Dr Jes 2016

DrJes

The Dawson Research Journal of Experimental Science Winter 2016, Volume 11

Features Vestibular Adaptation to Vertigo in Ballet Dancers and Figure Skaters Antibacterial Effects of Natural Flavanones from Citrus Peel Extract on Streptococcus salivarius The Effect of Mozart's Music on Spacial Intelligence A Reversed Cauchy-Schwarz-Bunyakowsky Inequality

Editors: Mazzn Ali, Alexandra Breton-Piette, Jessica Di Bartolomeo, Erica Bugden, George Vlad Calapod, Zachary Dionisopoulos, Alexa Eberle, Sarah Ferrier, Katerina Giannios, Andrew Hamilton, Sonia Israel, Anne-Marie Langlois, Divine Malenda, Eloise Passarella, Michael Ralph, Salima Ramdani, Khalil Rifai, Janna Shapiro, Elena Skothos, Artsiom Skliar, Ana Maria Sochirca, Georgia Stavrakis, Khandideh Williams, Anna Wong, Sahar Zamani Referees and Consultants: Pierre Chuard (Concordia), Kathleen Church (Concordia), Chiara Gamberi (Concordia), Nicolas Giguère (UdeM), Mohammadmehdi Haghdoost Manjili (INRS), Ian M. Ferguson (Concordia), Mindy Melgar (Concordia), Sylvain Muise (Dawson), Ghislain Paka Djiokeng (INRS), Alex Vallerand (Concordia), Denise Wernike (Concordia), Yu Zhan (Concordia)

About the Cover Our cover, White Matter Fibers, HCP Dataset Red Corpus Callosum, features a color-coded white matter fiber that has been constructed from a large collection of brain images gathered by the Human Connectome Project. The colors are coded so that red represents the orientation of the x-axis, green, the y-axis and blue, the z-axis. With the Connectome Scanner dataset, the white fibers in the brain are distinguished from neighboring regions by individually selecting the targeted parts via connectomic neuroimaging. The result depicts all the functional and structural neural connections of the white matter in vivo in the human brain.

Considered as the first-large scale attempt to provide compilations of neural data, the Laboratory of Neuro Imaging and the Martinos Center for Biomedical Imaging at Massachusetts General Hospital have collaborated to work on their data collection over a 5-year period. Both sites have used many different techniques in order to come up with various connectomic maps. Their goal is to provide tools and data for a better understanding of the living human brain.

Specifically, they use special connectomic neuroimagery devices to provide the first means of accessing the brain’s essential circuitry. The large amount of data generated is then processed by advanced software devices into connectomic maps. Finally, by means of cutting-edge scanner hardware, analytic tools, and software, the analysis of the amassed images is made efficient and rapid. Such mapping can then be used to study the behavioral variation of the white matter fiber pathways, as well as their correlation to entire groups. Hence, these complex, large-scale mappings enable the Massachusetts General Hospital team to create a unique image of the many neural connections constituting our brain.

It is not by chance that we have selected the brain as our cover page; rather, it is closely related to the rigorous scientific community here at Dawson College. Indeed, we hope that, by publishing research conducted by our peers, students may showcase individual minds and their work. Hence, there is nothing more appropriate than an image of the brain to represent the scientific learning illustrated in our journal.

Courtesy of the USC Laboratory of Neuro Imaging and Athinoula A. Martinos Center for Biomedical Imaging, Consortium of the Human Connectome Project. <www.humanconnectomeproject. org> 2

The Dawson Research Journal of Experimental Science (DrJes) is a student publication of Dawson College’s Science Program. Its aim is to publish experimental research undertaken by college students, either independently or as part of their program of study, to increase their familiarity with the scientific method. Subscriptions are available at cost plus postage and handling. Advertising matters, subscriptions, changes of address, and submission should all be forwarded to the mailing address provided below. For further information, please visit the DrJes webpage.

Submissions: For submissions, please refer to the guidelines available on the DrJes web page. Submit articles or editorials with a selfaddressed stamped envelope to the address below, along with an electronic copy of your work on a CD or as an email attachment.

DrJes c/o Jaleel Ali 3040 Sherbrooke St. W. Suite 6B.19-2 Montreal, QC Canada H3Z 1A4 Web: http:// place.dawsoncollege.qc.ca/~drjes Email: jali@place.dawsoncollege.qc.ca The Editorial Board gratefully acknowledges the financing provided

by Dawson Colleges’s Office of Academic Development that made this publication possible.

DrJes Articles

Contents

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Letter from the Editors

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En savoir plus Ă propos de la maladie dâ&#x20AC;&#x2122;Alzheimer Doran Vermette St-Pierre

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Clostridium difficile: A Healthcare Challenge Vanessa Bujwid and Faten Yazbek

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TRIZIVIR Tritherapy, Abacavir, Lamivudine, Zidovudine: HIV/AIDS Treatment Olivier Larochelle

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Antibacterial Effects of Natural Flavanones from Citrus Peel Extract on Streptococcus salivarius Nensi Alivodej, Noah Cohen, Maegan Grossman and Samantha Shapiro

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The Effect of Mozart's Music on Spacial Intelligence Samantha Rosenthal, Kelly Perlman, Jennifer Banon and Roy Hilzenrat

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Vestibular Adaptation to Vertigo in Ballet Dancers and Figure Skaters Joanie Papillon

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Growth of mung bean (Vigna radiata), a salt intolerant plant, in a salty environment when paired with a salt-tolerant plant Darel Bouhadana, Rachel Korman, Roxana Wong and Rachel Hayes

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An Investigation of Skin Flora Growth Patterns Post Ultraviolet Radiation Exposure Fatima Bahsoun, Jonah Elbaz, Jessica Hier, Noah Itovitch

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A Reversed Cauchy-Schwarz-Bunyakowsky Inequality Jason Da Silva Castanheira and Richard Fournier

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Solutions to First-Order Partial Differential Equations Dylan Cant and Alexander Hariton

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Letter from the Editors It is with relief and joy that we present this, the eleventh issue of DrJes. This volume represents a collection of the comprehensive examinations and independent study projects of our fellow Dawsonites. In order for the contributors, most of whom will be moving on to university studies, to see the fruit of their efforts, our editors have worked diligently to prepare this issue

by Winter 2016.

DrJes, for 17 years, has published research conducted by College students, giving spotlight to their work. The journal provides our fellow students with a rare and valuable opportunity, not only to have their papers published, but to receive feedback from professionals and experts from a variety of scientific fields. These professional experts who accepted the task of refereeing the articles guarantee the credibility and quality of these articles.We are incredibly grateful to the referees who hail from the Université de Montréal, Concordia University, the INRS and Dawson College for taking the time to read through and evaluate the articles prior to publication.

Our authors pride themselves in having put together a combination of unique papers that shed light on topics that strech across many scientific disciplines. Some of the questions featured in this volume include: "Do people recover from vertigo differently?", "How do citrus peels benefit our health?", "Does listening to Mozart's music improve our concentration?". These questions can be answered once you turn these pages. We hope that as you read through the articles you will recognize the quality of the work, the efforts that went into bringing this publication to light, and most of all the opportunity to deepen your understanding of diverse phenomena.

Finally, this year’s DrJes team consisted of devoted, efficient, effective and hardworking members. We cannot thank every single member of DrJes enough for taking the time from their busy school and personal schedules to complete their biweekly edits. Most importantly, a special word of thanks to our faculty advisors, Jaleel Ali and our newest recruit Brid Nic Niocaill, for providing support to the DrJes team.

Finally, without further ado, please enjoy the issue!

Salima Ramdani and Anna Wong Co-Editors-in-Chief, 2015-2016

A Note of Clarification Only the abstracts of the following papers were published in Issue 10: Stress: A Silent Killer, Megan Comeau, Jenefer Dhanaswar and Helen Vouyioukas Ultraviolet Light Exposure: The Primary Cause of Melanoma, Samira Khatiwada and Alice Qhang Friedreich’s Ataxia: Should Newton Screening Be Implemented?, Victoria Harding and Vanessa Licursi The full version of these articles will soon be made available on the DrJes website.

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En savoir plus à propos de la maladie d’Alzheimer Doran Vermette St-Pierre Introduction Le cerveau est l’organe le plus important chez les animaux, puisqu’il gère le système nerveux et tous les autres organes du corps humain. Lorsque ce centre de contrôle est atteint d’une maladie, les lésions provoquées peuvent être à l’échelle du corps entier. La maladie d’Alzheimer est une de ces maladies.

Cette maladie se caractérise par le décès de neurones1 et elle est de plus en plus courante chez les humains. Dans le texte qui suit, la découverte de la maladie par Alois Alzheimer et ses effets sur les neurotransmetteurs dans le cerveau seront abordés. Ensuite, les conséquences physiques et psychologiques sur la personne en fonction des sept stades de la maladie seront évoquées. Finalement, il sera question de la recherche pharmaceutique ayant pour but de développer un médicament pour enrayer la maladie d’Alzheimer, ainsi que de la progression de cette maladie dans la société québécoise.

La découverte de la maladie d’Alzheimer Docteur Alois Alzheimer est né le 14 juin 1864 à Marktbreit et est décédé le 19 décembre 1915 à Breslau, en Allemagne2. Suite à ses études médicales, il devient le pionnier de l’utilisation du microscope en psychiatrie. Passionné par le cerveau, il effectue plusieurs biopsies sur le cerveau des patients ayant souffert d’une maladie mentale, pour finalement devenir membre de l’équipe de l’hôpital psychiatrique le plus important d’Allemagne à Francfort-sur-le-Main2. En novembre 1901, Alois Alzheimer rencontre la patiente Auguste Deter, dont l’état pique rapidement la curiosité du psychiatre. La dame se rappelle de son nom et celui de sa fille, toutefois, elle ne se rappelle plus de son année de naissance, de l’endroit où elle se trouve et du nom de son mari. Son époux raconte qu’auparavant, sa santé physique était excellente. Cependant, elle a dû être hospitalisée, car elle avait d’importantes pertes de mémoire et d’autonomie au quotidien2. Alzheimer a l’opportunité d’analyser le cerveau d'August Deter lorsqu'elle décède d’une pneumonie en avril 1906. Alois son cerveau au microscope. Il observe une perte de cellules neuronales, ainsi que la présence de plaques séniles2. À la suite d’observations de plusieurs autres cas identiques dans le monde médical allemand, la démence sénile devient reconnue internationalement en 1910 comme étant la maladie d’Alzheimer2.

Ses effets neurologiques Deux types de lésions au cerveau apparaissent chez quelqu’un souffrant de la maladie d’Alzheimer : les plaques séniles et la dégénérescence neurofibrillaire. Les plaques séniles sont aussi connues sous le nom de plaques amyloïdes, car elles sont formées par des amas de la protéine beta-amyloïde. Cette protéine est formée par la séparation de la protéine transmembranaire de cellules nerveuses, appelée peptide précurseur de l’amyloïde. Elle est très adhésive, donc s’agglutine facilement3.

Quant à la dégénérescence neurofibrillaire, elle se produit à l’intérieur des neurones. Les microtubules, qui forment une traverse par laquelle l’influx nerveux circule, sont retenus par la protéine tau qui subit des modifications à cause de la maladie.

Ainsi, le transfert d’information ne s’engendre plus, car la traverse s’est refermée3. Généralement, le dépôt de plaques séniles dans le cerveau affecte les neurotransmetteurs. Ces derniers ont pour rôle de maximiser l’efficacité des connections entre les neurones4. Le neurotransmetteur principalement ciblé est l’acétylcholine, qui a la fonction de favoriser la mémorisation.

Sa présence est diminuée de 40% chez l’individu qui commence à démontrer les premiers symptômes de la maladie d’Alzheimer4.

Au début, la dégénérescence des neurotransmetteurs se produit au niveau de l’hippocampe, qui s’occupe de traiter l’information verbale et visuelle4. Par la suite, le lobe pariétal est affecté par le développement de plaques séniles. Selon le lobe en question, droit ou gauche, les symptômes peuvent différer. Par exemple, si le côté gauche est touché, le patient aura tendance à mélanger ses mots et à ne plus comprendre ce que les gens lui disent. Ultimement, le cerveau entier est envahi par les plaques séniles, qui occupent beaucoup d’espace, et c’est à ce moment que les symptômes sont les plus graves4.

Les sept stades de la maladie d’Alzheimer Les effets de la maladie d’Alzheimer dépendent du degré des lésions qu’elle provoque. L’échelle de détérioration globale de Docteur Barry Reisberg est celle qui est la plus utilisée dans le monde. Normalement, ces étapes s’écoulent sur une période de 8 à 10 ans5. Toutefois, la durée et la gravité de chaque étape varient d’une personne à l’autre. Les sept stades décrivant l’évolution de la maladie sont décrits dans le Tableau 1.

Plus les séquelles sont importantes, plus le patient sollicite les services de professionnels pour l’aider dans sa vie quotidienne.

La solution la plus envisageable demeure le centre d’hébergement avec des soins soutenus. Au septième stade, le cerveau ne contrôle plus les organes efficacement et la mort est imminente, car le corps ne peut se maintenir en vie6.

Les traitements et la recherche pharmaceutique Pour tenter de soigner les gens atteints de la maladie d’Alzheimer, la recherche pharmaceutique est essentielle. Les médicaments symptomatiques les plus utilisés aujourd’hui sont de type cholinergique, notamment l’Aricept, le Reminyl et l’Exelon2. Ils atténuent efficacement les symptômes en stimulant la mémoire, mais ils n’arrêtent pas la progression normale de la maladie. Au courant de la recherche, les plaques amyloïdes sont la cible de la plupart des médicaments. Jusqu’à ce jour, tous les médicaments testés pour arrêter la production de la toxine amyloïde ont trop d’effets secondaires, ceux-ci impliquant des vomissements et des maux de tête2. Les chercheurs sont donc revenus au point de départ et ils doivent trouver un nouveau procédé biologique que les médicaments devront cibler pour arrêter la maladie. Une nouvelle idée est l’utilisation de facteurs de croissance. Les scientifiques cherchent à activer ces molécules, inactives depuis l’enfance, pour régénérer le

Figure 1: Illustration de la dégénérescence neurofibrillaire

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Tableau 1. Descriptif des différents stades de l’évolution de la maladie Stade Déficit cognitif 1 Aucun 2 Très léger 3 4 5 6 7

Description5 La vie quotidienne de la personne n’est pas affectée.

La personne commence à oublier des noms d’individus, les endroits où elle range certains objets, ainsi que certains mots.

Léger La personne ne fonctionne plus normalement dans son milieu de travail et elle est désorientée dans un milieu inconnu.

Modéré Les tâches plus complexes, par exemple la finance et le magasinage, deviennent difficiles à accomplir.

Relativement grave La personne doit se faire rappeler de s’occuper de son hygiène quotidienne, comme prendre sa douche.

Grave La personne perd la mémoire à court terme et elle ne peut plus prendre soin de son hygiène personnelle seule.

Très grave Le vocabulaire de la personne est restreint à quelques mots seulement. De plus, elle est incapable de se nourrir et de se déplacer par elle-même.

réseau neuronal2. Les facteurs de croissance encourageraient la régénération et la création de nouvelles cellules neuronales.

Pour l’instant, l’absence de médicaments efficaces et l’augmentation du nombre de personnes âgées causent une augmentation du nombre de gens affectés par la maladie d’Alzheimer.

Références 1.

Douglas Institut Universitaire en Santé Mentale. «Maladie d’Alzheimer: causes, symptômes et évolution » (Mai 5, 2014) [Online] Available: http://www.douglas.qc.ca/info/ alzheimer

La progression de la maladie d’Alzheimer dans la société québécoise

2.

Poirier, Judes., Gauthier, Serges..La maladie d’Alzheimer: le guide, (Éditions du Trécarré, Montreal, 2011), p. 19-22, 27-28, 128-136.

3.

Dubuc, Bruno. «Les plaques amyloïdes et la dégénérescence neurofibrilaire» (October 20, 2013). [Online] Available:http://lecerveau.mcgill.ca/flash/d/d_08/d_08_cl/d_08_ cl_alz/d_08_cl_alz.html

4.

Micas, Michèle. Alzheimer: prévention, causes et symptômes, au quotidien, conseils Pratiques, (Éditions Josette Lyon, Paris, 2008), p. 90-92.

5.

