Manhattan Scientist 2014

The Manhattan Scientist Series B Volume 1 Fall 2014

A journal dedicated to the work of science students

Series B

The Manhattan Scientist

Editorial Staff Student Editors

Andrew Baumgartner

Managing Editor / Physics Editor

Paul Markaj Chemistry Editor

Sana Saeed Biology Editor

Kimsy Tor

Mathematics Editor

Faculty Advisor and Editor in Chief

Constantine E. Theodosiou, Ph.D.

Manhattan College

4513 Manhattan College Parkway, Riverdale, NY 10471 Student Handbook manhattan.edu

MANHATTAN COLLEGE • RIVERDALE, NY 10471

Volume 1 (2014)

Series B

The Manhattan Scientist

Volume 1 (2014)

A note from the dean The first volume of the Manhattan Scientist was published in 1947. For almost forty years, students and faculty from the School of Science at Manhattan College presented the results of their scientific research performed on campus in this journal. They highlighted the importance of such efforts in the enrichment of the student learning environment and the preparation of future scientists, in their quest to understand the natural world. While the publication was interrupted for a number of years, the students have continued to be engaged in research activities with their faculty. The present edition of the journal reaffirms the paramount significance of such activities and that our students are capable of conducting high quality theoretical and experimental research across all disciplines, under the valuable guidance of their professors.

The present Volume includes seventeen papers, covering all disciplinary subjects of the School. These activities are aligned with the College’s mission, to “provide a contemporary, person-centered educational experience that prepares graduates for lives of personal development, professional success, civic engagement, and service to their fellow human beings.” The quality of the projects is indicative of our students and faculty and their commitment to research as part of the students’ educational experience.

This work would not be possible without financial support of our students. The support came from the School of Science Research Scholars Program, the Jasper Scholars Program of the Office of the Provost, the Catherine and Robert Fenton endowed chair in Biology, the Michael J. ’58 and Aimee Rusinko Kakos endowed chair in Chemistry, and Jim Boyle, ’61.

The student editors, all volunteers, worked hard to learn in a short time frame the intricacies of LaTeX and typesetting, along with the proper scientific style necessary for publishing in their professional journals. I would like to express my deep appreciation for their efforts. We are all honored to showcase our students’ contribution to the body of scientific knowledge. It is, therefore, with great pleasure that the editors present the publication of Series B, Volume 1, of the Manhattan Scientist.

Constantine Theodosiou Dean of Science

Series B

The Manhattan Scientist

Volume 1 (2014)

Table of Contents Biology Xylem conductivity of petioles and primary stem tissues at stem terminals of Herbaceous plant species Christopher Auricchio .................................................................................................................................................... 1 Development of epidermal and hypodermal cells in shoot apical meristems of cactus species from South America Elisa Behrami ................................................................................................................................................................. 9 Dynamics of eccentric stem development of Artemisia tridentata var. wyomingensis Hayley Graney .............................................................................................................................................................. 19 Dynamics of xylem cell and vascular bundle development in a stem node of Agrostis stolonifera Diana Luzuriaga .......................................................................................................................................................... 29 Range expansion of the non-native Asian shore crab in the Hudson River Angelica Romero ......................................................................................................................................................... 45 Investigation of the interactions between antimalarial and antiretroviral drugs Sana Saeed ................................................................................................................................................................... 53 Xylem conductivity in stems of 22 species of columnar cacti of South America Kristen Skonieczny ....................................................................................................................................................... 63 Mechanical stresses of primary branches and tree branch morphology Lydia Wehrli .................................................................................................................................................................. 75

Chemistry and Biochemistry Water remediation using analogs of Vitamin C Monika Gruca ................................................................................................................................................................ 85 Remediation of ground water containing chromium (VI) Paul Markaj .................................................................................................................................................................... 89 DFT investigation of the structural and energetic features of the protoribosome Daniel McCloskey ......................................................................................................................................................... 95 Trash to treasure: Optimization of heterogeneous catalyst systems for biodiesel synthesis Adrienne Perea ............................................................................................................................................................. 99 Footprinting of CMG at the replication fork Andi Wallick .............................................................................................................................................................. 105

Mathematics Pitch perfect: Re-analyzing the passing networks of Manhattan College women’s soccer Andre Oliveira ............................................................................................................................................................. 109 Monte Carlo studies of ideal three dimensional polymers Greg Zajac .................................................................................................................................................................. 117

Physics Systematic transition rate cancellations in quasi one-electron atoms Andrew Baumgartner ................................................................................................................................................. 123 Study of rare muon decay: µ+ → e+ e− e+ νe ν¯µ with polarized muons Dylan Gray and Thomas Reid .................................................................................................................................... 133

On the cover: The hydrated structure of Vitamin D with its binding protein, modeled from the x-ray structure, using MOPAC2012 on the facilities of the Kakos Center for Scientific Computing.

Xylem conductivity of petioles and primary stem tissues at sstem terminals of herbaceous plant species Christopher Auricchio∗ Department of Biology, Manhattan College Abstract. Parts of the plant like Stem tissues, leaves and flowers are produced by the shoot apical meristem. Cell production of meristems is dependent on cell maturity and developmental functions of newly formed cells produced by the meristems. Relationships between xylem contributions to leaves versus xylem conductivity solely in the stem were determined by examining xylem conductivity of terminal shoot meristems. Stem and petiole xylem conductivity analyses for the 29 species were restrained to observing stem terminal that only have primary xylem cells and less than five leaves more than 15 mm in length. Cumulative leaf areas ranged from 3.1 to 82 cm2 , stem diameters ranged from 0.82 to 3.88 mm, and maximum leaf xylem conductivities ranged from 0.0019 to 0.549 g cm MPa−1 s−1 . Petiole xylem conductivities (in g cm MPa−1 s−1 ) with leaf areas (cm2 ) for individual plant species was scaled well, with all R2 values above 0.92. Scaling of petiole xylem conductivity of the oldest leaf sampled with xylem conductivity of the stem subtending the oldest leaf sampled of each species tested. (R2 = 0.92). Cumulative petiole xylem conductivities (cumulative starting with terminal petioles) with xylem conductivities of subtending stems among the species tested was scaled also well (all R2 above 0.90). For pooled species, scaling of cumulative petiole conductivity (sum of all petiole conductivities) with the xylem conductivity of the stem subtending the oldest leaf sampled of each species tested was scaled incredibly well (R2 = 0.99). Overall, there is a strong correlation between stem xylem conductivities as petioles are added stem conductivities at shoot apices for the 29 plant species.

Introduction Shoots of plants are responsible for growth in length and thus height so that plants can compete for light. The structure and function of shoot apical meristems are stem terminals that are important for these functions. There are three basic functions for shoot apical meristems. Shoot apical meristems generate more stem cells and they also produce new leaves and new flowers.

However, these three functions in the meristem cause the plant to have tradeoffs. The meristem contains cell proliferation characteristics that depend on the maturation and development of the newly formed cells created by the meristem. Water and nutrients are provided for the meristem via xylem conduits that are just formed in the young stem. Structures like flowers and developing leaves cause the water conductivity to be distributed to these structures instead of the meristematic cells at the shoot apical meristem.

Effectiveness in the use of water in shoot apical meristems as well as young leaves are very important because they are what initiate primary growth and possibly the rate of producing new leaves. (Banavar et al., 1999; McCulloh et al., 2004; McCulloh and Sperry, 2005). A key element of leaf area is leaf venation (Scoffoni et al., 2011). The larger the leaves are, the major vein density decreased. However, leaf area and minor leaf vein density were not associated with each other.

Higher order leaf veins had greater length per unit area while the lower order leaf veins had a larger diameter with greater conduit numbers (Scoffoni et al., 2012). ∗

Research mentored by Lance Evans, Ph.D.

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Much research has been focused at water conductivity in woody tissues. (Anfodillo et al., 2006; Weitz et al., 2006; Atala and Lusk, 2008). Leaf specific conductivity was scaled well with the diameter of wood and the cross sectional area of the stems throughout tree branches. Due to Murray’s Law of tree branches, leaf specific conductivity and conduit taper across branches are correlated. The only time when woody stems may not conform to Murray’s Law is when the woody stems need to provide mechanical support (McCulloh and Sperry, 2004; 2005).

Vessel characteristics are very different for tree trunks and new twigs of the same trees. Diameters of the vessels increased linearly within trunks as well as with tree length of twigs. The diameters of the vessels ranged from 75 to 220 while for tree heights from 10 to 45 in trunks.

Meanwhile vessel diameters ranged from only 40 to 70 for young twigs (branch terminals). Vessel densities ranged from 20 per mm2 to less than 5 per mm2 for trunks and from 80 to 20 per mm2 for twigs (Zach et al., 2010).

Zach et al. (2010) found that whole-plant water transport was restricted due to the hydraulic conductance of the lamina of the leaf. With this particular study, the Klamina and Kplant were scaled together. The Klamina ’s range was 0.2 to 15 x10−4 kg m−2 MPa−1 while the Kplant range was from 0.2 to 2.5 x10−4 kg m−2 MPa−1 . The leaves in the sun had values about 15 to 65% higher Klamina than shade leaves. The water fluxes, leaf irradiance, petiole conductance, and guard cell lengths for sun leaves were higher when compared to shade leaves. Leaf dry mass per area, leaf density, osmotic potential and cuticle conductance was autonomous with Klamina .

The width of vascular bundles was scaled with vessel diameters that were hydraulically weighted within major axes of 10 species of oak leaves (Coomes et al., 2008). Coomes’ study displays the importance of bearing in mind leaf veins. McCulloh et al. (2009) compared leaf areas and specific leaf conductivities with stem sizes among all groups of trees.

All of the above studies deal with small to large stems. None address issues of xylem conductivity in shoot apical meristems that involve small leaves. Xylem conductivity characteristics of stems and leaves of shoot apical meristems may lead to a better understanding of stem growth and leaf initiation. Water availability is so important for the growth of young stems tissues. The current study was examined if (1) if petiole xylem conductivities were related to leaf areas for each species, (2) if cumulative petiole xylem conductivities of successive leaves were related to cumulative leaf areas for stems, (3) if there was a relationship between petiole xylem conductivities among the largest leaves of plants, (4) if values of stem xylem conductivities were related to cumulative petiole xylem conductivities for plants, and (5) if stem xylem conductivities among species were related to mean radius of conduits.

Materials and Methods

Plant Sampling. From May until September from 2011-2015 samples were taken from natural plant species on the Manhattan College campus (Table 1). The scientific names were verified using INPI. The amount of rainfall was ample and normal in the area for good samples. No noticeable blemishes were on the plants collected. Species were identified with several sources.

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(http://dendro.cnre.vt.edu/dendrology/main.htm; Uva et al., 1997; Leopold, 2005; Kersher et al., 2008; Gargiullo, 2010). Pictures of the plants as a whole and parts of each sampled were archived.

Tissue Sampling For Anatomy. Three plants were sampled for each species of plant. The primary determinant at the beginning of the experiment was assumed to be leaf area; therefore the plants chosen had related leaf areas. For the first six internodes the length and diameters were measured. For the first six leaves the midrib lengths were measured on fresh tissues respectively for each of the plants. Xylem tissue diameters were measured as well. The most expressive plant from each of the species was further processed for histology. At the most six leaves and six internodes were sampled basipetally to leaf #1. Samples of the internodes were taken in the middle between successive leaves. A digital caliper was used to determine length and diameter of all petioles and internodes. (Model (NC 9261865, Fisher Scientific, fishersci.com). The diameter of fresh xylem tissue was measured using a digital caliper that was at 30x magnification. A leaf area meter was used to determine leaf blade areas (LI-3000 surface area meter; LI-COR Corporation, Lincoln, NB).

Histological Procedures. Samples of tissues were fixed in FAA (Jensen, 1962) within 40 minutes of plant samples entering the lab. The samples were then processed in a tertiary butanol series to pure tert-butanol after 5 to 24 hours in the original fixative (BX1805-1, Fisher Scientific, fishersci.com). The tissue samples were put in a liquid Paraplast-Xtra (McCormick Scientific, Richmond, IL) and then positioned in an oven at 56◦ C. Tissues were then embedded in Paraplast after several changes to it. Microtome cross sections of stems and petioles were cut at 30 µm. Sections of tissue were placed on slides with adhesive and safranin (Jensen, 1962) stain for the xylem cells. Canada Balsam made the tissue sections permanent (Acros #CAS 8007-47-4, Acros.com).

Microscopic Analyses. From each plant the stem samples were processed. The first phase was to exclude stem segments with secondary xylem due to the purpose of the study to only focus on primary xylem. The magnification was either 100x or 400x for viewing the microscopy samples. The total number of xylem conduits for each stem and petiole sample was counted. Pictures were taken of each slide and the images were moved to ImageJ (National Institutes of Health, http://rsb.info.nih.gov/ij) to calculate radii of the conduits. For each of the tissue samples’ measured radii, at least 50 xylem conduits were evaluated for each of the tissue samples. Sampled conduits were selected randomly in the all species to measure them. The weighted tissue conductivities were then averaged together. The calculation of xylem conductivity was calculated using this formula: π ∗ number of conduits ∗ (average radius of conduits, in cm)4 (1) 8 ∗ viscosity of water in units of g cm MPa−1 s−1 (McCulloh et al., 2009). Xylem conductivities of cumulative petioles were found through adding petiole xylem conductivities starting at the stem apex.

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Table 1. Characteristics of the plant species of this study Largest leaf area (cm2 ) Ailanthus altissima Swingle 22.4 Asclepias syriaca 61.6 Astragalus canadensis L. 3.10 Betula papyrifera Marshall 19.5 Bidens frondosa L. 14.9 Boehmeria cylindrica L. 15.9 Buddleja davidii Franch.

21.0 Chenopodium album L. 13.8 Zelkova sinica 23.6 Coleus sp. Morton 30.0 Cucumis sativus L. 82.0 Cucurbia moschata Duchesne 17.6 Dendranthema grandiflorum 3.80 Eupatorium hyssopifolium L. 4.30 Fallopia japonica 48.0 Helianthus tuberosus L. 10.6 Ligustrum obtusifolium Siebold &Zucc.

2.34 Mentha arvensis L. 13.4 Mentha dahurica Bentham 7.18 Mentha Piperita 6.20 Morus alba L. 50.2 Nicotiana tabacum 3.90 Piper nigrum 11.0 Rhododendron ferrugineum 20.9 Rubus occidentalis L. 32.2 Sassafras albidum Esenbeck 45.5 Solanum lycopersicum L. 44.7 Sonchus arvensis L. 31.5 Zelkova sinica C.K. Schneid.

23.6 All scientific names were verified with INPI (inpi.org).

Plant Species tested

Largest stem xylem conductivity (g cm MPa−1 s−1 ) 0.1240 0.3190 0.0773 0.0266 0.0412 0.0149 0.0199 0.0484 0.0478 0.1850 0.5490 0.362 0 0.0241 0.0210 0.3060 0.1210 0.0019 0.1020 0.0245 0.0090 0.3040 0.0055 0.0115 0.1130 0.1471 0.1490 0.1170 0.0400 0.0183

Largest stem diameter (mm) 1.64 3.97 1.24 1.36 2.54 1.65 2.55 1.80 1.08 3.41 3.88 1.90 1.97 1.80 2.40 3.36 0.82 2.28 2.07 2.02 1.88 3.01 3.20 3.20 2.88 3.83 3.23 3.25 1.37

Results

The examination of stems was limited to stem terminals that only had primary xylem cells.

Each stem for every species had at least four leaves with the smallest leaf only greater than 15 mm in length. For the 29 plants species examined, Cumulative leaf area reached around 2.3 to 80 cm2 , stem diameters were ranged to about 0.82 to 3.88mm, and maximum leaf xylem conductivities ranged from 0.0019 to 0.549 g cm MPa−1 s−1 (Table 1).

The scaling of petiole xylem conductivities (in g cm MPa−1 s−1 ) with leaf areas (cm2 ) for individual plant species was done overall(Fig. 1). The R2 values for all species was larger than 0.92. In addition, from the pooled species from Fig. 1, petiole xylem conductivity of the largest (oldest) leaf sampled was scaled against the subtending stem of the largest (oldest) leaf for each individual species (Fig. 2). These values found were well scaled (y = 0.47x + 0.003 with an R2

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0.40 0.30 0.20 0.10 0.00

0.30

leaf

Petiole Conductivity of largest

0.50 Cumulative Petiole Conductivity

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0.20 0.10 0.00 0.00

0.20

0.40

0.60

Stem conductivity of subtending leaf 0

50

100

150

200

250

Cumulative Leaf Area (cm2) -1 -1 s ) with Fig. 1. Scaling1.of cumulative xylem conductivities (g cm MPa Figure Scalingpetiole of cumulative petiole xylem con−1 −1 2 2 ductivities (in(cm g cm s species. ) with leaf cumulative leaf areas ) for MPa individual plant Allcumulative r values were larger than 2 2 areas (cm ) for individual plant species.

All R val0.92.

ues were larger than 0.92.

-1 -1 Figure 2. For pooled species, scaling cm ofMPa petiole Fig. 2. For pooled species, scaling of petiole xylem conductivity (g s ) of −1 −1 xylem conductivity (in g cm ) ofsubtending the the largest leaf sampled with xylem conductivity (g cmMPa MPa-1 s-1) ofsthe stem

largest leaf sampled with xylem conductivity of the stem subtending the largest leaf sampled of each 0.003 with an r2 of 0.92. species tested. The equation of the line was y = 0.47x + 0.003 with an R2 of 0.92.

the largest leaf sampled of each species tested. The equation of the line was y= 0.47x +

of 0.92). This high R2 value between these two parameters represents that there is an important relationship between them.

The data in Fig. 4 shows max cumulative petiole conductivity (in g cm MPa−1 s−1 ) (sum of all petiole conductivities) being scaled with the xylem conductivity of their subtending stems of the oldest leaves sampled of each species tested. The equation of the line and R2 value was well scaled (y = 1.1453x+0.023 with an R2 of 0.99). Showing us that there is an important relationship between these two factors.

The xylem conductivity of subtending stems for each individual species was scaled with cumulative petiole xylem conductivity (cumulative starting with terminal petioles) among the species tested. As cumulative petiole conductivity increased, so did stem conductivity. The R2 for all species were at least 0.90 or larger showing an important relationship.

Discussion The primary focus of this study was concentrated on xylem conductivity of stem terminals including small leaves at the terminals. The largest leaf in the study was 82 cm2 and the largest stem was 3.88 mm in diameter. McCulloh et al. (2009) for petioles and petiolules of fourteen species of tropical and temperate plants had similar xylem conductivities values similar to this particular study. Xylem Conductivity of individual leaves ranged from 0.01 to 70 g cm MPa−1 s−1 (McCulloh et al., 2009). Meanwhile, in this current study xylem conductivity of the leaves ranged from nearly 0.0019 to 0.549 g cm MPa−1 s−1 , way below the xylem conductivity of the largest compound leaf (70 g cm MPa−1 s−1 ) in McCulloh et al. (2009) Leaf areas with stem diameters and leaf specific conductivities were compared by McCulloh et al (2010). Both specific conductivities and leaf areas scaled similarly with stem size among all

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Cumulative Stem Conductivity

1

0.1

0.01

0.001

0.0001 0.00001

0.0001

0.001

0.01

0.1

1

Cumulative Petiole Conductivity Figure 3. Scaling of cumulative petiole xylem Fig. 3. Scaling of cumulative petiole xylem conductivities (g cm MPa-1 cons-1) (cumulative ductivities (in g cm MPa−1 s−1 ) (cumulative starting with terminal petioles) with xylem conductivities of 2 stems among the speciesstems tested. among All r2 values larger than 0.90. All R subtending thewere species tested. values were larger than 0.90.

starting with terminal petioles) with xylem conductivities (g cm MPa-1 s-1) of subtending

Fig. 4. For pooled species, scaling of cumulative petiole conductivity (g cm MPa-1 s-1)

Figure 4. For pooled species, scaling of cumu(sum of all petiole conductivities) with the xylem conductivity (g cm MPa s ) of the lative petiole conductivity (sum of all petiole constem subtending the largest leaf sampled of each species tested. The equation of the line ductivities) with the xylem conductivity of the stem was y= 1.1649x + 0.036 with an r value of 0.99. subtending the largest leaf sampled of each species tested. The equation of the line was y = 1.1649x + 0.036 with an R2 value of 0.99.

-1 -1

2

groups. Stem diameters ranged from less than 1 mm to almost 40 mm for the study.

For this study, stem and petiole conductivity at shoot apical meristems was used under the assumption that stem conductivities should increase proportionally as conductivities of successive petioles were considered for each species and that primary xylem conduits would have little involvement in mechanical support.

The data from Fig. 1 has very identical slopes among all species studied. Showing us that leaf area is very important in determining petiole conductivity. Leaf areas varied from 2.0 to 82 cm2 among all leaves for the species sampled. Therefore regardless of morphology differences, the species all show an identical relationship of petiole conductivity increasing, as the leaf gets larger. Meanwhile in Fig. 2 the leaf gets about 50% of stem conductivity for all species. Although leaf morphologies varied (2.0 to 80 cm2 ) for the species just like in Fig. 1, the leaf area still drives petiole conductivity. Therefore from the data in Figs. 1 and 2, petiole conductivity becomes greater in order to accommodate leaf area where for each leaf; the stem will give nearly half (50%) of its conduits in order to provide adequate water for the leaf.

Plants have high stem conductivity and any variation seen in Fig. 2 comes from the theme where larger conductivity stems retain lower percentage of their conductivity and give the rest to the leaves. Fig. 3 allows us to observe that all of these relationships are equivalent. Stems create conductivity in order to supply leaves with water while the plant grows. Therefore, if we were to include even larger leaves, we would expect the lines to just extend on the figure and remain straight showing the same relationship seen in the figure.

When you add all of the leaf petiole conductivity together, they add up to the stem conductivity amongst all species. Therefore, as cumulative petiole conductivity grows larger, the stem creates

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sufficient conductivity to supply enough water for their leaves as observed from our high R2 value in Fig. 4.

All species in this study regardless of size and morphology show the same exact pattern exactly. All these processes (xylem conductivity, petiole conductivity arrangement, etc.) are happening at the same time because all the plants are growing. Therefore, in the real world, as leaves get larger and more numerous over time, the stem conductivity must increase to counterbalance this process.

Acknowledgement The author is grateful for financial support from the Catherine and Robert Fenton Endowed Chair to Dr. Lance Evans.

References Anfodillo, T., V. Carraro, M. Fior, and S. Rossi. 2006. Convergent tapering of xylem conduits in different woody species. New Phytologist 169: 279-290.

Atala, C. and C. Lusk. 2008. Xylem anatomy of Betula pendula Roth seedlings: relationship to physical vascular models. Gayana Botanica 65: 18-27.

Banaver, J. R., A. Maritan, and A. Rinaldo. 1999. Size and form in efficient transportation networks. Nature 399: 130-132.

Coomes, D.A., S. Heathcote, E.R. Godfey, J, J. Shepard and L. Sack. 2008. Scaling of xylem vessels and veins within the leaves of oak species Biol. Letters 4: 302-306.

Gargiuillo, M. A. 2010. Guide to native Plants of the New York City Region. Rivergate Books, New Brunswick, NJ. INPI inpi.org.

Jensen, W.A. (1962). Botanical Histochemistry. Principles and Practice. W.H. Freeman. San Francisco, CA. Kersher, B., Matthews, D. and Nelson, G. 2008. Field Guide to Trees of North America. Sterling Publ. Co., New York.

Leopold, Donald, J. 2005. Native Plants of the Northeast, Timber Press, Inc. McCulloh, K.A., John S. Sperry, F.R. Adler. 2004. Murray’s law and the hydraulic vs mechanical functioning of wood. Functional Ecology 18: 931-938.

McCulloh, K.A. AND J. S. Sperry. 2005 Patterns in hydraulic architecture and their implications for transport efficiency. Tree Physiology 25: 257-267.

McCulloh, K.A., J. S. Sperry, F.C. Meinzer, Barbara Lachenbruch, and Christian Atala. 2009.

Murray’s Law, the ’Yarrum’ Optimum, and the Hydraulic Architecture of Compound Leaves.

New Phytologist 184: 234-44.

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McCulloh, K.A., J.S. Sperry, B. Lachenbruch, F.C. Meinzer, and P. Reich. 2010. Moving water well: comparing hydraulic efficiency in twigs and trucks of coniferous, ring-p[orous, and diffuse-porous saplings from temperate and tropical forests. New Phytologist 185: 1-12.

Scoffoni, C., M. Rawls, A. D. McKown, H. Cochard, and L. Sack. 2011. Decline of Leaf Hydraulic Conductance with Dehydration: Relationship to Leaf Size and Venation Architecture. Plant Physiology 156: 832-843.

Scoffoni, C., A. D. McKown, M. Rawls, and L. Sack. 2012. Dynamics of Leaf Hydraulic Conductance with Water Status: Quantification Analysis of Species Differences under Steady State.

Journal of Experimental Botany 63: 643-58.

Uva, Richard H., Neal, Joseph C., and DiTomaso, Joseph M. 1997. Weeds of the Northeast, Cornell University Press.

Weitz, J., K. Ogle, and H. Horn. 2006. Ontogenetically stable hydraulic design in woody plants.

Functional Ecology 20: 191-199.

Zach, A., B. Schuldt, S. Brix, V. Horna, and H. Culmsee. 2010. Vessel diameter and xylem hydraulic conductivity increase with tree height in tropical rainforest trees in Sulawasi, Indonesia.

Flora 205: 506-512.

Development of epidermal and hypodermal cells in shoot apical meristems of cactus species from South America Erisa Behrami∗ Department of Biology, Manhattan College Abstract. Cactus plants produce dermal layers such as a thick cuticle, epidermis and hypodermis by shoot apical meristems. These layers cover stem tissues in order to restrict water loss. Dermal layers of stems from twelve species of columnar cacti from South America were analyzed to determine if they were similar to cactus samples from previous studies. Cuticles from the twelve species ranged from 3 to 51 µm thick, epidermal layers ranged from 18 to 72 µm thick, and hypodermal layers ranged from 64 to 530 µm thick. These thicknesses were similar to dermal layers from published scientific papers. Data show that thicknesses of epidermal layers were positively correlated with thicknesses of cuticular layers among the twelve species. Likewise, thicknesses of hypodermal layers were positively correlated with thicknesses of epidermal layers among the twelve species. Studies also determined the distances required for dermal layers to become mature after they were produced by the shoot apical meristem. In general, cuticles, epidermal layers and hypodermal layers became completely developed between 2.3 to 87, 3.7 to 71, and from 2.4 to 94 mm from the meristem, respectively, among the species tested. These distances appear rather large considering that much water loss by transpiration could occur from shoot apical meristems.

Introduction The plant family Cactaceae encompasses the largest number of species and the most varied life forms and habits of any plant family (Garcia, et al., 2012). Cactus plants are known for their vast variability in size and shape throughout their geographic distribution from Patagonia to south Canada (Altesor and Ezcurra, 2002).

There are two morphological features prominent in cacti: their spine-bearing areoles and succulent cortex (Fig. 1, Schwager, et al., 2013). The areole is the vegetative structure in Cactaceae.

It is responsible for producing spines, glochids, and tufts of hair that are usually uniserate and develop at the base (Boke, 1980) and they are changed axillary buds found on tubercles (Altesor and Ezcurra, 2002). Most spines are found on the abaxial side scattered throughout juvenile areoles and the majority of cacti have areoles that are similar to each other, are located on one tubercle and have only one meristem that yields spines and either flowers or vegetative branches (Boke, 1980).

Since, the majority of cacti are found in deserts and semiarid locations where precipitation is limited, water management is essential to surviving in these conditions (Gibson and Nobel, 1986).

As Cacti evolved to be stem succulents, they have almost entirely eliminated their petioles and leaf blades, while manipulating their leaf base (Boke, 1980). Cacti stems are entirely made up of ribs and or tubercles transmissible with each other and the internodes are eradicated. Cacti are deemed as succulent because of the presence of dense, water-storing tissues (Nobel, 1988). A trait unique to Cactoideae is the make-up of their dermal system (Darling, 1989; Loza-Cornejo, 2003). ∗

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Figure 1. An image of cacti that were cultivated in the Singapore Botanic Gardens. The image is taken from http://en.wikipedia.org/wiki/Cactus in order to illustrate typical characteristics associated the apical meristems of cactus plants. Note the large number of spines near the meristems.

In cactus plants, the dermis is made up of the cuticle, epidermis, hypodermis and helps to restrict water loss from the stem of the plant (Gibson and Noble, 1986). The stem of cacti typically has a thick cuticle and consists of a uniserate epidermis made up of square or rectangular cells (Garcia, et al., 2012). A smooth cuticle is present in the stem of the majority of cacti species (Loza-Cornejo, 2003). In Cacti, the hypodermis is an elastic tissue responsible for adapting to varying stem volume levels as a result of retention and reduction of water (Garcia et al., 2012) and is made up of many cell layers that have thick cell walls (Soffiatti and Angyalossy, 2007). However, the hypodermis also tries to keep pathogens from attacking inner tissues by defending them (Gibson and Nobel, 1986).

The purpose of this study is to determine the steps involved in the development of the dermal structures near the shoot apical meristems of cactus plants (Fig. 1). These tissues need to rapidly develop close to the apical meristems since most cacti are found in very arid environments. This study is significant because the rapid development of the epidermis and hypodermis near the shoot apical meristems helps cactus plants limit water loss and survive.

Materials and Methods Species Studied. The samples of the species of cactus plants that were studied were collected from Peru in May 2013 and from Argentina and Chile in January 2013. The field location data from Anderson (2001) and (http://cludwigfr.dyndns.org) was used to help to locate and identify the species. Species were also identified by comparing characteristics observed to those in Anderson (2001). Photographs of a wide range of physical characteristics such as cactus ribs, tubercles, spines, areoles, height, distances between each section taken from stem, etc. were taken. A Garmin eTrex Legend (REI.com) was used to record the latitudes and longitudes and IPNI (www.IPNI: Plant Name Search) and Tropicos (www.tropicos.org) were used to verify species names. The species Argentina were Cereus aethiops var. landbeckii (Phil.) Backeb. (near the junction of Route 9 and Route 34 near Salta, S 24◦ 43.8, W 65◦ 01.7), Cereus spegazzinii F.A.C. Weber (near Route 34 north of General Guemes, S 24◦ 37.9, W 65◦ 03.9), Cereus validus Haw. (near junction of Route 9 and Route 34/ Salta, S 24◦ 43.8, W 65◦ 01.7). Echinopsis thelegona (F.A.C. Weber) H.

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Table 1. Mean characteristics of cuticles, epidermal and hypodermal cells of 12 cactus species, in mm.

Species Eulychnia iquiquensis Eulychnia breviflora Weberbauerocereus winterianus Espostoa nana Echinopsis coquimbana Echinopsis thelegonia Cereus aethiops Neoraimondia arequipensis Cereus validius Echinopsis skottsbergii Cereus spegazzinii Eulychnia acida

Distance to 95% maturity from terminal meristem cuticle epidermis hypodermis 3.86 3.47 4.21 3.21 3.59 3.28 5.13 5.12 4.56 5.96 5.86 5.69 3.22 3.61 3.28 3.05 2.97 2.45 2.36 2.40 2.82 3.69 4.41 4.22 2.86 3.53 3.28 87.9 71.6 94.0 2.61 3.67 3.8 66.3 38.7 70.5

Cuticle depth 3.4 7.3 25.5 5.9 18 30 35 18 30 45 25 51

Epidermis depth 18 32 31 20 33 33 40 32 44 72 60 63

Hypodermis depth 64 66 85 110 141 150 220 250 350 370 480 530

Friedrich G.D. Rowley (junction of Route 9 and Route 34 near Salta, S 24◦ 43.8, W 65◦ 01.7). The species obtained in Chile were Echinopsis coquimbana (Britton Rose) A.E. Hoffm. (near Route 5 south of Coquimbo, S 30◦ 01.9, W 71◦ 22.9), Echinopsis skottsbergii (Backeb.) H. Friedrich G.D. Rowley var. breviata (Backeb.) H. Friedrich G. D. Rowley (near road east of Fray Jorge National Park, S 30◦ 48.4, W 71◦ 21.8), Eulychnia acida Phil. Var. procumbens F. Ritter (north of Illapel near Route 5, S 31◦ 58.7, W 71deg 29.8), Eulychnia breviflora Phil. var. tenuis F. Ritter (near Route 5 north of Coquimbo, S 290 59.5, W 710 21.8), Eulychnia iquiquensis (K. Schum.)

Britton Rose subsp. ritteri (Cullmann) D.R. Hunt (near Route 5 south of Coquimbo, S 30◦ 01.9, W 71◦ 22.9). Samples obtained from Peru were Neoraimondia arequipensis (Meyen) Backeb. subsp. roseiflora (Werderm. Backeb.) Ostolaza (near Nazca, S 14◦ 49.6, W 74◦ 49.1), Espostoa nana F. Ritter (road from Celendin to Balsas, S 6 51.5, W 78◦ 3.8), Weberbauerocereus winterianus F. Ritter (near Nazca, S 14◦ 49.6, W 74◦ 49.1).

Tissue Sampling and Histological procedures. Before individual tissue samples were taken, cactus surfaces were photographed to document the overall physical characteristics. Tissue samples were taken at a variety of distances from the shoot apical meristems. Tissue samples were normally 25 mm2 on surfaces only. The location of each sample relative to the apical meristem was recorded. Samples were fixed in FAA (Jensen, 1962) for a minimum of 24 hours and then processed through a tertiary-butanol series (Jensen, 1962) to paraffin wax, embedded in paraffin and sectioned with a microtome at 30 µm.

Measurements. In order to measure the depths of the cuticle, epidermis and hypodermis for each sample, images of tissue samples were taken under a microscope. The depths were measured using imageJ (www.rsb.info.nih.gov/ij/). The data for the depths were taken beginning at the tip

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of the cactus plant and continuing along the surface of the stems for each species sampled. The data measurements collected were taken to follow the development of the cuticle, epidermis and hypodermis from the shoot apical meristem to farther distances down the stem of every species sampled.

Results

Cactus plants are known for the presence of areoles, tubercles, and spines on their surfaces. All species of cacti studied had these same physical characteristics (Fig. 1). The cuticles, epidermal and hypodermal characteristics for three species will be described in depth. These three species represent the range of characteristics of all the species tested. All species of cacti studied had dermal structures composed of the cuticle, epidermis and hypodermis (Fig. 2). However, the thickness of these cells differs depending on species and distances from the shoot apical meristems (Fig. 2). At the meristem tip of Cereus validus a cuticle was present and was about 30 µm (Fig. 3).

The epidermis was a single layer and contained cuboidal cells with a five-to-six layered hypodermis (Fig. 2A). The same dermal tissues were present five mm from the meristem in which tissues were matured (Fig. 2B). The epidermis was uniserate with cuboidal cells of 26 to 48 µm thick (Fig. 4).

The hypodermis of Cereus validus had seven-to-nine-layers and ranged between 250 to 400 µm thick (Figs. 2B and 5).

For the meristem of Echinopsis skottsbergii, the cuticle was less than 5 µm (Fig. 7) and the epidermis wavy and one-to-two layered (Figs. 6A and 8). The hypodermis was thick with dense cell walls (Fig. 6A) and a thickness of less than 80 µm at the meristem (Fig. 9). For mature tissues of Echinopsis skottsbergii, 152 mm from the tip, the cuticle was thick (between 35 and 60 µm; Fig. 7) with a biserate epidermis of 55 to 82 µm (Fig. 8). For mature stem tissues of Echinopsis skottsbergii, the hypodermis was between 325 and 470 µm thick (Fig. 9) and the cell layers were difficult to differentiate because the cell walls were very thick (Fig. 6B).

At the meristem tip of Espostoa nana (Fig. 10A), the cuticle was thin (less than 3 mm) and the epidermis was uniserate with globular cells. The hypodermal cells had thick cell walls that were less than 30 µm at the meristem. In mature stem tissues seven mm from the meristem (Fig. 10B), the cuticle was about seven µm (Fig. 11) while the uniserate epidermis with globular cells was 25 µm (Fig. 12). For mature tissues, the hypodermis was composed of flattened cells with thick cell walls about 175 µm thick (Fig. 13).

Thicknesses of cuticles and epidermal cells were compared among the 12 species These two parameters were well correlated in which species with thicker cuticles had thicker epidermal layers (Fig. 15; R2 = 0.69). In a similar manner, species with thicker epidermal layers had thicker hypodermal layers (Fig 16; R2 = 0.77).

Thicknesses of cuticles, epidermal layers and hypodermal layers were compared as a function of distance from the apical meristem (Fig. 14; Table 1). For this comparison, maturity was set to be 95% of the distance of maximum thickness for each tissue. Thereafter, depths of tissues at 95% and distances of 95% maturity were established for the data. There was a wide range of

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Fig. 2 A)

B)

Figure 2. Images of stem dermal structures of Cereus validus. A) Image shows a thin cuticle (arrow) and a uniserate epidermis made up of cuboidal cells (thick-arrow) and a five-to-six-layered hypodermis at the meristem tip (brackets). B) Image shows a thin cuticle and a uniserate epidermis made up of cuboidal cells and a seven-to-nine-layered hypodermis of a mature sample five3 mm from the meristem tip.

Fig. 5.

5

4

Fig. 3.

600

Epidermis Thickness (µm)

40 30 20 10 0 0

1

2

3 4 Distance (mm)

5

60 50 40 30 20 10 0 0

6

2

4

6

Hypodermis Thickness (µm)

70

50 cuticle thickness (µm)

Fig. 4.

60

300 200 100 0 1

2

3

4

5

Distance (mm)

Figure 4. Data of epidermis thickness versus distance from meristem tip of Cereus validus. The equation was y = 5.39 ln(x) + 36.0 with R2 = 0.55.

Figure 6.

