PennScience Volume 9 Issue 1

Interviews

Research Articles

Dr. David Roos DEPARTMENT OF BIOLOGY

Dr. Helen C. DaviesDEPARTMENT OF MICROBIOLOGY

Features

Parental care as seen in foraging bouts of mo-nogamous owl monkeys (Aotus azarai azarai)RACHEL GITTELMAN

Two-Player Zero-Sum Poker Models with One and Two Rounds of Betting HANZHE ZHANG

Low Energy Ultrasonic Irradiation: Potential Applications in Oil Refinement JAMES MANDAGLIO

How Vaccines are Made

Vaccines: Why People Say ‘No’

The H1N1 PandemicBRIAN LAIDLAW & VARUN PATEL

SANDERS CHANG & ISABEL FAN

SALLY CHU & ANGELO LEE

Research at Penn

A Good Infection: Using Bacteria to Fight Cancer

Understanding the Yersinia pestis bacterium

Quorum-Sensing Bacteria in Cholera Patho-genesis

Contents

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About

Journal Staff EXECUTIVE BOARD

Editors-In-ChiefVishesh AgrawalAJ Argall

Layout ManagersIsabel FanHijoo Karen Kim

Editing ManagersBrian LaidlawNikhil Shankar

Publicity ManagerIris BraunsteinSteven Chen

Assistant Layout ManagersSteven Chen

Assistant Editing ManagersVarun PatelZhu WangEmily Xue

Writing ManagersBrian LaidlawIsabel Fan

WebsiteRaghav Puranmalka

EditingAbraham ChanalesSanders ChangSally ChuRachel GrosserSarah JohnsonJenny LinQinnan LinSusan ShengJiaming Zhang

WritingSanders ChangSally ChuAngelo LeeSusan Sheng

Faculty AdvisorsDr. M. Krimo BokretaDr. Jorge Santiago-Aviles

Cover DesignMaggie Edkins

GENERAL STAFF

PennScience is a peer reviewed journal of undergraduate research published by the Science and Technology Wing at the University of Pennsylvania. PennScience is an undergraduate journal that is advised by a board of faculty members.

PennScience presents relevant science features, interviews, and research articles from many disciplines including biologial sciences, chemistry, physics, mathematics, geological sciences, and computer sciences.

PennScience is a SAC funded organization.

For additional information about the journal including submission guidelines, visit http://www.pennscience.org.

PennScience

Dr. Helen C. DaviesDEPARTMENT OF MICROBIOLOGY

Copyright © 2010 PennScience Journal of Undergraduate Research. The authors of the individual re-search articles published in this journal retain all rights to their work. No part of PennScience Journal of Undergraduate Research may be reprinted, reproduced, or transmitted in any form or by any means without permission in writing from PennScience or the individual authors, whichever is appropriate.

Research Laboratory at the Hos-pital of the University of Pennsyl-vania ca. 1940. Photo courtesy of University Archives.

Letter from the EditorsDear Readers,

We are proud to introduce you to our 9th volume of PennScience and our first as Editors in Chief. We have dedicated ourselves to continuing the strong tradition of PennScience by further improving upon the quality of the journal and its content in order to better inform our readers about important and in-teresting topics in science.

The theme of this issue, Infectious Diseases, was inspired by a resurgence of interest following the H1N1 pandemic. Most notably, Vice President Joe Biden encouraged Americans to avoid confined areas, and many Penn upperclassmen will remember long lines of students waiting to get vaccinated. To an ex-tent, this was justified: the WHO approximates 17,000 deaths were caused by the virus. However, H1N1 symptoms rarely exceeded those of the typical seasonal flu.

The PennScience staff decided to examine infectious diseases from a range of viewpoints. We spoke with two Penn faculty members, Professors David Roos and Helen Davies, who are doing groundbreak-ing research in the field of infectious disease. Additionally, our Writing committee has written a series of compelling articles on the issue. Isabel Fan and Sanders Chang examine how vaccines are made and tested, and why they work. Other articles include an account of the H1N1 pandemic and an analysis of why people are often skeptical of vaccines. We also present a series of features examining the exiciting research happening in the Microbiology Department. Challenging the widespread view that microbes are bad, one article explains a cancer treatment proposal using bacteria to initiate an immune response against tumors. Additional articles delve into the complexities of quorum sensing bacteria and novel ways to prevent the harmful effects of potential bioweapons.

As always, this semester’s PennScience has several terrific undergraduate research papers. Hanzhe Zhang presents an analysis of poker play using game theory. Rachel Gittelman has studied a rare spe-cies of owl monkey that exhibits male paternal care. Finally, James Mandaglio presents a review of low energy ultrasonic radiation and how it might be used in oil refinement.

We would like to thank the groups and individuals that make our work at PennScience possible. First, we owe our funding to the Student Activities Council and the Science and Technology Wing, without which we could not publish a high-quality journal in full color. Second, we would like to thank our fac-ulty advisors for their constant support and insight. Lastly, we would like to thank the Penn faculty that took the time to meet with us to discuss their research.

Thank you for reading PennScience, and we hope you enjoy our latest issue!

Sincerely,

Arthur Argall and Vishesh AgrawalCo-Editors-in-Chief

www.pennscience.org 4

The 2009 H1N1 PandemicBRIAN LAIDLAW & VARUN PATEL • University of Pennsylvania

THE VIRUS EMERGED FROM THE MOUNTAINS OF MEXICO, RAPIDLY DESCENDING ON AN UNSUSPECT-ING AND VULNERABLE POPULATION. As the virus’ reach extended to more countries, panic spread along

with it as governments resorted to quarantines and the mass slaughter of pigs in an attempt to slow the

virus down (1). It had begun in April of 2009, a time of year normally associated with the end of flu season,

as large numbers of Mexicans suddenly became sick with a flu-like illness (2). However, unlike the seasonal

flu, which most people have some immunity against, this flu seemed to be an entirely different strain. By the

end of April, 113,000-375,000 Mexicans had already become infected with the new virus, and the number of

cases was still increasing (3). Despite the aggressive actions of the Mexican government, which by the end of

April had closed all schools and public gathering places in the country, the virus would not be contained. The

first cases in the United States were reported as early as late March with confirmed cases in all fifty states by

the end of May (4). In June 2009, as the outbreak spread to all corners of the globe and the total number of

cases continued to increase, the World Health Organization (WHO) declared the H1N1 influenza outbreak a

pandemic, the first since the 1968-69 flu season which claimed an estimated one million people worldwide.

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PennScience Journal of Undergraduate Research VOL 9 ISSUE 1, FALL 2010

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The H1N1 virus differs from the normal seasonal flu by its genetic makeup. Each flu season, one to two different strains of influenza circulate within the general popula-tion causing infections. As the flu season progresses and

people gain immunity, the strain loses its ability to infect new in-dividuals. However, through a process known as antigenic drift, the virus is able to mutate itself in such a way that individuals are no longer protected against that strain. It is for this reason that a vaccine against the flu is only effective for one or possibly two years, forcing scientists to constantly develop new vaccines against strains circulating in a given year. Despite this constant mutation, people maintain a certain base level of protection since they have been exposed to a similar strain of the flu, thereby limiting the potential for an outbreak to occur. On rare occasions, however, through a process called antigenic shift, influenza undergoes a complete change in genetic makeup into a strain never exposed to humans and to which we have no immunity. This complete lack of protection leaves people extremely vulnerable to infection and creates the kind of conditions necessary for a pandemic.

It was exactly this type of scenario that occurred in the spring of 2009. Through a gene reassortment between North American and Eurasian swine H1N1 viruses, as well as the avian flu, a novel strain of influenza emerged against which people had very little to no immunity (2). This lack of protection allowed the virus to sweep across the world at a rapid pace, reaching pandemic status within months of its emergence. In addition to this rapid spread, several other disturbing characteristics of the virus soon began to emerge. Typically, influenza heavily affects the young and elderly, leaving those with a strong immune system relatively unaffect-ed. However, H1N1 exhibits the reverse pattern of infection and seems to target those who are most healthy. The unique pathogen-esis of the virus became increasingly clear throughout the fall as the pandemic swept through college campuses, infecting students by the hundreds. Another ominous observation was that there al-ready were a high number of cases by November, whereas there are normally few cases during this time. Given that the flu season generally peaks in February, it seemed possible that the situation would continue to worsen. Since a hallmark of the 1918 influenza pandemic, which killed an estimated fifty million people world-wide, was its ability to infect those with healthy immune systems, many were concerned that the virulence of the H1N1 virus could be similar to that strain of influenza (5).

With this concern in mind, many researchers have studied the virulence of the H1N1 virus using animals. Using mamma-lian models, one group found that H1N1 was more pathogenic than the seasonal flu and had an ability to replicate in the lung and cause appreciable damage, a trait shared by highly pathogenic viruses. It was suggested that sustained person-to-person trans-mission of the virus could result in the emergence of more patho-genic strains (6). This result was confirmed using ferrets, finding that H1N1-infected ferrets had higher levels of virus then those

infected with seasonal strains (7). While the ferrets infected with seasonal flu only had viral replication in the nasal cavity, H1N1 infected ferrets had replication in the trachea, bronchi, and bron-chioles. Despite this increased virulence compared to the seasonal flu, H1N1 was determined to be a relatively mild virus compared to more pathogenic strains such as the 1918 flu (7).

H1N1 was able to efficiently replicate in human immune cells such as macrophages and primary dendritic cells and displayed an ability to avoid the activation of the innate immune response (1). The replication speed of H1N1 was determined to be compa-rable to that of the seasonal flu but it failed to generate the type of robust cytokine response that is a distinguishing characteristic of pathogenic strains. For example, it was found that H1N1 in the vast majority of cases only resulted in a mild respiratory tract illness similar to that of the seasonal flu. H1N1 infection did re-sult in gastrointestinal symptoms in a significant number of cases which is atypical in the seasonal flu (2). The mortality rate for H1N1 is comparable to the less than 0.1% rate of the seasonal flu with estimates ranging from 0.4% by the WHO to a more recent estimate by Dr. Marc Lipsitch of Harvard of 0.007-.045% (8).

In addition to the relatively low mortality rate of the virus, the number of new cases has also declined since reaching its peak of about 10,000 new cases per week, reported by the CDC in Oc-tober 2009. This drop is largely attributable to the introduction of the H1N1 vaccine along with the fact that most of the people susceptible to the virus had already been infected. This allowed the number of positive cases in 2010 to stay below 500 per week as of March 13th (9). The mortality rate due to pneumonia and influenza has also dropped below epidemic threshold and is once again comparable to the seasonal baseline. Considering that the mortality rate before the vaccine was produced was on pace to be well above the epidemic threshold, this result is a testament to the effectiveness of vaccines in limiting the number of new infections (10).

Despite the worst of the H1N1 pandemic seemingly being be-hind us, there is still cause for concern. Due to influenza’s ability to swiftly mutate, there is a constant threat of the emergence of a more virulent form of the virus. One mutated influenza strain D222G has already been identified and was found in 11 out of 61 severe cases in Norway. This mutation is hypothesized to al-low the virus to bind more efficiently to lung cells and cause symptoms similar to those found in infection with the 1918 flu (11). However, doubts remain towards the ability of this mutated strain to allow efficient transmission of the virus. Furthermore, it is unclear whether this mutation is associated with increased virulence, as Dr. Nancy Cox of the CDC commented: “If you look globally you can see that this mutation is neither necessary nor sufficient for a severe or fatal outcome” (12, 13, 14). In addition to this mutation, numerous cases of antiviral resistant H1N1 strains have been found, raising the possibility that our current antivirals


may lose much of their potency in treating those infected with H1N1 (15). Thus, while the pandemic seems to have ended, it is still necessary to be vigilant for any changes which might result in the emergence of a new and potentially more virulent form of the virus.

References

1. Ballantyne C. 2010. Will Egypt’s plans to kill pigs protect it from swine--sorry, H1N1 flu? Scientific American. <http://www.scientificamerican.com/blog/60-second-science/post.cfm?id=will-egypts-plans-to-kill-pigs-prot-2009-05-01>

2. Osterlund P, Pirhonen J, Ikonen N, Rönkkö E, Strengell M, Mäkelä SM, et al. 2009. Pandemic H1N1 2009 Influenza A Virus Induces Weak Cyto-kine Responses in Human Macrophages and Dendritic Cells and Is High-ly Sensitive to the Antiviral Actions of Interferons. Journal of Virology. 84(3):1414-22

3. Lipsitch M, Lajous M, O’Hagan JJ, Cohen T, Miller JC, et al. 2009. Use of Cumulative Incidence of Novel Influenza A/H1N1 in Foreign Travelers to Estimate Lower Bounds on Cumulative Incidence in Mexico. PLoS ONE 4: e6895.

4. Fox M, Whitcomb D. 2009. US swine cases hit all 50 states. Reuters. <http://www.reuters.com/article/idUSN01480382>

5. Morens DM, Fauci AS. 2007. The 1918 influenza pandemic: insights for the 21st century. J Infect Dis. 2007 Apr 1;195(7):1018-28.

6. Itoh Y, Shinya K, Kiso M, Watanabe T, Sakoda Y, Hatta M, Muramoto Y, et al. 2009. In vitro and in vivo characterization of new swine-origin H1N1 influenza viruses. Nature. 460(7258):1021-5.

7. Munster VJ, de Wit E, van den Brand JM, Herfst S, Schrauwen EJ, Beste-broer TM, van de Vijver D, Boucher CA, Koopmans M, Rimmelzwaan GF, Kuiken T, Osterhaus AD, Fouchier RA. 2009. Pathogenesis and transmis-sion of swine-origin 2009 A(H1N1) influenza virus in ferrets. Science. 325(5939):481-3.

8. Fox M. 2009. Swine flu death rate similar to seasonal flu: expert. Reuters <http://www.reuters.com/article/idUSTRE58E6NZ20090916>

9. Center for Disease Control. 2009. CDC Estimates of 2009 H1N1 Cases and Related Hospitalizations and Deaths from April 2009 - January 16, 2010, By Age. <http://www.cdc.gov/h1n1flu/estimates_2009_h1n1.htm>

10. Center for Disease Control. 2010. 2009-2010 Influenza Season Week 9 ending March 6, 2010. < http://www.cdc.gov/flu/weekly/>

11. Kiland A, Rykkvin R, Dudman SG, Hungnes O. 2010. Observed associa-tion between the HA1 mutation D222G in the 2009 pandemic influenza A(H1N1) virus and severe clinical outcome, Norway 2009-2010. Euro Sur-veill. 15(9):2

12. World Health Organization. 2009. Preliminary review of D222G amino acid substitution in the haemagglutinin of pandemic influenza A (H1N1) 2009 viruses. <<http://www.who.int/csr/resources/publications/swine-flu/cp165_2009_2812_review_d222g_amino_acid_substitution_in_ha_h1n1_viruses.pdf>

13. Racaniello V. 2009. The D225G change in 2009 H1N1 influenza virus is not a concern. < http://www.virology.ws/2009/11/24/the-d225g-change-in-2009-h1n1-influenza-virus-is-not-a-concern/>

14. CIDRAP. 2010. H1N1 mutation’s proposed link to severe illness de-bated. <http://www.cidrap.umn.edu/cidrap/content/influenza/swineflu/news/mar0410mutation.html>

15. Janies DA, Voronkin IO, Studer J, Hardman J, Alexandrov BB, Treseder TW, Valson C. 2010. Selection for resistance to oseltamivir in seasonal and pandemic H1N1 influenza and widespread co-circulation of the lineages. Int J Health Geogr. 9(1):13.Photo credit: @istockphoto.com/bovinicus

FIGURE: Progression of laboratory confirmed H1N1 influenza cases and deaths by May 2009. Courtesy of the World Helath Organization.


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EVERY YEAR, MILLIONS OF FLU SHOTS ARE ADMINISTERED IN SCHOOLS AND CLINICS. In response to major outbreaks

like avian flu, SARS, and H1N1, governments, health organiza-

tions, and research institutions collaborate to distribute vac-

cines to those at risk. Vaccines play a critical role in the well-

being of countless people each year, whether they are being

used to suppress the seasonal flu or prevent a major global

epidemic. However, it is crucial that we do not overlook the

research and testing involved in vaccine development in or-

der to better appreciate their contributions to global health.

SANDERS CHANG & ISABEL FAN • University of Pennsylvania

HowVaccines

areMade


The human body is trained to induce an immune response whenever it comes in contact with a foreign pathogen. Antibodies are synthesized that can specifically bind to the antigens or the

surface proteins of the pathogen. These antibodies then mark the pathogen for destruction by white blood cells. To prepare the body for future invasions of the same pathogen, memory cells are created that can immediately synthesize these antibodies, allowing the body to respond more quickly to infections of this pathogen (1). A vac-cine works by introducing a manageable, weakened form of the pathogen to the body. The body responds to the weakened pathogen as if it were an actual infection, pro-ducing memory cells that can prepare it from actual in-fections of the pathogen. Depending on the way they are made and their safety, vaccines are divided into five differ-ent categories: attenuated, inactivated, subunit, conjugate, and toxoid.

The attenuated vaccine uses a live, weakened form of the virus. This virus can still reproduce within the body but at a reduced rate. Attenuated vaccines have been used to protect against relatively common diseases such as measles, mumps, and chickenpox. One common way to create this vaccine is to grow generations of it in cultured cells. This environment causes the virus to accumulate a wide range of mutations, which reduces its reproduc-tive capability to the point that it can safely be introduced to the human body (2). An advantage of this vaccine is that with the virus still alive, the body can produce a full-fledged immune response. One or two vaccinations can thereby assure lifelong immunity to the virus. However, the fact that the virus can still reproduce suggests that it can mutate back to its highly virulent form. Therefore, at-tenuated vaccines are usually not administered to indi-viduals with weakened immune systems.

Used to create immunity against polio, Hepatitis A, and influenza, an inactivated vaccine is composed of a pathogen that has been killed through the use of radia-tion, heat, or chemicals (2). This process prevents patho-gens from mutating back to their virulent forms. Chemi-cal inactivation can also be used to produce immunity against bacteria that secrete toxins . These toxoid vaccines utilize bacterial toxins which have been inactivated by an aqeous formaldehyde solution called formalin (2). As a result, the im-mune system develops immunity against the active form of the toxin as well. These vaccines are used in the immunization of teta-nus and diphteria.

