1866: Rust College Journal of Student Research

J our na l 1 8 66: Rus tCol l e g e

o fSt u d e n tRe s e a r c h Vol .I I I ,No.1 ,201 3

Sc i e nc e

Acknowledgements Our deepest appreciation goes to Dr. Paul Lampley, Vice President for Academic Affairs, for encouraging the faculty to continue interesting our students in involving themselves in research and in making the research activities of our students known to the public. Sincere gratitude is also extended to Mrs. Nilse Furtado-­‐Gilliam, the College’s new webmaster, who has gone beyond the call of duty in helping to make our transition from a print to online format seamless.

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Editorial Committee

Alisea Williams McLeod, Ph.D., General Editor LaTanya Foreman, M.S.S.W., Social Work Rhonda Kuykindoll, Ph.D., Biology Meghann Oglesby, M.S. M.C., Mass Communications Helen Oliver, Ph.D., Education V.T. Samuel, Ph.D., Social Work Nellie Smith, Ph.D., Business/Education Nilse Furtado-­‐Gilliam, M.A., Journalism, Technical Assistance

Disclaimer: All submissions to this journal were initially selected and approved by the individual divisions, represented by appropriate members of the editorial committee. All citation formats are as per the requirements of the divisions. Therefore, the divisions assume responsibility for the documentation and legitimacy of any submission. The General Editor has been responsible for proofreading final submissions.

Copyright © 2013 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or storing without written permission from Rust College. To obtain permission, please write: Alisea Williams McLeod, Ph.D., General Editor, Rust College, 150 Rust Avenue, Holly Springs, MS 38635, or amcleod@rustcollege.edu.

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Table of Contents Acknowledgements ………………………………………………………………………………………….… 2 Editorial Committee …………………………………………………………………………………………... 3 Letter from the General Editor ……………………………………………………………………………. 5 Research Papers ………………………………………………………………………………………………… 6 Stress Responses in the Unicellular Alga Chlamydomonas reinhardtii by Treetenia Williams ……………………………………………………………………….. 7 Helping Eve Overcome Adam: Targeting the Promoter G-­‐Quadruplex of ADAM-­‐15 by Taesha Simmons ………………………………………………… 17 Analysis of Round Robin Tournaments with a Focus on Odd Numbered Participants by Cherlinca Boyd ………………………………………………………... 30 Description of the Ronald McNair Program …………………………………………………..…… 44 Abstracts: Ronald E. McNair Program ……………………………………………………………….. 45

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Letter from the General Editor Early in the school year, I had an opportunity to listen to several Rust College students present their work at the Earnest A. Smith Research Symposium. I was blown away then as I am now by the brilliant thinking of our students. I shared with them then what struck me most about their presentations-­‐-­‐their obvious zest for research. I was inspired by their enthusiasm, and being a part of that moment of sharing reminded me that education is in fact a two-­‐way street, dynamic and mutually beneficial.

Because our students are producers of knowledge, rather than mere consumers of it, they have something to offer the world. The College would be remiss if it did not look for opportunities such as a student journal to broadcast our young people’s many talents and interests.

As someone who spends lots of time these days online-­‐-­‐seeking each day to increase my “flow,” I am more and more a believer that those of us who intend not to hide our lights under a bushel will need to push ourselves to develop active online lives. Too many developments are taking place literally every minute of the day for any of us, even avowed scholars-­‐-­‐to opt out of the numerous cyber spaces in which creative people are creating and sharing. Ideally then, the journal’s transition from a print to an online format will be accompanied by inter-­‐connectivity. In order for the ideas found within the journal not to sit on a virtual shelf, readers and producers of it must get the word out, and that once-­‐challenging task has been made very convenient through social networking.

Lastly, the journal has undergone a name change. Its new name-­‐-­‐1866: Rust College Journal of Student Research. The slight change has to do with more than recognizing the year of the College’s founding. Rather, 1866 is intended to signal to our readers a time of transition, an opening. After all, 1866 was the beginning of freedom for millions of African Americans. Though the year followed the end of the Civil War, it remained a time of tumult and possibility, and within the temporal space of raging ideas, forward-­‐minded individuals on the right side of history envisioned a college. Members of the Rust College family and friends of our beloved institution most surely will meditate on the fact that each day in the life of the College is an opening into which new ideas might be born. Certainly, the work represented in this first online version of our journal of student research nicely meets this goal.

I look forward to continuing to play a part in exposing the world to our students’ and our institution’s academic excellence in the form of student research.

Alisea Williams McLeod, Ph.D., General Editor

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Research Papers

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RUNNING HEAD: STRESS RESPONSES IN THE UNICELLAR ALGA CHLAMYDOMONAS

Stress Responses in the Unicellular Alga Chlamydomonas reinhardtii

Treetenia Williams

Published with permission of Ames Research Center, NASA

ABSTRACT The unicellular green alga, Chlamydomonas reinhardtii, is widely used as a model for research for various topics including cell motility, photosynthetic pathways, and responses to environmental stimuli. Responses to certain stimuli, such as extreme temperatures, include the use of intracellular pathways that produce reactive oxygen species (ROS). The space environment of high UV radiation and extreme temperatures also affects intracellular oxidation. Stress responses of algae in space are essential for understanding key biological effects, as well as providing a platform for life support, ISRU (in situ resource utilization) and synthetic biology for NASA. While ROS are commonly known for damaging cellular components, studies have shown that C. reinhardtii is capable of strongly acclimating to singlet oxygen after being pretreated with a sub-­‐lethal level of the ROS. Such data is significant because it proves that specific genes are responsible for the resistance of the damaging outcome of ROS. This project specifically looks at the stress response in C. reinhardtii under heat shock to determine changes in ROS production, gene expression and photosynthetic efficiency. The specific gene expression will be monitored by quantitative polymerase chain reaction (qPCR), in parallel with Pulse Amplitude-­‐Modulated (PAM) Fluorometry to measure the photosynthetic activity, and ROS assays.

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INTRODUCTION A representative example of the evolution of multicellularity is the lineage of volvocine green algae. This lineage starts with the unicellular alga Chlamydomonas reinhardtii, continues with same cell-­‐type colonial algae, and includes the cell-­‐ differentiated multicellular Volvox cartieri. Previous studies examined the elemental and genetic fluctuations in V. carteri due to the accumulation of reactive oxygen species (ROS) under heat stress (Nedelcu, 2004). Performing similar studies with C. reinhardtii can partially bridge the gap by identifying how the mechanisms of responding to ROS changes from unicellular to cell-­‐differentiated multicellularity within the same lineage (Proschold, 2005, Ledford, 2007). In this study, monitoring of oxidative stress due to the accumulation of ROS was observed by using pulse amplitude modulated fluorometry.

MATERIALS AND METHODS Strains and Growth Conditions.

The C. reinhardtii wild type strain cc-­‐1690 mt + (Chlamydomonas Resource Center, U. Minessota) and a cell wall deficient cc-­‐503 cw92 mt + were used. Cells were grown in P49 medium (University of Texas at Austin) in an incubator at 29⁰C, with constant shaking at 80 RPM and a light regime of 14 hours light/10 hours dark, to synchronize the cultures. In order to determine at what wavelength on the spectrometer gave a maximum peak, a spectral scan was completed at wavelengths ranging from 400-­‐800nm in increments of 25 for both C. reinhardtii strains. To complete a standard growth curve for C. reinhardtii cc-­‐1690, the corresponding optical density samples were fixed and counted using a hemocytometer counting chamber.

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Fixation and Cell Counting.

In order to fix 1ml of culture, 121µl of 37% formaldehyde was added and allowed to sit for 15 to 20 minutes. The sample was then centrifuged for 1 minute at 8000 RCT and the supernatant was discarded. The pellet was resuspended in 1ml of P49 medium and centrifuged at 8000 RCT for 1 minute. The supernatant was discarded and the remaindering pellet was resuspended in 250µL of medium. The Fuchs Rosenthal hemocytometer counting chamber was used under a bright field microscope in order to calculate the number of cells per ml at the corresponding optical density.