A)

400

0

Distance (mm) .

Figure 3. Data of cuticle thickness versus distance from tip of Cereus validus.

The equation for the line was y = 2.76 ln(x) + 25.6 with R2 = 0.24.

500

Figure 5. Data of hypodermis thickness versus distance from tip of Cereus validus.

The equation for the line was y = 52.5 ln(x) + 270 with 6 R2 = 0.70.

B)

Figure 6. Images of stem dermal structures of Echinopsis skottsbergii. A) shows a thick cuticle and a one-to-twolayered, wavy epidermis made up of cuboidal cells with very thick cell walls near the meristems tip. B) shows a thick cuticle and biserate epidermis of cuboidal cells and a hypodermis with very thick cell walls in a mature sample 152 mm from the tip.

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Figure 7.

Figure 8.

Epidermis Thickness (µm)

Cuticle Thickness (µm)

60 50 40 30 20 10 0 0

50

100 Distance (mm)

150

Figure 7. Data of cuticle thickness versus distance from tip of Echinopsis skottsbergii.

The equation of the line was y = 5.47 ln(x) + 18.3 with R2 = 0.85.

Fig. 10.

A)

200

100 90 80 70 60 50 40 30 20 10 0

450 Hypodermis Thickness (µm)

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Figure 9.

0

20

40

60 80 100 Distance (mm)

120

140

Figure 8. Data of epidermis thickness versus distance from tip for Echinopsis skottsbergii.

The equation of the line was y = 6.57 ln(x) + 40.3 with R2 = 0.82.

160

400 350 300 250 200 150 100 50 0 0

20

40

60 80 100 Distance (mm)

120

140

160

Figure 9. Data of hypodermis thickness versus distance from tip for Echinopsis skottsbergii.

The equation of the line was y = 32.0 ln(x) 10 + 206 with R2 = 0.84.

B)

Figure 10. Images of stem dermal structures of Espostoa nana. A) shows a thick cuticle and a uniserate epidermis made up of globular cells and a hypodermis with thick cell walls at the meristem tip. B) shows a thick cuticle and uniserate epidermis made up of globular cells and a multi-layered hypodermis with very thick cell walls and flattened cells in a mature sample seven 7 mm from the tip.

depths and distances. Overall, species with larger depths had larger distances (Fig. 14; Table 1).

The exponential plots of thicknesses of cuticles, epidermal layers and hypodermal layers for all twelve species had R2 values of 0.40, 0.49, and 0.33 respectively. These results suggest that in all species studied, at 95% maturity, most of the cuticles were between 0 − 51µm thick and all but two species matured by 5 mm from the tip. For the epidermis, and hypodermis similar results were seen. For the epidermis and hypodermis, species thickness varied from 18-72 µm and 64-530 µm respectively (Fig. 14).

Discussion This study analyzed the development of dermal tissues in stems of twelve cacti species from South America in relation to location to the shoot apical meristem. Cuticle, epidermis, and hypodermis depths vary among species. However, correlations between the cuticle and epidermis and epidermis and hypodermis exist. In general all species showed that dermal structures were 95%

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Fig. 11.

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30 Epidermis Thickness (µm)

7 Cuticle Thickness (µm)

12

Fig. 12

6 5 4 3 2 1 0 0

2

4 Distance (mm)

6

25 20 15 10 5 0 0

8

Figure 11. Data of cuticle thickness versus distance from tip of Esposta nana. The equation of the line was y = 1.72 ln(x) + 2.54 with R2 = 0.72.

2

4 Distance (mm)

6

8

Figure 12. Data of epidermis thickness versus distance from tip of Esposta nana. The equation was y = 6.02 ln(x) + 8.36 with R2 = 0.71.

14 Figure 14.

600

Hypodermis Thickness (µm)

Fig. 13.

200 180 160 140 120 100 80 60 40 20 0

500 Cuticle thickness (m)

13

300 200 100 0 0

0

2

4 Distance (mm)

6

8

Figure 13. Data of hypodermis thickness versus distance from tip of Esposta nana. The equation of the line was y = 37.2 ln(x) + 39.8 with R2 = 0.49.

15

20

40 60 80 Cuticle (95%) distance (m)

100

Figure 14. Data of cuticle (circle), epidermis (square), and hypodermis (triangle) thicknesses versus the distances from tip when tissues are 95% mature for all 12 species sampled. The equation for the line for the cuticle thickness versus 95% of tissues mature relationship is y = 7.63 ln(x) + 11.1 with R2 = 0.40. For the epidermis, the equation for the line is y = 11.2 ln(x) + 20.0 and the R2 value is 0.49. The equation for the line for the hypodermis thickness versus 95% of tissues mature distance rela16 tionship is y = 76.1 ln(x) + 96.6 with R2 = 0.33.

Fig. 16

Fig. 15

600

80

Hypodermis thickness (m)

70 Epidermis thickness (m)

400

60 50 40 30 20 10 0 0

10

20 30 40 Cuticle thickness (m)

50

60

Figure 15. Data of cuticle thickness versus epidermal thickness for all twelve species observed. The equation of the line was y = 0.941x + 16.8 with R2 = 0.69.

500 400 300 200 100 0 0

20 40 60 Epidermis Thickness (m)

80

Figure 16. Data of epidermal thickness versus hypodermis thickness for all twelve species of this study.

The equation of the line was y = 8.41x–100 with R2 = 0.77.

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completed within five mm of the apical meristem.

Loza-Cornejo and Terrazas (2003) observed dermal structures in seventy different species of North American cacti. Their results show that for most of the species they studied, cuticle thicknesses varied from 1-49 µm thick. However, cuticles thicker than 20 µm were present in twenty-six species. Soffiatti and Angyalossy (2007) and Garcia et al. (2012) and Torres-Boeger et al. (2010) also observed a thick cuticle present above the epidermis. A study on cacti species Lepismium cruciforme and Lepismium lumbricoides also reported cuticle thicknesses to be 10.73 and 11.37 µm respectively (Torres-Boeger et al., 2010). These results are similar to those obtained in this study. All of the twelve species studied had epidermal cells that were covered by a thick cuticle and the cuticle depths ranged from 0 to 51 µm thick, which is similar to the cuticle depths reported in other studies.

Darling (1989) observed epidermal and hypodermal structures in Carnegiea gigantia. For C. gigantia, the epidermis and hypodermis combined were one mm thick. Similarly, Loza-Cornejo and Terrazas (2003) found that the epidermis of most species was uniserate with cuboidal or rectangular cells, but wavy epidermal walls existed in two species, Echinocereus pensilis and Aricarpus retuse. Similary, Lemos and Melo-de-Pinna (2011) also saw wavy epidermal walls present in two of their species, Hatiora salicornioides and Epiphyllum phyllanthus. In studies done by Loza-Cornejo and Terrazas (2003), epidermis depths ranged from 11 to 69 µm thick in 70 species studied and Torress-Boeger, et al. (2010) observed epidermal depths in L. cruciforme and L. lumbricoides to be 29.97 and 11.15 m respectively. These results are similar to the epidermis depths observed in this study, which ranged from 18 to 72 µm thick in the species used for this study.

Some cactus species have a 10-12 cell-layered hypodermis with very thick cell walls (Darling 1989). Soffiati and Angyalossy (2007) observed that in the species Arrojadoa bahiensis, Brasilicereus markgraffti, and Arrojadoa penicillata the hypodermis is comprised of cells with asymmetrically thick walls that ranged from one-to-six layers. Loza-Cornejo and Terrazas (2003) obtained similar results. They found that the hypodermis was one to several layers thick with thick cell walls and twenty-eight species had a hypodermis more than 200 µm thick. In all cactus species studied, the hypodermis was several layers and consisted of cells with very thick cell walls.

In some species, such as Echinopsis skottsbergii the cell walls were so thick that the number of layers present in the hypodermis could not be determined. The depths of the hypodermis ranged from 64-530 µm thick in the twelve species used for this study, comparable to those observed by Loza-Cornejo and Terrazas (2003) and Torres-Boeger, et al. (2010), 10 to 626 µm and 75.33 and 89.81 µm respectively.

Although the depths of the cuticle, epidermis, and hypodermis are similar to those published in other studies, no studies have shown the development of the dermal structures relative to the shoot apical meristem. The findings in this study show that in all species studied, cuticle thickness were 0-51 µm thick and the epidermis and hypodermis thickness varied from 18-72 µm thick and 64-530 µm respectively. However, this study also shows that ten of the twelve species studied had tissues

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95% mature by 5 mm from the tip (Fig. 14). This study also observes that cuticle and epidermal cell thickness and epidermal and hypodermal thicknesses are well correlated because species with thicker cuticles had thicker epidermal layers and species with thicker epidermal layers had thicker hypodermal layers.

However, the development of the epidermis and hypodermis in cactus plants also shows the role these dermal structures serve in water retention. Darling’s study revealed that two structures known for their role in water conservation in Cactus plants are the thick epicuticular wax and cuticle (Conde 1975; Darling 1989). The presence of the thick epicuticular wax constricts water loss and prevents surface water (Gibson and Nobel 1986). However, the structure of the epidermis and hypodermis reveals how crucial it is for cacti to retain water. In cactus plants, the epidermis functions in limiting water loss, especially in species where the epidermal cells have thick cell walls (Crawley 1986; Loza-Cornejo 2003). Wavy anticlinial walls show no selective advantages, however, they may help in the expansion and contraction of epidermal cells in the absorption and reduction of water (Mauseth 1988; Mauseth 1984; Loza-Cornejo 2003). In cacti, the hypodermis functions in retaining water and is present from the apical meristem to the bottom of the plant.

Large levels of pectin, a water-retaining element is present in the cell walls of the hypodermis. The large amount of pectin found in these cell walls also contributes to the density of the hypodermal cell walls (Gibson and Nobel 1986).

Since the epidermis and hypodermis are the main tissues that limit water loss, these cell types need to develop close to the shoot apical meristems in order for the plant to resist losing water.

The results of this study show that in all but two species of the cactus plants studied, the epidermis develops 2.4 to 5.86 mm away from the tip. In the species Echinopsis skottsbergii and Eulychnia acida, the epidermis develops 71.6 and 38.7 mm from the tip respectively. Similar results are found for the hypodermis development. The development of the hypodermis ranges from 2.45 to 5.69 mm from the tip and in Echinopsis skottsbergii and Eulychnia acida, the development occurs 94 and 70.5 mm away respectively. These results conclude that since the epidermal and hypodermal tissues function in constricting water loss, they develop close to the apical meristems.

Acknowledgement The author is grateful for financial support from the Catherine and Robert Fenton Endowed Chair to Dr. Lance Evans.

References Altesor, A., Ezcurra.E., 2003. Functional morphology and evolution of stem succulence in cacti. J. of Arid Environ. 53, 557-56.

Anderson, E.F., 2001. The Cactus Family. Timber Press, Portland, OR. Boke, Norman H. (1980). Developmental Morphology and Anatomy in Cactaceae. BioScience 30, 605-610

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Conde, L. F., 1975. Anatomical comparisons of five species of Opuntia (Cactaceae). Ann. Missouri Bot. Gard. 61, 425-473 Crawley, M. J. (ed.) 1986. Plant Ecology. Blackwell Scientific Publications. Oxford, UK. Darling, M. S., 1989. Epidermis and hypodermis of the saguaro cactus (Cereus giganteus): Anatomy and spectral properties. Amer. J. Bot. 76, 1698-1706.

Garcia, dos Santo, J., Scremin-Dias, E., Soffiatti, P., 2012. Stem and root anatomy of two species Echinopsis (Trichocereae: Cactaceae). Rev. Mex. Biodiversity 83, 202-221.

Gibson, A.C., Nobel, P.S., 1986. The cactus primer. Harvard University Press. Cambridge, MA. “IPNI: Plant Name Search.” IPNI: Plant Name Search. International Plant Names Index, 13 Jan. 2014. Web. 08 Apr. 2014. http://www.ipni.org/ipni/plantnamesearchpage.do Jensen, W.A. 1962. Botanical Histochemistry. W.H. Freeman and Co. University of California, Berkeley.

Lemos, R., Melo-de-Pinna, G., 2011. Morpho-anatomical variations during stem development in some epiphytic Cactaceae. J. Torrey Bot. Soc. 138, 16-25.

Loza-Cornejo, S., Terrazas, T., 2003. Epidermal and hypodermal characteristics in North American Cactoideae (Cactaceae). J. Plant. Res. 116, 27-35.

Mauseth, J., 1984. Introduction to cactus anatomy, part 7, epidermis. Cact Succ J (USA) 56, 33–37 Mauseth, J. ,1988. Plant anatomy. Benjamin/Cummings Publishing. Redwood City, California Nobel, P.S. ,1988. Environmental Biology of agaves and cacti. Cambridge University Press. NY. Schwager H, Masselter T, Speck T, Neinhuis C. (2013) Functional morphology and biomechanics of branch stem junctions in columnar cacti. Proc R Soc B 280: 2013-2244.

Soffiatti, P., Angyalossy, V., 2007. Anatomy of Brazilian Cereeae (subfamily Cactoideae, Cactaceae): Arrojadoa Britton and Rose, Stephanocereus A. Berger and Brasilicereus Backberg.

Acta Botanica Barsilica 21.

Torres-Boeger, M., Soffiatti, P., Gomes-Souto, M., Budchen, M., Bagatini, K., Forno, M., 2010.

Functional morphology of two Lepismium species (Rhipsalideae, Cactaceae). Rev. Mex. Biodiversity 81, 393-400

Dynamics of eccentric stem development of Artemisia tridentata var. wyomingensis Hayley Graney∗ Department of Biology, Manhattan College Abstract. This research determined the eccentric nature of a stem segment of Artemisia tridentata in order to understand xylary ring development. A stem segment of 288 mm in length was selected for this research. The stem segment was from a naturally occurring plant near Fremont Canyon, Utah. This stem segment was cut into 32 equally spaced samples. Each sample was photographed and placed into Microsoft Paint. Thereafter measurement of ten equally spaced transects 36 degrees apart (0 degrees, 36, etc.) were drawn on each image. The depth of each xylary ring for each of the transect was determined with ImageJ. The basal portion of this stem had 36 xylary rings whereas the more acropetal portion had 18 xylary rings. All rings except the two inner most rings were eccentric. The xylary depths fluctuated along the stem. For example in stem samples 18 mm apart some xylary rings present in one sample were not present in the adjacent sample. This happened in five of the ten transects between these two samples. Many other examples are presented. This eccentric growth begins in the second year of stem growth and is maintained throughout the life of individual stems. This eccentric growth is the result of the allocation of resources from vegetative growth to reproductive growth to produce a large number of seeds each year.

Introduction One of the main events in plant evolution was the development of woody tissues that allowed plants to grow tall and obtain sunlight above ground level. Woods are composed of vessel and tracheids that function to take water from the soil to the upper reaches of trees (Mauseth 2014; Hopkins & Huner 2004). Wood for tall trees is produced by a vascular cambium that provides secondary growth. The vascular cambium produces both secondary xylem cells (wood) and secondary phloem for the transport of sugars (Mauseth 2014; Hopkins & Huner 2004). The vascular cambium normally produces these tissues in a seasonal manner and thus wood shows annual growth rings.

Wood or secondary xylem of a stem can vary. This variability can be differences in widths of growths rings as well as wood textures (Darling, 1912). The vascular cambium is responsible for secondary growth as well as new phloem and xylem production. In temperate climates, both spring and summer woods are produced (Borner et al., 2006). Spring wood is produced in the early spring of the annual cycle and is more porous and less compact compared with summer wood that is produced during the summer and is less porous and denser (Darling, 1912). Spring wood has its characteristics because sugars that are present in stems over the winter are readily available and growth is rapid in the spring. During the summer (summer wood), growth is slower. Spring and summer wood combined result in a single growth ring. Normal xylary ring development can be seen in Fig. 1 which shows both the first year growth (Fig. 1A) and the second year growth (Fig. 1B) of a Tilia stem. The two years of growth both appear as separate and relatively uniform rings. ∗

Research mentored by Lance Evans, Ph.D.

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Graney

Figures

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Figure 1 A. First year growth of a Tilia stem. This stem illustrates normal xylem growth.

Figure 1 B. Second-year growth of Tilia stem in which there are two layers of normal xylem cells.

Figure 1. A (left): First year growth of a Tilia stem. This stem illustrates normal xylem growth. .

B (right): Second-year growth of Tilia stem in which there are two layers of normal xylem cells

3

Figure 3. Stem wood section of Artemisia triden-

Figure 2. Stems of Artemisia tridentata sampled in this study

Figure 5. Stem wood section of Artemisia tridentata showing extensive eccentric growth. The tata showing extensive eccentric growth. The biologbiological center (location of primary stem tissues is in the lower right-hand corner where the lines cross. Lines demarking the annual rings wereof added.

Note transects 0, 36, 72, is 108,in144, ical center (location primary stemattissues the180, 216 252, 288 and 324 degrees.

ms of Artemisia tridentata sampled in this study.

Figure 4. Stem sample of Artemisia tridentata used in the experiments

lower right-hand corner where the lines cross. Lines demarking the annual rings were added. Note transects at 0, 36, 72, 108, 144, 180, 216 252, 288 and 324 degrees.

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Big sagebrush (Artemisia tridentate) is an evergreen shrub (Fig. 2) that ranges in size from 2 to 13 feet with multi-branched stems (USDA plant guide). Prior to Anglo-Americans, most of the states of Arizona, California, Colorado, Idaho, Montana, Nebraska, Nevada, New Mexico, North Dakota, South Dakota, Oregon, Utah, Washington and Wyoming were covered with numerous subspecies of sagebrush (Welch, 2005). Thus, sagebrush is the plant that most typically describes our “American West.�

Stems of all subspecies of Artemisia tridentata do not show the typical pattern of growth rings described above. Stems show eccentric growth (Fig. 3) or the uneven growth pattern of xylem rings (Diettert, 1938). Thus, during eccentric growth normal circular growth rings are not produced because portions of the vascular cambium die. To better understand eccentric growth of stems, there are two types of branches that occur. If a branch grows year after year it has indeterminate growth. In contrast, if a branch naturally ceases growth because it produces only flowers it is termed determinate growth. Flowering branches are determinate because after flower and seed production the branches die at the end of the season. Determinate and indeterminate branches may also be referred to as flowering and vegetative branches, respectively (Welch, 2005).

It is the growth of these flowering branches that causes death to the vascular cambium in main stems at the point of branch attachment (Evans et al, 2012). In other words, death of the vascular cambium within the main stem is caused by the death of determinant flowering (Evans et al., 2012).

The vascular cambium does not die at all locations only at the attachment point of the branch.

Therefore, eccentric growth occurs year after year as a stem grows. This eccentric growth is magnified as stems become larger. The purpose of the current research is to determine the extent of eccentric behavior among the xylary rings along the stems of Artemisia tridentata var. wyomingensis. Artemisia tridentata Nutt. ssp. wyomingensis (Beetle and Young) is native to many parts of Utah and it is used here. Overall, this research will try to quantify the dynamics of eccentric stem development over a typical stem segment of Artemisia tridentata.

Materials and Methods The stem samples for this study were from Artemisia tridentata var. wyomingensis. They were obtained from Fremont Canyon, Utah (N 40.0; W 112.1). The stem was selected randomly among ten stems. All stems exhibited eccentric growth. One entire stem (1.5 meters long) was selected. A stem segment of 288 mm was selected for analysis. From this stem, 32 individual wood samples were removed for analysis (Table 1). Some of the extraneous bark was removed from the stem prior to sawing of samples along the branch. A black line with a permanent marker (Sharpie Fine Point Permanent Marker) was drawn along the length of the stem (Fig. 4) so that when samples were removed, their orientation would be retained. Small wood samples were cut

by Jason Durney from the wood shop at Manhattan College with a thin fine toothed Dewalt Saw DWHT 205 (mscdirect.com/dewalt). Each wood sample was labeled and archived (Table 1).

Each wood sample was viewed with a dissecting microscope (Leica EZD4 model) to view the xylary rings. Several images of each sample were cataloged. Images were then transferred

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into Microsoft Paint (www.Microsoft.com) where each of the xylem rings was traced in black using a tracing tool (Fig. 3). Ten transects (every 36 degrees) were drawn on each image (Fig. 3). Each transect was drawn from the biological center to the outside bark with Microsoft Paint (www.Microsoft.com) (Fig. 3).

Table 1. Thirty-two wood samples of Artemisia tridentata used in this experiment Sample Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

cumulartive Distance (cm) 0.00 22.2 31.8 38.1 44.4 54.0 63.5 69.8 79.4 89.0 98.4 108 117 125 135 141 151 160 170 181 190 200 210 220 227 235 244 252 262 271 281 289

Diameter (mm) 30 26 25 30 30 35 32 35 35 20 24 18 20 21 20 20 20 20 20 25 20 17 20 23 15 20 16 15 15 15 14 16

Number of xylem rings 36 36 36 35 35 34 34 34 34 33 33 32 32 31 30 29 28 28 28 27 27 27 25 23 22 22 21 21 20 20 19 18

Images were then transferred into Image J (imagej.nih.gov/ij/ ) in order to measure the depth of each xylary ring along each transect line. All depths were entered into Microsoft Excel files (www.Microsoft.com). A ring was considered to be eccentric if the standard deviation/mean among the ten transects was 25% or larger (Evans et al., 2012). For the final portion of the study the patterns of growth were modeled using Sigma Plot (www.sigmaplot.com).

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Results Characteristics of the 32 wood samples are shown in Table 1. As expected, more acropetal stem samples had fewer xylary rings. Specifically, sample 1 had 36 rings while sample 32 had only 18 rings. More acropetal stem samples had smaller diameters. All stem samples of this study showed eccentric growth. Recall that the criterion for eccentric growth is when the standard deviation divided by the mean is greater than twenty five percent (see above). Among all of the samples rings 1 and 2 showed normal growth in only six of the thirty-two samples. All other rings showed eccentric growth in all samples. Data in Table 2 shows data for rings 5 and 7 for wood sample number 22. Data in Table 2 shows depths for rings 5 and 7 for the ten transects. Note the percentage standard deviation is 70% and 162% for rings 5 and 7, respectively.

7

Sample 13

Sample 17

Sample 22

Sample 32

Figure 6. Collage of four samples for comparison.

Figure 5. Collage of four samples for comparison.

The above explanation viewed the eccentric nature for two xyalry rings. This approach does not give a good view of the overall pattern of eccentric growth that can occur. The views in Figure 5 show marked changes in the overall pattern of eccentricity from sample 13 (117 mm from base) to sample 32 (289 mm from base). Thus the distance form sample 13 to sample 32 is 172 mm

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8 9

xylary ring #5

0.6

Xylem Depths (mm)

Xylem Depths (mm)

0.8

0.4 0.2 0 0 ‐0.2

100

200

300

1.2 1 0.8 0.6 0.4 0.2 0

xylary ring #7

10

0

Distance from lowest sample (mm)

100 200 300 Distance from lowest sample (mm)

11

1.2

xylary ring #11

1

Xylem Depths (mm)

Xylem Depths (mm)

7B.2Squares Depths represent of xylem rings for 0 transects 0 and 72 for xylary ring #7. Squares represent transect 0 Figure 7A. Depths of xylem rings for transects 0 and 72 for xylaryFigure ring #5. transect xylary ring #14 circles 72. Distances were calculated from the distance from the lowest stem 1.5 represent while circles the distance from thetransect lowest stem 0.8 represent transect 72. Distances were calculated fromwhile sample. 1

sample.0.6

0.4 0.2 0 ‐0.2 0

100 200 300 Distance from lowest sample (mm)

0.5 0 ‐0.5

0

100

200

300

Distances from lowest sample (mm)

Figure 7C. Depths of xylem rings for transects 0 and 72 for xylaryFigure ring #11. transect 7D.Squares Depths represent of xylem rings for transects 0 and 72 for xylary ring #14. Squares represent transect

Figure 6. Depths of xylem rings for transects 0 and 72 for xylary rings #5, #7, #11, and #14. Squares represent transect 0 while circles represent transect 72. Distances were calculated from the distance lowest 0 while circles represent transectstem 72. Distances were calculated from the distance from the lowest stem 0 while circles represent transect 72. Distances were calculated fromfrom thethedistance from the lowest stem sample. sample.

sample.12

Figure 8. Sample 22 rings 1-20

Figure 7. Sample 17 rings 1-20

14 Radar Plot

108 1-20.

Figure 8. Sample 17 rings

72

108

144

36

0 0

1

2

3

216

4

5

6

7

40 38 36 34 32 30 28 26 24 22 20 18 16 14 12

vs vs vs vs vs vs vs vs vs vs vs vs vs vs vs

Col Col Col Col Col Col Col Col Col Col Col Col Col Col Col

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

36

180

0 0

8

324

Col Col Col Col Col Col Col Col Col Col Col Col Col Col Col

72

144

180

252

15

Figure 9. Sample 22 rings 1-20.

Radar Plot

4

216

6

8

10

324

252

288

Figure 9. Representation of xylary rings for wood sample #17 rings for xylary rings 1 through 20.

2

Col Col Col Col Col Col Col Col Col Col Col Col Col Col Col Col

40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10

vs vs vs vs vs vs vs vs vs vs vs vs vs vs vs vs

Col Col Col Col Col Col Col Col Col Col Col Col Col Col Col Col

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

288

Figure 10. Representation of xylary rings for wood sample #22 rings for xylary rings 1 through 20.

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D i s ta nc e a l on g the s te m (m m )

350 300 250 200 150

18

100 50 0 15

20

25

30

35

N u m be r o f x yl a r y rin g s a lo ng s te m

40

Figure 11. Decrease in the number of xylary rings along the stem. ring was produced every 14.5 mm.

Each 17

Figure 12. Decrease in the number of xylary rings along the stem. Each ring was produced every 14.5 mm.

Figure 12. Left: Sample 27. Right: Sample 28. Demonstrates how rapidly changes occurred across the stem sample one successive sample to the next)

Figure 13A. Sample 27 (from

(Table 1).

Figure 13B. Sample 28. Demonstrates how rapidly changes occurred across the stem sample (from one successive sample to the next).

Four xylary rings (rings 5, 7, 11, 14) were chosen at random among the first twenty rings for detailed analysis. These four xylary rings were tracked along the stem samples from the base of the stem segment selected to the tip (a total of 289 mm). Of the ten transects present in each sample, two transects (0 and 72 degrees) were chosen for observation. Figs. 6 shows the changing xylem depths for the four rings at transect 0 and transect 72 starting from the base of the stem. A general pattern cannot be drawn from the data. That being said, Figs. 6 show that all of the four rings go through a series of increases and decreases. For example at ring 5 for transect 0 the ring depth was 0.52 mm at the base of the stem and 0.32 mm at the top of the stem. In general there was a decrease in the depth of ring 5 however there were points near the middle of the stem where the depth of the ring was smaller than both the starting and ending depths. There were also points where the ring was not present. For example this occurred at 125 mm from the base of the stem for ring 5 at transect 72.

Ring 7 at transect 0 started fairly large at the base of the stem but by the end of the stem the depth greatly decreased. At transect 72 the depth of ring 7 at the base of the stem was the same as the depth at the tip of the stem. The depths of ring 7 between the two ends of the stem fluctuated greatly. The depths of ring 11 at both transects were quite large at the base of the stem however at the other end of the stem the depths decreased. The same pattern of fluctuation of ring depths seen

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Table 2. Depths of rings 5 and 7 for the ten transects of wood sample #22 Transect 0 36 72 108 144 180 216 252 288 324 Mean %SD

Ring 5 (mm) 0.33 0.25 0 0 0 0.36 0.33 0.38 0.33 0.30 0.23 70%

Ring 7 (mm) 0.51 0.43 0 0 0 0 0 0 0 0.46 0.14 162%

Table 3. Changes of ring areas from Sample 17 and Sample 22 Ring Number 5 7 11 14

Sample 17 Areas (mm2 ) 1.29 2.58 4.52 9.68

Sample 22 Areas (mm2 ) 1.94 1.94 3.87 6.45

Area Differences 17 to 22 0.65 -0.64 -0.65 -3.23

% change 50 -25 -14 -33

in the previous rings, 5 and 7, was also seen in ring 11 for both transects. Ring 14 also showed great variety in terms of ring depth. For example at the base of the stem along transect 72, ring 14 was not present but as the distance from the stem base increased ring 14 reappeared along transect 72. The ring then disappeared again by the time the end of the stem was reached. In conclusion there is no general pattern for xylary depths for the thirty-two wood samples.

The areas of the individual rings also changed along the stem. Fig. 7 shows sample 17 that was used in the area comparison with the respective rings (rings 5, 7, 11 and 14). Table 3 shows how the total areas of these four rings changed from sample 17 to sample 22 (Fig. 8). The area of ring 5 increased while the areas of rings 7, 11 and 14 all decreased (Table 3). The percent change for each ring is also show in Table 3. While ring 5 increased by 50%, ring 7 decreased by 25%, ring 11 decreased by 14% and ring 14 decreased by 33% (Table 3).

The changes in the xylary rings were also modeled using Sigma Plot. Fig. 9 shows the model for sample 17 and Fig. 10 shows the model of sample 22. The two images were modeled after Figs. 7 and 8, respectively. The models were compared to actual sample images. They showed an accurate depiction of the xylem ring positions and presence at each of the ten transects.

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Discussion The current study shows that (1) eccentric growth of stems of Artemisia tridentata can be quantitatively evaluated, (2) all rings except the two inner most rings were eccentric, (3) there was no uniform pattern of ring depth among samples, and (4) eccentric behavior can be modeled.

The stem used for this analysis was 288 mm long and had between 18 and 36 xylary rings ranged throughout its length. Moreover, the growth rate of the stem was small (14.5 mm per year; Fig. 11).

As stated above rings 1 and 2 showed normal, non-eccentric growth. All other rings exhibited eccentric growth patterns. They were considered eccentric based on the fact that their values of standard deviation/ mean were greater than 25%. Most xylary rings varied greatly (by as much as 500%) in their depths across the ten transects. These variations produced very high standard deviation to mean values.

As mentioned above, the presence of determinant branches in second year stems causes eccentric growth (Evans et al., 2012). Subsequent growth of stems in later years would only exacerbate the eccentric nature stem anatomy that could occur over very short distances along branches. To illustrate changes in eccentric nature over short distances, data from two successive wood samples will be presented. Views and data of samples 27 and 28 that differed by a distance of 8 mm distance will be illustrated (Fig. 12). At transect 0, rings 10 - 14 were present in sample 28 but absent in sample 27. At transect 72, depths of rings 13 - 18 all decreased 50% from sample 27 to sample 28. At transect 108, ring depths for rings 15 - 19 increased markedly from sample 27 to sample 28. Rings 18 and 19 were not present in sample 27 but they were in sample 28 (Fig. 12). For the transects of 144, 180, and 324 degrees xylary rings were present in sample 28 but were not present in sample 27. For example, rings 7 - 17 were present in sample 28 but not sample 27 at transect 144. At transect 180, rings 8 - 15 were present in sample 28 but they were not present in sample 27. At transect 324, rings 16 - 19 were not present in sample 27 but they were present in sample 28. Clearly, marked differences in eccentric growth occurred over distances of as small as 8 mm.

Models of eccentric growth were created in Sigma Plot to determine if they provide additional visual perspectives of xylary patterns in wood samples A. tridentata. The models showed clear representations of the xylary rings and their orientations about the various transects. However, they did not offer better images than the actual wood images.

The present research centered on demonstrating eccentric growth with the use of 10 transects.

The idea of 10 transects is useful for the purposes of the present research. However, data from only ten transects does not address the issue of overall xylary growth or stem growth. When eccentric growth is present, it is difficult to determine the rates for individual growth rings. Stated another way, since whole sectors of xylary rings of stems are not present while other sectors show growth, it is difficult to calculate xylary growth rates. Future research should focus on determining if the overall areas of xylary rings are constant even with the presence of eccentric portions. It would be interesting to see how eccentric growth at one portion affects the entire stem’s growth rate.

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Vascular cambium death, which is related to eccentric growth, is responsible for the weakening of stem segments of Artemisia tridentata (Evans et al., 2012). Stem weakening could possibly limit the stem segment’s vegetative growth. The low rates of stem growth (14.5 mm per year) characteristic to A. tridentata may therefore be caused by the eccentric growth. It seems reasonable then that eccentric growth would have a deleterious effect on vegetative stem growth. As stated earlier the growth of the flowering branches causes the vascular cambium to die at the point of attachment. A. tridentata sacrifices its vegetative growth for reproductive growth by producing more flowering branches. These flowering branches then cause death to the vascular cambium and hence limit the overall growth of the plant.

The findings from the present research are the first to document eccentric growth along a stem at various transects or angles. The stems of this variety of Artemisia tridentata show growth that is very eccentric. Previously there were few if any quantitative descriptions of eccentric growth just qualitative descriptions. By looking at the stem from this study we can conclude that almost every ring from the sample showed eccentric growth, that Artemisia tridentata appears to sacrifice vegetative growth for reproductive growth and that the dynamics of eccentric growth occur over very short distances.

Acknowledgement

The author is grateful for financial support from the Catherine and Robert Fenton Endowed Chair to Dr. Lance Evans. She would also like to thank Dr. Stanley Kitchen for obtaining and shipping the Sage brush samples.

References

Borner, A. Schulze, E.-D. Schweingruber, F.H. 2006. Atlas of Woody Plant Stems Evolution, Structure, and Environmental Modifications. Springer-Verlag Berlin Heidelberg, Germany.

Darling, C.A. 1912. The Determination of Woods. Torrey Botanical Society. Torreya, Vol. 12, No. 9 (September, 1912), pp. 201-208.

Diettert, R.A. 1938. The morphology of Artemisia tridentata Nutt. Lloydia 1:3-74 Evans, L.S., A. Citta, and S.C. Sanderson. 2012. Flowering branches cause injuries to secondyear main stems of Artemsia tridentata Nutt. subspecies tridentata. Western North American Naturalist. 72: 447-456.

Hopkins, W.G.. Huner, N.P.A. 2004. Introduction to Plant Physiology 3rd Edition. John Wiley and Sons, inc. New York.

Mauseth, J.D. 2014. Botany An Introduction to Plant Biology 5th Edition. Jones Bartlett Learning, LLC. Burlington, MA. United States Department of Agriculture, Natural Resources Conservation Service, Plant Guide. http://plants.usda.gov/ plantguide/pdf/pg artr2.pdf Welch, B. 2005. Big Sagebrush: a sea fragmented into lakes, ponds, and puddles. General Technical Report RMRS-GTR-144, Fort Collins, CO

Dynamics of xylem cell and vascular bundle development in a stem node of Agrostis stolonifera Diana Luzuriaga∗ Department of Biology, Manhattan College Abstract. Grasses are important plants. Corn, rice, wheat, sorghum and sugarcane are very important crops that make up the bulk of human and food animal diet. Grasses have various levels of water use efficiency. Understanding water use efficiency and the process of water movement in grasses is critical to their ability to provide grains. Water is conducted in grasses through xylem vessels within individual vascular bundles. There are no current studies that look at the entire developmental process of individual vascular bundles within grass stem nodes. Previous publications only addressed the anatomy of cells within bundles, the structure of bundles but did not provide a tracking of xylem vessels or vascular bundles within a stem. This experiment tracked entire developmental processes of all vascular bundles through a node. This tracking included changes in the number and location of each vascular bundles and the number of xylem elements within each bundle. Overall, 91 serial tissue sections (total length of 2.7 mm) were processed from a nodal plexus for a stem of Agrostis stolonifera. Forty bundles already present and sixteen bundles that emerged spontaneously within the node were placed into a variety of categories. Of the forty original bundles, 45% bifurcated and stayed within the stem, 13% bifurcated and contributed bundles to the leaf. Fifteen percent of bundles did not bifurcate but stayed within the stem. Fifteen percent of bundles did not bifurcate but moved into the leaf. The remaining 12% had a variety of fates. Sixteen bundles arose spontaneously within the node and they terminated or merged with other bundles. The number of xylem vessels was recorded for each bundle within each tissue section for this study. Overall, the number of vessels in bundles increased prior to bundle bifurcation and decreased before bundles terminated spontaneously. This is the first study that tracked all xylem vessels and all vascular bundles within a nodal plexus of a grass species.

Introduction Grasses play a very significant role in today’s economy. Corn, rice, wheat, sorghum and sugarcane are very important crops that make the bulk of human and food animal diet. In many societies, these grass plants form the main carbohydrate source. Norman Borlaug, an agronomist, investigated grasses and developed a variety of wheat cultivars that were used in many developing countries worldwide. Borlaug’s research revolved around water use efficiency of wheat varieties that could be utilized in arid climates. Borlaug received the Nobel Peace Prize and the Congressional Gold Medal in 1970 for his research for wheat improvement. Therefore, the study of water use in grasses will continue to be an important research area that could contribute to food production.

Evolution plays a large role in the development of vascular structures in plants. Plants species have to compete with their neighbors for sunlight to optimize photosynthesis. With competition, the demand for water increases and therefore, the demand for cells and tissues that can provide water to all plant parts. Thus, vascularization evolved. The development of a variety of vascular bundles, in turn, provided for further evolution into the diversity of plants of today. In dicotyledonous ∗

Research mentored by Lance Evans, Ph.D.

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plants, xylem and phloem tissues are separated by the vascular cambium. Primary xylem tissue is obscured when the vascular cambium produces secondary xylem. Secondary xylem evolved to provide mechanical support and facilitate water conduction. In contrast, monocotyledonous plants have only primary xylem and phloem arranged in vascular bundles.

The anatomy of vascular bundles is well understood in grass plants (Evans, 1928; Arber, 1930; Sharman, 1942; Esau, 1943; Kumazawa; 1958; 1961; Zimmerman and Tomlinson, 1965; Hitch and Sharman, 1971; Dormer, 1972; Zimmerman, 1983, Mauseth, 1988; Shane et al., 2000).

