July 30-August 2, 2008
Society for Mathematical Biology Conference

hosted by the Centre for Mathematical Medicine, Fields Institute
held at University of Toronto, Medical Sciences Bldg.


Accepted Contributed Posters

Instructions for posters:
Posters will be mounted on a form core board, provided at the conference. Authors can use push-pins to attach their posters, but please bring your own. Each poster presenter will be assigned to and share a poster board. Poster mounting supplies (pushpins and Velcro) will be supplied at the Meeting.
The space allocated for each poster will be 36 X 42 inches wide.
The poster session to follow Friday August 1, please mount posters in the the Stone Lobby in the morning for viewing during lunch and break periods.

Poster Abstracts

Name Title
Alexandra Agranovich Influence of Spatial Factor on Hysteresis in Immune system.
Luay Almassalha Understanding the formation of the arabidopsis root epidermis through an intimate collaboration between modeling and experiment
Tyler Aten An Investigation of Tyrosine Kinase Tnk1 Substrates and Function
Marine Aubert Marine Aubert Simulating the growth patterns of Bacillus subtilis with a cellular automaton
Seunghyeon Baek Mathematical analysis on the diffusive models incorporating immunotherapy in the tumor-immune interaction
Jacob Barker, Naomi Pollica A statistical approach to population studies of Chagas Disease
Ian Besse A model of cardiac action potential: incorporating the caveolae-associated sodium current
Bruno Bieth Analysis of a Drug-Drug Interaction Problem from Pharmacokinetic
Richard Brown A meta-population model for the growth of nassella tussock
Tung Bui A Model of the BMP4 and FGF Signaling Pathways in Embryonic Xenopus laevis
Anna Cai Modeling a cell population with intracellular threshold dependent differentiation
Thomas W. Carr An SIR epidemic model with partial temporary immunity modeled with delay
David Chan Modeling of gene dispersal in a natural forest system
Ching-Shan Chou Robust Cell Polarization
John Contompasis The Role of Flightin in Drosophila Native Thick Filament Flexural Rigidity and Assembly
Katie Ferguson A model of CA1 hippocampal neurons with astrocytic input
Ben Fitzpatrick Parameter Estimation and Data Analysis in an Ecosystem Model of College Drinking.
Yu-yu Ren and Bo Forrester Determining the Correlation between Temporal Changes in Gravitropism and Auxin Sensitivity in Flax (Linum usitatissimum) Roots: A Mathematical Approach
Farshid S. Garmaroudi Systems Properties of Signaling pathways in CVB3-infected Cardiomyocytes
Moritz Gerstung Estimating mutational pathways of carcinogenesis
Jana Gevertz Growing Heterogeneous Tumors in Silico
Jennifer Glenister Individual based model of factors influencing the territorial boundary between the harvester ant Pogonomyrmex spp. and related hybrid lineages
Pranay Goel The geometry of bursting in the dual-oscillator model of pancreatic beta-cells.
Pace S. Goodman Habitat segregation between two species of Harvest Ants and their interspecific hybrids
Heather Hardway Models for Robust Protein Gradients in the Drosophila Embryo
Andreas Hellander Simulation of spatially inhomogenous cellular reaction networks on unstructured meshes
Jonathan A. Johnson Modeling the dependence of radial oxygen losses from arterioles on hematocrit
Istvan Karsai The Importance of Simulation in Freshman Education
Caner Kazanci Indirect relations in ecosystems: An individual based approach
Daniel Kern Optimal Control Model for Cancer Chemotherapy Subject to Drug Resistance
Yangjin Kim Glioma invasion in vitro
Ilya Kobelevskiy Bifurcation analysis of a system of Morris-Lecar neurons with time delayed gap junctional coupling
Karen O'Connell and Dianne Kopp Separating the Effects of Genetic Drift and Natural Selection Using a Modification of Tajima's D Statistic
Stephanie Kuelbs Mathematical Modeling of the Transcriptional Network Controlling the Cold Shock Response in Saccharomyces cerevisiae
Dr Anil Kumar Mathematical Modelling of Blood Flow Through Magnetic Effects
Omid Massoudifar Use path analysis and regression for wheat characterizes in dry land condition
Ramit Mehr Models for Antigen Receptor Gene Rearrangement: CDR3 Length
Jason E. Miller Interdisciplinary Training in Mathematical Biology at Truman State University
Jonathan L. Mitchell Recurrent intrahost epidemics in a model of Malaria with binary immune response
Erandi Castillo Montiel Analysis of tumor vascular networks using nonlinear dynamic.
Marcio Duarte Albasini Mourao Stochastic simulation of interphase microtubule dynamics in plant systems
Aniel Nieves-Gonzalez Mathematical model of interactions between cell volume regulation and transport in cortical TAL cells
Onyeka Obi An Application of Mutational Analysis to Cancer Morphology
Yuanyi Pan Linear assumption or dynamic system - A study to sex ratio in China
Colin Phipps Efficient combination of antiangiogenic therapy and chemotherapy: A mathematical modeling approach
Nataliya Portman Estimation of growth parameters of the Drosophila's wing disc development from a sequence of micrographs using the Growth as Random Iterated Diffeomorphisms Model
Tim Preece Harmful Mating Strategies in Hermaphrodites
Erin Prosk Models of the EGF-Gradient Sensing Cofilin Pathway in Metastasizing Mammary Tumour Cells
Joseph Rhoads Parallel Biological Simulations on the Graphics Processing Unit
Suzanne Robertson Spatial patterns in stage-structured populations with density-dependent dispersal
Timothy Schlub Methods to analyse nucleotide sequence data on HIV retroviral recombination.
Pinal Shah The Dynamics of a One-Predator Two-Prey Model for Integrated Pest Management
Abhinav Singh Inverted fish biomass pyramid in coral reefs
Vladas Skakauskas Modelling of the population dynamics with complex structure
Molly Smith Analyzing, Mining and Modeling Medical Therapeutic Data for Quantification and Reproducibility
Chengjun Sun Carnivore Hunting Mode and Plant Species Coexistence
Terry Tang Simulation of mRNA Migration in Subnuclear Environment
Jeremy Thibodeaux A Mathematical Model of Erythropoiesis Subject to Malaria Infection
Spencer Tipping Modeling the Effects of Genetic Drift and Natural Selection with Discrete Simulation
Naveen K. Vaidya The Interaction Between Influenza Hemagglutinin (HA) Fusion Peptides and a Lipid Bilayer Membrane
Vanessa Venturi Analytical methods for comparing samples of the T cell receptor repertoire
Xujing Wang The hyperbolic effect of density and strength of inter-beta cell cell coupling in islet bursting
Zhian Wang Fast diffusion prevent blow up in chemotaxis
Zoe Ward Heterogeneity and HIV drug resistance
Alexandra Wehrman A Semi-Automated Procedure for Segmenting Early Embryogenesis in Caenorhabditis elegans
Brett L. Wiley Inside GIS: Habitat Parameterization and Metapopulation Modeling of a Rare Winter Annual
Lev Yampolsky Game theory of female guarding: the role of female choice
Lev Yampolsky Teaching Math to Biologists and Biology to Mathematicians: When Needed and As Much As Needed
Suellen Yin, Alex Jacobson A Mathematical Model to Relate Serum-Mediated Bacterial Killing with Anaphylatoxin Elaboration
Karen Yip Quantifying the fitness of influenza drug-resistant mutants from plaque assay data
Eiichi Yoshimoto Mathematical modeling of animal morphogenesis; pattern formation on the cell-based growing field
Jiaxin Yu To Investigate the Genetic Variability and Spatial Distribution of Tubifex tubifex
Ruijun Zhao A New View of CDC's Plan of Elimination of Syphilis
Tae-Soo Chon Cross-correlation analysis and spatially explicit models in dispersal of forest pest populations

Influence of Spatial Factor on Hysteresis in Immune system.
Alexandra Agranovich

Bar Ilan University, Ramat Gan, Israel
Coauthors: Yoram Louzoun

We study a spatial extension of the classical predator – prey model with an independent source of prey in the context of lymphocyte - pathogen dynamics. We found the regimes,where the mean field theory is wrong. We show using stochastic simulations that such regimes exist and study the mechanism leading to the stabilization of the point with zero prey density in regions of parameter space where the mean field prediction is that the coexistence fix point is the stable one.

Understanding the formation of the arabidopsis root epidermis through an intimate collaboration between modeling and experiment
Luay Almassalha

University of Michigan, Department of Mathematics
Coauthors: Asha Radhamohan, Andrew Cheng, Yana Panciera, David Gammack, Patrick Nelson, John Schiefelbein

Our model modifies the Meinhardt-Gierer model of activator-inhibitor interaction to study the role of position cues, such as those produced by SCM in Arabidopsis Thaliana, on the production of heterogeneous steady-states patterns. In A. thaliana, the WER/MYB23 complex acts as a non-mobile activator and CPC/TRY as the mobile inhibitor. Using sensitivity analysis and parameter identification techniques, we look to see if the application of the position cues will produce the wild-type pattern observed in nature. Using experimental techniques, we look for the criteria for differentiation into the pattern of hair and non-hair fates and examine the ability of the model to reproduce this pattern. A. thaliana, a variety of mustard plant, is an ideal organism for study because of its fully sequenced genome and its short growth period. Experimental evidence suggests that an epidermal cell of A. thaliana differentiates into a hair-cell when the activator to inhibitor ratio is sufficiently high and this ratio inside the cell is 10x magnitude higher than the activator to inhibitor ratio in neighboring cells.

An Investigation of Tyrosine Kinase Tnk1 Substrates and Function
Tyler Aten

University of Vermont

Protein tyrosine kinases (PTKs) play essential roles in many aspects of cell signaling (1). PTKs are utilized during a wide diversity of multi-cellular functions including; cell growth, differentiation, adhesion, motility, and apoptosis (2). Tnk1 is a non-receptor tyrosine kinase apart of the Ack protein family (3). It was originally cloned from human umbilical cord blood hematopoietic stem/progenitor cells (3). Tnk1 is expressed broadly in fetal tissues while expression in adults is limited to select tissues (3). The majority of signaling pathways involving Tnk1 have not been identified (4). However, Tnk1 is known to interact with Phospholipase C-?1 by means of its SH3 domain to inhibit the transactivation of nuclear- factor-?B via tumor-necrosis-factor-a (TNF-a), allowing TNF-a induced apoptosis to take place (5). Unpublished data revels that Tnk1 is capable of inducing phosphorylation in a number of substrates (6). We aim to identify these substrates and define if Tnk1 phosphorylates these substrates in primary neurons during fetal brain development.