Pulse Amplitude-­‐Modulated (PAM) Fluorometry.

A Jr. PAM chlorophyll fluorometer (Walz) was used to measure the photosynthetic efficiency of C. reinhardtii under normal growing temperatures at 29⁰C and under heat shock at 42.5⁰C. Such an experiment is important because it provides data about how oxidative stress has an effect on the metabolism of C. reinhardtii over time. Each test spanned a three hour time period in which the photosynthetic efficiency was measured in one-­‐minute increments. In order to test which density of cells yielded the best results, three different optical densities of C. reinhardtii cc-­‐1690 wild-­‐type were tested. Before starting the actual PAM experiment, an OD of the culture was taken at 700nm and 2ml was put in a small glass bottle with a mini stir bar and wrapped in aluminum foil. This was done twice, one for the control and one for heat shock, and placed in the incubator at 29⁰ C for 30 minutes. Both the control and heat shock experiments were completed in the dark in order to minimize the amount of photosynthesis happening at the time of the test.

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RUNNING HEAD: STRESS RESPONSES IN THE UNICELLAR ALGA CHLAMYDOMONAS

RESULTS Chlamydomonas growth.

In order to determine the optimal cell density for the biochemical, physiological and genomic assays, a spectral scan for wild-­‐type and cell wall deficient strains was completed at varying wavelengths of 400nm-­‐800nm (Fig. 1).

The absorbance of cc-­‐1690 mt + cultures at 700nm was correlated to the cell density

0.5

Spectral Scan of Chlamydomonas

0.4 0.3 0.2 9 Days Old cc-­‐503

0.1 0

400 425 450 475 500 525 550 575 600 625 650 675 700 725 750 775 800

Op#cal Density

counted by a hemocytometer, giving a standard growth curve (Fig. 2).

6 Days Old cc-­‐1690

Nanometer

Figure 1. The absorbance spectral curve of wild-­‐type and cell-­‐wall deficient strains demonstrate the absorbance peaks at 575 and 700 nm.

Op#cal Density

Op#cal Density of Cultures: cc-­‐1690 1.2 1 0.8 0.6 0.4 0.2 0 0

10000000

20000000

30000000

40000000

50000000

Cell Number/mL

Figure 2. Calibration curve for C. reinhardtii strain grown in P49 medium based on absorbance at 700 nm. The curve plateaus and is no longer linear after approximately 25 million cells/ml (OD ~ 0.7).

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RUNNING HEAD: STRESS RESPONSES IN THE UNICELLAR ALGA CHLAMYDOMONAS

Photosynthetic efficiency.

The photosynthetic efficiency of cc-­‐1690 cultures was measured with the Jr. PAM (Walz) as an indicator of the response to heat-­‐shock stress. To determine at which optical density yielded the best results, three different tests were conducted with absorbance values of 0.318, 0.645, and 0.876 (Fig. 4) at 700nm. Below is the setup of the apparatus used (Fig. 3).

Figure 3. With the purpose of regulating the temperature during control and heat-­‐shock stress and keeping the cultures homogeneous throughout, a water bath was placed on top of a stirrer.

Aluminum foil was placed over the entire top of the water bath while experiments were in process to ensure that the cells were in complete darkness while testing the photosynthetic efficiency.

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RUNNING HEAD: STRESS RESPONSES IN THE UNICELLAR ALGA CHLAMYDOMONAS

Photosynthe#c Effeciency: cc-­‐1690 0.9 0.8

[Y(II)]

0.7 0.6

Control: 29⁰ C OD 0.645

0.5

Heat-­‐Shock: 42.5⁰C OD 0.645 Control: 29⁰ C OD 0.318

0.4

Heat Shock: 42.5⁰C OD 0.318

0.3

Control: 29⁰C OD 0.876

0.2

Heat-­‐Shock: 42.5⁰C OD 0.876

0.1 0 0

10

20

30

40

50

60

70

Time (Min)

Figure 4. Three different optical densities of C. reinhardtii were tested. The intensity of chlorophyll fluorescence indicates a decrease in photosynthetic efficiency within minutes of heat-­‐shock stress.

After this period the cultures lose the ability to photosynthesize.

Identifying oxidative genes involved in the stress response.

The C. reinhardtii genome (Joint Genome Institute, Walnut Creek, CA) was queried for genes involved in quenching reactive oxygen species. By studying the genes expressed during heat-­‐shock stress, it could provide details about the mechanisms the cells undergo in response to oxidative stress. Multiple peroxidase genes, one catalase, and a Mn superoxide dismutase are shown in the table below (Ledford, 2007).

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RUNNING HEAD: STRESS RESPONSES IN THE UNICELLAR ALGA CHLAMYDOMONAS

Table 1. Chlamydomonas genes involved in oxidative stress

Function

Protein

Comments

ID GPX3

glutathione peroxidase

137012

putative, mitochondrial

GPX4

glutathione peroxidase

188373

putative, chloroplastic

GPXH=GPX5

glutathione peroxidase

143122

induced by singlet oxygen

GSTS1

glutathione peroxidase

193661

induced by oxidative conditions

GSTS2

glutathione peroxidase

152438

induced by oxidative conditions

GSTS3

glutathione peroxidase

193691

putative GST

Cat1

catalase

150104

involved in detoxification of H2O2

MSD1

Mn superoxide

53941

superoxide dismutase activity

dismutase

Primer design.

The transcript sequence of each gene was used to design primers for qPCR. Forward and reverse primers in the exon region, flanking an intron, should amplify the cDNA but not the genomic DNA. The programs Primer 3 and Reverse Complement were used to pick the best primer in a specified exon region and to identify the right primer in the exon sequence respectively.

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RUNNING HEAD: STRESS RESPONSES IN THE UNICELLAR ALGA CHLAMYDOMONAS

Table 2. Genetic primers for Chlamydomonas reinhardtii

Gene

Left Primer

Right Primer

GPX3

5'-­‐CTGGCTTAAGACCCAGAAGG-­‐3'

5'-­‐GCCCTCCTTGTTGATCAGG-­‐3'

GPX4

5-­‐'CGGCTACACCGATGAGAACT-­‐3'

5'GGGAAGCCCAGAATCTCAAG-­‐3'

GPXH=GPX5

5'-­‐GCCACAATACAAGGGTCTGG-­‐3'

5'TTCACGTCCGACTTCTCCAT-­‐3'

GSTS1

5'-­‐GCCGGAGCAGAAGTCAAAGT-­‐3'

5'ACGTCCTGAACCAGGAACAC-­‐3'

GSTS2

5'-­‐GTCTTCCACGTGACCGACTT-­‐3'

5'TCTCCAGCTGCTTCAGTTTG-­‐3'

GSTS3

5-­‐'GATCTGGCCCTGTTTGTGTC-­‐3'

5'GCGGGGTAGTTCTTGAACAG-­‐3'

Cat1

5'-­‐AAGTGCGGCGAGAAGTACC-­‐3'

5'CGGGGTCCATGGTCTGTA-­‐3'

MSD1

5'-­‐GATGAAGGCCAAGTTCAACG-­‐3'

5'GTAGTAGGCGTGCTCCCACA-­‐3'

DISCUSSION This preliminary data shows that the stress response in C. reinhardtii upon heat shock can be quantified by the photosynthetic efficiency of the algae. The best results from the Jr. PAM show that C. reinhardtii with an absorbance value ~ 0.645 at 700nm can withstand the harmful effects of heat-­‐shock stress for up to 40 minutes. Because genetic changes occur within an hour, it is important that the cells can withstand heat-­‐shock stress for at least two hours. To solve this, future experiments will be conducted at 37⁰ C. When compared to V. carteri, which is able to endure heat-­‐shock at 42.5⁰ C for up to two hours, it is clear that the evolution of cell-­‐differentiated multicellularity in the volvocine lineage provides survival advantages.