Development of xylem vessels have been described (Evans, 1928; Sharman, 1942; Esau, 1943; Zimmerman and Tomlinson, 1965; Dormer, 1972; Mauseth, 1988; Shane et al, 2000). However, despite some anatomical investigations, there is vague understanding in the overall vascularization systems in monocot plants. There is little information on the initiation of vascular bundles, bifurcation of vascular bundles and the division of bundles between stems and leaves. For this latter situation, only about one-half the number of all vascular bundles in stems is present in each leaf.

The process in which bundles in the stem give rise to bundles in leaves is bifurcation (McCulloh et al., 2003). Other interesting issues involve the origination of new xylem cells and new vascular bundles in stems studied (Evans, 1928; Sharman, 1942; Esau, 1943; Zimmerman and Tomlinson, 1965; Dormer, 1972; Mauseth, 1988; Shane et al, 2000, Sharman, 1942; Esau, 1943) and the ending of vascular bundles (Zimmerman and Tomlinson, 1965).

Investigation of the distribution of vascular bundles in stem and leaf sheath sections has suggested that the leaf sheath contains about half of bundles than the stem. It has also been observed that stem sections below and above a node contain similar numbers of bundles. Therefore, it seems that half the number of bundles in the stem below the node bifurcates to provide one vascular bundle in the sheath and one in the stem above the node, while the other half remains intact through the node. However, in order to investigate this hypothesis, the vascular bundles must be observed carefully in all the consecutive sections throughout a node. It is important to not only track each bundle throughout the node, but to track the number of vessels in each bundle. This would allow a deeper understanding of the bifurcation process. The purpose of this study is to understand the bifurcation process by observing each bundle and their vessels throughout an entire node. This was done by cutting 30 Âľm sections of stem/leaf cross-sections through a node and observing each section in succession under a microscope. Ninety successive sections were evaluated.

Materials and Methods Plants of Agrostis stolonifera were collected in a natural field setting, near the road to Haleakala National Park (N 20â—Ś 46.322, W 156â—Ś 18.452), Maui, Hawaii during July 2013. Agrostis stolonifera was chosen for this research for its limited number of vascular bundles, its hollow stem internodes and its distinct nodes. Each sample composed of a portion of the internode below the node, the node and a portion of the internode above the node. The sample chosen for this study has an indentation at the internode (Fig. 1). The presence of this indentation was important to orient each tissues section taken from the stem.

Fig. 1

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Figure 1. Stem sections of Agrostis stolonifera showing the orientation of bundles. Note the indentation of the stem (the location of a tiller) in each section. This indentation was used to assist in the orientation of bundles. Labels indicate the bundles that were followed in detail. These bundles belong to the four scenarios with the highest percentage of occurrence. A shows the section at the internode basipetal at 0 µm. B shows the section at 1980 µm. In both A and B, the bar equals 200 µm

Table 1. Characterization of the various types of vascular bundles through the nodal tissues of Agrostis stolonifera.

Scenario 1 2 3 4 5 6 7 8 Total 9 a b 10 Total

Description of scenario Present below the node Bifurcated to form bundles that ended, remained in the stem and went into the sheath.

Bifurcated to form bundles that ended and remained in the stem.

Bifurcated to form bundles that ended and went into the sheath.

Bifurcated to form bundles that stayed in stem.

Bifurcated to form bundles that stayed in stem and went into sheath.

No bifurcation. Ended in the stem without change.

No bifurcation. Stayed in the stem without change.

No bifurcation but went into sheath.

Emergent within the node Emergent in stem and ended Without change With bifurcation Emergent and bridged into other bundles.

Number of bundles

Percentage of bundles

1

2.5

11

27.5

5

12.5

7 2

17.5 5

2

5

6

15

6 40

15 100

9 3 4 16

22.5 7.5 10 40

Three stem segments containing an entire node were randomly selected for this study. The stem segments were labeled segment #1, #2 and #3. These tissue samples were fixed in FAA (Jensen, 1962) for 24 hours. Thereafter, samples were dehydrated with a series of tertiary butanol

Fig. 2

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Figure 2. Diagram of the ninety serial microtome segments through the node of segment #1 of Agrostis stolonifera L. All sections were part of the nodal plexus. Section #1 is at the internode basipetal while section #91 is at the internode acropetal.

Luzuriaga

Fig. 3

Figure 3. Normal vascular bundles of Agrostis stolonifera. A. shows a bundle of Agrostis stolonifera with 4 xylem vessels, some parenchyma cells and some phloem cells. B. shows another bundle of Agrostis stolonifera with 5 xylem vessels, some parenchyma cells and some phloem cells. All xylem vessels have Fig. 4 a thick, red stained cell wall, a typical circular appearance and cell enlargement. In all images, the bar equals 20 µm

Figure 4. Process of parenchyma cells giving rise to immature and mature vessels. Bundle BB from the sample of this study is used as an example of this process. Circled in red are mature xylem vessels; circled in green are immature vessels; and circled in black are new mature vessels. A. shows bundle BB at 330 µm. There are parenchyma cells surrounding the 4 xylem vessels. B. shows bundle BB at 420 µm. The immature vessel circled in green is developing a thick cell wall and is growing in size; however, it is not quite large enough and circular enough to be considered a mature vessel. C. shows that the immature vessel has developed a thick cell wall, a circular shape and is enlarged by 450 µm. It is now a mature vessel and is circled in black. In all images, the bar equals 20 µm.

Luzuriaga

Fig. 5

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Figure 5. Bundle KK is used as an example from scenario 2. KK bifurcates into blinding bundles (bundles that end) and leaf trace bundles. Step 1 shows bundle KK at 0 µm. Step 2 shows an enlarged KK and bundle 2 that had emerged independently at 1980 µm. Step 3 shows the result after bridging vessels move from KK into 2 at 2200 µm. At 2250 µm, Step 4 shows that KK has bifurcated into 3 different vascular bundles – KK1, KK2 and KK3. Bundle 2 still remains. Step 5 shows an expanded KK2 at 2430 µm. Step 6 shows that at 2460 µm KK2 has bifurcated into KK2 and KK4; and bundle 2 has started to taper. At 2580 µm, Step 7 shows KK3 becoming more regularly shaped; KK1, KK2 and KK4 have tapered; and bundle 2 has ended. Step 8 shows only KK3 remaining and has moved into the stem while all other bundles have ended.

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Figure 6. Bundle FF is used as an example from scenario 4. FF is an axial bundle and bifurcates into 2 axial bundles.

Step 1 shows bundle FF at 0 µm. Step 2 shows that FF has expanded by 2430 µm. Step 3 shows that bundle FF has bifurcated to produce FF1 and FF2 at 2460 µm. Step 4 shows FF1 and FF2 remain in the stem at 2700 µm.

Fig. 7

Figure 7. Bundle BB is used an example from scenario 8. BB is an axial bundle and becomes a leaf trace bundle through the node. Step 1 shows BB at 0 µm. Step 2 shows that BB has expanded and many parenchyma cells have become mature xylem vessels by 1950 µm. At step 3, at 2070 µm, many xylem vessels end. Step 4 shows that by 2700 µm the leaf sheath has appeared and bundle BB has move into the sheath.

Luzuriaga

Fig. 8

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Figure 8. Bundle 3 is an example from scenario 9(a). Bundle 3 emerges and ends within the node. Step 1 shows the section before bundle 3 emerges at 1950 µm. There are no vascular elements. Step 2 shows the emergence of bundle 3 in the next serial section at 1980 µm. Step 3 shows an elongated bundle 3 at 2070 µm. Step 4 is the section at 2220 µm before bundle 3 disappears. Bundle 3 is tapering in this step. Bundle 3 is no longer found in subsequent sections.

Fig. 9

Figure 9. Bundle 7 is an example from scenario 9(b). Bundle 7 bifurcates and resultant bundles end in the stem. Step 1 shows the section at 2220 µm before bundle 7 emerges and the absence of any vascular elements. Step 2 shows that bundle 7 has emerged in the next serial section at 2250 µm. Step 3 shows bundle 7 has bifurcated to provide 2 bundles – 7a and 7b at 2340 µm. Step 4 shows the section at 2430 µm before both bundles end spontaneously. Bundle 7 is no longer found in sections after 2430 µm.

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Figure 10. Vascular bundles of various grass species. Vascular bundles consist of xylem vessels, phloem cells and parenchyma cells. A shows a vascular bundle from Agrostis stolonifera stems. There are 4 xylem vessels in this bundle.

B shows a vascular bundle from Hordeum vulgare stems.

There are 4 xylem vessels. C shows a vascular bundle from Miscanthus sinensis stems. There are 4 xylem vessels. D shows a vascular bundle from Saccharum officinarum stems with 3 xylem vessels. All species have vascular bundles with about 4 xylem vessels, undifferentiated parenchyma cells that surround the xylem cells and many phloem cells. All xylem vessels have a thick, red stained cell wall, a typical circular appearance and cell enlargement. In all images, the bar equals 20 µm.

solutions. After dehydration, samples were placed in molten paraffin wax (Paraplast X-tra Tissue Embedding, McCormick, Leica Biosystems Richmond, Inc., Richmond, IL) and placed in a 56◦ C oven. The paraffin solution was changed and after 24 hours, tissues were embedded in paraffin.

Embedded tissues were cut with a rotary microtome at 30m, placed on microscope slides with diluted Knotts gelatin and placed on a slide warmer for 24 hours. Ninety-one, 30 µm serial sections were successfully obtained from segment #1 (Fig. 2). Inconsecutive sections were obtained from segments #2 and #3. These tissue sections were used to confirm findings from segment #1. Later, tissues were stained with 30% safranin solution and eventually covered with Canada Balsam.

The ninety-one sections from segment #1 were used primarily for this study. Tracking of the vascular bundles throughout all consecutive sections was made convenient because there was an indentation in the stem that indicated the orientation of the stem. This indentation was the previous location of a tiller. Tillers are side stems that grow after the main stem grows. Each serial section was photographed so that each bundle may be labeled with a letter or number and tracked throughout all sections. All bundles present in the first section (section #1) were assigned letters.

Bundles that emerged in later sections within the node were assigned numbers. In each section, the number of xylem vessels in each bundle was recorded.

Within a vascular bundle, the number of xylem vessels may increase or decrease among sections. Xylem cells may arise from parenchyma cells and may eventually end in later sections.

Therefore, each cell was identified as a xylem cell or a parenchyma cell. In cross-sectional view, typical traits of xylem vessels were (1) a thick, red stained cell wall, (2) a typical circular appearance and (3) cell enlargement. Parenchyma cells may only satisfy one or two of these criteria.

Images of the vessels were uploaded and ImageJ software was used to determine radii of the vessels.

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Results Tracking axial bundles. Grass stems consist of nodes and internodes (Fig. 2). The node is the site of stem where each leaf forms. Internodes are the regions between nodes. For many grasses, internodes of A. stolonifera are hollow with the vascular bundles lining the perimeter of the stem.

For all grasses, including A. stolonifera nodes have septa that form a tissue bridge that links all portions of stems. All stem tissue sections of this study were within the nodal region so a septum was present in all sections.

Stems of Agrostis stolonifera were similar to stems of other grass species (Esau, 1960). All grasses have axial bundles arranged adjacent to the outer stem surface. As stated above there were 91, 30 Âľm, consecutive tissue sections for this study. The most basal section was designated section #1. Section #1 had 40 axial bundles mostly located near the outer stem surface (Fig. 1).

Stems of A. stolonifera had normal vascular bundles (Fig. 3). A normal vascular bundle is circular with about four or five large xylem conduits, some xylem tracheids, many parenchyma cells and many phloem cells (Fig. 3). The xylem vessels were cylinders that were continuous along the stem and were normally arranged in their own cluster. The parenchyma cells were individual spherical cells that surround the xylem cells. Parenchyma cells are usually undifferentiated cells but they can differentiate to become xylem conduits (Esau, 1960). When parenchyma cells differentiate to become xylem vessels or tracheids, they enlarge, lose their cell contents, and they develop a thick secondary cell wall. Many times, cell walls of developing xylem cells fuse with other xylem cells (Fig. 4). Once the secondary cell wall forms, the cell can no longer enlarge.

They then become conduits to move water. Parenchyma cells that are about to differentiate and only satisfy one or two of the criteria stated above were called immature vessels. The main objective of this study was to track axial vascular bundles and all vessel cells within these vascular bundles throughout the nodal region. Ten scenarios were observed (Table 1). Eight scenarios were assigned for the 40 vascular bundles present in section #1 of the node while an additional two scenarios were assigned for the 16 vascular bundles that emerged within the nodal plexus.

The 40 initial axial or cauline bundles at the nodal plexus were assigned letter designations.

For these 40 axial bundles, 26 bundles underwent at least one bundle bifurcation (Table 1; Scenarios 1 through 5) . Among these 26 bundles, eight bundles bifurcated to provide leaf trace bundles (bundles to leaf sheath; Scenarios 1,3 and 5). Seventeen of the initial 40 axial bundles bifurcated to provide axial bundles that ended spontaneously within the node (Scenarios 1 through 3). Twentyone of the initial bundles bifurcated to provide bundles that remained in the stem (Scenarios 1, 2, 4 and 5). Fourteen initial axial bundles did not bifurcate (Scenarios 6 through 8). Of these fourteen bundles, eight stayed within the stem while six were contributed to the leaf sheath.

Sixteen axial bundles that spontaneously emerged within the nodal region were assigned number designations and tracked through subsequent sections. Among these 16 emergent bundles, twelve ended spontaneously within the stem while four bundles merged with the existing axial bundles. None of these emergent bundles contributed bundles or vessels to leaf traces.

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Bundles from the four scenarios with the most frequent occurrence will be illustrated further.

Scenario 2 involved an axial bundle present that either ended spontaneously within the nodal plexus or went to the stem. For this scenario, the fate of bundle KK was followed (Fig. 5). In step 1, at 0 µm, bundle KK had four xylem vessels and several parenchyma cells. At step 2, at 1980 µm, KK had 23 vessels and bundle 2 emerged spontaneously with 6 vessels. Step 3, at 2200 µm, vessels bridged from bundle KK laterally into bundle 2, resulting in 16 vessels each. At step 4, at 2250 µm, KK bifurcated to produce KK1, KK2 and KK3 with 4, 6 and 7 vessels respectively. Bundle 2 was still present with 13 vessels. Step 5, at 2430 µm, bundles KK1, KK3 and 2 change little with 5, 8 and 8 vessels respectively, while bundle KK2 expanded significantly with 19 vessels. At step 6, at 2460 µm, bundles KK1 and KK3 do not change much with 5 and 7 vessels respectively. Bundle KK2 has now bifurcated into bundles KK2 and KK4 with 5 and 9 vessels respectively. Bundle 2 starts to taper and only 3 vessels remain. At step 7, at 2580 µm, bundles KK1, KK2 and KK4 start to taper with 6, 5 and 2 vessels respectively. Bundle KK3 starts to become more regular-shaped and circular with 5 vessels. Bundle 2 has ended. At step 8, 2700 µm, bundles KK1, KK2 and KK4 have all ended and KK3 moves into the stem with 5 vessels.

Scenario 4 involved axial bundles present at the internode that bifurcated into two axial bundles. For bundle FF (Fig. 6), bundle FF has four vessels with some parenchyma cells at 0 µm. By step 2, at 2430 µm, FF expanded significantly and had 17 vessels. At step 3, at 2460 µm, bundle FF had bifurcated to produce bundle FF1 and FF2 with 9 and 6 vessels, respectively. By step 4, at 2700 µm, FF1 and FF2 remained in the stem with 9 and 8 vessels respectively.

Axial bundles of Scenario 8 provided bundles to leaf sheaths without bifurcation. Step 1 of axial bundle BB had four vessels and some parenchyma cells at 0 µm here (Fig. 7). At step 2, at 1950 µm, bundle BB enlarged and had 21 vessels. At Step 3 bundle BB had seven vessels at 2070 µm. By step 4, at 2700 µm, bundle BB is present in the leaf sheath with 13 vessels.

Tracking emergent bundles. Scenario 9 involved bundles that emerged spontaneously within the nodal plexus. Scenario 9(a) involved emergent bundles that ended spontaneously within the nodal plexus with or without bifurcation while Scenario 9(b) involved emergent bundles that bridged with existing axial bundles.

For scenario 9(a), the fate of bundle 3 is followed (Fig. 8). At Step 1, at 1950 µm, shows parenchyma cells. Within the next tissue section, at 1980 µm, (Step 2) bundle 3 had 16 vessels.

At step 3, at 2070 µm, bundle 3 has enlarged with 13 vessels. Step 4, at 2220 µm, bundle 3 had decreased in area and had only six vessels. In subsequent sections, bundle 3 was no longer present.

For scenario 9(b), the fate of bundle 7 was followed (Fig. 9). Step 1, at 2220 µm, only parenchyma cells were present. Similar to bundle 3, no vascular elements were found in this region. Step 2 shows the next section at 2250 µm. Bundle 7 emerged and had 30 vessels. At step 3, at 2340 µm, bundle 7 bifurcated to provide 2 bundles – 7a and 7b with 5 and 13 vessels respectively. Step 4, at 2430 µm, shows bundle 7a with 4 vessels and bundle 7b with 10 vessels in

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the section right before both bundles spontaneously end. In subsequent section, bundle 7a and 7b and their vascular elements were no longer found.

Table 2. Number of vessels per bundle for 15 randomly selected bundles through the node.

Distance (in Âľm) from most basal tissue section Original Bundle (scenario number)

derived bundles

A (5)

A1 A2 A3 A4 A5 A6 A7 F1 F2 H1 H2 H3 M1 M2 M3 M4 M5 O S1 S2 T1 T2 W1 W2 W3 AA1 AA2 AA3 EE1 EE2 NN1 NN2 NN3 GG1 GG2 II 3 KK1 KK2 KK3 KK4 MM

F (2) H (5) M (4)

O (6) S (2) T (2) W (4) AA (2) EE (3) NN (2) GG (3) II (8) KK (2)

MM (7) Total

0 5

1950

1980

11

17

2130

2310

2430

2520

Number of vessels per bundle 10 17 8 5 9 5 10 9 5 11 5

4

8

10

11

4

11

18

5

8

15

16 17 17 16

5 5

10 10

9 10

11 11

4

10

16

26

4

8

9

4

10

19

3

10

12

4

7

12

9 4 23 8 6 5 8 4 9

5

9

24

8 4

10 6

4 63

8 134

6 6 8 9 7 7

2670

2700

2 6 11 7 ended 5 3 6 4 8 2 3 6 3 13 3 4

6 6 6 4 ended ended 4 ended 8 3 2 7 5 9 4 ended

7

6

9 11 10 4 4 10 7 6 6

6 ended 7 2 ended 7 6 ended 3 2 ended 6 ended 5 ended ended 7 134

7 8 10 6 6 7 6 8

8 6 11 6 6 10 3 9

9 7 19 7 7 7 10 8 10

19 7 6 25 8 10 3 12 13 7 3 9 6 18

15 11 7 15 9 10 7 14 12 15 2 86 3 22

8 10 ended 20 6 10 6 5 12 8 7 7 ended 8 6

15 9 8 3 9 7

13 ended 6 5 19 7

13

12 13

16 3 14 14

7 5 3 10

10 204

9 263

8 298

5 294

6 5 5 8 10 5 284

7 3 5 2 5 9 216

Tracking numbers of vessels in bundles. Additionally, 15 random bundles were then tracked to estimate the total number of vessels in several sections throughout the node (Table 2). This was done to observe how the total number of vessels changed along the node of Agrostis stolonifera. 15

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bundles were randomly selected and tracked at 9 sections across the node. The number of vessels in each of these 15 bundles and in the bundles they gave rise to was recorded. For example, bundle A from scenario 5 gave rise to a total of seven bundles (A1 – A7) within the node. At 0 µm, bundle A had 5 vessels. By 2700 µm¸ the 4 remaining bundles (A1 - A4) had 22 vessels. Therefore, the sum of the number of vessels that arose from these 15 bundles was taken at nine different sections.

At 0 µm, the 15 bundles possessed a total of 63 vessels. At 2700 µm, the 15 bundles gave rose to 25 remaining bundles with 134 vessels.

The data from Table 2 allow estimations of the total number of vessels in all bundles along the node (Table 3). It can now be observed how the total numbers of bundles and vessels change along the node of Agrostis stolonifera. The 40 initial bundles at the internode basipetal gave rise to 65 bundles at 2700 µm, in which 50 bundles remained in the stem and 15 bundles went into the sheath.

This is consistent with the claim that the number of bundles in the stem remains about constant through a node, while the number of bundles in the leaf is about half the number of bundles in the stem (unpublished results). The total number of bundles increases from 40 to 83 by 2520 µm. As 18 bundles end spontaneously, 65 bundles are left at 2700 µm. Essentially, the total number of bundles doubles from 100% to 208% ( 200%). 45% then end spontaneously resulting in the 163% ( 150%). Furthermore, table 4 shows that as the number of bundles doubles, the number of vessels quadruples, indicating that the number of vessels per bundle also doubles. At 2520 µm, the mean vessels per bundles increased from 4.2 to 8.4. Lastly, table 4 also indicates that the resulting 65 bundles have more vessels per each bundle than the initial 40 bundles.

Tracking vessels in emergent bundles. Since the 15 bundles that were randomly selected from the initial 40 bundles did not account for emergent bundles, three randomly selected emergent bundles were also tracked at 9 locations along the stem (Table 4). For example, bundle 7 from scenario 9b was tracked. Bundle 7 emerged at 2250 µm with 20 vessels, bifurcated at 2340 µm to produce bundle 7a with 5 vessels and bundle 7b with 13 vessels and both these bundles ended spontaneously at 2460 µm.

Discussion Many grass species such as Hordeum vulgare, Miscanthus sinensis and Saccharum officinarum have vascular bundles that each consists of about four xylem conduits, some tracheids, parenchyma cells and phloem tissue (Fig. 10). Bundles of Agrostis stolonifera have normal vascular bundles and vessels for grass species. Therefore, this study can provide a general model for vascularization for grass species.

Both vessels and tracheids were present in all bundles in this study. However, only numbers of vessels were counted for this analysis. This is because the xylem vessels made the largest contribution to xylem conductivity for Agrostis stolonifera. Data from bundle A of this study was used to show this. Bundle A at the internode basipetal was observed. The xylem conductivity (McCulloh and Sperry, 2005) of bundle A was obtained from four xylem vessels and five tracheids. The mean

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and standard deviations of radii for the xylem vessels were 9.94 and 2.73 µm, respectively. The xylem conductivity of the four vessels alone was 0.00200 g cm MPa−1 s−1 . The mean and standard deviations of radii for the five tracheids were 3.27 and 0.74 µm, respectively. The conductivity for the five tracheids was added to the conductivity of the four vessels, giving 0.00214 g cm MPa−1 s−1 . Therefore, this shows that the five tracheids only contributed 1.4% of the conductivity of four vessels.

Table 3. Total number of bundles and estimated total number of vessels in 9 sections across the node. (*50 bundles were found in the stem and 15 bundles were found in the leaf sheath.)

Total distance from section 1 (in µm) 2700 2670 2520 2430 2310 2130 1980 1950 0

Total number of bundles in stem 65* 66 83 77 69 58 48 40 40

Number of vessels from initial 15 bundles 134 216 284 294 298 263 204 134 63

Number of bundles from initial 15 bundles 25 36 34 33 30 24 15 15 15

Mean number of vessels per bundle from initial 15 bundles 5.4 6.0 8.4 8.9 9.9 11.0 13.6 8.9 4.2

Estimated total number of vessels in all bundles 348 396 693 686 685 636 653 357 168

There are no existing publications that explain this process thoroughly. Certain publications only address the anatomy of vascular systems and the development of its elements without relating it to the pathway of the vascular bundle through a node. Others vaguely track individual bundles across the node without addressing the changes in structure of the vascular bundle and its elements. This study aims to address both matters. This experiment tracks the entire developmental process of each vascular bundle through a node while addressing changes in number and structure of vascular elements.

There has been research that developed general paths for vascular bundles throughout the internode and node (Evans, 1928; Sharman, 1942; Esau, 1943; Zimmerman and Tomlinson, 1965; Dormer, 1972; Mauseth, 1988). These previous research show that in the internode, axial bundles that later bifurcate to produce a leaf trace bundle, commonly move from the perimeter of the stem towards the center of the stem cross-section. This occurs at the internode below the node. At the nodal plexus, bifurcation takes place to produce a leaf trace bundle (Zimmerman and Tomlinson, 1965; Dormer, 1972; Mauseth, 1988). This current study does not observe this process. The sample collected contained sections that were all part of the nodal plexus. The processes viewed were within the nodal plexus, and not the internode. Most research only focused on a few sections throughout the stem. Zimmerman and Tomlinson (1965) viewed each tenth section in Rhapis excelsa. At the internode basipetal to a node, R. excelsa bundles were found near the stem periph-

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Table 4. Number of vessels per bundle for three randomly selected emergent bundles through the node. (* indicates the occurrence of bridging) Distance (in Âľm) from most basal tissue section Original bundle (scenario number) 3 (9a) 7 (9b) 2 (10)

Derived bundles

7a 7b

0 0 0

1950 1980 2070 2130 2220 2250 2310 2340 2430 2460 2520 2580 0 0

16 0

0

6

13 0

Number of vessels per bundle 6 ended 0 20 18 5 4 13 10 13* 16 13 8

3

ended ended

ended

ery. Zimmerman and Tomlinson (1968) have developed a six-step process to show the individual bundles development across the stem internode and nodal plexus. First, bridging was revealed to occur at the internode. Bundles then started to move towards the center of the stem at position #2.

As bundles move towards the middle of the internode (position #3), protoxylem tends to appear.

By position #4, bundles have enlarged significantly. Towards the nodal plexus (position #5), the existing bundles have developed into one of four fates – axial bundles, leaf trace bundles, satellite bundles and bridges. By position #6, leaf trace bundles move into the leaf sheath; and the satellite bundles are now found between the axial bundle and the leaf sheath.

Shane et al. (2000) used particulate tracers to study the xylem pathways for water in maize stems. Their research shows that tracers were not found in all bundles in stem section. This result is clearly related to the current study. The lack of tracers in some bundles (Shane et al., 2000) is consistent with the significant percentages of emergent and blinded bundles found in this study.

Another study conducted by Dong et al. (1997) revealed that tracers in sugarcane stem did not reach leaves caused by filters in vessel pit membranes. The presence of the emergent and blinded bundles and the effect of its decreased ability for water transport are unknown. Clearly, emergent and blinded bundles are present in significant numbers but there have been no explanations as to their function or functions.

Zimmerman and Tomlinson (1965) and Mauseth (1988) show bridging of bundles in grass stems and leaves. In other research, filters in pit membranes of vessels are shown (Dong et al., 1997). There is the question of whether filters are similar among bridging vessels as for vessels not part of bridge. Currently, there are no publications that support this. More research needs to be performed with tracers to study the anatomy of these structures.

Dormer (1972) reexamined Evans (1928) data and concluded that there was no single general rule for the behavior of individual bundles within the node of Zea mays. Dormer (1972) suggested a statistical approach to examine the origin and track of individual bundles. This study has applied that recommendation and revealed several complex bundle scenarios. Therefore, this study is consistent with the conclusions of Evans (1928) and Dormer (1972). Furthermore, Evans (1928) and Zimmerman and Tomlinson (1968) decided that their methods would only provide reliable data

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for observing large bundles but not smaller bundles. Evans (1928) made use of a retting process while Zimmerman and Tomlinson (1968) employed an optical shuttle method. This current study uses several serial microtome sections that allow the tracking of large and smaller bundles and emergent and blinding bundles.

This study also concentrated on the change in the number of vessels in individual bundles within the nodal plexus (Table 2). For example, bundle K had four vessels at 0 µm. By 2310 µm, the number of vessels within KK had increased to 14 vessels. At 2310 µm, KK has bifurcated to provide three bundles. KK1 had three vessels; KK2 had nine vessels; and KK3 had seven vessels.

At 2520 µm, KK2, which previously had nineteen vessels, had bifurcated to form two bundles – KK2 and KK4. KK2 had 5 vessels while KK4 had ten vessels. By 2700 µm, KK1, KK2 and KK4 have all ended and KK3 remains. This shows that serial anatomical sections are capable of showing and allowing the tracking of smaller bundles.

Table 2 and Table 3 also show more than the tracking of vessels. These tables reveal how different events happen at different locations and sections across the nodal plexus. They also show how vessels decrease as a bundle starts to taper before it ends; how vessels increase as a bundle starts to expand before it bifurcates; and how vessels are allocated among the resultant bundles after bifurcation.

This study did not show the horizontal traces in stem sections of Agrostis stolonifera that were present in Zea mays (Strasburger, 1891; Esau, 1942). This absence could be due to the fact that, unlike Zea mays, bundles of A. stolonifera were found near the periphery of stem section.

Horizontal traces could also have been present within the stem internode, however, intermodal sections were not considered for this study.

Agrostis stolonifera stems were used in this study because there were only forty clearly demarked vascular bundles with only sixteen emergent bundles within the nodal plexus. Stems from other monocotyledonous plants, such as sugarcane (Dong et al. 1997), maize (Esau, 1943; Kumazawa; 1958; 1961; Shane et al., 2000), palms (Zimmerman and Tomlinson, 1965; Zimmerman et al., 1982) and bamboo (Liese, 1980; McClure, 1966), have large numbers of vascular bundles compared to A. stolonifera. Stems with a large number of bundles may have a corresponding larger number of scenarios compared to this study. Furthermore, monocot plants also have a large diversity of leaf morphology that can also account for the diversity of vascular bundles.

Acknowledgement The author is grateful for financial support from the Catherine and Robert Fenton Endowed Chair to Dr. Lance Evans.

References Arber, A. 1930. Studies in the Gramineae IX 1. The nodal plexus. 2. Amphivasal bundles. Annuals of Botany 44:593-619.

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Dong, Z., M.E. McCully and M.J. Canny. 1997. Does Acetobacter diazotrophicus live and move in the xylem of sugarcane stems? Anatomical and physiological data. Annuals of Botany 80: 147-158.

Dormer, K.J. 1972. Shoot Organization in Vascular Plants. Syracuse University Press. 240 pages.

Esau, K. 1943. Ontogeny of the vascular bundle in Zea mays. Hilgardia 15: 327- 368.

Esau. K. 1960. Plant Anatomy. John Wiley Sons, Inc. New York.

Evans, A.T. 1928. Vascularization of the node in Zea mays. Bot. Gaz. 85: 97-103.

Hitch, P.A. and B.C. Sharman. 1971. The vascular pattern of festucoid grass axes, with particular reference to nodal plexi. Bot Gazette 132:38-56.

Jensen, W.A. (1962). Botanical Histochemistry. – Principles and Practice. W.H. Freeman. San Francisco, CA. Kumazawa, M. 1958. Vascular connection of the axillary shoot and the adventitious root with their mother axis. Vascular anatomy in maize. Bot. Mag. Tokyo 71:70-6.

Kumazawa, M. 1961. Studies on the vascular course in maize plant. Photomorphology 11:128139.-76.

Liese, W. 1980. Anatomy of bamboo. 161-164. In: Proc. Workshop on Bamboo Research in Asia.

Singapore. (Eds.) G. Lessard and A. Chouinard. IDRC, Ottawa, Canada.

Mauseth, J. D. 1988. Plant Anatomy. The Blackburn Press. Caldwell, NJ. McClure, F.A. 1966. The Bamboos. Harvard Univ. Press, Cambridge, USA. McCulloh K, Sperry J and Alder F. 2003. Water transport in plants obeys Murray’s law. Nature 421: 939-942.

McCulloh, K.A., J. S. Sperry 2005 Patterns in hydraulic architecture and their implications for transport efficiency. Tree Physiology 25: 257-267.

Shane, M. W., M.E. McCully and M.J. Canny. 2000. The vascular system of maize stems revisited: Implications for water transport and xylem safety. Annals of Botany 86: 245-258.

Sharman, B.C. 1942. Developmental anatomy of the shoot of Zea mays. Annals of Botany 6:245281.

Strasburger, E. 1891. Ueber den Bau die Verrichtungen der Leitungsbahnen in den Pflanzen. Histologische Beltrage 3. 1000 p. Gustav Fischer, Jena.

Zimmerman, M.H. 1983. Xylem structure and the ascent of sap. Springer-Verlag, Berlin. 143 pages.

Zimmerman, M.H., and P.B. Tomlinson. 1965 Anatomy of the palm Rhapis excelsa I. Mature vegetative axis. J. Arnold Arbor. 46: 160-178.

Zimmerman, M.H., and P.B. Tomlinson. 1968 Vascular construction and development in the aerial stem of Prionium (Juncaceae). Amer. J. Bot. 55: 1100-1109.

Zimmerman, M.H., K. F. McCue and J.S. Sperry. 1982. Anatomy of the palm Rhapis excelsa VIII. Vessel network and vessel length distribution in the stem. J. Arnold Arbor. 63: 83-95.

Range expansion of the non-native Asian shore crab in the Hudson River Angelica Romero∗ Department of Biology, Manhattan College Abstract. Hemigrapsus sanguineus, the Asian shore crab, is an invasive species first noted in 1988 (New Jersey) and now fully established on the outer coast of the northwestern Atlantic from the Carolinas to Maine. Earlier experiments have shown that the larvae stage of these crabs cannot survive in salinities lower than 25 psu. The purpose of this research was to document the local distribution of H. sanguineus by using the Hudson-Raritan estuary as a natural salinity gradient from oligohaline to euryhaline conditions. At four sites along the Hudson and one reference site in western Long Island Sound, both population density and individual size distribution were documented by using quadrat and catch per unit effort methods. The results of these sampling efforts showed an increasing abundance of crabs along the salinity gradient ranging from 0.8 to 5 m−2 at the highest saline Hudson site, but 74 m−2 at the reference site.

Interestingly, individual crab sizes tended to be smaller at the higher salinity sites. Additional laboratory experiments tested the effect of salinity on larval hatching success. Ovigerous females were placed in a jar of either 5, 15 or 25 psu.

The results of these tests showed individuals in 15 and 25 psu treatments had approximately triple the survival rate than those in 5 psu treatments. Lastly, no differences among the amount of days it took to hatch were found among the three treatments. In many life stages, H. sanguineus is able to tolerate lower salinities than previously reported.

Introduction Hemigrapsus sanguineus, the Asian shore crab (Fig. 1), is an invasive species first noted in 1988 in New Jersey at the Townsends Inlet Bridge in Cape May County (McDermott, 1991) and now fully established on the outer coast of the northwestern Atlantic (Epifanio, 2013). It is native to Western Pacific, where it is found in the upper and middle intertidal zones of rocky beaches or in the lower parts of estuaries (McDermott, 1998). Eventually this species of crab may displace the native mud crabs on the East Coast and create the localized extinction (Lohrer and Whitlatch, 2002).

The purpose of this research is to investigate if the population of H. sanguineus has expanded its local range into lower saline estuarine habitats. The Hudson-Raritan estuary offers a salinity gradient from oligohaline (Riverdale) to euryhaline (Governor’s Island) conditions. Many organisms have a difficult time changing from water with high salinity to low salinity because they have limited osmoregulatory abilities. Crustaceans can use osmoregulation but not to a great extent.

Adult H. sanguineus have been recorded by Epifanio and his team (Epifanio et al., 1998) in areas with salinities over 25 psu. They are especially sensitive to changes in salinity when they are larvae. However, the larvae stage would be the presumed stage that these crabs move great distances since this is the dispersal stage. Further experiments have shown that the larvae stage of these crabs cannot survive in salinities lower than 25 psu (for a review, see Epifanio, 2013). ∗

Research mentored by Michael Judge, Ph.D.

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In conjunction with population density estimates, we also looked at egg survivorship of these crabs in the extreme portion of their local range along with the salinity and temperature of the water in these areas.

Materials and Methods

For this research, four sample sites were used along the Hudson River, these include: Riverdale, George Washington Bridge, 125th Street and Governor’s Island. These sites were chosen because they formed a salinity gradient within the Hudson from north to south. A fifth site, Clason Point, was used as a reference site due to its high abundance of H. sanguineus and previous census efforts (2001 and 2008). All sites were sampled three times during the summer of 2013 at less than 0.4 ft. During each sampling period, salinity (via refractometer), temperature (air and water), arrival and departure time were recorded.

Because some sites possessed sloping beaches and other rip rap, two types of sampling methods were used, quadrat sampling and catch per unit effort (CPUE). In order to compare sampling methods both sampling methods were used at Riverdale and Clason Point to establish a standard curve.

The first method, quadrat sampling, consists of using 1-m2 plots (PVC pipe) to establish the sampling area. Placements for the quadrats were split, half at the low tide mark and half slightly higher. During the quadrat sampling, researchers flipped over rocks and collected all crabs. After collection, all crabs were identified for species, sex, and presence of eggs. In addition, carapace width was recorded to the nearest 0.05mm using vernier calipers. All crabs were released after sampling. Quadrat sampling was conducted at Riverdale, Clason Point and George Washington Bride.

The second method sampling method, CPUE, entailed the researchers collecting all crabs as quickly as they were encountered. This was used at locations that had a terrain difficult to set a quadrat down at such as 125th Street and Governor’s Island. The amount of time spent searching for crabs ranged from 10 minutes to 60 minutes depending upon the relative abundance of crabs at each site. CPUE was expressed as # crabs caught / #collectors / collection time. If the site was known to have a high abundance of crabs the time would be shorter than a site with a known lower abundance.

The second part of this research dealt with egg survivorship relative to salinity in a laboratory setting. This was done over a period of 19 days. Females carrying eggs (24) were collected at Clason Point on July 17, 2013 between 12:26 and 13:30 hours in a site away from those used for abundance sampling. Once in the lab the crabs were split into three groups based on the maturation of their eggs (i.e. colorscale). The salt water treatments of consisted of 5, 15 and 25 psu. Before placed in the jars each crab’s carapace width was measured. Each treatment was replicated 8 times (one measured crab per jar) were placed in an incubator set at 21◦ C and 12 hour light/dark cycle.

