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UTTER Research Directions

The central theme of the UTTER project's research directions is mathematical ecology, including aquatic and plant ecology, and epidemiology. Undergraduate research training in the program involves not only work with faculty and advanced student researchers in the usual lab and field settings but also regular participation in program seminar courses where all participants share and discuss work regularly, thereby providing models of the scientific endeavor at every step. New students in the program benefit from interaction with advanced students already engaged in research, and with faculty in both seminar and research settings. This structured environment in which all project participants mentor collectively as a learning community helps keep new students' training from being overdependent on interaction with a single individual. Through the UTTER research activities, students pursuing a mathematics major are engaged with empirical science, while students pursuing a biology major are engaged with quantitative and theoretical approaches. Thus these students have the rare opportunity to develop deep understanding of perspectives outside their home discipline.

Each of the UTTER research teams involves a mix of students majoring in mathematics and biology, and each is advised by faculty and Ph.D. students with related research interests.


A Mathematical Examination of the Relationship Between Visceral Leishmaniasis Incidence and the Proportion of Post-Kala-Azar Dermal Leishmaniasis Cases Treated into Remission
Andrea, Ryan, Ileana, and Nhan (UTTER Scholars)
    Visceral Leishmaniasis (VL) is a fatal disease caused by species of the Leishmania protozoan parasite. This disease is a health problem for the very poor and it results in the death of thousands and illness of hundreds of thousands every year. Some countries, for example India and Bangladesh, have started programs to reduce the occurrence of VL by focusing on early diagnosis and complete treatment. Post-kala-azar dermal leishmaniasis (PKDL) is a cutaneous manifestation of Leishmaniasis following the treatment of VL. Diagnosis of PKDL is based on one's history with VL, distribution of lesions, and by parasitological confirmation when in doubt. This study focuses on the relationship between VL incidence during a given period and the proportion of PKDL cases treated into remission during the same period using a dynamical system to model VL and PKDL infection dynamics over a fixed period of time where the assumption is that the infection has reached an endemic state. Here the proportion of PKDL cases treated is defined as the ratio of cumulative number of PKDL cases treated to the incidences of PKDL over the time period. This study indicates that with the current treatments available and considering achievable levels of treatment the impact of treating new PKDL cases on incidences of visceral leishmaniasis cases does not diminish at higher proportions of new cases treated, however the ability to treat new cases is precipitously inhibited at high proportions. Considering the rate of treatment as a simple proportion of cases treated does show a diminished efficacy at higher treatment levels due to a depletion of the population presenting with PKDL.

Mathematical Modeling and Simulation of Staphylococcus Aureus and its Small-Colony Variant
Amitpal, Logan, Whitney, and Kevin (UTTER Scholars)
    Staphylococcus aureus, known as golden staph, is a Gram-positive bacterium that is known to exist in two forms: its wild-type and a Small-Colony Variant (SCV). S. aureus is a very prevalent bacterium in the human body, as is Pseudomonas aeruginosa, which produces a signal molecule that causes the transition from wild-type to SCV. The SCV phenotype is understood to be more resistant to standard antibiotics, therefore cause recurring infection, as seen in individuals with Cystic Fibrosis. Our research aims to provide a mathematical model for the transition between the wild-type and SCV S. aureus in a chemostat culture which is influenced by a signal molecule. We used a system of differential equations to demonstrate the population dynamics of these variants of S. aureus. We examined the equilibria of the two variants in relation to the critical nutrient, iron, and the stability of their respective equilibria to establish how the transition from wild-type to SCV influences S. aureus population dynamics.


Quorum Sensing Interaction and the Effect of Antibiotic on the Dynamics of Two Types of Bacteria
Stephanie, Sarah, Mark, An, and Tina (UTTER Scholars)
    Quorum sensing plays an important role in cell-to-cell communication. Bacteria that employ this mechanism produce a signal molecule that can initiate transcription, causing phenotypic changes such as biofilm formation. In this study, we examine two types of bacteria of the same species that have different growth and mortality rates. Only one of the two types produces the signal molecule. The other type has the ability to form biofilms, allowing it to gain more protection from the antibiotic treatment. If the antibiotic can inhibit quorum sensing, the biofilm will be unlikely to form and the infection may be eliminated efficiently. Four differential equations were derived to model the effects of autoinduction and antibiotic on the quorum sensing between the bacteria. Autoinduction induces the maximum rate at which signal molecules are produced; higher signal molecule concentration implies higher possibility of converting one type of bacteria into another type capable of forming biofilm. However, the analysis and numerical simulations of this theoretical study indicate that autoinduction plays no significant difference in the conversion. In addition, the antibiotic eliminates both types of bacteria at different rates.