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RUNNING HEAD: STRESS RESPONSES IN THE UNICELLAR ALGA CHLAMYDOMONAS

The next steps are: 1. to correlate the change in photosynthetic efficiency with the change in the production of ROS 2. to quantify the expression of oxidative genes involved in the heat shock response This project provides the tools for future studies on the role of reactive oxygen in the response to environmental stress. The experimental foundation is designed to support space biology’s question of stress responses in the space environment and addresses the fundamental astrobiology question of the evolution of complexity and multicellularity.

AKNOWLEDGEMENTS We would like to thank the CIPAIR Program for support during the summer internship, the Space Biosciences Division for providing the laboratory access for this work, and Brad Bebout in the NASA Ames Exobiology Branch for providing access and training in the use of the PAM fluorometer.

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RUNNING HEAD: STRESS RESPONSES IN THE UNICELLAR ALGA CHLAMYDOMONAS

Cited References 1. Kirk, D.L., A twelve-­‐step program for evolving multicellularity and a division of labor. Bioessays, 2005. 27 (3): p. 299-­‐310.

2. Ledford, H.K., B.L. Chin, and K.K. Niyogi,Acclimation to singlet oxygen stress in Chlamydomonas reinhardtii. Eukaryot Cell, 2007. 6 (6): p. 919-­‐30.

3. Nedelcu, A.M., O. Marcu, and R.E. Michod, Sex as a response to oxidative stress: a twofold increase in cellular reactive oxygen species activates sex genes. Proc Biol Sci, 2004. 271 (1548): p. 1591-­‐6.

4. Proschold, T., E.H. Harris, and A.W. Coleman,Portrait of a species: Chlamydomonas reinhardtii. Genetics, 2005. 170 (4): p. 1601-­‐10.

5. Shao, N., et al. A reporter system for the individual detection of hydrogen peroxide and singlet oxygen: its use for the assay of reactive oxygen species produced in vivo.

Plant, 2007. 50 (3): p. 475-­‐87.

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RUNNING HEAD: HELPING EVE OVERCOME ADAM

Helping Eve Overcome Adam: Targeting the Promoter G-­‐Quadruplex of ADAM-­‐15

Taesha Simmons

Published with permission of The Ronald McNair Program, University of Mississippi

ABSTRACT Breast cancer is a very common malignant disease found in women. Various types of breast cancers have a poor prognosis and/or initial response to treatment, followed by resistance. One of these types is the Her2/neu-­‐positive breast cancer, which represents 15 to 20 percent of breast cancers. Women diagnosed with this type cancer are some of the most advanced patients with the poorest outcome.

Although there have been many therapeutic advances, patients often progress in the cancer, and, for this reason, there is still a dire need for new treatments.

It has been noted that in patients overexpressing the Her2/neu receptor, there is frequently concurrent overexpression of another transmembrane protein – ADAM-­‐15. ADAM-­‐15 is a sheddase protein that increases metastasis and functions with Her2/neu to increase cellular growth. Within the ADAM-­‐15 promoter lies a G-­‐ rich region capable of forming a unique non-­‐B-­‐DNA structure called a G-­‐quadruplex (G4), which was hypothesized to be a silencer element. To test this theory, the current study utilized luciferase plasmids with a wild-­‐type or mutated ADAM-­‐15 promoter as well as an in vitro breast cancer system. Luciferase studies confirmed the G4 to be a silencer element. Stabilization with the pan-­‐G4-­‐binding compounds, quindoline i (Q-­‐i) demonstrated moderate cytotoxicity in MCF-­‐7 and BT474 breast

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RUNNING HEAD: HELPING EVE OVERCOME ADAM

cancer cells with a concurrent abrogation of ADAM-­‐15 mRNA expression. These studies demonstrate that stabilization of the G4 within the ADAM-­‐15 promoter will decrease its expression and that it is a viable option to develop new targeted drugs to increase the survival of Her2/neu-­‐positive breast cancer.

INTRODUCTION Breast cancer is the most common cancer found in women. In 2011, there were an estimated 232,600 new cases and 40,000 deaths according to the American Cancer Society. Breast cancer is categorized according to the expression of various proteins, including the Estrogen receptor (ER), the progesterone receptor (PR), and the human epidermal growth factor 2 (Her2/neu). Patients are then stratified into ER/PR+ (79%), Her2/neu+ (8%), or triple negative, which is none of the above (13%). These different subgroups correspond to different treatment options and patient outcomes. Her2/neu+ patients that express no other receptor are 5+-­‐fold more likely to have distant metastases, 10+-­‐fold more likely to have poorly differentiated disease, and 2+-­‐fold more likely to experience recurrences (Onitilo, AA, et. al. 2008).

Her2/neu is a transmembrane protein expressed on the surface of some breast cancer cells. This protein is an important part of the pathway for cell growth and survival. The function of Her2/neu in a normal cell is to send signals into the cell nucleus that then triggers Her2/neu Figure 1: Her2/neu (purple) spans the cell membrane. It can pair with other expression in breast cancer cells increases the transmembrane proteins, signaling (green cellular growth and may protect cancer cells jugged line) to the nucleus to trigger cell growth (http://newspaper.li/herceptin/). from the effects of some chemotherapy. cellular

growth

(Figure

1).

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RUNNING HEAD: HELPING EVE OVERCOME ADAM

Her2/neu overexpression is effectively targeted by the antibody Herceptin, which is currently being used to treat Her2/neu+ breast cancer. Herceptin halts the progression of cancer by binding to receptors of Her2/neu proteins on the surface of cancer cells (21st Century Cancer Drugs). It shrinks Her2/neu+ tumors when used as an adjuvant before surgery, treats the Her2/neu+ cancer cells that have spread beyond the original tumor, and helps prevent tumor recurrence. However, studies have shown that the effectiveness for this anti-­‐tumor antibody is limited, and breast cancer patients may eventually develop resistance to the genetic drug, leading to recurrence (21st Century Cancer Drugs). Her2/neu overexpression has also been shown to correlate with a member of the ADAM family (ADAM-­‐15) in cases of breast cancer that are more advanced and that have a poorer prognosis.

The ADAM family is a group of sheddase proteins that cut off, or shed, extracellular portions of other transmembrane proteins (Figure 2). (Abram, Clare Figure 2: Diagram of an ectodomain shedding ADAM metalloprotease.

L. et al). Currently there are 29

members in the ADAM family that function in various ways,

including the control of membrane fusion, cytokine and growth factor shedding, and cell migration, as well as processes such as muscle development, fertilization, and cell fate determination (Primakoff P, Myles DG). Pathologies such as inflammation and cancer also involve aberrant control of ADAM family members, including ADAMS-­‐10, -­‐17, and -­‐15. ADAM-­‐15 functions in breaking down the extracellular matrix which increases metastasis. It also cleaves another transmembrane protein, E-­‐cadherin, to release a soluble form called sE-­‐cadherin. That sE-­‐caderhin can then

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RUNNING HEAD: HELPING EVE OVERCOME ADAM

bind to and stimulate the Her2/neu receptor in either a nearby, or the same, cell.

When ADAM-­‐15 is co-­‐overexpressed with Her2/neu, it allows for the completion of an autocrine-­‐loop, stimulating growth of the breast cancer cells. Previous work has been done to show that if ADAM-­‐15 is decreased, then there is increased cell kill of breast cancer cells and that in particular, there is synergy with anti-­‐Her2/neu therapy.

However,

no

current methods have been identified

to

decrease

ADAM-­‐15.

For the current study, it Figure 3: G4 formation from Hoogsteen hydrogen bonded guanines (left) to build a tetrad (center), stacked into a intramolecular G4 (right).

is important to note that within the ADAM-­‐15 core promoter lies a guanine

(G)-­‐region of DNA. Such G-­‐rich regions have been shown to be able to form unique non-­‐B-­‐DNA secondary structures called G-­‐quadruplexes (G4s). G4s form when guanines pair with each other using Hoogsteen hydrogen bonding. This forms tetrads that can then stack upon each other (Figure 3). The energetics for G4 formation is supplied when two DNA complementary strands melt apart due to torsional stress.