1. Manning, G., Whyte, D. B., Martinez, R., Hunter, T., and Sudarsanam, S. (2002). The protein kinase complement of the human genome. Science, 298(5600):1912-1934.

2. Robinson, D. R., Wu, Y.-M., and Lin, S.-F. (2000). The protein tyrosine kinase family of the human genome. Oncogene, 19(49):5548-5557.

3. Hoehn, G. T., Stokland, T., Amin, S., Ramírez, M., Hawkins, A. L., Griffin, C. A., Small, D., and Civin, C. I. (1996). Tnk1: a novel intracellular tyrosine kinase gene isolated from human umbilical cord blood cd34+/lin-/cd38- stem/progenitor cells. Oncogene, 12(4):903-913.

4. Felschow, D. M., Civin, C. I., and Hoehn, G. T. (2000). Characterization of the tyrosine kinase tnk1 and its binding with phospholipase c-[gamma]1. Biochemical and Biophysical Research Communications, 273(1):294-301.

5. Azoitei, N., Brey, A., Busch, T., Fulda, S., Adler, G., and Seufferlein, T. Thirty-eight-negative kinase 1 (tnk1) facilitates tnfa-induced apoptosis by blocking nf-?b activation. Oncogene, aop(current).

6. Lionel Arnold (Unpublished results).

Simulating the growth patterns of Bacillus subtilis with a cellular automaton
Marine Aubert

Laboratoire IMNC, 15 rue Georges Clemenceau, bat 104, 91406 Orsay Cedex, France
Coauthors: Mathilde Badoual, Patrick Derbez, Basile Grammaticos

We introduce a cellular-automaton based model for the description of the migration and growth patterns of colonies of Bacillus subtilis. The two phases, associated to processes of migration and consolidations, are described by appropriate rules for the update of the automaton. We show that it is possible to reproduce the patterns present in the morphological diagram for Bacillus subtilis and in particular the ring-like structure that the colonies adopt in the case of a not very hard medium and under nutrient abundance.
Mathematical analysis on the diffusive models incorporating immunotherapy in the tumor-immune interaction
Seunghyeon Baek

Department of Mahtematics Korea University 1 Anam-dong, Sungbuk-ku Seoul, Korea
Coauthors: Inkyung Ahn, Wonlyul Ko

In this presentation, we consider a parabolic system incorporating treatment terms of effector cells and cytokine interleukin-2(IL-2) in the dynamics among tumor cells, immune-effector cells and IL-2. In this system, we investigate sufficient conditions that the tumor cell could be eliminated. These phenomena can be interpreted by the effect of treatment terms. Furthermore, we demonstrate a numerical simulation to present the mathematical results.--------------------------------------------------------------------------------

A statistical approach to population studies of Chagas Disease
Jacob Barker, Naomi Pollica

University of Vermont
Coauthors: Robin Hicks, Lauren Gilligan, Dr. Lori Stevens

Chagas Disease is an endemic in the South American countries that has affected millions of people. It is transmitted by the vector Triatoma infestans which feeds at night when the victims are caught unaware. It may take several years for the disease to present itself with heart disease, megaesophogus, and megacolon. In this study, we used micro satellite markers with the help of cluster analysis to determine the clonal distribution of the parasite, T. cruzi. Along with the micro satellites, we used the blood meals of the vectors to determine the lineage of the parasite. We used artificial neural networks and contingency test to look for association of the parasite cloned particular feeding types.


A model of cardiac action potential: incorporating the caveolae-associated sodium current
Ian Besse

University of Iowa
Coauthors: Colleen Mitchell, Ph.D. Erwin Shibata, Ph.D.

The contraction of a cardiac cell is initiated by a transient depolarization of the cell membrane called an action potential. Action potentials result from the rapid movement of ions across the membrane through pores called ion channels. Recent electrophysiological data regarding caveolae, small invaginations of the cell membrane, reveal that caveolae are reservoirs of ‘recruitable’ sodium ion channels. As such, caveolar ion channels constitute a substantial and previously unrecognized source of sodium current that can significantly influence action potential morphology. While many mathematical models of cardiac action potential exist, none take into account this caveolae-associated sodium current. In this talk, a three-compartment ODE model of cardiac action potential incorporating a caveolar component will be introduced. I will demonstrate that this model yields results that are consistent with experimental data and that this model promises to offer insight into the composition of the caveolar membrane at the molecular level and into the biophysical mechanisms underlying some cardiac arrhythmias.

Analysis of a Drug-Drug Interaction Problem from Pharmacokinetic
Bruno Bieth

Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis
Coauthors: Raymond C.Y. Chin, Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis Lang Li, Division of Biostatistics, Department of Medicine Indiana University

A two drug interaction is usually predicted by individual drug pharmacokinetic. An improved drug-drug interaction prediction method based on a three-level hierarchical Bayesian meta-analysis model uses Monte Carlo Markov chain pharmacokinetic parameter estimation procedure. Underlying present the parameter estimation procedure is a fast integration method of the stiff pharmacokinetic equations. In this presentation, we report the establishment and computation of some lower and upper bounds using quasi linearization method. We are able to prove the existence and uniqueness of the solution by using the perturbation theory of a two real autonomous system. We discuss the interrelation and the interaction between the Monte Carlo Markov Chain Pharmacokinetic parameter estimation procedure and the numerical integration scheme.

A meta-population model for the growth of nassella tussock
Richard Brown

Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
Coauthors: Alex James Britta Basse Graeme Bourdot Shona Lamoureaux Mick Roberts Dave Saville

Nassella tussock is a major pest plant in Australia and New Zealand. In the Hurunui area of NZ Nassella is managed by over 800 individual property owners by grubbing (manual removal) of plants. We develop a meta-population model of growth on each property. We show that a mean field model is not a suitable simplification and variation between properties, particularly for some model parameters is essential for realistic results. We present some ideas for management and control strategies.

A Model of the BMP4 and FGF Signaling Pathways in Embryonic Xenopus laevis
Tung Bui

University of Houston-Downtown
Coauthors: Akif Uzman, Jeong-Mi Yoon

A mathematical model of the BMP4 and FGF signaling pathways during the neural and epidermal development of Xenopus laevis is presented in this talk. The model consists of a system of coupled, nonlinear ordinary differential equations. By using linear stability analysis and bifurcation theory, the properties of this model are described. Numerical computations include bifurcation studies, which may be helpful in elucidating the interactions within the biochemical signaling network in embryonic Xenopus laevis.

Modeling a cell population with intracellular threshold dependent differentiation
Anna Cai

Department of Mathematics, University of California, Irvine
Coauthors: Qing Nie, Department of Mathematics University of California, Irvine qnie@math.uci.edu Xing Dai, Department of Biological Chemistry University of California, Irvine xdai@uci.edu

The maintenance of a stable stem cell population in the epidermis is important for the constant regeneration of the stratified epithelium. Stable cell population size is regulated by intra-celluar proteins e.g. c-Myc, and also by secreted diffusible extra-cellular signalling molecules e.g. TGF-b. Extra-celluar molecules are produced by the cell population and directly regulate the intra-cellular proteins. In this talk we focus on the intra-celluar protein, c-Myc, with a threshold value that allows cell differentiation. A structured model incorporating both levels of regulation will be presented, and the balance between growth and differentiation will be discussed.

An SIR epidemic model with partial temporary immunity modeled with delay
Thomas W. Carr

Southern Methodist University
Coauthors: Michael L. Taylor (Southern Methodist University)

The SIR-epidemic model for disease dynamics considers recovered individuals to be permanently immune, while the SIS-epidemic model considers recovered individuals to be immediately resusceptible. We study the case of temporary immunity in an SIR-based model with delayed coupling between the susceptible and removed classes, which results in a coupled set of delay-differential equations. We find conditions for which the endemic steady state becomes unstable to periodic outbreaks. We then use analytical and numerical bifurcation analyses, specialized for delay-differential equations, to describe the severity and period of the recurrent epidemics.

Modeling of gene dispersal in a natural forest system
David Chan

Virginia Commonwealth University
Coauthors: Rodney Dyer

Due to the growth of using genetically modified plants, the drastic decline in bee populations, and increase in habitat fragmentation understanding the movement in genes via insect pollinators is vital. Using an agent-based model we examine various biological parameters (e.g. turning probabilities, target perception, pollen carryover, etc.) and physical parameters (e.g. target density, target size, flower density, etc.) on the effects of gene dispersal. We study how these affect measurements of expected distance, search area covered, and genetic dispersal within the population.

Robust Cell Polarization
Ching-Shan Chou

University of California, Irvine
Coauthors: Travis Moore, Qing Nie, and Tau-Mu Yi

Cells localize (polarize) internal components to specific locations in response to external signals such as spatial gradients. For example, yeast cells form a mating projection toward the source of mating pheromone. There are specific challenges associated with cell polarization including amplification of shallow external gradients of ligand to produce steep internal gradients of protein components (e.g. localized distribution), response over a broad range of ligand concentrations, and tracking of moving signal sources.

In this talk, we will propose models that investigate the tradeoffs among these performance objectives. With our models, strategies for balancing the tradeoffs will be presented. We will also highlight the critical role of lateral diffusion of proteins in the membrane on the robustness of polarization.


The Role of Flightin in Drosophila Native Thick Filament Flexural Rigidity and Assembly
John Contompasis

University of Vermont
Coauthors: Lori Nyland J.O. Vigoreaux

Drosophila Indirect Flight Muscle (IFM), responsible for wing movement, is widely considered among the most powerful muscles in the animal kingdom. Power output of the muscle is highly dependent upon the muscle’s stiffness due to the process of stretch activation. Muscle stiffness is reliant upon the primary proteins in muscle; myosin and actin. We isolated native thick filaments from wild-type Drosophila melanogaster as well as mutants lacking the thick filament accessory protein flightin (fln0). Atomic Force Microscopy images of these filaments were evaluated with an automated analysis algorithm that precisely identifies filament position and shape. The curvature of these filaments was analyzed using statistical polymer chain mechanics in order to ascertain their specific persistence length (SPL), which is an index of filament flexural rigidity. Our data suggests the presence of flightin yields a significant increase (p<.05) in SPL (fln0:1,301µm ?1,805µm, wild-type: 2,446µm ?2,450µm) for newly eclosed flies. The same trend (p<.05) is also seen in 2-5 day old flies (fln0: 637µm ?557µm, wild-type: 1,672µm ?1,660µm). Our data also shows differences in filament length between the wild-type and fln0 newly eclosed flies (fln0: 3.90µm ?1.33µm, wild-type: 3.00µm ?0.38µm), which suggests that flightin has a role in the assembly of thick filaments. These results raise the possibility that thick filaments are a major contributor to the high resting stiffness of IFM, a characteristic feature of this muscle that underlies Drosophila’s ability to be activated by stretch and oscillate at high wing beat frequencies.--------------------------------------------------------------------------------

A model of CA1 hippocampal neurons with astrocytic input
Katie Ferguson

University of Waterloo
Coauthors: Sue Ann Campbell (University of Waterloo)

Over time astrocytes have been thought to function in an auxiliary manner, providing neurons with metabolic and structural support. However, recent research suggests they may play a fundamental role in the generation and propagation of focal epileptic seizures by causing synchronized electrical bursts in neurons. It would be helpful to have a simple mathematical model that represents this dynamic and incorporates these updated experimental results. We have used ordinary differential equations to create a two-compartment model of a typical neuron found in the hippocampal CA1 region, an area often thought to be the origin of these seizures. The focus is on properly modelling the astrocytic input to examine the pathological excitation of these neurons and subsequent transmission of the signals.