The crabs were checked each weekday for proper aeration, egg color, larval release. Once a crab released her eggs, the amount of larvae (dead and alive) were counted.

sites also contained the largest recorded body sizes for individuals. Between these two sites Clason Point

Romero

seems to show a slightly larger mean body size than the individuals at Governor’s Island. The lower The Manhattan Scientist, Series B, Volume 1 (2014) saline sites, Riverdale, George Washington Bridge and 125th Street all showed a larger mean body size.

Using the Kolmogorov-Smirnov test, cumulative frequency distribution showed no difference among Riverdale, George Washington Bridge and 125th Street. Both Governor’s Island and Clason Point differed from each other and all over sites. Governors Island did not show a heightened peak like the lower saline sites.

and C. sapidus. At George Washington Bridge, about one-half of the crabs were R. harrisii, followed by

Figure 1. Hemigrapsus sanguineus

30% H. sanguineus, and a smaller proportion U. minax, spp, and C. sapidus. At 125th Street Hemigrapsus Body SizePanopeidae Distribution 0.4

the proportion of H. sanguineus found jumped to about 80% with the rest of the population of crabs 0.35

being R. harrisii0.3and Panopeidae spp. At Governor’s Island the proportionRiverdale found to be H. sanguineus 0.25 George Washington Bridge 0.2to about 92% and the rest of the population consisted of Panopeidae spp and C. Proportion increased again 125th Street 0.15 Governor's Island 0.1

maenas. At Clason Point the proportion of H. sanguineus reached almost 100% with one C. sapidus Clason Point

0.05

found.

0 0

10

20 30 Carapace Width (mm)

40

Frequency of Crab Species Among Sites

2. Hemigrapsus body distribution The types of crabsFigure found varied at each of the five sitessize (Figure 3). Each crab species along the salinity gradient starting with Rithropanopeus harrisii, found at relatively low salinity, and Carcinus 1 maenas which is0.9 typical of higher saline waters. Of all the crabs, Hemigrapsus sanguineus is the only one 0.8 0.7 found at each of0.6 the five locations. For Riverdale, the majority of crabs were proportion Riverdale found to be R. Proportion 0.5 0.4 George Washington Brdge harrisii, followed by a small amount of H. sanguineus and an even smaller proportion of Panopeidae spp 0.3 0.2 125th Street 0.1 0 Governor's Island Clason Point

Species

Figure 3. Frequency of crab species among sites Hemigrapsus Frequency Along Salinity Gradient proportion of H. sanguineus among all crab species. Overall, the proportion of Hemigrapsus increased

The salinity recorded for all sampling days was averaged for each site (Figure 4). To express the

Riverdale 1 with salinity up to 25psu. Thus, those sites such as Riverdale, George Washington Bridge and 125th 0.8 G. Washington Bridge 0.6salinity averages exhibited a lower proportion of H. sanguineus relative to sites such as Street with lower 125th Street Proportion 0.4 Clason Point or Governor’s Island.

0.2 Governor's Island 0 0 10 20 30 Clason Point Mean Salinity (psu)

Figure 4. Hemigrapsus frequency along salinity gradient

In order to establish a standard curve to facilitate comparison of density estimates, the

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Results Individual size distribution among sites, between sex, and among dates, were analyzed by using the Kolmogorov-Smirnov test (see Chakravarti et al., 1967). For maximum differences between cumulative frequency distribution no significant difference in size distribution were attributed to sex with a value from all four sites higher than 0.2. When tested for differences among dates for each site, none of the sites showed a significant difference except for Clason Point where the July date differed from the other two dates with a value of 0.049. Once all of the sites were tested against each other there was no significant difference between Riverdale, George Washington Bridge and 125th Street with values all greater than 0.1. However, Clason Point differed from all others as well as Governor’s Island.

The overall body size distribution varied among sites (Fig. 2). The sites are organized along a salinity gradient starting from low (Riverdale) to high (Clason Point). It appears that the higher saline sites had an average body size smaller than the lower saline sites. Of the all the sites, H. sanguineus appeared to have the smallest mean size at Clason Point followed by Governor’s Island.

However, these sites also contained the largest recorded body sizes for individuals. Between these two sites Clason Point seems to show a slightly larger mean body size than the individuals at Governor’s Island. The lower saline sites, Riverdale, George Washington Bridge and 125th Street all showed a larger mean body size. Using the Kolmogorov-Smirnov test, cumulative frequency distribution showed no difference among Riverdale, George Washington Bridge and 125th Street.

Both Governor’s Island and Clason Point differed from each other and all over sites. Governors Island did not show a heightened peak like the lower saline sites.

The types of crabs found varied at each of the five sites (Fig. 3). Each crab species along the salinity gradient starting with Rithropanopeus harrisii, found at relatively low salinity, and Carcinus maenas which is typical of higher saline waters. Of all the crabs, Hemigrapsus sanguineus is the only one found at each of the five locations. For Riverdale, the majority of crabs were proportion found to be R. harrisii, followed by a small amount of H. sanguineus and an even smaller proportion of Panopeidae spp and C. sapidus. At George Washington Bridge, about one-half of the crabs were R. harrisii, followed by 30% H. sanguineus, and a smaller proportion U. minax, Panopeidae spp, and C. sapidus. At 125th Street the proportion of H. sanguineus found jumped to about 80% with the rest of the population of crabs being R. harrisii and Panopeidae spp. At Governor’s Island the proportion found to be H. sanguineus increased again to about 92% and the rest of the population consisted of Panopeidae spp and C. maenas. At Clason Point the proportion of H. sanguineus reached almost 100% with one C. sapidus found.

The salinity recorded for all sampling days was averaged for each site (Fig. 4), to express the proportion of H. sanguineus among all crab species. Overall, the proportion of Hemigrapsus increased with salinity up to 25 psu. Thus, those sites such as Riverdale, George Washington Bridge and 125th Street with lower salinity averages exhibited a lower proportion of H. sanguineus relative to sites such as Clason Point or Governor’s Island.

Riverdale to Governor’s Island (figure 6). Once at Clason Point the density of crabs increased to about 80 correlation line had an equation of y = 0.0689x + 0.2805 to describe the relationship between quadrat ten times the amount of any other site sampled. and CPUE. The standard curve was used to estimate the density of 125th street and Governor’s Island.

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9 8 7 6 Count Per Unit 5 Effort 4 (#/person/min) 3 2 1 0

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110

0100 5

90

-20 80

y = 0.0689x + 0.2805 R² = 1

0

20

40

60

15

80

100

120

Density (#/m²)

Figure 5. Comparison of density estimates

25

Salinity (%)

70

Density (#/m²) 60 50 40 30 Of the three different treatments none differed when it came to amount of time it t 20 10 0 140 larvae to hatch (Figure 7). When looking at the maturity of the eggs those that were less ma Riverdale George 125th Street Governor's Clason Point Washington Island took longer to hatch than those more mature.

Bridge Site

Figure 6. Hemigrapsus density among sites

Hatching success of the larvae was measured at 3 different salinities (Figure 7). Individuals in

Hatching Success

Days to Hatching

120

both the 15psu16 and 25psu treatments had the highest survival rate. Individuals in the 5psu treatment

100

14 times less likely to survive when compared to the other treatments. The 15psu were about three 12

80

treatment showed 10 close to 100% success in surviving larvae.

20 0 -20

Immature

Number of 8 Days 6 4 2 0

Proportion 60 Alive 40

5

15

25

Young Intermediate Ready to Hatch 0

5

10

15

20

25

30

Salinity (psu)

Salinity (%)

Figure 7. Hatching success

Of the three different treatments none differed when it came to amount of time it takes for the

Figure 8. Days to hatching

larvae to hatch (Figure 7). When looking at the maturity of the eggs those that were less mature to start

In order to establish a standard curve to facilitate comparison of density estimates (Fig. 5), the took longer to hatch than those more mature.

Riverdale and Clason Point sites were sampled twice using both sampling techniques (quadrat and CPUE). For Riverdale the mean CPUE was found to be 0.34 while the mean density was about to Hatching 0.89 #/m2 with Days a standard deviation of about 0.38. At Clason Point the mean CPUE was found 16 to be 5.4 while the results for quadrat sampling were found to average around a density of 74.35 14 #/m2 . When graphed, the correlation line had an equation of y = 0.0689x + 0.2805 describing the 12 10 Immature relationship between quadrat and CPUE. The standard curve was used to estimate the density of Number of 8 Days Young 125th street and Governor’s Island.

6 4

Intermediate

The densities of 125th Street and Governor’s Island were calculated as #/m2 using the standard 2 Ready to Hatch curve (i.e.0 0the 5inverse of 20the 25above correlation) mean. The standard deviation was then found by 10 15 30 Salinity (psu) using the calculated densities for each day. The density of crabs gradually increased with salinity from Riverdale to Governor’s Island (Fig. 6). Once at Clason Point the density of crabs increased to about ten times the amount of any other site sampled.

Hatching success of the larvae was measured at 3 different salinities (Fig. 7). Individuals in both the 15 psu and 25 psu treatments had the highest survival rate. Individuals in the 5 psu treatment were about three times less likely to survive when compared to the other treatments. The 15 psu treatment showed close to 100% success in surviving larvae.

Of the three different treatments none differed when it came to amount of time it takes for the

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larvae to hatch (Fig. 7). When looking at the maturity of the eggs those that were less mature to start took longer to hatch than those more mature.

Discussion The focus of this investigation was to document H. sanguineus by using the Hudson River as a natural salinity gradient. To do so the densities, individual size, and hatching success of crabs at various sites of low salinity along the coast of New York were sampled in order to identify whether H. sanguineus has expanded its range into lower salinity habitats.

To test differences in individual size distribution, the cumulative carapace width frequencies were tested for maximum difference using the Kolmogorov-Smirnov test. At each site, there were no difference among sexes; therefore body size among days by site was likewise tested. Again, little difference was seen among days. Lastly differences in size distribution among sites were tested. This test showed that Riverdale, George Washington Bridge and 125th Street appeared to have similar average body sizes. Both Governor’s Island and Clason Point differed from both each other and all other sites.

The proportion of crabs that were H. sanguineus differed among the five sample sites (Fig. 2) and was consistent with the salinity gradient from, Riverdale to Clason Point. As you move along the salinity gradient the proportion increases gradually going from 0.2 at Riverdale, 0.3 at George Washington Bridge, 0.8 at 125th Street, 0.92 at Governor’s Island, and reaching 0.998 at Clason Point. This pattern is seen where proportion of H. sanguineus is graphed against the mean salinity at each site (Fig. 3). At mean salinities greater than 15 psu, at least 80% of all crabs caught were H. sanguineus.

In order to compare each of the five sampling sites the measurements were all converted to density (#/m2 ). To do so the CPUE and density calculations for Riverdale and Clason Point for the last two days were utilized to create a standard curve shown in Fig. 4. The equation of this line, y = 0.0689x + 0.2805, gave the equation to find CPUE with the x-value being the density. However, in order to compare each of the five sample sites the inverse equation was needed, y = 14.507x − 4.0691, to find the density. Once the density was calculated for 125th Street and Governor’s Island all five sites were able to be graphed side by side as shown in Fig. 5. This agrees with the rest of the data showing that along the salinity gradient as the salinity increases the density of H. sanguineus also increases.

Overall the data points to a rise in Hemigrapsus sanguineus as the salinity of the water increases. However, with larger densities the average carapace width goes down. This could be caused by competition for resources. In locations with higher densities of crabs larger crabs would have a harder time finding enough food to maintain a large body size. In comparison, areas with a low density of crabs, competition is also lower, therefore allowing for crabs to maintain larger body sizes easier From the data collected it does look like in the higher salinity sites the major proportion of crabs is H. sanguineus. Clason Point, Governor’s Island and 125th Street were ideal

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habitats for the crabs because the range of salinity average remained above 10 psu. Where in comparison Riverdale and George Washington Bridge’s salinity averaged below 10 psu. In both of these locations H. sanguineus was not the dominant species of crab and lived amongst other crabs.

This could be because it had not yet lived in these habitats long enough to dominate the resources.

It could also be that H. sanguineus is cohabitating with other crabs.

The increase of H. sanguineus along the coast has been a concern because it is thought that they might out-compete other species causing them to go extinct (Lohrer and Whitlatch, 2002).This could be done through competition for food with other crabs. H. sanguineus eat a wide range of prey including but not limited to blue mussels, soft-shell clams and oysters (Bordeau and O’Connor, 2003). Of these they prefer the smaller organisms, which are normally those that are less mature. This was because the crabs could open the shells of the smaller ones and had a difficult time opening the larger ones. Due to this, the organisms could be forced to mature at smaller sizes in order to reproduce effectively causing the sizes in the population to decrease (Brousseau et al., 2001). It is difficult to track where invasive species will thrive. There are many people who attempt to predict the spread of H. sanguineus. Delaney et al. (2012) have come up with a method that seems to be successful in predicting the spread of H. sanguineus through the use of a biological- physical oceanographic model. However it could only predict the drift cards and was unable to predict the spread of the larvae stage (Delaney et al., 2012). Therefore more research is still needed to be done to predict where invasive species are likely to spread in hopes to prevent the spread and preserve the native species which may not survive an invasion.

Acknowledgement The author thanks the School of Science Research Scholars Program and the Jasper Scholars program for financial support.

References Bordeau, P. E., and N. J. O’Connor. 2003. “Predation by the nonindigenous Asian shore crab Hemigrapsus sanguineus on macroalgae and molluscs.” Northeastern Naturalist 1010:319-334.

Brousseau, D. J., Filipowicz, A., and J. A. Baglivo, “Laboratory Investigations of the Effects of Predator Sex and Size on Prey Selection by the Asian Crab, Hemigrapsus Sanguineus.” Journal of Experimental Marine Biology and Ecology 262 (2001): 199-210.

Chakravarti, Laha, and Roy, (1967). “Handbook of Methods of Applied Statistics,” Volume I, John Wiley and Sons, pp. 392-394.

Delaney, D.G., Edwards, P.K., and B. Leung, 2012. “Predicting regional spread of invasive species using oceanographic models - validation and identification of gaps.” Marine Biology 159: 269282.

Epifanio, C. E., Dittel, A. I., Park, S., Schwalm, S., and A. Fouts. 1998. Early life history of Hemigrapsus sanguineus, a non-indigenous crab in the Middle Atlantic Bight (USA). Marine Ecology Progress Series 170:231-238.

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Epifanio, C. E., 2013. Invasion Biology of the Asian Shore Crab Hemigrapsus Sanguineus: A Review. Journal of Experimental Marine Biology and Ecology 441: 33-49.

Lohrer, A. M., and R. E. Whitlatch, 2002. “Interactions among aliens: Apparent replacement of one exotic species by another. Ecology 83:719-732.

McDermott, John J., “A Breeding Population of the Western Pacific Crab Hemigrapsus Sanguineus (Crustacea: Decapoda: Grapsidae) Established on the Atlantic Coast of North America.” Biol Bull 181 (1991): 195-98.

McDermott, John J., “The Western Pacific Brachyuran (Hemigrapsus Sanguineus: Grapsidae), in Its New Habitat along the Atlantic Coast of the United States: Geographic Distribution and Ecology.” ICES Journal of Marine Science 55.2 (1998): 289-98.

Investigation of the interactions between antimalarial and antiretroviral drugs Sana Saeed∗ Department of Biology, Manhattan College Abstract. Malaria and AIDS are two infectious diseases that are prevalent in sub-Saharan Africa due to geographic overlap. Malaria, caused by the protozoan parasite Plasmodium, is transmitted to humans by the female Anopheles mosquito. The Human Immunodeficiency Virus (HIV), which can lead to AIDS, is a retrovirus that damages the immune system by destroying CD4 T-cells. It is transmitted both parentally and sexually. Previous research in our laboratory has shown that co-infected patients in Benin City, Nigeria, taking both antiretroviral and antimalarial drugs, still had Plasmodium present in their bloodstream. We have demonstrated that P. falciparum was the only species present in these patients at a 28.7% prevalence. We have also shown a lack of correlation between the levels of CD4 T-cells and Plasmodium in these patients suggesting no interaction between HIV and Plasmodium. Therefore, we hypothesized that antiretroviral drugs are inhibiting the antimalarial drugs. This was tested by performing a 3 Hhypoxanthine incorporation assay in the presence of antimalarial and antiretroviral drugs, used individually and in combination. We found that the antimalarial drugs, sulfadoxine and lumefantrine, were inhibited by the antiretroviral drugs, zidovudine, lamivudine, and stavudine, respectively. We also found that stavudine had the most inhibitory effects on all of the antimalarial drugs, except for artemisinin.

Introduction Co-infection occurs when there is a geographic overlap of multiple pathogens. Many in subSaharan Africa and sub-tropical regions are co-infected with multiple pathogens. Malaria and other diseases are common co-infections in sub-tropical regions of the world [1, 2, 3, 4, 5]. After malaria, schistosomiasis is the second worldwide in parasitic disease morbidity [6]. Like malaria, lymphatic filiarias is a disease transmitted by the Anopheles mosquito and affects 120 million people worldwide [7]. Another common co-infection is malaria with tuberculosis, which affects 1/3 of the world population [8, 9]. All of these co-infected diseases are suspected to have interactions in vivo.

Malaria and AIDS are widespread diseases affecting the world [10], specifically in subSaharan Africa, South America, and South Pacific Asia [11]. Ninety percent of malaria cases are found in sub-Saharan Africa [12, 13], while 70% of HIV deaths have are in sub-Saharan Africa [14]. Together AIDS and malaria result in two million deaths annually and no effective vaccine exists for either disease [15, 16].

Malaria is caused by the protozoan parasite, Plasmodium. There are five species that infect human hosts, P. falciparum, P. ovale, P. vivax, P. malariae, and P. knowlesi. P. falciparum is the deadliest of all four human malarial species [17]. It can cause severe health complications including acute anemia and cerebral malaria [17]. The parasite is introduced into the human host by ∗

Research mentored by Ghislaine Mayer, Ph.D.

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Figure 1. Life cycle of Plasmodium falciparum (www.cdc.gov/malaria)

the bite of a female Anopheles mosquito. When the mosquito takes a blood meal from the human, it subsequently releases the parasite into the human’s bloodstream. The parasite travels to the liver where it undergoes asexual reproduction releasing thousands of parasites into the bloodstream. The parasite can then infect red blood cells; one parasite can release dozens of parasites after 48 hours.

The release of parasites into the bloodstream produces the symptoms of malaria, including fever, chills, nausea, and headache. The uncontrolled reproduction in red blood cells can cause anemia, one of the characteristic symptoms of malaria. The parasite can also develop into a gametocyte in a red blood cell, which can be taken up by another mosquito and can continue the life cycle of Plasmodium (Fig. 1).

HIV is the human immunodeficiency virus and infection with HIV can progress into the disease AIDS. The virus is transmitted to others through affected bodily fluids. The virus binds to the CD4+ T cells, also known as helper T cells, and integrates itself into the DNA of the host, with the help of enzymes integrase and reverse transcriptase. As the virus uses the helper T cells to replicate itself, it damages the host cells. By further invading helper T cells, the virus weakens and destroys the immune system. Symptoms include swollen lymph nodes, weight loss, fever, coughing, and diarrhea [10]. If the virus is not controlled, AIDS and opportunistic infections can occur in individuals.

For the treatment of P. falciparum malaria, WHO recommends artemisinin combination therapy (ACT). Antimalarial drugs attack the parasite during the liver and blood stages to eradicate the parasite and prevent transmission and severity of the disease. Artemisinin is the primary con-

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stituent of ACT along with multiple derivatives: artesunate, arthemether, artelinic acid, artemoil, and dihydroartemisin, which efficiently kill the parasite [15]. Along with artemisinin,the antimalarial drugs lumefantrine and sulfadoxine are also used in combination for the treatment of malaria.

The treatment recommended by WHO for HIV is highly active antiretroviral treatment. These drugs include non-nucleoside reverse transcriptase inhibitors (NNRTI) and nucleoside analogue reverse transcriptase inhibitors (NRTIs) which inhibit the retroviral functions. Protease inhibitors are used to disable the reverse transcription of RNA into DNA [11].

To understand the relationship between malaria and HIV in co-infected patients, research has been conducted to calculate the prevalence of malaria in HIV patients. Dr. Akinbo, of Benin City Nigeria has studied the prevalence of malaria in HIV patients’ not taking HAART medication [18, 16] and those on HAART [11]. Forty six percent of malaria was found in HIV-positive patients not taking HAART medication, while 2.6% prevalence of malaria was found in patients taking HAART. The study was conducted with 285 individuals with HIV on antiretroviral treatment. A correlation between CD4+ T-cell count and malaria was reported. Mastanna Eraifej, of Manhattan College continued the research by asking which specific species of Plasmodium is prevalent in HIV infected patients. Using molecular techniques, we found a 28.7% prevalence of textitP. falciparum [19]. No significant correlation between CD4+ T-cell count and parasitemia was found in patients following both anti-retroviral and anti-malarial treatments.

Based on these findings, it was hypothesized that the drug treatments administered to coinfected patients were interfering in vivo. This was tested by performing drug assays with individual and combination antimalarial and antiretroviral drugs. In vitro drug interference was assessed by analyzing parasite viability with microscopy. Microscopy is the gold standard in malaria diagnosis, but can be limiting in accuracy. To test the validity of the microscopy results, this research focuses on utilizing a radio-labeled metabolic compound to assess parasite viability. Hypoxanthine is a purine derivative necessary for parasite nucleic acid synthesis, and used as a nitrogen source.

A healthy parasite will actively uptake hypoxanthine while a dead parasite will not be able to. We used a tritiated hypoxanthine so that parasite viability could be assessed with the amount of incorporated 3 H-hypoxanthine measured [20]. Utilizing a scintillation counter to measure incorporated 3 H-hypoxanthine is a more precise and objective method. A more objective approach would allow us to assess drug inhibition more accurately.

Materials and Methods P. falciparum Culture. We acquired the 3D7 clone of parasite P. falciparum from Dr. Thomas Wellems of the Laboratory of Malaria and Vector Research at the National Institute of Health (NIH). The parasites were frozen with human erythrocytes at 1% hematocrit. 3D7 parasites were grown in malaria culture medium containing RPMI 1640 (Lifetechnologies, Carlsbad, CA), buffered with HEPES, and supplemented with 0. 005% hypoxanthine. The culture was gassed for three minutes to maintain a micro-aerobic environment for parasite growth. The gas contains 5%

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CO2 , 1% O, and 94% N2 . The culture flask was placed in the 37◦ C incubator until use.

Assessing Parasite Viability. Parasitemia was assessed using microscopy of Giemsa-stained blood smears. Briefly, the smears were stained in 10% Giemsa solution after being fixed in methanol.This was necessary to perform a successful drug assay. Depending on the health and parasitemia, the infected red blood cells were diluted to less than or equal to one percent parasitemia.

In vitro Drug Assay. The antimalarial drugs used in the assay were artemisinin, lumefantrine, and sulfadoxine (Sigma Aldrich, St. Louis, MO). The antiretroviral drugs used were zidovudine, lamivudine, stavudine, nevirapine, provided by Dr. Akinbo of Benin City Teaching Hospital, Nigeria. Prior to preparing the assay, the drugs were diluted in distilled H2 O and DMSO based on their solubility properties. Working solutions of the drugs were aliquotted and were used at a final concentration of 10 µM. Drug assays were performed in a biosafety cabinet to maintain sterile conditions. Assays were performed in duplicate, in four independent experiments. Briefly, with washing media, P. falciparum-infected erythrocytes were washed three times and centrifuged prior to placing into wells in order to remove all non-radioactive hypoxanthine from the media.

Fresh media were prepared using complete media without hypoxanthine and supplemented with 3 H-hypoxanthine solution. The final concentration of 3 H-hypoxanthine in each well was 32.5 µci/mL. This ensured the incorporation of only tritiated hypoxanthine by the parasite. As a control, parasites were grown in absence of drugs. After the wells were filled with specific drug cocktails, the 96-well plate was placed in a Modular Incubator Chamber (Billups-Rohenberg Inc.), with a wet paper towel to maintain humidity. The chamber was gassed with 5% CO2 , 1% O2 , and 94% N2 for five minutes before placing in the incubator at 37◦ C for 48 hours.

Assessment of P. falciparum Viability. To determine the effects of the drugs on P. falciparum viability, the incorporation of 3 H-hypoxanthine was assessed by using Tri-carb Scintillation analyzer (Packard, Meriden, CT). Briefly, P. falciparum-infected erythrocytes were washed three times to remove unincorporated 3 H-hypoxanthine. The infected erythrocytes were lysed by freeze-thaw to release the parasite content and measure incorporated 3 H-hypoxanthine. Lysed erythrocytes were spotted onto filter paper and place into scintillation vials and allowed to dry for 1 h at room temperature. Ecolume scintillation fluid (MP Biomedical, Salem, OH) was added to the scintillation vials before placing the vials into the scintillation counter. The data was measured in counts per minutes (CPM). The higher the CPM, the greater hypoxanthine incorporation, therefore less inhibition of parasite growth. All values were compared to the control, which were parasite incubated in the absence of drugs.

Results Effect of Anti Malarials (ACTs) on P. falciparum Growth. Each antimalarial was individually tested to observe the effects they would have on parasite growth. All the drugs used in patients co-infected with HIV and malaria from Benin City Teaching Hospital were used in the assay.

These drugs were found to have an inhibiting effect on parasite growth, both individually and in

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combination. As expected, the amount of 3 H-hypoxanthine incorporated in the antimalarial assays are much less than the control where there were no drugs present (Fig. 2). The antimalarial drug, lumefantrine, decreased parasite growth number by 60%, while sulfadoxine and artemisinin decreased parasite growth number by 41% and 45%, respectively.

Percent Inhibition of P.falciparum Growth

90

Control Sulfadoxine

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50

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60%

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Percent Inhibition of P. falciparum Growth

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24%

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0%

Control

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Zidovudine

Lamivudine

Stavudine

Nevirupine

All Antiretrovirals

Antiretroviral Drugs

control

Antimalarial Drugs

Figure 2. All antimalarial drugs decrease P. falciparum growth

Figure 3. Antiretroviral drugs exhibit antimalarial activity. Zidovudine, lamivudine, nevirapine, individually, exhibited low lovels of antimalarial activity.

Stavudine had no effect on parasite growth.

60

Control

41%

20

40% 26%

0% 0

control

Control ‐20

‐37%

Sulfadoxine ‐58%

Sulfa+Z Sulfa+Lam

‐40

Sulfa+Stav ‐60

Percent Inhibition of P.falciparum Growth

Percent Inhibition of P.falciparum Growth

100

40

Lum+Z 60

Figure 4. Individual antiretroviral drugs combined with the antimalarial sulfadoxine exhibited inhibition on the antimalarial property of sulfadoxine. Both zidovudine and stavudine expressed complete inhibition of sulfadoxine.

Lum+Lam Lum+Stav

40

Lume+Nev

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0%

15%

1%

10%

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control ‐29% ‐20

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Lumefantrine

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Drugs ‐60

Figure 5. Individual antiretroviral drugs combined with the antimalarial lumefantrine exhibited inhibition. In the presence of the antiretroviral stavudine, lumefantrine was completely inhibited.

Effect of Anti Retrovirals on P. falciparum Growth. The antiretrovirals were tested individually and altogether to observe the effects they had on parasite growth. We compared the effect on parasite growth to the control, which had no drugs. All of the individual antiretrovirals except stavudine had an inhibiting effect on parasite growth compared to the control (Fig. 3). Antiretrovirals used in combination had the highest inhibition on parasite growth, leading to a 24% decrease

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in parasite growth (Fig. 3). This suggests possible low antimalarial properties of HAART drugs.

Individually, nevirapine had the highest inhibitory effect causing a decrease of parasite growth by 21%, followed by zidovudine with 19%, and lamivudine with 11% ( Fig. 3). In the presence of stavudine, parasite growth increased by 26% (Fig. 3). Parasite growth is sensitive to stavudine, as seen by increasing parasite growth as compared to the control.

The Antimalarial Sulfadoxine is Inhibited by Antiretroviral Drugs. The antimalarial drug sulfadoxine was tested in the presence of individual antiretroviral drugs to test possible interactions. As expected, sulfadoxine alone inhibited parasite growth by 41% (Fig. 4). Sulfadoxine in the presence of the antiretroviral drug nevirupine has no observable change on parasite growth compared to sulfadoxine alone, indicating no interaction between the two drugs. Sulfadoxine in the presence of lamivudine has a decreased effect on parasite growth compared to sulfadoxine alone, indicating low levels of inhibition on sulfadoxine by lamivudine. Sulfadoxine in the presence of zidovudine and stavudine, respectively, doesn’t inhibit parasite growth at all. Therefore, sulfadoxine’s antimalarial property is inhibited by both zidovudine and stavudine when used in a 1:1 combination.

The Antimalarial Lumefantrine is Inhibited by Antiretroviral Drugs. The antimalarial lumefantrine was assessed individually with antiretroviral drugs. As expected, lumefantrine alone inhibited parasite growth by 60% (Fig. 5). In the presence of zidovudine and nevirapine, lumefantrine only decreased parasite growth numbers by 15% and 10%, respectively (Fig. 5). In the presence of lamivudine, lumefantrine only decreases parasite growth numbers by 1%. This indicates the slight inhibition of lumefantrine by zidovudine, lamivudine, and nevirapine. In the presence of stavudine, the antimalarial property of lumefantrine is completely inhibited (Fig. 5).

The Antimalarial Artemisinin is Inhibited by Antiretroviral Drugs. The antimalarial drug artemisinin was assessed individually with antiretroviral drugs to study any possible inhibition.

As expected, the antimalarial artemisinin inhibited parasite growth by 45%. In the presence of lamivudine, stavudine, and nevirapine, the parasite growth number decreased by 43%, 45%, and 34% respectively (Fig. 6). This indicates no inhibitory interaction of these antiretroviral drugs on the artemisinin. In the presence of zidovudine, the antimalarial property of artemisinin is less that artemisinin alone indicating the slight inhibition of artemisinin by zidovudine. Therefore, artemisinin is the least susceptible to inhibition by individual antiretroviral drugs.

Testing Interactions Between Anti Retrovirals and ACTs. To ascertain if all antimalarial drugs used in combination (ACTs) are inhibited by individual antiretroviral drugs, ACTs were tested in the presence of individual HAART drugs. When all antimalarials are tested with each individual antiretroviral drug, ACTs in the presence of stavudine has the highest inhibition on parasite growth. P. falciparum growth was inhibited by 74% (Fig. 7). Individual antiretroviral drugs have a negligible effect on the antimalarial property of ACTs. Inhibition of ACT by HAART. To determine whether ACTs are inhibited by HAART, P. falciparum parasites were grown in the presence of both. In the presence of ACTs a significant

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decrease of 61% in parasite growth number was observed (Fig. 8). All antiretrovirals, exhibit low levels of antimalarial property by decreasing parasite growth number by 24% (Fig. 8). In the presence of HAART, the ACT drugs were not as effective as parasite growth was only decreased by 35%. This data mimics the high prevalence of P. falciparum in treated co-infected patients from Nigeria. Finally, HAART completely inhibited the antimalarial property of lumefantrine (Fig. 8).

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Percent Inhibition of P.falciparum Growth

Artemisinin Art+Z

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Art+Lam Art+Stav

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Art+Nev 40

30

45%

20

34% 43%

10

45%

20% 0%

0

control

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70

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61% 61%

59%

58%

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0% 0

control

Drugs

ACTs

ACTs + Zidovudine

ACTs + Lamivudine

ACTs + Stavudine

ACTs + Nevirupine

All Antimalarial Drugs Figure 6. Individual antiretroviral drugs in combination with the antimalarial artemisinin express no inhibition of antimalarial property. In the presence of the antiretroviral zidovudine, artemisinin has a slight decrease in its antimalarial property.

Figure 7. Individual antiretroviral drugs combined with ACTs dod not inhibit parasite growth. Stavudine seems to have a synergistic effect on ACTs

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Control Percent Inhibition of P.falciparum Growth

Percent Inhibition of P.falciparum Growth

Control 70

All R

60

All M 40

61%

All R+Lu

20

35% 0%

0

All R+M

24%

control ‐26%

‐20

‐40

Drugs

Figure 8. ACTs are inhibited by HAART

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Discussion The objective of this research was to determine whether antiretrovirals (HAART) are inhibiting the antimalarials (ACTs) in vitro, and to identify which component of HAART was the most inhibitory. The inhibition was assessed by the presence of live parasite. P. falciparum prevalence was high in co-infected patients as observed by Akinbo in 2009 [18]. Additional research testing the interaction in vitro by microscopy supported the claim [19]. In this study, we tested the inhibition of ACTs by HAART by using the accurate method of 3 H-hypoxanthine incorporation. As expected, we found that ACTs are the most effective in killing P. falciparum. When ACTs were used in combination with HAART the parasites were not killed completely, indicating inhibition of ACTs by HAART between the drugs in vitro. This mirrors what was observed in co-infected patients from Benin City, Nigeria [11].

The inhibiting effects of antiretrovirals on antimalarials were seen in 1:1 combinations. There were four strong negative drug interactions which inhibited antimalarial properties of both drugs used in combination. The highest inhibition was seen in sulfadoxine by stavudine. This data supports previous data found in our lab [19]. Sulfadoxine was also inhibited by zidovudine. Sulfadoxine is the most susceptible ACT to inhibition by HAART. Artemisinin is the least susceptible to HAART, exhibiting little inhibition due to HAART. According to the data, 1:1 combination therapy of these drugs do not inhibit parasite growth and in fact increase parasite growth number.

They are not effective at killing P. falciparum.

In conclusion, we have observed that antiretroviral drugs inhibit antimalarial property in vitro.

Sulfadoxine is the most susceptible antimalarial drug to antiretroviral inhibition, while artemisinin is the least susceptible. We have identified stavudine as the inhibitory component of HAART. All antimalarial drugs are not affected in the presence of individual antiretrovirals or all antiretrovirals.

There were two classes of HAART drugs used: nucleoside reverse transcriptase inhibitors (NRTIs) and non-nucleoside reverse transcriptase inhibitors (NNRTIs). NRTIs mechanism of action is to competitively bind to the HIV reverse transcriptase enzyme to block the formation of DNA, it also is activated via phosphorylation [21]. NNRTIs also inhibit HIV reverse transcriptase but it binds to a different site and also is not activated via phosphorylation. None of the targets of the antiretroviral drugs are the same as the antimalarial drugs [21]. There are several mechanisms by which HAART could inhibit ACTs. In our study we only observed NRTIs inhibiting individual ACTs, it is also the class of drugs that are activated via phosphorylation, the addition of a phosphate group to a protein which can turn protein enzymes on or off. Phosphorylation may be interfering with the effectiveness of the ACTs or the resistance of P. falciparum to ACTs. Moreover, another mechanism of inhibition could be the ineffective uptake of the ACTs due to the presence of HAART. HAART may be degrading the ACTs in vivo and deactivating its function.

These are all possible explanations of the drug inhibition observed and will be studied in the future.

We observed that the HAART and lumefantrine assay had the highest inhibition on lumefantrine. Our data suggests that for co-infected patients, it is discouraged to use lumefantrine.

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Stavudine is only suggested to be used in a 1:1 combination with artemisinin as seen by its sensitivity to drug interactions. In the future, we want to test the effect of HAART on ACT using different parasite clones. We also want to determine the mechanism of inhibition of HAART on ACTs. Results from these studies will help in developing treatment guidelines of co-infected individuals in endemic areas.

Acknowledgement The author thanks the School of Science Research Scholars Program for financial support.

References [1] K. E. Lyke and Dicko Alassane, “Association of Schistosoma haematobium Infection with Protection against Acute Plasmodium falciparum Malaria in Malian children,” The American Journal of Tropical Medicine and Hygiene, 78:1124-80 (2005) [2] M. Lemaitre and M. Watier, “Coinfection with Plasmodium falciparum and Schistosoma haematobium: additional evidence of the protective effect of Schistosomiasis on malaria in Senegalese children,” American Journal of Tropical Medicine and Health 90:329-34 (2014) [3] S. K. Ghosh and R. S. Yadav, “Naturally acquired concomitant infections of bancroftian filariasis and human plasmodia in Orissa,” Indian Journal of Malariology 32:32-36 (1995) [4] E. J. Muturi and B.G. Jacob and C. H Kim and C. M. Mbogo and R.J. Novak, “Are Coinfections of Malaria and Filariasis of Any Epidemiological Significance?” Parasitology Research Journal 102:175-181 (2008) [5] A. K. Mueller and J. Behrends and K. Hagens and J. Mahlo and U. E. Schaible and B. E. Schneider, “Natural Transmission of Plasmodium berghei Exacerbates Chronic Tuberculosis in an Experimental Co-Infection Model,” PLoS One, 7:e48110. (2012) [6] CDC “Schistosomiasis,” Center for Disease Control and Prevention: Atlanta, Georgia (2012) [7] CDC, “Lymphatic Filiriasis,” Center for Disease Control and Prevention: Atlanta, Georgia (2013) [8] CDC, “Tuberculosis (TB),” Center for Disease Control and Prevention, Atlanta, Georgia (2014) [9] R. Colombatti and M. Penazzato and F. Bassani and C. S. Vieira and A. A. Lourenco, et al., “Malaria prevention reduces in-hospital mortality among severely ill tuberculosis patients: a three-step intervention in Bissau, Guinea-Bissau,” Biomed Central Infectious Diseases 11 (2011) [10] WHO, “HIV/AIDS,” World Health Organization: Geneva, Switzerland (2013) [11] F. O. Akinbo and R. Omoregie, “Plasmodium falciparum Infection in HIV-Infected Patients on Highly Active Antiretroviral Therapy (HAART) In Benin City, Nigeria,” Journal of Research in Health Sciences, 12:15-18 (2012)

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[12] UNICEF, “Malaria is alive, well and killing more than 3000 children a day in Africa,” United Nations Children’s Fund: New York City (2003) [13] “Malaria,” Centers for Disease Control and Prevention.