Torsional stress is strain that is induced by transcription, affecting the activity of nearby genes or even inducing structural transitions in the DNA strands (Nelson).

This leads to single-­‐stranded DNA, which is energetically unfavorable. In G-­‐rich DNA, the guanines can pair as described above and form a G4, alleviating the stress of single stranded DNA. Thus G4s form when there is more transcription, likely regulating a feedback loop.

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RUNNING HEAD: HELPING EVE OVERCOME ADAM

G-­‐rich regions have shown to

cluster

around

the

transcriptional start site, which indicates that G4s play a vital role in regulation (Figure 4).

This phenomenon has been shown to persist throughout evolution, as noted in rodents and primates. In addition, G4s are found more commonly in Figure 4: (Top, B) Evolutionary conservation of putative G4-forming sequences (PG4) clustering at the transcriptional start site (TSS). (Bottom, D) Clustering of PG4s around the TSS in humans, observed across all chromosomes.

cancer related genes and appear to represent a new class of molecular targets for pharmaceutical development.

Since G4s are more globular than double-­‐stranded-­‐B-­‐DNA, they are capable of being specifically targeted.

Preliminary studies have shown that the ADAM-­‐15 promoter is capable of forming multiple equilibrating G4s, and have identified two major structures. Both G4s have parallel, and small, loops, and are formed from the end 4-­‐runs of guanines (Figure 5). Although two major G4 structures have been identified, what has not been known is the biological role of these G4s in ADAM-­‐15 regulation. To address this question, I examined the biological role of G4s in ADAM-­‐15 regulation Figure 5: Two major G4s (bottom) found within the ADAM-15 core promoter (top).

by

conducting a luciferase expression assay. I also

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RUNNING HEAD: HELPING EVE OVERCOME ADAM

ran a cell viability assay and a quantitative real time polymerase chain reaction (qRT-­‐ PCR) to see if the G4 in the ADAM-­‐15 promoter can be stabilized in an intact breast cancer cells using the MCF-­‐7 and BT474 cell lines.

METHODOLOGY Chemicals, compounds, and cells.

Quindoline i was kindly provided by the laboratory of Dr. Laurence Hurley at the University of Arizona. BT474 and MCF-­‐7 breast cancer cells were purchased from ATCC and provided at low passage from colleagues at the University of Mississippi Medical Center Cancer Institute in Jackson, Mississippi. Cells were maintained in exponential growth in DMEM media supplemented with 10% FBS and 1x Pen/Strep solution at 37 °C, 5% CO2 throughout the duration of these studies. Except where noted, all chemicals were purchased from Sigma-­‐Aldrich of St. Louis, Missouri.

Transformation of e. coli.

Two ADAM-­‐15 plasmids, containing a wild-­‐type (WT) or mutant (MT) promoter, were suspended in 300 ml of TE buffer and vortexed; 2ml of suspended plasmids was then added to thawed DH5a e. coli and incubated for 30 minutes on ice.

The mixture was heated in a 40°C water bath for 45 seconds and then placed on ice for 2 minutes. 900mL of SOC media was then added, and mixture was incubated at 175rpm, 37°C for 1 hour. After incubation, 150mL was spread on 100mm3 plates containing LB Agar and 1x Ampicillin. Plates were left overnight in incubator at 37°C.

Extraction of Plasmids.

Single clones were then chosen from the plates and expanded over night in Luria Broth (LB) Agar and 1x Ampicillin at 37°C. The next day, plasmids were extracted using the Qiagen Maxi Kit (Qiagen, Valencia, CA) as follows: the e.coli clones were pelleted by centrifugation at 5,000rpm for 15 minutes. Pellets were then resuspended in 10ml of Buffer P1. 10ml of Buffer P2 was added and the tube was

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inverted and incubated at room temperature for 5 minutes. 10ml of the chilled Buffer P3 was added to the lysate and poured into the barrel of the QIAFilter cartridge and then incubated at room temperature for 10 minutes. After 10 minutes, the cap was removed from the QIAFilter cartridge and the plunger was inserted to filter the cell lysate into a 50ml tube. Once filtered, 2.5ml of Buffer ER was added to the lysate, inverted 10 times, and incubated on ice for 30 minutes. After 30 minutes, 10ml of Buffer QBT was applied to Qiagen tip 500 and allowed it to empty by gravity flow for equilibration. After equilibration, the filtered lysate was applied to the QIAGEN-­‐tip and entered the resin by gravity flow. After filtered lysate entered the resin, the tip was washed with 2x 30ml of Buffer QC. DNA was then eluted with 15ml of Buffer QF. 10.5ml of room temperature iso-­‐propanol was added to eluted DNA, mixed, and then centrifuged at 5,000 x g for 60 minutes at 4°C. After centrifuged, supernatant was removed and DNA pellet was washed with 5ml of room temperature 70% ethanol and centrifuged for 10 minutes at 5,000 x g for 60 minutes at 4°C. After centrifuge, supernatant was decanted and tube air dried for 5-­‐10 minutes. After air drying DNA pellet, it was redissolved in 150mL of TE buffer.

Transfection and Luciferase Expression Studies.

HEK-­‐293 cells were plated in 6-­‐well at 7x106 c/well in 1mL of media and were incubated at 37°C overnight. The next day, media was changed to OPTI-­‐MEM low serum media and cells were transfected with 3 mg/well of target plasmids (empty vector, wild-­‐type or mutant ADAM-­‐15 promoters inserted into a pGL3.basic vector), plus 500 ng of renilla plasmid/well, with Fugene HD (Promega, Madison, WI) in a 3:1 DNA:lipid ratio. Cells were incubated overnight, and then OPTI-­‐MEM was removed and 1mL of DMEM media or DMEM media containing 5 mM of Q-­‐i was added. Plates were gently swirled and placed back into incubator. After 24 or 48 hours, media was removed from HEK-­‐293 plates, washed 2x with PBS (~1mL/well), paraffined, and placed in -­‐80°C. For measurement of luciferase expression, plates were thawed and cells were lysed with 1x passive lysis buffer from Promega. The

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dual-­‐luciferase reporter assay system from Promega was used with a Lumat LB-­‐905 (Berthold Technologies, Bad Wildbad, Germany) luciferase machine to determine firefly and renilla luciferase activity. For all samples, firefly luciferase activity was normalized to the corresponding renilla activity, and then normalized again to the controls as described in the results section.

Cell Viability. Cells were plated in 96-­‐well plates (15,000 cells/well) and incubated at 37°C overnight. Q-­‐i was added (0.015-­‐100 mM in ½ log steps) and plates were incubated at 37°C. After 24 hours, 20mL of 3-­‐(4, 5-­‐dimethylthiazol-­‐2-­‐yl)-­‐5-­‐(3-­‐ carboxymethoxyphenyl)-­‐2-­‐(4-­‐sulfophenyl)-­‐2H-­‐tetrazolium

(MTS)

and

5%

of

phenazine methosulfate (PMS) was added. Plates were incubated for 2 hr and absorbance was read at 490 nm. Once absorbance was read, absorbance was normalized to no-­‐compound controls and GraphPad Prism software was used to calculate (using non-­‐linear regression modeling) and graph the IC50s in both cell lines.

mRNA Expression Assay.