Parameter Estimation and Data Analysis in an Ecosystem Model of College Drinking
Ben G. Fitzpatrick

Clarence J. Wallen, S. J., Professor of Mathematics
Loyola Marymount University

Recently we developed a model composed of five impulsive differential equations that describes the changes in drinking patterns amongst college students. Many of the model parameters cannot be measured directly from data; thus, an inverse problem approach, which chooses the set of parameters that results in the “best” model to data fit, is crucial for using this model as a predictive tool. Here we present a procedure for parameter estimation in this model. The results show that our model provides a good fit to survey data for 32 campuses.


Determining the Correlation between Temporal Changes in Gravitropism and Auxin Sensitivity in Flax (Linum usitatissimum) Roots: A Mathematical Approach
Yu-yu Ren and Bo Forrester

Truman State University
Coauthors: Dr. John Ma and Dr. Todd Hammond

The successful development of plants depends on the downward growth of the emerging root, and the upward growth of the shoot. Such orientation of plant organs in response to the gravity vector is known as gravitropism. The gravity-induced spatial configuration is essential for plant growth and development since it establishes a root system for anchorage, water acquisition and mineral uptake from the soil, and a shoot system for the capture of sunlight for photosynthesis aboveground. We observed that both the gravity response and sensitivity of flax seedlings deteriorates as roots age, and we examined the potential correlation with changes in the sensitivity of root tissue to auxin. Roots of different ages were tested for their elongation rate, gravitropic response, and gravitropic sensitivity under a wide range of auxin concentrations. For curvature measurements, roots were isolated using image segmentation techniques, and the angles of curvature were obtained using methods from differential geometry of curves on the Blum medial axis of the roots. Accurate characterization of gravity perception and response under varying conditions would allow us to further investigate the gravisensing machinery in plant roots.

Systems Properties of Signaling pathways in CVB3-infected Cardiomyocytes
Farshid S. Garmaroudi

The University of British Columbia
Coauthors: Xiaoning Si, David Marchant, Abbas Khalili, Aline Tabet, Raymond Ng, Kevin Murphy, Honglin Luo and Bruce M. McManus.

Background: Coxsackievirus serotype B3 (CVB3), a small non-enveloped single-stranded RNA enterovirus in the Picornaviridae family, is the most significant causative agent of viral myocarditis. The intimate relationship between virus and host makes it difficult to discuss one without considering the other. Viruses must extensively manipulate host cell machinery to support viral replication. Meanwhile, infected cells induce an array of defence mechanisms to battle the invader. We and others have already shown how distinct signaling pathways are exploited by virus or infected cells. Now, we speculate cell signaling pathways are not autonomous units, but conjoined networks. Many host-virus events are mediated by interaction and cross-correlation between cellular signaling cascades.

Hypothesis: Cross-talk between signaling pathways determines the fate of CVB3-infected cardiomyocytes and enable CVB3 to progress through its life cycle.

Methods: Murine cardiomyocytes were pretreated and infected with signaling inhibitors and CVB3, respectively, at various timepoints. Viral protein synthesis and progeny release were determined by Western blot and plaque assay, respectively. Virus-induced cell death was assessed by cell viability assay and caspase activity assay. Host protein phosphorylation status was determined by individual phospho-ELISA kits. We generated 3-dimensional data: 1) components: ten signaling molecules, four host apoptotic responses, and two virus replication indicators; 2) timepoints: sham-infected cells [0h post-infection (p.i.)], viral receptor interaction (0.17h p.i.), internalization (1h p.i.), viral RNA synthesis (8h p.i.), viral protein synthesis (16h p.i.) and virion progeny release (24h p.i.), and 3) 23 different experimental conditions. We utilized the following computational tools: 1) Least Angle Regression Analysis (LARS); 2) Principal Components Analysis (PCA), and 3) Gaussian Graphical Modeling (GeneNet ®), to process generated data.

Results: 1) At 0h p.i., the only cross-talk between signaling pathways that we detected was a negative correlation between JNK and NFkB; 2) at 0.17h and 1h p.i., we did not detect a correlation between any of other signaling components ; 3) at 8h p.i., there was a negative correlation between JNK-NFkB and positive correlation between Akt-NFkB, JNK-p38 MAPK, Akt-JNK; both GSK3b and ERK1/2 share CREB as a transcription factor; 3) at 16 h p.i., there were positive correlations between NFkB-GSk3b, ??p38 MAPK-GSk3b, p38 MAPK-NFkB, ERK1/2-GSk3b ??and? negative correlation between Akt-p38 MAPK, JNK-NFkB, and 4) at 24 h p.i., there was a positive correlation between ERK1/2-GSk3b ?and a negative correlation between Akt-Hsp-27. On the one hand, GSK3b and p38 MAPK merged on CREB as transcription factor; on the other hand, p38 MAPK, JNK and Hsp-27 share ATF-2 as a substrate.

Conclusion: The systematic cataloging of signaling pathways allows us to understand the behaviour of signaling networks in CVB3-infected cardiomyocytes. We determined that some of signaling components played more interactive roles than others for instance, NFkB, GSK3b ?and JNK. Applying a systems approach to study complex interactions in signaling networks is yielding novel insights into the interplay between virus and host, and allows for the generation of new hypotheses.


Estimating mutational pathways of carcinogenesis
Moritz Gerstung

Dep. of Biosystems Science and Engineering, ETH Zurich
Coauthors: Seth Sullivant and Niko Beerenwinkel

The development of cancer is thought to be a multistep process of accumulating mutations. We describe this process by an exponential waiting time model in which the chronology of events is constrained by a partial order. This mathematical structure defines the conjunctive Bayesian network, a probabilistic model accounting for multiple pathways of carcinogenesis. We introduce a censored version of this model and estimate model parameters and the underlying partial order from observed mutation data by an EM algorithm. The expected waiting time of a given mutational pattern measures the genetic progression of the tumor and presents a marker of disease progression. We apply our model to comparative genomic hybridization (CGH) data from different cancer types revealing characteristic mutagenetic pathways. Furthermore we evaluate the prognostic value of the genetic progression score using patient survival data.

Growing Heterogeneous Tumors in Silico
Jana Gevertz

Princeton University
Coauthors: Salvatore Torquato

An in silico tool that can be utilized in the clinic to predict neoplastic progression and propose individualized treatment strategies is the holy grail of computational tumor modeling. Considering the highly complex nature of cancer progression, a multitude of inter-tumor processes and host tumor-interactions must be incorporated into any computational model that will be of use in a clinical setting. With this goal in mind, we have developed a novel two-dimensional hybrid cellular automaton model of cancer growth that incorporates two distinct types of interactions between the tumor and the host. First, the algorithm couples the remodeling of the microvasculature with the evolution of the tumor mass. Second, the algorithm considers the impact that organ-imposed physical confinement and heterogeneity have on tumor growth. By incorporating the effects of tissue structure, tumor shape and spread is more accurately predicted than when radially symmetric growth is assumed. Finally, we illustrate how genetic mutations can be incorporated into the model and explore the likelihood that different advantageous and deleterious mutations survive in the tumor cell population. Together, this algorithm is a first step in the direction of developing a clinically relevant cancer simulation tool that can be used to test how perturbing certain aspects of the tumor system impact its growth and survival.


Individual based model of factors influencing the territorial boundary between the harvester ant Pogonomyrmex spp. and related hybrid lineages
Jennifer Glenister

University of Vermont
Coauthors: Sara Helms Cahan, Pace Goodman

Hybridization between species can lead to speciation if the hybrids are able to successfully compete ecologically with their parent species. Interbreeding between harvester ants Pogonomyrmex rugosus and P. barbatus has produced hybrid lineages whose geographic ranges meet with both parent species at contact zones. An individual based model will be developed to investigate the local characteristics of the boundaries between the parent and hybrid lineages and determine which biotic and abiotic factors may influence their ecological success. The model will be validated against distribution patterns observed in the field. If the model reproduces the same types of distributions as seen in the field, the processes included in the model may be important in the competition between the hybrid and parent lineages.

The geometry of bursting in the dual-oscillator model of pancreatic beta-cells.
Pranay Goel

Laboratory of Biological Modeling, NIDDK, NIH
Coauthors: Artie Sherman

The rapid increase in the occurrence of Type 2 Diabetes Mellitus (T2DM) is a major health concern throughout the developed nations, and most of the world. Impaired insulin secretion from the endocrine beta-cells of the pancreatic Islets of Langerhans is central to the development of T2DM and is the subject of much investigation. Despite great advances in the field, the mechanism underlying the pulsatility of insulin secretion continues to remain controversial. The work of Artie Sherman et al. has been systematically elucidating the biophysical basis of secretion for over two decades. In a recent development, calcium and metabolism have been proposed as being jointly implicated in controlling the intracellular dynamics leading to hormone release. A mathematical model, termed the Dual-Oscillator Model (DOM), has been put forward that successfully explains much available data on islet bursting activity.
Glycolysis and ion-channel mediated calcium entry are both ancient systems: it is plausible that beta-cells may have evolved by coupling these two systems together to achieve regulated, glucose-stimulated insulin secretion. The characteristic bursting of the pancreatic beta-cell is now thought to reflect the complex interaction of the two systems. We have developed a systematic mathematical analysis of the DOM: we use bifurcation theory to map out the the properties of the two subsystems, metabolic and electrical, which can each be either stationary or oscillatory. We then extend our analysis to understand how bursting patterns of different frequencies, and of different waveforms, can be orchestrated by their coordinated action.
Our mathematical analysis of the DOM not only explains the complex bursting patterns observed physiologically, it also provides insight into how beta-cells exploit the timescale separation inherent in electrical (fast) and metabolic (slow) processes to regulate the signaling pathways involved in insulin secretion with changes in glucose.