Société Alzheimer du Canada. «La maladie» (October 20, 2013). [Online] Available: http://www.alzheimer.ca/fr/ About-dementia/Alzheimer-s-disease/What-is-Alzheimers-disease/Global-Deterioration-Scale

6.

Société Alzheimer de Montréal «La maladie d’Alzheimer» (October 20, 2013). [Online] Available: http://www. alzheimermontreal.ca/maladie/maladie_introduction.php

7.

Société Alzheimer de Montréal «La maladie d’Alzheimer» (October 20, 2013). [Online] Available: http://www. alzheimermontreal.ca/maladie/statistiques.php

Au Québec, la progression de la maladie est très avancée, surtout avec le vieillissement de la population. Selon la Société Alzheimer de Montréal, 105 600 personnes de 65 ans et plus étaient atteints de la maladie d’Alzheimer en 20077, 74 700 de ces individus sont des femmes et 30 900 sont des hommes7. Il est donc évident que les femmes sont plus affectées, mais l’explication de ce phénomène demeure un mystère. De plus, les projections sont très peu encourageantes. En 2031, la Société Alzheimer s’attend à voir plus de 187 500 personnes affectées par les maladies dégénératives. Au Canada, 750 000 personnes seront touchées par la maladie d’ici à 20317. Il est donc impératif de trouver une solution pour guérir les patients.

Conclusion En conclusion, cette maladie neurologique dégénérative découverte par Alois Alzheimer atteint les neurotransmetteurs dans le cerveau. Les plaques séniles causent la dégénérescence dans le cerveau. La recherche pharmaceutique qui tente de trouver un remède pour cette maladie est en progression, mais manque de résultats positifs. Cela cause une augmentation du nombre de cas d’Alzheimer dans les populations vieillissantes, incluant celle du Québec. Du côté de la famille, beaucoup de temps doit être consacré aux soins du malade et plusieurs décisions sont à prendre lors de la dégénérescence. Est-il raisonnable de dire que la maladie a un impact très important sur l’entourage de la personne altérée, voire même plus important que sur la personne elle-même?

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Referee and Editor’s Comment Even if this article presents a good summary of this pathology, there is still room for improvement. Further explanations of how the disease affects the patient would have been appreciated, namely in what way can Alzheimer’s lead to death. Also, it is said that until this day, all medications tested to stop the production of the amyloid toxin have too much side effects. On the contrary, the use of nanotechnology (polymeric nanoparticle) targets the brain and reduces such side effects! Furthermore, the conclusion is too close to the literature. The authors only repeat their main points and end with a question that is somewhat off topic.

Clostridium difficile: A Healthcare Challenge Vanessa Bujwid and Faten Yazbek Canadaâ&#x20AC;&#x2122;s public healthcare system is a massive and intricate organization forced to meet high expectations within an increasingly challenging financial reality. Chief among the issues facing Canadian hospitals is the prevalence of healthcareassociated infections (HAIs): pathogens which are acquired within the very same institutions designed to provide a healing environment. Of these nosocomial infections, the rising incidence and severity of Clostridium difficile infection (CDI) is of primary concern.

Over the past few decades, the mortality rate associated with CDI has quadrupled, while infection rates persist at unprecedented levels1. The appearance of the hypervirulent BI/ NAP1/027 strains of C. difficile (FQR1 and FQR2) in the early 2000s,has resulted in multiple outbreaks of a markedly severe form of CDI which is resistant to traditional antibiotic therapies. As the leading cause of nosocomial infectious diarrhea, the Public Health Agency of Canada estimates the cost of CDI in health care to be 46.1 million dollars annually2. This disturbing trend affects all domains of the healthcare sector. When developing an effective strategy for the management of CDI, the following three levels need to be addressed: prevention, diagnosis and treatment.

Prevention measures offer the most potential benefit, as, when implemented effectively, the downstream costs and sufferings associated with cases of CDI are eliminated before they begin.

This would logically translate into decreased infection rates, a reduced number of deaths associated with these infections, shorter hospital stays, reduced antibiotic therapies and surgical interventions, a decrease in the risk of the development of resistant bacterial strains, less physical and emotional distress experienced by the patient and reduced economic burden on society as a whole. Successful reform in the hospital setting would involve collaboration between all levels of the healthcare system with a focus on management involvement in the design, execution and enforcement of an effective and universal infection control program3. Aspects of a comprehensive program, described by the Public Health Agency of Canada, include organizational controls, an effective means of risk assessment and surveillance, established isolation protocols and contact precautions, an aggressive hand hygiene initiative, personal protective equipment, cleaning and disinfection standards for both equipment and the environment and the education of healthcare workers, residents, families and visitors as to the dangers and prevention guidelines concerning CDI4.

Rapid diagnosis and timely treatment of CDI are important in improving patient outcome. Methods used in the past include toxigenic culture, cell cytotoxicity neutralization assays (CCNAs), and enzyme immune assays (EIAs). Nucleic acid amplification assays (NAATs) are the newest methods to achieve widespread use in the clinical setting due to their high sensitivity, high specificity and short turn-around time. Although they are relatively costly, many consider these assays to

be superior to other available tests. Each technique possesses its strengths and weaknesses in relation to sensitivity, specificity, speed and cost-effectiveness. It is the laboratoryâ&#x20AC;&#x2122;s goal to find a balance between these parameters which best serve the patient's interests. With this objective in mind, a number of algorithms have been developed which combine multiple methods that complement each other in order to optimize detection while minimizing associated costs. These algorithms typically begin with a rapid, inexpensive and sensitive test as a screening tool, followed by more specific confirmatory tests to diagnose a positive result for CDI5, 6.

When a patient begins treatment for CDI, the primary concern is supportive care, as the initial symptoms may be life-threatening if left uncorrected. The two first-line antimicrobial drugs generally used in the treatment of CDI are metronidazole and vancomycin7, 8. If C. difficile infection recurs, the same treatment used during the primary infection may be used to treat the secondary infection. In the event of a third infection (second recurrence) a pulsed vancomycin therapy is the treatment to be used. An alternative drug, fidaxomicin, was recently approved by the FDA in May 2011. However, the drug is very expensive and not practical as a first line of therapy9. When a third recurrence of CDI occurs after pulsed vancomycin therapy, fecal microbiota transplant (FMT) should be considered. FMT involves infusion of stool from a healthy individual to the intestine of a patient in an attempt to restore the normal microbiota balance that has been disrupted by the administration of antibiotics10.

In CDI patients who progress into an advanced, complicated, fulminant state of systemic toxic effects, surgical intervention remains the only salvage therapy11. Subtotal colectomy and end-ileostomy have been established as the operations associated with improved survival, although postoperative mortality rates remain quite high12. Procedures such as laparoscopic diverting loop ileostomy are probably preferable from the patientâ&#x20AC;&#x2122;s perspective because it is minimally invasive, preserves colon integrity and decreases patient morbidity. Measures should be taken to evaluate the effectiveness and the risk associated with these newer procedures13, 14.

A proactive approach is required to decrease the mortality and morbidity associated with C. difficile, with a focus on the exploration of new options for testing and treatment as well as the improvement of practices already in place. The initiatives taken today in the context of the Canadian healthcare system will have a direct impact on the prevalence of CDI within the coming years.

References 1. Communicable Disease Report: Quarterly Report. Available from: http://www.health.gov.nl.ca/health/publichealth/cdc/ CDR%20-%20Vol%2030%20-%20No.%203%20Final.pdf .

2. Ibid.

3. Walters P, Zuckerbraun B. "Clostridium difficile Infection: Clinical Challenges and Management Strategies". Critical Care Nurse , 34(4), (2014), p. 24-35.

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4. He M., et al. "Emergence and global spread of epidemic healthcare-associated Clostridium difficile". Nature Genetics, 45(1), (2013), 109-113.

5. Kufelnicka A and Kirn T. "Effective Utilization of Evolving Methods for the Laboratory Diagnosis of Clostridium difficile Infection. Clinical Infectious Diseases, 52(12), (2011), p. 1451-1457.

6. Walters, P. and Zuckerbraun, B. "Clostridium difficile Infection: Clinical Challenges and Management Strategies", Critical Care Nurse, 34(4), (2014), p. 24-35.

7. Ibid.

8. C Diff Foundation (March 2014). Available: http://cdifffoundation.org/category/infection-control/page/2/ 9. Ibid.

10. Ibid.

11. Ibid.

12. Walters, P. and Zuckerbraun, B. "Clostridium difficile Infection: Clinical Challenges and Management Strategies", Critical Care Nurse, 34(4), (2014), p. 24-35.

13. Ibid.

14. C Diff Foundation (March 2014). Available: http://cdifffoundation.org/category/infection-control/page/2/

Trizivir Tritherapy: Abacavir, Lamivudine, Zidovudine HIV/AIDS Treatment Olivier Larochelle Abstract With the high infection rate and lethality of the HIV retrovirus, pharmaceutical companies find that synthesizing drugs to fight this pathogen has significant commercial value. Thanks to an indepth understanding of the HIV lifecycle and structure, antiviral research finally brought productive results.

Antiviral therapy has existed since the 1980s. With the research that has been and continues to be done to understand the virus’ lifecycle, new and more effective drugs are being introduced into the market. The latest drugs not only slow down HIV replication, but also target multiple aspects of the HIV lifecycle, preventing mutations that would be beneficial to the retrovirus.

Tritherapy is the newest advancement in antiviral technology. It consists of a specific ratio of three antivirals mixed in one drug.

HIV has one tritherapy treatment: TRIZIVIR. TRIZIVIR targets reverse transcriptase, an enzyme found in various viruses to transcribe RNA to DNA before integration.

By mimicking deoxynucleosides, the three drugs in TRIZIVIR terminate the nucleotide chain formation because of their molecular structure. It is antiviral research at its finest: a combination of chemistry and biology fighting viruses.

Introduction Therapeutic medicine has improved greatly over the years, from the simple days of the first antibiotics to modern chemotherapy.

Constantly evolving helps bacteria and viruses survive as beneficial mutations make it more and more difficult to terminate them.

Human Immunodeficiency Virus (HIV) is a relatively new retrovirus that dupes helper T cell receptors into taking in the virus. As a retrovirus, HIV inserts a DNA copy of itself into its host’s DNA to “hijack” it, producing numerous copies of itself at the expense of its host’s resources. This is similar to someone hijacking a hospital (the helper T cells) and turning it into a bomb factory (HIV production center). The issue arises with the fact that helper T cells are responsible for warning other white blood cells about incoming pathogenic threats so that they can attack pathogens with antibodies, such as killer T cells that target infected cells.

Without this precautionary action, the body gradually loses most of its “scouts” and becomes immunologically deprived.

This condition is known as Acquired Immunodeficiency Syndrome (AIDS). In short, this would make anyone affected more prone to catching any pathogen and/or producing cancerous cells!

According to the World Health Organization, HIV was responsible for the deaths of 1.6 million individuals in 20121. Thankfully, public awareness campaigns and advances in therapeutic

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drugs have led to a gradual decrease in the number of deaths linked to the retrovirus. By knowing the lifecycle of HIV and the possible methods of treating an HIV infection, TRIZIVIR, a tritherapy drug, is the latest used in HIV treatment.

HIV retrovirus composition and lifecycle A mature HIV virus’ lipid membrane holds several gp41 transmembrane glycoproteins, which are bound to the membrane along with gp120 docking glycoproteins. These docking glycoproteins match the helper T cell’s CD4 receptors’ active site, stimulating receptor-mediated fusion between the viral lipid membrane and the host’s lipid membrane [Fig. 1].

Figure 1: Fusion of a Virus with a Host Cell2 The fusion process opens the viral membrane “envelope,” emptying its contents into the host cell, merging and mixing the viral and host lipid membranes together. Next, the virus’ matrix is broken down within the cytosol, revealing the HIV capsid, a membrane that houses the virus’ functional components. Within the capsid of the retrovirus, there are two strands of RNA, two integrase proteins, two reverse transcriptase proteins, and two protease proteins [as shown in Fig. 2].

DNA. Integrase proteins are used to attach the viral DNA into the host cell’s DNA, akin to severing a rope (host DNA) and mending the severed parts back together using another rope (viral DNA to host DNA) to create a single seamless rope (with mixture of viral DNA ). Protease proteins are used during the maturation of the virus. This includes breaking the produced protein into chains once outside the host cell, so that every component can assume their proper shape in order to function.

All of these components have functions, and all of these functions are vital to the virus’ survival. Thus, biologists and chemists work to develop methods to inhibit these components from carrying out their job properly. An antiviral drug will target a stage of the virus’ lifecycle and inhibit it from carrying out its function. There are entry inhibitors, which target the docking glycoproteins or CD4 receptors to prevent HIV from entering the host cell. There are nucleotide reverse transcriptase inhibitors that mimic nucleotides to terminate the reverse-transcription phase (turning RNA to DNA prior to integration). There are nucleoside reverse transcriptase inhibitors, which, like the nucleotide reverse transcriptase inhibitors, imitate a nucleoside to prevent reverse transcription. Non-nucleoside inhibitors mimic nucleosides during the reverse transcription phase. However, they bind directly to the reverse transcriptase enzyme, making it unusable. Integrase inhibitors target integrase proteins, binding to the protein and preventing it from integrating the viral DNA into the host DNA. Finally, protease inhibitors inhibit the protease enzyme, preventing the emerging HIV virus from maturing, essentially making the virus collapse on itself, since it cannot take its final shape. Thus, inhibitors can effectively slow the virus' replication so as to prevent the contraction of AIDS. With a relatively wide database of anti-HIV drugs, complete with information about their resistance patterns and toxicity profiles, drugs can be combined to be an effective option. Combination therapy requires a particular sequence of drugs in order to benefit the patient4. Tritherapy, the use of three antiviral drug types simultaneously, is a recommended method to effectively “prevent the development of antiretroviral drug resistance”5.

Trizivir, a popular HIV tritherapy drug, will be covered in detail.

Synthesizing an HIV antiviral drug “The HIV pandemic has been a major stimulus of the rapid development of new antiviral drugs over the last decade”6. Finding a drug to counter HIV was a response to the research done on the structure of viral enzymes and proteins7. The severity of the HIV infection and its incidence rate created a commercial interest for making a drug.

Figure 2: HIV Retrovirus Component (HHMI)3 The RNA strands contain the complete set of genetic information required to produce an HIV viral agent. Reverse transcriptase proteins transcribe the RNA into single stranded DNA, which is transcribed again to form a double stranded, integrable

The first HIV drug, Zidovudine, had already been identified as “an inhibitor of retrovirus replication,” so the drug testing and approval was greatly quickened8. Zidovudine, Lamivudine, and Abacavir were approved for consumer use in 19879, 199610, and 1999 respectively11. Shortly thereafter, in 2000, a drug utilizing specific proportions of all three of these molecules was used to synthesize Trizivir, one of the first antiviral tritherapy drugs to be prescribed, one that is still in use today12.

7

TRIZIVIR Pathway TRIZIVIR is synthesized from three nucleoside analog reverse transcriptase inhibitor molecules; Abacavir, Lamivudine, and Zidovudine. Each one mimics a deoxyribonucleoside found in DNA, namely deoxyguanosine, deoxycytidine, and thymidine (respectively). These molecules enter the host cell through passive diffusion or active transport13. Before being useful, these drugs are phosphorylated within the cytosol three times, to transform them into their functional triphosphate form. The following are pictures of the three drugs, and below them are the normal deoxynucleosides that they mimic. Note the differences in the ribose.

Figure 3: Carbovir and Abacavir14

Figure 4: Lamivudine15

Figure 6: Deoxyguanosine17

Figure 5: Zidovudine16

Figure 7: Deoxycytidine18

Figure 9: Nucleotides Linked By a Phosphate Backbone20 Since the virus cannot produce its own nucleosides for the reverse transcription phase, the virus uses the host cell’s naturally occurring nucleosides in the cytosol. Since these drugs mimic a type of nucleoside, the reverse transcriptase enzyme will use them to build its DNA. When the enzyme adds the molecule, a dehydration reaction occurs with the 3’ carbon forming a phosphodiester linkage between the molecule’s phosphate group and the 5’ hydroxyl group on the last nucleoside. A phosphodiester bond is a strong covalent bond using phosphate groups to link nucleotides with one another, forming the phosphate backbone in DNA [Figure 9] Lamivudine, mimicking cytidine, has its 3’ carbonhydroxyl substituted by sulfur. Since sulfur has a full octet with its neighbouring carbons, it would be very unreactive. For this matter, sulfur is unable to form a phosphodiester bond with the next nucleoside. Carbovir, the metabolized form of the prodrug abacavir, mimics guanosine. Its 3’ carbon is in a double bond with the 2’ carbon. With no hydroxyl group, there can be no phosphodiester bond formed with the next nucleoside.