BT474 and MCF-­‐7 cells were each plated in 6-­‐well plates (5x105 cells/well in 2mL of media) and were incubated overnight at 37°C. 5, 10, or 15 mM of Q-­‐i was added to the cells. After 24 hours, the cells were washed with 500mL of PBS and then 500mL of TrypLE was added to allow the cells to detach from the wells. Cells were incubated for 3-­‐5 minutes, and 1mL of PBS was added. The mixture was transferred to Eppendorf tubes, which were then centrifuged at 13,000rpm for 5 minutes. After centrifugation, the supernatant was removed, 1mL of PBS was added, and the tubes were vortexed and centrifuged again at 13,000rpm for 5 minutes. The mRNA was then extracted using the Qiagen RNeasy Mini Kit as follows: 350mL of Buffer RLT and 1% b-­‐Mercaptoethanol was added to each pellet, which was then ran through the Qiashredder. 1 equivalent of 70% ethanol was then added to each sample to precipitate DNA. RNeasy columns were then placed in a vacuum manifold, to which the 700mL of sample was added. Columns were washed with 350mL of Buffer RWI, and then the vacuum was stopped. 500mL of RPE was added to the columns and

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allowed to incubate for approximately 3 minutes. Vacuum pressure was reapplied and another 500mL of RPE was added. Samples were removed from the manifold, placed in eppendorf tubes, and the RNA was eluted with 50mL of RNase free water by centrifugation at 13,000rpm for 3 minutes. 100ng of extracted mRNA was reverse transcribed into cDNA using the Bio-­‐rad iScript cDNA Synthesis Kit (Bio-­‐rad, Hercules, CA). When cDNA was ready, 6 mL of water were added to each sample. The qRT-­‐PCR master mix was made for 35 samples by adding 350mL of Ssofast probe mix (TAQ Buffer) and 35mL each of primer pair (ADAM-­‐15-­‐FAM and GAPDH-­‐VIC) into tube.

12ml of Master mix was then aliquoted into 96 well PCR plate, to which, 8mL of cDNA was added into corresponding well, vortexed, and centrifuged in mini plate spinner for 30 seconds. After centrifugation, cDNA was then amplified by qRT-­‐PCR, using the Biorad CFX Connect. For each sample, ADAM-­‐15 expression was normalized to the corresponding GAPDH expression (DCq) and then normalized again to the cell specific DMSO vehicle control (DDCq). Expression was calculated as equal to 2^(-­‐DDCq).

RESULTS Transformation of E.coli After transformation of e. coli with the ADAM-­‐15 WT or MT plasmid, there were approximately 26 and 11 clones, respectively, selected under ampicillin pressure. From the single clones chosen, 815.4 and 937.8 ng/mL of plasmid were recovered, respectively.

Luciferase Expression Data In order to assess potential biological regulation of ADAM-­‐15 by a G4, the basal luciferase expression of the WT and MT plasmids, along with an empty vector (EV) were measured at 24 and 48 hours. Relative luciferase expression was normalized to the co-­‐transfected Renilla, and then to time-­‐matched WT expression. At both time points, luciferase expression was higher in both the MT and EV. Notably, knocking out G4 formation in the MT plasmid lead to significant increases in luciferase expression

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from 1 ± 0.1 to 1.7 ± 0.04 and 1 ± 0.05 to 3.2 ± 0.05 – fold expression at 24 and 48 hours, respectively (p<0.05)(Figure A).

Further studies were undertaken adding a pan-­‐G4-­‐stabilizing compound, termed quindoline i (Q-­‐i) to the transfection study. The anticipated outcome from these works was a decrease in luciferase expression in the WT, but not the MT or EV plasmids. However, what was noted was an increase in luciferase expression in the MT and EV 2.9 ± 0.9 and 4.7 ± 0.2 – fold expression, respectively (reaching significance only in the EV), but not in the WT system.

Q-­‐i Toxicity (MTS Assay) and mRNA expression Q-­‐i is a pan-­‐G4-­‐binding compound that blocked an Figure 7: Q-i-induced inhibition of cellular growth in MCF-7 and BT474 breast cancer cell lines. 24 hr IC50’s were determined to be 14.1 and 6 µM, respectively.

increase

in

expression

of

luciferase in the ADAM-­‐15 WT plasmid that was noted in the MT and EV. It was further

examined in the breast cancer cells, BT474 and MCF-­‐7, to measure cytotoxicity. Cells were exposed to a range of Q-­‐i concentrations for 24 hours and the IC50’s were calculated to be 6 and 14.1mM, respectively (Figure 7). To correlate the inhibition of cell growth to ADAM-­‐15 mRNA regulation, both cell lines were treated with 5, 10, or 15 mM of Q-­‐i for 24 hours; mRNA was measured by qRT-­‐PCR. At all concentrations tested, ADAM-­‐15 mRNA was markedly decreased from 1 in the DMSO vehicle controls to 0-­‐0.09-­‐fold in the MCF-­‐7 cells and 0-­‐0.17-­‐fold in the BT474 cells (Figure 8).

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Figure 8: Abrogation of ADAM-15 mRNA expression by Q-i (5-15 µM) in MCF-7 and BT474 breast cancer cells within 24 hr.

DISCUSSION

In the current study, we used luciferase plasmids to examine if the ADAM-­‐15 G4 element silences transcription. We noted that with the loss of G4 formation in the MT plasmid, the luciferase expression was greater than with the WT plasmid, which confirms the G4 as a silencer element. We further used a pan-­‐G4-­‐stabilizing compound, Q-­‐i, which we expected to further decrease luciferase expression in the WT, but not MT promoter. This was not found to be the case but it was noted that in the WT plasmid Q-­‐i was able to block the increase in luciferase expression noted with the mutant promoter and the empty vector. It is likely that the color of the Q-­‐i compound, a light yellow, is interfering with the luciferase assay and thus skewing these results. More studies are justified to confirm this hypothesis.

We further examined the cytotoxicity of Q-­‐i in two breast cancer cell lines and found a moderate IC50 at 24 hr. At the concentration which inhibited cellular growth (5-­‐15 mM), we observed a notable decrease in ADAM-­‐15 mRNA expression in both the MCF-­‐7 and the BT474 cell lines. These works confirm that the ADAM-­‐15 G4 is a viable new molecular target for further development for novel therapeutics.

Using an antibody that stabilized all G4s throughout the genome, researchers noted both an up-­‐ and a down-­‐regulation of transcription, highlighting the potential

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various regulatory functions that G4s can have (Fernando, H, et.al. 2009). Therefore, when looking at various G4s in cancer for potential targeting, it is important to understand its biological function, to determine if a G4 is a silencer or an activating element. If a G4 is a silencer in an oncogene (a gene that is capable of promoting cancerous growth), then a compound should be developed to stabilize the G4 promoter in order to turn off the gene. If the G4 is an activating element for a tumor suppressor gene, then again the G4 should be stabilized for anti-­‐cancer therapeutics.

However, if the oncogene G4 is an activator, or the tumor suppressor gene G4 is a silencer, then the overall goal with a compound would be disruption. This highlights how important it is to understand the biological role of G4 formation for each potential cancer target.

Our works demonstrated that the ADAM-­‐15 promoter G4 is a silencer element; therefore the future work will be to find a new therapeutic drug to specifically stabilize it. In order to develop such a drug, a specific compound would be developed in the lab through rigorous testing, including tests in breast cancer cell lines similar to what was done in this study. After in vitro testing, the compound will then be developed using animal models, which is required for FDA approval, and finally in Her2/neu+ breast cancer patients in combination with Herceptin.

Studies have shown ADAM-­‐15 and Her2/neu are concurrently overexpressed in breast cancer patients with a more dire prognosis and more advanced disease.

Furthermore, laboratory studies have demonstrated that decreasing ADAM-­‐15 can synergize with anti-­‐Her2/neu therapies, but to date there are no methods to do so.

Our current works show that the unique G-­‐rich region of the ADAM-­‐15 promoter, which is capable of forming a non-­‐B-­‐DNA structure called a G-­‐quadruplex, represents a potential target for achieving downregulation. Successful drug development focusing on this target has high probability to lead to significant advances for breast cancer treatments, especially in the more advanced Her2/neu+ cases.