[14] UNAIDS, “Report on the Global AIDS Epidemic” (2012) [15] WHO, “World malaria report,” World Health Organization, Geneva, Switzerland (2013) [16] F. A. Fehintola and O. O. Akinyinka and I. F. Adewole and C. C. Maponga and Q. Ma and G. D. Morse, “Drug Interactions in the treatment and chemoprophylaxis of malaria in HIV infected individuals in sub-Saharan Africa,” Current Drug Metabolism, 12:51-56 (2011) [17] MVI, “Fact Sheet: Plasmodium falciparum malaria,” PATH (2014) [18] F. O. Akinbo and C. E. Okaka and R. Omoregie and R. Mordi and O. Igbinumwen, “Prevalence of malaria and anemia among HIV-infected patients in Benin City, Nigeria,” New Zealand Journal of Medical Laboratory Science 63:78-80 (2009) [19] M. Eraifej. “Interactions between Antimalarial and Antiretroviral Drugs in Plasmodium falciparum,” unpublished observations (2014) [20] In vitro Module, WWARN 3H-hypoxanthine uptake inhibition assay to evaluate P. falciparum ex vivo isolate susceptibility to antimalarial drugs, WorldWide Antimalarial Resistance Network Procedure (2012) [21] D. W. Wilson, C. Langer, C. D. Goodman, G.I. McFadden, and J. G. Beeson, “Defining the Timing of Action of Antimalarial Drugs against Plasmodium falciparum,” Antimicrobial Agents and Chemotherapy, 7:1455-1467 (2012)

Xylem conductivity in stems of 22 species of columnar cacti of South America Kristen Skonieczny∗ Department of Biology, Manhattan College Abstract. Cactus plants are native to environments in which availability of water is limiting to plant growth. Examples of such environments are deserts and arid environments. For several tall cactus species, it may be necessary that water be transported a large distance, sometimes several meters, from their roots all the way up to their terminals. Due to this fact, species of columnar cacti that are tall may possibly be more sensitive to availability of water. The purpose of conducting this study was to determine if simplifications exist concerning vascular bundles, water conduits, as well as xylem conductivity values in twenty-two columnar cactus species from South America. Vessel cells, or conduits, are oriented in vertically-aligned bundles contained within cactus stems and transport water from roots to tips. The number of vascular bundles for each plant is constant; however, the number of vessels in these bundles varies. Information obtained as a result of this study shows that the magnitude of vascular bundle diameters was correlated positively with the magnitude of stem diameters. For each of the species tested there was a unique relationship between the overall number of conduits within the stem and stem volumes. However, these relationships pertaining to conduits and volume differed by ten-fold among the tested species. The study revealed that there were two times as many conduits located a distance 300 mm from stem tips as at 150 mm. Although the total amounts of conduits varied extensively among the selected species, data shows that within each of the species, the amount of conduits was heavily regulated in accordance to the previously mentioned configuration. In addition, xylem conductivity values differed markedly among species.

However, the largest stem conductivity values were well correlated with the total volumes of the terminal portions of sampled cactus stems. The data displays a wide array of individual relationships among the tested species, but overall, they demonstrate that the amount of conduits and xylem conductivity values are predictable when considering stem volume.

Introduction Cactus plants typically live in deserts. Deserts occupy approximately 20% of all land surfaces on Earth (Mauseth, 1988; MacMahon, 1992, Anderson, 2001). For arid climates, evapotransporation rates exceed precipitation rates (Bender, 1982). Understanding cactus plants may help scientists understand plant survival when water is limiting.

A major issue for plants living in arid climates is the efficiency of water usage (Nobel, 1988).

During dry periods, cactus plants may store significant amounts of water, when available, in order to aid in preventing desiccation. Some cactus species are able to survive for prolonged periods of time without precipitation (Anderson, 2001). Cactus plants have distinctive characteristics that limit water loss. These characteristics include thick cuticles, thick epidermal layers, and thick hypodermal layers. (Gibson and Nobel, 1968; Evans et al., 1994). Interior to these cells are cells containing the chlorophyll necessary for photosynthesis. Beneath these layers, parenchyma cells are found with vascular bundles that have xylem and phloem cells for nutrient transport (Gibson, 1973; Mauseth, 1993a). Gibson (1973) described the features of secondary xylem cells ∗

Research mentored by Lance Evans, Ph.D.

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(cells that transport water) in the stems of over one-hundred cactus species. In addition, Mauseth (1993a,1993b) looked at xylem cell anatomy for cactus species from an evolutionary standpoint.

Xylem cells with vascular tissues, arranged in vascular bundles, are responsible for delivering water from roots to terminals (Gibson, 1973; Gibson and Nobel, 1968; Mauseth, 2004).

Vascular bundles are distinct and vertically-aligned. These bundles are organized in rings inside the stems (Figs. 1 and 2). These bundles may contain several cell types including vessel cells, tracheids, wide-band tracheids, fibers, and phloem cells (Gibson, 1973; Mauseth, 2004). Stems might also contain medullary (cortical) bundles (Mauseth & Sajeva, 1992; Mauseth, 1993b) dispersed throughout stems, but the centrally-located, vertically-lined vascular bundles are responsible for water transport from roots to terminal stems (Fig. 3).

Recently, several studies have demonstrated relationships between morphological structures of plants with both numbers of xylem conduits and with xylem conductivity (Hacke and Sperry, 2001; McCulloch and Sperry, 2005; Sperry et al., 2006; McCulloh et al., 2009). The foundation of these research studies is the impression that plants should obey Murray’s Law (Murray, 1926; Sherman, 1981) in respect to water distribution (McCulloh et al., 2009). Murray’s Law was applied to animal blood vessels and states that blood flow is proportional to the cubic of vessel diameter. Because all water transport that takes place within plants occurs inside the xylem cells, the application of Murray’s Law to plants is difficult to apply directly. Thus, for plants Murray’s Law needs to take into account the number and diameter of individual conduits. Through analyzing plant height and leaf area, xylem-specific conductivity was well predicted (Gleason et al., 2012). Therefore, xylem conductivity explains many water transport phenomena in plants (Gleason et al., 2012).

Xylem conductivity has been a topic of study in numerous species recently. For example, Zach et al. (2010) revealed that vessel characteristics appeared different for vessels located in tree trunks from those found in young twigs from the same trees. Vessel diameters increased in a linear fashion within trunks and twigs in accordance to tree height. For instance, vessel diameters in trunks spanned from 75 to 220 µm for trees with heights that ranged from 10 to 45 m. Vessel diameters in twigs, in contrast, spanned from 40 to 70 µm in the same tree. Vessel compactness, for trunks, ranged from 20 per mm2 to lower than 5 per mm2 , while for twigs vessels, densities ranged from 80 to 20 per mm2 . In addition, Weitz et al. (2006) showed that vessel distances from the tops of trees and vessel radii of Fraxinus americana were nicely correlated. Over a distance from 2 to 14 meters, vessel radii differed from 60 to 140 µm. Overall, vessel radii measurements were found to not be well correlated with tree height or tree age. Amid cactus growth types, the large trees had vessels with lengths over 300 µm, in addition to vessels with diameters over 65 µm. Prostrate and caespitose cactus species had vessel lengths of 250 µm and diameters of 42 µm (Gibson and Nobel, 1986).

In oak leaves, vessel diameters that were hydraulically weighted and widths of vascular bundles in major axes of ten distinct species were nicely scaled (Coomes et al., 2008). The study by Coomes et al. (2008) established the significance of taking leaf veins into account. McCulloh et

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Figure 1. A diagram illustrating the constant vascular bundles from the most basal stem sections up to terminal portions of columnar cactus species. Typically, the quantity of vascular bundles is uniform and does not change from the base to the tip.

Figure 2. An image of a freshly sampled stem section of Lasiocereus rupicola displaying the inner ring containing the vascular bundles. The diameter of the vascular bundle ring was approximately 20 mm.

Figure 3. Image of a Cleistocactus smaragdiflorus stem portion demonstrating the vascular bundle ring.

Bar = 200 Âľm

Figure 4. Diagram portraying the sampling of stem tissues along a stem. The first sample taken from the stem was generally within three mm from the tip. Other segments were obtained from an assortment of positions along the stem. For individual stems, one sample was cut at 150 mm from the terminal end and another at 300 mm from the tip.

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al. (2010) looked at leaf specific conductivities in addition to leaf areas and compared them with stem diameters for various forest tree saplings. Among all groups of trees, stem diameters were well correlated with both leaf areas and with leaf specific conductivities. The overall purpose for this research study was to comprehend the structure of the “devices” which deliver water to the terminals of stems of several columnar cacti species. These “devices” being vascular bundles and the conduits located within these bundles. The explicit objectives of these tests were to determine (1) the features of vascular bundles found in cactus species, (2) if vascular bundle ring diameters were well correlated with stem diameters amid cactus species, (3) if vascular bundles amongst species were similarly spread out, (4) if the total number of conduits correlated with cactus lengths among species, (5) if xylem conductivity was correlated with stem volumes for each individual cactus species, and (6) if a relationship existed between maximum xylem conductivity with total stem volumes among the tested cactus species. If coalescing principles are found in the experimental data, then the data would propose that characteristics of xylem conductivity are comparable among cactus species. These studies are significant because the rate of water conductivity within cactus stems may hinder general plant growth rates.

Materials and Methods Species Analyzed In January 2013 cactus samples were obtained in Argentina and Chile while in May 2013 samples were obtained in Peru. Species were recognized in the field with the aid of records of field locations (Anderson, 2001; http://cludwigfr.dyndns.org), an extensive variety of physical features including plant height, rib structures, areole and spine appearances, stem widths, stem color, etc.

(Anderson, 2001). Identifications were made with confidence since the majority of the species are found in defined regions and do not look like other cactus species at a given location. Latitude and longitude were documented from a Garmin eTrex Legend (REI.com). All of the names of the species found were confirmed with IPNI (www.IPNI: Plant Name Search) and Tropicos (www.tropicos.org).

Sampling Technique and Field Measurements Several photographs were taken prior to sampling, including photos of the landscape and the general morphologies of the selected plants. For each stem that was sampled, terminal sections along with four to five supplementary stem segments were acquired (Fig. 4). The distances between the segments obtained were documented. Numerous photographs of each individual stem segment were taken. Immediately following the photographs, the sections were fixed in FAA fixative (Jenson, 1962) for a minimum of 24 hours. After the fixation period, samples were kept in 50% ethanol until additional processing.

Stem Measurements Several measurements were made during this study. From pictures of fresh tissue samples, diameters and perimeters of the vascular bundle ring were determined using the computer program

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imageJ (www.rsb.info.nih.gov/ij/). Using data from the perimeter of the vascular bundle ring in addition to the mean distance between vascular bundles, the number of vascular bundles in each stem sample was determined. ImageJ was also used to determine the area of each stem segment obtained. Using the areas of individual samples as well as the distances between sequential segments, the volume of cactus stems was calculated.

Table 1. Cactus species sampled in Argentina Species

Location

Cereus validus Hav

Junction of Route 9 and Route 34 near Salta, S 24◦ 43.8, W 65◦ 01.7 Near Cafayate, S 25◦ 37.8, W 65◦ 37.8

Cleistocactus smaragdiflorus Britton & Rose f. royoi (Cardenas) F. Ritter Echinopsis angelesiae (R. Kiesling) G. D. Rowley Echinopsis thelegona (F.A.C. Weber) H. Friedrich & G. D. Rowley

Near Cafayate, S 25◦ 53.7, W 65◦ 42.5 Junction of Route 9 and Route 34 near Salta, S 24◦ 43.8, W 65◦ 01.7

Table 2. Cactus species sampled in Chile Species

Location

Echinopsis chiloensis (cholla) H. Friedrich & G.D. Rowley Echinopsis coquimbana (Britton & Rose) A.E. Hoffm.

Echinopsis litoralis (Johow) H. Friedrich & G.D. Rowley Echinopsis skottsbergii (Skottsb.) H. Friedrich & G.D. Rowley Eulychnia acida Phil.

Eulychnia breviflora Phil. var. tenuis F. Ritter Eulychnia iquiquensis (K. Schum.) Britton & Rose subsp. ritteri (Cullmann) D.R. Hunt

Near Route 5, S 32◦ 39.6, W 71◦ 13.2 Near Route 5 south of Coquimbo, S 30◦ 01.9, W 71◦ 22.9 Near Route 5, S 32◦ 15.6, W 71◦ 28.4 East of Fray Jorge National Park, S 30◦ 48.4, W 71◦ 21.8 North of Illapel near Route 5, S 31◦ 58.7, W 71◦ 29.8 Near Route 5 north of Coquimbo, S 29◦ 59.5, W 71◦ 21.8 Near Route 5 south of Coquimbo, S 30◦ 01.9, W 71◦ 22.9

Table 3. Cactus species sampled in Peru Species

Location

Armatocereus arduus F. Ritter Browningia columnaris F. Ritter Browningia pilleifera (F. Ritter) Hutchison Cleistocactus pachycladus (Rauh & Backeb.) Ostolaza Cleistocactus serpens (Kunth) F.A.C. Weber Espostoa calva F. Ritter Espostoa nava F. Ritter Lasiocereus rupicola F. Ritter Neoraimondia arequipensis (Meyen) Backeb. subsp. roseiflora (Werderm. & Backeb.) Ostolaza Weberbauerocereus weberbaueri (K. Schum. ex Vaupel) Backeb. var. horridispinus (Rauh & Backeb.) F. Ritter

Route 26 near Nazca, S 14◦ 49.4, W 74◦ 51.1 Route 26 near Nazca, S 14◦ 51.1, W 74◦ 44.7 Road from Celendin to Balsas, S 6◦ 51.4, W 78◦ 3.8 Road from Arequipa to Puno, S 16◦ 6.8, W 71◦ 37.9 Road from Celendin to Balsas, S 6◦ 51.5, W 78◦ 3.8 Road from Cajamarca to San Marcos, S 7◦ 19.01, W 78◦ 11.1 Road from Celendin to Balsas, S 6◦ 51.5, W 78◦ 3.8 Road from Arequipa to Puno, S 16◦ 13.6, W 71◦ 39.6 Near Nazca, S 14◦ 49.6, W 74◦ 49.1 Near Nazca, S 14◦ 49.7, W 74◦ 41.26

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Histological Procedures Small tissue samples, approximately 100 mm2 , were processed for histology for each of the stem segments that were taken (Jensen, 1962). After water removal procedures with tert-butanol solutions, tissues were treated in paraffin (Paraplast X-tra Tissue Embedding, McCormick, Leica Biosystems Richmond, Inc., Richmond, IL). All tissues that were processed were then embedded and microtomed at 30 µm. Safranin was used to stain the tissues while Canada Balsam was used to cover the tissues on slides.

From the histological samples, the overall number of conduits was calculated for each stem segment. This was achieved by calculating the average number of conduits in each bundle and multiplying this value by the number of bundles in that particular sample. Three to five bundles per segment were chosen for the purpose of determining the average number of conduits. For this particular study, a conduit entails all vessel cells in addition to any wide-band tracheids (Mauseth, 2004) without distinction amongst the two cell types. Vessel cells accounted for the majority of conduits in the samples. With the accessibility of imageJ, each conduit’s radius was calculated as one-half of the measured diameter. Two diameter measurements were taken per conduit, and the average of those two values was used in determining the conduit radius. In contrast to conduits, fiber cells were not of concern in this particular study. The average conduit radius (McCulloh, 2005) for each segment was determined from the average of a minimum of fifty conduits radii in the stem sample. Xylem conductivity was determined from the subsequent formula: π ∗ total number of conduits ∗ (average radius of conduits)4 8 ∗ 10−9

(1)

The units of xylem conductivity are g cm MPa−1 s−1 (McCulloh and Sperry, 2005).

Results The studied cactus species displayed diversity among vascular bundles. Bundles located near stem tips were circular (Fig. 5A) or pointed (Fig. 5B) in cross-sectional assessment. In contrast, the majority of bundles observed in more mature cross-sections were found to be rectangular upon assessment (Fig. 5C). Bundles proximate to terminals were quite evenly spaced.

As demonstrated in Fig. 1, all species used in this study contained vertically-aligned vascular bundles organized in rings. Stem segments near the tip had a smaller quantity of conduits than stem sections more distant from the tip (Fig. 6). For example, stem segments within 12 mm from the tip for Echinopsis coquimbana had six conduits per bundle, while E. chiloensis had eight conduits per bundle from the same tip distance. In contrast, stem sections of 130 and 150 mm from the tips for the two species mentioned above averaged 61 and 81 conduits in each bundle, respectively.

There was a large variety among the species sampled regarding vascular bundle diameters. For example, when analyzing Cleistocactus tenuiserpens, the largest stem section contained a vascular bundle diameter of 4 mm. In contrast, Echinopsis chiloensis had a vascular bundle diameter of

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Figure 5. Three different vascular bundles are shown. A: Stem portion a distance of 38 mm from the tip of Espostoa calva. Bar length = 200 µm. B: Stem portion a distance of 37 mm from the tip of Cleistocactus pachycladus. Bar length = 200 µm.

C: Stem portion a distance of 356 mm from the tip of Echinopsis angelesiae. Bar length = 300 µm.

Figure 6. Image of the vascular bundles of two distinct cactus species in effort to demonstrate the changes in the amounts of conduits observed per bundle. A: Stem section a distance of 25 mm from the tip of Echinopsis coquimbana. Each bundle contained fewer than 10 conduits. Bar length = 200 µm.

B: Stem section a distance of 180 mm from the tip of Echinopsis coquimbana. It is noted that there is a larger number of conduits contained within each bundle. Bar length = 400 µm. C: Stem section a distance of 50 mm from the tip of Echinopsis chiloensis. Each bundle contained fewer than 30 conduits.

Bar length = 200 µm. D: Stem section a distance of 150 mm from the tip of Echinopsis chiloensis. It is noted that there is a larger number of conduits contained within each bundle. Bar length = 200 µm.

63 mm for its largest stem segment. However, when the twenty-two species were grouped and analyzed, vascular bundle diameter and stem diameter were well related with one another (Fig. 7).

The vascular bundle diameter and stem diameter relationship possessed a line with an R2 value of 0.77 and the equation y = 0.313x–1.11. These results propose that, for the studied species, vascular bundle diameters were roughly 31% of stem diameters.

The quantity of vascular bundles differed strikingly among species. For instance, Cleistocactus serpens had merely 38 bundles while Browningia columnaris had 269 bundles. It was found that the numbers of vascular bundles within vascular rings were well correlated to maximum stem diameters (Fig. 8). Species with lesser stem diameters had fewer bundles in comparison to species possessing larger diameters (R2 = 0.45). Near stem tips, where there were small conduits (Fig. 6), the bundles were quite evenly spaced around the vascular ring (Fig. 3). Conversely, in more mature stem sections, bundles were not as evenly spaced. Therefore, some vascular bundles had a close to other bundles, while some were more evenly spread out.

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Figure 7. Interspecific scaling relating vascular bundle diameter magnitudes with stem diameter measurements regarding the most basal segments of each of the tested cactus species. The equation of this relationship was y = 0.313x–1.11 with an R2 of 0.77.

Figure 8. Interspecific scaling relating the number of vascular bundles with measurements of stem diameters regarding the most basal segments of each of the tested cactus species. The line had an equation of y = 1.45x + 31.1 presenting an R2 value of 0.45.

Figure 9. Intraspecific scaling of overall amounts of conduits contained within vascular bundles with collective stem volumes of each individual cactus species. The greatest slope was 0.032 while the lowest slope was 0.0023, with and average slope of 0.011 among all of the tested species.

Figure 10. Interspecific scaling of amounts of conduits at a distance of 300 mm from the stem tip with amounts of conduits at a distance of 150 mm from the tip. The relationship generated a line with the equation y = 1.98x − 277 with an R2 value of 0.99.

The general pattern in all of the tested species was that the quantity of conduits essentially doubled from 150 mm to 300 mm from stem tips.

Figure 11. Intraspecific scaling of each tested species regarding xylem conductivity values and cumulative stem volumes. The highest and lowest slope values were 0.032 and 0.0023, respectively. The average slope value of all species was 0.011.

Figure 12. Interspecific scaling relating maximum stem conductivity values with maximum volume of each of the tested stem samples. The relationship displayed an equation of y = 0.00090x–3.91 presenting an R2 value of 0.75.

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For each species tested, numbers of conduits within the vascular bundles were well related to cumulative stem volumes (Fig. 9). Among the species examined, the slopes of the graphs plotting the number of conduits against cumulative stem volume ranged broadly. For illustration, Cereus validus had a slope of 0.0023, the lowest slope, while Echinopsis angelesiae had a slope of 0.032, expressing the largest slope. All of the tested species had their own respective R2 values, all of which exceeded a value of 0.93. As anticipated, cactus species possessing larger stem diameters contained more conduits than those species with smaller stem diameters. Similar relationships arose concerning conduit radii and cumulative stem volume.

There was an extensive array of conduit numbers within the species tested. For instance, Cleistocactus serpens had merely 670 conduits at the position 150 mm from the stem tip while Echinopsis chiloensis had 21000 conduits at the same position. When all of the species were analyzed as a group, the numbers of conduits that were 300 mm from the stem tip were well related with the numbers of conduits located 150 mm from the stem tip (Fig. 10). This relationship exhibited the equation y = 1.98x − 277 along with an R2 of 0.99. In general, the amount of conduits essentially doubled from 150mm from the stem tip to 300 mm from the tip for all species that were tested. These data demonstrate that within individual stems, the number of conduits was controlled and all species presented the same distribution arrangement regardless of the overall number of conduits.

Values of xylem conductivities near stem tips of the examined species ranged from a minimum of 0.0011 g cm MPa−1 s−1 for Eulychnia iquiquensis, to a maximum of 1.43 g cm MPa−1 s−1 for Browningia columnaris. Nonetheless, xylem conductivity was nicely correlated with stem volume (Fig. 11) for individual species. All species had separate R2 values beyond 0.90. Differences in the numbers of conduits, not in the weighted average of conduit radii, accounted for the majority of the variances in xylem conductivity values among species. When grouped together, conductivity values of species with the largest stem samples were nicely correlated with collective stem volumes (Fig. 12).

Discussion The purpose of this research study was to demonstrate if any generalizations exist concerning vascular bundles, xylem conduits, and xylem conductivity amongst twenty-two species of South American columnar cacti. This study was driven by the notion that the rates of water conductivity could possibly restrict growth rates of the cactus stem terminals. The relationships presented from this study show that the features of conduits and xylem conductivity values were comparable among cactus species. Although the amount of bundles varied strikingly among the species, the amount was associated with stem diameters. Additionally, quantities of conduits were linearly correlated with collective stem volumes for all of the tested species.

Remarkably, the amount of conduits amid the species differed from fewer than 1,000 to greater than 20,000 at 150 mm from the terminal end among the species examined. Nevertheless, among all species there were two times as many conduits at 300 mm from the terminal end compared

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with sections at 150 mm from the stem terminal end. This linear correlation with a slope of 1.98 is noteworthy considering that each of these species was acquired from three countries, each containing particularly different environments. This similarity among all of the species may be the result of a uniform response to common desert or arid conditions instead of the specific local environmental conditions for different species.

As anticipated, slopes of xylem conductivity values set against cumulative stem volumes differed among the species tested. Conductivity values varied markedly near stem tips based upon the diversity of stem diameters. E. chiloensis, for example, had a terminal segment conductivity value of 0.001 g cm MPa−1 s−1 with a collective volume of 2.49 x 104 mm3 . C. serpens, in contrast, had a xylem conductivity of 0.112 g cm MPa−1 s−1 in addition to a cumulative stem volume of 1,980 mm3 . However, at the basipetal stem segments, conductivity values were more similar for the species sampled. For E. chiloensis, the utmost basal section sampled revealed a conductivity value of 362 g cm MPa−1 s−1 along with a collective volume of 3.69 x 106 mm3 . C. serpens, in comparison, possessed a xylem conductivity of 18.1 g cm MPa−1 s−1 with a collective volume of 2.63 x 105 mm3 . Therefore, there was not an apparent relationship between xylem conductivity as a function using cumulative stem volumes.

Although individual slopes varied among the species analyzed, maximum stem conductivities values were well correlated with the total volume of the sampled stems. With this uniform reaction of xylem conductivity among the twenty-two species tested, it is suggested that, overall, cactus stems have similar conductivities. The findings of this study support the notion of a joined reaction for xylem cell development within the stems of cactus plants under arid, desert conditions. To our understanding, these are unique findings that quantify the xylem conduits in twenty-two cactus species as well as relate xylem conductivity amongst columnar cactus species.

Studies regarding xylem characteristics in relation to xylem conductivity within plants are new and novel. Woody stem conduits are area and volume conserving because stem evade unnecessary networks limiting hydraulic efficiency by just providing mechanical support (McCulloh et al., 2005; Atala and Lusk, 2008). In a few cases, xylem vessels might make a substantial contribution to the mechanical properties observed in stems. Accordingly, for woody plant stems, keeping water conduction and mechanical assets of xylem cells separated could be an issue. A study by McCulloh et al. (2009) of xylem conductivity in both leaf petioles and leaf petiolules may possibly propose a unique incident because the xylem vessels within these tissues ought to provide minute mechanical support. We feel as though xylem vessels in tip segments of cactus stems offer little mechanical support due to the fact that there are low numbers of conduits and few xylem fibers in these terminal segments. In more basal sections, the amounts of xylem fibers were greater than ten times the quantity of xylem conduits (Gibson and Nobel, 1986). The amounts of xylem fibers also differed distinctly among the tested cactus species. Thus, xylem fibers possibly make the principal contribution to the mechanical properties presented in the terminal stems of columnar cacti.

Consequently, we believe that the chief function of xylem conduits in cactus stem terminals is for water transportation. The comparable xylem conductivity relationships displayed here also help to

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support the impression that xylem conduits are predominantly involved in transportation of water and not with mechanical support.

Acknowledgement The author is grateful for for financial support from the Catherine and Robert Fenton Endowed Chair to Dr. Lance Evans, travel funds and a summer stipend for research.

References Anderson, E. (2001). The Cactus Family. Timber Press, Portland, Oregon.

Atala, C. and Kusk, C.H. (2008) Xylem anatomy of Betula pendula Roth saplings: Relationships to physical vascular models. Gayana Botanica 65: 18-27.

Bender, G.L. (1982). Reference Handbook on the Deserts of North America. Greenwood Press.

Westport, CT. Coomes, D.A., Heathcote, S., Godfey, E.R., Shepard, J.J. and Sack, L. (2008). Scaling of xylem vessels and veins within the leaves of oak species. Biol. Letters 4: 302-306.

Evans, L. S., Cantarella, V.A., Kaszczak, L., Krempasky, S.M. and Thompson, K.H. (1994). Epidermal Browning of Saguaro Cacti (Carnegiea gigantea). Physiological Effects, Rates of Browning and Relation to Sun/Shade Conditions. Environ. and Exp. Botany 34: 107-115.

Gibson, A. C. (1973). Comparative anatomy of second xylem in Cactoideae (Cactaceae). Biotropica 5: 29-65.

Gibson, A. C. and Nobel, P.S. (1968). The cactus primer. Harvard Univ. Press. Cambridge, MA. Gleason, S. M., Butler, D.W., Ziemiriska, K., Waryszak, P. and Westoby, M. (2012). Stem xylem conductivity is key to plant water balance across Australian angiosperm species. Functional Ecology 26: 343-352.

Hacke, U., and Sperry, J. (2001). Functional and ecological xylem anatomy. Perspectives in Plant Ecology, Evolution and Systematics 4: 97-99.

Jensen, W.A. (1962). Botanical Histochemistry. Principles and Practice. W.H. Freeman. San Francisco, CA. MacMahon, J. A. (1992). Deserts. National Audubon Society. New York.

Mauseth, J. D. (1988). Plant Anatomy. The Blackburn Press. Caldwell, NJ. Mauseth, J. D. (1993a). Water-storing and cavitation. Annals of Botany 72: 81-89.

Mauseth, J. D. (1993b). Medullary bundles and the evolution of cacti. Amer. J. Bot. 80: 928-932.

Mauseth, J. D. (2004). Wide-band tracheids are present in almost all species of Cactaceae. J. Plant Res. 117: 69-76.

Mauseth, J. D., and Sajeva, M. (1992). Cortical in the persistent, photosynthetic stems of cacti.

Ann. Bot. 70: 317-324.

McCulloh, K.A., and Sperry, J. S. (2005) Patterns in hydraulic architecture and their implications for transportation efficiency. Tree Physiology 25: 257-267.

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McCulloh, K.A., Sperry, J. S., Meinzer, F.C., Lachenbruch, B., and C. Arala, C. (2009). Murray’s law, the ‘Yarrum’ optimum, and the hydraulic architecture of compound leaves. New Phytologist 184: 234-244.

McCulloh, K.A., Sperry, J.S., Lachenbruch, B., Meinzer, F.C., and Reich, P. (2010). Moving water well: comparing hydraulic efficiency in twigs and trucks of coniferous, ring-porous, and diffuseporous saplings from temperate and tropical forests. New Phytologist 185: 1-12.

Murray, C. D. (1926). The physiological principle of minimum work. I. The vascular system and the cost of bold volume. Proc Natl. Acad. Sci. 12: 207-214.

Nobel, P.S. (1988). Environmental Biology of agaves and cacti. Cambridge University Press. New York.

Sherman, T. F. (1981). On connecting large vessels to small. J. Gen. Physiol. 78: 431-453.

Sperry, J. S., Hacke, U.G., and Pitterman, J. (2006). Size and function of conifer tracheids and angiosperm vessels. Amer. J. Bot. 93: 1490-1500.

Weitz, J., Ogle, K., and Horn, H. (2006). Ontogenetically stable hydraulic design in woody plants.

Functional Ecology 20: 191-199.

Zach, A., Schuldt, B., Brix, S., Horna, V. and Culmsee, H. (2010). Vessel diameter and xylem hydraulic conductivity increase with tree height in tropical rainforest trees in Sulawasi, Indonesia.

Flora 205: 506-512.

Mechanical stresses of primary branches and tree branch morphology Lydia Wehrli∗ Department of Biology, Manhattan College Abstract. Tree branches contain leaves that photosynthesize to produce sugars for overall branch growth. Tree branches exhibit a wide variety of morphologies. The purpose of this research was to understand relationships between the presence of leaves and mechanical stresses of tree branches. Branches from ten tree species were analyzed.

Stresses were determined along each branch and analyzed relative to the placement of leaves along branches. Among the tree species cumulative leaf area was positively correlated with distances along the branch. Among the tree species maximum tree stress with leaves was positively correlated with leaf masses. Analyses were done comparing stresses on branches with and without leaves. Branch stress with leaves was ten times greater than when leaves were not present.

These data indicate that weights, distributions and arrangements of leaves are the main determinants of branch stress.

Mechanical stresses of branches with leaves can be accurately predicted based upon stresses of branches without leaves and vice versa. These data provide a unifying view of the relationships between leaf arrangements and branch stresses.

Introduction Land plants have an almost infinite number of growth forms. Evolution has favored tree species that grow tall so they can intercept life for photosynthesis. In order to grow tall however, considerable energy must be diverted to make wood to support the leaves for photosynthesis.

Thus, the resources for photosynthesis must be diverted to several processes. One of these processes is the production of wood (secondary xylem cells) that will support branches. Primary or terminal branches will produce leaves so that the leaves can be exposed to sunlight for maximum photosynthesis, thus, maximum carbon gain by the plant.

The chemical and physical components of wood are critical for the support of these primary branches. Thus, the wood of theses primary branches must provide mechanical support for the leaves but at the same time evolution would favor branching patterns that would not use an excessive amount of resources for that mechanical support. Thus, each plant species must have an optimum for these two opposite processes.

Mechanical design plays an important role in tree growth (Read et al., 2006). The leaves have to be positioned so that they can get enough sunlight without hindering the other leaves. The leaves cannot be too heavy, since the stems have to be able to support them. This same weight restriction is observed when it comes to the number of leaves along a same branch. The presence of leaves adds considerable weight and as such leads to greater mechanical stress to branches. Therefore, not only the weight of individual leaves will be observed but also the number of leaves along a same branch. ∗

Research mentored by Lance Evans, Ph.D.

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In this study we see that more weight on the branch leads to more mechanical stress, whereas large stem diameters lead to less mechanical stress. Overall, this study focuses on tree morphology, by looking at the leaf placement along branches. It also focuses on several aspects of mechanical stress of tree branches. This study had four aims. They were: (1) cumulative leaf area along branches is similar for all tree species (2) the average maximum branch stress with leaves is well correlated with total mass of leaves on branches among tree species (3) mechanical stresses on branches with leaves are about ten times larger than branches without leaves present, and (4) branch stresses with leaves can be accurately calculated from data of branch stresses with no leaves present.

Materials and Methods Data collection Tree species for this study were located on campus of Manhattan College, Bronx, NY 10471 (Table 1).

All tree species selected had simple leaves. Trees with compound leaves were not tested. For each tree, one primary (main) branch was selected. Main branches were between 40 cm and 90 cm long. In general, each branch had between two and eight secondary branches.

There were not visible injuries on each of the branches.

Selected branches had adequate sunlight exposures.

Table 1. The 10 tree species studied Genus Acer Alnus Cornus Crataegus Fagus Magnolia Quercus Tilia Tilia Viburnum

Species palmatum viridis drummondii calpodendron grandifolia soulangeana alba cordata platyphyllos lentago

Authority Raf. Regel C.A. Mey Medik Ehrh.

Hort.

Houba Bush Scop.

L.

Many images were obtained for each branch. At least four images of the entire tree in situ were obtained so we could relocate the tree if necessary. These images were also used to document that the branches were exposed to full sunlight. At least six images were taken of the branch on the tree before it was separated from the tree. Extracted branches were immediately taken to the laboratory and a series of additional images (at least 10 images) were obtained (Fig. 1). Drawings of the branch were also made in the laboratory (Fig. 2). Each species was identified by comparing tree, branch, leaf and fruits with Kershner et al. (2008).

Laboratory tape was placed along the branches to mark important points like branch points, bends in the branches and locations of all leaves. The area of each leaf (LI-3100, LI-Cor Corp., Lincoln NB) was obtained. The weight of each leaf was obtained (OHAUS Adventurer, www.ohaus.com). Images of the bare branches with tapes attached provided the best view of branch morphology (Fig. 3).

A digital caliper [Fisher Scientific Catalog # S405032D, www.FisherSCI.com] was used to measure stem diameters along each branch. These measurements were used to calculate mechanical stress. To measure mechanical stress, values of length, width and the length of the branch, as

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well as the same measurements for each individual point. In order to obtain these measurements, the whole branch was fixed in a horizontal position. White paper sheets were placed under the elevated branch and each node were drawn on the sheets.

The height, the width and the depth 1 of each node were measured with a meter-long wooden ruler. Stem density (mass per unit volume) was calculated for many points along branches. Mass was determined with an analytical balance (OHAUS Adventurer) and volumes were determined by water displacement. Finally, all data collected were placed into excel files (Microsoft Excel) to allow their analysis.

Figure 1. Image of a branch of Fagus grandifolia before labeling

Figure 2. Drawing of the branch Magnolia x soulangeana after labeling

Fig 1. Image of a branch of Fagus grandifolia before labeling.

Stress calculations Branch stresses were determined with standard techniques (Shahbazi et al., in press). All the 3 units of stress will be expressed in Pascals (Pa).

Figure 3. Image of a bare branch of Tilia cordata. Each leaf node and morphological changes are labeled with laboratory blue tape.

Fig. 3: Image of a bare branch of Tilia cordata. Each leaf node and morphological changes are labeled with laboratory blue tape.

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Figure Maximum stress values were well correlated with the total mass of leaves for ten plant species.

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Fig. 6: Maximum stress values are proportional to the total mass of leaves for Tilia Figure 6. Maximum stress values are proportional platyphyllos, a species with a maximum stress value of 1,200,000 Pa. to the total mass of leaves for Tilia platyphyllos, a 8 species with a maximum stress value of 1,200 kPa.

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Fig. 5: Maximum stress values are proportional to the total mass of leaves for Alnus viridis, a Figure Maximum stress are proportional species with5. a maximum stress value of 600,000 values Pa. to the total mass of leaves for Alnus viridis, a species 6 with a maximum stress value of 600 kPa.

Average of max stress with leaves (kPa)

Maximum stress values with leaves (kPa)

species show similar slopes meaning that the leaf distribution followed a similar pattern Figure 4.species.The cumulative leaf area increased from among tree the tip of the main stem to its base. All 10 species show similar slopes meaning that the leaf distribution followed a similar pattern among tree species.

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Fig. 8: Data of branch stress values versus cumulative distance for Tilia platyphyllos. The

Figure 8. from Data of ofbranch stress values versus cumuvalues increase the base the branches to their tip.

Although the stress values (circles) without leaves are lower (means equal 6000, 6800, 10900, and 8570 Pa) than the stress values lative distance for Tilia platyphyllos. The values in(squares) with leaves (means equal 71000, 80000, 58000, and 73000 Pa). crease from the base of the branches to their tip. Although the stress values (circles) without leaves are lower (means equal 6, 6.8, 10.9, and 8.57 kPa) than the stress values (squares) with leaves (means equal 71, 80, 58, and 73 kPa).

-100 0

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DataData of branchof stress values versus cumulative distance for Alnuscumuviridis. The values Figure branch stress values versus increase from the base of the branches to their tip. Although the stress values (circles) without lative distance for equal Alnus ThePa)values increase leaves are lower (means 7200,viridis.