Habitat segregation between two species of Harvest Ants and their interspecific hybrids
Pace S. Goodman

University of Vermont
Coauthors: Dr. Sara Helms Cahan

For hybridization to lead to persistent hybrid populations, there must be some niche differentiation between the hybrids and parental species. However, hybrid harvester ant populations originally derived from Pogonomyrmex rugosus and P. barbatus co-occur regularly with their parental species in the southwestern region of the United States. In this study we examined a variety of abiotic and biotic factors that may be involved in niche differentiation between parental species and hybrid lineages on a microgeographic scale using six contact sites, three for each parent species, where both a parental species and hybrid lineage co-occur in comparable numbers. The parental and hybrid lineages clustered geographically in patterns predictable by the environmental factors examined in this study. Our results suggest that habitat variability may allow for hybridization to act as a mechanism of speciation.

Models for Robust Protein Gradients in the Drosophila Embryo
Heather Hardway

Rice University
Coauthors: Bibhash Mukhopadhyay (Baylor College of Medicine), Timothy Burke (Rice), Theron James Hitchman (University of Northern Iowa), Robin Forman (Rice)

In early Drosophila development, one of the first specifications made in determining cell location is the formation of the anterior-posterior axis, and this event is carried out with incredible precision, despite many variations of the genetic regulatory network and environmental fluctuations. My focus is on the first step in this process, where the protein, Hunchback (Hb), forms a very sharp boundary at the midpoint of the embryo, despite receiving ‘noisy’ information from its known upstream regulator, Bicoid (Bcd). Using systems of partial differential equations to model the gene network, we seek an answer to the following inverse problem: given the ‘robust’ Hb boundary, what conditions does this place on the regulatory network? While a simple answer does not likely exist, we provide examples of such networks, as the result of both numeric searches and analytic techniques, and an interpretation of the conditions in terms of the biological system.

Simulation of spatially inhomogenous cellular reaction networks on unstructured meshes
Andreas Hellander

Div. of Scientific Computing, Dept. of Information Technology, Uppsala University
Coauthors: Stefan Engblom, Lars Ferm, Per Lötstedt

Stochastic simulation of reaction-diffusion processes inside living cells are computationally very expensive. We extend an existing algorithm in two ways. First, by making connections to the finite element method (FEM) we are able to conduct simulations on unstructured meshes. The jump propensities can be conveniently obtained by using existing FEM software, and thus the treatment of complicated geometries is made possible. Secondly, in the spatially homogeneous case, hybrid methods have been introduced to facilitate the study of stiff models. We propose a hybrid method for the reaction-diffusion master equation where the diffusion is treated deterministically, when appropriate, for some or all of the species. The connection to FEM has the potential of making this approach highly efficient by utilizing the capabilities of state of the art solvers.

We show that the method qualitatively reproduces results obtained with an existing software (mesoRD) that uses Cartesian meshes. In a first Matlab implementation, the hybrid approach is three orders of magnitude faster for a model problem. The results suggest that the method will be an efficient alternative to pure stochastic simulation. Ongoing work includes the integration of the method with finite element software in order to obtain a generic, easy-to-use framework for both stochastic and hybrid simulation of reaction-diffusion models.


Modeling the dependence of radial oxygen losses from arterioles on hematocrit
Jonathan A. Johnson

Department of Medical Biophysics, University of Western Ontario
Coauthors: Daniel Goldman

Erythrocyte O2 saturation levels at the entrances to capillaries are known to be substantially lower than arterial values. A number of proposed mechanisms for this phenomenon exist, such as the effect of radial O2 losses from arterioles. The goal of this model is to attempt to quantify these radial oxygen losses that take place at the arteriolar level. In particular, three effects were studied for their influence on radial oxygen losses: 1) Spatial distribution of hemoglobin, 2) P50 value of the hemoglobin-oxygen dissociation curve, and 3) PO2 of the surrounding tissue. This was modeled by considering a time-dependent diffusion equation with a nonlinear source term. The model was studied numerically, through the use of a finite difference approach, with steady state cases evaluated analytically through the use of Green's functions. Using this model, the dependence of oxygen saturation levels on hematocrit was found. In future work, this result will be used in conjunction with an existing model to study the regulation of capillary O2 delivery. This work was supported by NIH grant HL089125.


The Importance of Simulation in Freshman Education
Istvan Karsai

ETSU Istitute of Quantitative Biology
Coauthors: George Kampis; McKayla Johnson; Tashauna Gilliam

Since 1998, studies using models in scientific literature have increased by more than a fourfold (Keeling and Rohani, 2007). We predict that the strongest effect of math on biology and biology education will be the extensive use of models and simulations. Today, integrated platforms and information systems ranging from Visual Cell to Netlogo and others provide templates where data, models, simulations, theories, mechanisms, different pieces of qualitative and quantitative knowledge are represented in a uniform and transparent fashion, which makes it easy to experiment, form and evaluate models and alternative hypotheses. Students without knowledge of advanced math are able to access and experiment quantitative biology problems and acquire skills and understanding of basic math problems. We provide examples of research projects we did with freshman biology students to introduce them into interdisciplinary research. These methods are particularly prone to study the dynamics of such complex and socially important phenomena as diseases where experimentation is not possible.

Indirect relations in ecosystems: An individual based approach
Caner Kazanci

University of Georgia, Department of Mathematics and Faculty of Engineering
Coauthors: E. William Tollner (University of Georgia, Biological and Agricultural Engineering) Bernard C. Patten (University of Georgia, Institute of Ecology) Stuart J. Whipple (University of Georgia, Institute of Ecology) John Schramski (University of Georgia, Faculty of Engineering)

A common way to represent an ecosystem is to build a graph (or a digraph), where vertices represent compartments and edges represent specific relations, such as flow of biomass or energy. However, two disconnected compartments can still be highly correlated, as they might have multiple common neighbors. Therefore a graph representation of an ecosystem may provide a misleading visualization of the actual relation strength among compartments. There has been efforts to quantify these so called indirect relations, mostly through linear algebraic arguments that aggregate flows among all compartments. Here, we present a novel way to compute the indirect effects precisely, using a stochastic individual based algorithm. Particle Tracking Simulation (PTS), a highly capable numerical algorithm, enables us to track individual particles that flow in the system, providing very detailed information on ecosystem organization and function. PTS results are compatible with the differential equation representation of the ecosytem, providing an accurate comparison between our method and currently available measures for indirect relations. This work is applicable to a wide range of ecosystem models, as long as the currency is a conserved entity, such as biomass, energy, N, C, P, etc.

Optimal Control Model for Cancer Chemotherapy Subject to Drug Resistance
Daniel Kern

University of Nevada, Las Vegas

Optimal control techniques are used to optimize a chemotherapy treatment regime. Cell cycle-specific chemotherapy is examined when drug resistance reduces the effectiveness of treatment over time, and toxicity levels place limitations on the course of treatment. The governing state equations are developed from a compartmental model that shows the development of resistance over time. The optimal control is characterized for the system, allowing for some numerical simulations.

Glioma invasion in vitro
Yangjin Kim

Mathematical Biosciences Institute
Coauthors: Yangjin Kim(1), Sean Lawler(2), Michal O. Nowicki(2), E.A. Chiocca(2), Jed Johnson(3), John Lannutti(3), Hans Othmer(4), and Avner Friedman(1); Mathematical Biosciences Institute(1), Dardinger Lab for Neuro-Oncology and Neurosciences,OSU(2), Lannutti Lab, OSU(3), Mathematics, U of Minnesota(4)

Multicellular tumor spheroids (MCTS) have been used as a model system because of their remarkable ability of reproducing the properties of tumors in vivo. Glioma cells, already at an early growth of the tumor, tend to migrate from the primary tumor into the surrounding tissue in different patterns. For example, cells from U87 cell-line have been shown to disperse in a radially symmetric fashion from a spherical tumor, whereas mutant U87DeltaEGFR cells form branching patterns similar spokes from a hub. Several models have been suggested to explain the different modes of migration, but none of them, so far, has explored the important role of cell-cell adhesion. The present paper develops a mathematical model which includes the role of adhesion and provides an explanation for the various patterns of cell migration. It is shown that, depending on critical adhesion and chemotactic parameters, the migration patterns exhibit a gradual shift from branching to dispersion, as observed in experiments.


Bifurcation analysis of a system of Morris-Lecar neurons with time delayed gap junctional coupling
Ilya Kobelevskiy

University of Waterloo
Coauthors: Sue Ann Campbell, University of Waterloo

We consider a system of two identical Morris-Lecar neurons coupled via electrical coupling. We focus our study on the effects that the coupling strength, g, and the coupling time delay, t, cause on the dynamics of the system.

For small g we use the phase model reduction technique to analyze the system behavior. We determine the stable states of the system with respect to g and t using the appropriate phase models, and we estimate the regions of validity of the phase models in the g, t plane using both analytical and numerical analysis.


Separating the Effects of Genetic Drift and Natural Selection Using a Modification of Tajima's D Statistic
Karen O'Connell and Dianne Kopp

Truman State University
Coauthors: Spencer Tipping (spencer.tipping@gmail.com) Pam Ryan (pjryan@truman.edu) Anton Weisstein (weisstae@truman.edu)

A number of statistical measures have been devised to infer past evolutionary forces from patterns of genetic diversity in sequence data. One of these measures, Tajima's D statistic, detects changes in overall genetic diversity, but cannot distinguish between the impacts of genetic drift versus natural selection. By analyzing synonymous (Dsyn) and nonsynonymous (Dnon) mutations separately, we can isolate the effects of these two evolutionary forces. For codons bearing only a single observed mutation, that mutation can be easily classified as synonymous or nonsynonymous. However, this classification becomes ambiguous for codons in which multiple mutations have occurred. In this talk, we explore three strategies for resolving this issue of ambiguity: (i) the Nei & Gojobori method, which extrapolates synonymous:nonsynonymous ratios from single-mutation codons to ambiguous codons; (ii) a genetic code-based method that employs expected frequencies based on the observed set of codons; and (iii) a mutation pathway-based method that averages the number of synonymous and nonsynonymous mutations over all possible pathways connecting observed codon pairs. Distributions for Dsyn and Dnon will be generated under models of specific evolutionary and demographic scenarios and will then be used to measure our method's ability to correctly infer the population's history.