Another type of vaccine is the subunit vaccine. The subunit vaccine is made from the surface antigens of the pathogen (2). There are several ways to create the subunit vaccine. One way is to

chemically disintegrate the pathogen into its individual parts and filter out its antigens. Another way is to manufacture the antigens separately from the virus via DNA recombination. This method is utilized in creating hepatitis B vaccines by genetically transform-ing yeast with viral genes coding for its antigens. A special type of the subunuit vaccine is the conjugate vaccine, which makes use of the sugar coating of the infectious bacteria in question. Some-times, immunity against certain bacteria relies on the ability of the body to recognize this sugar coating of the bacteria (3). How-ever, it is found that the immune systems of infants and children

FIGURE: The process of developing a West Nile Virus VaccineSource: National Institute of Allergy and Infectious Diseases (NIAID)


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are unable to recognize this sugar coating. Scientists devised a way to avoid this problem by creating vaccines that have the sugar coating linked to the antigens and toxins of the bacteria that can be easily recognized by the immune system (2). Some examples of conjugate vaccines include Haemophilius influenza B and pneu-mococcal vaccines.

Current research is beginning to focus on the DNA vaccine. This vaccine makes use of the phenomenon that foreign DNA in-troduced to the body can be taken up by cells. This causes these cells to manufacture and display these antigens on their surfaces, thus inducing an effective immune response (2). This vaccine does away with the need to use the physical form of the pathogen to induce an immune response. Moreover, this vaccine is generally cheaper and easier to make than other vaccines being used. Meth-ods of ensuring that cells in the body take up the DNA include shooting DNA-containing gold particles into the body’s cells or linking the DNA with molecules that can be easily taken up by the cells (2). However, there is still the concern that this method of vaccination can induce an unwanted autoimmune response or mutagenesis of the cells (4).

Once a vaccine is developed, rigorous testing is conducted that may last from a couple of months to many years before the vaccine can be licensed and provided to the public. The National Institute of Allergy and Infectious Diseases (NIAID), a branch of the National Institutes of Health, oversees the entire process of vaccine testing, monitoring the thousands of individuals who volunteer to be a part of these clinical trials and maintaining ef-fective communication of research laboratories, pharmaceutical companies, and clinics involved (3, 5). The first level of testing is done with a subject pool of around one hundred patients or less who have relatively little susceptibility to the illness. The purpose of this phase is to simply determine whether the vaccine is safe to administer and whether it has any effect on physiological defense mechanisms. Vaccine safety is more firmly validated in the sec-ond level of testing, where it is tested by hundreds of people who tend to be at a higher risk of contracting the disease (3).

Rather than just testing whether the vaccine induces a re-sponse, the third level truly determines if the vaccine has the ex-pected effects. This phase of testing utilizes thousands of subjects from a large geographic distribution and can take years to verify whether the vaccine successfully results in the correct immune response (3). The Food and Drug Administration (FDA) must confirm the clinical design and the validity of the data (5). The FDA then passes this information to the Advisory Committee on Immunization Practices (ACIP) of the Centers for Disease Con-trol and Prevention (CDC) and other coalitions who then decide whether the vaccine should be licensed, and if so, how it should be distributed (3). If the vaccine receives acknowledgement and validation from the ACIP and the other committees, it can be dis-tributed to the public.

After the vaccine is provided to the public, the Food and Drug Administration along with the Centers for Disease Control and Prevention continue to monitor test subjects from all three lev-els of testing for any side effects that might arise after testing has concluded. The FDA and CDC also collects reports of adverse re-sponses to the vaccines among the public. Consequently, no mat-ter how many trials of testing are conducted, there always exists the possibility that vaccines go awry (5). People have argued that some vaccines have resulted in detrimental and sometimes fatal effects. For instance, some have argued of a strong link between meningococcal vaccine and Guillain-Barre syndrome, hepatitis B vaccine and multiple sclerosis, and other vaccines to disorders such as autism and even sudden infant death syndrome (6). As a result, there is a significant population who prefer not to receive vaccines and risk contracting infections. (7).

“A vaccine works by introducing a manageable, weakened form of the pathogen to the body. The body responds to the weakened pathogen as

if it were an actual infection.”

References

1. “Immune System: Mounting an Immune Response” National Institute for Allergy and Infectious Diseases. Web. 20 Feb 2010. <http://www3.niaid.nih.gov/topics/immuneSystem/response.htm>.

2. “Types of Vaccines” National Institute for Allergy and Infectious Dis-eases. Web. 1 Mar 2010. <http://www3.niaid.nih.gov/topics/vaccines/understanding/typesVaccines.htm>.

3. “How Are Vaccines Made?” The Children’s Hospital of Philadelphia. Mar 2008. Web. 20 Feb 2010. <http://www.chop.edu/service/vaccine-educa-tion-center/vaccine-science/how-are-vaccines-made.html>.

4. Hunt, Dr. Richard. “Vaccines: Past Successes and Future Prospects.” Uni-versity of South Carolina School of Medicine. 24 Nov 2009. Web. 1 Mar 2010. <http://pathmicro.med.sc.edu/lecture/vaccines.htm>.

5. “Vaccine Development and Testing” U.S. Department of Health and Hu-man Services. Aug 2001. Web. 10 Mar 2010. <http://www.hhs.gov/nvpo/factsheets/fs_tableII_doc1.htm>.

6. “Vaccine Safety” Centers for Disease Control and Prevention. 24 Mar 2010. Web. 26 Mar 2010. <http://www.cdc.gov/vaccinesafety/Concerns/Index.html>.

7. Seppa, Nathan. “What’s Behind Latest Phobia Towards Vaccines?” Science News. U.S. News and World Report. 4 Nov 2009. 26 Mar 2010. <http://www.usnews.com/science/articles/2009/11/04/whats-behind-latest-phobia-towards-vaccines.html>.

8. “Annual Influenza Vaccine Production Timeline.” Figure. Influenza.com, Flu Information and Influenza Prevention. 09 Mar 2007. Web. 26 Mar 2010.<http://www.influenza.com/Index.cfm?FA=Science_History_6>.

Photo credits: @istockphoto/batman2000, @istockphoto/svengine


SALLY CHU & ANGELO LEE • University of Pennsylvania

IN 1950, THERE WERE 50 MILLION CASES OF SMALLPOX WORLDWIDE. TODAY, THERE ARE NONE. While

this may be one of the more striking examples of vaccines’ success, it is far from the only one. Vaccines were

developed in order to minimize the illness and death that often ravaged unprotected populations. They are

able to do this by training the human body to resist a disease through exposure to a weakened or altered form

of that disease. This prevents future infections and helps stop the spread of disease. This quest to eradicate

disease through vaccination is largely responsible for the increase in life span experienced in most parts of the

world during the last century, and is a vast improvement over gaining immunity to a disease by surviving it (2).

Vaccines: Why People Say No


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Despite the overwhelming success vaccines have had, they are still looked upon with suspicion by many people. This is largely due to misconceptions people hold towards vaccines. One common misconception

is that because there is better hygiene in the world today and no recent cases of a disease, vaccines are unnecessary. However, those who believe this tend to neglect to consider that people from other countries could be carriers of the disease, or that the disease could mutate and reemerge (3). As a result, these peo-ple are shocked when they find that people are still becoming ill with the disease, and falsely conclude that the vaccine is to blame for the new cases of the disease. They presume that vac-cines are 100% effective, even though immunity successfully de-velops in only 85-95% of the vaccine’s recipients (4). They ignore the fact that in the vast majority of cases vaccines only have tem-porary or minor side effects, and they focus on a few select cases where side-effects are major or vaccination failed, and therefore they resist getting a vaccine. These exaggerated thoughts may develop from irrational belief persistence.

Irrational belief persistence occurs when people insist on be-lieving something that has been proven to be false. Even work-ers in health care are prey to this phenom-enon. In a survey of physicians, nurses and administrators, respon-dents “in all three pro-fessional groups who were unvaccinated dur-ing the current season were significantly more likely than the vaccinated respondents to overestimate several of the surveyed adverse-effect rates” (5). Similarly, at Penn, although the H1N1 flu vaccine is available to Penn students, not everyone chooses to get it; this may be be-cause of overestimation of the adverse effects of the H1N1 vac-cine. In particular, there have been reports linking thimerosal, an ingredient in some vaccines, to autism in children (6). While these reports have since been discredited and the paper with-drawn, people still persist in believing the H1N1 vaccine causes autism, especially due to media coverage and the comments of public figures (7). President Obama announced, “We’ve seen just a skyrocketing autism rate. Some people are suspicious that it’s connected to the vaccines. The science right now is incon-clusive, but we have to research.” (8) Since negative statements tend to resonate more with people, the second part of President Obama’s statement is likely overshadowed by the first, thereby fueling the phenomenon known as availability bias. Availabil-ity bias is a human cognitive bias in which people overestimate probabilities of events associated with memorable or vivid oc-currences (9). People often subconsciously use the availability bias when making decisions by considering the readiness with which similar memorable events come to mind (10). For in-

stance, although plane crashes are exceedingly rare, many peo-ple overestimate their occurrence because the media extensively covers such a tragedy when it does occur.

It is true that if a vaccine is given to someone in poor health or someone who has been immunosuppressed, he or she may experience serious side effects. However, that is no reason for those with healthy immune systems to refuse vaccinations. Yet many people still do refuse vaccines because they believe the vaccine will give them the very disease it is protecting them against. Part of the reason for this is because there is no placebo against which vaccines are tested. Also, people tend to learn only some of the facts surrounding vaccines, and thus they are not aware, for instance, of the extent to which the FDA tests every vaccine before permitting its release to the public. According to one survey conducted in Pittsburgh, PA, almost one-third of the health care workers, excluding doctors and nurses, believed that vaccines were not a safe and effective way to prevent infec-tion. 36% of those surveyed believed that vaccines are safe in pregnancy (many are not) (11). In addition, this survey found that in many cases the most experienced nurses were not the people who were most knowledgeable about symptoms of in-

fluenza. This proves that within health care, just as in the public, there are some people who are unaware of, or mis-informed about, impor-tant health information

As mentioned ear-lier, the link between vaccines and thimerosal is an example of people falling victim to misinformation. Despite the paper link-ing these two being since disproven and withdrawn, there are still many adults who know nothing of the removal of the paper and still tend to believe that thimerosal causes autism. This is due to lack of general public knowledge - while thimerosal has a mercury ingredient in it, it is generally harmless. People know mercury can be harmful to the body, but they don’t know that mercury comes in different types, including methylmercury and ethylmercury. The latter is used in vaccines, and is pro-cessed more quickly than the former so that there is minimal accumulation in the body. This greatly reduces the possibility of it having any harmful effect on the body. However, most simply believe that because thimerosal has mercury in it, the vaccine is dangerous and could induce autism in unborn children; thus, many parents allow their children to go unvaccinated.

The media in many cases exacerbates this problem through

coverage that employs fear tactics to draw in viewers. As people tend to find negative stories more memorable then positive ones more due to cognitive biases, coverage focusing on the fears about vaccines rather than the facts can result in people per-

“Irrational belief persistance occurs when people insist on believing something that

has proven to be false. Even workers in health care are prey to this phenomenon.”


FIGURE: Decline of Scarlet Fever, Diphtheria, Whooping Cough, and Measles

ceiving vaccines as dangerous. This bias against vaccines is what viewers take away from the program causing them to ignore those who encourage people to get vaccinated. People seem to put more weight on the consequences of their actions, as op-posed to those of their inactions. This is called the omission bias. Professor Jonathan Baron of the University of Pennsylvania psy-chology department defines omission bias as “the tendency to favor omissions (such as letting someone die) over otherwise equivalent commissions (such as killing someone actively).” It seems that parents feel more guilt if their child dies from a vac-cination received at their urging than if their child dies from the disease naturally. From a normative standpoint, the parents should feel equal guilt for the death caused by administering or failing to administer the vaccine.

I. Ritov and J. Baron, in an experiment to find the connection between omission bias and vaccination, found that “subjects are reluctant to vaccinate a child when the vaccination itself can cause death, even when vaccine-related mortality is far less likely than death by the would-be-vaccinated disease.” (13) This study was conducted by surveying the responses of 53 under-graduates to situations in which they had a choice between vac-cinating their children against dangerous disease using a vac-cine which in very rare cases can lead to death, or allowing their children to go unvaccinated. From this, the two concluded that parents would be unwilling to vaccinate their children if the death rate from the disease was less than 10 times higher than the death rate from the vaccine (14). However, since hypotheti-cal questions were used to obtain the results, generalizing the

validity of the results to real world vaccination is not completely valid. To test the validity of omission bias in the real world, Baron conducted another survey concerning parents’ thoughts in administering the DPT vaccine to their children. Baron also found that some respondents who believed the DPT vaccination was beneficial still resisted vaccination and others resisted vac-cination because they believed the vaccine was harmful, proving that “omission bias is not confined to hypothetical cases pre-sented in the laboratory.” (16)

In order to minimize the number of deaths from viral ill-nesses, it is important to compare the relative costs and benefits of vaccination and nonvaccination without favoring inaction over action. Perhaps people should heed the advice of Benjamin Franklin. In his autobiography, Franklin said, “In 1736 I lost one of my sons, a fine boy of four years old, by the small-pox, taken in the common way. I long regretted bitterly, and still regret that I had not given it to him by inoculation. This I men-tion for the sake of parents who omit that operation, on the sup-position that they should never forgive themselves if a child died under it; my example showing that the regret may be the same either way, and that, therefore, the safer should be chosen.” (17)

References

1. “Disease Decline before Introduction of Immunization.” Vaccination. Web. 17 Mar. 2010. <http://www.whale.to/vaccines/decline1.html>.

2. “Vaccine Benefits.” National Institute of Allergy and Infectious Dis-eases. Web. 1 Mar. 2010. <http://www3.niaid.nih.gov/topics/vaccines/understanding/vaccineBenefits.htm>.

3. “Vaccines: Vac-Gen/Why Immunize?” Centers for Disease Control and Prevention. 6 Aug. 2009. Web. 1 Mar. 2010. <http://www.cdc.gov/vac-cines/vac-gen/why.htm>.

4. “Vaccines.” Centers for Disease Control and Prevention. Web. 20 Mar. 2010. <http://www.cdc.gov/vaccines/pubs/vis/default.htm>.

5. Ehrenstein, M.D., Boris P., Frank Hanses, M.D., Stefan Blaas, M.D., Falitsa Mandraka, M.D., Franz Audebert, M.D., and Bernd Salzberger, M.D. “Per-ceived Risks of Adverse Effects and Influenza Vaccination: a Survey of Hospital Employees.” Oxford Journals | Medicine | European Journal of Public Health. 20 Jan. 2010. Web. 10 Mar. 2010. <http://eurpub.oxford-journals.org/cgi/content/full/ckp227v1>.

6. Betz, Ph.D., RN, FAAN, Cecily. “Educating the Public About H1N1.” Journal of Pediatric Nursing 24.6 (2009): 445. ScienceDirect. Web. 1 Mar. 2010. <http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WKM-4XR8SRH-5&_user=489256&_coverDate=12%2F31%2F2009&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docaPhoto credit: @istockphoto.com/markchentx

“People seem to put more weight on the consequences of their ac-tions, as opposed to those of their

inactions.”


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SARS, AVIAN FLU, AND SWINE FLU are just some of the diseases that have hit

the news headlines in recent years. Over the years, various infectious diseases

have risen to infamy; at the same time, as doctors and scientists study these dis-

eases, some have fallen to obscurity as new treatments and preventative meth-

ods are discovered. At the University of Pennsylvania, many researchers are study-

ing different aspects of various disease-causing agents in the hopes of finding

vaccines and treatments. Read on to learn more about three of these researchers.

Research at Penn


Since the anthrax attacks in 2001, researchers such as Dr. Dieter Schifferli, Associate Professor of Microbiology at the University of Pennsylvania, have become interested in studying the Yersinia pestis bacterium because of its

potential for use as a bioweapon.

Yersinia pestis is perhaps best known for causing the “Black Death” that swept through Europe during the 14th century, killing 25 million people (25% of Europe’s population) over a 5 year period (3). Several centuries earlier, in the 6th century, the plague traveled throughout much of the known world, causing 100 million deaths over a 50 year period. Y. pestis is responsible for causing bubonic, septicemic, and pneumonic plague; the manifestation of the disease is dependent on the method and location in which the bacterium infects the host. With modern antibiotics, individuals with bubonic plague can be treated ef-fectively if the disease is detected early. Primary pneumonic plague however, which results from aerosolized Y. pestis enter-ing the lungs, is much more deadly, and often kills the patient within 3-5 days. Thus, there is much concern currently over the potential weaponization of Y. pestis into an aerosolized form.

The fear of the weaponization of Y. pestis is not without his-torical precedence. As early as 1346, the bodies of plague victims were being used as weapons as the Tartars catapulted the bod-ies over the walls of the city now known as Feodosia in a battle against Genoese merchants, hoping to create an epidemic in-side the city (6). During World War II, records indicate that the Japanese successfully tested different variations of a “flea bomb” on Chinese villagers and prisoners, with the intent of dropping the bomb – a “ceramic container filled with plague-infested fleas and flour” – on San Diego, California (4). Furthermore, both the United States and Soviet Union experimented with aerosolized Y. pestis during the 1950s and 1960s.

There is currently no licensed vaccine against the disease in the United States. During the Vietnam War, a formalin-killed Y. pestis vaccine was used by the US military. Although effective against bubonic plague, this vaccine did not efficiently protect

against pneumonic plague. A vaccine used in other countries (including the former Soviet Union) is based on an attenuated strain – a strain of the bacteria missing a large region of DNA, which renders it less harmful – but that vaccine is not used in the U.S. due to severe secondary side effects. An experimental vaccine which targets two proteins associated with Y. pestis is currently being developed and tested. While this new vaccine appears promising, Dr. Schifferli and other researchers are working to find additional bacterial proteins to target, which would make a vaccine even more effective in protecting against infection by a greater variety of Y. pestis strains.

The long-term goal of Dr. Schifferli’s lab is to understand how bacterial pathogens initiate their infectious process. The lab studies bacterial ligands that bind the bacteria to receptors on host cells, mediate colonization, host cell signaling, and/or opti-mal toxin delivery. The hope is that an improved understanding of how bacteria infect the host and promote infection will lead to new targets for prophylactic and therapeutic treatments. For instance, one type of ligand being studied is bacterial fimbriae, which are hair like protein structures on the surface of the bac-teria. These structures, which coil in a helical formation, help the bacteria adhere to each other and to host cells. In Y. pestis, the structure of a major type of adhesive fimbriae (designated Psa) is comprised of only one repeating subunit protein. These fimbriae are being examined as a potential target for a vaccine or therapeutic treatment; if the fimbriae are unable to attach to host cells, then infection can be delayed or even prevented.