Zidovudine, mimicking thymidine, has its 3’ hydroxyl group substituted with an azide group. Again, no phosphodiester bond can be formed to link the next nucleoside. With the molecule added, the result is a chain termination; there cannot be another 5’-3’ phosphodiester bond to continue the chain. As a result, the reverse transcription stops, and the RNA degrades, killing the virus.

TRIZIVIR Overall Effectiveness

Figure 8: Deoxythymidine19 8

Only few of the molecules will successfully be converted into their functional form, and most will be metabolized in other pathways. Although these quantities are quite limited in the host cell, they can react and create adverse effects. In terms of symptoms, Lamivudine has less side effects than Abacavir. However,

10. Drugs.com. “Epizivir” (May 11, 2014). [Online]. Available: http://www.drugs.com/uk/epivir.html 11. Drugs.com. “Ziagen” (May 11, 2014). [Online]. Available: http://www.drugs.com/uk/ziagen.html 12. Drugs.com. “Trizivir” (May 11, 2014). [Online]. Available: http://www.drugs.com/uk/trizivir.html 13. Ghodke et al "PharmGKB Summary: Zidovudine Pathway" Pharmacogenetics and genomics, (2012). [Online]. Available: https://www.pharmgkb.org/pathway/PA166104634, https://www.pharmgkb.org/pathway/PA165860384, https:// www.pharmgkb.org/pathway/PA165859361

Figure 10: Reverse Transcriptase Enzme Making a DNA Copy21 Zidovudine’s highly reactive azide group is known to cause anemia and neutropenia (among other symptoms) (HIVInSite)22.

Despite the side effects, Trizivir creates a scenario where the viral reverse transcriptase must have three successive beneficial mutations in order to survive and propagate. This extremely unlikely event is the main reason TRIZIVIR has unprecedented antiviral efficacy.

References 1.

“Global Health Observatory (GHO) data” (May 11 2014).

[Online]. Available: http://www.who.int/gho/hiv/epidemic_status/deaths_text/en/

2. Swiss Institute of Bioinformatics. “Fusion” (n.d.). [Online].

Available: http://education.expasy.org/images/Fusion.jpg 3. Walker and Ojikutu. “HIV Life Cycle and Drug Targets” (2007). [Online]. Available: http://www.hhmi.org/biointeractive/poster-hiv-life-cycle-and-drug-targets 4. Littler and Oberg. “Achievements and challenges in antiviral drug discovery” (2005). [Online]. Available: http:// www.intmedpress.com/servefile.cfm?suid=7ab6afa5-005446ce-a39a-30640a7a8328

14. “Patentimages Googleapis” (n.d.). [Online]. Available: http://patentimages.storage.googleapis.com/ WO2005063751A1/imgf000002_0001.png 15. Ibid. http://patentimages.storage.googleapis.com/ WO2010023676A2/imgf000002_0001.png 16. Ibid. http://patentimages.storage.googleapis.com/ EP0550714B1/imgb0003.png 17. Wikimedia Commons. “Description: Chemical structure of Deoxyadenosine” (April 11, 2005). [Online]. Available: https://commons.wikimedia.org/wiki/File:DA_chemical_ structure.png 18. Wikimedia Commons. “Description: Chemical structure of Deoxycytidine” (April 11, 2005). [Online]. Available: https://commons.wikimedia.org/wiki/File:DC_chemical_ structure.png 19. Wikipedia. “Desoxythymidin” (n.d.). [Online]. Available: http://wpcontent.answcdn.com/wikipedia/commons/ thumb/3/34/Desoxythymidin.svg/200px-Desoxythymidin. svg.png 20. Biospring. “Oligos 1” (n.d.). [Online]. Available: http:// www.biospring.de/images/oligos_1.jpg 21. Chemistry. “HIV” (n.d.). [Online]. Available: http://www. chemistry.wustl.edu/~edudev/LabTutorials/HIV/images/ rt.jpg

5. Rathbun et al “Antiretroviral Therapy for HIV infection” Medscape, (August 15, 2013). [Online]. Available: http://emedicine.medscape.com/article/1533218-overview#aw2aab6c10

22. McNicholl, Ian. “Adverse Effects of Antiretroviral Drugs” HIV Insite, (October 19, 2012). [Online]. Available: http:// hivinsite.ucsf.edu/insite?page=ar-05-01

6. Littler and Oberg. “Achievements and challenges in antiviral drug discovery” (2005). [Online]. Available: http:// www.intmedpress.com/servefile.cfm?suid=7ab6afa5-005446ce-a39a-30640a7a8328

Referee and Editor’s Comments

7. Ibid.

8. Ibid.

9. Drugs.com. “Generic Retrovir Availability” (May 11, 2014). [Online]. Available: http://www.drugs.com/availability/generic-retrovir.html

The authors asserted that Abacavir, Lamivudine and Zidovudine are phosphorylated within the cytosol three times and transformed into their functional triphosphate form. They should further elaborate on its mechanism. Was the phosphorylation specific to only that compartment? Why did the phosphorylation occur three times? Also, the authors should opt for well-known scientific publications in their references. The acceptability of sources that are not scholarly articles can be very subjective and therefore lack validity.

9

Antibacterial Effects of Natural Flavanones from Citrus Peel Extract on Streptococcus salivarius Nensi Alivodej, Noah Cohen, Maegan Grossman and Samantha Shapiro Abstract Flavonoids are natural phenolic compounds composed of plant metabolites and, therefore, have the potential to provide numerous health benefits. In this experiment, flavanones, a specific type of flavonoid mainly found in the albedo and flavedo of citrus fruits, were studied. The aim of this experiment was to observe if a solution of citrus peel extract inhibited the growth of Streptococcus salivarius bacteria and if so to identify which.

This was determined by recording the zone of inhibition created by the citrus peel extract on S. salivarius. The experiment was carried out by preparing a solution of equal parts of methanol and acetone, and various citrus fruitsâ&#x20AC;&#x2122; powdered flavedo and albedo. A piece of gauze was immersed into the lemon, lime, orange and grapefruit peel extract solutions and was placed in four petri dish replicates that were previously plated with S. salivarius. A mean zone of inhibition of 8.25 mm and 8.75 mm was observed for the orange and lime respectively. The results of an ANOVA test concluded that two out of four results, the orange and lime, are statistically significant (p < 0.05). The results of the experiment coupled with the knowledge of citrus fruitsâ&#x20AC;&#x2122; antibacterial properties and flavanone content suggest that lime and orange have a significant effect on the growth of S. salivarius.

Introduction The study of natural phenolic compounds has garnered a great amount of attention in biochemistry due to their promising antimicrobial and chemopreventive properties for use in in the development of medicinal treatments1. Phenols are chemical compounds that have a hydroxyl group attached to an aromatic carbon ring2. There are many natural phenols, especially in plants, some of which are flavonoids. Flavonoids are a group of similarly structured polyphenols that contain fifteen carbon atoms and are synthesized by plants3.They are found as aglycones (with no sugar attached), as glycosides (with sugar attached), and as methylated derivatives (CH3 functional group attached)4.

They all have 3 carbon rings but can differ in bond-position and attached functional groups4. The different backbones of flavonoid groups are shown in Figure 1.

Flavonoids are known to be nutraceuticals: natural ingredients that provide health benefits, which in this case include antioxidant, antiviral, anticarcinogenic, and antibacterial properties4.

Studies have demonstrated that flavonol quercetin completely inhibits Staphylococcus aureus growth and that most flavanones having no sugar moiety had inhibitory activity on microorganisms4. Also, a new flavanone named Flemingiaflavanone, from Flemingia strobilifera, has shown significant antimicrobial activity against some Gram-positive and Gram-negative bacteria5.

Previous studies have focused on the development of non-nat10

ural flavanones as antimicrobial agents by adding or removing functional groups during their biosynthesis9. However, the fact that natural flavonoids can act as nutraceuticals may prevent the undesirable growth of common bacterial species. A prominent bacteria found in the oral flora of humans is Streptococcus salivarius, which is responsible for bad breath and commonly colonizes dental plaque10. It is a non-pathogenic Gram-positive bacteria that helps control oral diseases, but can cause serious infections like bacteremia when it enters the bloodstream, which can lead to sepsis for people at risk11. The bacterium creates favorable conditions for colonisation of other bacteria that are potentially harmful to oral health and creates a capsule of glucan from sucrose as it is greatly exposed to sugars10. There is no known correlation between the accumulation of S. salivarius and infectious diseases caused by the microorganism, but its accumulation on dental plaque attracts other microorganisms that may influence the progression of cavities10. If flavonoids, particularly flavanones, could inhibit S. salivarius growth, they may naturally regulate the number of S. salivarius bacterial colonies in the oral cavity, which could prevent the undesirable accumulation of harmful bacteria.

Since flavonoids are known to have antibacterial properties, the flavedo and albedo extracts of citruses that have a higher flavanone concentration will show a greater zone of inhibition on S. salivarius. Fruits account for one of the major food groups consumed daily and contain a great variety of flavonoids, especially in citrus fruits such as the grapefruit. In fact, flavanones are the dominant group of flavonoids in the genus Citrus and are found in high concentrations such as hesperidin, naringin, and eriocitrin6. Flavanones have a hydroxyl group at positions 5 and 7 in ring A, and a double bonded oxygen at position 4 in ring C. The sole difference between flavanone types is in their R1 and R2 functional groups that give different chemical properties4.

The backbone of flavanones is shown in Figure 2. Grapefruits are known to have a higher total flavanone content among citruses at 50+ mg/100 g, followed by lemons and oranges with 10 to 50 mg/100 g, and limes with less than 5mg/100 g7. The

Figure 1: Backbone of Flavonoid (2-phenylbenzopyrans) groups

flavanone content profile of limes and sweet oranges is dominated by hesperidin, that of lemons is dominated relatively equally by eriocitrin and hesperidin, and that of grapefruit is dominated by naringin6. Hesperetin, naringenin, and eriodictyol are respectively the aglycones of flavanone glycosides hesperidin, naringin and eriocitrin, and are also present in citruses8.

The highest flavanone concentration in citruses is found in the flavedo (the external colorful part of the peel) and in the albedo (the inner white part of the peel)6. It is predicted that grapefruit will have a greater zone of inhibition considering that it has a higher concentration of flavanones compared to the other citruses lemon, lime, and orange.

towel. The flavedo and the albedo of each fruit were peeled with a potato peeler sterilized with 70 % ethanol. The pieces of peel were dried for four days in an environment with constant temperature and pressure. Each citrusâ&#x20AC;&#x2122; dried peel was then ground individually in a coffee grinder sterilized with 70 % alcohol to make the powder12. The peel was ground until it was in the form of powder. Five 100.0 mL beakers were used to make the solutions. 10.0 g of each citrusâ&#x20AC;&#x2122; powder was added to one of the five 100.0 mL beakers. 30.0 mL of acetone and 30.0 mL of methanol was then added to each beaker. Each piece of sterile gauze was then cut into four squares of 2.5 cm Ă&#x2014; 2.5 cm. Next, one piece of sterile gauze was submerged into one of the solutions (control, lemon, lime, orange and grapefruit peel) for four to five seconds with the use of tweezers that had been soaked in 70% alcohol. The gauze was afterwards positioned in the middle of the petri dish that was inoculated with S. salivarius. This was replicated twenty times: four times per citrus solution. The bacterial cultures were then incubated for three days. The zone of inhibition on the right side of the gauze was measured with a ruler three days after the experiment took place. An ANOVA test was used in order to determine whether the results were statistically significant.

Results

Figure 2: Chemical Structure of Flavanone Aglycone Materials and Methods Twenty samples of S. salivarius were cultured on agar plates.

The petri dishes were separated into five columns with four replicates in each row. The columns were labeled control, lemon, orange, grapefruit and lime respectively. This experiment was performed in room 5A.18, a laboratory at Dawson College.

Three tubes of S. salivarius were held in a base plate for test tubes. Aseptic technique was used in order to culture the bacteria. Gloves were used at all times to ensure that the experiment was not compromised by contamination. The sterile swabs were opened carefully and the tube was quickly flamed above the Bunsen burner. The sterile swab was then quickly placed into one of the tubes of S. salivarius. It was then flamed again, and closed. The petri dish was opened (keeping the side with agar face down), and the S. salivarius was spread, making sure that the entire surface area of the agar plate was covered.

Each fruit was washed with tap water and dried with paper

Table 1 shows that the mean zones of inhibition of S. salivarius for the lime and orange were 8.75 mm (with a standard deviation of 1.50 mm) and 8.25 mm (with a standard deviation of 2.63 mm) respectively. The control had a mean zone of inhibition of 4.25 mm (with a standard deviation of 1.44 mm). An ANOVA test with an alpha value of 0.05 was used to analyze the data collected. The results of the between-groups ANOVA test showed that, compared to the control treatment, both the lime and orange gave statistically significant results. When the control was compared with the experimental lime, d.f. = 3, p < 0.01. Furthermore, when the control was compared with the experimental orange, d.f. = 3, p < 0.04. It was thus concluded that both the lime and orange inhibited the growth of S. salivarius.

However, the mean zones of inhibition of S. salivarius created by the grapefruit and lemon were 3.50 mm (with a standard deviation of 0.41 mm) and 5.50 mm (with a standard deviation of 1.00 mm) respectively. The results of the ANOVA test state that these results were not statistically significant

Table 1: Mean zone of inhibition of S. salivarius on the right side of the saturated gauze in the petri dish (n = 4) Control

Lime

Grapefruit

Lemon

Orange

Mean zone of inhibition (mm)

4.25

8.75

3.50

5.50

8.25

Standard deviation (mm)

1.44

1.50

0.41

1.00

2.63

p Value Compared to Control

N/A

p < 0.01*

p < 0.36

p < 0.20

p < 0.04*

*Statistically significant (p < 0.05)

11

Discussion We hypothesized that the flavedo and albedo extract solutions from citruses that have higher flavanone concentrations would be the most effective antibacterials. Since flavonoids are known to have antibacterial properties, we believed that the concentration of flavanones affected the efficacy of an antibacterial agent.

When comparing the mean zone of inhibition of the control group to that of the experimental groups, only the lime and orange solutions had a statistically significant difference according to the ANOVA test. The lemon solutionâ&#x20AC;&#x2122;s mean zone of inhibition was greater than that of the control group, but the difference was not significant. The grapefruit solutionâ&#x20AC;&#x2122;s mean zone of inhibition was actually less than that of the control solution, but the difference was, once again, not significant.

The four citruses have different dominant flavanones. Sweet oranges and limes are both dominated by hesperetin; lemon is dominated about equally by hesperetin and eriodictyol; grapefruit is dominated by naringenin7. Table 2 gives the different flavanone contents of sweet orange, lime, lemon, and grapefruit.

The different types of flavanones may have different antibacterial properties because of the differences in their chemical structures.

Table 2:

The flavanone aglycones are all structurally similar in the respect that they have no sugar moiety, but differ in their function according to what two functional groups (R1 and R2) are attached4. We believed that all of the aglycones, in other words, all of the flavanones that have no sugar attached, would be an effective antibacterial agents4. We observed that the citruses dominated solely by hesperetin (orange and lime) were the only ones that had significant antibacterial properties, an idea that does not seem to have been previously presented. The functional groups of hesperetin may be more effective antibacterial agents than those of eriodictyol and naringenin. Therefore, the different aglycones extracted may have had different effects on

Flavanone content of sweet orange, lime, lemon and grapefruit.

Hesperetin (mg/100 g)

Naringenin (mg/100g)

Eriodictyol (mg/100g)

Sweet orange

21.87

7.10

/

Lime

43.00

3.40

/

Lemon

27.90

0.55

21.36

Grapefruit

0.35

32.64

/

When a flavanone attaches to a disaccharide via an oxygen atom in position 7, it is called a flavanone-7-O-glycoside13. An aglycone is a flavanone without the attached disaccharide14.