11600, and 4600 than the stress values (squares) with leaves (means equal 40600, 63700, and 32600 Pa). from the base of the branches to their tip. Although the stress values (circles) without leaves are lower (means equal 7.2, 11.6, and 4.6 kPa) than the stress values (squares) with leaves (means equal 40.6, 63.7, and 32.6 kPa).

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Results Cumulative leaf area along branches is similar for all tree species studied The first results we got were focused on the branch morphologies. We entered the cumulative leaf areas from the tip of each individual branch to the base. All side branches were included in the data. The data for all ten species were entered on the same graph to allow a better comparison of their leaf placement (Fig. 4). As shown, all leaf areas are increasing from the tip to the base of the branches. All ten species show similar slopes. Similar slopes means similar pattern. Therefore, all tree species have similar leaf distributions along their branches.

Average maximum branch stress with leaves is well correlated with total mass of leaves on branches among tree species studied The average of the maximum stress at each leaf node was recorded for each branch as well as the total mass of each leaf along that same branch. The data for Alnus viridis, a species with a relatively low maximum stress value, were plotted (Fig. 5). The same was made for Tilia platyphyllos, a species with a relatively high maximum stress value (Fig. 6). For both species we see a clear correlation between the average maximum stress value on the branch and the mass of the leaves along that same branch.

The same data for all 10 species were obtained (Fig. 7). All species showed an increase in leaf mass as they show an increase in their average maximum stress. Therefore, maximum stress values are well correlated with the total mass of leaves for ten plant species.

As shown, the smaller the average maximum stress, the lighter the leaves are. The same is observed with heavier leaves leading to heavier average maximum stress. Thus, the mass of the leaves and the average maximum stress are directly proportional to one another, meaning that the average maximum stress with leaves is related to the total mass of leaves among tree species.

Mechanical stresses on branches with leaves are about ten times larger than branches without leaves present Maximum stress values with and without leaves along the branch were calculated for each tree species. Data in Fig. 8 shows results for Tilia platyphyllos. The upper part of the graph shows us the stress values with leaves, whereas the lower part of the graph shows us the stress values without leaves. As shown, the stress values with leaves are higher than the stress values without leaves. The average slope of the stress value with leaves was 71,000 and the average slope of the stress value without leaves was 8,100. Also, the slopes of the lines representing the stress values with leaves are similar, showing that the trend among the stress values with leaves are similar. The same results are observed for Alnus viridis (Fig. 9). The stress values with leaves are higher than the stress values without leaves. The average slope of the stress value with leaves was 45,600 and the average slope of the stress value without leaves was 7,800. Also, the slopes among the results of the stress values with leaves are similar, and the slopes among the stress values without leaves

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0.00 0.05 0.10 0.15 0.20 0.24 0.29 Figure 11. The stress values Distance along branch (m) with leaves (red) and the stress Figure 10. The stress valFig. 11: The stress values with leaves (red) and theleaves stress values without leaves (blue) along values without (blue) ues with leaves (red) and the Fig. 13: The stress values with leaves (red) and the stress values without leaves (blue) along the main branch of Tilia cordata.

Figure The stress valthe main branch of Celtis 12. occidentalis. along the main branch of Tilia stress values without leaves Fig. 10: The stress values with leaves (red) and the stress values without leaves (blue) along ues with leaves (red) and the cordata. (blue) along the main branch the main branch of Viburnum lentago. stress values without leaves of Viburnum lentago. (blue) along the main branch of Celtis occidentalis.

are similar as well. Therefore, stress values without leaves show the same pattern and stress values with leaves show the same pattern among them as well.

The averages of the slopes for each graph were recorded (Table 2). The ratio of the average slope with leaves over the average slope without leaves was calculated (Table 2, “slope ratio mean”), as well as the standard deviation for those values (Table 2, “slope ratio S.D.”). Overall, the mechanical stresses on branches are on average 10.3 times larger with leaves compared with branches without leaves. Thus, overall, mechanical stresses with an without leaves are easily calculated when the above means are known.

Data in Figs. 10 through 12 show stresses for locations along branches where stresses changed.

For each species, a regression equation was constructed to compare stress with and without leaves.

Once the best-fit equation was known, an analysis was done to compare the predicted values with actual values. The pattern of stresses for Viburnum lentago (Fig. 10) was derived from data in Table 3. When actual data were compared the predicted values, the error was 11.3%. This value can be compared with the mean ratio value (7.0) for all locations along the branch (Table 2). The pattern of stresses for Tilia cordata (Fig. 11) was derived from data in Table 4. When actual data were compared the predicted values, the error was 0.61%. This value can be compared with the mean ratio value (6.3) for all locations along the branch (Table 2). The pattern of stresses for Celtis occidentalis (Fig. 12) was derived from data in Table 5. When actual data were compared the predicted values, the error was 1.1%.

Discussion The purpose of these experiments was to determine the relationships between the distribution of leaves along branches and mechanical stress properties of branches for branches of ten branch species. This study has shown that the leaf distributions were similar among ten species, the maximum stress values were directly proportional to cumulative leaf masses, the branch mechanical

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Table 2. The average slopes from the stress values with the leaves are in all 10 species larger than the average slopes of the stress values without the leaves. The ratios varied from 4.7 for Crataegus calpodendron to 23.4 in Cornus drummondii. However, the overall average of the species shows slopes about 10.3 times higher with the leaves than without the leaves.

Species Acer palmatum Alnus viridis Cornus drummondii Crataegus calpodendron Fagus grandifolia Magnolia soulangeana Quercus alba Tilia cordata Tilia platyphyllos Viburnum lentago mean

average slope with leaves 11000 46000 33000 140000 7200 53000 39000 5900 71000 2800

average slope without leaves 2000 7800 1300 30000 890 5000 1900 980 8100 450

slope ratio mean 6.3 6.1 23.4 4.7 8.6 12.2 19 6.3 9.1 7

slope ratio S.D. 1.5 0.9 8.1 1 2.1 7.1 6 1.2 1.9 1.5

10.3

3.13

stresses were ten times higher for branches with leaves than without leaves, and mechanical stresses of branches without leaves were accurately predicted from mechanical stresses with leaves.

The data for all ten species observed show similar slopes in leaf distribution along main branches. In general, species with many leaves clumped together have small leaf areas. In contrast, most species with larger leaves have more distance among leaves along branches. However, most species showed similar slopes when the cumulative leaf area was plotted with distance along the main branch. Therefore there must be compensative mechanisms so that leaves are appropriately spaced along branches.

In this study maximum stress values of branches was highly correlated with leaf masses for all species. For example, with Tilia platyphyllos, a species with relatively high average maximum stress values, the correlation coefficient for the relationship between the average maximum stress value with leaves and leaf mass along the branch was 0.84. When data from all ten species were grouped the relationship between average maximum stress and total mass of leaves had a correlation coefficient of 0.81. Thus overall, maximum stress along the branches was highly correlated with mass of leaves.

This correlation can be explained by the fact that branches are made to display the leaves.

Their role is to hold the leaves such as they receive as much light as needed and as little shade as possible, in order to produce sugars via photosynthesis. In order to be efficient, the branch has to use as little energy as possible. Therefore, the branch has to be thin and short, but also has to be resistant enough to hold the leaves. If the leaf mass is to large, the branch might break. However, if the leaf area available is not large enough the tree might not survive. The maximum stress values give us a numerical value of the amount of the resistant forces the branch has to bear. By increasing

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Table 3. The stress values with and without leaves for Viburnum lentago. The ratio is able to show us how much higher the values with leaves are compared to the values without leaves. The estimated values without leaves were calculated using the best-fitted line.

Stress with leaves 177000 177000 180000 180000 176000 177000 23000 17000

Stress without leaves 50000 50000 49000 48000 50000 51000 2000 1500

Predicted stress without leaves 49400 49400 50300 50300 49100 49400 2710 891

% error 1.19 1.19 2.67 4.81 1.79 3.13 35.5 40.5 11.3

Table 4. The stress values with and without leaves Tilia cordata. The ratio is able to show us how much higher the values with leaves are compared to the values without leaves. The estimated values without leaves were calculated using the best-fitted line.

Stress with leaves 201000 181000 223000 218000 162000 152000 142000 141000

Stress without leaves 29000 25000 34000 33000 21000 19000 17000 17000

Predicted stress without leaves 29200 25100 33800 32800 21100 19000 16900 16700

% error 0.94 0.40 0.406 0.549 0.653 0.269 0.204 1.43 0.607

the leaf mass, we thus increase the stress value, since we increase the resistant forces needed by the branch.

Since maximum branch stress is highly correlated with mass of leaves, experiments were performed to determine calculated differences in stress with and without leaves. Our analysis shows that stress with leaves was ten times greater than branch without leaves for the ten species tested. Thus, leaves are a major contribution to overall branch stress.

For the ten species of this study, branch stress data considers the weight of leaves was an excellent predictor of stress when leaves were not present. Overall stress values with leaves predicted stress without leaves within 5%. These data are important because, based upon the close relation between leaf mass and stress, we can predict the amount of extra wood that a tree branch will produce to support leaves. Although the data were not shown the stress values with leaves were accurately predicted, with 5%, from branch data without leaves.

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Table 5. The stress values with and without leaves for Celtis occidentalis. The ratio is able to show us how much higher the values with leaves are compared to the values without leaves. The estimated values without leaves were calculated using the best-fitted line.

Stress with leaves 490000 489000 370000 370000 941000

Stress without leaves 59000 59600 49700 49700 102000

estimated stress without leaves 60100 60000 49000 49000 101000

% error 1.91 0.73 1.25 1.25 0.32 1.10

Table 6. Data show average leaf areas and distances between leaves for Cornus drummondii and Tilia platyphyllo.

C. drummondii has smaller leaves than Tilia platyphyllo. Distances between leaves were similar for the two species.

Leaves of C. drummondii were evenly spaced, whereas the leaves of T. platyphyllos were overlapping.

Species Cornus drummondii Tilia platyphyllos

Average leaf area per leaf (cm2 ) 17.03 48.79

Average distance between leaves (cm) 2.56 3.25

Leaf areas in deciduous trees vary among tree species. Small leaves are advantageous in dry and warm environments, whereas large leaves are advantageous in cool and moist environments (Niinemets et al., 2006). In species such as Tilia platyphyllos, the total leaf area is large, whereas in species such as Cornus drummondii, the total leaf area is much smaller. Another difference in tree morphology is the distance among the leaves. If the distance is short and the leaf area big, we can assume that the leaves are overlapping. However, if the distance between leaves is large, we can assume that the leaves are not overlapping, independently of their leaf areas. Tilia platyphyllos has a greater leaf area than Cornus drummondii along its branches; however, the distance between the leaves is about the same in Tilia platyphyllos as it is in Cornus drummondii (Table 6). This shows that leaves in Tilia platyphyllos are overlapping whereas leaves in Cornus drummondii are evenly spaced. This aspect is important in determining the light capture. In other words, leaf size and the distance between leaves are important factors in determining the investments for efficient light capture (Niinemets et al., 2006). Finally, leaf areas determine the amount of surface available for photosynthesis. Thus, determining the branch morphology gives us an indication on the photosynthetic potential along the branches (Grier et al., 1977). Since the branches show similar patterns in the leaf distribution, we can infer that they show similar photosynthetic potential.

The correlation between leaf mass and maximum stress value gives an indication of amounts of mass that single tree branches can hold. External loads are applied to tree branches. These external loads may be animals, snow, rime ice and debris. The most documented external loads

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have been snow loads for storms in which leaves of deciduous trees remained on the trees. A good example is the Halloween storm in the New England state during 2011. Previous to the storm there was plenty of soil moisture. The addition of snow loads to these deciduous trees caused many branches to break ad for trees to be uprooted to result in storm costs that ranged from $1-3 billion (Wikipedia, 2011). It is hoped that studies like the current study may help in understanding the limits of branch failure.

Acknowledgement The author is grateful for financial support from the Catherine and Robert Fenton Endowed Chair to Dr. Lance Evans. We gratefully acknowledge the collaboration of Dr. Zahra Shahbazi, Allison Kaminski, and Simon Mysliwiec of the Mechanical Engineering Department, Manhattan College, for assistance with the process of obtaining branch stresses.

References Evans, L., Z. Kahn-Jetter, J. Torres, M. Martinez, and P. Tarsia. 2008. Mechanical stresses of primary branches: a survey of 40 woody tree and shrub species. Trees 22:283-289.

Grier, Charles G. and Steven W. Running.“Leaf area of mature northwestern coniferous forests: relation to site water balance.” Ecology (1977): 893-899 Kershner, B., Mathews, D., and Nelson, G. 2008. Field Guide to Trees of North America. Sterling Publishing Co., Inc. New York ¨ Angelika Portsmuth, and Mari Tobias. “Leaf size modifies support biomass distriNiinemets, Ulo, bution among stems, petioles and midribs in temperate plants.” New Phytologist 171.1 (2006): 91-104 Read, Jennifer, and Alexia Stokes. “Plant biomechanics in an ecological context.” American journal of botany 93.10 (2006): 1546-1565.

Shahbazi, Z., A. Kaminski, and L. Evans. in press. Mechanical Analysis of Tree Branches. American J. of Mechanical Engineering.

Wikipedia. “2011 Halloween Nor’easter.” Wikipedia. Wikimedia Foundation, 2011. Web. 10 Mar. 2015. (a) Transmission Facility Outages During the Northeast Snowstorm of October 29-30, 2011, Federal Energy Regulatory Commission and North American Electric Reliability Corporation, 2012-05-12, pages 5-8. Retrieved 2014-05-03. (b) Transmission Facility Outages During the Northeast Snowstorm of October 29-30, 2011, Federal Energy Regulatory Commission and North American Electric Reliability Corporation, 2012-05-12, page 5. Retrieved 2014-05-03.

Water remediation using analogs of vitamin C Monika Gruca∗ Department of Chemistry and Biochemistry, Manhattan College

Abstract. Chromium (VI) is a health hazard found in drinking water in the United States. The research was focused on identifying a new chemical compound that would allow for the conversion of chromium (VI) to a more beneficial form chromium (III). This conversion can be done through the addition of Vitamin C. It was planned to create a reusable analog of Vitamin C that could be filtered out once the conversion was completed. However, an insoluble compound has yet to be identified.

Introduction Chromium (VI) can be found in the drinking water of major US cities. This is primarily due to the tanning of leather, production of stainless steel, and wood treatment. This is a health hazard since chromium (VI) was found to be carcinogenic by the US Environmental Protection Agency and therefore labeled a priority pollutant (Wielinga et al., 2001; Yurkow et al., 2002). One way to solve the problem is to convert chromium (VI) to chromium (III). This is accomplished through an oxidation-reduction (redox) chemical reaction. Chromium (III) is beneficial to the body’s health.

So, having this done on a large industrial scale would allow for health-beneficial chromium (III) to be present in the drinking water. Studies done by Xiang-Rong Xu and associates (Xu et al., 2003), show that chromium (VI) can be converted to its less harmful counterpart chromium (III) by the addition of Vitamin C, aka ascorbic acid.

However, the addition of excess amounts of ascorbic acid to the water supply has unknown consequences. Therefore research needs to be done on how to form an insoluble ascorbic acid analog that can convert the chromium and be removed once the reaction has been completed.

The ideal analog is a filterable compound that could be easily removed from the water source.

Ascorbic acid contains six oxygen atoms making it a polar molecule. This causes it to be highly water-soluble. Therefore it cannot be readily removed from an aqueous environment and an analog must be formed. In order to prevent the ascorbic acid from dissolving some of the polar domains have to be converted to hydrophobic ones. This allows for the molecule to become less hydrophilic and less likely to dissolve in an aqueous environment. It is important to leave two oxygen atoms on the furanone nucleus of ascorbic acid available to convert chromium (VI) to chromium (III) (Fig. 1). These two atoms cannot be modified or else the redox chemistry will be unfavorably affected.

Using the correct chemical reagents ascorbic acid can be adjusted to change its physical properties without interfering with its chemical reactivity. ∗

Research mentored by John Regan, Ph.D.

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1. Ascorbic acid reaction with Cr(VI) Figure

Figure 2.

Figure 2. General Structure of Prototypes This research is specifically designed to investigate the acylation of ascorbic acid. It will

provide new hydrophobic molecules that are expected to retain their redox abilities. After the redox it is important to be able to collect the new ascorbic acid derivative (Fig. 2.). The molecule can be chemically reduced and then be recycled for additional uses.

Results and Discussion

The formation of 5,6-isopropylidene-L-ascorbic acid was successful. This specific ascorbic acid was formed with the use of acetone and trifluoroacetic acid (TFA) (Fig. 3). This specific derivative is necessary for the formation of the desired compound. It is allows for the ascorbic acid to be acylated. This is done through a reaction with a compound that will change the physical properties of the ascorbic acid without changing the chemical properties of the compound.

During research 2-naphthoyl chloride and biphenoyl chloride were both tested to see which formed the most insoluble compound (Fig. 4.).

In the case of both reactions the acylation was successful. However, the recrystallization of 2-O-naphthoyl-L-ascorbic acid leads to difficulties in recollecting the product. The particles were

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too fine to be recovered. In the case of 2-O-biphenoyl-L-ascorbic acid the product was recovered after recrystallization. After 2-O- biphenoyl-L-ascorbic acid was obtained a rearrangement was to occur under basic conditions to form 6-O-biphenoyl-L-ascorbic acid (Fig. 5).

The rearrangement is necessary to allow for both the 2 and 3 oxygen atoms on the molecule to be able to react during the redox reaction. However, the rearrangement was never successfully completed. Based on our results there wasn’t enough of the desired final product to allow for a redox reaction to occur when the product was introduced to a solution of dilute chromium (VI).

This means that the conditions in which this rearrangement occurs has to be altered in order to provide an optimal situation where the desired product can be formed.

Figure 3.

Figure 3. Reaction Mechanism Figure 4.

Figure 4. Prototypes created

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Figure 5. Reaction Mechanism for Step 2

Conclusion Even though the formation of 2-O-naphthoyl-L-ascorbic acid was successful the recovery of the product after recrystallization proved to be difficult. The product is too fine to be easily filtered after recrystallization, which would also lead to difficulties in the collection of the compound if it went through the redox reaction with chromium (VI). In the case of 2-O-biphenoyl-L-ascorbic acid being rearranged to 6-O-biphenoyl-L-ascorbic acid the conditions need to be altered in order to allow for this to occur. A large part of this difficulty that needs to be overcome is the fact that 2-O-biphenoyl-L-ascorbic acid does not readily dissolve. This could be why the rearrangement does not occur uniformly.

Acknowledgement The author would like to thank the School of Science Research Scholars program for financial support to perform this work.

References Xu, X. R., Li, H. B., Li, X. Y. , and Gu., J. D. , “Reduction of Hexavalent Chromium by Ascorbic Acid in Aqueous Solutions,” Chemosphere 57, 609-613 (2003) Yurkow, E. J., Hong, J., Min, S., Wang, S., “Photochemical reduction of hexavalent chromium in glycerol-containing solutions,” Environ. Pollut. 117, 1-3 (2002) Wielinga, B., Mizuba, M.M., Hansel, C.M., Fendorf, S., “Iron promoted reduction of chromate by dissimilarity iron–reducing bacteria,” Environ. Sci. Technol., 35, 522-527 (2001)

Remediation of Ground Water Containing Chromium (VI) Paul Markaj∗ Department of Chemistry and Biochemistry, Manhattan College Abstract. Chromium (VI) is a known carcinogen and is a deadly contaminant. Chromium (VI) is a byproduct of industrial processes such as tanning leather and steel production. It has been found in the water supplies of United States cities. Chromium (III), in contrast, is a beneficial form of chromium; it is found in everyday multivitamins. It has been shown that ascorbic acid, also known as vitamin C, can reduce chromium (VI) to chromium (III). Alteration of the ascorbic acid structure can yield a water insoluble analog that can still reduce chromium (VI), which can then be recycled. Acetal and ketal formation of oxygen atoms at C-5 and C-6 was used to add non-polar groups to make a water insoluble version of ascorbic acid. Some acetals were formed from aldehyde which was then combined with a diol and a strong acid. The analogs successfully convert chromium (VI) to chromium (III), as the UV-VIS charts show, but there is a very poor recovery and there has been little progress in terms of recycling the analog.

Introduction The byproducts of many industrial processes can be harmful to the environment and its inhabitants. Chromium (VI), also known to some as hexavalent chromium, is the third most common pollutant at hazardous waste sites and is the second most common inorganic contaminant [1, 2].

It is a byproduct of many processes such as tanning leather, stainless steel production, refractory industries, pigment industries and wood treatment. The movie ‘Erin Brockovich’ depicted the negative health consequences due to exposure to chromium (VI) in Hinkley, California. The company, Pacific Gas and Electric, had been dumping waste water with dissolved chromium (VI) into the town’s groundwater which caused a rise in the number of people with cancer. Along with cancer, chromium (VI) can also lead to organ damage, dermatitis, and respiratory impairment. Hexavalent chromium is deadly, not only because of its effects on people and the wildlife, but also because it is soluble and therefore does not precipitate easily. Its tendency to bind to the soil and travel through the ground to local aquifers and wells makes makes its effects widespread. Chromium (III) on the other hand has a tendency to precipitate out and does not travel through the sediment very well, and is an essential nutrient for humans and animals[3, 4, 5].

The purpose of this experiment was to chemically convert hexavalent chromium to chromium (III) in solution. Even if it does manage to make it to a town’s water supply it would be reduced to chromium (III). There have been many different methods of reducing chromium (VI) to chromium (III). For example one method was using biological enzymes found in bacteria. But the environments where chromium (VI) is present would not allow these enzymes to survive. Therefore in order to reduce chromium (VI) to chromium (III) other non-biological reducing agents must be used . But, commonly used reducing agents: (H2 S, SO2 , Fe+ , glycerol) are either too toxic or would not work in the environments where the chromium (VI) would be present, the toxic and ∗

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O

O

Cr

O

O

O O

Markaj

O-

Cr

O OH

O

+

H 2O

Cr3+

H

H

O

Ascorbic Acid Vitamin C

O

OH

Dehydroascorbic Acid

Cr(III)

Figure 1. the reaction between dichromate ions and ascorbic acid Figure 1. The reaction between dichromate ions and ascorbic acid

O

O OH

O

OH

O

H

H

H HO

OH

OH

H HO

Dichromate: Cr(VI)

O

O

+

H O

O

R

R

OH

R = hydrophobic group to provide crystalline and water insoluble solid

while not affecting redox reaction.

H O

OH

O

Initial Prototype

Figure 2. Proposed reaction for altering the structure of ascorbic acid

Figure 2. our general proposal for altering the structure of ascorbic acid alkaline environment would degrade the reducing agents. The ideal reducing agent would be safe for humans and animals, and work in the alkaline environments where chromium (VI) would be found. Vitamin C has been proven to be used as a successful reducing agent on chromium (VI), see Fig. 1. The only downside to this is that vitamin C is very water soluble and it will completely dissolve. There could be unintended side effects of adding all that vitamin C, it also would not be cost effective to just throw all that vitamin C in without hesitation. It is hypothesized that a derivative of vitamin C can be created that will reduce chromium (VI) into chromium (III), and be insoluble enough to be separated.

Our goal would be to chemically alter the structure of vitamin C to make it less water soluble, which gave us our initial prototype (Fig. 2). This would then permit us to filter out the vitamin C, recycle it, and then reintroduce it back into water contaminated with chromium (VI). This would then take care of any possible side effects of excess vitamin C and also would reduce the cost of reducing the chromium (VI). We will use different hydrophobic side chains to alter the solubility

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of vitamin C and then we will test its effects on a solution of potassium dichromate. The solubility effects of different side chains were recorded and the presence of chromium (VI) was evaluated with UV-Vis spectroscopy. We will then attempt to reduce the vitamin C analog’s dehydrogenated form by using sodium borohydride (Fig. 3). The results indicate that vitamin C’s structure can be successfully altered, but some of the hydrophobic side chains are more effective than others and they all retain their strong reducing agent properties.

Materials and Methods The source of our dichromate ions was a solution of potassium dichromate that was dissolved in water to make a 12.5 mM solution. The analogs themselves were created by combining the acetals/ketals with ascorbic acid in Dimethylformamide (DMF) with a catalytic amount of triflouroacetic acid (TFA). This reaction was then allowed to stir for 120 hours (Fig. 4). We had used 3 - 5 grams of the acetal or ketal and then a 1.5 molar excess of ascorbic acid. We then used a ratio of 1 gram of ascorbic acid to 1 mL of DMF. We used a ratio of 10 g of ascorbic acid to half a gram of TFA. The resulting solution was mixed with water to allow the analog to precipitate out; it formed a viscous, gelatinous solid. The solution was then extracted with ethyl acetate and the ethyl acetate layers were washed with some saturated sodium chloride solution. The ethyl acetate was then evaporated leaving behind the ascorbic acid analog. Some of the acetals/ketals had to be created from their aldehydes. This was done by combining the aldehydes with methanol and a catalytic amount of TFA. We again used a 3 - 5 g scale of the aldehyde and 50 mL of methanol.

We used roughly the same ratio of TFA for this reaction as well. The reaction was allowed to stir overnight. The resulting acetal or ketal was then filtered out and then used to prepare the acid analog.

The newly formed analog was then added to a few milliliters of the potassium dichromate solution. There was an excess of the analog and the reaction was allowed to stir for half an hour.

After the half hour mark the solution was filtered, and the liquid was then diluted and a sample was analyzed by UV-Vis spectroscopy. The solid that had been filtered out was then combined with sodium borohydride in water and allowed to stir overnight. The analog was then collected and the solvent was evaporated off. The solid was then tested to verify that the recycling had worked.

Results The analogs that developed were very stable, high melting solids. They did not dissolve in water and did not decompose in a pH 4.01 buffer solution. The results of the reaction with our vitamin C analog and chromium (VI) are shown in Fig. 5. As you can see the dashed line represents our 12.5 mM stock solution of potassium dichromate. The distinct peak at 372 nm is an identifying characteristic for chromium (VI). The solid line represents the 12.5 mM solution after it reacted with the vitamin C analog for half an hour. As you can see there is no peak at 372 nm and therefore all the chromium (VI) was converted to chromium (III). We had attempted to filter out the solid after the reaction had been completed and then recycle the vitamin C analog, but the percent yield was low and we were not successful.

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O

OH

O

O

H

H H

O

O

O

Cr(VI)

OH

H

NaBH4

O

O

O

O

Figure 3. Initial hypothesis for reducing the dehydro form back to ascorbic acid

Figure 3. Initial hypothesis for reducing the dehydro form back to ascorbic acid

O

O

OH

O H

+ H

HO

OH

OH

O H 3 CO

OH

OCH 3

H

H2SO4 (cat)

H O

DMF room temp.

5-7 days

OH

O

Mp 184-190 oC Stable at pH 4.0 for 2 hours

Figure 4. Experimental synthesis for our analog

Figure 4. Experimental synthesis for our analog

Figure 5. Spectroscopic results of the chromium (VI) reaction with our ascorbic acid analog

Discussion The projects objective was to create a derivative of ascorbic acid that can be separated from water, ideally by filtration and still retain its redox properties. We created a stable water insoluble

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analog of vitamin C. Our results show that the conversion of chromium (VI) to chromium (III) can be completed with the ascorbic acid analogs in a heterogenous environment. The redox reaction occurred in less than 30 minutes. We filtered the solid out of solution which gave us a low recovery rate. This could be due to the fact that the dehydroascorbic acid version of our analog is very polar and is more soluble in water. The same reasoning could be said about why the percent recovery is also very low. The next step would be to try different methods at reducing the dehydroascorbic acid analog. We will also try to examine different hydrophobic groups to make it even less soluble in water. In addition, changing the physical properties from solids to hydrophobic oils is also under consideration.

Acknowledgement The author would like to thank the Jasper Scholars Program for financial support to perform this work.

References [1] B. Wielinga and M. M. Mizuba and C. M. Hansel and S. Fendorf, “Iron Promoted Reduction of Chromate by Dissimilatory Iron-reducing Bacteria,” Environmental Science and Technology 35, 522-527 (2001) [2] E. J. Yurkow and J. Hong and S. Min and S. Wang, “Photochemical Reduction of Hexavalent Chromium in Glycerol-containing Solutions,” Environmental Pollution 117, 1-3 (2002) [3] S. E. Fendorf and G. C. Li, “Kinetics of Chromate Reduction by Ferrous Iron,” Environmental Science and Technology 30, 1614-1617 (1996) [4] I. J. Buerge and S. J. Hug, “Influence of Organic Ligands on Chromium (VI) Reduction by Iron(II),” Environmental Science and Technology 32, 2092-2099 (1998) [5] C. Kim and Q. H. Zhou and B. L. Deng and E. C. Thornton and H. F. Xu,“Chromium(VI) Reduction by Hydrogen Sulfide in Aqueous Media: Stoichiometry and Kinetics,” Environmental Science and Technology 35, 2219-2225 (2001)

DFT investigation of the structural and energetic features of the protoribosome Daniel McCloskey∗ Department of Chemistry and Biochemistry, Manhattan College Abstract. There exists an RNA sequence in the peptidyl transferase center of the modern day ribosome that is well conserved among all domains of life. Such an enduring, shared structure is a likely candidate for the prebiotic origin of the present-day ribonucleoprotein. Geometric optimizations as well as vibrational frequency and transition state geometry calculations were performed on this protoribosome structure using the B3LYP hybrid functional, and the dispersion corrected B97D functional, with the Synchronous Transit-Guided Quasi-Newton method in order to investigate its structural and energetic features. Stable reactant and product geometries, and their respective energies, were obtained through the B3LYP process, though the transition state could not be determined from the acquired structures.

The thermodynamic information gathered supposes that the conversion from reactant to product is an entropy driven process. Calculations utilizing the B97D method have reached 42 iterations and are continuing.

Introduction The ability to construct the various proteins needed for the ordinary functioning of all living cells rests upon the uninhibited and proper functioning of the ribosome. An ancient and complex molecular machine, the modern ribosome is present within all domains of life and consists of over 33,000 atoms arranged in a collection of various interrelated proteins and rRNA molecules organized into two distinct moieties that together perform the complex task of peptide bond formation.

The inner site responsible for overseeing protein translation, the peptidyl transferase center, consists solely of rRNA material, thus characterizing the ribosome as a ribozyme [1]. Additionally, this center contains a universally conserved RNA sequence [2]. This shared structure represents a likely candidate for the prebiotic origin of the modern cellular factory. Such a protoribosome, consisting solely of the conserved RNA sequence, would need to embody the characteristics of the modern ribosome without the luxury of many of the distinctive features of its contemporary counterpart. Lending further support to this notion are studies showing that ribozymes consisting of RNA sequences isolated from a synthesized pool of RNA molecules are indeed capable of inducing peptide bond formation [3].

In the present experiment, we sought to model the structural features of the protoribosome before the accumulation of its many “protein shields” via chemical evolution. The principles of density functional theory were utilized in order to perform geometric optimizations as well as vibrational frequency and transition state geometry calculations. Solvent effects were expected to have a significant effect on the bare RNA structure and its function as a ribozyme. Also sought were insights into the enzymatic mechanism of the protoribosome. ∗

Research mentored by Joseph Capitani, Ph.D.

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Figure 1. Protoribosome reactant optimized using B3LYP/3-21G*. Dotted lines indicate hydrogen bonds.

McCloskey

Figure 2. Protoribosome product optimized using B3LYP/3-21G*. Dotted lines indicate hydrogen bonds

Computational Methods Geometry Optimization and Transition State Geometry The geometric optimizations and resulting vibrational frequencies of the protoribosome reactant [4] (Fig. 1) and product (Fig. 2) were calculated using the B3LYP hybrid functional method with the 3-21G* basis set. The basis set included polarizable functions in order to accurately reproduce chemical bonding of electronegative elements. The resulting optimized structures were then used in the QST2 option of the Synchronous Transit-Guided Quasi-Newton (STQN) method in order to nd a transition state geometry. After failure to nd a true transition state structure, the QST2 result was used as a guess transition state along with the optimized product and reactant in the QST3 option of the STQN method.

Geometry Optimization of the Solvated Protoribosome The geometric optimization of the solvated protoribosome reactant (Fig. 3) and solvated product (Fig. 4) were calculated using the B97D standalone method with the Def2SVP basis set and with water as the specified solvent of the solvent reaction eld. All calculations were performed using Gaussian 09 [3].

Results Geometry Optimization and Transition State Geometry The optimization of both the reactant and product utilizing B3LYP/3-21G* resulted in the optimized geometries depicted in Figs. 1 and 2 respectively. No imaginary vibrational frequencies were found in either case indicating that the optimized geometries had settled at true minima of the potential energy surfaces. The energy of the reactant was determined to be -8,591.3327 Hartrees while the energy of the product was determined to be –8,591.3275 Hartrees yielding an energy

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Figure 3. Protoribosome reactant under optimization using B97D/Def2SVP after 42 iterations. Dotted lines indicate hydrogen bonds

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Figure 4. Protoribosome product under optimization using B97D/Def2SVP after 54 iterations

difference of only 3.257 Kcal/mol indicating a mildly endothermic process. No transition state could be determined as the QST3 option of the STQN method was killed after 721 iterations without making a positive move towards a transition state structure. Reasons for failure include poor choice of functional and a lack of solvent. (1 Hartree unit = 625 Kcal/mol) Geometry Optimization of Solvated Protoribosome Final geometric results of the solvated protoribosome have yet to be determined as the reactant and product have reached 42 and 54 iterations, respectively, and are ongoing. The currently determined structures are visible in Figs. 3 and 4.

Conclusions Several interesting conclusions were able to be drawn from the gathered data. The introduction of the solvent had a profound effect on the protoribosome reactant geometry yet curiously provided an analogous structure for the product. This both supported, though not necessarily to the degree imagined, the initial expectations that solvent effects would play a large role in shaping the bare RNA structure. Examination of the final geometric results of the solvated protoribosome should yield conclusive data.

The thermodynamic information gathered allowed for the supposition that the process is entropy driven. This is due to ∆G = ∆H–T ∆S where the extremely small H value of 3.257 Kcal/mol indicates that ∆S is the main driver of ∆G. This information provides an interesting parallel to the modern day ribosome, which has been found to be driven by such an entropic process [5]. This also highlights the importance of nding a transition state which, with the introduction of a better set of functionals as well as solvent, is hoped to be achieved in the near future.

All calculations were performed on Hermes, the GNU/Linux GPU server located in the Kakos Center for Scientific Computing, Hayden Hall, at Manhattan College.

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Acknowledgments The author thanks the Michael J. ’58 and Aimee Rusinko Kakos endowment for financial support. He would like to thank Dr. Joseph Capitani for guidance during his summer research experience, Dr. Lou Massa (Hunter College/CUNY) for helpful discussions, and Dr. Constantine Theodosiou for encouragement and valuable assistance with the preparation of this manuscript.

References [1] Rodnina MV, Beringer M, Wintermeyer W., “How Ribosomes Make Peptide Bonds,” Trends Biochem. Sci. 32 (1), 20–6 (2007). doi:10.1016/ j.tibs.2006.11.007 [2] Huang L, Krupkin M, Bashan A, Yonath A, Massa L, “Protoribosome by Quantum Kernel Energy Method,” PNAS, 110 (2013) [3] Zhang, B. & Cech, T. R. “Peptide Bond Formation by In Vitro Selected Ribozymes,” Nature, 390, 96–100 (1997) [4] A. Sievers, et al.,“The Ribosome as an EntropyTrap,” Proc. Natl. Acad. Sci. U.S.A, 101, 78977901 (2004)

Trash to treasure: optimization of heterogeneous catalyst systems for biodiesel synthesis Adrienne Perea∗ Department of Chemistry and Biochemistry, Manhattan College Abstract. The most effective oil/catalyst system for biodiesel synthesis was investigated in this paper. Traditionally biodiesel is produced by using edible oils such as soybean oil with a homogeneous catalyst in transesterification process. In this study, the effect of using more cost-efficient oils with heterogeneous catalysts was investigated. Oils used during this research were vegetable, camelina and waste vegetable oils and the catalysts used were KOH, decomposed CaCO3 , CaO and eggshells. Experimental results show that the reaction of camelina oil with eggshells was the most effective oil/catalyst system, resulting in a yield of 100 %. IR and NMR spectroscopy were used to analyze the biodiesel.

Introduction The transesterification process is one in which the triglycerides of vegetable oils react with an alcohol, in the presence of a catalyst, to produce biodiesel and its byproduct, glycerol, also known as glycerin. The process is shown in Fig. 1 [1].

Figure 1. Transesterification process of triglycerides

Methanol is used as the alcohol for producing biodiesel because it is the least expensive alcohol [2]. Biodiesel has become a reasonable candidate as a renewable alternative fuel over the years, because of its fuel properties. It is biodegradable, free of sulfur and aromatics, and as it is obtained from renewable sources, it reduces the lifecycle of carbon dioxide emissions by almost 70% compared to conventional diesel fuel [3]. Biodiesel can also be produced from a great variety of feedstocks including vegetable oils, animal fats and waste oils [2]. This is very helpful, because the high cost of vegetable oils, especially edible oils, is the main barrier for expansion of biodiesel applications [4]. Therefore, this barrier can be reduced with the use of more cost-efficient oils such as camelina and waste vegetable oil. Camelina oil is a good alternative for the edible oils, because ∗

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it grows quickly in areas that are not used for farming, thus making it lower than the cost of other oil crops. Waste vegetable oil is also a promising alternative fuel because it can be obtained for free at restaurants [5].

Traditionally, homogeneous catalysts, typically KOH, are used for the synthesis of biodiesel.

Homogeneous catalysts have many disadvantages such as soap formation, emulsion formation and excessive water usage. They cannot be reused since the catalysts are consumed in the reaction.