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Cited References 1. Abram, Clare L. et al. The Adaptor Protein Fish Associates with Members of the ADAMs Family and Localizes to Podosomes of Src-­‐treansformed Cells. Journal of Biological Chemistry. 2003 May; [cited 2012 July 6]. Available from URL: http://www.jbc.org/content/278/19/16844.full 2. Fernando, H; Sewitz, S; Darot, J; Tavare S; Huppert JL; Balasubramanian S. Genome-­‐wide analysis of a G-­‐quadruplex-­‐specific single-­‐chain antibody that regulates gene expression. NAR. 2009 Nov; 37(20):6716-­‐22. Available from URL: http://nar.oxfordjournals.org/content/37/20/6716.long 3. Nelson Phillip. Transport of Torsional stress in DNA. PNAS. 1999 Dec; [cited 2012 July 6]. Available from URL: http://www.pnas.org/content/96/25/14342.abstract 4. Onitilo, AA; Engel, JM; Greenlee, RT; Mukesh, BN. Breast Cancer Subtypes Based on ER/PR and Her2 Expression: Comparison of Clinicopathologic Features and Survival. Clinical Medicine & Research V7, No1/2: 4-­‐13, 2008. Available from URL: http://www.clinmedres.org/content/7/1-­‐2/4.long.

5. Primakoff, P. Myles, DG. The ADAM gene family: surface proteins with adhesion and protease activity. Trends Genet. 2000 Feb; 16(2):83-­‐7 [cited 2012 July 6]. URL: http://www.nlm.nih.gov/pubmed/10652535

http://newspaper.li/herceptin/ st 21 Century Cancer Drugs; http://www.targetedcancerdrugs.com/herceptin.htm

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Analysis of Round Robin Tournaments with a Focus on Odd Numbered Participants

Cherlinca N. Boyd Published with permission of Rust College

Abstract This research considers the usefulness of mathematics in sports, an area of life that influences every individual in some way. Specifically, this research analyzes the theory of mathematics behind round robin tournaments with a focus on an odd number of total participants participating in the round robin tournament where only two participants face off at a time. The first portion of the mathematical method involved organizing a round robin tournament for an even number of participants. When round one of the analysis was complete, the next object of analysis was round robin tournaments with an odd number of participants. After completion of both scenarios, the conclusion showed that there is little difference between the two scenarios.

INTRODUCTION

Sometimes referred to as the “Prince of Mathematics,” Johann Carl Friedrich Gauss stated, “Mathematics is the queen of the sciences.” There is a heated debate stirring through the mathematical community as to whether it was the discovery of mathematics or invention of mathematics for which Gauss is to be credited. On the one hand, there is Plato, a distinguished Greek philosopher and mathematician who made major contributions to the field of mathematics; he believed in the invention of mathematics. On the other hand, there is Aristotle, another distinguished mathematician and philosopher, who believed in the discovery of mathematics.

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Regardless of which belief is judged most true, all that matters is that mathematics exists, and through its existence, mathematics has made major contributions to life as we know it. There is arguably no area of life that can avoid the use of mathematics, and this reality includes sports.

Although sports have not been around nearly as long as math, the two still

come together forming a unique relationship. Some may say that through mathematics, sports exist. For example, in order to win a basketball game, one team must score more baskets than the opposing team scores. It takes shooting a ball at the correct amount of degrees in order for the ball to go through the hoop and the basket to count. During a golf tournament, it takes accuracy to win. A player must take into consideration which size golf club would provide them with the best chances of sinking the shot within their first few swings according to the distance of the hole. Another factor that is common to a game of golf is the wind. Calculating the wind velocity is a necessity in order for a golfer to attempt the best shot possible.

There are many more cases in sports where the determining factor relates to mathematics.

Instead of just during particular actions involving sports, mathematics can

apply to general cases as well, such as creating regular season schedules. The Kirkman Tournament is a popular brainteaser in the field of combinatorics that Rev. Thomas Penyngton Kirkman created during the 1800s. It was from study of Kirkman’s tournament brainteaser that an essay written by Dalibor Froneck from the University of Minnesota Duluth, entitled “Scheduling a Tournament,” came.

Froneck’s research was actually an extension of Mr. Kirkman’s research on tournaments. The difference between this research and the previous research done

by Mr. Kirkman and Mr. Froneck is that it focused on an odd total number of participants in the tournament with only two of those participants facing off and with one game played per round. Another stipulation is that each participant faced the remaining tournament participants only once while still only playing one game per round. This type of tournament is known as a round robin tournament.

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Before a clear understanding of the data within this research is complete, a few key terms must be clarified. Below is a list of key information.

•

Often referred to as an all-­‐play-­‐all tournament, the round-­‐robin tournament is a competition in which all of its participants must face off with each of the remaining participants.

•

There will be many methods involved during the analysis of the data in this research, but the primary methods/patterns are the methods necessary to finding the simplest way of completing a round-­‐robin table.

•

Other than the primary methods/patterns, there are subsidiary methods/patterns. These patterns play vital roles in finding the speediest, yet correct, way of completing tournament tables.

•

When tables list teams according to games and rounds, it is vital that we explain how to visualize it. The first team listed is the primary team, which relies heavily on the primary and subsidiary methods.

•

When there is a reference to a bye team, this means that that particular team does not face an opponent in that particular round. In this research, a team is a bye team only once per tournament.

LITERATURE REVIEW This research closely relates to the field of combinatorics. Combinatorial mathematics, also known as combinatorial analysis or combinatorics, is a mathematical discipline that began in ancient times (Ryser, 2010, p. 1).

Conbinatorics is the study of finite or countable structures. Being new to this field requires the understanding of its basic knowledge. Books such as Combinatorics Mathematics offer elementary definitions and examples easy for lay readers to understand.

Although not as much as it does on combinatorics, this research also relies on Graph Theory. The connectedness of the graphs within the text of Mr. Froneck’s essay on round-­‐robin tournaments proves this. Graph Theory focuses on the

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connectedness of things or objects. In the text “Networks, Crowds, and Markets: Reasoning about a highly Connected World,” this text thoroughly details what it means for something to be connected. According to” Networks, Crowds, and Markets (2010),” when people talk about the “connectedness” of a complex system, in general they are really talking about two related issues (p. 4). One is connectedness at the level of structure –who is linked to whom-­‐ and the other is at the level of behavior –the fact that each individual’s action has implicit consequences for the outcomes of everyone in the system (Easley and Kleinberg, 2010, p. 4). The graphs that depict tournament participants as vertices and games played between two teams as edges are examples of this connectedness.

The use of these two textbooks allows for easy comprehension of the data in this research.

LIMITATIONS Rev. Kirkman laid out a detailed format of his version of a round robin tournament. He even created a famous combinatorial mathematics problem, called the Kirkman Schoolgirls Problem, (Ryser, 2010, p.1) related to the process of scheduling round robin tournaments. Like Kirkman, Froneck went into detail about round robin tournaments in his essay. However, what makes Froneck’s research a little more significant was his use of Graph Theory. Using Graph Theory, the credibility of his research may evoke less doubt. Due to limited resources, the author was unable to apply graph theoretical methods as Froneck did during his research. This research was also limited due to time. The time constraint prevents a deeper analysis into the mathematics behind round robin tournaments.

Nonetheless, the presentation of this research is accurate and unbiased.

METHODOLOGY The research focuses on the mathematical concepts behind a round-­‐robin tournament with an odd number of participants. The only stipulation to the

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tournament is that it mandates every team to play every other remaining team and each team is only allowed to play one game per round. While this may seem simple, it is actually a little more complex than that. Before getting into the analysis of an odd team round-­‐robin tournament, there must be an understanding of even round-­‐robin tournaments.

Below is an example of a chart detailing a round-­‐robin tournament between four teams.

Friday

Saturday

Sunday

Game 1

1-­‐2

1-­‐3

1-­‐4

Game 2

3-­‐4

2-­‐4

2-­‐3

Table 1

Here we will allow the numbers 1-­‐4 to signify four different teams. With a tournament so small, it is fast and easy to complete. On Friday, game one will be between teams 1 and 2, and game 2 will be between teams 3 and 4. On Saturday, game one will be between teams 1 and 3. Game two will be between teams 2 and 4.