Hesperidin, naringin, and eriocitrin are flavanone-7-O-glycosides; hesperetin, naringenin, and eriodictyol are their respec-

Figure 3: 12

tive flavanone aglycones15. The chemical structure of hesperetin and naringenin with their formal glycosides are presented in Figure 3. The acetone-methanol solution was selected for extraction for several reasons. The two substances are miscible with each other and with water, making it suitable for a solid-liquid extraction16. The solution is polar and therefore extracted more polar glycosides, but some less polar aglycones were also dissolved. Acetone is flammable but not toxic, and methanol is flammable and toxic17, 18. This was not optimal, as ideal extracting solvents are not flammable or toxic, but it was the best available combination19.

the bacteria: they may not all be equally strong antibacterial agents. The different functional groups of aglycones naringenin, eriodictyol and hesperetin are illustrated in Figure 4.

Additionally, the flavanone-7-O-glycosides are separated into two different classes according to which disaccharide is at-

Chemical structure of hesperetin and naringenin with their respective glycosides

tached to the flavanone: 7-O-rutinosides have rutinose attached, and 7-O-neohesperidosides have neohesperidose attached.

Hesperidin and eriocitrin are 7-O-rutinosides while naringin is a 7-O-neohesperidoside6. The zone of inhibition of the grapefruit solution, the only solution containing 7-O-neohesperidosides, was smaller than that of the control group. This leads us to believe that S. salivarius possibly uses the disaccharide neohesperidose as a nutrient.

Figure 4: General chemical structure of a flavanone and R-group specification On one hand, neohesperidose is a 2-O-alpha-L-Rhamnopyranosyl-D-glucopyranose, meaning it has a rhamnose sugar connected to a glucose by a (1→2) linkage20. S. salivarius, being Gram-positive, has a thick peptidoglycan layer that consists of oligoglycan strands crossed-linked by short peptides (glycoproteins)21. This means that S. salivarius may have used the flavanone glycosides for the formation of its peptidoglycan layer, and according to our results, it may have had a preference for 7-O-neohesperidoside; therefore, its bacterial growth was not inhibited.

On the other hand, the flavanone aglycone hesperetin, having no sugar attached, may have cross-linked the glycoproteins in the peptidoglycan layer to form flavanone glycoside hesperidin, which blocked peptidoglycan synthesis and caused bacterial cell death. Also, hesperetin is the only flavanone aglycone with a methyl group attached. It may have been easier for the methyl group to detach from its backbone in the solvent containing methanol and interact with the bacterial cell peptidoglycan layer than the other flavanones that only have a hydroxyl group and a hydrogen attached. Thus, hesperetin may have acted as a bacteriostatic agent. Although limes have the highest total amount of flavanones, this explains the greater inhibition zone from lime’s flavanone solution, which contains the highest concentration of hesperetin, and sweet oranges that also contains a high concentration of hesperetin. Although lemons contain a greater amount of hesperetin than sweet oranges, the reason they did not show any significant results may be due to the presence of eriodictyol.

Only lemons have eriodictyol; oranges have solely hesperetin in greater amount and little naringenin. It has been suggested, by previous literature, that all of the bitter glycosides from Citrus, including eriodictyol derivatives, were characterized by the presence of 7-O-neohesperidose22. From our results, the presence of neohesperidose doesn’t suggest any antibacterial

property. Therefore, the presence of more eriodictyol derivatives may have overshadowed the presence of the aglycones eriodictyol and hesperetin.

Further experimentation must be performed in order to reach a conclusion; however, our data suggests two possible new discoveries. One, different aglycones are not identically effective antibacterials: the different functional groups may affect their efficiencies. Hesperetin shows the greatest antibacterial property. Two, S. salivarius may be able to use the disaccharides present in certain flavanone-7-O-glycosides as nutrients for their peptidoglycan layer, rendering them helpful to their growth rather than a hindrance to it.

Our results may have been influenced by several factors. Although the flavedo and albedo of all the citruses were dried in the same controlled environment, it was not sterile. They may have been exposed to contaminants; however, if they were, they all would have been exposed to the same ones. The dried peel was also ground very crudely in a coffee bean grinder.

Eventually, the grounds could not get any smaller. The grounds of lemon and lime were a bit larger than those of orange and grapefruit, and the size of the particles may have affected how the aglycones and glycosides were extracted. Additionally, the citruses that the flavedo and albedo came from are of unknown cultivars. Different cultivars’ flavanone concentrations vary, some quite greatly6. Averages of all cultivars were used to determine flavanone concentration, but these numbers may have been considerably inaccurate. During the experiment, we soaked the gauze in the prepared solutions, but when pressing the gauze into the petri dish, some solution spilled out of the gauze: the zone of inhibition may take into account some area where the bacteria were directly exposed to the solution. There were also several major problems with our method. The extract solution still contained methanol and acetone, which our findings show a clearing on the starch plates with S. salivarius. The two solvents are volatile enough that the solutions should have been distilled in order to isolate the flavanone extract and therefore test the effect of only flavanones on the bacteria19. The solvents are also polar and most likely extracted more glycosides than aglycones. Using a non-polar solvent may extract more aglycones, which are said to be stronger antibacterial agents4.

Finally, we cultured S. salivarius to test the antibacterial effects of the peel extract solutions. S. salivarius is actually able to make a capsule from sucrose: if any sucrose was available either from the glycosides or the starch plate, it would have been able to protect itself22. S. salivarius is not a usual model organism, and the experiment would have been conducted better had it been performed on one. In future experiments, the peel should be air-dried in a sterile environment and grounded with a mortar and pestle; the citruses should be of known cultivars; the gauze should be dry before applying to the petri dish. Also, the extract solution should be distilled and the tested bacteria should be a model organism like Escherichia coli23.

The hypothesis could be modified for future experiments in two ways. We could hypothesize that citruses with high concentrations of hesperetin or of flavanone-7-O-glycosides or both are effective antibacterials, and that aglycones are antibacterial 13

while glycosides are not.

In order to further research this topic, new experiments could be performed. Instead of making extract solutions of different citrus species, the same experiment could be performed with extract solutions of different known cultivars of one citrus species.

The same experiment could also be performed with a different extraction process. Instead of extracting both aglycones and glycosides in one solution, two different solutions—one of only extracted aglycones and one of only extracted glycosides— could be prepared and tested on bacteria. This could either be done for a known cultivar of several different species like in this experiment, or for several different known cultivars of one species.

References 1. Huang, Wu-Yang, Cai, Y.Z. and Zhang, Y. “Natural Phenolic Compounds from Medicinal Herbs and Dietary Plants: Potential Use for Cancer Prevention” Taylor and Francis Online, (2010). [Online]. Available: http://www.tandfonline.com/doi/full/10.1080/01635580903191585 2. Wade, Leroy G. Jr. “Phenol - Chemical Compound” (January 16, 2014). [Online]. Available: http://www.britannica. com/EBchecked/topic/455507/phenol 3. Peluso, Micheal R. “The Definition of Flavonoid” (2015).

[Online]. Available: http://healthyeating.sfgate.com/definition-flavonoid-5235.html 4. Tapas, A.R., Sakarkar, D.M., and Kakde, R.B. “Flavonoids as Nutraceuticals: A Review” Tropical Journal of Pharmaceutical Research 7(3), (September 2008). [Online]. Available: http://www.bioline.org.br/pdf?pr08030 5. Madana et al. “A New Flavanone from Flemingia Strobilifera (Linn) R. Br. and its Antimicrobial Activity” Tropical Journal of Pharmaceutical Research 7(1), (March 2008). [Online]. Available: http://www.tjpr.org/vol7_no1/ 718Madan.pdf 6. Berhow et al. “Survey of Phenolic Compounds Produced in Citrus” United States Department of Agriculture Technical Bulletin 1856, (December 1998). [Online]. Available: http:// www.ars.usda.gov/SP2UserFiles/person/34764/MABSurveyCitrus.pdf 7. Bhagwat, S., Haytowitz, D.B. and Holden, J.M. “USDA Database for the Flavonoid Content of Selected Foods” (2011). [Online]. Available: http://www.ars.usda.gov/nutrientdata/flav

14

8. Kanaze, et al. “Pharmacokinetics of the Citrus Flavanone Aglycones Hesperetin and Naringenin after Single Oral Administration in Human Subjects” US National Library of Medicine National Institutes of Health, (April 2007).

[Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/17047689 9. Fowler, et al. “M.A.G.Development of Non-Natural Flavanones as Antimicrobial Agents” US National Library of Medicine National Institutes of Health, (October 2011).

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[Online]. Available: https://microbewiki.kenyon.edu/index. php/Streptococcus_salivarius 11. "Streptococcus Salivarius - Fiches Techniques Santé-Sécurité: Agents. Pathogènes” (April 30, 2012). [Online].

Available: http://www.phac-aspc.gc.ca/lab-bio/res/psds-ftss/ streptococcus-salivarius-fra.php 12. “Beauty DIY: How to Make Orange Peel Powder for Face” (2015). [Online]. Available: http://healthmunsta.hubpages. com/hub/How-to-Make-Orange-Peel-Powder-for-Face 13. “Glycoside - Biochemistry” (December 15, 2014). [Online].

Available: http://www.britannica.com/EBchecked/topic/236171/glycoside 14. “Aglycone” (2011). [Online]. Available: http://www.thefreedictionary.com/aglycone 15. “Eriocitrin” (2008). [Online]. Available: http://www.neohesperidin-dc.com/pages/eriocitrin.htm 16. "Solvent miscibility table” (2015). [Online]. Available: https://www.erowid.org/archive/rhodium/pdf/solvent.miscibility.pdf 17. "Acetone - C3H6O” (2015). [Online]. Available: http://pubchem.ncbi.nlm.nih.gov/compound/acetone#section=Top 18. “Methanol - CH4O” (2015). [Online]. Available: http://pubchem.ncbi.nlm.nih.gov/compound/methanol 19. “Apparatus And Technique” (2015). [Online]. Available: http://www.chem.ualberta.ca/~orglabs/Interactive%20Tutorials/separation/Theory/theory6_2.htm 20. Bohm, Bruce A. Introduction to Flavonoids, (CRC Press, Boca Raton, January 18th 1999).

21. Vollmer, W., and Holtje, J.V. “The Architecture of the Murein (Peptidoglycan) in Gram-Negative Bacteria: Vertical

Referee and Editor’s Comment The abstract should contain the main results and its significant implication instead of very detailed experimental description. In the Materials and Methods section, the variables are not clearly accounted for. There are several questions concerning the scientific description. For example: did the bacteria grow evenly on the all the plates? Did the three tubes of bacteria come from the same culture? Did all the peel power dissolve in the chemical solvent? Will the gauzes get the same amount of liquid from each fruit?

Furthermore, the authors say that an ANOVA test was used for statistical analysis. If they used software for this purpose, they should mention the name of software in this section. If they calculated manually, they should briefly explain how they did the ANOVA calculation. Also, an equal amount of power from peels to the organic solvent does not assure an equal amount of extract put on the plate. They should find a way for proper quantifying the extract for each kind of fruit.

Finally, an emphasis of the antibacterial function of flavanones would make the article even more relevant.

The Effect of Mozart's Music on Spatial Intelligence Samantha Rosenthal, Kelly Perlman, Jennifer Banon and Roy Hilzenrat Abstract In recent studies, Mozart’s music, which has a very specific rhythmic pattern, was found to have performance-enhancing effects on cognition due to its influence on certain human brain functions and wave patterns. We conducted an experiment with the goal of determining whether the first movement “Allegro con spirit” of Mozart’s Sonata for Two Pianos (K448) in D major improved spatial-temporal reasoning. We did so by observing the time that it took for six participants to complete three puzzles in two different conditions: once in silence and the other after listening to Mozart’s sonata for 10 minutes. Our results suggest that the sonata did temporarily improve the participants’ spatial reasoning. Therefore, we accepted our alternate hypothesis, although we acknowledge that the small sample size was a limit of the study. These results further substantiate previous studies conducted and give further findings to the study of the Mozart effect.

Introduction The effect of classical music on cognitive functions is a widely discussed topic among researchers. A specific theory called "The Mozart Effect" has been of interest to many since claims were made that listening to the first movement “Allegro con spirito” of Wolfgang Amadeus Mozart's Sonata for Two Pianos (K448) in D major improved spatial intelligence (Rauscher et al. 1993). With regards to Mozart in particular, his sonata for two pianos may have had significant results on spatial-temporal reasoning because his music tends to have sequences that repeat themselves every 20-30 seconds (Glass 1995). This relates to brain processing because many neural functions and brain wave patterns are repeated at intervals of 30 seconds. This synchronization between the rhythm of the music and brain functions may explain why Mozart’s music can affect cognition.

Findings demonstrate that certain components of the music such as pitch, tone, tempo, rhythm, and melody have a direct effect on the way the human brain processes information. Our hypothesis is that Mozart’s music will improve cognition and allow the participants of the experiment to perform better on the tests used. As hypothesized by Rauscher et al., listening to types of complex music, such as Mozart’s sonata, may stimulate neural transmitters in areas of the brain that control both the processing of spatial images and the processing of music.

This hypothesis was based on the “Trion model” of the cerebral cortex developed by Shaw, which suggests that the neural firing patterns of the nerve cells associated with processing music are analogous to that of the nerve cells associated with processing spatial images. Thus, by stimulating certain areas of the brain and activating these neural firing patterns, it was hypothesized that spatial task performance could be enhanced for 10-15 minutes following a listening period of Mozart’s sonata. However, a second hypothesis exists as to why Mozart’s music might lead 15

to enhanced performances in spatial temporal tasks. According to a study conducted by Salimpoor et al. (2010), published in Nature Neuroscience, music evokes an emotional response, which releases the neurotransmitter dopamine at its peak of arousal. This relates to the Mozart effect as noted by a different study by Thompson et al. (2001) called “Arousal, Mood and the Mozart Effect”. The study concluded that the release of neurotransmitters that affect mood and arousal, such as dopamine and norepinephrine, can moderately increase performance in tasks requiring spatial intelligence. Therefore, the music enhances an individual’s mood, which in turn releases the neurotransmitters (from the ventral tegmental area of the brain to the locus ceruleus area) that enhance the performance of spatial tasks. In 1994, at the University of Aukland, Stough, Kerkin, Bates, and Mangan were unable to yield the same results as in the original study by Rauscher et al and no difference was found in the performance of subjects who listened to Mozart’s music, disco music or no music at all. Additionally, recent alternate findings have shown that the effects of Mozart’s sonata on spacial intelligence are either statistically insignificant or non-existent (Pietschnig, Voracek, & Formann, 2010). This research used a meta-analysis that analyzed 40 studies that tested the viability of the Mozart effect and concluded that listening to Mozart’s sonata does not significantly improve cognitive processes and behavior.

Materials and Methods For this project, we conducted 6 tests. In three of these, we began by letting our participants complete a set of three spatial-temporal tasks, which took a maximum of fifteen minutes. The first task consisted of a spatial intelligence puzzle called IQ fit, where the participants had to fit irregularly-shaped, 3-dimensional rounded pieces into a fixed board in order to form a flat 2-D image without any protruding pieces. The second puzzle was called Super Mind, where the participants had to fit various shapes to fill out a specific image, and the final test was a 24-piece jigsaw puzzle. All of these tests were timed, and the participants were urged to do them as quickly as possible.

Each of the three participants’ results was recorded. The participants were asked to listen to Mozart’s Sonata for Two Pianos K448. The same song was played from the same laptop at the same volume, using the same source of music (YouTube). Each participant listened for ten minutes, which is the amount of time used in prior studies (mentioned above). After the ten-minute period, the participants were asked to complete the set of tests again by using different variations of the same puzzle of equal difficulty. This was the first of two measures we took to make sure that the participants’ improvement was not results of practice.

The second set of participants listened to the sonata for ten minutes before completing the first round of tests. They each completed one variation of each game (IQ Fit, Super Mind, and Jigsaw Puzzle). They were then asked to wait fifteen minutes (until the effects of the music were shown to wear off), without doing any sort of activities involving music or intellectual tasks to avoid influencing our results for the next round of testing.

After the rest period, the participants were asked to complete 16

the different variations of the same tests. The results (time to complete the puzzle) were recorded and an unpaired t-test was used.

Figure 1. Mean time it took for participants to complete the IQ Fit test, both with and without having listened to Mozart’s sonata.

The mean time taken for IQ fit test in the experimental group was lower than the mean time taken for the test in the control group (calculated t = 2.100; critical t = 2.015). This difference in means is shown in Figure 1. The full t-test procedure and calculations can be found in Appendix 1. The results here were significant.