Death of the Bees: A Mathematical Model of Colony Collapse Disorder
Lindsey, Brian, and Christopher (UTTER Scholars)
    A mysterious problem has developed within honey bee populations; in a worst case scenario, bee hives will spontaneously collapse as the entire population disappears from the hive. This phenomenon has been named Colony Collapse Disorder (CCD). The problem is recent and has no known cause, though it is surmised to stem from one or multiple infections. In order to gain insight into its dynamics and possible causes, we have attempted to create a mathematical model. First, we establish a baseline model for the population dynamics of a single healthy hive, using a system of ordinary differential equations. To this model we then add equations which account for the disease affecting the population. Here we must take some liberties regarding assumptions of the disease source given how little is known about CCD, but our model accommodates both direct (bee-to-bee) and indirect (via contaminated plants as vectors) transmission. An analysis of the model's six equilibria including disease-free, endemic, and extinction states develops criteria for distinguishing among several scenarios, including both survival and extinction due to CCD. These criteria identify several key parameters which could offer insight into the nature of the cause of this colony collapse. All theoretical results are supported by a set of numerical simulations and are consistent with raw data regarding the dynamics of the disorder.


A General Model of the Innate Immune Response
Jackie, Katie, Kaytee, Souad, and Thuy (UTTER Scholars)
    This project involves the dynamics of innate immune system, represented as a predator-prey interaction in which prey have a refuge. Phagocytes (the predator) can prey on free, infectious bacteria in a planktonic stage, but not on the stage in a refuge that either represents a biofilm or an intracellular niche. Analysis of this model focused on conditions for feasibility and stability of a semi-trivial equilibrium (phagocytes present, but no bacteria) versus an equilibrium where the infection persists (phagocytes and both bacterial stages present).

A Mathematical Model of Bacteria and Nutrients in a Batch and Chemostat Culture
Andrew, Tyler, and Wilber (UTTER Scholars)
    This project involved dynamics of a microbial population in batch or chemostat culture when an inactive (non-reproducing) stage is produced. This project is linked to experiments on the harmful alga Prymnesium parvum, which can produce an inactive stage that appears neither to reproduce nor make the toxin produced by active cells.


A small sample of general interdisciplinary research directions, including: that students can pursue in the UTTER program is provided below.

Simple Models of Resource Competition and Allelopathy
    The coexistence of species competing for one ore more resources is a classical issue in ecology, dating from early findings that competition for one resource can lead to extinction of all but a single superior species. Since the forceful statement of the Competitive Exclusion Principle by Hardin, ecologists have proposed many exceptions, because the natural world is far too rich in species for the Competitive Exclusion Principle to apply generally. Many of these exceptions involve tradeoffs between the ability to compete for a resource and other biological properties affecting species interactions, such as allelopathy - the production of toxins that affect one or more competitors. Resource competition is often studied in the context of the chemostat, a well-mixed laboratory microcosm. An elegant body of mathematics based on ordinary differential equations (ODE) predicts that the species best able to deplete the resource will exclude other species asymptotically, a prediction well verified by experiments. Recent extensions of the traditional chemostat theory, by incorporating production of a toxin by one of two competitors, show that an inferior competitor for a resource that produces a toxin selectively killing its competitor can avoid extinction, and in some cases can drive the superior competitor extinct. Such ODE models find a natural application in the study of harmful algae, which produce a variety of toxins some of which can kill other algae. They are sufficiently simple to permit local stability and bifurcation analyses in addition to numerical studies. They are also interesting not only by virtue of their applications but because despite their similarity to conventional chemostat theory, global analyses derived from that body of work do not always apply, motivating deeper theoretical exploration. Our goal in this research direction will be to provide UTTER program participants with projects focused on numerical simulations and local analyses of relatively simple models constructed to represent biologically plausible patterns of population growth, resource competition, and toxin production.