Mathematical Modeling of the Transcriptional Network Controlling the Cold Shock Response in Saccharomyces cerevisiae
Stephanie Kuelbs

Loyola Marymount University
Coauthors: Kevin Entzminger, Kenny Rodriguez, Dr. Ben Fitzpatrick, Dr. Kam Dahlquist

Gene expression is a complex biological process in which cells translate their genetic code into proteins. In this process, cells first transcribe their DNA into an intermediary code known as mRNA, and then the cell translates mRNA into proteins. Involved in this process are transcription factors, which are proteins that increase or decrease the rate at which a cell transcribes a gene. We used mathematical modeling to describe the interactions between transcription factors thought to play a role in controlling the environmental stress response in Saccharomyces cerevisiae. We created a network of 15 active transcription factors that regulate one another, a model that we analyzed by running forward simulations in MATLAB. The concentrations of the individual transcription factors are modeled using ordinary differential equations, which we solved as a system in order to identify the optimal combination of parameters. Each transcription factor’s equation includes a production rate and a degradation rate. The production rate for each gene depends nonlinearly on other genes influencing its production. This nonlinear function is parameterized with a sigmoidal response. The production rates and degradation rates were inferred from experimental data, and the remaining parameters in the sigmoidal response were optimized using a least-squares algorithm that compares yeast cold-shock microarray data to the mathematical model. We performed sensitivity analysis on the model by running the forward simulations with systematically perturbed parameters. We also compared the fold changes of each gene in the original model to fold changes generated when a transcription factor is deleted from the model. This may predict the behavior of a mutant strain of yeast (a strain with the same transcription factor deleted) to cold shock.


Mathematical Modelling of Blood Flow Through Magnetic Effects
Dr Anil Kumar

Department of Mathematics, Dronacharya college of Engineering , Greater Noida UP India

In this paper a two layered blood flow model is investgated. The flow of blood and plasma take place in the core and peripheral regions respectively. In the present study the effect of a magnetic field on the blood flow is investigated using the equation of a magnetic fluid model.The governing equations are solved by the finite difference method. The influence of the magnetic field on blood flow in the core region affects the flow of non magnetic plasma in the peripheral regions.

Use path analysis and regression for wheat characterizes in dry land condition
Omid Massoudifar

Agriculture Eng. & adviser

In this study , the effect of different density ( 250, 300, 400 and 450 seed per m2 and 3 row space : 15 ,25 ,40 cm ) of wheat ( Kohdasht cultivar) on some morphological, physiological and biochemical properties on dry land farming is evaluated by using regression and path analysis. The experiment was arranged as a randomized complete block design. The results of path analysis and regression showed leaf area, stem length , seed per spike , protein accumulation , water-soluble carbohydrates were effected and decreased by an increase in density. Multiple regression and path analysis indicated that the maximum yield showed in 400 seed per m2 density. The coefficient of correlation between harvest index and density was negative and significant; and correlation between root and shoot dry weight was positive. Therefore on the basis of this data and compared with normal conditions we can conclude that wheat in dry land farming conditions is sensitive to density.

Key word : path analysis , regression , correlation , wheat, dry land

Models for Antigen Receptor Gene Rearrangement: CDR3 Length
Ramit Mehr

The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan, Israel
Coauthors: Ravit Saada, Moran Weinberger and Ramit Mehr

Despite the various processing steps involved in V(D)J recombination, which could potentially introduce many biases in the length distribution of complementarity determining region 3 (CDR3) segments, the observed CDR3 length distributions for complete repertoires are very close to a normal- like distribution. This raises the question of whether this distribution is simply a result of the random steps included in the process of gene rearrangement, or has been optimized during evolution. We have addressed this issue by constructing a simulation of gene rearrangement, which takes into account the DNA modification steps included in the process, namely hairpin opening, nucleotide additions, and nucleotide deletions. We found that the near-Gaussian- shape of CDR3 length distribution can only be obtained under a relatively narrow set of parameter values, and thus our model suggests that specific biases govern the rearrangement process. In both B-cell receptor (BCR) heavy chain and T-cell receptor beta chain, we obtained a Gaussian distribution using identical parameters, despite the difference in the number and the lengths of the D segments. Hence our results suggest that these parameters most likely reflect the optimal conditions under which the rearrangement process occurs. We have subsequently used the insights gained in this study to estimate the probability of occurrence of two exactly identical BCRs over the course of a human lifetime. Whereas identical rearrangements of the heavy chain are highly unlikely to occur within one human lifetime, for the light chain we found that this probability is not negligible, and hence the light chain CDR3 alone cannot serve as an indicator of B-cell clonality.

Interdisciplinary Training in Mathematical Biology at Truman State University
Jason E. Miller

Truman State University
Coauthors: Jon Beck, Michael Kelrick, and Laura Fielden

Truman State University's new program in Mathematical Biology trains students to work at the intersection of the life and mathematical sciences through a combination of coursework and undergraduate research, with an emphasis on the latter. This poster will describe the program with an emphasis on some of its more novel aspects, including its summer research community, its minor degree, and its field trip program.

Recurrent intrahost epidemics in a model of Malaria with binary immune response
Jonathan L. Mitchell

Southern Methodist University
Coauthors: Thomas W. Carr (Southern Methodist University)

We study the intrahost immune response to infection by a single species of the Malaria parasite by considering a mathematical model that accounts for both variant-specific and cross-reactive immune response. We first determine the biological conditions that lead to damped oscillations in the host's viral load, which corresponds to recurring but weakening bouts of sickness. In particular, we find that the ratio of the efficacy of the variant-specific immune response to the cross-reactive immune response is critical in determining the characteristics of the disease dynamics. We then find that a slow responding immune system, modelled with a fixed delay, can lead to undamped and persistent oscillations in the viral load. We use analytical and numerical bifurcation analyses, specialized for delay-differential equations, to describe the severity and period of the recurrent intrahost epidemics, i.e., bouts of high-viral load and sickness.


Analysis of tumor vascular networks using nonlinear dynamic.
Erandi Castillo Montiel

Laboratory of Mathematical Modelling and System Simulation
Center for Computing Research of the National Polytechnic Institute, México City

Angiogenesis is a process that involves the growth of new vascular networks in tumor malignant,
we present a study about this networks in patient with liver cancer. We used image of tomography
in order to obtain de vascular networks. The image were analyzed and converted into a binary skeletonized
form. The analysis experimental include the measure of dynamic, structure and gemometry of network in diferents size. Our preliminary results show that networks have power law relation.


Stochastic simulation of interphase microtubule dynamics in plant systems
Marcio Duarte Albasini Mourao

Indiana University School of Informatics, Bloomington
Coauthors: S. Shaw 2 and S. Schnell 1 1 Indiana University School of Informatics and Biocomplexity Institute, Bloomington, IN, USA, maralbas@indiana.edu, schnell@indiana.edu 2 Indiana University, Department of Biology, Bloomington, IN, USA sishaw@indiana.edu

Microtubules (MT) are a critical component of the cytoskeleton. They serve as structural components within cells and are involved in many cellular processes including mitosis, cytokinesis, and vesicular transport. Plant cells create highly structured MT arrays at the cell cortex without a central organizing center to anchor the microtubule ends. Microtubules are created by polymerization of tubulin. In vivo imaging of individual microtubules in Arabidopsis plants revealed that new microtubules exhibit dynamics at both ends. Polymerization biased dynamic instability at one end and slow depolymerization at the other end constitute a hybrid treadmilling mechanism(1) that results in sustained microtubule migration across the cell cortex. Using the measured polymerization and depolymerization rates and estimated tubulin concentrations, the dynamic properties of the plant interphase array will be simulated.

In order to test the organization of the cortical microtubule array, we require an accurate model for the dynamics of the individual MT polymers. Here, we present the results of a dynamic engine that accurately recapitulates the dynamic properties of the MTs as they have been measured in live cells.

(1) Shaw, S. L., Kamyar, R., Ehrhardt, D. W., “Sustained Microtubule Treadmilling in Arabidopsis Cortical Arrays”, Science, 300, 2003.


Mathematical model of interactions between cell volume regulation and transport in cortical TAL cells
Aniel Nieves-Gonzalez

Stony Brook University- Dept. of Applied Mathematics & Statistics
Coauthors: Chris Clausen, Harold E Layton, Leon Moore.

We develop a mathematical model of a cortical thick ascending limb (cTAL) cell to study the interactions between ion transport and cell volume (CV) regulation. Because the Na+-K+-2Cl- cotransporter (NKCC2) mediates the Na+ uptake, and its activity is regulated by CV-dependent kinases, we hypothesize that transport-related CV changes should result in compensatory regulation of NKCC2 activity and Na+ reabsorption. The cTAL cell model is based on mass conservation and includes models for the Na+-K+-ATPase, the Na+-H+ exchanger, Cl_-HCO3- exchanger, the NKCC2 (A isoform), the K+-Cl- cotransporter (KCC1), and passive ion fluxes. CV-sensitive regulation of the activities of NKCC2 and KCC1 is represented with empirical functions. Model parameters were chosen to yield potentials, cytosolic concentrations, and ionic fluxes consistent with published data. To test our hypothesis, we simulated published experiments which measured the relationship between short circuit current (Isc) and luminal [Cl-]. Simulations were done with and without NKCC12 and KCC1 regulation. The agreement between the predicted and measured responses was significantly improved, particularly at luminal [Cl-] greater than 75mM, by inclusion of NKCC2 and KCC1 regulation. Moreover, the gain that provided the best fit to the Isc curve yielded regulatory volume decreases consistent with published data. These findings support the idea that CV regulatory responses modulate Na+ transport in cTAL cells.


An Application of Mutational Analysis to Cancer Morphology
Onyeka Obi

University of Pittsburgh
Coauthors: Paul Gartside

We use Jean-Pierre Aubin's theory of mutational equations to develop spatial models of cancer growth. As an initial investigation, we consider a model of a single solid tumor growth in the avascular phase as well as a model of solid tumor growth in the presence of a nearby vascular supply to model the vascular phase.


Linear assumption or dynamic system - A study to sex ratio in China
Yuanyi Pan

Department of Mathematics and Statistics, York University, Toronto
Coauthors: Jianhong Wu

The sex ration in human population is often assumed to be equal in the study of sexually transmitted disease (STD). It is not always true in developing country like China. A mathematical model is constructed to describe the change of human population. The simulation shows that the growth of male and female population in sexually mature stage could be estimated linearly while the total population and other sex-gender groups behave differently.