Figure 2. Mean time it took for participants to complete the Supermind Shapes game, both with and without having listened to Mozart’s sonata.

The mean time taken for Supermind Shapes test in the experimental group was higher than the mean time taken for the test in the control group (calculated t = 0.9250; critical t = 2.015). This difference in means is shown in Figure 2. The results here were not significant.

Figure 3. Mean time it took for participants to complete the 24-piece jigsaw puzzle, both with and without having listened to Mozart’s sonata.

The mean time taken for Jigsaw puzzle test in the experimental group was lower than the mean time taken for the test in the control group (calculated t =2.570; critical t = 2.015). This difference in means is shown in Figure 3. The results here were significant.

Discussion Our findings suggest that listening to Mozart’s sonata for two pianos for ten minutes has transient performance-enhancing effects on spatial intelligence. After the listening period, the participants were able to complete the tests more quickly than when they completed the tests without having listened to the music. Two of the tests, the IQ Fit challenge and the 24-piece jigsaw puzzle, yielded statistically significant results. However, the Supermind Shapes test results were inconclusive. The critical t-value, which was obtained using the t-test for repeated measures, was 2.0150. Our calculated t-values for the IQ fit test and the 24-piece jigsaw puzzle were 2.1000 and 2.5700 respectively. The Supermind Shapes test, however, gave us a calculated t-value of 0.9250.

One possible explanation for the results of the two tests where the results were statistically significant is related to the way in which the human brain processes music and spatial imaging.

Positron emission tomography (PET) scans, as well as magnetic resonance (MRI) brain scans, show that the perception of music is localized and that music activates certain areas of the brain depending on the rhythm, pitch, meter, melody, and timbre of the music (Jenkins 1994). The stimulated locations in the brain include the prefrontal, temporal and precuneus regions.

Similarly, PET scans showed that the areas in the brain that are activated during spacial image processing correspond to those activated during music processing (Mellet, Tzourio, Crivello, et al. 1996). Since these areas overlap, we can infer that listening to music enhances overall spacial intelligence.

The results for the two statistically significant tests can be explained alternatively based on observations during the testing period. It was observed that some participants became more

alert during the listening period and displayed a higher level of concentration after the listening period. They were observed to enjoy the music more than other participants. These participants showed a greater improvement with regards to the speed at which they were able to complete the puzzles after the listening period. Researchers at the University of Toronto who conducted a study on the Mozart effect concluded that: “listening to Mozart’s music causes either an increase or decrease in someone’s arousal and moods to a level that is more optimal for testing” (Steele, 2000; Thompson, Schellenberg, & Husain, 2001). As aforementioned, when emotional arousal occurs, the consequential release of dopamine and norepinephren into the brain results in improved spatial and temporal reasoning skills. Thus, the fact that music evokes an emotional response and arousal directly correlates with the release of dopamine, which relates to increased spatial intelligence (Thompson 2001).

The Supermind Shapes test yielded insignificant results according to the t-test for repeated measures. Since the experimental group was only composed of six participants, unlike other studies on the topic of the Mozart effect that tested hundreds of participants, each participant had a significant effect on our results. Thus, the one person out of six whose performance level decreased after the listening period altered the expected outcome. Had there not been an outlier, the second test may have been statistically significant as well since all other participants showed improvement after the listening period. The fact that there was an outlier is due to normal fluctuations that occur during a testing period. This participant could have been distracted by some uncontrolled external factors, such as lighting, stress or other emotions.

During our experiment, the person administering the tests, the age range of the participants (16-19 years old), and the materials and activities used were kept constant. Also, it was ensured that none of the participants had extensive musical training.

This would have been an uncontrollable factor because music training may have an effect on cognitive function. In addition, the placebo effect was minimized by not informing the participants about what the expected outcome would be, nor who the composer was, in case they had previously heard of the Mozart effect. They were unaware of which test they were supposed to do better on and, therefore, performed honestly.

There were several sources of error in this experiment. Firstly, the time of day could have had an effect on our results. If the tests took place later in the day, the participants could have been tired which could have potentially affected the participants’ concentration level and performance and most likely affected our results. Secondly, there were discrepancies in the amount of hours of sleep obtained by each participant. If one participant was more tired, it could have affected the outcome of their scores. In addition, we noticed that some of our participants were more anxious than others and expressed that they felt pressured because they were being timed. This anxiety could have affected their performance due to their lack of concentration, or general nervous demeanor. This would have most probably affected our obtained results. Another source of error in this experiment is the fact that a small sample size was used. A large 17

sample size is very important because it increases the accuracy of the conclusions that can be drawn from the patterns observed. We did not increase our sample size because the length of each test took up to 40 minutes. The constraints due to time interfered with our ability to recruit enough participants to have a large sample size.

There is a significant amount of further research that can branch out of this study. Firstly, one could explore the effects of a person’s favorite type of music, rather than classical music, on their spatial-temporal skills. Secondly, the effects of listening to the Mozart Sonata, classical music or non-classical music while taking the tests, as opposed to taking the tests only after listening to the music could be investigated. Other factors, such as the effect of the length of the listening period on cognitive function and the effect of Mozart on other realms of intelligence could also be evaluated.

References 1. Jenkins, J. S. "The Mozart Effect", Journal of the Royal Society of Medicine, (1994), [Online].Available http: //jrs. sagepub.com/content/94/6/316.2.full 2. Mellet E et al. “Functional anatomy of spatial imagery generated from verbal instructions”, J Neurosci. 16 (20): 6504-12 (1996).

3. Pietschnig, Voracek, Formann. “Mozart effect–Shmozart effect: A meta-analysis”, Intelligence 38, Issue 3, 314-323, (May–June 2010). [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0160289610000267.

4. Rauscher, Shaw, Ky. “Listening to Mozart enhances spatial-temporal reasoning: toward a neurophysiological basis”, Neurosci., 185: 44-7 (1995).

5. Rauscher, Shaw, Ky. “Music and spatial task performance”, Nature, 365: 611 (1993).

Referee and Editor’s Comment Upon reviewing this experiment, some issues have been noticed. A major problem is in the statistical analysis. A t-test was used. Instead, a more fitting analysis could have been done using ANOVAs. In the performed t-test, p-values were not provided by the authors, which has compromised the analysis.

Another major issue is the very small sample size, which also compromises the validity of the results, although this was acknowledged in the report. Generally, however, this experiment was interesting and the report was good.

Vestibular Adaptation to Vertigo in Ballet Dancers and Figure Skaters Joanie Papillon Abstract The vestibular system, responsible for balance and movement, can be accustomed to vertigo through repeated stimulation.

For ballet dancers and figure skaters, turning is a key element of training that they perform regularly and repetitively, which allows them to adapt to the sensation of vertigo and diminishes their perceptual responses to dizziness. This experiment aims to compare the time of recovery from vertigo in ballet dancers, figure skaters and other athletes. When measuring the time taken to recover from dizziness after turning blinded for 20 seconds, for each of the individuals from those 3 groups, results significantly demonstrated that figure skaters (M=6.12s) recover significantly faster than ballet dancers (M=13.87s). Furthermore, figure skaters themselves recover significantly faster than the control group (M=22.88s). This leads to the conclusion that the training of figure skaters provides a different rotational stimulation than that of ballet dancers, which generates a more effective habituation to vertigo.

Introduction The vestibular system holds a very important role in the human body, since it is responsible for maintaining balance and posture, as well as regulating the body’s spatial orientation and its coordination of movement. Vertigo is closely related to the vestibular system and is defined as the impression of movement, whether it is linear, rotational or tilted. Vertigo is also often supplemented by sensations of imbalance or nausea (Grapinet). In this experiment, it is also referred to as the feeling of dizziness.

The vestibular system is composed of the peripheral sensory apparatus, which sends information to the vestibular nucleus complex and the cerebellum of the nervous system, and of an output mechanism connected to the eyes and the spinal cord. This output device allows three important reflexes: the vestibule-ocular reflex (VOR), which permits clear vision with motion of the head; the vestibulocollic reflex (VCR), which keeps the head steady; and the vestibulospinal reflex (VSR), which produces movement to maintain balance (Hain & Helminsky, 2007).

It has been observed that the vestibular system is adaptable, since VOR and the impression of rotation can be conditioned through repeated rotational stimulation. Furthermore, this accommodation to the sensation of turning has been verified to be long-term, since it persists even after the cessation of the rotational training (Clément et al., 2008) In light of these observations, we study the vestibular responses of individuals who continuously experience rotational stimulus.

In figure skaters, VOR was shown to be be 27% lower than in others and their motion sickness after stimulation would be significantly smaller than normal (Tanguy et al., 2008). Moreover, the analysis of vestibular nystagmus, which is defined by oscillatory involuntary jerky movements of the ocular globe, has

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revealed that skaters have developed the ability to reduce their eye movement frequency faster after rotation than non-skaters (Collins, 1967). In ballet dancers, vestibular responses are completely inhibited, meaning that after performing pirouettes, dancers feel absolutely no vertigo. In fact, the duration of their VOR responses have been tested longer than those of non-dancers, but their perceptual responses would be much briefer. This would be due to a reduction of the density of grey matter in the vestibular cerebellum (Nigmatullina et al., 2013) The purpose of this experiment is to compare the perceptual responses of figure skaters, ballet dancers and other athletes.

The hypothesis to be tested is that both figure skaters and ballet dancers demonstrate a quicker recovery from vertigo, but that skaters likely exhibit an enhanced adaptation over dancers, because of their ability to better control VOR. Material & Methods The individuals chosen to participate in this experiment are females aged between 18 and 21 years old and are non-sedentary people who train at least 10 hours per week. Care was given to ensure that none of them suffered from low or high blood pressure, diabetes, anemia, hyperventilation, heart conditions, dehydration or were pregnant at the time of the study, since these conditions could enhance dizziness. The experiment was performed upon two experimental groups: figure skaters and ballet dancers. The control group was made of female athletes of different disciplines who do not imply repeated rotations, such as hockey, rowing, soccer and running.

The subjects were blindfolded with a scarf and asked to position themselves with their arms crossed over their shoulders and their feet hip width apart. They were then asked to turn on themselves as fast as they could for 20 seconds and then find their balance on one foot. The time of vertigo measured was the time needed by the subject to recover from their rotation; that is, the time from the moment the participant stopped turning until he succeeded in holding his equilibrium position for a duration of 3 seconds Results Based on our research done about the vestibular system, we postulated that athletes engaging in intense training that involves spinning may have had the ability to faster recover from vertigo. In order to bring further evidence to this notion, we wanted to determine the time that figure skaters (etc) needed to recover from vertigo after rotation. The mean time of recovery from vertigo was significantly less for the figure skaters (M=6.12s) and for the ballet dancers (M=13.87s) than for the control group (M=22.88s, calculated t-values=6.51617 and 3.11113 > critical t-value=1.83311; Figure 1). Moreover, the practice of figure skating had a significantly greater effect than that of ballet dancing on the adaptation to dizziness (calculated t-value=5.26044 > critical t-value=1.83311). As shown in Figure 1, the mean variations of the three groups are relatively consistent, which is supported by the low standard deviations: SD=8.01 for the control group, SD=1.41 for the figure skaters, and SD=4.44 for the ballet dancers.

Figure 1: Average time of vertigo recovery for each group Discussion The purpose of this study was to determine whether or not there is a correlation between athletes who engage in activities that include spinning and their ability to recover from vertigo. The results of this experiment support the hypothesis that figure skaters and ballet dancers develop a vestibular adaptation to vertigo that other athletes do not have, which allows them to recover faster from rotation. This conclusion agrees with previous studies’ findings that the vestibular system can be conditioned to the sensation of vertigo (Clément et al., 2008) and that both figure skaters and ballet dancers exhibit this type of adaptation (Tanguy et al., 2008; Nigmatullina et al., 2013). The results also show a significant difference between the two groups of individuals accustomed to rotational movements. Indeed, figure skating training seems to be a more effective exercise in the conditioning of the vestibular system to vertigo than ballet dancing. This could be explained by the different techniques used by the groups: ballet dancers “spot” when they turn, meaning that they keep their sight on a precise point throughout the pirouette, while figure skaters do not spot, but rather, fix their gaze only when finishing their spin.

Although efforts were made to ensure the accuracy of this experiment, it should be noted that some factors may have limited the exactitude of the results. First, the ballet dancers who participated in the study trained 17 hours per week, which was much more than the individuals of the two other groups who trained 9 hours per week on average. In future studies, this variable should be controlled. Secondly, the speed of revolution of the subjects during the experiment might have varied, since they were asked to turn on their feet and they were the initiators of the movement. It is possible that this turning speed influenced the results, so for replication of the experiment, external forces with the capability of regulating the speed should instead perform the subjects’ spin. Finally, it is possible that the method used to measure the time of vertigo recovery, which involved maintaining balance on one foot for 3 seconds, may have introduced error in the results. In fact, individuals might have more or less difficulty in maintaining their balance, depending on their natural dispositions and their training. In further research, the time measurement should be based on a more accurate observation, such as ocular reflexes.

Taken together, this data suggests that athletes who engaged in spinning were about to recover from vertigo more rapidly, 19

and underlines the importance of undertaking further studies to better understand the vestibular system. By better elucidating its physiology and mode of adaptation/ability to cope with vertigo, crucial information can be obtained to help us identify cures of vestibular related diseases.

Growth of Vigna Radiata in a salty Environment when Paired with a Salt-tolerant plant Darel Bouhadana, Rachel Korman, Roxana Wong and Rachel Hayes

References

Abstract

1. Herdman, Susan J. Vestibular Rehabilitation, 3rd ed., (F.A. Davis, 2007), p. 2-18.

Climate change and other anthropogenic phenomena have been causing the salinity levels in the soil to rise. This increase in salinity can have devastating impacts on trees and plants, and can cause major losses of crop yields. Research has shown that soybeans can be introduced into salty environments to maintain other plants’ salt tolerance.

2. Clément, G., Tilikete, C., Courjon, J.-H. “Retention of Habituation of Vestibulo-Ocular Reflex and Sensation of Rotation in Humans” Experimental Brain Research 190, 3, 307-315 (2008).

3. Tanguy, S.et al “Vestibolu-Ocular Reflex and Motion Sickness in Figure Skaters" European Journal of Applied Physiology, 104, 6, 1031-1037 (2008, August 14).

4. Collins, W.E. “Adaptation to Vestibular Disorientation: VII. Special Effects of Brief Periods of Visual Fixation on Nystagmus and Sensations of Turning” Federal Aviation Agency (1967).

5. Nigmatullina et al “The Neuroanatomical Correlates of Training-Related Perceptuo-Reflex Uncoupling in Dancers.”

Oxford University Press (2013).

6. Collins, W.E. “Adaptation to Vestibular Disorientation: II. Nystagmus and Vertigo Following High-Velocity Angular Accelerations.” Federal Aviation Agency (1965).

7. Grapinet, J. “Entries: Vertigo, Vestibular system” ( February 9th, 2014). [Online] Available: http://www.vestibulaire.com/ glossary/Glossaire_gi1318.html Referee and Editor’s Comment Despite this being a sound and interesting experiment, some issues have been brought up that could not be rectified. Further descriptions of the experiment would have been preferred, namely whether or not the test subjects knew they were being tested and information on the equipment used to measure the time. More primary research articles, as well as the replacement of some of the more outdated sources would also have been an asset. In regards to the t-test performed, there were some concerns with the assumptions that the t-test makes and its viability in this experiment. Instead, some other forms of testing might have been employed, such as ANOVA.

The purpose of this experiment is to determine the effects of salt on the growth of non salt-tolerant plants when a salt-tolerant plant is present.

Two salt-intolerant seeds, radish and mung bean, were planted in ten pots and radish was planted with a soybean, a salt-tolerant seed, instead of the mung bean in ten other pots. The pots were then placed in the same area with identical temperature and sunlight and their growth was monitored for five weeks while they were watered with 30 mL of the same solution of tap water and sodium chloride (concentration = 2g/L) every three days. The data collected was the root length of the mung bean from each pot and a t-test was performed.

The mung bean paired with the non salt-tolerant plant had a low survival rate and the mean root length was 2.7cm. The mung bean paired with the salt-tolerant plant had a higher survival rate and had a mean root length of 5.1cm. The results of the t-test conclude that the mung beans showed a more significant growth in a salty environment when planted alongside a soybean, a salt-tolerant plant. These results support the hypothesis that a salt-intolerant plant will have a higher survival rate when watered with a sodium chloride aqueous solution and paired with a salt-tolerant plant rather than a non salt-intolerant plant.