Spatial and Temporal Trends in Coral Diversity and Decline in the Florida Keys
    Coral reef decline is occurring on a global scale, and mass coral mortality is observable in all of the world's tropical oceans. However, little is known about the timing or spatial variability of the loss of reef-building corals on both global and local scales. One region particularly hard hit are the Florida Keys, which have experienced dramatic changes over the past decade, including a significant decline in stony coral cover and substituent fluctuations in community structure. As a result, Florida Keys National Marine Sanctuary and Protection Act designated over 2,800 square nautical miles of coastal waters as the Florida Keys National Marine Sanctuary (FKNMS) and the Florida Keys Coral Reef Evaluation and Monitoring Project (CREMP) was initiated in 1994 to provide data on the status of coral reef resources. The CREMP data is a large data set collected over 10 years from 1996 to 2005 of coral abundance, species richness and disease over 40 locations and 3 geographic regions (defined as Upper Keys, Middle Keys, and Lower Keys) in the FKNMS. The collaboration between Mydlarz and Hawkins will expose students to this extensive and rich data set to answer ecological questions concerning the rate and spatial trends underlying coral decline in the Florida Keys. In addition a coincident data set on the spatial and temporal trends in water quality (water temperature, salinity, dissolved oxygen, nitrate, nitrite, ammonium, total nitrogen, total phosphorus and total organic carbon) of the Florida Keys is available from the FKNMS Water Quality Monitoring Project (WQMP). To date these two data sets have not been extensively studied for the potential relationships between water quality and coral decline. Therefore students will work on stochastic modeling to link specific metrics of water quality to the net increase or decrease in stony coral percent cover and stony coral species richness, overall net change in measurable reef community parameters and relating these changes to local land use as well as global climate change issues. UTTER participants will be developing relevant hypotheses within the ecological context of coral reef degradation and models for exploring the hypotheses. The models considered will span those studied in the proposed stochastic modeling course: Poisson processes and continuous-time Markov chains for the dynamic evolution of the disease/coral loss processes, in addition to regression models relating the parameters of these processes to potential drivers, such as water quality data.

Stoichiometric Modeling of Microbial Interactions
    This research direction elaborates a class of biological details that can be represented in models of species interactions such as those outlined in the first interdisciplinary research direction. The stoichiometry of elements within organisms can vary with consequences for a variety of ecological processes. For example, storage of nutrient elements commonly produces stoichiometric variation in algae. Similar stoichiometric variations in bacteria, and the protozoa that prey on bacteria are currently under study in our labs. Theory predicts that such stoichiometric variation has consequences for predator-prey and competitive dynamics, and these theoretical predictions being tested with parameterized mathematical models and experiments. Extending this research direction provides a number of projects for participants in the proposed program. Experiments testing published theory would involve running microbial cultures and analyzing the results, applying statistical principles of experimental design and analysis, including nonlinear parameter estimation. Extending theory to incorporate such complications as mixtures of dissolved organic substrates and mixotrophic nutrition would involve reformulating theory and exploring the consequences. To support experimental work, several microbes are currently under study in our labs, including the bacterium Pseudomonas fluorescens, and the protists Ochromonas danica and Prymnesium parvum. The latter is a harmful alga whose blooms are notorious for causing fish kills.