Using mouse models and attenuated strains of Y. pestis, Dr. Schifferli and his team have been working to develop a method that would target the bacterial fimbriae and improve the prog-nosis of infected individuals. If the progression of pneumonic disease can be slowed down, then the ability of medical profes-sionals to recognize and treat infected individuals in time is improved. Additionally, Dr. Schifferli has been looking at ways to mimic the specific region of host receptors that are targeted by the bacteria. If successful, therapeutic treatments such as a nasal spray could be developed. The spray could be provided to individuals at high risk for exposure (e.g. soldiers or research-ers); in the event of exposure, individuals could quickly use the

SUSAN SHENG, University of Pennsylvania

Understanding the Yersinia pestis bacterium


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spray, which would enter the respiratory system and coat it with molecules mimicking host receptors. Y. pestis would then bind to the mimic receptors instead of host cells, and the severity of infection would be reduced.

Inevitably as our knowledge of the world increases, the po-tential for that knowledge to be harnessed for malicious pur-poses also increases. Fortunately, researchers including Dr. Schifferli are already developing ways to counter these emerg-ing threats.

References

1. Dieter M. Schifferli, Description of Research Expertise. [Internet] Philadelphia (PA): University of Pennsylvania School of Veterinary Medicine; c2010 [cited 2010 March 20] Available from: http://www.vet.upenn.edu/FacultyandDepartments/Faculty/tabid/362/Default.aspx?faculty_id=4382134

2. Division of Vector-Bourne Diseases. Information on Plague. [In-ternet]. Fort Collins (CO): Center for Disease Control and Prevention; [modified 2005 March 30; cited 2010 March 20]. Available from: http://www.cdc.gov/ncidod/dvbid/plague/info.htm

3. Douglas Fix, Yersinia [ Internet] Carbondale (IL): Southern Illinois University Carbondale; c1997-2010 [cited 2010 March 20] Available from: http://www.cehs.siu.edu/fix/medmicro/yersi.htm

4. GlobalSecurity.org, Plague (Yersinia pestis) [Internet]. GlobalSecu-rity.org; c2000-2010 [modified 2007 October 23; cited 2010 March 20] Available from: http://www.globalsecurity.org/wmd/intro/bio_plague.htm

5. Tami Port, What Are Bacterial Fimbriae? [Internet] Microbiology: Suite10; 2009 March 9 [cited 2010 March 20] Available from: http://microbiology.suite101.com/article.cfm/what_are_bacterial_fimbriae

6. Thomas Johnson, A History of Biological Warfare from 300B.C.E. to the Present [Internet] Irving (TX): American Association for Respira-tory Care; [cited 2010 March 20]. Available from: http://www.aarc.org/resources/biological/history.aspPhoto credits: @istockphoto.com/theasis, @istockphoto.com/janrysavy

FIGURE: The 987P-like CS18 fimbriae of human enterotoxi-genic Escherichia coli ON phase variants. (Molecular Mi-crobiology, Volume 48, Number 1, 2003, cover illustration)

Dr. Jun (Jay) Zhu, an assistant professor in the Penn De-partment of Microbiology, is studying the process of “quorum sensing” in bacteria, specifically in Vibrio cholerae, the bacterium responsible for the disease chol-

era. Research on cholera can have profound and pressing health implications. In addition, the study of quorum sensing can shed light on an important and prevalent function of a wide range of bacteria.

Quorum sensing is not unique to V. cholerae and was in fact first described in V. fischeri, a strain of bacteria that produces biolumi-nescence only when the bacteria achieves a high density of cells in the light organs of certain species of marine fish. The behavior im-plies a method of communication between single-celled bacteria, usually through a diffusible molecule produced by the bacteria that “autoinduces” their neighbors. This autoinduction process was dis-covered in the late 1970’s, but it wasn’t until Dr. Zhu’s mentor, Dr. Steve Winans, a professor at Cornell University, coined the term “quorum sensing” in the 1990’s to describe it, that the process be-came more widely researched and was found to occur in a number of different bacterial strains.

Dr. Zhu has focused his study of quorum sensing on the bacte-ria that cause cholera, a disease that poses a serious global health threat even though it is no longer common in the United States (2). Cholera is most often acquired from drinking water contami-nated with V. cholerae, especially in developing countries without sophisticated methods of waste treatment. If left untreated, it can lead to death within days from dehydration due to diarrhea and vomiting. Cholera is also a disease particularly prone to epidemics, as waste carrying the V. cholerae bacteria from infected patients can contaminate a local water supply and increase the rate of infec-tion, often to the thousands of cases (3). Partly because of its high pathogenicity, the CDC has listed cholera amongst potential agents of bioterrorism, making understanding its transmission and infec-tious behavior even more crucial (4).

Dr. Zhu explains that the quorum sensing process employed by V. cholerae is notably different from the system used by other in-fectious disease-causing bacteria, which do not become pathogenic until a critical mass of the bacteria has been reached in the host. This is achieved through an auto-inducing molecule produced by the bacteria that in high concentrations activates concentration-dependent gene transcription of a “virulence factor” that actually

Quorum-Sensing Bacteria in Cholera PathogenesisEMILY XUE, University of Pennsylvania


causes the disease. Though V. cholerae follows the same concen-tration-dependent model of transcription, its pathogenesis is just the opposite, as quorum sensing is actually used to repress the virulence factor. Due to the relatively fast progression of the disease, the bacteria produce the cholera toxin shortly af-ter colonizing the intestine, sickening the host and allowing the bacteria to multiply rapidly. The resulting high concentration of V. cholerae’s auto-inducing molecules causes these molecules to diffuse back into the bacteria, and quorum sensing deactivates pathogenesis and allows the bacteria to escape from the diseased host. Dr. Zhu notes that this unusual method of quorum sensing behavior could lead to treatments for cholera by targeting the quorum sensing pathway, effectively minimizing the virulence of a V. cholerae infection – though he also notes that such treat-ments would require more research.

Dr. Zhu’s research focuses on the complex gene regulatory network in V. cholerae as a result of quorum sensing. There are inherent difficulties in studying the behavior of bacteria that cause disease in living organisms, especially because this behav-ior may be quite different in vitro. Dr. Zhu’s lab uses in vivo mod-els to most accurately reflect the variety of environmental fac-tors that affect bacteria in the host, measuring the expression of genes through a recombinant genetic reporter system.

In addition to the virulence controlled by quorum sensing in Vibrio cholerae, Dr. Zhu also has an interest in biofilm for-mation, another factor related to quorum sensing. Biofilms can be defined as microorganisms attach to a surface to form 3-D complex structures. Both bacterial biofilms and quorum-sensing systems fundamentally blur the distinction between unicellular and multicellular forms of life. V. cholerae bacteria form bio-films in aquatic environments to help them resist harsh condi-tions. Biofilms also protect V. cholerae when traveling through the low pH environment of the host’s stomach. Once the bac-teria reach the target site, quorum sensing allows the bacteria to detach from the biofilm, aiding colonization of the intestine, an integral step in the progression of the disease.

In gaining a greater understanding of quorum sensing in V. cholerae, Dr. Zhu can shed light on various stages in the course of a cholera infection through knowledge of both pathogenesis and bacterial environmental survival. This understanding may one day lead to novel methods of combating cholera and is in-creasing our knowledge of an integral and widespread function of bacteria.

References

1. Dr. Jun Zhu. Personal interview. 10 March 2010.

2. National Center for Zoonotic, Vector-borne, and Enteric Diseases. Chol-era. [Internet]. Centers for Disease Control and Prevention; [modified 2009 July 17; cited 2010 March 21]. Available from: http://www.cdc.gov/nczved/divisions/dfbmd/diseases/cholera/

3. World Health Organization. Global Epidemics and Impact of Cholera. [Internet]. World Health Organization; [modified 2010; cited 2010 March 21]. Available from: http://www.who.int/topics/cholera/impact/en/in-dex.html

4. National Center for Zoonotic, Vector-borne, and Enteric Diseases. Bac-terial Zoonoses Branch. [Internet]. Centers for Disease Control and Pre-vention; [modified 2009 August 11; cited 2010 March 21]. Available from: http://www.cdc.gov/nczved/divisions/dfbmd/bzb/

FIGURE: “We love quorum sensing.” An example of bioluminescent quorum sensing bacteria in vitro (picture provided by Dr. Zhu)

“Dr. Zhu has focused his study of quorum sensing on the

bacteria that cause cholera, a disease that poses a serious

global health threat...”


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VISHESH AGRAWAL, University of Pennsylvania

A Good Infection: Using Bacteria to Fight Cancer

Traditional cancer therapies such as chemotherapy and radiation therapy often have detrimental side effects due to the treatments’ lack of specificity. Research con-ducted by Dr. Yvonne Paterson in the Department of

Microbiology at the University of Pennsylvania may present an alternative approach to treating cancer. Instead of using radia-tion therapy, surgery or chemotherapy, Dr. Paterson’s research seeks to use bacteria to activate the body’s own immune response against cancer cells. Her lab uses the pathogen Listeria monocy-togenes to activate the innate immune response toward particular tumor factors.

Listeria is an unusual pathogen that can live and replicate in the cytosol of Antigen Presenting Cells (APCs). APCs are a group of cells that include macrophages, dendritic cells and B cells that can activate CD4+ and CD8+ T cells. Dr. Paterson has geneti-cally engineered these bacteria to preferentially express a tumor antigen after the bacteria have infected cells. Tumor antigens are proteins which are usually expressed at very high levels in cancer cells and include BCR/ABL, Her2-Neu, and HPV-16 oncogenes. These proteins are often oncogenic and overexpressed, which causes cancerous growth.

When Listeria bacteria produce tumor antigens within the cytosol of APCs, these immunogenic peptides are transported to the endoplasmic reticulum and then exported to the cellu-lar membrane of APCs complexed with Major Histocomptabil-ity Complex (MHC) proteins. T-cells bind to the MHC-peptide complex and recognize the tumor antigen as a threat.

These T-cells then activate an immune response towards cells that display these proteins. Because tumor cells usually express these proteins at high levels, these peptide MHC complexes are more likely to be found on the surface of cancer cells than on normal human cells. As a result, the immune system is activated to eliminate tumors. This is especially useful because tumors themselves are not particularly immunogenic. Human cells are designed to be recognized as “self” by the immune system and avoid being attacked by immune cells, and because tumors arise from normal humancells, they often do not invoke a strong im-mune response. However, by infecting a patient with Listeria the immune system is preferentially activated to target cancer cells expressing the antigen expressed by both the cancer cell and the Listeria bacterium.

The use of Listeria for the treatment of cancer has been great-ly helped by the work of Dr. Paterson. Experiments done in mice have demonstrated that Listeria-based immunotherapy is effec-

tive in treating cancer. This research has also moved into human clinical trials with a Phase I clinical trial using Dr. Paterson’s research having recently been completed. This is the first clinical trial to use live-attenuated Listeria for the treatment of cancer (1). Patients in this study had advanced stage, metastatic, cervi-cal squamous cell carcinoma and had failed to respond to che-motherapy, radiotherapy, and/or surgery. These patients were infected with tumor antigen expressing Listeria. The tumor an-tigen used in this trial was HPV-16, E7, a protein specific for cer-vical cancer. Patients in this trial showed an increase in survival with over half showing disease stabilization while a third of the patients showed tumor regression.

This immunotherapy method presents an interesting and novel approach to fighting cancer. It can be used to specifically target cancer and has been shown to be effective in causing tu-mor regression. An added benefit is that this approach is likely to cost much less than traditional cancer therapies. Additionally, perhaps the most interesting outcome of this research is the rela-tively decreased severity of side effects. Most patients displayed flu-like symptoms after infection with Listeria, a much less se-vere side effect than cancer patients normally experience.

References

1. Maciag PC, Radulovic S, Rothman J. (2009). Vaccine. 27(30):3975-83.

2. Personal interview with Dr. Yvonne Paterson.

FIGURE: Listeria bacteria living inside Antigen Presenting Cells. Courtesy of the Paterson Lab.


Interview with David S. Roos, Ph.D.

David Roos is the E. Otis Kendall Professor of Biol-ogy at Penn, where he runs a research laboratory integrating cell biology, biochemistry, immunol-ogy, genomics, and computational approaches to explore eukaryotic evolution and the genetics of host-pathogen interactions. Focusing on the proto-zoan parasites Plasmodium falciparum (malaria) and Toxoplasma gondii, the Roos lab studies molecular mechanisms of drug action and resistance, the origin of subcellular organelles, immune effector pathways, and comparative genomics. Dr. Roos also directs the Eukaryotic Pathogen Genome Database (EuPathDB.org), one of four national bioinformatics resource centers for biodefense and emerging pathogens, and was Founding Director of the Penn Genomics Institute. Roos graduated from Harvard College in 1979, received his Ph.D. in Virology from The Rocke-feller University in 1984, and did post-doctoral work at Stanford University before joining Penn in 1989.

Your lab work focuses on host-pathogen interac-tions, and you also teach a course on infectious disease biology. Can you give us an overview of what your research is about?

My laboratory studies protozoan parasites – unicellular eu-karyotes (cells with nuclei) that are responsible for diseases like malaria. While Plasmodium has been eliminated from the US, malaria remains a huge problem globally, causing more than one million deaths each year – and the problem is growing, due to the emergence and spread of drug resis-tance. Toxoplasma is even more common: about 30% of the U.S. population is thought to be chronically infected. Unlike malaria, which is transmitted by mosquitoes, Toxo-plasma is carried by cats, which shed oocysts in the feces that can survive in the environment for decades. Dogs, pigs, sheep, and other animals get infected by nosing around in contaminated soil. Humans can become infected by play-ing in sandboxes, gardening, or eating improperly washed vegetables. Infected animals develop a ‘tissue cyst’ form that can be transmitted in undercooked meat – so both veg-etarians and carnivores are at risk for infection! Toxoplas-mosis isn’t usually a problem in healthy adults, but it’s a se-rious concern if you are immunosup¬pressed (in AIDS, or for cancer chemotherapy). Toxoplasma is also a notorious congenital pathogen, since primary infections can cross the placenta during pregnancy.

Beyond the clinical importance of these parasites, our re-search is also driven by the insights that these parasites pro-vide into basic cell biological processes and evolution. We would like to understand the interactions between patho-gens and their hosts, and Toxoplasma turns out to be a very convenient experimental system, allowing us to carry out the same kinds of manipulative experiments that biologists use to study E. coli, or fruit flies, or guinea pigs. We can use these parasites to learn what is shared among all eukaryotic cells (including ourselves), and also about the diversity of life … keeping in mind that whatever distinguishes a para-site from its host provides a possible target for killing the pathogen without harming the patient.

Are there clinical applications of your studies on mechanisms of drug action and resistance?

Contrary to popular opinion, there is no shortage of effective treatments for infectious diseases. Thousands of drugs can kill TB, or flu, or malaria – or cancer, for that matter – but they’re not much use if they kill the patient as well! The chal-

INTERVIEWS


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lenge is to discriminate between healthy cells and the disease. What makes penicillin so effective is that it prevents the syn-thesis of the cell wall that is necessary for bacterial survival, but this structure is completely lacking in humans. Similarly, sulfa drugs inhibit the enzymes used by bacteria to make folic acid – which we eat as a vitamin (as the side of your cereal box will tell you). Sulfonamides are also effective against Toxoplasma and Plasmodium, but unfortunately, their target enzymes can acquire mutations that block drug binding without inhibiting function. That’s the basis of drug resistance. We are trying to discover what genes are targeted by effective drugs whose mechanism of action is unknown, what mutations might lead to resistance, and ways of combating this, by developing better inhibitors or new treatment strategies.

How do you integrate computational biology into your research?

It turns out that computational approaches aren’t all that different from the many other strategies we pursue in the lab. Immuno-logical, molecular genetic, cell biological and biochemical studies all use distinct techniques to provide complementary answers to biological questions, like the parable of the blind men and the elephant. Technological advances have brought about an infor-mation explosion in biology and medicine – as in many other ar-eas of life, from weather forecasting to the financial sector – and advances in computer hardware, software, databases, and algo-rithm development helps us to make sense of this data, allowing us to conduct experiments in silico. We now know the complete sequence of the human genome, the Toxoplasma genome, the malaria genome, and even the mosquito genome. We are learn-ing where every gene is, when it is turned on, and the distribution of different alleles in individuals from all over the world. That’s a lot of information! And things get even more challenging – and more interesting – when we start to put these pieces together to figure out how entire biological systems operate. I have always been keen to adopt new technologies, and have been interested in computers for a long time, so my lab has used computational approaches to make sense of genomic-scale datasets for the para-sites we study, helping to identify genes, determining when and where they are used, developing algorithms to figure out what they might do, and analyzing potential functions in the context of the many other activities taking place simultaneously in the same biological system.

The demand for computational biologists is increas-ing. Where do you see this area going in the future?

You’re certainly right to notice the increasing demand for compu-tational biologists. We live in a data-rich age, and I don’t see any signs that this is about to change. When I was a gradate student, it was difficult to do experiments, but the results were usually easy

to understand. Now we can probe all of the genes in a parasite (or a person) in a single afternoon, generating millions of data points. Instead of spending years trying to figure out how to do an experi-ment and days figuring out what our data means, we now spend days on the experiment … but months or years in data analysis.

Computational biology provides many challenges, and many op-portunities. One challenge is that the scientists most familiar with isolating culturing parasites from an infected animal may be less familiar with statistical and computational approaches … and vice versa. On the positive side, computational experiments have the advantage that they can often be carried out rapidly, and with-out expensive reagents. It is easy to waste thousands of dollars on an unsuccessful ‘wet’ lab experiment, and changing the param-eters means further financial investment, but on the computer, we can simply run the analysis again.

Were you trained as a computational biologist?

No, I wasn’t. This field didn’t really develop as a distinct discipline until fairly recently. We established one of the world’s first pro-grams in computational biology at Penn, in 1993. As it happens, however, I had the good fortune of growing up in an area that was part of a pioneering computer education project developed at Dartmouth College. Local students were introduced to com-puters in grade school: like many of my classmates, I wrote my first computer program in the second grade, which was unheard of in the 1960s! I wasn’t as heavily into computers as many of my friends, but I certainly developed some familiarity with what computers can do, so that when I was confronted with large-scale datasets in my career as a biologist, I was perhaps more familiar than some of my colleagues with how computers might help us to connect the dots. With a sense of what should be possible, I have been able to assemble a spectacular group of colleagues to help put this vision into practice.

Can you tell us about your decision to go to graduate school? What advice do you have for undergraduates thinking about pursuing a PhD?

There are lots of people who have always known that they wanted to go into biomedical research. Not me. I knew something about biology, because my father was an endocrinologist, and I grew up pretty close to nature as a kid in rural New Hampshire, but I had no idea what I wanted to do as an undergraduate. I started out as an art major. Science classes do a great job of teaching a lot of information, but they tend not to be so good at getting students to understand how anyone ever figured all that stuff out. I ended up working in a laboratory almost by accident, and found out that I really enjoy the process of scientific discovery. It’s like a giant puzzle that you get to work on all the time, with a lot of smart people. I think that if you enjoy doing crossword puzzles, or play-


ing Scrabble, you might find that you are good at science. I try to teach a bit about how scientists think to my students in Biology 406 (Molecular Mechanisms of Infectious Disease Biology).