Introduction Species of plants vary in their ability to tolerate different salt levels in soil. The addition of salt in an environment places a lot of stress on plants and can cause major crop losses1,2,3,4,5. Climate change and anthropogenic greenhouse gas emissions have caused soil salinity to drastically increase, which puts many plants under a lot of stress3. The agricultural area that is currently affected by an increase in salinity is estimated to double in the next thirty five years4,5.

Soil salinity can cause ion toxicity, osmotic stress, mineral deficiencies, and drastic physiological and biochemical changes in plants5. In some cases, this stress can even cause plants to conserve water by closing their stomata, therefore restricting the entry of carbon dioxide into leaf5. The photosynthetic process is therefore interrupted, which leads to the death of the plant. Soil salinity is constantly increasing, claiming farmland and rendering it unusable5. Meanwhile, the human population continues to grow and demand more food6. To resolve this problem, scien-

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tists must find a sustainable way to reduce the effects of salt on salt-sensitive plants6.

While many plants do not have the capacity to tolerate higher salt levels, some, such as soybeans, contain a specific gene that allows them to have a greater threshold for salted soil2,3,4. The presence of this gene allows soybean crops to survive in these environments and improves crop yields2,4. Some studies suggest that once this gene has been identified it can be used to improve salt tolerance of many other crops, and has the potential to better global food security2,4.

This new information regarding on soybeans can be used to make genetic markers in breeding programs to find similar genes in different types of plants such as wheat and grapevine4.

By identifying these genes, future cultivators of soybean can survive in areas that are prone to soil salinity4.

Another study observed how urban-landscape plants are affected by environmental conditions that are different from their natural habitats2. Since increased salinity levels can have harsh impacts on plants, salt-tolerant species were introduced to the environment to reduce plant stress and loss of salt-intolerant plants2. In other words, by simply adding a salt-tolerant species into an environment, the salt-intolerant plants had a better chance of survival.

The breeding of salt tolerant plants has also been used to contribute to research in sustainable food production3. The survival of salt-tolerant plants in these environments is attributed to salt bladders which take up salt and deposit it inside a safe external balloon-like structure3. Recent research on salt bladders has allowed scientists to conduct more experiments in order to see if salt-loving plants, which contain these bladders can be used to modify the genes of salt-intolerant plants3. According to ScienceDaily, this would allow crops, such as wheat and rice, to develop salt bladders that will allow their survival in salty environments3.

Previous research and experimental evidence suggests that genetically modifying plants to contain the soybean salt bladder gene will allow them to survive in salted terrain2,3,4. We wish to observe the growth of salt-intolerant plants on salted terrain without genetic modification. We hypothesize that planting the salt-tolerant soybeans seed will improve the growth and yield of the salt-intolerant horticultural crop, the mung bean7.

Materials and Methods In the experiment, mung bean plants were paired with either salt-tolerant or non salt-tolerant plants and watered with salt water to determine if they would have a higher growth rate when paired with the salt-tolerant plant. First, forty mung bean seeds, twenty soybean seeds, and twenty radish seeds were purchased and planted in conditions that were prepared to allow the seeds to germinate. A paper towel was dampened and then rung out to avoid excess water, which could have damaged the seed or lead to mold growth8. A maximum of ten seeds were evenly distributed on the top half of the paper towel, the other half of the paper towel was folded over the top of the seeds8. The seeds were then placed inside a small sized Ziploc bag to avoid water

loss8.This was done to the twenty radish seeds, twenty soybean seeds and forty mung bean seeds. The bags were then placed on a table that was not in direct sunlight since all the seeds needed darkness to germinate9,10,11. The door to the room remained shut and a heater was set up to go on every half hour for a fiveminute interval to ensure that the room had a high temperature.

The seeds germinated for 24 hours. After the 24-hour period, the seeds were uncovered. The seeds that failed to germinate were disposed of.

The seeds that germinated were then planted. A total of twenty identical 400 cm3 plastic pots were used. Small rocks lined the bottom of each pot to assist with drainage. Each pot was filled ¾ full with Miracle-gro® soil from the same bag. In the control group, which was made up ten of the pots, a mung bean seed and a radish seed (both salt-intolerant) were planted together, approximately 3 cm apart from each other. In the experimental group, which was also made up of ten pots, a mung bean was planted with a soybean seed (a salt-tolerant plant). All twenty pots were placed on a windowsill, 4 by 5 to ensure they all had the same exposure to light.

The plants grew for a period of five weeks. During this period the plants were watered every three days with 30 mL solution of tap water and 2g/L sodium chloride.

At the end of the time period, all the plants were unearthed and the root length of the mung bean plants that survived were recorded. Descriptive statistics (means and standard deviation) were calculated and a one-tailed t-test was used to determine if the data was statistically significant.

Results In figure one, the mean value of the root length of the mung bean (± standard deviation) is demonstrated. The standard deviations for the control and experimental groups were 0.31 and 1.19 respectively. In the control group, the mean root length (2.7 cm) was significantly lower than the mean root length (5.1 cm) in the experimental group. A t-test was used to analyze the data (the degree of freedom was 2, the calculated t-value was 4.28, the critical t-value was 2.920 and the alpha value was 0.05). The calculated t-value was greater than the critical t-value, 4.28>2.920, therefore, p≤0.05. Thus, it was concluded that the data is statistically significant. Therefore, salt tolerant plants can aid in the survival of intolerant to salt plants when subjected to saline water conditions.

Discussion The experiment was conducted to determine whether there is a relation between the presence of a salt-tolerant plant and the growth of a salt-intolerant plant in a salty environment. As predicted, it was observed that the average root length of the mung bean planted with a soybean seed was larger than the average root length of those planted with a radish seed (5.1cm > 2.7cm), which indicates it displayed greater tolerance for higher salt concentrations in the soil2,3,4. When a t-test was performed, the difference between the means was shown to be statistically significant. Previous experiments and research showed that soybean crops have a considerably larger threshold for saline 21

yields over time22. The removal and treatment of excessive salt in the soil is costly and damaging to the ecosystem22,23,24. The introduction of a salt-tolerant crops may be able to help reduce crop loss caused by soil salinization and increase the productivity of the land. Likewise, but on a much smaller non-industrial scale, using a salt-tolerant plant in the garden could also benefit salt-intolerant plants in combating the ever increasingly saline soil caused by climate change.

Figure 1: Mean value of mung bean root length (+/- standard error) when grown (paired) with a salt tolerant plant (soybean) versus an intolerant to salt plant (radish), while all plants were watered with a salt-water solution. soil than radish crops7,12. We believe this may explain why the mung beans planted with the radish showed significantly less root growth. Based on the knowledge that some plants can survive in salted terrains thanks to a special gene that codes for salt bladders, it is possible that the soybean plants absorbed and stored the salt in their bladders and therefore reduce the impact on the salt-intolerant plants2,3,4. Another contributing factor could’ve been that since plants have the ability to interact with neighbouring plants not only for competition but also to work together, the soybean plants could have communicated with the mung beans to aid in the growth13,14. Ultimately, both of these factors could be responsible for the survival of the mung beans in saline soil, whereas it would not have survived otherwise, as observed in the control group.

High salinity levels in the soil are known to be a factor that reduces crop yield since there is a decrease in the plant’s capacity to absorb water, in the available water supply and the water quality, which inhibit growth and development in numerous plants7,15,16. This is because the osmotic pressure of the soil increases as soil salinity increases, making it challenging for plants to extract water7,16,17. Furthermore, the intake of salt ions may be toxic to certain plants, and can also reduce the amount of essential nutrients absorbed12,17. Some plants, such as soy beans18, are able to yield crops at a higher salinity level than other species by undergoing osmotic adjustment in order to retrieve more water in salt concentrated soil environments19. As confirmed from the results of our experiment, it is advantageous to plant soybeans with salt intolerant plants where soil salinity is an issue.

This issue is common in the agricultural sector, where irrigation is widely used20,21. Irrigation consists of the artificial watering of farm fields in order to promote plant growth, in order to increase crop yield to match the demand of a constantly rising global population21. This agricultural practice contributes greatly to salinization. The salt gradually accumulates in the soil and the high concentration stunts plant growth, resulting in smaller 22

Salt-tolerant plants may be especially useful in our planet’s state today. As global warming becomes a progressively urgent issue, soil salinity has augmented with it; in regions where precipitation is decreasing and temperature is rising, salinization will intensify25. It is estimated that 50% of the world’s fertile land will be lost to soil salinity by the middle of the 21st century25.

The nations relying heavily on agriculture will suffer. While we have yet to find better ways to tackle climate change, the ability for salt tolerant plants to sustainably remediate saline ecosystems and help salt-intolerant plants grow is an aspect of optimism for biologists and environmentalists alike26. In the midst of what looks to be an era of environmental desolation and food shortages, perhaps there are biological ways to overcome it.

Although major parts of the experiment were carried out with consistency, challenges arose in creating an ideal environment and temperature for the growth of the plants, considering the lack of sunlight and warmth in the winter months. This may offer an explanation as to why some seeds did not grow. The short time frame allotted for the experiment may have led to rapidly drawn conclusions and is an area for improvement. Perhaps a different outcome would have arisen if the plants were monitored for a longer period of time and under more ideal conditions.

A possible future experiment is to test a multitude of other salt-tolerant plant species, both higher and lower in threshold than the soybean, using the same procedure, and compare the results to those of this experiment to potentially discover connections that will further support our findings.

References 1. Bischoff, J. and Werner, H. “Salt Salinity Tolerance of Common Agricultural Crops in South Dakota”. (March 1999). [Online]. Available: http://www.sdstate.edu/abe/wri/ water-quality/upload/FS903.pdf 2. American Society for Horticultural Science. “Clues to trees' salt tolerance found in native habitat, leaf traits.” ScienceDaily. (2014) [Online]. Available: http://www.sciencedaily. com/releases/2014/11/141117130727.htm 3. Cell Press. “Salt-loving plants may be key to global efforts for sustainable food production.” ScienceDaily. (2014).

[Online]. Available: http://www.sciencedaily.com/releases/2014/10/141028122600.htm 4. University of Adelaide. "Salt tolerance gene in soybean found." ScienceDaily. (2015). [Online]. Available: http:// www.sciencedaily.com/releases/2015/01/150109100949. htm

5. American Society for Horticultural Science. "Salt-tolerant crops show higher capacity for carbon fixation." ScienceDaily. (2011). [Online]. Available: http://www.sciencedaily. com/releases/2011/12/111212124703.htm 6. Pimentel, D. and Pimentel, M. “Population Growth, Environmental Resources, and the Global Availability of Food.”

Social Research: An International Quarterly 66(1). (1999).

[Online]. Available: https://epay.newschool.edu/C21120_ ustores/web/product_detail.jsp?PRODUCTID=1571 7. FAO Corporate Document Repository. “Agricultural Drainage Water Management in Arid and Semi-Arid Areas." Natural Resources Management and Environment Department.

(1999) [Online]. Available: http://www.fao.org/docrep/005/ y4263e/y4263e0e.htm 8. Gerard, Jack. “How to Germinate Soybeans Without Soil” (n.d.) [Online]. Available: http://homeguides.sfgate.com/ germinate-soybeans-soil-44278.html 9. Westover, Jessica. “How Long Does it Take for Radishes to Germinate” (n.d.) [Online]. Available: http://homeguides. sfgate.com/long-radishes-germinate-68498.html 10. Li, Piper. “Factors for the Germination of Mung Beans to Grow”. [Online]. Available: http://www.ehow.com/ list_7018530_factors-germination-mung-beans-grow.html 11. “Growing Soy Bean Sprouts” (n.d.). [Online]. Available: http://sproutpeople.org/growing-soy-bean-sprouts/ 12. "Salinity Problems: Agricultural Drainage Water Management in Arid and Semi-Arid Areas.” FAO Corporate Document Repository. (n.d.) [Online]. Available: http://www.fao. org/DOCReP/003/T0234e/T0234E03.htm 13. McGowan, Kat. “How Plants Secretly Talk to Each Other.”

Conde Nast. (2013) [Online]. Available: http://www.wired. com/2013/12/secret-language-of-plants/ 14. Merchant, et al. “Plant–Plant Interactions. American Society of Plant Biologists.” (2013). [Online]. Available: http:// www.plantcell.org/content/25/5/tpc.113.tt0513 15. Hill, Robert W., and Richard T. Koenig. “Water Salinity and Crop Yield.” Utah State University (1999). [Online].

Available: https://extension.usu.edu/files/publications/publication/AG-425_3.pdf 16. Mass, E. V., and G. J. Hoffman. “Crop Salt Tolerance.”

U.S. Salinity Laboratory Agricultural Research Service. (n.d.) [Online]. Available: http://www.waterrights.ca.gov/ baydelta/docs/southerndeltasalinity/hist_exhibits/1977bdh_p2ex1.pdf 17. Podmore, Cynthia. “Irrigation Salinity - Causes and Impacts.” (Oct. 2009). [Online]. Available: http://www. dpi.nsw.gov.au/__data/assets/pdf_file/0018/310365/Irrigation-salinity-causes-and-impacts.pdf 18. Silvente, Sonia, Anatoly Sobolev, and Miguel Lara. “Metabolite Adjustments in Drought Tolerant and Sensitive Soybean Genotypes in Response to Water Stress.” Public

Library of Science. (2012). [Online]. Available: http:// www.ncbi.nlm.nih.gov/pmc/articles/PMC3369847/ 19. Chen, Hui, and Jian-Guo Jianga. “Osmotic Adjustment and Plant Adaptation to Environmental Changes Related to Drought and Salinity”. “Environmental Reviews.” (Aug. 2010). [Online]. Available: http://www.nrcresearchpress. com/doi/abs/10.1139/A10-014#.VULrOSFVikp 20. “Water.” Eating Ecologically. (n.d.) [Online]. Available: http://www.eateco.org/Environment/Water.htm 21. Nevada Division of Water Planning. "Some Irrigation Methods." USGS. (n.d.) [Online]. Available: https://water. usgs.gov/edu/irquicklook.html 22. “AIC White Papers on California Agricultural Issues.” University of California Agricultural Issues Center. (November 2009). [Online]. Available: http://aic.ucdavis.edu/publications/whitepapers/Soil%20Salinization.pdf 23. Cardon et al. “Managing Saline Soils. Colorado State University.” (December 2014). [Online]. Available: http:// www.ext.colostate.edu/pubs/crops/00503.html 24. Hasanuzzaman et al. “Potential Use of Halophytes to Remediate Saline Soils.” BioMed Research International.

(2014). [Online]. Available: http://www.hindawi.com/journals/bmri/2014/589341 25. Várallyay, G. “The Impact of Climate Change on Soils and on Their Water Management.” Research Institute for Soil Science and Agricultural Chemistry (RISSAC) of the Hungarian Academy of Sciences, Budapest. (2010). [Online].

Available: http://agronomy.emu.ee/vol08Spec2/p08s214. pdf 26. Ashraf, M. Yasin, Abdul Rasul Awan, and Khalid Mahmood. “Rehabilitation of Saline Ecosystems Through Cultivation of Salt Tolerant Plants.” Soil Science Division, Nuclear Institute for Agriculture and Biology (NIAB), Faisalabad, Pakistan. (May 2012). [Online]. Available: http:// www.pakbs.org/pjbot/PDFs/44(SI2)/10.pdf Referee and Editor’s Comment Some assumptions made by the authors require further referencing to assure relevant conclusions. Although appearing logical, such statements still need to be validated by other sources.

The explanation of the soybean salt bladder gene is unclear.

In the introduction, the authors explain that adding this gene would help the salt-intolerant plants, which has been done and studied. However, a few paragraphs before, it is written that this gene has not yet been discovered. The facts seem inconsistent.

The authors hypothesize that planting a salt-tolerant soybean seed will improve the growth and yield of the salt-intolerant plant. Yet, this study has been previously done as stated in the introduction. Preferably, there needs to be something that could differentiate them from the other studies. The high temperature condition to which the plants were exposed to and the number of seeds that has geminated or that has roots are unknown.

23

An Investigation of Skin Flora Growth Patterns Post Ultraviolet Radiation Exposure Fatima Bahsoun, Jonah Elbaz, Jessica Hier and Noah Itovitch Abstract Human exposure to UV radiation is associated with various health risks and the most common source of UV radiation is the sun. This experiment was designed to test the effects of ultraviolet radiation on the growth of bacterial colonies, mainly bacteria found on the skin, such as P. acnes and S. epidermis.