Heterogeneous catalysts are more environmentally benign alternatives compared to homogeneous catalysts. Heterogeneous catalysts do not require a water-washing step and they could be easily separated from the reaction mixture by filtration and then reused [6]. They are less corrosive, leading to safer, cheaper, and more environment-friendly operations [6].

The main component of waste eggshells is CaCO3 and when it is calcined, it decomposes to CaO. CaO is a basic heterogeneous catalyst that has a higher basicity, lower solubility, lower price, and is easier to handle than KOH [5]. When using CaO for biodiesel production, it should be pretreated with methanol, because a small amount of CaO gets converted into Ca(OCH3 )2 that acts as an initiating reagent for the transesterification reaction and produces glycerin as a by-product [7].

Materials and Methods Materials Vegetable oil, camelina oil and waste oil, which were obtained from the school’s cafeteria, were utilized as starting material. The homogeneous catalyst used was potassium hydroxide and the heterogeneous catalysts used were calcium oxide, decomposed calcium carbonate and eggshells. Methanol was employed as both solvent and a reactant.

Transesterification Reaction with Homogeneous Catalysts Specific chosen oil, methanol and potassium hydroxide placed in a 250 mL round bottom flask at 60◦ C for an hour. Upon the reaction completion, the contents were transferred into a separation funnel in which the biodiesel and glycerol phases were able to separate overnight.

Transesterification Reaction with Heterogeneous Catalysts The catalysts used for the reaction had to be calcined in a furnace at 900◦ C for four hours.

After calcination, the catalyst was added to 100 mL of chosen oil and 50 mL methanol in a 200 mL round bottom flask with stirring at 65◦ C. This reaction was heated for approximately one hour, and then the contents were cooled to room temperature, vacuum filtered and placed into a separation funnel so that the layers could separate. Magnesium sulfate was used as a drying agent when needed to remove any water or alcohol residue.

Transesterification Reaction with eggshells Eggshells was rinsed several times, broken into smaller pieces and dried at 100C for 12 hours [8]. Before calcination, the dried eggshells were ground until they became a powder form. Then,

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eggshells were calcinated at 800◦ C for four hours. Once the calcination procedure was done, 120 mL of oil and 80 mL of methanol (methanol:oil molar ratio 9:1) using 3% eggshells were placed in a round bottom flask. After the reaction was completed, contents were vacuum filtered and layers were separated using the separation funnel. Magnesium sulfate was used as a drying agent when needed to remove any water or alcohol residue.

Purification of Glycerol All of the glycerols produced during the reactions were combined. The glycerol was distilled by using a simple distillation apparatus at 100◦ C. The distilled glycerol and potassium hydroxide solution were mixed at 50◦ C for 10 minutes. After 10 minutes, the glycerol solution cooled to room temperature was poured into a porcelain bowl and left to cure.

Results Homogeneous Catalyst While the reaction with vegetable oil and KOH resulted in a 66.7% yield, the reaction with waste vegetable oil and KOH resulted in a 99% yield of biodiesel. The reaction with camelina oil and KOH resulted in a 97% yield.

Heterogeneous Catalysts In the reaction of vegetable oil and calcium oxide using a 1:9 oil to methanol ratio, a 95.8% yield was obtained. Throughout the heating process, the oil, methanol, calcium oxide mixture was dark in color. Once vacuum filtration occurred, a lot of calcium oxide was recovered. 115 mL of biodiesel and 16 mL of glycerol were obtained at the end of the reaction. 1.2032 g of calcium oxide was also recovered.

A 91.67% yield was obtained from the reaction of vegetable oil and eggshells with 110 mL of biodiesel production that was yellow in color. In the reaction of camelina oil with eggshells, 100% conversion was achieved as 120 mL of biodiesel was obtained. In the reaction of waste vegetable oil with eggshells, a 90.8% yield was obtained. 109 mL of biodiesel was obtained and its appearance was a light brown. Table 1 summarizes the conversion yields for each reaction.

Discussion Potassium Hydroxide as a Homogeneous Catalyst From prior research about the production of biodiesel, it was known that potassium hydroxide was mainly used as the homogeneous catalyst [2]. However, the goal of the project was to show that heterogeneous catalysts, such as calcium oxide or eggshells, were more environment friendly, because it could be reused. Not only could calcium oxide or eggshells be reused but also it would result in a better yield, since a homogeneous catalyst such as potassium hydroxide requires water washing. Water washing results in soap formation, which reduces the yield of biodiesel obtained [3].

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Table 1. Conversion yields for each transesterification process

Oil

Catalyst

Percent Yield

Vegetable Oil

KOH

66.7%

Waste Vegetable Oil

KOH

99.0%

Camelina Oil

KOH

97.0%

Vegetable Oil (1:9)

CaO

95.8%

Vegetable Oil

Eggshells

91.7%

Camelina Oil

Eggshells

100.0%

Waste Vegetable Oil

Eggshells

90.8%

As mentioned in the results, the reaction of waste vegetable oil with a homogeneous catalyst resulted in a 99% yield and the reaction of camelina oil with a homogeneous catalyst resulted in a 97% yield. The reaction of vegetable oil with a homogeneous catalyst had a 66.67% yield.

I attribute this low yield to the fact that the catalyst was not mixed with the methanol before being placed into the vegetable oil. Typically, the catalyst is dissolved into the alcohol to make a solution, which is activated and can then be placed in the starting oil. I also believe this low yield is because I washed all of the biodiesel with water. When this washing occurred after the glycerol was separated, a large amount of soap formed, thus leading me to believe that I had decreased the amount of biodiesel produced.

Calcium Oxide as a Heterogeneous Catalyst In this reaction, a 90% yield was obtained, to find out that the oil that I have collected at the end of the reaction was not biodiesel, but vegetable oil. In order to activate the catalyst, it must be dissolved in the methanol with stirring for one hour at 65◦ C. After mixing the catalyst with methanol at 65◦ C, the solution was added to specific oil and stirred at 65◦ C. The first reactions conducted using calcium oxide were the 1:9 and 1:12 ratios using vegetable oil. When I used calcium oxide as a catalyst and allowed it to form a methoxide solution with the methanol, I found that not only did I get a 95.8% yield from the 1:9 ratio and a 90% yield from the 1:12 ratio, but the IR’s from these products resembled that of biodiesel. Therefore, these two reactions went to completion and the vegetable oil was converted into biodiesel. Since the 1:9 ratio resulted in a better yield, I tried to use that same ratio for the reactions of camelina oil as well as waste vegetable oil with calcium oxide. However, during the first trial, the reactions did not go to completion according to IR analysis. I then redid the experiments, but this time used 65 mL of methanol opposed to the original 55 mL. After using 65 mL of methanol, I saw that the camelina oil and the waste vegetable oil pretreated with ferric sulfate had converted to biodiesel. The waste

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vegetable oil was pretreated with ferric sulfate before transesterification reaction.

Eggshells as a Heterogeneous Catalyst For the three reactions involving eggshells as a catalyst, a large excess of methanol was used.

In previous experiments, I have mostly used 55 mL and 65 mL of methanol. However, it seemed that the more methanol I used, the better chance that the trial would work. Therefore, after using 80 mL of methanol for the eggshell reactions, I saw that each reaction went to completion during the first trial. Although I did not let the reactants heat overnight as in previous reactions, I did let them heat for approximately seven hours and then stir overnight. In the morning, I found that two layers were present and IR analysis proved that the reactions of vegetable oil, waste vegetable oil and camelina oil with eggshells worked. The percent yields obtained were 90.8% for the waste vegetable oil, 91.7% for the vegetable oil and 100% for the camelina oil. Sample FTIR and NMR spectrum is shown in Fig. 2 and Fig. 3.

Figure 2. FTIR spectra of biodiesel produced by a heterogeneous catalyst

Figure 3. NMR spectra of biodiesel produced by a heterogeneous catalyst

Purification of Glycerol Glycerol is a product used in cosmetics such as in soaps and lotions [9, 10]. Glycerol was distilled at 100â—Ś C and then converted into liquid soap by using KOH solution.

Conclusion The purpose of this project was to identify which oil and catalytic system resulted in the best conversion to biodiesel. Traditionally, soybean oil is used with methanol and potassium hydroxide

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to synthesize biodiesel. Since potassium hydroxide is a homogeneous catalyst, it is hard to separate the catalyst from the biodiesel and glycerol phases. The use of a heterogeneous catalyst is more favorable because it can be easily separated through vacuum filtration and thus, can be reused. The reaction with camelina oil and eggshells resulted in the best yield out of all of the experiments for biodiesel synthesis. Camelina oil reduces the competition that is seen with vegetable oils, which are used both for fuel and food. The eggshells as catalysts resulted in the best yield. They can be reused to synthesize another product and thus become more environmentally benign.

Acknowledgement The author would like to thank the School of Science Research Scholars Program for financial support during the performance of the present research.

References [1] G. Knothe (2001). Historical Perspectives on Vegetable Oil-Based Diesel Fuels. The AOCS Lipid Library. Retrieved August 22, 2014.

[2] G. Knothe (2005). Introduction. In The biodiesel handbook (p. 1). Champaign, Ill.: AOCS Press.

[3] Z. Hillion, et al. (2003). Biodiesel Production by a Continuous Process using a Heterogeneous Catalyst. Am. Chem. Soc., Div. Fuel Chem., 48(2), 636.

[4] P. Patil, V. Gnaneswar Gude, and S. Deng (2009). Biodiesel Production from Jatropha Curcas, Waste Cooking, and Camelina Sativa Oils. Ind. Eng. Chem. Res., 48, 10850-10856.

[5] A. Gnanaprakasam, et al. (2013). Recent Strategy of Biodiesel Production from Waste Cooking Oil and Process Influencing Parameters: A Review. Journal of Energy, vol. 2013, Article ID 926392, 1-10.

[6] L. Yang, A. Zhang, and X. Zheng (2009). Shrimp Shell Catalyst for Biodiesel Production.

Energy & Fuels, 23, 3859-3865.

[7] A. Kawashima, K. Matsubara, and K. Honda (2008). Acceleration of catalytic activity of calcium oxide for biodiesel production. Bioresource Technology, 100 (2009), 969-700.

[8] A. Buasri et al. (2013). Application of Eggshell Wastes as a Heterogeneous Catalyst for Biodiesel Production. Sustainable Energy, 1(2), 7-13.

[9] C. Tiangeng (2013) Purification of Crude Glycerol from Waste Cooking Oil Based Biodiesel Production by Orthogonal Test Method. China Petroleum Processing and Petrochemical Technology, 15(1), 48-53.

[10] D. Johnson, K. Taconi The glycerin glut: Options for value-added conversion of crude glycerol resulted from biodiesel production. J. Environ. Prog., 2007, 26: 338-348.

Footprinting of CMG helicase at the replication fork Andi Wallick∗ Department of Chemistry and Biochemistry, Manhattan College Abstract. During DNA replication, the double stranded DNA is separated into two single strands by a helicase. In eukaryotes the helicase is an eleven-subunit complex called CMG. How CMG loads and works at the replication fork is still matter of study. In this report we investigate the location of CMG helicase at the replication fork using footprinting experiments with different nucleases.

Introduction

During DNA replication the helicase separates the double stranded DNA into two single strands that become the templates for the leading and lagging strands synthesis . In eukaryotes the helicase is called CMG. CMG is an eleven- subunit complex composed of Cdc45, Mcm2-7, and Gins. Mcm2-7 forms a hetero-exameric complex that encircles one or both strands of DNA and unwinds the duplex DNA by breaking the hydrogen bonds connecting the two strands. The role of Cdc45 and Gins is still under investigation, but many in vivo and in vitro studies indicatea that rthey ticle are indispensable for helicase unwinding activity. CMG, as shown in Fig. 1 (from Georgescu et al.

(2014)), is thought to be loaded on the leading strand at the replication fork but a conclusive proof is missing. In this study we investigate the position of the helicase complex at the fork by using a nd replisome with CMG, Pol ε, + + + + + a b RPA: footprinting approach.

ATP: + + + – + assay. The 3.2-kb forked DNA RFC–PCNA + + – + + a synthetic primed replication 3′ Leading Pol ε: + – + + + eotide bias to enable specific CMG: – + + + + 3 kb CTP. CMG was assembled on Time (min) 2 4 8 12 20 20 20 20 2 ncubation; then Pol ε, PCNA Mcm2–7 5′ MW (kb) CMG cold dATP and dGTP before Lagging 3.0 RPA, ATP, dTTP and [ 32P]dCTP. Cdc45 2.0 rations are in Online Methods.

GINS 1.5 AMP-PNP cts. Lanes 1–5, time course CMG 1.2 1.0 with indicated components s of DNA product at 2 and 0.7 Pol ε PCNA upplementary Figure 2.

Figure 1.

RFC CMG dA, dG

0.5 0.4 0.3

Nucleases are enzymes that digest DNA. There are two types of nucleases: exonucleases and to endonucleases.

Exonucleases degrade the DNA from the 3’ (Exo I) or 5’ (RecJ) termini. ty similar that of Drosophila

substrate,∗ Research we constructed mentoredlin­

by Chiara Indiani, Ph.D. each having the same synthetic ed a DNA 37-mer primer to the

RPA, dT, dG 32 [α- P]dC

0.2

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Figure 2.

Endonucleases (DNase I) can break both single and double stranded DNA from the inside of the duplex.

At the replication fork, the segment of DNA that is bound to CMG complex is protected from nuclease digestion. If CMG, loads on the leading strand, as shown in Fig. 1, the nuclease would not be able to bind and digest the DNA coated with CMG. To test leading strand CMG loading, we use an exonuclease, Exo I, to specifically degrade the leading strand from the 5’end, The CMG present would prevent degradation of the base pairs leading up to the fork. If the helicase is loaded on the lagging strand, we would use the lagging strand exonuclease, RecJ, to specifically degrade the lagging strand.

Methods Primer labeling: The synthetic replication fork used in this study is formed by 80 base pair fork with 40 of them being DNA dT tails. To label the fork, we use radioactive Phosphorus, [Îł32P] ATP. After we have our labeled replication forks, we were able to have the nucleases degrade the DNA. We would track the degradation of DNA during time course digestion reaction. CMG bound to DNA would protect the base pairs from nucleases and generate longer digestion fragments in a 10% Urea/polyacrilamide sequency gel.

Results Our first step in performing these experiments is finding the right concentration of Exo I needed to not displace the CMG from the replication fork.. Since Exo I is a leading strand nuclease, we use the leading strand labeled replication fork to track the DNA degradation. We used three different concentrations: 10, 50, and 100 nM as shown in the picture. In Fig. 2, we found that the 1:50 concentration was ideal for our situation since it does not degrade the DNA too fast and you can see the degradation of the DNA along the time course.

For our next experiments, we use the 1:50 dilution of the Exo I stock solution. A control sample that does not contain CMG is run beside the time course digestion experiment of the synthetic

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replication fork in the presence of CMG. The results show no difference between the experiments indicating that there is no protection of the DNA base pairs by CMG (Fig. 3). These results could

Figure 3.

Figure 4.

be explained in three ways: first the CMG was never loaded, second the Exo I concentration is too concentrated, and third, the CMG does not load on the leading strand but instead on the lagging strand.

To address the first possibility we increase incubation time of CMG loading at the replication fork (data not shown) and its concentration (Fig. 4). The results indicate that neither a longer incubation time of the helicase nor higher concentrations can produce different digestion fragment of the labeled replication fork. Indeed the digestion fragments obtained in the presence and absence of CMG are the same.

We conclude that Exo I is not a good reagent for these specific footprinting experiments.

Since exonucleases do not give a clear answer to the questions of CMG loading, endonucleases, which degrades the DNA from the inside, are tested. The endonuclease we use is DNase I. As for Exo I, we need to find the appropriate concentration of the DNase I so that the CMG is not displaced from the replication fork by the addition of the endonuclease, and the nuclease also degrades the DNA only one time. To find the experimental conditions for the endonuclease in the footprinting experiment, we performed a titration of DNaseI in the absence of CMG and found that the best concentration of DNase I is 50 nM. As seen in Fig. 5, the DNase I endonuclease shows a progressive time course degradation of DNA. However, 100 nM concentration degrades the DNA too fast and the 100 nM concentration is too slow. From this experiment, we also found that DNase I is specific for double stranded DNA as indicated by the bands that traveled farther in the gel. If the single DNA was cut, there would be bands in the upper part of the gel. Once found the experimental conditions we perform footprinting

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Figure 5.

Wallick

Figure 6.

experiment in the presence of CMG loaded at the replication fork.

In this experiment, we want to have a control of + and – CMG. We also want to have two proteins, RPA and SSB, that bind single stranded DNA tightly and do not get easily removed. As shown in Fig. 6, CMG does not bind to the double stranded DNA because there is not protection of the DNA. When RPA is added, it indeed binds to the single stranded DNA and protect it from degradation as indicated by the intense band at the top of the gel corresponding to uncut DNA. Unfortunately, SSB protein shows a gel shift making the results difficult to interpret. These results indicate that DNase I is not ideal to address because it preferentially cut double strand DNA.

Discussion In this study we found that both Exo I and DNase I are not ideal nucleases that can be use in a footprinting experiment to determine the how and where CMG is loaded at the replication fork. Future experiments might include the use of RecJ, a 3’-5’ exonuclease, to investigate the possibility of CMG binding to the lagging strand. Moreover, more experiments will be required to optimize the loading of CMG at the replication fork. Although we were unable to find how the CMG loads on the replication fork, the results of this study lead us to conclude that both nucleases, Exo I and DNase I, are not suitable reagents for footprinting method.

Acknowledgement The author thanks the Jasper Fellows Program for financial support.

References Georgescu, R. E., Langston, L., Yao, N. Y., Yurieva, O., Zhang, D., Finkelstein, J., O’Donnell, M. (2014). Mechanism of Asymmetric Polymerase Assembly at the Eukaryotic Replication Fork.

Nature Structural and Molecular Biology, (8), 664-70.

Pitch perfect: Re-analyzing the passing networks of Manhattan College women’s soccer Andre Oliveira∗ Department of Mathematics, Manhattan College Abstract. Network Theory has a store of real world applications, incuding in the sport of soccer. This paper extends the work of Pena and Touchette in “A network theory analysis of football strategies” [1]. Their methods of analysis are re-applied to the Manhattan College Women’s soccer team; with modifications that attempt to correct for the differences between men’s international and women’s collegiate style of play.

Introduction In recent work by J. Pe˜na and H. Touchette [1], they apply Network Theory notions to passing networks of international men’s soccer teams. A naive approach to perform their analysis on the Manhattan College Women’s Soccer team, The Jaspers, quickly shows some of the fundamental differences between the collegiate and international levels of play.

During a research seminar, “Applied Network Theory,” taught by Dr. Tyler in the Fall 2013 semester, of which I was a student; The class covered the basics of Network Theory, read through Pe˜na and Touchette’s paper [1], and attempted to reapply their analysis to the school’s womens soccer team, the Jaspers. We found the fundamental differences between the levels of play being substitutions, skill level, and fitness; affecting the overall amount of passes and substitutions during a game.

In professional men’s soccer, each team is allowed up to three substitutions per match and once a player is substituted off he cannot reenter the game. Meanwhile in collegiate women’s soccer, each team is allowed an unlimited number of substitutions per match, but if a player is substituted off she can reenter the game in the next period.

Throughout this paper I will use the word player, when I should instead use the word position.

This is a conscious decision and makes the language and ideas easier to understand. However it is important to bear in mind the difference between a set of players, grouped under one position, and a single player.

A Team’s Performance A passing network is a directed graph where the nodes correspond to players, and weighted arrows to the number of completed passes between respective players. For our computations we use a weighted adjacency matrix, a representation of a passing network, where the (ij)-th entry is the number of passes from player i to player j. ∗

Research mentored by Helene Tyler, Ph.D.

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We give the definitions of three measures for individual players, and a measure of how tightknit the players are, as defined by Pe˜na and Touchette; and discuss their use in a passing network’s analysis. As well as define two new measures to better understand the roles each position plays in the team.

Closeness A player j is said to be “close” to a player i if it is relatively easy to move the ball from player i to player j. Formally we define the closeness score of player i, Ci , as the inverse of her geodesic distance to and from every other player. Hence, Ci = P

j6=i

20 P , dij + dji j6=i

where the geodesic distance, dij , is given by the length of the shortest path connecting the nodes i and j; and the length of a path is obtained by adding the lengths lij of the arrows according to ( 0 if i = j . lij = 1 if i 6= j Aij Ideally one would want every player in a team to have a high closeness score. As this would mean it is extremely easy for the team to move the ball among themselves.

Betweenness An important attribute of a player is their ability to help the team move the ball from one player to another, in the shortest amount of passes. The betweenness score of a player i, CB (i), measures this attribute. Specifically, the betweenness of a player, is the extent to which she lies on the shortest path between other players. If nijk denotes the number of geodesic paths from j to k going through i and gjk gives the total number of geodesic paths from j to k, then 1 X nijk .

CB (i) = 90 j6=k6=i gjk It is not bad for a player to have a high betweenness score, it can however be bad for the team.

A team composed of players with unbalanced high betweenness scores heavily relies on the highscore players to distribute the ball. This makes the team more easily defendable as the opposing team can simply mark these players more heavily. Disrupting the passing ability of the team. On the other hand, a team with low and balanced betweenness scores does not rely so heavily on any one player. The balanced team could lose a player to injury, penalty, or good defense and not have its performance suffer.

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Pagerank We say that a player is “popular”, or important, if other “popular” players pass to her. This recursive notion of popularity is measured by PageRank. Formally the PageRank of a player i, xi , is defined as X Aji xi = p x + q, out j L j j6=i

where Lout j is the total number of passes made by player j. Because of this recursive definition, computing the PageRank of a player reduces to solving for an eigenvector. The PageRank of a player is also the probability that she will have possession of the ball after a reasonable number of passes.

Clustering We define a cluster as a directed triple of players, i, j, k. Where j passes to i and k, and i passes to k. The clustering score of a player i, cw i , is a notion of how well that player helps complete these triples; they can be viewed as directed triangles. Formally, p X 3 Ajk Aji Aik 1 w , ci = ui (ui − 1) j,k max(A)

where ui is the number of passes made by player i. We scale each triangle by the geometric mean of the passes involved; this also discounts non-completed triangles.

If a player has a high clustering score, they are consistently providing an alternate path to move the ball from one player to another. Note that this alternate path only consists of one player, while there might exist longer paths with the same source and destination. In a soccer context, this is a helpful characteristic of a team. Imagine a defender blocking the pass between player j and k; note here this is the physical passing lane, not a path of passes. If player i has a high clustering score she will typically be in a position to allow player j to pass to her and then pass to player k. This is a helpful attribute for a teams’ players for it adds resiliency to the network, making it difficult for opponents to defend.

Heat Score The mention of passes from and to players leads to the question, “how many passes did a player contribute?” This is exactly the heat score of player i, heat(i), written as X X heat(i) = Aij + Aji . i6=j

i6=j

With regard to heat, we are considering players to be the intersections of a city. A “busy intersection” corresponds to a player with a high heat score. This can be used in combination with Closeness and PageRank to find players that are consistently in good positions, on the field, to make and receive passes.

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Defensive Score After defining heat, the definition below easily follows, X X def(i) = Aij − Aji , i6=j

i6=j

where def(i) is the defensive score of a player i. We say a player with a high defensive score is a good defender. The idea being, if def(i) is high then player i must be passing the ball more than she is receiving. To do so, she must be generating the ball from somewhere, we assume that she is winning the ball from the other team, and thus a good defender.

Analysis To perform our Analysis, and avoid our previous problems, we recollected the passing data from the 2013 season by position. This solves the problem of players changing positions throughout the game as well as being substituted on and off the field.

Looking inward The Manhattan College Jaspers are part of the Metro Atlantic Athletic Conference (MAAC), which is affiliated in NCAA Division I. The MAAC is comprised of eleven schools from three states. During the 2013-14 season, 3 of the 10 regular conference games were played using a 4-3-3 formation. That is, players occupy four defending positions, three midfield positions, and three forward positions, plus a goalkeeper. Our analysis is based on the games in which the Japsers played in this formation; the first 3 games of the season. We chose to analyze these games due to time constraints.

Table 1 contains the computed measures for our players; there are a few non-intuitive results in this table.

Naively one makes a few assumptions about how a soccer team plays. For example, the ball is passed the most in the midfield, the midfielders should be the closest to other players, the Table 1. Computed scores for individual players.

Player G LOB LCB RCB ROB LDCM RDCM ACM CF RF LF

Ci 0.88 0.75 0.6 0.68 0.75 0.34 0.36 0.47 0.58 0.68 0.58

CB (i) 0.0 4.3 1.77 0.5 3.54 2.3 2.3 0.72 0.58 0.27 0.72

xi 0.02 0.07 0.06 0.04 0.08 0.09 0.1 0.12 0.14 0.14 0.13

cw i 0.15 0.2 0.23 0.25 0.24 0.28 0.3 0.24 0.28 0.31 0.32

heat(i) 4.33 28.0 16.0 12.0 21.67 25.0 29.0 27.33 28.0 28.0 32.67

def(i) -0.33 -11.33 2.0 -3.33 -5.0 -3.67 -3.67 4.67 8.67 9.33 2.67

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defenders are the best defenders, etc. However not every team plays in the same fashion, they don’t all employ these techniques; the Jaspers are one such team that do not follow an intuitive game plan.

As mentioned, one would naturally think the midfielders would have the highest closeness and heat scores, considering they should be in the middle of the field. This is not the case for the Jaspers. The highest closeness scores are for the goalkeeper, then the outside-backs, followed by the center-backs, the forwards, and then the midfielders. The highest heat scores belong to the outside backs and then forwards. These strange results can be attributed to the Jaspers playing a long-ball and outside-in style of play. A long-ball style is where the team attempts to pass the ball directly from the defenders to the forwards, bypassing the midfielders; and, an outside-in style is where the team pushes its outside-backs up the field, to then pass the ball to the forwards, again bypassing the midfielders.

Also, the Jaspers’ ability to win the ball from opposition is most prominent among the forwards. Note that this is not a bad property of a team, the forwards here are simply very aggressive and do well stealing the ball.

Observing the PageRank scores, as we move down the column, xi , the scores seem to consistently increase. Recall that as well as measuring how popular a player is, PageRank also gives an estimate of how probable it is a player will be in possession of the ball. Applying this to our data set we see that it is most probable for one of our forwards to be in possession of the ball. Again, we must remind ourselves that this is not physical positions; it does not mean the ball is at the front of the field, only that a forward is most probably in possession. However, it is fair to assume that a forward is most likely to be at the front of the field, and so the ball is also most likely to be there. This of course is a great attribute for the team, because one needs possession of the ball by the other goal to score and win.

While the Jaspers display these characteristics of a good soccer team, it is clear from the betweenness scores that they rely heavily on a few key positions, specifically, the outside backs.

While this is part of the style of the play the Jaspers wish to emulate, the extremely unbalanced scores in the betweenness column hint that the team relies too heavily on this strategy. An opponent that successfully defended these positions would most certainly overpower the Jaspers’ offense.

Along with considering the information we can extract from Table 1, we can also analyze the team’s passing network, Fig. 1 below. It is immediately clear that there is an imbalance in the team.

The left-hand positions as well as the forward positions dominate in number of passes. There is a disconnect between players in the defense. As well as a partial connection through the midfield, but it is not as strong as one would except.

While we can extract these facts from our table of measures, we would not be able to find that there exists a clear path of passes from left-outside-back (LOB), left-center-mid (LCM), attckingcenter-mid (ACM), and left-forward (LF). An interesting fact that we are not able to explain. While we focused mainly on the analysis of Table 1, there remain a numerous amount of details to extract

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Mexico Last formation against Uruguay.

GermanyScientist, v The Manhattan Series B, Volume 1 (2014) England

Oliveira Player

Holland v Spain England

1 - Oscar

Germany Holland

2 - Franc

Spain

3 - Carlos

Other teams

4 - Rafae

Notes

5 - Ricard

Press release News coverage

6 - Gerar

14 - Javie

16 - Efrai

17 - Giov

18 - Andr

21 - Adol

Figure 1. The Jasper’s 4-3-3 formation

Figure 2. Mexico’s passing network USA

Last formation against Ghana. from the passing network, and only the passing network.

Looking outward Player We compare ourselves to the Top 16 teams from the 2010 World Cup. The data for these teams was available in [1]. We directly compare ourselves to these teams by inserting the Jaspers’ data1- Tim HO alongside these teams, in Table 2.

3 - Carlos

Notice that while our connectivities, average clustering, and average betweenness are on par with these team, our average passes and largest clique are out of the norm. The Jaspers have the4 - Micha third lowest average number of passes, as well as the highest largest clique. We are not certain6 - Steve why the Jaspers have the highest largest clique. We assume this is because they play much more compactly, whereas the international teams would have players more evenly spread throughout the8 - Clint D field. However the low number of average passes can be explained by the Jaspers being a collegiate10 - Land team. They are neither as skilled nor as fit as these international teams.

12 - Jona

To quantify the comparison between the Jaspers and the Top 16 we develop a similarity score based on a Borda Count. A Borda Count is a preferential voting system, where voters rank each13 - Rica candidate on some point-scale. A candidate’s score is then the sum of the voters’ rankings. The 15 - Jay D winner is the candidate with the best ranking.

In our similarity score, we take the voters to be the measures, and the Top 16 teams as candi-17 - Jozy dates. For each measure, m, define the distance ∆m (t) as the absolute value of the difference, of20 - Robb

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measure m, between team t and the Jaspers. We then order this list of distances and assign a team its ranking. A team’s similarity score is the sum of all their rankings.

We compute similarity scores with and without regard to average number of passes. Regardless Mexico has the highest similarity score, as seen on Table 3. However, the Jaspers and Mexico’s passing networks share nothing in common, see Fig. 2. While Mexico is strong in their defense, the Jaspers are strong in the offense. Why then are we most similar to Mexico? This abnormality is hidden in our definition of similarity. We compute similarity scores using averages. To be more exact, Mexico is not the most similar team to the Jaspers, they are however the team with the most similar averages. The exemplifies problem of using averages, they introduce artifacts.

Table 2. Data for the teams in the round of 16, taken from Table 1 in [1], including The Jaspers’ scores. P : average number of passes; k: edge connectivity; ku : undirected connectivity; cw : average clustering; CB : average betweenness; Cq : largest clique. The highest two values (except for clique) are highlighted, and the Jasper’s scores are emphasized.

Team

P

k

ku

cw

CB

Cq

Argentina Brazil Chile England Germany Ghana Japan Jaspers Korea Rep. Mexico Netherlands Paraguay Portugal Slovakia Spain USA Uruguay

227 321 120 239 220 184 180 126 227 225 266 103 175 166 417 160 117

4 5 0 2 2 3 1 2 3 0 5 0 3 3 3 1 2

5 7 1 3 2 4 5 2 5 0 7 2 4 6 5 4 3

27.9 26.2 18.9 28.0 24.7 15.5 28.9 25.4 24.4 27.2 29.7 20.4 14.6 18.5 30.0 16.0 14.3

2.7 2.0 5.1 3.6 4.6 3.5 3.3 1.7 2.6 1.9 1.9 7.5 4.1 3.0 1.9 4.6 4.8

8 8 6 7 6 8 8 10 8 7 8 5 7 7 9 7 6

A better similarity score definition would rank each team by how close respective positions play. This however limits us, only allowing similarity scores to be computed for teams playing in the same formation.

Obtaining Our Results To aggregate, order, and compute the values of our measures we created custom Python classes, and implemented our Similarity Score voting system in iPython Notebook. Sage was used to compute the Jaspers’ connectivity. And, Mathematica was used to create the Jaspers’ passing network.

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Future Work Ideally one would be able to have every piece of information available; by tagging each pass with player from, player to, position from, position to, time, position on the field, etc. However, this seems beyond the possibility for an undergraduate project. This method may already be employed by international teams.

One key fact to keep in mind during our analysis is that we only consider the actions of the Jaspers. We disregard all effects of having an opponent on the pitch. Thus, a collaboration between schools to gather inter-team data would lead to a completely new branch of analysis we have not yet considered.

Acknowledgement The author would like to thank the School of Science for financial support to perform this work.

Table 3. Similarity scores with and without regard for average number of passes. A higher score, a closer similarity.

Team Mexico Korea Brazil Germany Spain Argentina England Japan Netherlands Slovakia Ghana USA Chile Paraguay Portugal Uruguay

with passes 1 2 6 3 7 5 7 4 9 7 11 10 8 10 12 11

without passes 1 1 2 3 3 4 5 6 6 7 8 9 10 10 10 11

References [1] J. L´opez Pe˜na, H. Touchette, A network theory analysis of football strategies, In C. Clanet (ed), Sports Physics: Proc. Euromech Physics of Sports Conf., Editions de l’ecole Polytechnique, Palaiseau, 2013.

Monte Carlo studies of ideal three dimensional polymers Gregory Zajac∗ Department of Mathematics, Manhattan College Abstract. Computer modeling is an important skill for engineering and science students to acquire. Monte Carlo simulations of ideal three dimensional polymers provide an opportunity for students to develop their computer skills while deepening their knowledge of the behavior of such materials.

Introduction In a previous publication in this journal, Varriale II and Bishop [1] used a Monte Carlo growth method to simulate two dimensional ideal linear and star polymers. They computed polymer properties such as the mean-square radius of gyration, hS 2 i, and the mean asphericity, hAi, of both linear and star polymers and found excellent agreement with theoretical values. Perrelli and Bishop [2] extended this simulation method to investigate ideal two dimensional H-comb polymers and found similar good agreement with theoretical predictions. In this work, the Monte Carlo growth method is used to examine ideal linear polymers in three dimensions. A wide variety of properties are computed and compared to theoretical predictions.

Method The program has been written using a procedural approach. Three dimensional polymers are constructed on an integer coordinate system. Given the numbers N and M, the simulation is performed by creating M independent samples each containing N units (beads). Samples are constructed by starting the first bead at the origin (0, 0, 0). Subsequent beads are placed by randomly selecting one of six possible directions: North, South, East, West, Up, or Down. Each bead is placed one unit apart from the previously placed bead. In this study of ideal polymers, a location that has already been used by another bead is allowed to be chosen so that beads can overlap. After each polymer is completely constructed, a number of properties are computed for that configuration.

One important property of polymers is their shape, which can be determined from the matrix ↔ representation of the radius of gyration tensor, T . This is a 3 by 3 symmetric tensor with nine components but only six are unique. It can be written as N

1 X a [Qi (k) − Qa CMi (k)] Qbi (k) − Qb CMi (k) ; a, b = X, Y or Z. T (k) = N i=1 ab

∗

Research mentored by Marvin Bishop, Ph.D.

(1)

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Here, Qi (k) represents the X, Y, or Z components of the location of the i-th bead in the k-th sample and QCMi (k) represents the corresponding center of mass: N 1 X QCMi (k) = Qi (k).

N i=1

(2)

↔

The eigenvalues of T , λ1 , λ2 and λ3 , are the components of the radius of gyration along the principal orthogonal axes [3]. They are determined for a given sample by using the Cardano-Vieta solution to the cubic characteristic equation. The λ values of each conguration can be ordered by magnitude. One can envision [4] the polymer as enclosed in an ellipsoidal envelope with semimajor axis λ1 and semi-minor axes λ2 and λ3 . Rudnick and Gaspari [3] defined the asphericity of the k-th sample of a configuration, A(k), in three dimensions as A(k) =

(λ1 − λ2 )2 + (λ2 − λ3 )2 + (λ3 − λ1 )2 .

2(λ1 + λ2 + λ3 )2

(3)

The asphericity ranges from a value of 0 when λ1 = λ2 = λ3 and the polymer has the shape of a perfect sphere, to 1 when λ2 = λ3 = 0 and the polymer has the shape of a straight rod.

The overall size of a polymer is characterized by its radius of gyration and, in the special case of a linear chain, by its end-to-end distance. The squared radius of gyration of the k-th sample, S 2 (k), is equal to the sum of the diagonal elements of the radius of gyration tensor, S 2 (k) = λ1 + λ2 + λ3

(4)

and the squared end-to-end distance of the k-th sample of linear chains, R2 (k), is R2 (k) = (XN − X1 )2 + (YN − Y1 )2 + (ZN − Z1 )2 .

(5)

Here N and 1 refer to the last and first bead, respectively.

It is well-known [5] that for large polymers, both hR2 i and hS 2 i follow scaling laws: hR2 i = C1 (N − 1)2ν 2

hS i = C2 (N − 1)

2ν

(6a) (6b)

The coefficients, C1 and C2 , are model dependent amplitudes but the exponent, 2ν, is universal hS 2 i 1 and equal to 1.0 for ideal polymers. It is also well-known [5] that hR 2 i = 6 for long ideal linear chains.

Results The simulation has been developed using the Visual Studio C++ compiler on a PC. All the runs for N = 100, 150, 200, 250 and 300 in Tables 1 and 2 employed 10,000 samples. The program

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averages the data over all the samples. Since the polymer generation process provides independent samples, the mean and standard deviation of the mean of general properties can be computed from the usual simple equations [6], but more care is needed in computing the errors of the ratios. In these tables the number in parenthesis denotes one standard deviation in the last displayed digit; for example, hλ1 i = 12.86(8) means that hλ1 i = 12.86 ± 0.08.