One of the discoveries that my laboratory is best known for is figuring out that malaria and Toxoplasma parasites harbor a dis-tinctive subcellular organelle that they stole from an ancestral plant, and that this ‘apicoplast’ provides a novel target for drugs that don’t kill people. All of the pieces of this puzzle were already known: the parasite genome, the subcellular organelle, the drugs, but we were able to put these pieces together, which was pretty ex-citing. Science is full of such discoveries, which help to keep you going in the face of the frustrating fact that most of what we try to do in the lab doesn’t work, and everything takes much longer than expected!

I work in infectious disease biology for various reasons: because pathogens provide a fantastic way to explore how biology works, and because they are so important in human health on a global scale. I have run a five continent lab for many years, and the para-sitology area provides plenty of opportunity for travel. One of the unanticipated pleasures of computational biology is that so much of our work is internet-based, so we can easily collaborate with colleagues all over the world.

In the current state of economy, many labs are finding it difficult to find research funding. How do you think this will affect students who are applying to graduate school? And how will it affect their careers?

Based on my own experience, and the many students who have passed through my lab (now quite a large sample: about 50 un-dergraduates, 20 PhD students, and 30 post-doctoral fellows), I am quite confident in saying that if you work hard, keep your eyes open, and think imaginatively, there are always possibilities and opportunities. It is certainly a time of high anxiety for scientific research, as it is for other areas of the economy. But my experi-ence has been that there has never been anything I felt that we really needed to do for which it hasn’t been possible to obtain the necessary support, sometimes from unexpected sources.

Interview by Zhu Wang

Interview withHelen C. Davies, Ph.D.

Helen C. Davies, Ph.D. is a professor in the Univer-sity of Pennsylvania School of Medicine, where she serves as academic coordinator of Microbiology as well as Ombudsman for Graduate and Medical Stu-dents. She has been teaching at Penn since 1962, notably in an infectious diseases course that has won praise for her inventive use of music as a mem-ory device. She has been widely acclaimed for her passion and dedication in her work with students, as evidenced by her numerous teaching awards in-cluding the Lifetime Mentor Award of the American Association for the Advancement of Science, Penn’s All-University Lindback Award for Distinguished Teaching, and the American Medical Student As-sociation’s National Excellence in Teaching Award.

How did you become interested in the study of infectious diseases? Why study infectious dis-eases?

When I was in grade school and read books on micro-biology, I thought it was fascinating and that’s what I’ve wanted to do since I can remember. It’s important because as diseases emerge, as they become virulent, as we lose the ability to treat them, we will all be dying off.

“I work in infectious disease biol-ogy for various reasons: because pathogens provide a fantastic way to explore how biology works, and because they are so important in

human health on a global scale.”


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21

Would you say there is a disease or group of diseas-es that pose the most threat?

One is MRSA, which is methicillin resistant staphylococcus aureus; it’s very virulent and we have very few antibiotics that work for it, so it could kill off a large number of people. There’s ebola, which you may have heard about, where the pa-tient bleeds through every orifice. There are a number of very deadly diseases, and they are extremely important. There are also diseases like C. difficile, which you also may have heard of.

What are some of the things that are being done to combat these diseases?

We keep looking for new antibiotics for those that aren’t vi-ruses, as well as new antivirals, and so far we have managed to keep ahead of the really problematic emerging infectious diseases. But we’ve also seen the emergence of viruses, bac-teria, and parasites that have no antivirals, antibacterials, or anti-parasites that will work on these organisms, so that’s our big problem.

Might this have something to do with modern med-icine, such as by inadvertently causing resistant strains as we attempt to treat them?

Yes, one of our problems is that we feed animals antiviral, anti-parasitic, and antibacterial materials, and this builds up the amount of immunity to these organisms and causes problems for us. Most of the antibacterials that are sold in the United States, for instance, are sold for animal use, and that creates an enormous amount of resistant organisms. If we could stop that from happening, we’d be much better off. But at this point, “big pharma” – that is, the big pharmaceutical companies – don’t seem willing to give that up.

So, you believe that at this point trying prevent these diseases from arising in the first place is more effec-tive than the attempts to combat them after the fact. What other advances have there been in the field of infectious disease treatment or research?

What we’re looking forward to right now is a kind of personal-ized way of dealing with infectious diseases. We need to look at each of the infectious diseases, and see how they impinge upon a particular person, and deal with that. For instance, if we have a human being who has a genetic tendency to get a certain disease, we can deal with it for that person differently than we can for other people. So this is a personalized kind of method for dealing with infectious diseases.

For instance, people with Crohn’s disease have a tendency to get C. difficile, and we need to deal with it for those individuals

in a different way than we do for others. It’s a more personal-ized way of working, which will be more expensive, but will hit the disease in a more targeted way.

Would that be addressed with medicines? What other aspects are there in considering individuals?

Working with the individual is useful not just for infectious diseases, but for all types of medicine. It’s an exciting field to be in, so if you’re planning on going into medicine now is a great time to do it.

Infectious diseases have been especially prominent in the news lately. What was your take on how some of these issues, such as the recent H1N1 outbreak, were treated?

The whole business of the influenza was carried through pretty well. What happens with different viruses, for instance, is that they can get into a certain species and “mix” there and come out to be much more damaging than they were individually. What happened with H1N1 was that it started in Mexico and came from there to the US, and we tried very hard to make vaccines for it, and did make some pretty effective vaccines. But what happened in the mixing of flus is that we had to deal with things such as avian flu, which is much more harmful than swine flu. But we do now have vaccines for many differ-ent flu types. I would also urge anyone who hasn’t gotten the vaccine to do so. Another observation is that students of high school age and younger are much more aware of infectious diseases now than they used to be. Students from Sayre High School who come here to Penn and attend lectures in infec-tious diseases, are fascinated by infectious diseases and they want to know as much as you can tell them about staphylococ-cus, and streptococcus and various viruses; they are just fasci-nated and are constantly asking questions. I think infectious diseases have become something that even young kids want to know about, which is great.

Can you describe your teaching interests?

My interest is in teaching about emerging infectious diseases, and teaching in such a way that students will understand and retain the information.

I’ve heard you have some very interesting ways to help your students to remember the things you teach; can you give us some examples?

One thing I do is to teach with music, which is a good thing to use because your brain can remember so much more when it’s set to music.

Interview by Emily Xue


IntroductionMale parental care is more commonly seen among pri-

mates than in most other mammalian taxa, but is still quite rare when compared to the rest of the animal kingdom (Charpentier et al 2008; Fernandez-Duque et al 2009). It is hypothesized that male parental care will be observed more frequently when paternal certainty is high or as a mating strategy to demonstrate parental ability to a future mate (Fernandez-Duque et al. 2007). Among both human and nonhuman primates, parental care behaviors include car-rying, grooming, playing, sharing food, feeding, retrieving, huddling, babysitting, defending and teaching (Fernandez-Duque et al. 2009). All of these behaviors increase the prob-ability of infant survival and development.

The owl monkeys of the Argentinean Gran Chaco (Ao-tus azarai azarai) are one taxon of primates that do show intensive male parental care. Owl monkeys are monoga-mous and live in groups consisting of one pair-bonded adult male and female and two to four young (Fernandez-Duque et al. 2009). For most of the time in the several months af-ter a birth all infants are carried by a parent (ie. the mother and suspected father), with the father shouldering up to 90% of these carrying responsibilities (Fernandez-Duque 2009). Adult males have also been shown to transfer food to juveniles and infants in the group more often than females (Wolovich et al. 2007). While there is strong evidence for paternal care in terms of food sharing and carrying, less evidence has been reported in terms of babysitting, which is another important form of parental care. Additionally, little is known about how the parental responsibilities may shift as the infant gets older. This study examined social inter-actions during feeding bouts as a way to analyze the roles of adult males and females in the care of infants and older young. Because individuals tend to forage with their groups, the bouts provide a useful opportunity to observe individual relationships and group dynamics, all important factors in studying paternal care.

The groups included in this study reside in the Estancia

Guaycolec, a cattle ranch in the Province of Formosa, Ar-gentina that contains small forested areas in which the mon-keys reside. The owl monkeys in this region are cathemeral, meaning that they are most active at dawn and dusk but still show activity, including feeding bouts, throughout the day. During a feeding bout the group will move from tree to tree feeding on a variety of leaves and fruits. The order in which each monkey in the group enters and leaves the tree may thus become a proxy for babysitting, or in other words the posi-tion entering and leaving a tree will be related to the amount of care provided to the infant by that individual. If, for in-stance, the adult male and infant are typically seen entering and leaving in consecutive order, this may be seen as pos-sible evidence that the male is watching over the infant more than the other members of the group are. Previous studies have shown that during the months when the infant is most dependent and being carried, the parent doing the carrying is most frequently seen traveling in the middle of the group, sometimes first, but rarely last. After several months when the infant is independent but still quite young, it is never observed moving last in the group, but after around five months of age this reverses and it begins to travel last more often than not (Rotundo et al. 2005). The infant observed during the time of the study was well over six months old. Thus the position the male takes while traveling may change as an infant becomes more independent.

MethodsThe study was conducted between June 3rd and July 31st

2009, with most of the data collected during July. The study site was located within the Estancia Guaycolec, a large ranch just outside Formosa, Argentina. Four habituated groups of owl monkeys were observed for a full day at least twice a week during the month of July. An observer would enter the forest just before sunrise (approximately 7:00 hrs during the winter months) and locate one of the four study groups us-ing radio telemetry equipment. Once located the observer would follow the group for the entire day until sundown, or approximately 18:00 hrs.

Parental care as seen in foraging bouts of mo-nogamous owl monkeys (Aotus azarai azarai)Rachel Gittelman, University of Pennsylvania

Male paternal care is often hard to find in primates. A group of monogamous owl monkeys (aotus azarai aza-rai), one of the few species that does exhibit male paternal care, was followed for a two month period to docu-ment the extent to which each parent babysat their infant during foraging bouts. This data was also compared to the foraging bouts of a group without an infant to determine whether or not foraging behaviors change based on the presence or absence of an infant. The male in the group with an infant was found to babysit the infant significantly more than the female, and positions within the foraging bouts did seem to vary slightly between groups.

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While following the group the observer collected many types of data. During foraging bouts the observer noted the tag number of the tree each individual foraged in (nearly all of the trees in each group’s territory were tagged), the begin-ning and ending time of the foraging bout, the type of tree, the part of the tree being eaten and the order in which each individual entered and left the tree. The times the adult male and adult female entered and left the tree were also noted. Often times the group would split up and feed in separate trees so there was also an option to record if the record of the bout had a “late start” or an “early end.” Because it was often impossible to collect bout information for multiple in-dividuals in separate trees simultaneously these additional variables were useful when the endpoints of a bout went un-seen. Information on the demography and ranging of the group was collected in addition to foraging bouts.

Data AnalysisSeveral tests were conducted on the data collected. The

most frequent position (first, middle or last) was calculated for each individual in each group, except for the juveniles. Juveniles have only in extremely rare cases been observed to take care of siblings and often lag behind or go off on their own during foraging bouts (Fernandez-Duque, personal communication) so any analysis of group foraging effects, especially for the scope of this study, will simply assume minimal contribution by juveniles. This being said, most bouts included in these analyses involved either all of the members of the group or all of the members of the group mi-nus any or all of the juveniles. Additionally, even if all mem-bers were present bouts were still excluded from the analysis if the observer was unable to record the order in which any or all of the monkeys entered (for the most frequent position entering) or left (for the most frequent position leaving) the tree. This frequently occurred because a monkey moved too far from the observer’s view or because a bout was simply too short to reliably and accurately record all of the data.

Only data from two of the four groups was compared (E350 and E500) because very few bouts were observed for the other two. Because each group is different it is important that analysis be done for each group separately and there simply was not enough data to conduct tests for two of the groups. The two groups that were not used, D500 and CC, consist of one adult male, one adult female, one juvenile and one adult male, one adult female and two juveniles, respec-tively. Of the groups that were used, E500 consists of one adult male, one adult female, one juvenile and one infant. E350 consists of one adult male, one adult female and one juvenile. Thus E500 was used as the group with an infant and E350 as the group without an infant.

Finally, analysis was also conducted for the group that had an infant (E500) on how often the adult male and female moved from bout to bout in a consecutive position to the

infant. For instance, if the adult male left the tree third and the infant left the tree last this was used as a data point. This measure was used as a proxy for the degree to which each adult “babysat” or watched the infant.

ResultsIn total 110 feeding bouts were observed. After excluding

bouts for the reasons described above, only 51 bouts were actually used in various parts of the analyses (28 from E500 and 23 from E350).

In group E500, the infant never traveled first and most frequently traveled in the middle of the group, occasionally traveling last. In this group the female traveled first more often than the male (18 of 34 bouts vs. 8 of 34 bouts) while entering or leaving the tree. This difference was statistically significant as indicated by a two sample hypothesis test for proportions which was used for all of the other comparisons conducted as well (α =.05, p=.0075). The male traveled last in 11 of 34 bouts and the female traveled last in 4 of 34 bouts while entering or leaving. These values were also significant (α=.05 and P=.0202). There was, however, no significant dif-

Figure 1: Number of times individuals with an infant entered or left a feeding bout in each position

Figure 2: Number of times individuals without an infant entered or left a feeding bout in each position


ference between the number of times either traveled in the middle (Figure 1).

In the group without an infant (E350), the female trav-eled first in 25/41 bouts and the male did so in 17/41 bouts. The female traveled in the middle less often than the male with 9/41 bouts compared to the male’s 21/41 bouts. There was little difference between the position of the male and female while traveling last, the male traveling last in 3 out of 41 bouts and the female in 7 out of 41 bouts. The differences between male and female were significant for first (α=.05, p=.0384) and middle (α=.05, P=.0030). The last position was not significant with α=.05, p=.0885 (Figure 2).

A comparison of the individuals between both groups suggested that there was no notable difference between the number of times the male with the infant (E500) traveled first or in the middle compared to the male without an in-fant (E350; first: α=.05, p=.505, middle: α=.05, p=.2709). The male did, however, travel last more frequently in the group with the infant (11/34 bouts) than the male without the infant (3/41 bouts; α=.05, p=.0028). The female’s posi-tion in both groups did not differ significantly (α=.05, first: p=.2420, middle: p=.1210, last: p=.260). These results should certainly be interpreted cautiously because, as mentioned before, there is little reason the female of one group should be compared to the female of the other group. Many reasons besides the presence or absence of an infant may account for differences in the data

Regarding the position of the male and female relative to the infant, the adult male spent more time in a consecutive position with the infant (27/28 bouts) than did the adult fe-male (20/28 bouts) while either entering or leaving the tree. This sex difference was significant with an α value of .05 and a P value of .0054.

DiscussionThe results obtained do tend to support the observation

that males expend more parental care than females with infants. It has been shown previously that males may carry

the infant more often during the months immediately fol-lowing its birth (Fernandez-Duque et al 2009) and transfer food more often to infants and juveniles than do females (Wolovich et al. 2007). The data show that during the study the male of E500 traveled in a consecutive position with the infant more often than the female which may be interpreted as indicating that the male is babysitting or watching over the infant to a greater degree than the female.

The other results obtained, simply comparing the fre-quency of each position held during travel from tree to tree between the sexes, show more mixed results. In both groups the female traveled first more often than the male. If it is true that much of the parental care responsibilities fall on the male it may be that the female then fulfills a leadership position in making decisions on when to leave each tree and which tree to go to next. This division of labor would make sense especially during the harsh winter months which co-incide with the mating season (May - September) when a pregnant female would have additional nutritional demands (Rotundo et al 2005). Indeed, one hypothesis for the main-tenance of monogamy in these owl monkeys supposes that the female is unable to raise the young on her own and must have the continuing support of the male well after the birth of their young (Fernandez-Duque personal communica-tion). Thus it is possible that the female travels first in both groups regardless of the presence of an infant for both have important nutritional needs. Researchers also suspect that the males and females may have such different needs that they often feed on different foods during separate feeding bouts (Van der Heide personal communication). This may account for why many of the bouts recorded did not contain the entire group.

The results also indicate that the adult male traveled last more often in the group with the infant. Because the infant most often traveled in the middle of the group it would make sense that the male would increase his time spent at the back of the group in order to watch over the infant. Analyzing the middle position is more difficult because E500 consisted of four members at the time of the study and E350 consist-ed of only three. There are thus twice as many ways to be the “middle” animal entering or leaving for the E500 bouts. For instance, there was no significant difference between the number of times the adult males of each group traveled in the middle (15/34 bouts for the male with an infant and 21/41 bouts for the male without an infant). However, the fact that the male of E500 is expected to travel more often in the middle simply by chance (50% of the time) than the male in E350 (33% of the time) may have artificially affected the differences between groups. This does, however, also seem to make more robust the result that the male with the infant traveled last more often. This is because the male of E500 would actually be expected to travel last less frequently than the male of E350 simply by random chance. Any future re-

Figure 3: Number of times spent in a consecutive position (directly in front of or directly behind) with the infant while entering or leaving a foraging tree


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25

search should aim at correcting this problem by comparing groups of the same size.

Additionally, many bouts were counted twice in the anal-ysis as data were collected for entering and for leaving the tree. If, for instance, the adult female was first in a certain bout to enter and to leave the tree this was counted twice in the analysis. After doing separate analyses for entering and leaving that resulted in similar patterns the two types of data were combined for the presentation of final results here. One potential problem in doing so may be that the entering and leaving events are not independent of each other and thus should not be counted separately. If an individual enters first in to a tree it may then be more likely to leave first as they simply get satiated before the others. Future analysis of this dataset should consider this issue.

The data presented are a preliminary attempt at quanti-fying the degree to which babysitting changes as an infant ages. Rotundo et al 2005 states that after 5 months of age the infant travels last more frequently than in the middle. This was not the case for the infant of E500 during this study, who traveled last in only 8 out of 34 cases and middle in 24 out of 34 cases despite being over 5 months old. Such dis-crepancies highlight the dangers of drawing conclusions from small sample sizes. Only one infant was used in this study and simply may not be representative of other indi-viduals of the species. Results should only be seen as a guide for future research.

Sex differences in parental care, as well as the length of the period in which intensive parental care is needed are both important components in investigating the behavioral ecology of nonhuman primates. Such topics also contribute to that study of monogamy and why it is maintained in cer-tain species but not in others. As with much other nonhu-man primate research, owl monkeys have close evolutionary ties to humans and any results may eventually give us insight into our own behavioral ecology. In particular, as one of the few monogamous species of primate, owl monkeys offer a unique opportunity to study pair-bonding and bi-parental care, topics with important parallels and contrasts to mod-ern human societies.