Efficient combination of antiangiogenic therapy and chemotherapy: A mathematical modeling approach
Colin Phipps

University of Waterloo
Coauthors: Mohammad Kohandel

Recent experimental and clinical studies have shown that the combination of cytotoxic therapies and antiangiogenic agents will probably be the most effective strategy in the treatment of malignant tumors. However, there are vastly different outcomes based on, at least partially, dosages and treatment times. A mathematical model may help to better predict the results of a wide array of possible combinations. In this direction, we have developed a simple model including tumor cells and blood vasculature, as well as proangiogenic and antiangiogenic factors. The antiangiogenic therapy is considered either to be blocking/deactivating proangiogenic factors or removing endothelial cells directly while the chemotherapeutic agent attacks tumor cells. We also discuss nanocells that include both forms of treatment in one delivery system with appropriate drug release profiles.

Models of the EGF-Gradient Sensing Cofilin Pathway in Metastasizing Mammary Tumour Cells
Erin Prosk,

University of British Columbia

Cofilin, a protein that severs actin filaments to create new barbed and pointed ends, has long been identified as a regulator of steady state cytoskeleton dynamics by increasing the turnover of G-actin monomers. Recent work indicates that cofilin activity in carcinoma cells is stimulated by a transient phospholipase(PLC)-dependent response to a chemoattractant gradient, such as EGF. This cofilin pathway is responsible for an early peak of barbed ends at the leading edge of a cell which is further amplified by a coupled Arp2/3 pathway to sustain directional movement. Cofilin has then emerged as a key player in the directional sensing of invasive tumour cells and its overall activity is hypothesized as a major determinant of the metastatic phenotype of tumour cells. We propose several models of the dynamics of the cofilin pathway; the eventual objective being to work with existing cell polarity models in order to predict possible tumour cell phenotypes.


Estimation of growth parameters of the Drosophila's wing disc development from a sequence of micrographs using the Growth as Random Iterated Diffeomorphisms Model
Nataliya Portman

Department of Applied Mathematics, University of Waterloo, 200 University Ave West, Waterloo,ON, N2L 3G1
Coauthors: Prof. Ulf Grenander, Division of Appled Mathematics, Brown University, Providence,Rhode Island,USA, Prof. Edward Vrscay, Department of Applied Mathematics, University of Waterloo, Waterloo, Canada.

According to a mathematical model for biological growth, called GRID, growth patterns are composed of smaller, local deformations, each resulting from elementary biological events (e.g.,cell division). A large number of such biological events, each ocurring randomly and independently from one another, results in a visible growth pattern or biological shape changes observed from the image data. Given a sequence of micrographs reflecting the dynamics of Wingless expression pattern in the growing Drosophila's wing disc we estimate the underlying optimal diffeomorphic transformation using a visible growth law derived from the GRID Model. We demonstrate the estimation of the GRID parameter, called growth power directly from the image data of biological growth. Then the growth induced transformation is obtained from the estimated growth power distribution in the growing wing disc.

Harmful Mating Strategies in Hermaphrodites
Tim Preece

University of Nottingham
Coauthors: Y Mao, J P Garrahan, A Davison.

Cost to females due to damaging male mating behaviour is commonly associated with sperm competition and conflict, but the precise function is not well understood. This conflict between male and female is especially important in hermaphrodites, because individuals can simultaneously take both sexual roles. We consider the hypothesis that harm inflicted during mating is a negative side effect of a trait that benefits the male function. Here, we generalise an existing model for sperm competition to encompass the harmful mating tactics that are commonly found in simultaneous hermaphrodites. Harm is modelled by a probability of death for the sperm recipient following a mating. We calculate Evolutionary Stable Strategies (ESS) for the level of harm, along with resource allocation to male and female functions. We observe that harmful mating should be associated with multiply-mating species in which ability to displace sperm, without the use of a harmful mating tactic, is low. Alternatively, if the harmful mating tactic is more efficient at promoting sperm displacement, the ability to displace sperm without the use of a harmful mating tactic becomes less important. It has been previously shown that resource allocation to male and female function can tend to equality in hermaphrodites. An unexpected outcome is that the model predicts that harmful mating tactics favour a considerably more female biased resource allocation. Although Bateman's principle implies that an increased allocation to female function should increase the number of offspring produced and hence the fitness of the population, the model instead shows that harmful mating tactics more than counter-compensate, so leading to reduced fitness and a greater possibility of extinction when competing with other species for a limited resource.

Parallel Biological Simulations on the Graphics Processing Unit
Joseph Rhoads

Florida State University: Department of Mathematics
Coauthors: Richard Bertram bertram@math.fsu.edu Gordon Erlebach erlebach@scs.fsu.edu

Electrophysiological simulations and parameter estimation are areas where massively parallel simulations can have a profound impact. One method for massively parallel simulations is a network of computers. Here we describe an alternative method for massively parallel biological simulations using the Graphics Processing Unit (GPU). We are able to run excitable cell systems with thousands of cells in parallel on the GPU at a fraction of the time required for serial simulations on a workstation. We will discuss applications of the GPU to areas such as parameter searching and simulations of networks of coupled neurons.

Spatial patterns in stage-structured populations with density-dependent dispersal
Suzanne Robertson

University of Arizona
Coauthors: Jim Cushing (University of Arizona, cushing@math.arizona.edu)

Spatial segregation among life cycle stages has been observed to occur in some stage-structured species, including species of the flour beetle Tribolium. We explore stage-structured, integrodifference equation models that incorporate density-dependent dispersal and investigate the mechanisms that can lead to spatial patterns in a homogeneous habitat, including patterns that have separated life cycle stages.

Methods to analyse nucleotide sequence data on HIV retroviral recombination.
Timothy Schlub

University of New South Wales, Australia
Coauthors: Redmond Smyth (Macfarlane Burnet Centre, Australia) Johnson Mak (Macfarlane Burnet Centre, Australia) Miles Davenport (University of New South Wales, Australia)

Retroviral recombination plays an important role in the evolution of HIV-1 by diversifying the viral quasi-species. Recombination can accelerate escape from immune pressure and antiretroviral therapy, which can lead to treatment failure. Previous experimental approaches to measuring recombination have often employed large gene insertions, and measured gene activation or inactivation rates. We have developed a novel HIV-1 marker system by making a small number of codon modifications in gag and pol, to mimic the recombination between closely related viral quasi-species in an infected individual, where viral genome sequences and structure are highly related. We can thus obtain direct sequence data showing recombination over multiple gene segments. We formulate statistical tools to calculate an öptimal recombination rate" that reproduces experimental recombination frequencies, taking into account the length over which recombination is measured and the possibility of multiple template switches. We used a bootstrapping approach to give a robust estimate of recombination rates using 248 and 268 sequences for gag and pol respectively. Our system of multiple markers allows recombination rates to be estimated along different regions of the genes. We compared the optimal recombination rate over the entire gene to rates within specific gene segments to determine the existence of recombination hotspots. Although our preliminary results suggest that recombination rates may vary along the genes, this was not significant. We also investigated the effects of specific conditions and gene modification, and found that deletion of the dimerization initiation site (DIS) significantly reduced the recombination rate in gag (p < 0.05), and that recombination is significantly higher in macrophages than in lymphocytes in both gag and pol (p < 0.05 for both).

The Dynamics of a One-Predator Two-Prey Model for Integrated Pest Management
Pinal Shah

Benedictine University
Coauthors: Debra Witczak, Benedictine University

We present a one-predator two-prey model for integrated pest management. Features of this model include stage structure for the predator species and one of the prey species and a birth pulse (rather than continuous growth) for the stage structured prey species. We demonstrate the existence of total pest eradication solutions and permanent solutions. We also investigate the effects of model parameters through the analysis of bifurcation diagrams.

Inverted fish biomass pyramid in coral reefs
Abhinav Singh

Georgia Institute of Technology, Atlanta
Coauthors: Hao Wang, Howard Weiss

Global warming and fishing have made a negative impact on coral reefs around the world. The diversity and biomass of coral reef fish is directly connected to the magnitude of coral reef cover in their local environment. It has been recently observed in pristine coral reefs that the biomass of fish is dominated by carnivorous fishes. This inversion of the fish biomass pyramid is in contrast to coral reefs where commercial fishing is practiced. We provide a predator-prey model which shows the connection between the size of coral reefs and biomass pyramid of coral reef fishes.

Modelling of the population dynamics with complex structure
Vladas Skakauskas

Vilnius University, Lithuania
Coauthors: Sarunas Repsys

Many species of animals produce a small number of offspring and take care of them. This phenomenon is natural for many species of mammals and birds and forms the main difference between the behavior of a population taking care of offspring and that of a population without maternal or parental duties. Mammals and birds feed, warm, and defend their young offspring from enemies. If one of these natural duties is not realized, young offspring die, and the population vanishes. For many species of mammals only females take care of their young offspring. Some species of mammals and birds care of their offsprings in couples.

We discuss a discrete newborn set-based deterministic model taking into account age, number of offsprings, and care of them. The model consists of integro-partial differential equations subject to the conditions of integral type. The number of these equations depends on the biologically possible maximal newborn number of the same generation produced by an individual. Analytical and numerical results will be discussed.

Analyzing, Mining and Modeling Medical Therapeutic Data for Quantification and Reproducibility
Molly Smith

Truman State University
Coauthors: Dr. Brian Degenhardt, Dr. Jon Beck, Dr. Alan Garvey

Osteopathic manipulative medicine has been used for over 100 years to treat an array of medical conditions. Anecdotal reporting in osteopathic literature indicates significant therapeutic benefit; however, there has been little quantitative research conducted to verify these claims. Current work at the A.T. Still Research Institute focuses on providing a strong evidence base for manipulative diagnosis and treatment essential to the future of osteopathic practice. To assess the validity and accuracy of osteopathic diagnostic tests, specialized digital cameras and pressure-sensitive pads are used to collect precise three-dimensional coordinates of specific points on the practitioner's hands as well as the forces applied during palpation. This new instrumentation generates vast amounts of raw data available for mining, analysis and visualization, far too much to be processed by hand. Key challenges in this work include signal processing of the raw data and merging of multiple data streams into a coherent information stream, pattern recognition in the information stream to identify palpation session milestones, and data visualization strategies. Current work has focused primarily on signal processing, pattern recognition and visualization of the three-dimensional camera data stream during a diagnostic session. A system was developed to allow practitioners to visualize the three-dimensional movement of their hands and select points at where palpations begin and end. Visualization of those sections of data is then produced along with reports including displacement, duration between a single palpation, as well as the specific location of each identified landmark along the body. Future work aims to incorporate the pressure data stream.