Table 1. General Properties Property hλ1 i hλ2 i hλ3 i hS 2 i hR2 i hAi

100 12.86(8) 2.88(1) 1.07(1) 16.81(9) 99.75(81) 0.395(2)

150 19.12(12) 4.32(2) 1.60(1) 25.03(13) 149.19(122) 0.394(2)

200 25.71(16) 5.74(3) 2.14(1) 33.60(17) 200.79(162) 0.395(2)

250 31.84(20) 7.19(4) 2.66(1) 41.69(21) 250.98(204) 0.393(2)

300 38.45(24) 8.61(4) 3.20(1) 50.26(26) 302.45(250) 0.395(2)

Table 2. Ratio Properties Property hλ1 i/hS 2 i hλ2 i/hS 2 i hλ3 i/hS 2 i hS 2 i/hR2 i hR2 i/hRi2 hR4 i/hR2 i2 hR6 i/hR3 i2 hR6 i/hR2 i3 hR8 i/hR4 i2 hR8 i/hR2 i4

100 0.765(1) 0.171(1) 0.064(1) 0.169(1) 1.175(2) 1.657(12) 2.555(51) 3.838(95) 4.184(327) 11.494(700)

150 0.764(1) 0.172(1) 0.064(1) 0.168(1) 1.180(3) 1.667(12) 2.550(42) 3.853(81) 4.064(265) 11.291(512)

200 0.765(1) 0.171(1) 0.064(1) 0.167(1) 1.177(2) 1.653(11) 2.505(38) 3.761(74) 3.938(239) 10.762(433)

250 0.764(1) 0.173(1) 0.064(1) 0.166(1) 1.180(3) 1.662(11) 2.530(41) 3.818(79) 4.010(256) 11.082(490)

300 0.765(1) 0.171(1) 0.064(1) 0.166(1) 1.181(3) 1.682(12) 2.616(41) 3.977(82) 4.235(265) 11.988(484)

The hS 2 i and hR2 i data in Table 1 were fit by a weighted nonlinear least-squares program [6] to determine the exponent in the scaling laws, Eqs. 6a and 6b. It was found that 2ν had the value of 0.99 ± 0.01 for hS 2 i and 1.00 ± 0.01 for hS 2 i. These results are consistent with the theoretical value of 1.00.

The computer results in the Tables are for finite N whereas the theoretical results are for infinite N . Another scaling law for any property P r is

K (7) P r = P r∞ 1 − ∆ N Here P r∞ is the value of P r for infinite N, K is a constant, and ∆ is the finite scaling exponent.

In the ideal polymer regime ∆ has a value of 1.0. The P r∞ value can thus be found by fitting a weighted least-squares line [6] in N1 to each set of data in the Tables.

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The error in ratio calculations involving the division of separately averaged quantities which might be correlated has been determined by employing the equation derived by Bishop and Clarke [7]. They related the error in a ratio to the separate errors in the numerator and in the denominator.

If the ratio is given as Z = hYhXi , where P is any power, the standard deviation of the mean of iP Z, σhZi , is determined by the standard deviations of the mean of hXi and the mean of hY i, σhXi and σhY i , respectively. σhZi = Z

"

σhXi hXi

2

+ P2

σhY i hY i

2

−

2P covar (hXi, hY i) hXihY i

# 12

.

(8)

Here, covar (hXi, hY i) is the covariance of hXi and hY i. It is defined by covar (hXi, hY i) =

hXY i − hXihY i .

M −1

(9)

The various ratio values and their errors were determined from Eqs. 8 and 9. Note that the ratios involve the quotient of averaged quantities rather than the average of the quotient. The results appear in Table 2. Then the best linear fit was extrapolated in N1 to 0 (e.g. N → ∞).

The final extrapolated values are presented in Table 3 along with known results. Most of the simulation values reported in Table 3 are well within two standard deviations of the mean or in the 95% confidence interval. The error bars for the end-to-end distance moments grow larger as the exponent of the moment increases because of the large numerical values present in the quotient.

Table 3. Comparison of Simulation and Literature Results

Property hλ1 i/hS 2 i hλ2 i/hS 2 i hλ3 i/hS 2 i hAi 2 hS i/hR2 i hR2 i/hRi2 hR4 i/hR2 i2 hR6 i/hR3 i2 hR6 i/hR2 i3 hR8 i/hR4 i2 hR8 i/hR2 i4

Extrapolated Literature 0.764(1) 0.7646(5)[a] 0.172(1) 0.1721(1)[a] 0.064(1) 0.06333(5)[a] 0.394(2) 0.394[b] 0.164(1) 0.167[c] 1.182(3) 1.178[d] 1.675(14) 1.667[d] 2.568(52) 2.577[d] 3.892(100) 3.889[d] 4.034(330) 4.200[d] 11.409(644) 11.667[d]

[a] Ref. [8], [b] Ref. [9], [c] Ref. [5], [d] Ref. [7]

Solc [10] also simulated ideal linear polymers in three dimensions. He found that hλ1 i, hλ2 i

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and hλ3 i were in the ratio of 11.8:2.69:1.00. Our ratio of 11.9:2.69:1.00 is in fine agreement with his results.

Conclusion We have investigated three dimensional ideal linear polymers using a Monte Carlo growth method. Many different properties have been computed. There is fine agreement with theoretical results and other simulations. Modeling projects such as the one described here provide a clear demonstration of some aspects of polymers and thus strongly enhance student understanding and intuition.

Acknowledgement The author thanks School of Science Research Scholars Program for financial support.

References [1] R. Varriale II and M. Bishop, “Modeling and Simulation of Star Polymers in Two Dimensions,” Comp. Educ. J., XVII (3), 44 (2007).

[2] M. Perrelli and M. Bishop, “Monte Carlo Simulations of Ideal Two Dimensional H-Combs,” Comp. Educ. J., 5(3), 25 (2014).

[3] J. Rudnick and G. Gaspari, “The Asphericity of Random Walks,” J. Phys. A, 19, L191 (1986).

[4] A. M. Dunn and M. Bishop, “Modeling and Simulation of Two Dimensional Star Polymers with the Pivot Algorithm,” Comp. Educ. J., XVIII (1), 64 (2008).

[5] P. G. de Gennes, Scaling Concepts in Polymer Physics, (Cornell University Press, Ithaca, 1979).

[6] P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences, (McGraw-Hill, New York, 1969).

[7] M. Bishop and J. H. R. Clarke, “Investigation of the End-to-End Distance Distribution Function for Random and Self-Avoiding Walks in Two and Three Dimensions,” J. Chem. Phys., 94, 3936 (1991).

[8] G. Zifferer and O. F. Olaj, “Shape Asymmetry of Random Walks and Nonreversal Random Walks,” J. Chem. Phys., 100, 636 (1994).

[9] H. W. Diehl and E. Eisenriegler, “Universal Shape Ratios for Open and Closed Random Walks: Exact Results for all D,” J. Phys. A, 22, L87 (1989).

[10] K. Solc, “Statistical Mechanics of Random Flight Chains. IV, Size and Shape Parameters of Cyclic, Star-like and Comb-like Chains,” Macromolecules, 6, 378 (1973).

Systematic transition rate cancellations in quasi one-electron atoms Andrew Baumgartner∗ Department of Physics, Manhattan College Abstract. We present a detailed study of discrete atomic transitions using the Coulomb approximation of Bates and Damgaard. We focus our attention to monopole, dipole and quadrupole transitions, as functions of the effective quantum numbers n∗ of the initial and final states. As expected, the matrix elements display oscillatory behaviors as functions of the n∗ . Our focus has been in a systematic presentation is made of minima in the radial matrix elements in the (n∗ , n0∗ ) plane, with applications to quasi one-electron isoelectronic sequences.

Introduction One of the most important quantities in atomic physics is the radial matrix element between two state wave functions. With this quanity, one can calculate the transition probability, lifetimes, oscillator and line strengths and as well as certain optical properties of the atoms. For a transition of order s, the radial matrix element is defined as Z ∞ 0 0 s 0 0 Pnl (r)rs Pn0 l0 (r)dr (1) R(nl; n l ) = nlr n l = 0

where the reduced radial wave function Pnl = rRnl (r) is normalized to unity and s = 0, 1, 2 correspond to monopole, dipole, and quadrupole transitions, respectively.

In the present work, we aim to find a general expression for the location of the cancellations, or Cooper minima [1], of R(nl; n0 l0 ) as a function of the effective quantum numbers n∗ and n0∗ . Using the Numeric Coulomb Approximation, we calculate the radial matrix elements and systematically study their behavior in the (n∗ , n0∗ ) plane. We apply our method to the Li, Na, K, Rb, Cs, and Cu isoelectronic sequences.

Calculation of Radial Matrix Elements The exact calculation of (1) can only be carried out for one-electron systems, where the radial wavefunctions are known analytically. For more complicated systems, it is necessary to introduce approximation techniques to solve the radial Schr¨odinger equation and (1). The methodology used in this work was introduced by Bates and Damgaard [2] and is called the Coulomb approximation (CA). It has been proven to be an accurate approximation for atoms with one active electron orbiting a core cloud of electrons around the nucleus. However, this approximation breaks down for n∗ about 20. For cases with high quantum numbers, we use the method of Regemorter et al. [3, 4].

The two methods are in close agreement for small quantum numbers, differing by no more than 4%. We give a brief outline of both methods we used. ∗

Research mentored by Constantine Theodosiou, Ph.D.

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In the case of a quazi one-electron system, the wavefunction has a hydrogenic form [5], except for a phase shift at the ionization threshold, which is related to the quantum defect Âľ [6]. π¾n=∞,l = δ(E = 0).

(2)

The quantum defect is defined through the binding energy, given in atomic units by Enl = −

Îś2 Îś2 ≥ − 2(n − Âľnl )2 2n∗2 nl

(3)

where n∗ is the effective principle quantum number and Îś = Z − N + 1, the asymptotic charge of the core. Due to the nature of the operator rs , the large distances outside of the core dominate the value of the integral (1). tion

The wavefunction Pnl (r) describing the electron can be found by solving the differential equa

l(l + 1) d2 Pnl (r) + 2(Enl − V (r) − Pnl (r) = 0 (4) dr2 r2

where l is the orbital angular momentum quantum number, E is its energy and V (r) is the atomic potential, which by the Coulomb approximation assumed to be of the form Îś V (r) = − . r Atomic units are assumed throughout this work.

(5)

Bates and Damgaard Approach To give an accurate approximation, we must find where the potential reaches this asymptotic form. If we call the radial position where it occurs rc , we must compare the values of the integrals Z rc I1 = Pn0 l0 rs Pnl dr (6) 0

and

I2 =

Z

∞

rc

Usually I1 I2 and can be ignored.

Pn0 l0 rs Pnl dr.

(7)

For r > rc , the bound state solutions to (4) with (5) are proportional to the second Whittaker functions [7]. They are

−1/2

2 âˆ‚Âľ ∗ 1/2 ∗ ∗ ∗2 Γ(n + l + 1)Γ(n − l) . (8) Pnl (r) = Wn,l+1/2 (2Îśr/n )Îś Ă— n 1 + ∗3 n ∂

For the present study, we set the electron’s energy Enl equal to the ionization potential, i.e. we neglect core relaxation effects.

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The Whittaker function has the asymptotic form ∗ n∗ −ζr/n∗

Wn∗ ,l+1/2 ≈ (2ζr/n ) e

∞ X

bt (n∗ l)/(ζr)t

(9)

t=0

where b0 = 1 and bt = (n∗ /2t) [l(l + 1) − (n∗ − t)(n∗ − t + 1)] bt−1 .

(10)

For integer n∗ , the series in (9) terminates whenever bt = 0, or l(l + 1) − (n∗ − t)(n∗ − t + 1) = 0.

(11)

But for non-integer effective quantum numbers, the series in infinite.

The wavefunction (8), with non-integer n∗ , goes to zero at infinity but diverges at the origin.

This is because µ is not an eigenvalue of (4). Plugging (8) into (1), we get Z ∞ Z ∞ s Wn∗ ,l+1/2 (2ζr/n∗ )rs Wn0∗ ,l0 +1/2 (2ζr/n0∗ ) Pnl (r)r Pn0 l0 (r)dr ≈ 0 0 X (12) ∗ 0∗ = (2/n∗ )n (2/n0∗ )n (n∗ /2)i (n0∗ /2)j bi bj Iij ij

where Iij is an integral that can be calculated exactly [7] Z ∞ ∗ 0∗ ∗ 0∗ Iij = e−(1/n +1/n )r rn +n −i−j+s dr

(13)

0

∗

0∗ −(n∗ +n0∗ −i−j+s+1)

= (1/n + 1/n )

∗

0∗

× Γ(n + n − i − j + s + 1).

This leads to the expression

j ∗ i Z ∞ ∗ 0∗ 0∗ ∗ 2(n +n ) n∗(n +2) n0∗(n +2) X n∗ + n0∗ n + n0∗ s Pnl (r)r Pn0 l0 (r)dr ≈ (n∗ + n0∗ )(n0∗ +n∗ ) 2n∗ 2n0∗ 0 ij ∗

(14)

0∗

× Γ(n + n − i − j + s + 1)ai aj .

Here we see the limits of integration are from zero to infinity. As before, we could split this integral into two integrals from 0 to rc and rc to ∞. The former integral will be negligible compared to the latter if ∗ 0∗ r(n +n −i−j+s) rc .

(15) This implies that there is an upper limit on the summation indices. This can be seen from the dependence of Iij on r which is of the form r−(i+j) . This dependence yields small values of r for large values of i and j, and the integral becomes very sensitive inside of the core, where the

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wavefunction is not approximated by the Whittaker function. Thus, the series must truncated.

Bates and Damgaard used the condition i + j < nâ&#x2C6;&#x2014; + n0â&#x2C6;&#x2014; â&#x2C6;&#x2019; 1

(16)

for dipole transitions; in the general (multipole) case, (16) becomes i + j < nâ&#x2C6;&#x2014; + n0â&#x2C6;&#x2014; â&#x2C6;&#x2019; s.

(17)

This truncation condition allows us to turn the transition integral into a finite double sum in (14), which can be easily computed.

Burgess and Seaton [8, 9] have extended the Bates and Damgaard approach to discrete - continuum transitions. They expressed the continuum functions as superpositions of regular and irregular Coulomb functions, both of which have a periodic behavior. The relevant transition matrix elements display similarly an oscillatory behavior R(nâ&#x2C6;&#x2014; l; 0 l0 ) = G(nâ&#x2C6;&#x2014; l; 0 l0 ) cos Ď&#x20AC;[nâ&#x2C6;&#x2014; + Âľ0 ( 0 ) + Ď&#x2021;(nâ&#x2C6;&#x2014; l; 0 l0 )].

(18)

Their results can be extended to discrete - discrete transitions, yielding R(nâ&#x2C6;&#x2014; l; n0â&#x2C6;&#x2014; l0 ) = G cos Ď&#x20AC;[nâ&#x2C6;&#x2014; â&#x2C6;&#x2019; n0â&#x2C6;&#x2014; + Ď&#x2021;ll0 (nâ&#x2C6;&#x2014; , n0â&#x2C6;&#x2014; )]

(19)

where G and Ď&#x2021;ll0 (nâ&#x2C6;&#x2014; , n0â&#x2C6;&#x2014; ) are very slow functions of nâ&#x2C6;&#x2014; and n0â&#x2C6;&#x2014; and Ď&#x2021;ll0 can be fitted like Ď&#x2021;ll0 (nâ&#x2C6;&#x2014; ) = all0 + bll0 /nâ&#x2C6;&#x2014; + cll0 /nâ&#x2C6;&#x2014;2 .

(20)

Regemorter, Hoang Binh and Prudâ&#x20AC;&#x2122;homme Approach The method of Bates and Damgaard is useful because it involves a series that is easily calculated. However this method breaks down for nâ&#x2C6;&#x2014; around 15. A method to calculate the integral (1), especially for high nâ&#x2C6;&#x2014; values, was developed by Regemorter et al.[3] and is valid for any quantum number, provided that the matrix element (1) varies slowly with nâ&#x2C6;&#x2014; and n0â&#x2C6;&#x2014; with a fixed â&#x2C6;&#x2020;nâ&#x2C6;&#x2014; . This approach allows us to set n0â&#x2C6;&#x2014; = n0 where n0 is an integer and interpolate for a fixed â&#x2C6;&#x2020;nâ&#x2C6;&#x2014; . This approach takes one of the solutions, Pnl of (4) to be of the form (8) and the other, Pn0 l0 , to be of the hydrogenic form as solved by Gordon [10] Pn0 l0

1/2

l+1 1 Î&#x201C;(n0 + l0 + 1) 2Îśr 1 1 â&#x2C6;&#x2019;Îśr/n0 â&#x2C6;&#x161; 0 0 =(â&#x2C6;&#x2019;1) e Î&#x201C;(n0 â&#x2C6;&#x2019; l0 ) n0 Îś n (2l + 1)!

2Îśr Ă&#x2014; 1 F1 (â&#x2C6;&#x2019;n0 + l0 , 2l0 + 2, 0 ) n n0 +l0 +1

(21)

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where 1 F1 is the confluent hypergeometric function. These two forms for the reduced radial wavefunction transform (1) to [3, 4] l0 +1 n∗ 1 2 2 ∗ 0 0 n0 +l0 +1 1 Rs (n l, n l ) = (−1) ζ s n∗ n0 (2l0 + 1)! n0 n∗ 0 ∗ n∗ +l0 +s+2 nn Γ(n∗ + l0 + s + 2) × 0 n + n∗

1/2 Γ(n0 + l0 + 1) (22) × Γ(n∗ − l)Γ(n∗ + l + 1)Γ(n0 − l0 ) t0 X × gt (n∗ , l; n0 , l0 ) t=0

× 2 F1 (−n0 + l0 + 1, , n∗ + l0 + s + 2 − t; 2l0 + 2;

2n∗ ) n0 + n∗

where g0 = 1, gt =

n0 + n∗ 2n0

l(l + 1) − (n∗ − t)(n∗ − t + 1) gt−1 , (n∗ + l0 + s + 2 − t)t

(23)

and 2 F1 is the Gaussian hypergeometric function.

The hypergeometric function 2 F1 (α, β; γ; x) can be easily computed by application of recurrence relations, using 2 F1 (0, β; γ; x) = 1 and 2 F1 (−1, β; γ; x)

= 1 − (β/γ)x.

(24)

To evaluate the integral Rs (n∗ , l; n0∗ , l0 ), we calculate the values for Rs (n∗ , l; n0 , l0 ) and Rs (n∗ , l; n0 + 1, l0 ) where n0 < n0∗ < n0 + 1 and interpolate between the two values. As we verified by extensive comparisons with our direct methods, the accuracy of this approach is comparable to the BD approximation in the range where the latter is accurate.

Present Results Our objective was to create a comprehensive mapping in the (n∗ l, n0∗ l0 ) space of the cancellations of the monopole, dipole, and quadrupole transition radial matrix elements (1) using the Coulomb Approximation. This was attained by (i) calculating (1) for the full range of (n∗ , l, n0∗ , l0 , s) combinations, (ii) obtaining the lines of intersection of these data with the Rs (n∗ , l; n0∗ , l0 ) = 0 plane, and (iii) superimposing these graphs of zeroes with the graphs of (n∗ l, n0∗ l0 ) combinations of effective quantum numbers for all available energy levels of the isoelectronic sequences of the alkali metals Li, Na, K, Rb, and Cs, and that of the Cu isoelectronic sequence.

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Figure 1. Radial matrix element for the s − p dipole transitions

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Figure 2. Radial matrix element for the s − d quadrupole transitions

Figure 3. Radial matrix element for the p − p monopole transitions

We particularly calculated matrix elements for the dipole ns − n0 p, np − n0 d, nd − n0 f , for the quadrupole ns − n0 d, np − n0 f , nd − n0 g, np − n0 p and nd − n0 d, and for the monopole ns − n0 s, np − n0 p, nd − n0 d, and nf − n0 f transitions. We treated the effective quantum numbers as continuous variables. The ranges of n∗ were limited by n∗ > l + 1, because the approximation is valid only for electrons moving at large distances from the origin. We started with the method of Bates and Damgaard [2] for low effective quantum numbers but it breaks down at around n ≈ 15.

We then used the method of Regemorter et al. [3]. The programming for both is simple and they yield results in the low n∗ limit that differ by at most 3%. To visually exhibit the behavior of the matrix elements, we made 3-D plots for the multipole transitions and a representative plot from each class of transitions is presented in Figs. 1 and 2. The matrix element exhibits oscillatory behavior in the n∗ − n0∗ plane. We plotted R1/3 instead to accentuate the behavior of the small values.

There is a large maximum along the line n0∗ = n∗ , which dominates the graph. This explains the lack of points in the region near n0∗ = n∗ in Fig. 4.

Minima in the radial matrix elements, also known as Cooper minima [1], correspond to tran-

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14

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12

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n*(p)

n*(p)

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8

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6

6

4

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2 2

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Reduced Plot for Zeroes

Zeroes for Dipole S-P Transition

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2

n*(s)

4

6

8

10

12

14

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Figure 4. Location of zeroes in the s − p dipole transitions

Figure 5. Generalized location of zeroes in the s − p dipole transitions

sition that are unlikely to occur. Curtis and Ellis [11, 12] studied these Cooper minima, also called cancellation effects, in the potassium (KI) isoelectronic sequence. Their work implies a relation among n∗ and n0∗ in these cancellation effects. If experimental values fall on these curves, a cancellation occurs. Theodosiou [13] discovered such minima in ab initio calculations of atomic oscillator strengths and lifetimes in the KI and CsI and an explanation was proposed on the basis of the spatial features of the involved wavefunctions as functions of their energy, i.e. effective quantum numbers. Raftopoulos [14] used the Bates and Damgaard approximation to locate cancellation locations, as a precursor to the present research. Density plots of bound-bound, bound-free and free-free transitions are given by Beterov et al. [15] using analytical expressions for the matrix elements. Their results give Cooper minima as a function of energy of the states.

In the present work, we find the Cooper minima as a function of the effective quantum numbers n and n0∗ . We find that the minima lie along lines parallel to the line n0∗ = n∗ and differ by integral numbers. An example of the behavior of the minima in the n0∗ − n∗ plane is given in Fig. 4. ∗

However, it is interesting to note that the zeroes lie on lines parallel to this central maximum.

To find the exact behavior of the zeroes, we shifted the lines down onto one line and found a general fit. For lines that lie above n0∗ = n∗ one, n0∗ is shifted down modulo(1) and for lines that lie below it n∗ is shifted down modulo(1). The typical result for s − p transitions is shown in Fig. 5.

We found fits for the general equation c (25) n∗ where the c term accounts for the non-linearity of the fits at small n∗ .The general fits for multiple n0∗ (mod 1) = an∗ + b +

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Transition d0d d0d s1p p1s p1d d1p d1f f1d s2d d2s p2f f2p p2p p2p d2d d2d

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Numerical values for n0∗ (mod 1) = an∗ + b + c/n∗ a b c upper or lower fit 0.997303 1.08607 -0.602469 up 1.000060 0.99880 0.011308 low 0.998825 1.32991 -0.399411 up 0.998456 1.35343 0.195236 low 0.999676 1.30311 -0.553408 up 0.997701 1.37212 0.600467 low 1.997015 1.39265 -1.565930 up 0.996983 1.39298 0.975337 low 0.996398 1.68650 -1.243720 up 0.995691 1.72910 0.447167 low 0.998147 1.62969 -1.385060 up 0.994841 1.74554 1.259060 low 0.996025 1.69265 -0.280196 up 0.998543 1.64069 -0.034283 low 0.994431 1.73556 -0.439753 up 0.998424 1.63828 0.123140 low

transitions are given in Table 1.

All values for a are around 1 which is expected given the the fact that they are parallel to the line n0∗ = n∗ . Recall also the predicted behavior of Eq. 19 from [9]. To find if a cancellation occurs in a specific transition, we must see if its value differs by an integer multiple from one of these lines. This shows that the cancellation effects in the transitions is systematic.

Application to Alkali-Metal Isolectronic Sequences We applied this analysis to the Li, Na, K, Rb and Cs isoelectronic sequences. An example of the results is shown in Fig. 6 We found that the experimentally observed cancellations [16, 17, 18] in table 2 also follow these trends.

We gathered data on effective quantum numbers from the National Institute of Standards and Technology [19] and used the values in Table 1 to calculate the relationship. The results followed the fits, with negligible error. Some fits differ from the single lines found here due to the fact that we collapsed all the lines on to one line to find a single fit. If the calculated value of a transitions differs from the predicted values by an integer number, a cancellation occurred.

Conclusion The analysis presented here is to show that the occurrence of cancellation in the radial matrix element (1) is not a random occurrence, but an expected phenomena. Using the the fits obtained from calculations based on the Coulomb Approximation and the available experimental data for the quantum defects, we found that cancellation effects do in fact follow a simple linear relation-

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Figure 6. Overlap of minima locations with n∗p − n∗d combinations for the Na isoelectronic sequence

Spectrum I

II

III

IV

Table 2. Dipole transitions where minima occur Na K Rb Na K Rb 5p-3d 4p-4d 6p-3d 5p-6d 7p-3d 5p-7d 3s-4p 3s-5p 3s-6p 4s-5p 4s-6p 5s-6p 5s-7p

4s-5p 4s-6p 4s-7p 4s-8p 5s-6p 5s-7p 6s-7p 7s-8p 6s-8p 7s-8p

6s-9p 7s-9p

5s-6p 5s-7p 5s-8p 5s-9p 6s-7p 7s-8p 7s-9p 5s-6p

V VI

5s-6p 5s-7p 6s-7p

6p-4d 7p-4d 7p-5d 8p-4d 8p-5d

K

4d-6f

3p-4d

4d-6f 5d-8f

4p-7d

4p-5d 5p-6d 5p-7d 6p-7d

5p-6d 4p-6d 4p-7d 4p-5d

4d-5f 7d-8f

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ship. We hope the numerical analysis provided here will be a useful tool for experimentalists and theorists working in the field, in predicting atomic transitions.

Acknowledgement The author thanks the Jasper Scholars Program for financial support during this research.

References

U. Fano, J. Cooper 1968 Rev. Mod. Phys. 40 441 D. Bates, A Damgaard 1949 Phil. Trans. Roy. Soc. London A42 101 H. Regemorter, D. Hoang, M. Prud’homme 1979 J. Phys. B 12 7 H. Regemorter, D. Hoang, M. Prud’homme 1979 Astr. J. 230 L127 H. Bethe, E. Salpeter 1977 Quantum Mechanics of One- and Two-electron Atoms (New York: Plenum) [6] T. Gallagher 1994 Rydberg Atoms (New York:Cambridge University Press) [7] I. Gradshteyn and I. Ryzhik 1980 Table of Integrals, Series and Products (New York:Academic Press) [8] A. Burgess, M. Seaton 1958 Rev. Mod. Phys. 30 992 [9] A. Burgess, M. Seaton 1960 Mon. Not. Roy. Astron. Soc. 120 121 [10] W. Gordon 1929 Ann. Phys. Lpz. 2 1031 [11] L. J. Curtis, D. G. Ellis 1978 J. Phys. B 11 L453 [12] L. J. Curtis and D. G. Ellis 1980 J. Phys. B 13 L431 [13] C. E. Theodosiou 1980 J. Phys. B 13 L1 [14] V. Raftopoulos, 1986 “A systematic study of cancellation effects in atomic transition probabilities: Application to the Na, K, and Rb isoelectronic sequences,” MS Thesis, University of Toledo, OH [15] I Beterov 2012 et al arXiv:1207.3626 [16] E. Beamont 1976 Physica 81C 158 [17] R. Crossley 1969 Adv. in Atom. Mol. Phys 5 237 [18] C. Fisher 1975 Beam Foil Spectroscopy Vol. 1 (New York: Plenum Press) [19] A. Kramida, Y. Ralchenko, J. Reader, and NIST ASD Team (2013). NIST Atomic Spectra Database (ver. 5.1), [Online].

Available: http://physics.nist.gov/asd [2014, August 18].

[1] [2] [3] [4] [5]

Study of rare muon decay: µ+ → e+ e− e+ νe ν¯µ with polarized muons Dylan Gray∗ and Thomas Reid∗ Department of Physics, Manhattan College

Abstract. We studied the rare muon decay process µ+ → e+ e− e+ νe ν¯µ . This Standard Model process is the background with respect to the signal process µ+ → e+ e− e+ which is predicted by many extensions of the SM. We show that the process µ+ → e+ e− e+ νe ν¯µ could be suppressed by cuts on the total energy of charged leptons in the kinematic region where the signal of new physics such as µ+ → e+ e− e+ is expected to appear. Also, we demonstrated that angular distributions of decay products in the process µ+ → e+ e− e+ νe ν¯µ are sensitive to the muon polarization and could be used to distinguish the signal of new physics µ+ → e+ e− e+ from the background process µ+ → e+ e− e+ νe ν¯µ .

Introduction In the Standard Model of particle physics, Lepton flavor is conserved in all processes [1].

The net flavor of all resulting leptons must be the same as that of the leptons involved in the initiation of the process. However, Lepton Flavor Conservation (LFC) is not known to be a law of physics, and there exists room in the SM for LFC processes that violate this property. While insubstantial evidence now exists to disprove LFC, there are a few promising candidate-processes, whose discovery would demonstrate that the SM needs to be revised [2]. One such process is the decay of a muon into two positrons and an electron, µ+ → e+ e− e+ . µ+ → e+ e− e+ Theory and Experiment While µ+ → e+ e− e+ is not known to occur, the process µ+ → e+ e− e+ νe ν¯µ , is. This process, in line with the SM, does accord with the presumptions of LFC. However, due to its similarity to the theoretical process, the process µ+ → e+ e− e+ νe ν¯µ can mimic the signal of new physics.

As a result, in the pursuit of lepton flavor violating processes, we can rely upon natural signposts such as µ+ → e+ e− e+ νe ν¯µ to hint at the right path. By combing the energy range in which µ+ → e+ e− e+ is expected to occur, we may be able to distinguish it from the background process µ+ → e+ e− e+ νe ν¯µ [2]. Unfortunately, this is not a straightforward task. µ+ → e+ e− e+ νe ν¯µ is an extremely rare process – its branching ratio (the ratio of the number of times it occurs in a sample to all the processes in the same sample) is about 3.4 × 10−5 , but the branching ratio of µ+ → e+ e− e+ is lower by many orders of magnitude [2]. This would make detecting µ+ → e+ e− e+ very difficult even under ideal circumstances, and so we require means to circumvent its elusiveness [1]. ∗

Research mentored by Rostislav Konoplich, Ph.D.

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Table 1. Experimental limits on lepton flavor violating muon decays [3] Decay Channel µ → eγ µ → eγ µ → eee µA → eA

Experiment MEGA MEG SINDRUM SINDRUM II

Branching Ratio Limit < 1.2 × 10−11 2.4 × 10−12 < 1.0 × 10−12 < 7 × 10−13

In a study performed by Blondel et al. [3], the branching ratio so far achieved experimentally in searches for µ+ → e+ e− e+ is < 1.0 × 10−12 . Their study indicates the necessary sensitivity for experiments looking for µ+ → e+ e− e+ must reach a branching ratio of < 10−16 [3].This means that current experimental methods are more than four orders of magnitude too imprecise to acquire results that would show signs of the theoretical process. In our study, we developed a method that would improve techniques to search for µ+ → e+ e− e+ . It is known that µ+ → e+ e− e+ νe ν¯µ would mimic the theoretical process if the energy of the two neutrinos were close enough to zero to be negligible. Consequently, it is assumed that we would detect the theoretical process if we could limit the search for it to regions of energy in which this is the case, suppressing the occurrences of µ+ → e+ e− e+ νe ν¯µ , and exaggerating those of µ+ → e+ e− e+ . Previous research on the subject has considered the results only of muon decays in which the muon was neutrally polarized. We aim to verify the results and generalize them to positively and negatively polarized muons under the assumption that polarization would exert an influence on the expanse of signal-regions [4].

In order to study the polarized decays in nature, an analytical formula describing them must be employed. Unfortunately, none currently exist for polarized muons. However, there exist two methods for producing them – they can be derived “traditionally” (by hand) [2] or they can be estimated from a numerical analysis. Our research concerned the latter method.

Methods We used MadGraph 5, a particle decay and collision simulator, to model the behavior of µ+ → e+ e− e+ νe ν¯µ . In total, we performed three separate simulations, one for neutrally polarized muon decay, one for positively polarized muon decay, and one for negatively polarized muon decay. We modified MadGraph to perform cuts on the data set for certain energy ranges, allowing us discern the how the background process had been affected with greater precision. In order to process this data, we employed ROOT, the European Organization for Nuclear Research’s (CERN) data analysis framework.

All of the histograms to follow were made with ROOT, the structure of each one based on computational models composed in C. For each polarization, the number of decays sampled and graphed was one-million. We will briefly review the nature of the mechanics of the background process before proceeding. A µ+ → e+ e− e+ νe ν¯µ decay can occur in four different ways. Here we have Feynman diagrams depicting two of them. In Fig. 1a, the muon decays into two neutrinos and a virtual positron, which emits a photon. The photon is then converted to a e+ e− pair. In

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Figure 1. Feynman diagrams for the background process (left, 1a; right, 1b)

Figure 2. Normalized entries vs. the total energy of charged leptons (left, 2a); the same, but cut at 50 MeV with a base-10 log scale applied to the y-axis (right, 2b)

Figure 3. The normalized entries versus the cosine of the emission angle of the leading positron, for all 3 polarizations (left, 3a); a 2-D histogram of the energy of the leading positron versus the energy of the subleading positron (right, 3b).

Figure 4. The normalized entries versus the energy of the electron (left, 4a); the normalized entries versus the energy of a positron (right, 4b)

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Fig. 1b, the muon emits the photon and decays into a positron and two neutrinos. The other two permutations of this process differ slightly. In both cases, we would see the same orders of events, except the positions of the positrons in the aftermath would be inverted.

In Fig. 2, the number of events peaks at a total charged lepton energy of about 50 MeV, before steeply decreasing. In other words, we see suppression of the background process beyond 50 MeV. The results for polarized processes are not shown because polarization had a negligible effect on energy distributions. The cut evident in Fig. 2b simply highlights the behavior of the region in which µ+ → e+ e− e+ νe ν¯µ is being suppressed.

The muon polarization significantly affects angular distributions of decay products. In Fig. 3a, the negative curve corresponds to the positively polarized process, the positive curve corresponds to the negatively polarized process, and the flat curve corresponds to the non-polarized process. This indicates that muon polarization leads to significant asymmetry of angular distributions. Fig. 3a is important because it confirms that the behavior of µ+ → e+ e− e+ νe ν¯µ matches the predictions of the Standard Model. If we detect deviations from this behavior, it would be an indication of physics beyond the Standard Model including, perhaps, µ+ → e+ e− e+ .

In Fig. 3b, it is made clear that the greatest number of events occurs when the energy of the leading positron is between 10 and 50 MeV, and the energy of the subleading positron is no greater than approximately 13 MeV. Fig. 3b suggests that we can significantly reduce the incidence of the background process by ensuring that the energies of the leading and subleading positrons are outside this region.

Fig. 4. displays the normalized entries versus the energy of the electron (left, 4a) and the normalized entries versus the energy of a positron (right, 4b). In Figure 4a, the distribution shows that the background process most often occurred when the electron had an energy of about 5 MeV, and decreased as the electron energy increased. Figure 4a indicates that we can reduce the incidence of the background process by raising the electron energy above 5 MeV. In Figure 4b, most events occur when the positron energy is about 5 MeV, and they decrease in number as the positron energy increases, much as they do with respect to the electron energy.

The key difference is the visible hump, which results from a more gradual die-off in occurrence – there are more events when the positron’s energy is greater than the electron’s. This suggests we would have to raise the positrons’ energy more greatly than we would than the electron’s to see a significant reduction in the background process.

In Table 2, the branching ratios grow rapidly smaller as the cuts become severe. This means that, in the regions delineated by the cuts, the incidence of the background process is reduced. By searching in these regions, we may see greater incidence of the signal process.

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Table 2. Branching ratios of the background process for a series of cuts on (mµ − Etot ) where Etot is the total energy of all charged leptons, and mµ = 105.7 MeV and me = 0.511 MeV are masses of the muon and electron, respectively.

Cut 1 me 5 me 10 me 50 me 100 me None

# of Events 16296 1000000 1000000 1000000 1000000 1000000

Branching Ratio 2.85 × 10−19 4.94 × 10−15 3.27 × 10−13 7.62 × 10−9 2.25 × 10−6 3.84 × 10−5

Conclusion From these results we can draw two conclusions: The first is that the occurrence of the background process is highly suppressed when the data set is cut at 25 MeV, 5 MeV, 2.5 MeV, and particularly at 0.5 MeV. It is reasonable to assume that we would see higher incidence of µ+ → e+ e− e+ in the regions defined by these cuts. Note that this behavior was evident in all graphs of lepton energy presented, normalized events decreasing as the positron or electron energy increased. The second conclusion is that that angular distributions of decay products are sensitive to muon polarization. Muon polarization leads to asymmetry in angular distributions of charged leptons and could be used to distinguish theµ+ → e+ e− e+ process from the Standard Model processµ+ → e+ e− e+ νe ν¯µ that was studied in this work. Deviations observed in nature from the expected distribution of emission angles may be a sign of physics beyond the Standard Model.

For our purposes, keeping this in mind may be useful. µ+ → e+ e− e+ is a non-Standard Model process, and might be revealed by such deviations.

Acknowledgement Gray thanks the School of Science Scholars Program and Reid thanks the Jasper Scholars Program for financial support during this research.

References

[1] Y. Kuno and Y. Okada, “Muon Decay and Physics Beyond the Standard Model,“ Rev. Mod. Phys. 73, 151 (2001) [hep-ph/9909265].

[2] R. M. Djilkibaev and R. V. Konoplich, “Rare Muon Decay µ+ → e+ e− e+ νe ν¯µ ,” Phys.Rev., D 79 073004 (2009), [arXiv:0812.1355].

[3] A. Blondel et al., “Research Proposal for an Experiment to Search for the Decay µ → eee,” Research proposal submitted to the Paul Scherrer Institute Research Committee for Particle Physics at the Ring Cyclotron, 2013 [arXiv:1301.6113] [4] Y. Okada, K.-I. Okumura and Y. Shimizu, “µ → eγ and µ → 3e Processes with Polarized Muons and Supersymmetric Grand Unified Theories,” Phys. Rev. D 61, 094001 (2000) [hepph/9906446].

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