AcknowledgmentsThe author is greatful to the Center for Undergraduate

Research and Fellowships at the University of Pennsylvania for awarding the Pincus-Magaziner Family Undergraduate Research and Travel Award. The project was also supported by a Hewlett Award for Innovation in International Offer-ings Grant (Provost Office-Penn) and an NSF-REU grant (BCS-0924352) to E. Fernandez-Duque. This research was also made made possible by Fundación ECO of Formosa, the Estancia Guaycolec of Formasa, Argentina, Griette Van der Heide, Victor Davalos, John Lindo, Claudia Valeggia and El-lie and Arye Gittelman. A special thanks goes to Dr. Edu-ardo Fernandez-Duque, for without his continual support

and mentoring this project would have never been possible.

References

Charpentier M. J. E., Van Horn R. C., J. Altmann, Alberts S. C. (2008). Paternal effects on offspring fitness in a multimale primate society. Proceedings of the National Academy of Sciences of the United States of America. 105:1988-1992.

E. Fernandez-Duque, C. Juárez & A. Di Fiore (2008). Adult male re-placement and subsequent infant care by male and siblings in so-cially monogamous owl monkeys (Aotus azarai). Primates 49:81-84.

E. Fernandez-Duque, C. R. Valeggia & S.P. Mendoza (2009). The Biol-ogy of Paternal Care. Annual Review of Anthropology, Volume 38: 115-130.

C.K. Wolovich, J.P. Perea-Rodriguez, E. Fernandez-Duque (2008). Food sharing as a form of paternal care in wild owl monkeys (Aotus azarai). American Journal of Primatology 70:211-221.

Rotundo, M., Fernandez-Duque, E. & Dixson, A.F. (2005). Infant de-velopment and parental care in owl monkeys (Aotus azarai azarai) of Formosa, Argentina. International Journal of Primatology: 26 (6): 1459-1473.

Fernandez-Duque, E.; Rotundo, M & Ramirez-Llorens, P. (2002). En-vironmental determinants of birth seasonality in night monkeys (Aotus azarai) of the Argentinean Chaco. International Journal of Primatology 23 (3), 639-656.


Two-Player Zero-Sum Poker Models with One and Two Rounds of BettingHanzhe Zhang, University of Pennsylvania

IntroductionPoker is a complex multi-player game of chance and de-

ception. In order to gain insight into different aspects of the game, mathematical and psychological alike, we construct simple models of poker by making assumptions about their hands and restricting rules. Two-player zero-sum poker models with independent uniform hands are the simplest non-trivial ones. Von Neumann (1953) discusses his model in Theory of Games and Economic Behaviors (von Neu-mann & Morgenstern, 1953).

In this paper, in addition to presentation of the original model, it is extended to allow an additional round of raise by the second player. This modication makes the model closer and more applicable to real poker (Texas Hold’em), and pro-vides more information on optimal players by both players in a more complicated situation. In addition, discussion on allowing multiple rounds follows.

von Neumann’s ModelThis section presents the basic model of von Neumann,

and denitions and lemmas that are applicable in general. Two players each contribute an ante of $1, and are dealt “hands” x1 and x2, respectively independent and identically distrib-uted as U(0,1). Player I can check or bet a predetermined amount B, and player II can call or fold if player I bets. The only available information for each player is his own hand and the game structure. Strategies for two players are

Player I: s1 : x1 → {check, bet};Player II: s2 : x2 × s1(x1) → {call, fold}.A player’s payoff is dependent of x1; x2; s1(x1); s2(x2). Exten-

sive form of the game and optimal strategies are presented in Figure 1 with player I’s payoffs shown (their reciprocals are player II’s because the game is zero-sum).

We want to investigate how players play in equilibrium. They are going to play a pair of optimal strategies as de-scribed below. A strategy is optimal if given any hand and the other player’s strategy, there is no incentive to deviate to any other strategy.

Denition 2.1. For player i, a strategy si* is optimal if given any other strategy si’ and other player’s strategy sj,

For two similar hands, payoff from an optimal strategy should be the same. Otherwise, there is an incentive to de-viate to the strategy played if given the other hand. There-fore, hands slightly bigger and slightly smaller yield similar payoffs. This idea is embodied in the indifference condition (IC). For example in the optimal strategy above, player II is indifferent between folding and calling when he is dealt c.

Lemma 2.2 (IC). For si*, as Є →0+,

Theorem 2.3. An equilibrium strategy of von Neumann’s game is presented as follows. Player I checks when a x1 b and bets amount B otherwise; in case of raise, player II calls if x2 > c and folds otherwise, where

Two players’ optimal strategies are illustrated in Figure 2.

Proof. Optimal strategies are found by backward induc-tion. Player II’s optimal strategy is found first. When Player I raises, Player II calls if his expected payoff is greater than −1, which is his payoff from folding. Since his payoff depends piecewise-linearly on his hand strength x2, u2(x1, x2), player

Two-Player Zero-Sum Poker Models with One and

Two Rounds of Betting

Hanzhe Zhang ∗†

March 28, 2010

Abstract

The paper presents the basic von Neumann’s two-player zero-sum poker model with independentand identically distributed uniform hands, and extends it by allowing player II to re-raise. The analysisshows that both models favor the player who initially raises, but re-raising option cuts in player I’sadvantage, reducing his expected payoff. “Payoff square”, a square diagram that indicates the payoffsunder different hands and strategies, is introduced and used to derive players’ payoffs. Extensions tomultiple and infinite rounds of betting are discussed, and optimal strategies are conjectured. Relatedmodels are reviewed along the way.

1 Introduction

Poker is a complex multi-player game of chance and deception. In order to gain insight into differentaspects of the game, mathematical and psychological alike, we construct simple models of poker bymaking assumptions about their hands and restricting rules. Two-player zero-sum poker models withindependent uniform hands are the simplest non-trivial ones. von Neumann (1953) discusses his modelin Theory of Games and Economic Behaviors[von Neumann & Morgenstern, 1953].

In this paper, in addition to presentation of the original model, it is extended to allow an additionalround of raise by the second player. This modification makes the model closer and more applicable toreal poker (Texas Hold’em), and provides more information on optimal players by both players in a morecomplicated situation. In addition, discussion on allowing multiple rounds follows.

2 von Neumann’s Model

This section presents the basic model of von Neumann, and definitions and lemmas that are applicablein general. Two players each contribute an ante of $1, and are dealt “hands” x1 and x2, respectivelyindependent and identically distributed as U(0, 1). Player I can check or bet a predetermined amountB, and player II can call or fold if player I bets. The only available information for each player is hisown hand and the game structure. Strategies for two players are

Player I: s1 : x1 → {check, bet};Player II: s2 : x2 × s1(x1) → {call, fold}.

A player’s payoff is dependent of x1, x2, s1(x1), s2(x2). Extensive form of the game and optimal strategiesare presented in Figure 1 with player I’s payoffs shown (their reciprocals are player II’s because the gameis zero-sum).

We want to investigate how players play in equilibrium. They are going to play a pair of optimalstrategies as defined below. A strategy is optimal if given any hand and the other player’s strategy, thereis no incentive to deviate to any other strategy.

Definition 2.1. For player i, a strategy s∗i is optimal if given any other strategy s′i and other player’sstrategy sj ,

∫

xj

ui(xi, xj , s∗i (xi), sj(xj))dxj ≥

∫

xj

ui(xi, xj , s′i(xi), sj(xj))dxj ∀x1 ∈ (0, 1).

∗To whom correspondence should be addressed: [email protected].†Submatriculation Thesis Advisor: Professor Robin Pemantle, Department of Mathematics, University of Pennsylvania.

1

I

IIbetcall

fold

check u

1

(1+B)u

Figure 1: Extensive form of von Neumann’s game, where u = 1 if x1 ≥ x2; = −1 otherwise.

For two similar hands, payoff from an optimal strategy should be the same. Otherwise, there is anincentive to deviate to the strategy played if given the other hand. Therefore, hands slightly bigger andslightly smaller yield similar payoffs. This idea is embodied in the indifference condition (IC). Forexample in the optimal strategy above, player II is indifferent between folding and calling when he isdealt c.

Lemma 2.2 (IC). For s∗i , as ε → 0+,

∫

xj

ui

(xi, xj , s

∗i

(xi − ε

), xj

)→

∫

xj

ui

(xi, xj , s

∗i

(xi + ε

), xj

)∀xi. (2.1)

Theorem 2.3. An equilibrium strategy of von Neumann’s game is presented as follows. Player I checkswhen a ≤ x1 ≤ b and bets amount B otherwise; in case of raise, player II calls if x2 > c and foldsotherwise, where

a =B

(B + 1)(B + 4), b =

B2 + 4B + 2

(B + 1)(B + 4), c =

B(B + 3)

(B + 1)(B + 4).


Player I a c0 1c

bet(bluff) bet

fold callPlayer II

check

Figure 2: Optimal strategies of both players

Proof. Optimal strategies are found by backward induction. Player II’s optimal strategy is found first.When Player I raises, player II calls if his expected payoff is greater than −1, which is his payoff fromfolding. Since his payoff depends piecewise-linearly on his hand strength x2, u2(x1, x2), player II’s payoff,is a monotonic function of x2 if he calls. Therefore, player II’s optimal strategy is to call when x2 > cand to fold otherwise.

Given player II’s optimal strategy, player I should bet if his expected payoff of betting is greater thanof checking (Tie situations need not be considered because the density function is non-atomic). PlayerI’s payoff given x1

• from checking is (+1) · (x1 − 0) + (−1) · (1− x1) = 2x1 − 1.

• from betting is

∫ c

0

(+1)dx2 +

∫ 1

c

(−1−B)dx2 = c+ (−1−B)(1− c) = (B + 2)c−B − 1, x1 < c,

or ∫ c

0

(+1)dx2 +

∫ x1

c

(1 +B)dx2 +

∫ 1

x1

(−1−B)dx2 = (B + 1)(2x1 − 1)−Bc, x1 ≥ c.

Then by IC in Equation 2.1,

2x1 − 1 = 2c+Bc−B − 1, (2.2)

2x1 − 1 = (B + 1)(2x1 − c− 1) + c (2.3)

2

I

IIbetcall

fold

check u

1

(1+B)u




∫

xj

ui

(xi, xj , s

∗i

(xi − ε

), xj

)→

∫

xj

ui

(xi, xj , s

∗i

(xi + ε

), xj

)∀xi. (2.1)


a =B

(B + 1)(B + 4), b =

B2 + 4B + 2

(B + 1)(B + 4), c =

B(B + 3)

(B + 1)(B + 4).


Player I a c0 1c

bet(bluff) bet

fold callPlayer II

check





• from betting is

∫ c

0

(+1)dx2 +

∫ 1

c

(−1−B)dx2 = c+ (−1−B)(1− c) = (B + 2)c−B − 1, x1 < c,

or ∫ c

0

(+1)dx2 +

∫ x1

c

(1 +B)dx2 +

∫ 1

x1

(−1−B)dx2 = (B + 1)(2x1 − 1)−Bc, x1 ≥ c.


2x1 − 1 = 2c+Bc−B − 1, (2.2)

2x1 − 1 = (B + 1)(2x1 − c− 1) + c (2.3)

2

I

IIbetcall

fold

check u

1

(1+B)u




∫

xj

ui

(xi, xj , s

∗i

(xi − ε

), xj

)→

∫

xj

ui

(xi, xj , s

∗i

(xi + ε

), xj

)∀xi. (2.1)


a =B

(B + 1)(B + 4), b =

B2 + 4B + 2

(B + 1)(B + 4), c =

B(B + 3)

(B + 1)(B + 4).


Player I a c0 1c

bet(bluff) bet

fold callPlayer II

check





• from betting is

∫ c

0

(+1)dx2 +

∫ 1

c

(−1−B)dx2 = c+ (−1−B)(1− c) = (B + 2)c−B − 1, x1 < c,

or ∫ c

0

(+1)dx2 +

∫ x1

c

(1 +B)dx2 +

∫ 1

x1

(−1−B)dx2 = (B + 1)(2x1 − 1)−Bc, x1 ≥ c.


2x1 − 1 = 2c+Bc−B − 1, (2.2)

2x1 − 1 = (B + 1)(2x1 − c− 1) + c (2.3)

2

The paper presents the basic von Neumann’s two-player zero-sum poker model with independent and identically distributed uniform hands, and extends it by allowing Player II to re-raise. The analysis shows that both models favor the player who initially raises, but re-raising option cuts in Player I’s advantage, reducing his expected payoff. “Payoff square”, a square diagram that indicates the payoffs under different hands and strategies, is introduced and used to derive players’ payoffs. Extensions to multiple and infinite rounds of betting are discussed, and optimal strategies are conjectured. Related models are reviewed along the way.

I

IIbetcall

fold

check u

1

(1+B)u




∫

xj

ui

(xi, xj , s

∗i

(xi − ε

), xj

)→

∫

xj

ui

(xi, xj , s

∗i

(xi + ε

), xj

)∀xi. (2.1)


a =B

(B + 1)(B + 4), b =

B2 + 4B + 2

(B + 1)(B + 4), c =

B(B + 3)

(B + 1)(B + 4).


Player I a c0 1c

bet(bluff) bet

fold callPlayer II

check





• from betting is

∫ c

0

(+1)dx2 +

∫ 1

c

(−1−B)dx2 = c+ (−1−B)(1− c) = (B + 2)c−B − 1, x1 < c,

or ∫ c

0

(+1)dx2 +

∫ x1

c

(1 +B)dx2 +

∫ 1

x1

(−1−B)dx2 = (B + 1)(2x1 − 1)−Bc, x1 ≥ c.


2x1 − 1 = 2c+Bc−B − 1, (2.2)

2x1 − 1 = (B + 1)(2x1 − c− 1) + c (2.3)

2

I

IIbetcall

fold

check u

1

(1+B)u




∫

xj

ui

(xi, xj , s

∗i

(xi − ε

), xj

)→

∫

xj

ui

(xi, xj , s

∗i

(xi + ε

), xj

)∀xi. (2.1)


a =B

(B + 1)(B + 4), b =

B2 + 4B + 2

(B + 1)(B + 4), c =

B(B + 3)

(B + 1)(B + 4).


Player I a c0 1c

bet(bluff) bet

fold callPlayer II

check





• from betting is

∫ c

0

(+1)dx2 +

∫ 1

c

(−1−B)dx2 = c+ (−1−B)(1− c) = (B + 2)c−B − 1, x1 < c,

or ∫ c

0

(+1)dx2 +

∫ x1

c

(1 +B)dx2 +

∫ 1

x1

(−1−B)dx2 = (B + 1)(2x1 − 1)−Bc, x1 ≥ c.


2x1 − 1 = 2c+Bc−B − 1, (2.2)

2x1 − 1 = (B + 1)(2x1 − c− 1) + c (2.3)

2

Figure 1: Extensive form of von Neu-mann’s game, where u = 1 if x1 ≥ x2;= −1 otherwise.



RESEARCH ARTICLES

27

II’s payoff, is a monotonic function of x2 if he calls. There-fore, player II’s optimal strategy is to call when x2 > c and to fold otherwise.

Given player II’s optimal strategy, player I should bet if his expected payoff of betting is greater than of checking (Tie situations need not be considered because the density function is non-atomic). Player I’s payoff given x1

• from checking is (+1) ∙ (x1 − 0) + (−1) ∙ (1 − x1) = 2x1 − 1.

• from betting is


Since Player I’s payoff is also piecewise linear with respect to x1, Player I’s optimal strategy is to bet if x1 < a or x1 > b, and to check if a ≤ x1 ≤ b. Then x1 ≤ c in Equation 2.2, and x1 ≥ c in Equation 2.3,

Player II’s optimal strategy should obey the indierence condition,

Solving Equations 2.4 and 2.5 gives values a and b and substituting into Equation 2.6, c = B(B + 3)∕ [(B + 1)(B + 4)]. a and b as functions of B are obtained by re-substitution.

Payoffs of both players can be determined. Given that Player I determines his bet amount before hands are as-signed, the optimal B that maximizes the expected payoff is of interest. First, payoff squares that describe strategies and corresponding payoffs of players are introduced.

Definition 2.4. A payoff square is a two-dimensional square diagram with hands of player I in x-axis, and player II’s in y-axis. A point in the square indicates a hand pair (x1, x2), and the payoff, u1(x1, x2, s1(x1, x2), s2(x1, x2)), indicated at the point is resulted from the strategies played corresponding to the hands.

Remark 2.5. Payoffs of any strategy set can be depicted by the payoff square. It can also be generalized to n-dimension, which is equivalent to taking multiple integrals of n variables (Besides the payoff square, only a payoff “cube” depicting a three-player game is beneficial).

Corollary 2.6. Given that both players follow the optimal strategies described in Theorem 2.3, Player I’s payoff is u1(x1, x2, s1, s2) = a. Optimal bet amount is B* = 2.

Proof. Expected payoff from player I checking all hands is 0, +1 below x1 = x2 and −1 above x1 = x2. Equivalently, the payoff differential from this strategy is illustrated and ex-pected payoff would be the same overall, so we add 1 above x1 = x2, subtract 1, and cancel out a square region on the top of +B and −B to get the resulting square on the right. The original, complete payoff square as well as its geometric and algebraic manipulation are shown in Figure 3.

Expected payoff of Player I is

Maximizing u1(B) with respect to B, (4−B2)∕[(B+1)2(B+4)2 ] = 0; B*� = 2: u1(2) = 1∕9; a = 1∕9; b = 7∕9; c = 5∕9.

The result deserves some discussion. Player I’s payoff, B ∕(B2 +5B +4) is positive for all B > 0, and it achieves its maxi-mum at B *� = 2, the pot size. This means that the game favors player I who is given the chance to raise, and he maximizes his payoff to be 1∕9 by betting pot size every time. Player I has an advantage because he can bluff with his worst hands. More importantly, for real poker perhaps, he must bluff with his worst but not mediocre hands.

In contrast to von Neumann’s model in which the bet amount is pre-determined and fixed, Donald Newman pres-ents a model that has the same game structure but allows any bet amount (Newman, 1959). Set ξ = 2∕(B + 2). The opti-mal strategy is that Player I checks when 1∕7 ≤ x1 ≤ 4 ∕7, bets B with hands (1 − 3ξ2 + 2ξ3)∕7, or 1 − 3ξ2∕7; Player II calls if and only if x2 > 1 −6ξ ∕7. In this game, Player I’s value is 1∕7 because Player I bluffs 1∕7 of time. Optimality of the strategy is proven by showing that the given pure strategy is a saddle point of all strategies.