On Sunday, game one will be between teams 1 and 4 and game two will be between teams 2 and 3. It is clear that each team plays one game a day and does not play a team twice.

The goal of this table, to create a complete round-­‐robin tournament with the minimum number of rounds and games per day, was achieved. Tables of 32 or 64 participants are more complicated. Finding the strategic patterns within the tables can decrease hassles and the amount of time it takes to create the table. These strategic patterns also allow tournament creators to spend less time performing trial-­‐and-­‐error methods. In Table 2, we have increased the number of participants in the tournament to six teams. Table 2 shows an incomplete chart of a six-­‐team round robin tournament. An error lies in Round 4 game 2. Team 5 has only two

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opponents it could possibly face seeing as it has already played teams 2, 4, and 6 in the previous rounds. The only two remaining teams that team 5 could face that are within the stipulation are teams 1 and 3.

Round 1

Round 2

Round 3

Round 4

Round 5

Game 1

1-­‐2

2-­‐3

1-­‐4

1-­‐3

Game 2

3-­‐4

4-­‐5

2-­‐5

5-­‐?

Game 3

5-­‐6

6-­‐1

3-­‐6

Table 2

However, team 5 cannot play either team 3 or team 1 because they are playing each other in game one of the same round. Because of this problem, the rest of the tournament, specifically game three of round four and the entire round five, will be null and void. In Table 3, it will demonstrate the correct set-­‐up of how a six-­‐team round-­‐robin tournament should be. The author described the completion of Table 3 as an “exhaustive trial and error method,” but what the author did not realize is that Table 3 should not have been that exhaustive because it is full of simple patterns. These simple patterns are the primary and secondary methods necessary to achieve the goal of this research, which is to obtain a speedy and efficient table completion. Why is Table 2 incomplete, yet with the rearrangement of a few teams, Table 3 was able to be completed? It may not be obvious to some, but I noticed several patterns within Table 3 that were not in Table 2.

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Round 1

Round 2

Round 3

Round 4

Round 5

Game 1

1-­‐6

2-­‐6

3-­‐6

4-­‐6

5-­‐6

Game 2

2-­‐5

3-­‐1

4-­‐2

5-­‐3

1-­‐4

Game 3

3-­‐4

4-­‐5

5-­‐1

1-­‐2

2-­‐3

Table 3

Table 2 contains no organization on the specific order each team will play. In Table 3, the primary pattern is in game one of all five rounds with the subsidiary team.

The pattern is team 6 acting as a gatekeeper to all of the remaining teams, denoted by the numbers highlighted in blue. In this research, a gatekeeper is viewed as a team that allows for a pivotal point in filling out the rest of the tournament.

Another primary pattern is with the primary teams of the remaining two games of each round. Denoted in red are the primary teams of games two and three. The colors show that the primary teams follow ascending order. Aside from the two patterns mentioned, there is also another pattern visible. Highlighted in purple are the opponents to the primary teams in games two and three for rounds 1 through 4. While some may miss the pattern that lies within these numbers because of the way they start, there is still one just as with the red and blue numbers. The purple numbers also follow an ascending order. The numbers start with higher numbered teams and when the table reaches team 5, the pattern follows a loop. The loop is that the secondary team flows in ascending order and when team 5 is the secondary team, the next team to take its place in the next round is team one. From team one the pattern continues to team two and so forth.

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Round 1

Round 2

Round 3

Round 4

Round 5

Game 1

1-­‐6

2-­‐6

3-­‐6

4-­‐6

5-­‐6

Game 2

2-­‐5

3-­‐1

4-­‐2

5-­‐3

1-­‐4

Game 3

3-­‐4

4-­‐5

5-­‐1

1-­‐2

2-­‐3

Table 4

Now, in finding the simple patterns in a table for a six-­‐team round-­‐robin tournament, it is evident that these patterns also exist in a larger tournament tables. The proof lies within the table 8.

RESULTS The question this research centers around is whether the underlying mathematical factors of a round-­‐robin tournament with an even number of participants also apply to an odd number of participants in the same kind of tournament. Looking at Table 2, the incomplete chart of 6 teams, and comparing it to Table 5, the incomplete chart of 5 teams, there is evidence of great similarities, mainly the lack of organization.

Round 1

Round 2

Round 3

Round 4

Round 5

Game 1

1-­‐2

1-­‐5

4-­‐5

Game 2

3-­‐4

2-­‐3

1-­‐?

Bye

5

4

3

2

1

Team Table 5

In Table 5, there is a lack of organization between both the primary teams and their opponents. Although there is a pattern amongst the bye teams, in this

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simulation that pattern alone does not allow for table completion. Due to the lack of proper patterns, this simulation will not be able to go any further that game two of round 3. To show how important primary patterns are, Table 6 gives a completed example of a 5-­‐team round robin tournament table.

Round 1

Round 2

Round 3

Round 4

Round5

Game 1

1-­‐2

1-­‐5

1-­‐4

1-­‐3

2-­‐4

Game 2

3-­‐4

2-­‐3

2-­‐5

4-­‐5

3-­‐5

Bye

5

4

3

2

1

Team Table 6

Table 6 shows the completed chart for five teams. This table is complete, but it is not the best example of how significant patterns are for odd participants as it is for even participants. Tables 7 and 8 will do just as Tables 5 and 6 did with more detail.

Round

Round

Round

Round

Round

Round

1

2

3

4

5

6

Game 1

1-­‐2

1-­‐3

1-­‐4

Game 2

3-­‐4

4-­‐5

3-­‐6

Game 3

5-­‐6

7-­‐2

7-­‐?

Bye

7

6

5

Team Table 7

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The fact that the only remaining team that is free to play team 7 in round 3 is team 2. It is impossible for team 7 to play team 2 because they matched up 2 in the previous round. As previously established, a team can only play another team once during the entire tournament.

Game

Round

Round

Round

Round

Round

Round

Round

1

2

3

4

5

6

7

1-­‐6

2-­‐7

3-­‐1

4-­‐2

5-­‐3

6-­‐4

7-­‐5

2-­‐5

3-­‐6

4-­‐7

5-­‐1

6-­‐2

7-­‐3

1-­‐4

3-­‐4

4-­‐5

5-­‐6

6-­‐7

7-­‐1

1-­‐2

2-­‐3

7

1

2

3

4

5

6

1 Game 2 Game 3 Bye Team Table 8

In Table 8, the same patterns apply for the primary and subsidiary teams as in Tables 3 and 4. By looking at the teams highlighted in red, one can see a visible pattern lies in the table that is common in every completed tournament table created throughout this research. In game one of round one, the two teams that face off are teams 1 and 6. If the patterns are correct, the next two teams to face off in game one of round two are teams 2 and 7. According to Table 8, the teams are teams 2 and 7. The patterns are correct. Through the color code, the previously mentioned patterns all exist; there are even teams that exist in Table 8 that do not exist in Tables 1-­‐7, there are several gatekeepers. Highlighted in red on Table 8 are the primary teams. If focus is placed solely on them, the pattern that becomes visible is that gatekeepers place diagonally. For example, Team 2 is the primary

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team in Game 2 of Round 1. Team 2 is also the primary team in Game 1 of Round 2.

The pattern is continuous for each team as they placed in the primary team position.

This pattern is present in round-­‐robin tournament tables with seven or greater participants.

CONCLUSION This research may be valuable to various people such as coaches, athletes, athletic directors and fans. My relationship to sports is what actually sparked my interest in analyzing the round robin tournaments. For so long the author thought the trial and error method was the only way to construct round-­‐robin tournaments.