Bacteria samples from the skin were collected, using petri dishes and sterilized swabs, and then exposed to UVR using a UV torch. This experiment was composed of a control group, which was exposed to 0 s of UV radiation, and three experimental groups exposed to 30 s, 300 s, and 600 s of UV radiation.

Each group consisted of three samples. Results obtained from the data collected were robust and showed statistical significance, in which a decrease in the number of bacterial colonies present was observed as the UVR exposure time increased.

The mean of the control group (0 s) was 1466 ± 880.54, and the means of the experimental groups (30 s, 300 s, 600 s) were 106.33 ± 56.77, 0 ± 0, and 0.3 ± 0.47, respectively. The measure of bacterial colonies present post-UVR exposure may have been dependent on the source of the bacterial samples, in addition to the technique in which the bacteria was collected (may have caused contamination). To further back up the hypothesis presented, it would be necessary to do similar testing with flora taken from the skin of a greater number of volunteers.

Introduction: Ultraviolet Radiation affects human beings health-wise1. The source of ultraviolet radiation that humans are most commonly exposed to is the sun. In an adult lifetime, one’s exposure to UVR varies from season to season, in which 30% of their annual exposure is obtained from sun-seeking holidays, 40% from summer weekends and the remaining from daily exposure during the rest of the months3. The skin flora, mostly composed of bacteria, can provide benefits to an individual by preventing transient pathogenic organisms from colonizing the skin’s surface4. Herein, we designed an experiment to test the effects of UVR on the proliferation of skin bacteria in order to determine whether the UV rays eradicate the bacteria present.

An experiment conducted by H.L. Bank and colleagues in1990 was designed to test bacterial effectiveness of modulated UV light5. The results of this experiment showed a decrease in colony size from a confluent lawn to less than 20 colonies after their exposure to UV radiation5. Based on this experiment, it is expected that increased exposure to UV radiation decreases the number of bacterial cells that can develop into colonies, indicating an inversely proportional relationship between the time of UV radiation exposure and the measure of bacterial colonies. It is predicted that if the bacterial samples are exposed to UV radiation for longer periods of time, then the number of

24

bacterial colonies eradicated will increase. This experiment will add to the knowledge of the effects of UV radiation on humans by demonstrating the negative effect it has on bacteria and, therefore, on the beneficial skin flora of humans. The inspiration that lead to the test design came from a prominent concern in today’s society, which is that UV radiation is often associated with the development of a variety of skin diseases such as cancers. Further, what tends to be neglected is another potentially harmful effect of UV exposure. As previously mentioned, epidermal flora performs a specific function to the human body and, if eradicated, the consequences may prove harmful to one’s immune system.

Materials and Methods Bacteria swabs were taken from a male volunteer’s left and right cheek. This was done by using a cotton swab that was submerged in sterilized water prior to the collection of the skin bacteria. The sterilized swab was placed onto the face and swept horizontally across the cheek, then, by using the cross-hatching method, transferred onto the petri dish. A new swab was used for every new bacterial sample collected. This experiment was comprised of a control group (0s UVR exposure) and three experimental groups (30s, 300s, 600s); n=3 per group. Once the bacteria were collected and transferred onto the petri dishes, each sample was exposed to UV radiation for varying times (0-600s) for their allotted time using a UV torch. The control group was exposed to 0 seconds of UVR, the first experimental group was exposed for a time of 30 seconds, the second for 300 seconds and the third for 600 seconds. These chosen times were within 33.3% of the total eradication period of 30 minutes. This was due to the fact that it was necessary to make the exposure representative of the UV radiation absorbed by skin in everyday life, where complete skin flora is not killed. Afterwards, the petri dishes were placed in an incubator for 72 hours so that the bacterial cells present would develop into a macroscopic colony. Following incubation time, the number of colonies in each petri dish was recorded, and the cellular morphology of the bacteria was determined. A gram-stain test was also preformed and indicated that all samples were gram-positive. Once stained and observed under the microscope at a magnification of 1000X, results showed that each colony was composed of gram-positive bacterial cells that had a cellular arrangement of either diplococci or streptococci.

Results Figure 1 illustrates a decrease in the mean of bacterial colonies as the UVR exposure time increases with the mean of the control group (0s) being 1466 ± 880.54 and the means of the experimental groups (30s, 300s, 600s) being 106.33 ± 56.77, 0 ± 0, and 0.3 ± 0.47, respectively. This clearly indicates an inversely proportional relationship between the number of bacterial colonies present and UVR exposure time. The ANOVA test showed that the collected data displayed statistical significance, indicating that, as opposed to the null hypothesis, UV radiation indeed influences bacterial growth.

Figure 1: Mean of the bacterial colonies present after UVR exposure for 0s-600s.

Control (0s) 1466 ± 880.54, experimental (30s) 106.33 ± 56.77, experimental (300s) 0 ± 0, experimental (600s) 0.3 ± 0.47 Table 1: Colony Morphology of Grown Bacterial Colonies on Control and Experimental Groups Cell Shape

Cell Colour

Cell Texture

Cell Arrangement

Gram Positive or Negative

Control White

Circular

White

Smooth, glistening

Diplococci, single coccus, streptococcus

Gram Positive

UV White

Circular

White

Smooth, glistening

Diplococci, single coccus, streptococcus

Gram Positive

UV Yellow

Circular

Yellow

Smooth, glistening

Diplococci

Gram Positive

UV Big

Irregular

White

Wrinkled

Streptobacilli

Gram Positive

Discussion: Considering that previous tests have shown that there is an inversely proportional relationship between exposure to UV radiation and growth of bacterial colonies, the results, showing a statistically significant difference between treatment groups, make sense. This experiment has shown that the null hypothesis, which is that UV radiation does not hinder bacterial growth, can be rejected. Furthermore, there is the possibility that sun exposure can lead to other diseases besides skin cancer.

In this experiment, the main potential source of experimental error lies in the fact that one of the three different types of colonies that experienced growth was irregular in terms of its colony morphology. One type was white, circular and had a smooth surface, another was yellow, circular, and had a smooth surface, and the third type was a large white colony with an irregular shape and texture. The first two types had a coccus cellular shape, whereas the third type had a bacillus cellular shape, calling into question whether this colony originated from contamination. As this large irregular colony was only present once in all 12 samples, this infrequency further supports the possibility that it originated either from air contamination or from another substance that was present on the volunteer’s cheek.

If this was in fact a source of contamination, one can assume that the antiseptic technique was not performed as efficiently as necessary. This may have lead to bacterial growth of bacteria in the air as opposed to skin flora, which was not the design of the procedure followed.

Based on previously performed experiments and the potential source of error previously mentioned, the tentative conclusion obtained is relatively strong. The conclusion states that as the exposure time of skin flora to UV radiation increases, a higher percentage of the bacterial cells will be eradicated.

In conclusion, the results obtained have shown that it may be necessary to take precautions before the skin is exposed to the sun or another source of UV radiation. This therefore contributes to the already existing body of work surrounding the potential harmful effects of UV radiation on skin flora. Knowing this, in addition to protecting one’s skin from UV radiation with the use of sunscreen, it may be necessary to develop a form of similar protection for skin flora. In terms of future directions, one could repeat the experiment using a larger sample size of volunteers and use males and females of a variety of ages. More so, as opposed to simply looking at the rate of bacterial eradication as UV exposure time increases, it would be interesting 25

A Reversed Cauchy-SchwarzBunyakowsky Inequality

to take bacteria that have experienced light exposure to UV radiation and determine if mutations occur, and if so, how they affect the expression of human characteristics.

Jason Da Silva Castanheira and Richard Fournier

References: Bank HL, John J, Schmehl MK, Dratch RJ. "Bactericidal effectiveness of modulated UV light”. [Online]. Available: http:// www.ncbi.nlm.nih.gov/pmc/articles/PMC2746716/ Cogen AL, Nizet V, Gallo RL. "Skin microbiota: a source of disease or defence?". [Online]. Available: http://www.ncbi.nlm. nih.gov/pmc/articles/PMC2746716/.

Diffey, Brian L. "The Impact Of Topical Photoprotectants Intended For Daily Use On Lifetime Ultraviolet Exposure".

[Online]. Available: http://onlinelibrary.wiley.com/enhanced/ doi/10.1111/j.1473-2165.2011.00563.x Tenkate, Thomas D. "Ultraviolet Radiation: Human Exposure And Health Risks" [Online]. Available: http://courses.washington.edu/envh311/Readings/Optional_25.pdf.

Yanhan, Wang, et al. "The Response Of Human Skin Commensal Bacteria As A Reflection Of UV Radiation: UV-B Decreases Porphyrin Production". [Online]. Available: http://journals.plos. org/plosone/article?id=10.1371/journal.pone.0047798.

Referee and Editor’s Comment Ultraviolet radiation was never defined. The authors should have mentioned that it is a part of the electromagnetic spectrum which is emitted by the sun, and which has a wavelength ranging from 10nm to 380nm. They mentioned that future research on this topic should include a bigger sample of individuals but did not consider including other bacterial strains as well.

Another thing that was not specified was the type of solutions in the petri dish. Was it simply agar? The authors of this article also mentioned bacterial morphology in their discussion, but it was not mentioned in the results. This point should have been explained in greater detail. In addition, the null hypothesis was sometimes vague and should have been stated earlier in the text.

Lastly, the p value for the ANOVA test and the type of ANOVA test was not specified.

Abstract The classical Cauchy-Schwarz-Bunyakowsky inequality yields an upper bound for the absolute value of the dot product ‹u,v› of two vectors in an arbitrary pre-Hilbert vector space. In the present work, a lower bound for the same quantity was obtained in the case of a real pre-Hilbert space.

Introduction The Cauchy-Schwarz- Bunyakovsky (CBS) inequality asserts

{ }

that given two sequences, a j real numbers, 2

n

∑a b j

=j 1

j

n

{ }

n

and b j

j =1

n j =1

composed of

n

≤ ∑ a 2j ∑ b 2j (1)

=j 1 =j 1

{ }

with the equality if and only if the sequence a j

{ }

multiple of the sequence b j

n j =1

n j =1

is a

, that is if and only if there

exists a real number K such that aj = Kbj

j =1, 2, 3,…, n

This inequality has a long, rich history and many generalizations and proofs (see [1] and [2] for extensive background information). The following argument is in the spirit of this paper. It is clear that   n    a j −  ∑ ak bk  b j  ∑ =j 1 = k 1    n

0 ≤

2

(2) 2 2 n n n     ≤ ∑ a 2j − 2  ∑ a j b j  +  ∑ a j b j  ∑ b 2j =j 1 = j1 =   j 1=  j1 and the result follows for the special case where n b 2 = 1 The general case follows by considering the n

∑

j =1

.

j

sequence {b j / s}

n j =1

with s =

(∑

n j =1

b 2j

)

1/ 2

; the case of equal-

ity is a trivial consequence of the inequality (2). The purpose of this paper is to obtain a general lower bound for the sum,

∑

n j =1

a jbj

2

, as opposed to an upper bound as in the inequal-

ity (1). Such lower bounds are known to exist (a chapter of [2] is devoted to similar questions); however, it is to the best of our knowledge that they simply depend on additional hypoth-

{ }

eses pertaining to the sequences a j

n j =1

{ }

and b j

n j =1

. More

examples, including a statement slightly less general than the main result, may be found in the classical book of Beckenbach and Bellman [3, pp. 44-45]. It is our desire to obtain a general inequality, applicable to all sequences without constraints.

Note: for the purposes of this paper all vectors will be denoted 26

by u or v,while scalars will be denoted a or b.

Statement of the Result

N

To begin, we shall work in the broader context of the Bessel’s =j inequality. Let V be an abstract, real vector space endowed with 1/ 2

a dot product ‹ ∙ , ∙ › and an induced norm of v = v, v for each vector v∈V . As well-known, Bessel’s inequality consequently states that for any set of vectors {v j }

N

j =1

2

u −

j =1

1 =j 1

N

∑

j ⊂V = with

u, v j

2

N

= u − ∑ u, v j 2

2

1 =j 1 N

u, u − ∑ u, v j v j

=

u∈V,

∑

≤ u u − ∑ u , v j v j (7)

and

v j , vk = δ jk (such vectors are called orthonormal) and any N

N

u, u − ∑ u, v j v j

j =1

u, v j

2

2

≤ u . (3)

It should be obvious that the CBS inequality is simply a consequence of Bessel’s inequality with V = Rn, N = 1 and n

∑u jvj ,

= u, v

u, v ∈ R n

where u = (u1, u2, u3,… , un) and v = (v1, v2, v3,… , vn).

In the same spirit of the above proof of the CBS inequality, we have a quick proof of Bessel’s inequality (3): 2

0 ≤ u − ∑ u , v j v j (4) j =1

N

2

0 ≤ u − 2∑ u , v j 2

+

N

∑

=j 1 =j 1 N

2

0 ≤ u − 2∑ u , v j 2

2

u, v j v j

N

+ ∑ u, v j

2

=j 1 =j 1 N

0 ≤ u − ∑ u, v j 2

(5)

2

. (8)

Conclusion We will conclude this note with some relevant remarks. To begin, the inequality (8) is non-trivial in the sense that the lefthand side of (8) is always positive: indeed, this is equivalent to saying N

N

u − u u − ∑ u, v j v j ≤ ∑ u, v j 2

2

with the left-hand side of the above being equal to N

2

.

j =1

In conceiving our main objective, we shall prove the following ‘reversed’ Bessel’s inequality: Theorem: We have for {u}  {v j } ⊂ V and {v j } orthonorj =1 j =1 mal, N

N

u, v v ≤ ∑

N

j j j 1 =j 1 =

u, v j

2

.

Proof of the Theorem We shall make use of the general CBS inequality [2]

α, β ≤ α β

N

=j 1 =j 1

2

The case of equality in the inequality (3) follows directly from (4): the equality holds in (3) if and only if the right-hand side of (4) vanishes. Consequently, there is equality in Bessel’s inequality if and only if u belongs to the span (v1, v2, v3,..., vN), the vector space generated by the orthonormal vectors (v1, v2, v3,..., vN).

N

N

u − u u − ∑ u, v j v j ≤ ∑ u, v j

u − ∑ u, v j

2

In passing from equation (5) to (6), the Theorem of Pythagoras has been used.

2

i.e.,

=j 1 =j 1

2

v j (6)

j =1

u − u u−∑

j =1

2

j =1

N

N

≤ u u − ∑ u, v j v j

α , β ∈V

We therefore obtain

.

One may also identify all cases of equality of (8): our proof shows that this is equivalent to obtaining equality upholding in (7). It is well-known [2] that this will hold if and only if N

u − ∑ u, v j v j = Ku K is a real number j =1

i.e., if and only if 0 = ‹u, vj› – ‹u, vk› = K ‹u, vk› for all 1 ≤ k ≤ N. This implies that either u is perpendicular to any vector vk or K = 0. We therefore obtain that equality shall hold N in the statement of our theorem if and only if u ∈ span v j

(

{ }

or if u ∈ span v j

span {v j }

N j =1

N j =1

)

⊥

{ }

j =1

, the orthogonal complement of

.

Furthermore, there exists a geometric interpretation of the result: let Bu be the best approximation of the vector u in the vector space generated by the orthonormal vectors Consequently,

{v } j

N j =1

.

Bu = ∑ j =1 u , v j v j and our result amounts N

27

Solutions to First-Order Partial Differential Equations

to N

u − u u − Bu ≤ ∑ u , v j 2

2

Dylan Cant, Alexander Hariton

j =1

Lastly, it is notable to remark that our estimate gives birth to relatively exotic inequalities like

 n 2  n 2  n   n    ∑ a j  −  ∑ a j   ∑  a j −  ∑ a j b j  b j  =  j 1=   j 1=   j 1 = j1    1/2

 n  ≤  ∑ a jbj   j =1  under the assumption

2 1/2

   

2

∑

n j =1

b 2j = 1 . Another example is, using .

this time the vector space V of all functions continuous over an interval [a,b] endowed with the standard integral dot product, b

∫ a

1/2

b  2 2 f ( x ) dx −  ∫ f ( x ) dx  a 

1/2

2 b b    × ∫  f ( x ) − ∫ f ( t ) g ( t ) dt g ( x )  dx  a  a   

b  ≤  ∫ f ( x ) g ( x ) dx  a 

2

for all continuous real-valued functions f, g over the real interval [a,b] such that

b

∫ g ( x)

2

dx = 1

a

References 1. "Cauchy-Schwarz inequality". [Online]. Available: http:// en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality.