Extension: Re-raise by player IIThe key extension to the previous model is allowing Play-

er II to re-raise B2 after calling Player I’s bet B1, and Player I either calls or folds. This model is discussed in Ferguson’s

I

IIbetcall

fold

check u

1

(1+B)u




∫

xj

ui

(xi, xj , s

∗i

(xi − ε

), xj

)→

∫

xj

ui

(xi, xj , s

∗i

(xi + ε

), xj

)∀xi. (2.1)


a =B

(B + 1)(B + 4), b =

B2 + 4B + 2

(B + 1)(B + 4), c =

B(B + 3)

(B + 1)(B + 4).


Player I a c0 1c

bet(bluff) bet

fold callPlayer II

check





• from betting is

∫ c

0

(+1)dx2 +

∫ 1

c

(−1−B)dx2 = c+ (−1−B)(1− c) = (B + 2)c−B − 1, x1 < c,

or ∫ c

0

(+1)dx2 +

∫ x1

c

(1 +B)dx2 +

∫ 1

x1

(−1−B)dx2 = (B + 1)(2x1 − 1)−Bc, x1 ≥ c.


2x1 − 1 = 2c+Bc−B − 1, (2.2)

2x1 − 1 = (B + 1)(2x1 − c− 1) + c (2.3)

2

Since I’s payoff is also piecewise linear with respect to x1, player I’s optimal strategy is to bet if x1 < aor x1 > b, and to check if a ≤ x1 ≤ b. Then x1 ≤ c in Equation 2.2, and x1 ≥ c in Equation 2.3,

2a− 1 = 2c+Bc−B − 1 (2.4)

2b− 1 = (B + 1)(2b− c− 1) + c (2.5)

Player II’s optimal strategy should obey the indifference condition,

[a(1 +B) + (1− b)(−1−B)

]/(a+ 1− b

)= −1 (2.6)

Solve Equations 2.4 and 2.5 give values a and b and substitute into Equation 2.6, c = B(B + 3)/[

(B +1)(B + 4)

]. a and b as functions of B are obtained by re-substitution.

Payoffs of both players can be determined. In addition, given that player I determines his bet amountbefore hands are assigned, the optimal B that maximizes the expected payoff is of interest. First, payoffsquares that describe strategies and corresponding payoffs of players are introduced.

Definition 2.4. A payoff square is a two-dimensional square diagram with hands of player I in x-axis, and player II’s in y-axis. A point in the square indicates a hand pair (x1, x2), and the payoff,u1(x1, x2, s1(x1, x2), s2(x1, x2)), indicated at the point is resulted from the strategies played correspondingto the hands.

Remark 2.5. Payoffs of any strategy set can be depicted by the payoff square. It can also be generalizedto n-dimension, which is equivalent to taking multiple integrals of n variables (Besides the payoff square,only a payoff “cube” depicting a three-player game is beneficial).

Corollary 2.6. Given that both players follow the optimal strategies described in Theorem 2.3, playerI’s payoff is u1(x1, x2, s1, s2) = a. Optimal bet amount is B∗ = 2.

Proof. Expected payoff from player I checking all hands is 0, +1 below x1 = x2 and −1 above x1 = x2.Equivalently, the payoff differential from this strategy is illustrated and expected payoff would be thesame overall, so we add 1 above x1 = x2, subtract 1, and cancel out a square region on the top of +B and−B to get the resulting square on the right. The original, complete payoff square as well as its geometricand algebraic manipulation are shown in Figure 3.

c

0 1 1x

2x0

a b

1+B

-1-B

-1-B

+1+1

-1

c

0 1 1x

2x0

a b

-B

+2

Bb

Figure 3: Illustration of Player I’s payoff by payoff square.

Expected payoff of player I is

u1 = B(1− b)(b− c)−B(a)(1− c) + (2)(1/2)(c+ c− a)(a) = B/[

(B + 1)(B + 4)]= a.

Maximizing u1(B) with respect to B,(4−B2

)/[(B+1)2(B+4)2

]= 0, B∗ = 2. u1(2) = 1/9, a = 1/9, b =

7/9, c = 5/9.

3


2a− 1 = 2c+Bc−B − 1 (2.4)

2b− 1 = (B + 1)(2b− c− 1) + c (2.5)


[a(1 +B) + (1− b)(−1−B)

]/(a+ 1− b

)= −1 (2.6)


(B +1)(B + 4)







c

0 1 1x

2x0

a b

1+B

-1-B

-1-B

+1+1

-1

c

0 1 1x

2x0

a b

-B

+2

Bb



u1 = B(1− b)(b− c)−B(a)(1− c) + (2)(1/2)(c+ c− a)(a) = B/[

(B + 1)(B + 4)]= a.


)/[(B+1)2(B+4)2

]= 0, B∗ = 2. u1(2) = 1/9, a = 1/9, b =

7/9, c = 5/9.

3


2a− 1 = 2c+Bc−B − 1 (2.4)

2b− 1 = (B + 1)(2b− c− 1) + c (2.5)


[a(1 +B) + (1− b)(−1−B)

]/(a+ 1− b

)= −1 (2.6)


(B +1)(B + 4)







c

0 1 1x

2x0

a b

1+B

-1-B

-1-B

+1+1

-1

c

0 1 1x

2x0

a b

-B

+2

Bb



u1 = B(1− b)(b− c)−B(a)(1− c) + (2)(1/2)(c+ c− a)(a) = B/[

(B + 1)(B + 4)]= a.


)/[(B+1)2(B+4)2

]= 0, B∗ = 2. u1(2) = 1/9, a = 1/9, b =

7/9, c = 5/9.

3


2a− 1 = 2c+Bc−B − 1 (2.4)

2b− 1 = (B + 1)(2b− c− 1) + c (2.5)


[a(1 +B) + (1− b)(−1−B)

]/(a+ 1− b

)= −1 (2.6)


(B +1)(B + 4)







c

0 1 1x

2x0

a b

1+B

-1-B

-1-B

+1+1

-1

c

0 1 1x

2x0

a b

-B

+2

Bb



u1 = B(1− b)(b− c)−B(a)(1− c) + (2)(1/2)(c+ c− a)(a) = B/[

(B + 1)(B + 4)]= a.


)/[(B+1)2(B+4)2

]= 0, B∗ = 2. u1(2) = 1/9, a = 1/9, b =

7/9, c = 5/9.

3


2a− 1 = 2c+Bc−B − 1 (2.4)

2b− 1 = (B + 1)(2b− c− 1) + c (2.5)


[a(1 +B) + (1− b)(−1−B)

]/(a+ 1− b

)= −1 (2.6)


(B +1)(B + 4)







c

0 1 1x

2x0

a b

1+B

-1-B

-1-B

+1+1

-1

c

0 1 1x

2x0

a b

-B

+2

Bb



u1 = B(1− b)(b− c)−B(a)(1− c) + (2)(1/2)(c+ c− a)(a) = B/[

(B + 1)(B + 4)]= a.


)/[(B+1)2(B+4)2

]= 0, B∗ = 2. u1(2) = 1/9, a = 1/9, b =

7/9, c = 5/9.

3


2a− 1 = 2c+Bc−B − 1 (2.4)

2b− 1 = (B + 1)(2b− c− 1) + c (2.5)


[a(1 +B) + (1− b)(−1−B)

]/(a+ 1− b

)= −1 (2.6)


(B +1)(B + 4)







c

0 1 1x

2x0

a b

1+B

-1-B

-1-B

+1+1

-1

c

0 1 1x

2x0

a b

-B

+2

Bb



u1 = B(1− b)(b− c)−B(a)(1− c) + (2)(1/2)(c+ c− a)(a) = B/[

(B + 1)(B + 4)]= a.


)/[(B+1)2(B+4)2

]= 0, B∗ = 2. u1(2) = 1/9, a = 1/9, b =

7/9, c = 5/9.

3

I

IIbetcall

fold

check u

1

(1+B)u




∫

xj

ui

(xi, xj , s

∗i

(xi − ε

), xj

)→

∫

xj

ui

(xi, xj , s

∗i

(xi + ε

), xj

)∀xi. (2.1)


a =B

(B + 1)(B + 4), b =

B2 + 4B + 2

(B + 1)(B + 4), c =

B(B + 3)

(B + 1)(B + 4).


Player I a c0 1c

bet(bluff) bet

fold callPlayer II

check





• from betting is

∫ c

0

(+1)dx2 +

∫ 1

c

(−1−B)dx2 = c+ (−1−B)(1− c) = (B + 2)c−B − 1, x1 < c,

or ∫ c

0

(+1)dx2 +

∫ x1

c

(1 +B)dx2 +

∫ 1

x1

(−1−B)dx2 = (B + 1)(2x1 − 1)−Bc, x1 ≥ c.


2x1 − 1 = 2c+Bc−B − 1, (2.2)

2x1 − 1 = (B + 1)(2x1 − c− 1) + c (2.3)

2

I

IIbetcall

fold

check u

1

(1+B)u




∫

xj

ui

(xi, xj , s

∗i

(xi − ε

), xj

)→

∫

xj

ui

(xi, xj , s

∗i

(xi + ε

), xj

)∀xi. (2.1)


a =B

(B + 1)(B + 4), b =

B2 + 4B + 2

(B + 1)(B + 4), c =

B(B + 3)

(B + 1)(B + 4).


Player I a c0 1c

bet(bluff) bet

fold callPlayer II

check





• from betting is

∫ c

0

(+1)dx2 +

∫ 1

c

(−1−B)dx2 = c+ (−1−B)(1− c) = (B + 2)c−B − 1, x1 < c,

or ∫ c

0

(+1)dx2 +

∫ x1

c

(1 +B)dx2 +

∫ 1

x1

(−1−B)dx2 = (B + 1)(2x1 − 1)−Bc, x1 ≥ c.


2x1 − 1 = 2c+Bc−B − 1, (2.2)

2x1 − 1 = (B + 1)(2x1 − c− 1) + c (2.3)

2 Figure 3: Illustration of Player I’s payoff by payoff square.


works (Ferguson & Ferguson, 2003, Ferguson et al., 2007). The strategies given hands x1, x2 ~ U(0, 1), are

Player I: s1 : x1 × s2(s1) → {check, bet B1} × {fold, call} = {bet-fold, bet-raise, check},Player II: s2 : x2 × {check, bet} → {bet B2, check, fold}.

Theorem 3.1. Player I bet-folds when x1 Є (0, a] U (b, c], checks when x1 Є (a, b], and bet-calls when x1 > c. Player II folds when x2 ≤ d, calls when x2 Є (e, f], and re-raises when x1 Є (d, e] U (f, 1]. 0 ≤ a ≤ e ≤ b ≤ c ≤ f ≤ 1 and 0 ≤ d ≤ e (d can be larger or smaller than a), where

where Δ = B1(4 + B1)(2 + 2B1 + B2)2 + (1 + B1)(2 + B1)

2B2. The optimal strategies are illustrated in Figure 5.

Proof. First, apply the ICs for• I at a: −2a + (−2 − B1)d = B1;• I at b: 2B1b + (2 + B1)d + (−2B1 − 2)e = B1;• I at c: (−2 − 2B1 − B2)d + (2 + 2B1 + B2)e + B2f = B2;• II at d: (2 + B1)a − (2 + B1)b + (2 + 2B1 + B2)c = B1 + B2;• II at e: (−2 − 2B1)b + (2 + 2B1 + B2)c = B2;• II at f: −c + 2f = 1.

Solving six linearly independent equations of six un-knowns, we get results as presented in the theorem. Now suppose we ignore the antes contributed by the players by treating them as sunk costs. Given that Player II uses the conjectured optimal strategy, and Player I has hand x1, I’s “gain”

• from checking is 2x1.• from bet-folding is 2a if 0 < x < e; 2a + 2(1 + B)(x − e)

if e < x < f, and 2a + 2(1 + B1)(f − e) if f < x < 1.• from bet-calling is 2a − 2(1 + B1 + B2)(e − d) if 0 < x <

d; 2a − 2(1 + B1 + B2)(e − x) if d < x < e; 2a + 2(1 + B1)(x − e) if e < x < f; and 2a + 2(1 + B1)(f − e) + 2(1 + B1 + B2)(x − f) if f < x < 1.

We can verify that at every critical point, the payoffs from two strategies are equal. Then noting that the payoff func-tion is piecewise linear, we verify that Player I’s strategy is optimal. Similarly given Player I’s optimal strategy and Play-er II’s hand x2, Player II’s expected payoff from

• folding is 0 if 0 < y < a, 2(y − a) if a < y < b, and 2(b − a) if b < y < 1.

• calling is −2(1 + B1)(a − y) if 0 < y < a; 2(y − a) if a < y < b; and 2(b − a) + 2(1 + B1)(y − b) if b < y < 1.

• raising is 0 if 0 < y < a, 2(y − a) if a < y < b; 2(b − a) if b < y < c; and 2(b − a)+(1 + B1 + B2)(y − c) if c < y < 1.

Then with II’s boundary conditions verified, player II is proven to play an optimal strategy as well. Complicated op-erations were done by Maple 11.

Corollary 3.2. Expected payoff of Player I is a. Optimal bet for Player I, B1

* = 1 + √13∕3. Optimal bet for II is B2* = 2B1

* + 2 = 4 + 2√13∕3.

Proof. Applying the modied payoff square as illustrated in Figure 6,

Minimizing u1 with respect to B2 while B1 is fixed, is equivalent to maximizing B2 = (2 + 2B1 +B2)

2,

Substitute in, u1 = 8B12 ⁄ [(1+B1)(9B1

2 + 36B1 +4)]. Then maximizing u1 with respect to B1 yields 9B1

3 − 40B1 − 8 = 0. Three roots are B1 = −2, 1 + √13∕3, 1 − √13∕3. Clearly,

Substituting in B1* and B2

*, a = 0.0955; b = 0.8178; c = 0.909; d = 0.569; e = 0.592; f = 0.954.

Though the game still favors Player I, its payof (0.0955) is lower than that in the original von Neumann model (1∕9). This shows that allowing Player II to re-raise restricts Player I’s audacity of bluffing, thus decreasing his advantage and

The result deserves some discussion. Player I’s payoff, B/(B2 +5B+4) is positive for all B > 0, andit achieves its maximum at B∗ = 2, the pot size. This means that the game favors player I who is giventhe chance to raise, and he maximizes his payoff to be 1/9 by betting pot size every time. Player I hasan advantage because he can bluff with his worst hands. More importantly, for real poker perhaps, hemust bluff with his worst but not mediocre hands.

In contrast to von Neumann’s model in which the bet amount is pre-determined and fixed, DonaldNewman presents a model that has the same game structure but allows any bet amount [Newman, 1959]. Set ξ = 2/(B + 2). The optimal strategy is that I checks when 1/7 ≤ x1 ≤ 4/7, bets B with hands(1− 3ξ2 + 2ξ3)/7, or 1− 3ξ2/7; II calls if and only if x2 > 1− 6ξ/7. In this game, player I’s value is 1/7because player I bluffs 1/7 of time. Optimality of the strategy is proven by showing that the given purestrategy is a saddle point of all strategies.

3 Extension: Re-raise by player II

The key extension to the previous model is allowing player II to re-raise B2 after calling player I’s betB1, and I either calls or folds. This model is discussed in Ferguson’s works [Ferguson & Ferguson, 2003],[Ferguson et al., 2007]. The strategies given hands x1, x2 ∼ U(0, 1), are

Player I: s1 : x1 × s2(s1) → {check, bet B1}×{fold, call}={bet-fold, bet-raise, check},Player II: s2 : x2× {check, bet} → {bet B2, check, fold}.

II

IIbet

checkfold

betcall

foldcheck u

1(1+B1)u

-(1+B1)

(1+B1+B2)u

Figure 4: Extensive form of the two players with player I’s payoffs.

Theorem 3.1. Player I bet-folds when x1 ∈ (0, a] ∪ (b, c], checks when x1 ∈ (a, b], and bet-calls whenx1 > c. Player II folds when x2 ≤ d, calls when x2 ∈ (e, f ], and re-raises when x1 ∈ (d, e] ∪ (f, 1].0 ≤ a ≤ e ≤ b ≤ c ≤ f ≤ 1 and 0 ≤ d ≤ e (d can be larger or smaller than a), where

a =B2

1(2 + 2B1 +B2)2

(1 +B1)∆, b = 1− 2 +B1

B1a, c = 1− 2B1(2 +B1)(2 + 2B1 +B2)

∆,

d =B1 + 2a

2 +B1, e =

B1

1 +B1− a, f = 1− B1(2 +B1)(2 + 2B1 +B2)

∆

where ∆ = B1(4 +B1)(2 + 2B1 + B2)2 + (1 + B1)(2 +B1)

2B2. The optimal strategies are illustrated inFigure 5.

Player Ia b c0 1

d e f

bet-fold bet-fold bet-call

fold raise call raisePlayer II

check

Figure 5: Optimal Strategies of both players.

Proof. First, apply the ICs for

• I at a: −2a+ (−2−B1)d = B1;

• I at b: 2B1b+ (2 +B1)d+ (−2B1 − 2)e = B1;

• I at c: (−2− 2B1 −B2)d+ (2 + 2B1 +B2)e+B2f = B2;

• II at d: (2 +B1)a− (2 +B1)b+ (2 + 2B1 +B2)c = B1 +B2;

• II at e: (−2− 2B1)b+ (2 + 2B1 +B2)c = B2;

• II at f : −c+ 2f = 1.

4






II

IIbet

checkfold

betcall

foldcheck u

1(1+B1)u

-(1+B1)

(1+B1+B2)u



a =B2

1(2 + 2B1 +B2)2

(1 +B1)∆, b = 1− 2 +B1

B1a, c = 1− 2B1(2 +B1)(2 + 2B1 +B2)

∆,

d =B1 + 2a

2 +B1, e =

B1

1 +B1− a, f = 1− B1(2 +B1)(2 + 2B1 +B2)

∆

where ∆ = B1(4 +B1)(2 + 2B1 + B2)2 + (1 + B1)(2 +B1)


Player Ia b c0 1

d e f



check



• I at a: −2a+ (−2−B1)d = B1;

• I at b: 2B1b+ (2 +B1)d+ (−2B1 − 2)e = B1;

• I at c: (−2− 2B1 −B2)d+ (2 + 2B1 +B2)e+B2f = B2;

• II at d: (2 +B1)a− (2 +B1)b+ (2 + 2B1 +B2)c = B1 +B2;

• II at e: (−2− 2B1)b+ (2 + 2B1 +B2)c = B2;

• II at f : −c+ 2f = 1.