From this research, the reader should gain some comprehension of mathematical concepts behind round-­‐robin tournaments. They should also realize the importance of patterns, whether primary or secondary. Without each pattern, there is no complex table that will be able to be composed without an “exhaustive trial and error methods. In general, the presence of an ascending order is vital. A problem arises in trying to figure out the starting point of this order. The starting point may be at team 1 or it may be at team 7 and requires a loop. From team 7 the next team in line is team 1.

There is little difference between the composition of a round-­‐robin tournament with an even number of participants and a round-­‐robin tournament with an odd number of teams.

SUGGESTIONS FOR FURTHER RESEARCH No research is 100 percent complete. That is true for this paper. As a suggestion

to further this research, one can analyze the charts to tell whether there are specific formulas that can be used to create a round-­‐robin tournament table that allow for faster table completion than the patterns already given. Several formulas that I found in both even and odd tournament tables are given.

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Let N equal the number of participants in a round-­‐robin tournament. When n is odd, denote it as N0. In an even case scenario, the number of rounds in an entire tournament equals the total number of participants minus one. The number of games per round equals the number of participants divided by two. The total number of games each team play equals the number of rounds per tournament. The total number of games in a complete tournament equals the number of participants multiplied by the number of games per round. The total number of opponents each participant faces equals the number of rounds in a tournament. In an odd case scenario, the number of rounds per tournament equals the total number of participants in a tournament. The number of games per round equals the number of participants minus one divided by two. The number of games each participant play equals the total number of participants minus one. The total number of games each participant plays equals the number of rounds multiplied by the number of games in a round. The total number of opponents each participant has equals the total number of participants minus one. It also equals the number of games each team throughout the tournament. While these formulas may seem too simple to contain any important data within them, the definitive answer will not be certain until further inquiry is conducted.

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Rounds per

Even Number

Odd Number

Participants

Participants

N-­‐1

N0

N-­‐2

(N0-­‐1)/2

tournament (r) Games per Round (g)

= N-­‐2 Games per team

N-­‐1

N0-­‐1

Total number of

N*g

r*g

N-­‐1

N0-­‐1

games in tournament Number or opponents

Table 9

1866: Rust College Journal of Student Research – Science 42

RUNNING HEAD: ANALYSIS OF ROUND ROBIN WITH A FOCUS

References

1. Easley, David, & Kleinberg, Jon (2010). Networks, Crowds, and Markets: Reasoning about a highly Connected World. Cambridge, MA: Cambridge University Press.

2. Froneck, Dalibor (Feb. 9, 2010). Scheduling a Tournament. Retrieved from http://www.mathaware.org/mam/2010/essays/FroncekTournament.pdf 3. Ryser, Herbert John. (1963). Combinatorial Mathematics. New York, NY: The Mathematical Association of America.

1866: Rust College Journal of Student Research – Science 43

Description of The Ronald E. McNair Program

The Ronald E. McNair Post-­‐Baccalaureate Achievement Program at The University of Mississippi is a program for first generation, low-­‐income students who engage in scholastic undertaking which will increase their chances for success in graduate school.

The University of Mississippi has three major partner institutions: Alcorn State University, Rust College and Tougaloo College. Mr. Sana Sise, Computer-­‐Science Instructor, is the coordinator for the McNair Program here at Rust College. The 2012 accepted scholars at Rust College were: Cherlinca Boyd, Demitrius Moore, Chase Carr, Taesha Simmons, Jamishela Williams and Raven Ransom.

As program participants they: § received personal and academic counseling and assessment; § interacted with faculty and student mentors; § underwent intensive GRE preparation; § expanded library and research skills; § attended professional meetings and visited graduate schools; § presented research findings at regional and national research conferences; receive assistance with graduate admissions, financial aid applications, and § participated in admission workshops.

The students also compete for the opportunity to do an internship that includes a $2,500 stipend. Nineteen (19) scholars are chosen for this intense, six-­‐week research internship at the University of Mississippi. Included below are the abstracts of the research conducted by the 2012 McNair Scholars from Rust College

Mr. Sana Sise Rust College Instructor of Computer Science McNair Program Campus Liaison

1866: Rust College Journal of Student Research – Science 44

Abstracts A Graph Theoretic Analysis of the National Basketball Association Cherlinca Boyd -­‐ Memphis, TN Graduating Senior, Mathematics Major The web search engine Google is a relatively new tool for extracting information from the web.

Google returns searches of keywords and must rank the pages displayed in order of relevance. In this research, I used the same page-­‐ranking algorithm as Google does to analyze the results of the 2011-­‐2012 National Basketball Association (NBA) season. I then seeded the teams by these rankings into NBA playoff trees to determine if the PageRanks of the teams could be used to predict success in the playoffs as compared to the actual playoff results. As hoped, the PageRanks did closely follow the actual playoff results and playoff seeding with just a couple of discrepancies.

1866: Rust College Journal of Student Research – Science 45

Changes in Expression of CB1 in Human Cardiac Fibroblast

Chase Carr -­‐ Leland, MS Graduating Senior, Biology Major The endocannabinoid system is recently documented to play a role in various disorders, including cardiovascular, neuropsychological, metabolic and inflammatory disease (Pacher 2006). There are currently two known cannabinoid receptors identified which are cannabinoid receptors 1(CB1) and cannabinoid receptor 2 (CB2). These receptors were first discovered as the molecular targets of the psychotropic component of the plant Cannabis sativa, to participate in the physiological modulation of central and peripheral functions (Demuth, D. 2006).

CB1 receptor is expressed mainly in the brain, but also in the lungs, liver and kidneys. CB2 is expressed mainly in the immune system.

1866: Rust College Journal of Student Research – Science 46

Does the Committee Structure of the U.S. Senate Contribute to a Divided America?

Demitrius Moore -­‐ East St. Louis, IL Graduating Senior, Mathematics Major This research addresses the issue of partisan politics in America. Specifically it asks the question of whether a social network analysis can offer a clearer picture of political partisanship. In order to have a quantifiable measure of this partisanship, perhaps the most influential and powerful group in America, namely the U.S. Senate, is studied. The committee structure of the Senate is at the heart of its operations; therefore, the committee structure by a bipartite graph that matches senators to committees serves as the model for this research. In order to transform the graph into a social network, the adjacency matrix associated with this bipartite graph is multiplied by its transpose and unitized to make an adjacency matrix of the group of senators.

This graph forms a social network as the node set consists merely of senators and not of senators and committees. The graph is analyzed in Mathematica for closeness centrality and other measures of connectivity between the senators.

1866: Rust College Journal of Student Research – Science 47

Cell Passages Influence the Activity of Plasma Kallikrein Kinin

Raven Ransom -­‐ Leland, MS Graduating Senior, Biology Major Cell aging has been associated with DNA damage, unprocessed proteins, and cell surface damage.

However, the underlying mechanisms that promote aging in response to damage remains largely not understood. It was hypothesized that the activation of KKS is elevated with increasing cell passage number in-­‐vitro. To determine whether cell passages influence the activation of plasma kallikrein kinin system, a PK activation assay and a PRCP activation assay was performed. While PK activation was elevated with cell passages, PRCP activity was reduced, concluding that cell passages do influence the activation of plasma kallikrein-­‐kinin system.

1866: Rust College Journal of Student Research – Science 48

For Richer or For Poorer: How Does Financial Illiteracy Affect Newlywed Couples?

Jamishela Williams – Starkville, MS Junior, Business Administration Major The topic of financial illiteracy has become very popular in recent years. Some studies show that financial matters are the main cause of newlywed couples' disagreements. The question considered for this research is: How does financial illiteracy affect newlywed couples? The purpose of this study is to add to an expanding body of research and to gain a better understanding of the lack of communication among newlywed couples when it comes to their financial matters.

This research will go in depth about why couples have issues with communicating, merging their finances, spending, and dealing with debt. Suggestions on how to become financially literate will also be included in the research. Most studies focus primarily on married couples. However, this study will examine the financial habits of newly married couples. The main objective of this research is to focus in on newlywed couples because they are adjusting to the financial pressures of their new union.

1866: Rust College Journal of Student Research – Science 49

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