2. Dragomir, S.S., "A Survey on Cauchy- BunyakovskySchwarz Type Discrete Inequalities". [Online]. Available: http://emis.matem.unam.mx/journals/JIPAM/images/010_03_JIPAM/010_03.pdf 3. Beckenbach, E.F. and Bellman, R., Inequalities (Springer-Verlag, Berlin, Fourth printing, 1983).

Introduction Differential equations, which relate a function of one or more variables with its derivatives, play an important role in many subjects, including physics, engineering and economics. Such equations arise whenever a relation exists between a continuously varying quantity and its rates of change. If the unknown function is a function of a single variable, then the differential equation is called an ordinary differential equation (ODE). In contrast, a partial differential equation (PDE) is a differential equation involving a function of more than one variable and its partial derivatives. For both ordinary and partial differential equations, the order of the differential equation is the order of the highest derivative appearing in the equation.

However, solving a differential equation in general is not an easy matter. In this paper, we make use of two specific methods for solving differential equations. In the case of a first-order partial differential equation, one method that can be used is the method of characteristic strips [1]. In the case of a system of first-order partial equations involving more than one function, one possible method is the method of Riemann invariants [2,3].

The Method of Characteristic Strips If we consider a first-order partial differential equation of the form F (x, y, u, ux, uy) = 0

(1)

where we use the notation ux = ∂u/∂x and uy = ∂u/∂y, then we look for a solution u(x, y) which consists of an integrable surface in the space {(x, y, u)} consisting of the independent variable u. At each point along the surface the normal vector n to the surface is the gradient of the function Φ(x, y, u) = u(x, y) – u, so n = (ux, uy, –1).

This is so because the surface u = u(x, y) is just a level surface 0 = u(x, y) – u, and level surfaces of a function Φ(x, y, u) = u(x, y) – u are always normal to the gradient of Φ, since moving on a level surface does not change the value of a function. If we let p = ux and q = uy and consider the space involving the five variables x, y, u, p and q, then at each fixed point (x0, y0, u0) along the surface, we obtain a relation: F(x0, y0, u0, p, q) = 0

(2)

relating p and q. This relation eliminates a degree of freedom and allows us to write p and q in terms of a single parameter λ: p = p(λ) and q = q(λ). Therefore, the possible tangent planes at the point (x0, y0, u0) are those whose normal vector is n = (p(λ), q(λ), –1). This gives us a one-parameter family of tangent planes whose envelope is a cone, which we call the Monge Cone [1].

The Monge cone intersects the surface along a specific direc28

tion [4]. Thus, at every point along the surface one obtains a Monge cone together with a direction. The integral trajectory of these directions is a characteristic curve along the surface.

At each point along the characteristic curve lies a tangent plane.

The succession of tangent planes along the characteristic curve constitutes a characteristic strip. The integral surface corresponding to the solution can therefore be constructed from these various characteristic strips.

In order to reconstruct the surface, we begin with an initial curve Γ, which lies along the surface and is parametrized by a parameter s. Along this initial curve we have: x = x(s) y = y(s)

u = u(s) = u(x(s), y(s)). (3)

The first-order partial derivatives, p(s) and q(s) along the initial curve can be determined from the following initial conditions ∂x ∂y ∂u p ( s ) + q ( s ) = (4) ∂s ∂s ∂s F ( x ( s ) , y ( s ) , u ( s ) , p ( s ) , q ( s )) = 0 The characteristic curves and characteristic strips are then constructed from these initial conditions through the following five differential equations [5] for the unknowns x, y, u, p, q as functions of s and t

q =−q + q =0 (8e)

Here a dot signifies differentiation with respect to τ. Since p and q are both equal to zero, we can conclude that they are both functions of s only. That is p(s, τ) = p(s)

q(s, τ) = q(s) (9)

Since g is a function of only p and q we can also conclude that g(s, τ) → g(s) (10) Similarly, gp and gq do not depend on τ.

The equations for x, y, u, that is (8a), (8b) and (8c), become of the form v= v + A ( s ) v − v = A(s)

. (11)

The solution to this (which can be verified by direct calculation) is v(s, τ) = w(s)eτ – A(s) (12) Plugging in gp, gq and –g + pgp + qgq as A(s) for x, y and u, respectively, yields

∂x ∂y = Fp = Fq ∂τ ∂τ ∂u = pFp + qFq ∂τ (5) ∂p = − ( Fx + pFu ) ∂τ ∂q = − ( Fy + qFu ) ∂τ

x(s, τ) = θ(s)eτ – gp (13a)

Here τ parametrizes the characteristic strips, and each function at τ = 0 corresponds to its value along the initial curve.

u(s, 0) = ψ(s) + g(p(s), q(s))

– p(s)gp(p(s), q(s)) – q(s)gq(p(s), q(s)) (14c)

In this way, the solution u(x, y) is constructed as an integral surface.

y(s, τ) = ϕ(s)eτ – gq (13b) u(s, τ) = ψ(s)eτ + g –pgp – qgq (13c) Here p, q, g, gp, gq are all solely functions of s. To find θ(s), ϕ(s) and ψ(s), we need to solve the equations x(s, 0) = θ(s) – gp (s) (14a) y(s, 0) = ϕ(s) – gq (s) (14b)

Clairaut’s equation is [6,7]

We can find x(s, 0), y(s, 0), u(s, 0), p(s) and q(s) from the initial parametrization (initial conditions), and then solve equations (14) to find θ, ϕ and ψ, thereby solving for the parametrized solution completely. If we wish to obtain a non-parametrized solution, we require initial conditions and a choice for g.

u=xux+yuy+g(ux, uy) (6)

The Method of Riemann Invariants

Making the substitution p = ux and q = uy , we get

The method of Riemann invariants can be used to find solutions of systems of first-order partial differential equations of a particular form [2,3]. We suppose that our system of m first-order PDEs for l functions u1, u2, u3, ..., ul of n independent variables x1, x2, x3, ..., xn is of the form:

Example: Clairaut’s Equation

xp + yq – u + g(p, q) = 0

(7)

The characteristic strip equations (5) become x= x + g p (8a) y= y + g q (8b) u = px + qy + pg p + qg q = u − g + pg p + qg q

(8c)

p =− p + p =0 (8d)

α µ sj ( u )

∂u j ∂xµ

= 0 (15)

where we use the summation convention (repeated indices are summed over), and µ = 1, 2, ..., n, j = 1, 2, ..., l, s = 1, 2, ..., m and u = u1, u2, u3, ..., ul .

Riemann made the hypothesis that the partial derivatives can be written in the form [8] 29

∂u j (16) = γ j ( u ) λµ ( u ) ∂xµ We associate each uj with a γj and each xµ with a λµ. Replacing (16) into (15) yields the wave relation: αµsj(u)γjλµ = 0 (17) We can cast the entire system of equations into a matrix equation:  αµ11λµ    α λ  µ m1 µ

 α µ1l λµ   γ 1         = 0 l   αµ ml λµ   γ 

(18)

Example: One dimensional equation for an ideal gas It can be shown that a non-viscous fluid will obey the following equations [9]. The first equation is just F = ma:   ∇ p ∂v  1  ∇φ + + + ∇ × v × v + ∇ ( v ⋅ v) = 0 (26) 2 ρ ∂t

(

)

where ϕ is the external potential per unit mass, p is the pressure, ρ is the density and v is the velocity vector field. The second is the continuity equation:  ∂ρ ∇ρ v + = 0 (27) ∂t

or in shorter notation

First, we assume that v and ρ are functions of x and t only and that the velocity v has a component in the x-direction only, so

Asjγj = 0, for each s (19)

v ( x, y, z.t ) = v ( x, t ) x

where A is the matrix shown above. The m rows represent the m equations and the l columns represent the l unknowns uj or γj . Since this is a homogeneous equation, it will only have a non-trivial solution if

ρ(x, y, z, t) = ρ(x, t) (29)

Rank(A) < l

(20)

If m = l, then A is a square matrix, and this condition becomes detA = 0

(21)

(28)

We also suppose that the fluid is an ideal gas, so that p = c2ρ, where c2 = kT/µ [10], and that there is no external potential so  that ∇φ =0 . Then equations (26) and (27) simplify to ∂v c 2 ∂ρ ∂v + +v = 0 ∂x ρ ∂x ∂t

(30)

∂ρ ∂v ∂ρ Since the αµsj are given, this can only be made solvable by vary+ρ + = v 0 (31) ∂x ∂x ∂t ing the λµ. We choose our λµ such that (20) is satisfied, and then solve the wave-relation (17) for a set of vectors γj(u), λµ(u) that Let’s apply the Riemann hypothesis to (30) and (31): satisfy the wave-relation. ∂ρ ∂ρ ρ = γ= λt γ ρ λx Any two vectors γ, λ which satisfy the wave-relation satisfy ∂t ∂x

(32) equation (16) (by construction), and so the problem reduces to ∂v ∂v v v = γ= λt γ λx solving the system of equations. ∂t ∂x ∂u j (22) Substituting (32) into (30) and (31), we obtain the wave relation = γ j ( u ) λµ ( u ) ∂xµ c2 ρ γ λx + γ v λt + vγ v λx = 0 Noting the formal similarity between (33) ρ ρ v ρ ∂u j ∂ u ∂ u vγ λx + ργ λx + γ λt = 0 j j ∂R j (23) γ= ( u ) λµ ( u ) and ∂xµ ∂xµ ∂R ∂xµ or, in matrix form, we attempt to find a solution  c2  λx λt + vλx   γ ρ   0  ∂u j  ∂R j γ= λµ ( u ) (24) ( u ) and  ρ   γ v  =  0  (34) ∂R ∂xµ  λ + vλ ρλx      x  t (Where R is known as the Riemann invariant).

If this system is to have solutions, the determinant of the matrix The simplest case of R which satisfies (34) must be equal to zero. That is ∂R  c2  = λµ ( u ) λ λt + vλx   ∂xµ det  ρ x =0  is simply when ρλx   λt + vλx n

(35) 2 2 2 ( λt + vλx ) R = ∑ λµ ( R ) x µ (25) c λ= x µ =1

±cλx =λt + vλx

λt = ( ±c − v ) λx

30

If we let ±1 = ε, our λ vectors have the form

p(c(1 + lnρ) – k) – q = 0 (48)

λ = (1, εc–v)λx (36)

Our initial parametrization is x = s, t = 0, ρ = ρ0(s), and the strip equations are

Substituting these back into equation (34) yields  c2  λx ρ  ε cλ x 



ε cλ x   γ ρ   0    γ v  =  0  ρλx     

(37)

∂t = −1 (50) ∂t

from where we obtain c

γ ρ (38) ρ so our γ vectors take the form εγ v = −

 εc  γ 1, −  γ ρ = ρ 

(39)

To simplify our notation, we will write γ as γ and λx as λ. ρ

∂ρ = p ( c (1 + ln ρ ) − k ) −= q 0 (51) ∂t These equations can easily be solved (mainly because ∂ρ ∂t and we obtain

∂ρ = λγ (40) ∂x ∂ρ = λγ ( ε c − v ) (41) ∂t ∂v −ε c (42) = λγ ∂x ρ ∂v −ε c = λγ (ε c − v ) (43) ∂t ρ

Now we depart from the method of Riemann invariants, and look for a solution to the simplified system of equations (40), (41), (42) and (43). These can be combined to eliminate γ and λ.

Combining (43) and (41) together with (42) and (40) yields: −ε c ∂ρ ∂v −ε c ∂ρ = and (44) ∂t ρ ∂x ρ ∂t

x = τ(c(1+lnρ0(s)) – k) + s (52) ρ = ρ0(s) (54) And, after some simplification, x + t(c(1 + lnρ0(s)) – k) = s x + t(c – k) = s – ctlnρ0(s) (55) Now this equation implicitly defines s in terms of x, t. Given ρ0(s), we may be able to explicitly obtain s(x, t), and then plug that back into ρ to obtain ρ(x, t). Once we obtain ρ(x, t), we can substitute that back into v = k – clnρ to obtain v(x, t).

Let us try a solution of the form ρ0(s) = exp(–s/l), where l has units of length [11]. Then (55) can be solved to obtain s(x, t): x + t ( c − k ) =s − ct ln exp ( − s / l ) x + t ( c − k ) =s + x + t (c − k ) =s ct 1+ l

Note that we can impose a physical condition that the velocity changes in the direction of decreasing density (and thus pressure), which is a reasonable steady state condition, and then obtain ε = +1

And so

∂v c ∂ρ =− ∂x ρ ∂x

Then

(45)

This can be integrated to obtain v = –clnρ + k (46) We can then combine (45), (40) and (41) to obtain: ∂ρ ∂ρ = ( c + c ln ρ − k ) ∂t ∂x (47) ∂ρ ∂ρ 0= c (1 + ln ρ ) − k ) − ( ∂x ∂t This is a first-order partial differential equation which can be solved with the method of characteristic strips. With x and t as the independent variables, p = ∂ρ and q = ∂ρ , we obtain ∂x

∂t

= 0 ),

t = –τ (53)

Returning to (32), we obtain 4 differential equations:

∂v ∂x

∂x =( c (1 + ln ρ ) − k ) (49) ∂t

cts l

 x + t (c − k )   l + ct  

ρ ( x= , t ) exp  −

(56)

(57)

v ( x, t )= k − c ln ρ ( x, t ) v ( x, t )= k + c

x + t ( c − k ) (58)

l + ct And so our finished solution is  x + t (c − k )   (59) l + ct  

ρ ( x= , t ) exp  − v ( x, t )= k + c

x + t (c − k ) l + ct

(60)

Now we can verify that these indeed satisfy equations (30) and (31). Let 31

x + t (c - k ) f = l + ct Then ∂f ∂x

(61)

1 ∂f lc − lk − cx

= 2 l + ct ∂t ( l + ct )

(62)

And ∂ρ −ρ = ∂x l + ct ∂v ∂x

∂ρ lc − lk − cx = −ρ 2 ∂t ( l + ct )

∂v c ( lc − lk − cx ) c = 2 ∂t l + ct ( l + ct )

(63)

By substituting the values in (63) into the left sides of (30) and (31), you can see that they do indeed equal zero. So this solution does indeed satisfy the initial equations.

Acknowledgements A. Hariton would like to thank Professor A. M. Grundland for helpful discussions on the subject of this paper.

References 1. R. Courant and D. Hilbert, Methods of Mathematical Physics, Volume II, (New York, John Wiley and Sons, 1962).

2. A.M. Grundland and P. J. Vassiliou “On the solvability of the Cauchy problem for Riemann double-waves by the Monge-Darboux method”, Analysis, 11, 221-278 (1991).

3. B. Riemann “Uber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite”, Göttingen Ab- handlungen, Vol. viii, p. 43 (Leipzig, Werke, 2te Aufl., 1858) p.

157, 1892.

32

4. Specifically, the direction D = n(λ) × n(λ + dλ) ∝ (qλ, –pλ, pqλ –qpλ). But since F(p, q) = 0, F = Fppλ + Fqqλ = 0, and so pλ ∝ –Fq and qλ ∝ Fp. Rescaling the parameter λ can turn this proportionality into an equality. We obtain D = (Fp, Fq, pFp + qFq).

5. These equations are simply the requirements that the strip be tangent to the characteristic direction D = (Fp, Fq, pFp + qFq) and that the tangent strip be tangent to the tangent plane.

6. D. Zwillinger, Handbook of Differential Equations, (San Diego, CA, Academic Press, 1989).

7. S. Iyanaga and Y. Kawada, Encyclopedic Dictionary of Mathematics, (Cambridge, MA, MIT Press, 1980) p. 1446.

8. Some motivation for this assumption can be found in the ∂u j

formal similarity with: .

∂xµ

=

∂u j ∂R ∂R ∂xµ

9. R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lectures on Physics, Volume II (Chapter 40), (California Institute of Technology, 1964).

10. Here µ is the mass per atom, k is the Boltzman constant 1.38×10–23J∙K–1 and T is the temperature in Kelvin.

11. This initial condition could represent an infinitely dense well of gas to the left of the origin. We should add a prefactor of A0 in front of the exponential, where A0 has units of density, but here we just assume A0 = 1 for simplicity.

33

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