4






II

IIbet

checkfold

betcall

foldcheck u

1(1+B1)u

-(1+B1)

(1+B1+B2)u



a =B2

1(2 + 2B1 +B2)2

(1 +B1)∆, b = 1− 2 +B1

B1a, c = 1− 2B1(2 +B1)(2 + 2B1 +B2)

∆,

d =B1 + 2a

2 +B1, e =

B1

1 +B1− a, f = 1− B1(2 +B1)(2 + 2B1 +B2)

∆

where ∆ = B1(4 +B1)(2 + 2B1 + B2)2 + (1 + B1)(2 +B1)


Player Ia b c0 1

d e f



check



• I at a: −2a+ (−2−B1)d = B1;

• I at b: 2B1b+ (2 +B1)d+ (−2B1 − 2)e = B1;

• I at c: (−2− 2B1 −B2)d+ (2 + 2B1 +B2)e+B2f = B2;

• II at d: (2 +B1)a− (2 +B1)b+ (2 + 2B1 +B2)c = B1 +B2;

• II at e: (−2− 2B1)b+ (2 + 2B1 +B2)c = B2;

• II at f : −c+ 2f = 1.

4

Solving six linearly independent equations of six unknowns, we get results as presented in the theorem.Now suppose we ignore the antes contributed by the players by treating them as sunk costs. Given

that Player II uses the conjectured optimal strategy, and player I has hand x1, I’s “gain”

• from checking is 2x1.

• from bet-folding is 2a if 0 < x < e; 2a+ 2(1 +B)(x− e) if e < x < f , and 2a+ 2(1 +B1)(f − e) iff < x < 1.

• from bet-calling is 2a− 2(1+B1 +B2)(e− d) if 0 < x < d; 2a− 2(1+B1 +B2)(e− x) if d < x < e;2a+2(1+B1)(x− e) if e < x < f ; and 2a+2(1+B1)(f − e) + 2(1+B1 +B2)(x− f) if f < x < 1.

We can verify that at every critical point, the payoffs from two strategies are equal. Then noting thatthe payoff function is piecewise linear, we verify that player I’s strategy is optimal. Similarly given playerI’s optimal strategy and Player II’s hand x2, Player II’s expected payoff from

• folding is 0 if 0 < y < a, 2(y − a) if a < y < b, and 2(b− a) if b < y < 1.

• calling is −2(1 + B1)(a− y) if 0 < y < a; 2(y − a) if a < y < b; and 2(b− a) + 2(1 + B1)(y − b) ifb < y < 1.

• raising is 0 if 0 < y < a, 2(y−a) if a < y < b; 2(b−a) if b < y < c; and 2(b−a)+(1+B1+B2)(y−c)if c < y < 1.

Then with II’s boundary conditions verified, player II is proven to play an optimal strategy as well.Complicated operations were done by Maple 11.

Corollary 3.2. Expected payoff of player I is a. Optimal bet for player I, B∗1 = 1+

√13/3. Optimal bet

for II is B∗2 = 2B∗

1 + 2 = 4 + 2√13/3.

Proof. Applying the modified payoff square as illustrated in Figure 6,

u1 = B1

[− a(1− d)− (c− b)(e− d) + (1− c)(e− d) + (1− b)(b− e)

]+

2[(2d− a)(a

/2)− (c− b)(e− d)

]+B2

[(1− c)(e− d)− (f − c)(1− f)

]

= B21

/{(1 +B1)

[B1(4 +B1) + (1 +B1)(2 +B1)

2B2/(2 + 2B1 +B2)2]} = a.

b

0 1 1x

2x1

a b

1+B1

-1-B1

-1-B1

+1 +1

-1

d e c f

a

d

e

c

f

1+B1+B2

+1

-1-B1

1+B1+B2-(1+B1+B2)

-1-B1

b

0 1 1x

2x1

a b

B1

-B1

+2

d e c f

a

d

e

c

f

B1+B2-2-B1

-B2

Figure 6: Payoff of Player I by payoff square.

Minimizing u1 with respect to B2 while B1 is fixed, is equivalent to maximizing B2/(2+ 2B1 +B2)2,

(2B1 + 2 +B2)− 2B2

(2 + 2B1 +B2)2= 0 ⇒ B∗

2 = 2B∗1 + 2.

5














1 + 2 = 4 + 2√13/3.


u1 = B1

[− a(1− d)− (c− b)(e− d) + (1− c)(e− d) + (1− b)(b− e)

]+

2[(2d− a)(a

/2)− (c− b)(e− d)

]+B2

[(1− c)(e− d)− (f − c)(1− f)

]

= B21

/{(1 +B1)

[B1(4 +B1) + (1 +B1)(2 +B1)

2B2/(2 + 2B1 +B2)2]} = a.

b

0 1 1x

2x1

a b

1+B1

-1-B1

-1-B1

+1 +1

-1

d e c f

a

d

e

c

f

1+B1+B2

+1

-1-B1

1+B1+B2-(1+B1+B2)

-1-B1

b

0 1 1x

2x1

a b

B1

-B1

+2

d e c f

a

d

e

c

f

B1+B2-2-B1

-B2



(2B1 + 2 +B2)− 2B2

(2 + 2B1 +B2)2= 0 ⇒ B∗

2 = 2B∗1 + 2.

5Substitute in, u1 = 8B2

1

/[(1+B1)(9B

21 +36B1 +4)

]. Then maximizing u1 with respect to B1 yields

9B31 − 40B1 − 8 = 0. Three roots are B1 = −2, 1 +

√13/3, 1−

√13/3. Clearly,

B∗1 = 1 +

√13/3 ≈ 2.202, B∗

2 = 4 + 2√13/3 ≈ 6.404

Substituting in B∗1 and B∗

2 , a = 0.0955, b = 0.8178, c = 0.909, d = 0.569, e = 0.592, f = 0.954.Though the game still favors player I, its payoff (0.0955) is lower than that in the original von

Neumann model (1/9). This shows that allowing player II to re-raise restricts player I’s audacity ofbluffing, thus decreasing his advantage and profit. Obviously player I always has advantage given thathe makes a voluntary decision first because he can always checks to yield an expected payoff of 0. Alsonote that player I’s optimal bet is a little over the pot size, and player II is little under the added potsize, however very close. This gives some insight and justification to bet by pot size in real poker.

In addition, player II can bluff with his “good” hands. This is justified as follows. Player I will foldhis worst hands because he is caught bluffing, and fold some of his good hands because player II will alsoraise with his best hands. However, if player II simply calls, he has higher chance of losing to the goodhands that player I has raised with. Folding is even more disastrous as he is bluffed by the worst handsof Player I.

In both models, payoffs for player I are both a which corresponds to the initial bluff region by PlayerI in the first round. This fact needs to be further investigated in order to determine whether value ofplayer I is always a allowing additional re-raises.

4 Multiple Re-raises

The game tree allowing two raises by each player is illustrated in Figure 7, and model of more raises canextended by adding more “branches”.

I III II Ifoldcheck/call

bet

Figure 7: Game tree of two raises.

By forward induction, we conjectured the optimal strategies for both players to be as follows. Forplayer i, i = 1, 2, in round j, let fi,j be the folding threshhold, ci,j the calling threshold, and ri,j theraising threshold. fi,j < ci,j < ri,j < 1, dividing the hands into four intervals. Then player i in round jwill

fold if xi ∈ (0, fi,j ]raise if xi ∈ (fi,j , ci,j ]call/check if xi ∈ (ci,j , ri,j ]raise if xi ∈ (ri,j , 1]

fI,1 = 0 in this model because no hand will be folded by player I. Furthermore, 0 < fi,j , ci,j , ri,j < fi,Jfor all J > j, producing strictly smaller interval of remaining hands. Relationship of inequalities betweentwo players’ folding, calling and raising thresholds needs to be investigated. We can apply indifferenceconditions to each of the thresholds and solve for equilibrium conditions, but it will be complicatedalgebraically.

If the bet amount is restricted to be pot size, with unlimited number of bets and forbidding check-raises, Cutler solves an equilibrium using recursion [Cutler, 1975]. Recursion is feasible because eachtime a player pays the same ratio to win an equivalent amount when he calls.

5 Conclusion

We investigated von Neumann’s model to see that bluffing is an important strategy to gain advantage.Giving player II’s option to re-raise, thus option to bluff after possible bluff after player I, eliminatessome of player I’s advantage.

6














1 + 2 = 4 + 2√13/3.


u1 = B1

[− a(1− d)− (c− b)(e− d) + (1− c)(e− d) + (1− b)(b− e)

]+

2[(2d− a)(a

/2)− (c− b)(e− d)

]+B2

[(1− c)(e− d)− (f − c)(1− f)

]

= B21

/{(1 +B1)

[B1(4 +B1) + (1 +B1)(2 +B1)

2B2/(2 + 2B1 +B2)2]} = a.

b

0 1 1x

2x1

a b

1+B1

-1-B1

-1-B1

+1 +1

-1

d e c f

a

d

e

c

f

1+B1+B2

+1

-1-B1

1+B1+B2-(1+B1+B2)

-1-B1

b

0 1 1x

2x1

a b

B1

-B1

+2

d e c f

a

d

e

c

f

B1+B2-2-B1

-B2



(2B1 + 2 +B2)− 2B2

(2 + 2B1 +B2)2= 0 ⇒ B∗

2 = 2B∗1 + 2.

5

Figure 4: Extensive form of the two players with Player I’s payoffs.




RESEARCH ARTICLES

29

prot. Player I always has advantage given that he makes a voluntary decision first because he can always check to yield an expected payoff of 0. Also note that Player I’s optimal bet is a little over the pot size, and Player II is little under the added pot size, however very close. This gives some insight and justification to bet by pot size in real poker.

In addition, Player II can bluff with his “good” hands. This is justified as follows. Player I will fold his worst hands because he is caught bluffing, and fold some of his good hands because Player II will also raise with his best hands. However, if Player II simply calls, he has higher chance of losing to the good hands that Player I has raised with. Fold-ing is even more disastrous as he is bluffed by the worst hands of Player I.

In both models, payoffs for Player I are both a which cor-responds to the initial bluff region by Player I in the first round. This fact needs to be further investigated in order to determine whether value of Player I is always a allowing additional re-raises.

Multiple Re-raisesThe game tree allowing two raises by each player is illus-

trated in Figure 7, and model of more raises can be extended by adding more “branches”.

By forward induction, we conjectured the optimal strate-gies for both players to be as follows. For player i, i = 1, 2, in round j, let fi,j be the folding threshhold, ci,j the calling threshold, and ri,j the raising threshold. fi,j < ci,j < ri,j < 1, di-viding the hands into four intervals. Then player i in round j will

fI,1 = 0 in this model because no hand will be folded by Player I. Furthermore, 0 < fi,j , ci,j , ri,j < fi,J for all J > j, pro-ducing strictly smaller interval of remaining hands. Rela-tionship of inequalities between two players’ folding, call-ing and raising thresholds needs to be investigated. We can apply indifference conditions to each of the thresholds and solve for equilibrium conditions, but it will be complicated algebraically.

If the bet amount is restricted to be pot size, with un-limited number of bets and forbidding check-raises, Cutler solves an equilibrium using recursion (Cutler, 1975). Recur-sion is feasible because each time a player pays the same ra-

tio to win an equivalent amount when he calls.

ConclusionWe investigated von Neumann’s model to see that bluff-

ing is an important strategy to gain advantage. Giving Play-er II’s option to re-raise, thus option to bluff after possible bluff after Player I, eliminates some of Player I’s advantage.

Findings in this paper may be applied to real poker. The paper shows that in optimal strategies, a player should bluff with their worst hands, but not mediocre hands, because there is slim hope of winning with their worst hands. How-ever, when one raises with a mediocre hand, the opponent is likely to call with a better hand and fold worse hands. Thus raising by the first player magnifies his loss by losing more from inferior hands and gaining none from the other player folding worse hand. In addition, if the player is re-raised, he would have a hard time deciding whether to fold or call with a mediocre hand, because he could falsely think that the opponent is bluffing him. However, calling would result in even bigger loss. Checking in the beginning could avoid such a situation.

Since unlimited number of raises are allowed in real poker, extension to more rounds is important too. The ex-tensions can help us to conclude about players’ optimal strategies corresponding to different regions of cards, and whether Player I’s expected payoff from optimal strategy is always a, the proportion of hands he has bluffed in initial raise. In addition, it gains insight whether there is a better equilibrium play for either player. The paper also introduces the payoff square, which could be of important use for more complicated hand distributions in games of two or three players because of its straightforward presentation of pay-offs.

ReferencesCutler, W. H. (1975). The American Mathematical Monthly 82-4, 368{376.

Ferguson, C. & Ferguson, T. S. (2003). In Game Theory and Applica-tions vol. 9, pp. 17{32. Nova Science Publisher New York, NY.

Ferguson, C., Ferguson, T. S. & Garaway, C. (2007). In Game Theory and Applications vol. 12, pp. 17{37. Nova Science Publisher New York, NY.

Newman, D. J. (1959). Operational Research 7, 557{560.

Smith, G., Levere, M. & Kurtzman, R. (2009). Management Science 55-9, 1547{1555.

von Neumann, J. & Morgenstern, O. (1953). Theory of Games and Economic Behavior pp. 186{219. Princeton, NJ: Princeton University Press.

Substitute in, u1 = 8B21

/[(1+B1)(9B

21 +36B1 +4)



√13/3, 1−

√13/3. Clearly,

B∗1 = 1 +

√13/3 ≈ 2.202, B∗

2 = 4 + 2√13/3 ≈ 6.404









bet






5 Conclusion


6

Substitute in, u1 = 8B21

/[(1+B1)(9B

21 +36B1 +4)



√13/3, 1−

√13/3. Clearly,

B∗1 = 1 +

√13/3 ≈ 2.202, B∗

2 = 4 + 2√13/3 ≈ 6.404









bet






5 Conclusion


6



Low Energy Ultrasonic Irradiation: Potential Applications in Oil RefinementJames P. Mandaglio, Johns Hopkins University

Demand for heavy crudes is increasing as lighter crudes become more costly. Compared with light petroleum products, heavy crude is hydrogen deficient and contains a larger fraction of asphaltenes. Asphaltenes are com-plex mixtures of polyaromatic molecules containing most of the metals, sulfur, and nitrogen within crude oil. These molecules are difficult to convert to lighter fractions, and the metals within these molecules foul catalysts. In addition, asphaltenes adversely affect viscosity, and thereby cause clogging during production, refinement, and transport. There is great demand within the oil refinement industry for a cost sensitive method that can ef-ficiently convert heavy crudes into lower sulfur products through catalysts, including biocatalysts and other pro-cesses. Recent research suggests that ultrasonic irradiation with frequencies in the range of 15 kHz to 1 MHz are known to cause a variety of chemical transformations (1) that could prove useful in oil refinement. The present paper investigates this potential utility of ultrasonic irradiation and concludes that sonic energy could be useful for catalytic refinement.

Refinement Catalysts: Characteristics of Ultrasonic Irradia-tion/Rectified Diffusion

There are a variety of microorganisms, catalysts, and combinations thereof that could potentially be suitable for use in oil refinement systems. Studies suggest that extremo-philic microorganisms and their enzymes (extremozymes) are attractive catalysts for use in petroleum refining. The enzymes isolated from extremophilic microorganisms pos-sess unique properties that can be used for industrial appli-cations; they are extremely thermostable (i.e. not prone to structural changes both chemically and physically at high temperatures) and are generally resistant to organic sol-vents, high pressures, and extreme pH environments (2). Different extremophilic bacterial genera such as Thioba-cillus, Achromobacter, Pseudomonas, and Sulfolubus have been utilized in the process of converting heavy crudes into lighter fractions (3). It is clear that a multiplicity of potential bioremediators exist that can be used to degrade sulfur rich asphaltenes within heavy crude. It still remains to be seen which of these catalysts, in the presence of ultrasound and cavitation inception, will show increased reactivity and ash-paltene degradation rate.

A potentially viable solution to increase the longevity and reactivity of these catalysts is the implementation of ultra-sonic irradiation within the refinement process. The propa-gation of low energy ultrasound (i.e. greater than 20 kHz but less than 1 MHz) through a heterogeneous solid-liquid mix-ture (i.e. heavy crude and some other hydrocarbon solvent) in a manner such that it does not adversely affect the refine-ment process or produce any unwanted byproducts through a secondary reaction mechanism, can induce cavitation in-ception through rectified diffusion. Cavitation inception refers to the process by which the liquid pressure in a liquid flow system drops below the vapor pressure of the operating

fluid at some locations, resulting in unplanned vaporization (4). The vapor bubbles (called cavitation bubbles because they form “cavities” in the liquid) collapse as they are swept away from the low-pressure regions, generating extremely high-pressure waves (5). Under ideal conditions or those that best lower the cavitation number (σ) of the system, cavitation inception can potentially increase the reactivity, catalytic capability, and lifespan of these micro-organisms. This concept seeks to utilize the high energy output in the form of extreme pressure and temperature gradients (pre-viously mentioned) that occur during bubble collapse. The manner by which cavitation might enhance the catalytic re-activity of extremophilic microorganisms within the refine-ment process draws upon knowledge from a variety of fields of research such as sonochemistry and biology, and will be discussed later in this article following a brief description of the process of cavitation inception via ultrasonic irradiation.

The presence of cavitation nuclei and the advent of cavi-tation inception can be triggered through various means. When refining heavy crudes into lighter fractions, ultrason-ic irradiation within the heterogeneous solid-liquid mixture will promote cavitation nuclei and future inception. When a sound wave propagates through a heterogeneous mixture, the waveform is comprised of two half cycles. The first half cycle, called rarefaction, produces a negative pressure front that is capable of overcoming the adhesion and cohesion forces of the liquid itself. If this half cycle produces enough negative pressure, cavitation nuclei will form. After the neg-ative pressure rarefaction front, the second half cycle passes, producing a positive pressure front through the system. This positive pressure causes bubbles within the bulk liquid to col-lapse inward (6). During implosion, a tremendous amount of heat and pressure are released into the system (7). At lower acoustic intensities (i.e. low energy ultrasound), cavitation


RESEARCH ARTICLES

31

inception can occur through diffusion. When the bubble is subjected to an oscillating pressure field there is a net inflow of gas into the bubble (8). During the positive half cycle, gas diffuses out of the bubble. Conversely, during the following negative half cycle (rarefaction), gas flows back in (9). The surface area of the bubble is larger during the negative half cycle due to the pressure decease in the surrounding bulk liquid so that there is, over a number of cycles, a net inflow of gas (10). This process is known as rectified diffusion (11). In essence, rectified diffusion is the manner by which cavita-tion occurs in ultrasonically irradiated fluids. After the bub-ble has reached a critical radius, the tensile strength of the bubble is no longer able to overcome the forces it is subjected to during the positive pressure cycle (12). Its surface then tears and the bubble collapses (13). During the compression cycle all bubbles will be made to contract and collapse (14). If during growth, some gas or vapor has diffused into the void or bubble, complete collapse may not occur (15). Those bub-bles which collapse completely are considered transient and those which do not are considered stable (16). The objective is to manipulate the refinement environment such that rec-tified diffusion is complete and transient cavitation occurs. The efficiency of cavitation inception and collapse depends on a variety of variables. Certain experimental variables such as the bulk temperature and the viscosity of the system can be manipulated to improve the quantity of cavitation nuclei and energy output during bubble collapse.