Carnivore Hunting Mode and Plant Species Coexistence
Chengjun Sun

Department of Biology, McGill University
Coauthors: Oswald J. Schmitz, School of Forestry and Environmental Studies, Yale University
Michel Loreau, Department of Biology, McGill University

Indirect effects of top predators is increasingly being invoked as an important determinant of plant community structure and attendant ecosystem function. Top-down effects of predators on plants can be mediated by herbivore prey in two general ways that are related to predator hunting mode. Actively hunting predators cause largely density-mediated indirect effects by direct lowering the abundance of herbivores impacting plants. Sit-and-wait ambush predators largely cause trait-mediated indirect effects by causing herbivore foraging shifts to avoid predation risk. We explore here, using a series of dynamical systems models, the implications of indirect effects propagated by carnivore hunting mode on plant species coexistence. We then examine how these effects singly (i.e., an identity effect) and in combination (i.e., a multiple predator effect) influence plant species coexistence.


Simulation of mRNA Migration in Subnuclear Environment
Terry Tang

University of Lethbridge

We study a mathematical model for mRNA translocation in the nucleus from the site of synthesis to a nuclear pore where it is exported to the cytoplasm. The free diffusion model which has been the dominant hypothesis for quite some time is compared to one in which the nuclear skeleton and chromatins confine the mRNA movement. The results show that chromatin serves as a barrier to mRNA movement away from the nuclear pore complex, hence enhancing early exit but keeping entrapped particles for longer; on the other hand, a bias towards diffusing in the directions perpendicular to the nuclear envolope, simulating the effect of a proposed nuclear skeleton, has little effect on the exit time.

A Mathematical Model of Erythropoiesis Subject to Malaria Infection
Jeremy Thibodeaux

University of Central Oklahoma

There have been numerous mathematical studies on the dynamics of erythropoiesis. The same can be said of the dynamics of malaria infection within a particular host. Surprisingly, there are no detailed mathematical studies on how these processes affect each other. In this study, we develop a mathematical model of erythropoiesis under the influence of malaria infection. The model takes the form of six coupled equations. Two are first-order, hyberbolic, partial differential equations describing the precursor and mature erythrocyte populations. The remaining four are ordinary differential equations describing the erythrpoietin concentration, the parasite population, the infected erythrocyte population, and the body's immune response.

Modeling the Effects of Genetic Drift and Natural Selection with Discrete Simulation
Spencer Tipping

Truman State University
Coauthors: Karen O'Connell (keo332@truman.edu) Dianne Kopp (dek453@truman.edu) Anton Weisstein (weisstae@truman.edu) Pam Ryan (pjryan@truman.edu)

To obtain distributions against which to compare our calculated Dsyn and Dnon values, we constructed a simulation that models the effects of selection and genetic drift over time. This software provides the capability to integrate and model several different evolutionary patterns such as natural selection, genetic drift, or any combination of these. A model-specific function determines the reproductive fitness of each individual, and a real-valued matrix controls both the degree of reproductive isolation of subpopulations and changes in population size. By combining these parameters, we can simulate both simple and more complex scenarios; for example, directional selection occurring within partially isolated subpopulations. After many model runs under a specific scenario, we acquire statistical distributions of our modified D statistics. Using Bayesian analysis, we then calculate the likelihood of the observed D statistics under each of the evolutionary scenarios to infer the population’s demographic and evolutionary history. Although our model was constructed to reflect specific biological features of HIV evolution, we anticipate that our extension of Tajima’s analysis will have broad applicability.

The Interaction Between Influenza Hemagglutinin (HA) Fusion Peptides and a Lipid Bilayer Membrane
Naveen K. Vaidya

Department of Mathematics and Statistics, York University, 4700 Keele St., Toronto, M3J1P3 Canada
Coauthors: Huaxiong Huang, York University, Canada; Shu Takagi, University of Tokyo, Japan

The microscopic level interaction between influenza Hemagglutinin (HA) fusion peptides and a lipid bilayer membrane is important for the membrane fusion process, which is a key step of the viral infection. We use a coarse-grained molecular dynamics (CGMD) simulation method to study the interaction between HA fusion-peptides and a phospholipid bilayer membrane. With CGMD, we have been able to simulate a relatively large piece of membrane for a sufficiently long time period and with more than one peptide embedded in the membrane. We obtained a kinked-shaped conformation of the peptide with the kink at the level of phosphate group, consistent with experimental NMR study. A presence of fusion peptides inside the membrane may cause bilayer thinning and lipid molecule disorder, which are required for the fusion activity. Peptides tend to come close to each other required for forming clusters as seen in many experiments.

Analytical methods for comparing samples of the T cell receptor repertoire
Vanessa Venturi

Centre For Vascular Research, University of New South Wales, Australia
Coauthors: Mark M Tanaka (University of New South Wales, Australia) Miles P Davenport (University of New South Wales, Australia)

T cells bear a receptor on the surface that enables the detection of viral peptides. The diversity of T cell receptors (TCRs) responding to a given viral peptide is estimated to vary between 10 and 103 different TCRs and is an important factor in an immune response. For example, some vaccinations may focus the T cell response to involve fewer different TCRs. However, it may be easier for a mutant virus to escape immune recognition from a focussed T cell response than a diverse T cell response. Another important factor in an immune response is the evolution of the TCR repertoire over time and through the various stages of infection. Determining the stability of the TCR repertoire requires assessing the similarity (or overlap) between sequential TCR samples. Thus, a rigorous quantitative approach to comparing samples of the TCR repertoire is required to understand the effects of infection and vaccination in vivo. The most popular approach to comparing samples of the TCR repertoire is to count the number of different TCRs within a sample or the number of similar TCRs between samples. This approach is highly sensitive to differences in sample sizes, does not account for the number of copies of each different TCR, and often does not provide a measure of statistical significance. We present a robust approach to comparing the diversity and assessing the similarity between samples of the TCR repertoire. We propose the use of ecological measures of diversity (Simpson’s diversity index) and similarity (Morisita-Horn similarity index) and randomization techniques (for standardizing sample size and establishing statistical significance), that both avoid these problems and enrich the analysis of TCR data. These techniques are broadly applicable to the analysis of TCR repertoire in various studies.

The hyperbolic effect of density and strength of inter-beta cell cell coupling in islet bursting
Xujing Wang

Max McGee National Research Center for Juvenile Diabetes & Human and Molecular Genetics Center, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, WI, 53226, USA
Coauthors: Aparna Nittala

The insulin producing beta cells reside in pancreatic islets, with tight inter-beta cell couplings. Each human islet contains several thousands of beta cells. Synchronized bursting from all beta cells in each islet is the basis of regulated insulin release. Increasing evidence is indicating the importance of islet morphology in its function, and the need for quantitative investigation. In this study we utilized a new 3D hexagonal closest packing (HCP) cell cluster model to examine islet bursting characteristics and the cluster architectural parameters including number of beta cells n_beta, number of inter-beta cell couplings each cell has nc, and the coupling strength gc. We simulated beta cell clusters of different sizes ranging from 1-343, gc spanning from 0-1000 pS, and nc varying between 0-12. From the resultant beta-cell responses, we quantified three significant functional measures – fraction of bursting ?-cells fb, synchronization index lambda and bursting period Tb. Our results suggest that the bursting characteristics depend quantitatively on the cluster architecture in a non-linear fashion. Specifically, we investigated the role of nc and gc, as these are impaired under pathological conditions like diabetes. We discovered a hyperbolic response to the combined stimulus of nc and gc. Based on this we defined a “cluster coupling index” or CCI. CCI describes the mechanical integrity of gap junctions among beta-cells and is critical to the robustness of islet oscillation and synchronization.

We propose CCI as an important functional islet predictor that has the potential of providing insight into the compensatory mechanism of islets during the onset of diabetes and disease progression. It may also hold the key to targeted drug delivery for altering either gc or nc to preserve islet functionality.

Fast diffusion prevent blow up in chemotaxis
Zhian Wang

Institute for Mathematics and its Applications, University of Minnesota, USA
Coauthors: Yung-Sze Choi

In this work, we propose a new mechanism to prevent blow up in a chemotaxis model. Based on biological relevance, we show that fast diffusion in chemotaxis can generate pattern formation and solutions of the resulting model stay bounded. We will show both numerical and theorectical results.

Heterogeneity and HIV drug resistance
Zoe Ward

University of Bath
Coauthors: K A J White

The emergence of drug resistance for HIV patients has led to the development of a range of drug types, each targeting a different stage in the production of viral particles within the body. Amongst the most common drugs are reverse transcriptase inhibitors which reduce the infection rate of susceptible cell targets and protease inhibitors which reduce the production rate of virus particles from infected cells (Gazzard, 2006). In addition to selection pressure on HIV to produce drug resistance strains, the wild type virus has an unusually large mutation rate in the absence of any drugs (Larder et al., 2001) which significantly complicates the problem of developing drug regimes to minimize viral load in a patient.

When considering viral loads within the body, it is often useful to use a compartmental model which can distinguish loads in the blood stream and in key body organs. Previous models which have taken a compartmental approach have demonstrated the possibility for different viral loads in different compartments in the presence of drugs (Calloway and Perelson, 2002). Here we extend this idea using the standard viral dynamic model of Nowak and May (2000) and demonstrate that drugs are not necessary to obtain such heterogeneity. Instead, by considering different cell target types in the different compartments, heterogeneity in viral load can emerge. Parameter estimates obtained from published data are used to demonstrate this behaviour numerically.

We extend the idea to consider the competition of different viral strains within the body. We discuss the results of this modeling, in particular focusing on the way in which drug and cellular heterogeneity affect the proportions of wild type and resistant strains within the body.