Migration of Chagas' Disease
    This project examines mechanisms underlying transmission of the parasite Trypanosoma cruzi in the U.S. and an evaluation of the possibility of Chagas' disease (caused by this parasite) emerging in this area, using a wide variety of mathematical models in conjunction with field biologists and epidemiologists. T. cruzi, native to the Americas, is carried by several insect vectors and mammalian hosts such as raccoons, dogs, and humans. A virulent strain causes Chagas' disease throughout Latin America; this often fatal and widely underdiagnosed syndrome eventually causes failure of the heart or other vital organs. As some U.S. strains of T. cruzi are nonvirulent, little is known of the transmission cycle that sustains it. However, observed risk factors for the emergence of a virulent strain such as the immigration of infected individuals, gradual migration of such strains from the south, and changes in environmental conditions establish a need to understand this cycle better. The best understood transmission cycle for Chagas' disease involves vector feeding and defecation on hosts. Chagas' vectors in the U.S., however, appear inefficient at this kind of transmission, and preliminary data suggest alternative avenues: by hosts consuming infected vectors, by vertical transmission, and through differential behavior (increased biting rates or mobility) of infected vectors. The interaction of vectors with multiple hosts, as well as local and regional geography, may also play important roles here. Preliminary data also suggest that infection by one strain may provide cross-immunity against infection by another strain. Evaluation of the potential for disease emergence in the U.S. also includes a comparative study of climatic effects and rapid urban growth on transmission in the U.S. and Mexico. Ongoing collaborations with parasitologists in Georgia and a public health researcher in Colima, Mexico continue to refine hypotheses and provide opportunities for interaction with field researchers. This research direction provides several possible projects for students in the proposed program, such as (1) Modeling the epidemiology of Chagas' disease with classical approaches using nonlinear dynamical systems, involving both qualitative and numerical analysis; (2) Formulation and computational exploration of stochastic agent-based models to study complex interactions of multiple mechanisms; and (3) Collection and analysis of epidemiological data, in collaboration with field biologists and epidemiologists in the U.S. and Mexico, to generate model predictions of climate change effects on the transmission cycle.

Mathematical and Computational Methods for Modeling of Biofilm-Forming Microbes in Porous Media
    The behavior of biofilms in porous media is important to the design of bioreactors for water treatment, bioremediation, and other industrial applications. Such designs require mathematical modeling of transport and accumulation of biofilm-forming microbes, biodegradation, and flagellate predation on bacterial communities. There is much room for improvement of the present generation of models, from creating more accurate models based on better understanding of underlying processes to developing better analytical tools and more efficient numerical solvers. This research direction extends an existing interdisciplinary collaboration whose broad goal is to model the effect of spatial heterogeneity on population dynamics, species interactions, and microbial community structure. It leads to a number of possible projects in mathematical modeling and numerical simulation for the undergraduate participants in the UTTER program, such as (1) Examining the effects of different kinetic reactions on the behavior of the multi-species biofilms in porous media through a series of numerical simulations; (2) Investigating bacterial tolerance to antibiotics by examining mathematical models of susceptible and resistant bacteria, and simulating the changes in biofilm populations in the presence and absence of the antibiotic; and (3) Examining the effects of protozoan grazing on bacterial activity, in particular pollutant degradation. The mathematical modeling will be conducted using ground-water flagellates as predators and bacterial prey with different adhesion characteristics.

Statistical Analysis and Modeling of Short- and Long-Term Ecological Data
    This research direction represents a unique opportunity for students to get involved in an ecological research in northern Alaska while being exposed to sophisticated statistical analysis techniques. It is a part of the Arctic LTER project which maintains numerous long-term manipulations of soil nutrient availability, air temperature, light availability, and mammal access in several different tundra types in northern Alaska. Research efforts are currently underway to examine the interplay of soil and plant food webs in two common tundra ecosystems and to modify models of soil food webs to directly include plant variables using collected data. In addition, several long-term datasets of plant species diversity and community composition are available, that have been collected in numerous tundra ecosystems. Available funds will be used to provide transportation costs for students to Alaska for the summer as they can function as research assistants on this project while completing their requirements for the UTTER program. There will be a number of possible projects for UTTER students, such as (1) Conducting additional measurements on long-term manipulations (from 1-25 years) of arctic tundra plant communities to analyze effects of climate change using appropriate statistical techniques. Many of the ongoing experiments will provide opportunities for new data collection to supplement current research projects, including soil, plant and invertebrate sampling; (2) Helping implement and expand the models proposed by Moore by including plant variables to better simulate carbon and nitrogen dynamics. UTTER students will assist Moore in exploring new models of productivity and trophic dynamics; and (3) Analyzing long-term datasets with new approaches to detect effects of ongoing climate change. The Arctic LTER maintains an on-line database that can be easily accessed by students, and many possibilities exist for analysis.