The bulk temperature of the system as well as its viscos-ity are both integral in the quantity and energy of cavitation inception. As the bulk temperature of the system increases, surface tension and viscosity decrease and cavitation is more readily achieved (17). As the bulk temperature of the system increases, the vapor pressure also increases (18). This spike in vapor pressure creates a cushioning effect that will in-hibit the high energy output that is typically associated with a normal bubble collapse thus inhibiting transient rectified diffusion (19). Therefore, due to the extreme temperatures associated with the refinement process and the accompany-ing spike in vapor pressure described above, the operating liquid must have a high bulk boiling point. If the liquid’s boiling point is too low, cavitation inception will be futile due to large vapor pressures in the flow (remember, cavita-tion occurs only when the flow vapor pressure drops below that of the operating fluid). Therefore, uncovering a combi-nation of temperatures and pressures that maximize cata-lytic reactivity and cavitation inception at a given ultrasonic energy level is vital.

Potential Method for Enhancing Rectified Diffusion and Cat-alytic Reactivity

While attempting to refine heavy crude through ultra-sonic irradiation, one must utilize the “cleansing” charac-teristics of cavitation to help increase the reactivity and life spans of chosen catalysts and extremophilic micro-organ-

isms that degrade the sulfur rich asphaletenes commonly found within heavy crude. Distinct evidence or experimen-tal data suggesting that a technique is energetically feasible has yet to be found. However, one option for success might be to continuously implement low energy ultrasound (i.e. to instigate cavitation via rectified diffusion) so that refinement of heavy crude can occur at the wellhead, and that this use-ful crude can then be injected into existing oil pipelines. The efficiency of rectified diffusion and the quantity of cavitation nuclei may also be enhanced through hydrodynamical cavi-tational technique.

Hydrodynamical cavitation occurs when a liquid under-goes a dynamic pressure reduction due to the constriction of devices like venturi or orifice plates (20). In a recent textile wastewater study, researchers assessed the efficiency of this technique by comparing results with “. . . the cavitation gen-erated by ultrasound” (21). Researchers observed:

“[T]here is a substantial enhancement in the extent of deg-radation of this dye using hydrodynamic cavitation for the same level of energy dissipation. Thus, the present set-up of hydrodynamic cavitation using multiple hole orifice plates has been found to give cavitational yields, which are two times higher than the best acoustic cavitation device, tested earlier. Moreover, the capacity of the reactor in the present case (50 l) is also 66 times higher as compared to the largest ultrasonic equipment tested. In case of hydrodynamic cavita-tion, the efficiency of the pump is also likely to increase with an increase in the scale of the operation, which promises an effective scale-up of the reactor with the same or even better cavitational yields for a larger scale” (22).

Although this study suggests no means by which ultra-sonic irradiation and hydrodynamical cavitation can be coupled to enhance rectified diffusion, it seems logical that utilization of the two methods would help ensure higher cavitation rates. Furthermore, the study also demonstrates that cavitation is a viable way to implement large scale re-finement, and that the output of this process can be utilized in the commercial realm.

As previously mentioned, a tremendous quantity of en-ergy is exerted into the experimental system during bubble collapse. This energy includes shockwaves created during bubble implosion, high temperatures reaching nearly 5000 K, extremely high pressures (around 2000 Atm), and water jets (23). In a heterogeneous solid-liquid mixture, this energy output can be utilized to perform useful work. In the case of liquid-powder slurries, the shock waves created by homoge-neous cavitation can create high-velocity inter-particle colli-sions. Such inter-particle collisions are capable of inducing striking changes in the surface texture and reactivity of the microorganisms used to refine the heavy crude. Reactivity rate enhancements of more than 10-fold are common, yields are often substantially improved, and unwanted by-products avoided (24). The mechanism of the rate enhancements in reactions of metals has been unveiled by monitoring the ef-


fect of ultrasonic irradiation on the kinetics of the chemical reactivity of the solids, examining the effects of irradiation on surface structure and size distributions of powders and solids, and determining depth profiles of the surface el-emental composition (25). The power of this “three-pronged approach” has been proved in studies of the sonochemis-try of transition metal powders (26). Doktycz and Suslick found that ultrasonic irradiation of liquid compositions of nickel, zinc, and copper powders leads to dramatic changes in structure (27). The high-velocity interparticle collisions produced in such slurries can cause smoothing of individ-ual particles and agglomeration of particles into extended aggregates (28). Surface composition was probed by Auger electron spectroscopy and mass spectrometry to generate depth profiles of these powders (29). The profiles revealed that ultrasonic irradiation effectively removed the inactive surface oxide coating (30). The removal of such passivating coatings dramatically improves reaction rates (31).

Utilization of Ultrasonic Irradiation and Cavitation in As-phaltene Decomposition

In the case of bioremediation and asphaltene breakdown, which occurs during the refinement of heavy crude, ultra-sonic irradiation can capitalize on the possibilities bred by the high energy output associated with a typical bubble col-lapse. This energy can be utilized in a heterogeneous solid-liquid mixture to increase the reactivity, lifespan, and overall efficiency of any catalyst present in the experimental system. The “smoothing” of the surface of these catalysts is primar-ily caused by inter-particle collisions created by shockwaves produced in the system during bubble collapse. When these micromolecules strike each other directly, they bind to-gether due to the high temperatures and form agglomerates with larger surface areas. These agglomerates will have more binding sites and be potentially more reactive in nature be-cause of their larger surface areas. If the micromolecules do not strike each other directly, but rather ‘nick’ each other, they will not bind but will chip away at each other’s surfaces. This process will rid the microorganisms of protein mem-branes that encapsulate the species and mar their reactivity and catalytic nature. In this way the implementation of low energy ultrasound will have advantages that are two-fold. First, the high energy output associated with cavitation in-ception and bubble collapse will enable the emulsification of micro-molecules due to inter- particle collisions that are spurred on by shock waves produced within the system dur-ing bubble collapse. These agglomerates will have larger sur-face areas and more active sites, thus enhancing their reac-tive capabilities and ability to decompose asphaletenes.

Second, indirect inter-particle collisions will cause grad-ual cleansing and removal of protein rich membranes that surround the surfaces of the microorganisms and inhibit life spans and reactivity. This will increase the overall capability of the microorganisms introduced to the refining environ-

ment, and will allow for larger quantities of heavy crude to be refined (via asphaletene decomposition) in shorter periods of time. Furthermore, cavitation inception is not typically characterized by singular bubble formation and collapse. That is, usually, one is left with a remnant cloud of small bubbles that will continue to collapse collectively. Though no longer a single bubble, this remnant cloud will still ex-hibit the same qualitative dynamic behavior, including the possible production of a shock wave following the point of minimum cavity volume (32). Studies have been performed that have tried to quantitatively measure that amount of en-ergy that is released during bubble collapse within the rem-nant cloud. Kimoto (1987) was able to observe stress pulses that resulted both from microjet impingement and from the remnant cloud collapse shock. Typically, the impulsive pres-sures from the latter are 2 to 3 times larger than those due to the microjet, but it would seem that both may contribute to the impulsive loading of the surface [e.g of solid in hetero-geneous solid-liquid system] (33). Remnant cloud formation can be utilized during the refinement process. By initiating cavitation and varying the frequency of the ultrasonic irra-diation, optimal levels of remnant cloud inception can be achieved. It has been shown that the cumulative implosion of the bubbles within these clouds can create shock waves and microjets, which cause cavitational erosion, pitting, and inter-particle collisions. Christopher Earls Brennen suggests that remnant cloud formation can be maximized when the frequency of the ultrasound is close to the natural frequency of a significant fraction of the nuclei present in the liquid. Under such conditions, one might be able to increase the rate of “cleansing” by increasing the quantity of inter-parti-cle collisions that occur in the heterogeneous fluid.

A byproduct of the utilization of cavitation in heteroge-neous solid-liquid systems such as those at the wellhead is the process of intercalation. Chemical intercalation is de-fined as the insertion or reversible inclusion of a “molecule (or group) between two other molecules or groups” (34). Su-slick suggests that organic or inorganic compounds can be inserted into the atomic sheets of layered solid hosts. Inter-calation permits the systematic change of optical, electronic, and catalytic properties (35). This process is especially useful when working with asphaltenes. Asphaltenes have a chemi-cal structure that can be described as “sheet-like” in nature (36). In the crude, the asphaltene sheets remain dispersed (37). However, they have the tendency to be attracted to-wards each other thus resulting in the formation of an ag-glomeration (38). The structure of the agglomeration is simi-lar to that of a book: a compact stack of thin sheets (39). The possibility therefore exists that ultrasonic irradiation could be able to inject certain catalysts or micro-molecules into the “sheet” structure of the asphaltenes present within the heavy crude. These molecules, once secured within the ben-zene ring structure, may help in further breakdown of the


RESEARCH ARTICLES

33

asphaltene structure. Coupled with the processes describe above, this could increase the rate and quantity of heavy crude refinement. Studies have suggested that intercalation is a slow process that typically requires high energy inputs. Even the use of high-intensity ultrasonic irradiation might produce only modest results over long periods of time.

A variety of patents are currently available that utilize low and high energy sonochemistry to drive chemical re-actions. Of particular interest is a sonochemical reactor that has been developed under USPC class 20415715, which comprises of a scaled-up reaction chamber with a plurality of physically coupled externally mounted transducers. Ex-ternally mounted transducers overcome the many disadvan-tages that stem from directly initiating excitations within the fluid (40). That is, the externally mounted transducers sim-plify the delivery of electric power and avert the potential damage resulting from cavitation inception or from the fluid itself (41). Furthermore, such a configuration proves advan-tageous when trying to induce cavitation in heterogeneous mixtures, because there can be variations in the acoustic im-pedance of the mixture within the reaction chamber which can significantly mar the control of internally mounted transducers (42). The patent claims that substantial uni-form radial excitation ensures that input energy is focused near the center of the reaction chamber, and the intensity of the resulting cavitation is determined by the input power. The claim in also made that the device can be operated in a continuous mode that proves advantageous for water pu-rification, sewage sludge processing, and even hydrocarbon “cracking” and dispersal of nano-particles in fluid. The reac-tion chamber, which is in the form of a thin-walled right cir-cular cylinder, also permits cleaning and maintenance (43).

The concepts exhibited by the patent described above might bridge the gap between small scale laboratory so-nochemical reactions and the much larger industrial so-nochemical reactions needed to refine heavy crude at the wellhead. As previously mentioned, the efficiency of the re-finement process will depend on a combination of the rate of cavitation inception and intensity of bubble collapse. Since both are highly dependent on environmental conditions, a device allowing for some control over ultrasonic intensity and the refinement environment (the reaction chamber is a closed cylindrical vessel) is beneficial. Furthermore, it might be possible to couple multiple devices together and place them in the wellhead. From here, heavy crude can be pumped through each system and further refined sequen-tially. Having multiple devices enables us to support the needs of multiple customers who might desire varying levels of refined crude. Pumping crude through a system such as this will also enable us to capitalize on enhanced asphaltene decomposition by combining ultrasonic irradiation with hy-drodynamic induced cavitation. If we, for instance, insert venturis or orifice plates within the sonochemical reactor

and pump the heterogeneous mixture through these struc-tures, hydrodynamical cavitation will occur. Combining this with the ultrasonic irradiation will increase the quan-tity of cavitation nuclei and enhance the rate of refinement. The aforementioned device is promising in that it has dem-onstrated the feasibility and validity of inducing cavitation for prolonged periods of time in heterogeneous mixtures similar to those present during heavy crude refinement. The efficacy of asphaltene decomposition (and crude refinement) instigated by ultrasonic and hydrodynamically induced cavitation suggests that ultrasonically generated cavitation might be an economically viable way to refine crude oil.

ReferencesBrennen, Earls Christopher. (1995) Cavitation and Bubble Dynamics. Oxford University Press.

Cengel, Yunus A, Cimbala, John M. (2010) Fluid Mechanics Funda-mentals and Applications. 2nd ed. Boston: McGraw-Hill Higher Edu-cation.

Gallaher, Amanda B, Hannon, Dominic B. Hardie and David John Webster (USPC Class 20415715). Sonochemistry. 24 May 2009. http://www.faqs.org/pate nts/app/20080217160.

Hoffmann, Michael R., Inez Hua, and Ralf Hochemer. “Application of Ultrasonic Irradiation for the Degradation of Chemical Contami-nants in Water.” Ultrasonics Sonochemistry 3.3 (1996): S163-172. Sci-enceDirect. Elsevier Science B.V., 11 Feb. 1999. Web. 26 Mar. 2010.

“Intercalation (chemistry).” Wikipedia: The Free Encyclopedia. Ac-cessed August 15, 2008. http://en.wikipedia.org/wiki/Intercalation_(chemistry).

Le Borgne, Sylvie and Rodolfo Quintero. Biotechnological Process-es for the Refining of Petroleum, Programa de Biotecnologia del Petroleo, Instituto Mexicano del Petroleo 81: 15 May 2003: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TG3- 48FCG111&_user=1082852&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=1082852&md5=70a4508fccdc19e36428e35038490f7c.

Lickiss, D. Paul. (2000) The New Chemistry. Ultrasound in Chemical Synthesis. Cambridge University Press.

Mason, J. Timothy and John P. Lorimer. (2002) Applied Sonochem-istry: The Uses of Power Ultrasound in Chemistry and Processing. Wiley-VCH Verlag GmbH, Weinheim.

OTS Heavy Oil Learning Centre, Lloydminster Oilfield Technical So-ciety. “What Are Asphaltenes?.” http://www.lloydminsterheavyoil.com/asphaltenes.htm.

Sivakumar, Manickam and Aniruddha B. Pandit. 2002. “Waste Water Treatment: A Novel Energy Efficient Hydrodynamic Cavi-tational Technique.” Ultrasonics Sonochemistry 9, no. 3 (July 2002), http://www.sciencedirect.com/science?_ob=Art icleURL&_udi=B6T W344GM2JG2&_user=1082852&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000051401&_version=1&_urlVersion=0&_userid=1082852&md5=274acc4a4536576a351abc626f688f27 (accessed August 24, 2008).

Suslick, S. Kenneth. (1994) “The Chemistry of Ultrasound,” The Year-book of Science & the Future, 138-155. Encyclopedia Britannica: Chi-cago.

Trevena, D. H. (1987) Cavitation And Tension In Liquids, 63. IOP Pub-lishing Ltd.


Notes1. Hoffmann, Michael R., Inez Hua, and Ralf Hochemer. “Applica-

tion of Ultrasonic Irradiation for the Degradation of Chemical Contaminants in Water.” Ultrasonics Sonochemistry 3.3 (1996): S163-172. ScienceDirect. Elsevier Science B.V., 11 Feb. 1999. Web. 26 Mar. 2010.

2. Sylvie Le Borgne and Rodolfo Quintero. Biotechnological Pro-cesses for the Refining of Petroleum, Programa de Biotecno-logia del Petroleo, Instituto Mexicano del Petroleo 81: (15 May 2003): 155-169.

3. Le Borgne and Quintero, 2003, 155-169.

4. Cengel, Yunus A, Cimbala, John M. (2010) Fluid Mechanics Fundamentals and Applications. (2nd ed. Boston: McGraw-Hill Higher Education), 42.

5. Cengel, Yunus A, Cimbala, John M. 2010, 42.

6. D.H. Trevena, D. H. Cavitation And Tension In Liquids. (IOP Pub-lishing Ltd, 1987), 63.

7. Trevena, 1987, 63.

8. Trevena, 1987, 63.

9. Trevena, 1987, 63.

10. Trevena, 1987, 63.

11. Trevena, 1987, 63.

12. Trevena, 1987, 63.

13. Trevena, 1987, 63.

14. Trevena, 1987, 63.

15. Timothy J. Mason and John P. Lorimer. Applied Sonochemistry: The Uses of Power Ultrasound in Chemistry and Processing. Wi-ley-VCH Verlag GmbH, Weinheim, 2002), 44.

16. Mason and Lorimer, 2002, 44.

17. Paul D. Lickis, The New Chemistry. Ultrasound in Chemical Syn-thesis (Cambridge University Press, 2000), 79.

18. Lickis, 2000, 79.

19. Lickis, 2000, 79.

20. Manickam Sivakumar, and Aniruddha B. Pandit. “Waste Water Treatment: A Novel Energy Efficient Hydrodynamic Cavitation-al Technique.” Ultrasonics Sonochemistry 9, no. 3 (July 2002): 123-131, http://www.sciencedirect.com/science?_ob=Art icleURL&_udi=B6TW344GM2JG2&_user=1082852&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C00005140&_version=1&_urlVersion=0&_userid=1082852&md5=274acc4a4536576a351abc626f688f27

21. Sivakumar and Pandit, 2002, 123-131.

22. Sivakumar and Pandit, 2002, 123-131.

23. Kenneth S. Suslick, “The Chemistry of Ultrasound,” The Yearbook of Science & the Future, (Encyclopedia Britannica: Chicago, 1994), 138-155.

24. Suslick, 1994, 138-155.

25. Suslick, 1994, 138-155.

26. Suslick, 1994, 138-155.

27. Suslick, 1994, 138-155.

28. Suslick, 1994, 138-155.

29. Suslick, 1994, 138-155.

30. Suslick, 1994, 138-155.

31. Suslick, 1994, 138-155.

32. Brennen, Earls Christopher. Cavitation and Bubble Dynamics (Oxford University Press, 1995), 79.

33. Brennen, 1995, 79-80.

34. “Intercalation (chemistry).” Wikipedia: The Free Encyclopedia. Accessed August 15, 2008. http://en.wikipedia.org/wiki/Inter-calation_(chemistry).

35. Suslick, 1994, 138-155.

36. OTS Heavy Oil Learning Centre. “What Are Asphaltenes?,” Lloy-dminster Oilfield Technical Society. http://www.lloydminster-heavyoil.com/asphaltenes.htm.

37. OTS Heavy Oil Learning Centre.



40. Amanda B. Gallaher, Dominic B. Hannon, and David John Web-ster Hardie (USPC Class 20415715). Sonochemistry. 24 May 2009. http://www.faqs.org/pate nts/app/20080217160.

41. Gallaher, Hannon, and Hardie, 2009.



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