  • Calloway, D. S. and Perelson, A. S. HIV-1 infection and low steady state viral loads. Bulletin of Mathematical Biology, 64: 29-64, 2002.
  • Gazzard, B British HIV Association (BHIVA) guidelines for the treatment of HIV-infected adults with antiretroviral therapy. HIV Medicine, 7:487-503, 2006.
  • Gudelj, I, Beardmore, R. E, Arkin, S. S. and Maclean, R. C. Constraints on microbial metabolism drive evolutionary diversification in homogeneous environments. Journal of Evolutionary Biology,20:1882-1889, 2007.
  • Larder, B, Richman D, Vella S., editors. HIV resistance and implications for therapy. 2nd ed. Gilead Sciences. Atlanta, GA, USA: MediCom Inc, 2001.
  • Nowak, M. A and May, R. M. Virus dynamics: mathematical principles of immunology and virology. Oxford University Press, 2000

A Semi-Automated Procedure for Segmenting Early Embryogenesis in Caenorhabditis elegans
Alexandra Wehrman

Truman State University
Coauthors: Kurt Warnhoff, Dr. Scott Thatcher, and Dr. Tim Walston
An understanding of the forces acting on cells in the early embryo can provide important information for how cells interact to determine their shapes, movements and fates. These forces can be physical and genetic, as well as intracellular or extracellular. The early Caenorhabditis elegans embryo provides an excellent environment to explore the forces acting during embryogenesis and to develop techniques and models that can be applied later to more advanced biological events. We report the continued development of a four-dimensional GGH (Glazier-Granier-Hogeweg) model to simulate the four-cell stage of embryogenesis. In addition, a semi-automated procedure for the segmentation of four-dimensional differential interference contrast (DIC) microscopic data has been developed. A precise and accurate segmentation scheme offers many opportunities for the quantitative analysis of early embryogenesis and other cellular systems. Our segmentation technique incorporates a combination of level set and watershed methods to properly delineate cells and cellular components of the embryo in DIC micrographs. Segmented data serves as an input into the current GGH code and data from many embryos are needed as a source of calibration and validation for the model. This segmentation technique for DIC images of the C. elegans embryo should also be applicable to DIC images of other embryos or biological samples.
Date received: June 27, 2008

Inside GIS: Habitat Parameterization and Metapopulation Modeling of a Rare Winter Annual
Brett L. Wiley

Truman State University
Coauthors: Jonathan D. Vollmer, Truman State University; Dr. Michael J. Adams, Truman State University; Dr. Michael I. Kelrick, Truman State University
Metapopulation models have become standard tools for biological conservation. These models require knowledge of both occupancy and flux of individuals among patches of suitable habitat. For animal species, estimation of these parameters is reasonably straightforward. However, for plants, it is impracticable to follow seed fates, and therefore difficult to build realistic metapopulation models. Even so, we are assembling a metapopulation model for the federally threatened, rare, winter annual plant species, the microhabitat endemic Missouri bladderpod (Lesquerella filiformis). Our model simulates a permanent grid of 963 5- X 5-m cells. Using a Geographic Information System approach, we used four years’ empirical data characterizing percent cover of cells’ habitat attributes to classify a cell as one of four subjectively defined microhabitats for which microhabitat-specific demographic data had been collected, or to exclude it from the simulation. Microhabitat-specific vital rates are computed by intra-annual data that have been combined to form inter-annual transition values that preserve measurement error associated with the field data collection. Through model simulations incorporating environmental stochasticity we can produce a distilled probabilistic projection of the time trajectories of population size of the entire grid. Our model incorporates a novel approach to simulating seed dispersal and habitat conditions, such as removing young cedars, to provide land management prescriptions for suitable L. filiformis habitat.
Date received: June 30, 2008

Game theory of female guarding: the role of female choice
Lev Yampolsky

East Tennessee State University
Coauthors: Mahul Chakraborty, Daniel Scantlebury, Jing Zhu and Tracy Ivy
We present a game theory model of the evolution of monogyny in the form of female guarding by males, in the situation in which guarding is not 100% efficient and females can therefore exercise at least some choice. Investment of time and effort into guarding of a single female at the expense of future copulations is not beneficial unless there is some factor impeding polygynous males' fertilization success. Previous models, developed mostly to describe monogyny in redback spiders (Fromhage et al., 2005, 2008), focused on male-biased sex ratio and male mortality between matings as factors limiting success of polygynous males. We consider a situation in which females evaluate mates and the probability of mating depends on the duration of courtship, giving the advantage to female-guarding monogynous males. We also assume that females can mate more than once, so both monogynous and polygynous males can experience sperm competition. While applicable to a variety of organisms, the model is tailored to describe mate-guarding in gammarids. Unlike spiders, in which monogamy is enforced after mating, gammarid males have to guard a female before mating can occur. In a two-person game with pure strategies (monogyny, or "guard" and polygyny, or "seek"), depending on the shape of relationship between courship time and mating probability, either both or neither "guard" and "seek" strategies may be the ESS. Accelerating returns on courtship time create an advantage for the "guard" strategy, while diminishing returns benefit the "seekers". A multiplayer mixed strategy game, however, never predicts a mixed ESS, suggesting that female choice-mediated guarding evolves under a restricted set of circumstances as an all-or-nothing strategy.

Teaching Math to Biologists and Biology to Mathematicians: When Needed and As Much As Needed
Lev Yampolsky

East Tennessee State University
Coauthors: Istvan Karsai, Edith Seyer, Karl Joplin, Laura Catron and Brandy Warner
Traditional biology curriculum leaves a gap between introduction of mathematical concepts within Calculus and Probability courses and application of these concepts to biological situations. Likewise, a Math major willing to get exposed to biological applications will have to survive a lot of biology before mathematical tools and ideas can be put to work. Even less likely is a typical undergraduate student to have a chance to apply mathematical concepts in research situations. This results in poor retention of knowledge and, more generally, lack of a common language for collaboration between traditionally educated biologists and mathematicians. We report here two concurrent interacting projects unfolding at ETSU: an NSF-funded undergraduate research program Talent Expansion in Quantitative Biology and an HHMI-funded curriculum development project aiming at creating a three semester integrated Biology and Math course (SYMBIOSIS I, II, III) to replace introductory Biology, Statistics and Calculus classes traditionally taught to Biology majors. In the SYMBIOSIS curriculum, the students get credit for both the Biology and Statistics (SYMBIOSIS I) or Biology and Calculus (SYMBIOSIS II) in the same class. Traditional order of presentation of biological material has been significantly changed to accommodate the more logical order of introducing mathematical concepts, from algebra and probabilities, to elementary calculus, to differential equations and linear algebra. In Talent Expansion program emphasis is on application of mathematical tools to problem-solving situations. We present examples of research and exam problem highlighting this integrated approach.
Date received: June 24, 2008

A Mathematical Model to Relate Serum-Mediated Bacterial Killing with Anaphylatoxin Elaboration
Suellen Yin, Alex Jacobson

University of Michigan
Coauthors: Suellen Yin, Alex Jacobson, Patrick W. Nelson, John G. Younger
Our study aims to quantitatively analyze the kinetics of the Complement Cascade, the human body’s way of destroying foreign pathogens. The bacteria used in this study, Klebsiella Pneumoniae, are commonly found as a cause of blood infections. Using fluorescently labeled bacteria and enzyme-linked immunoassays, a reaction mixture of bacteria and human sera was created to obtain high-resolution measurements of bacterial growth and complement protein binding. This data and several assumptions about the interactions of the immune system were combined to develop and fit parameters for a pharmacokinetic mathematical model.

Quantifying the fitness of influenza drug-resistant mutants from plaque assay data
Karen Yip

Department of Physics, Ryerson University
Coauthors: Catherine Beauchemin, Ryerson University, and Guy Boivin, CHUQ-CHUL and Universite Laval
An increasing fraction of circulating and emerging influenza strains are resistant to anti-flu drugs. To assist in developing public health measures to contain a potential flu pandemic, epidemiological modellers will need to make accurate predictions of the size and rapidity of emergence of drug-resistant mutant strain populations. This requires accurate quantitative measures of the parameters responsible for the fitness impairments/enhancements of these mutants.

Differences in fitness between strains is typically assessed by comparing the diameter of the plaques produced by different strains in infection plaque assay experiments. The aim of our work is to develop a tool which could translate differences in plaque diameter to a difference in a parameter controlling viral reproduction in these strains (e.g., viral attachment rate, production rate, or release rate). Here, we present the first step of this project which consisted in developing an agent-based model to mimic an in vitro infection plaque assay set-up. Our approach should also be applicable to other infection systems (e.g., SARS, metapneumovirus), and could be used to rapidly quantify the virulence of emerging strains.
Date received: June 26, 2008

Mathematical modeling of animal morphogenesis; pattern formation on the cell-based growing field
Eiichi Yoshimoto

Nagoya University
Coauthors: Shigeru Kondo (Nagoya University)
There are many mathematical models proposed to explain the pattern formation of animal development. In many cases, the numerical simulation studying these models was done in the fixed and continuous fields. However, in the real morphogenesis, the field (embryo) is the aggregate of the cells, and the size and the shape of the field changes by the division, death and migration of the cells. To do a more realistic simulation of the animal morphogenesis, we need to incorporate these phenomena into the simulation of the pattern formation. On this purpose, we developed a platform of the simulation that deals the behavior of the cells and calculates the whole embryo shape automatically. This system enables us to simulate the morphological changes in more realistic condition. By applying a reaction-diffusion model to this system, it is possible to reproduce the early development of some animal species.
Date received: June 28, 2008

To Investigate the Genetic Variability and Spatial Distribution of Tubifex tubifex
Jiaxin Yu

University of Vermont
Coauthors: Lori Stevens (University of Vermont) Nilanjan Lodh (University of Vermont) Max Droppman (University of Vermont)
The objective of this research is to compare the prevalence of Myxobolus cerebralis infection in worms collected from Montana vs. Vermont, and to use GIS to determine if the spatial distribution of Tubifex tubifex in Vermont is different than in Montana. The Batten Kill in Manchester, Vermont was previously tested positive for Myxobolus cerebralis, and five sites on the river were chose as sample collection sites. During sample collection, streams will be divided into 100m sections, and samples will be collected using kick-nets. Twenty worms will be collected from each site. Habitat assessment will also be carried out on each site. Nested PCR for 18S rDNA of M. cerebralis and gel electrophoresis are used to screen the T. tubifex to determine whether they are positive for the parasite. GIS will be used to compile habitat information to determine whether there are similarities of habitat characteristics between Montana and Vermont. This research is still on-going, samples from Montana have been analyzed, the results are yet to compile.

A New View of CDC's Plan of Elimination of Syphilis
Ruijun Zhao

Purdue University
The CDC launched the National Plan to Eliminate Syphilis from US in October 1999. In order to reach their goal, a good understanding of transmission dynamics of the disease is necessary. Breben et al. supported the plan by showing that no cycling occurs for syphilis based on a SIRS model. We study three sub-optimal models, taking care of partial immunity, vaccination, and relapse of secondary lesions. Our models suggest that a backward bifurcation very likely occurs using the estimated epidemiological parameters for syphilis, which may explain the resurgence of syphilis after mass treatment. Occurrence of backward bifurcation brings a new challenge for the CDC's plan - a balance between treatment of primary and secondary infection and vaccination development and health education. Our models support the premise that development of effective vaccine and health education enhancing biological and behavioral protection against infection in risky populations is amongst the best ways to achieve the goal of elimination of syphilis from US.