42 LS06 Abstracts

CP1 [email protected] A One-Dimensional Model of Blood Flow in Arter- ies with Friction, Convection and Unsteady Taylor Alexander Anderson Diffusion Based on the Womersley Velocity Profile Department of Mathematics University of Dundee We present a one-dimensional model for blood flow in ar- [email protected] teries, without assuming an a priori shape for the velocity profile across an artery. We combine the one-dimensional equations for conservation of mass and momentum with CP1 the Womersley model for the velocity profile. The veloc- Simulating Cardiac Blood-Muscle-Valve Mechanics ity profiles produced are used to evaluate the friction, to by An Adaptive Version of the Immersed Boundary correct the nonlinear terms and in unsteady Taylor diffu- Method sion theory. We present flow simulations for numerical and disease modeling purposes. Cardiac mechanics can be modeled as the interaction of a viscous incompressible fluid (the blood) and a (visco- Charles S. Peskin )elastic structure (the walls and valves of the heart). The Courant Institute of Mathematical Sciences immersed boundary (IB) method is an approach to such New York University problems. We shall present an adaptive version of the [email protected] IB method and describe the application of this adaptive methodology to the three-dimensional simulation of blood Karim Azer flow in the heart. Computer animations of the beating Courant Institute of Mathematical Sciecnes, NYU heart will be shown. Karim [email protected] Charles S. Peskin Courant Institute of Mathematical Sciences CP1 New York University Simplified Models of the Respiratory Control Sys- [email protected] tem. David M. McQueen We have developed simplified mathematical models for the Courant Institute for Mathematical Sciences control of respiration in mammals. One component con- New York University sists of a model of the brainstem respiratory oscillator [email protected] that incorporates regulation of frequency and amplitude of breathing in response to physiological control signals (oxy- Richard Hornung gen and carbon dioxide). The neural model was coupled Lawrence Livermore National Lab to simplified models of the lungs incorporating oxygen and [email protected] carbon dioxide transport. The models explain some experimental observations on open- and closed-loop regulation of breathing. Boyce E. Griffith Courant Institute of Mathematical Sciences Alona Ben-Tal New York University Massey University griffi[email protected] Institute of Information & Mathematical Sciences [email protected] CP1 Jeffrey C. Smith Finite Elements and Operator Splitting Method NINDS, NIH for the Numerical Simulation of Fluid Flow in De- [email protected] formable Domains with Application to Blood Flow The modeling of blood flow in human arteries involves Ilya Rybak a Fluid-Structure Interaction problem (FSI) because the Drexel University region itself in which the fluid is confined changes as a School of Biomedical Engineering consequence of the fluid motion. Several approaches are [email protected] available to simulate FSI. Our goal is to explore the benefits and the applicability of a numerical algorithm based on finite elements method and operator splitting in order CP1 to avoid iterative procedures for the location of the de- An Evolutionary Hybrid Cellular Automaton formable boundary. Model of Solid Tumour Growth Tsorng-Whay Pan We propose a model of tumour growth, in which each cell Department of Mathematics is equipped with a micro-environment response network. University of Houstofn This network determines the cellular behaviour, and is sub- [email protected] ject to mutations and subsequently Darwinian evolution. Using this approach we have investigated the impact of Giovanna Guidoboni, Roland Glowinski the tissue oxygen concentration on the growth and evolu- University of Houston tionary dynamics of the tumour. The results show that the Department of Mathematics oxygen concentration affects both the genetic diversity and [email protected], [email protected] morphology of the tumour. Philip Gerlee Univeristy of Dundee LS06 Abstracts 43

CP1 of actin. An Arterial Blood Pressure Model Peter Kollman The arterial pulse pressure waveform analysis has impor- Department of Pharmaceutical Chemistry tant clinical applications. Some approximations of the flow UCSF described by Navier-Stokes equations can be written as [email protected] N-soliton solutions of a Korteweg-de Vries equation, com- pleted by a windkessel flow. Experiments show that N = Edward F. Pate 2 or 3, leading to a model with a small number of parame- Department of Mathematics ters that can be useful in new diagnosis methods based on Washington State University indexes of pulse pressure shape variability estimated from [email protected] non-invasive measurements. Roger Cooke Michel Sorine University of California, San Francisco INRIA [email protected] [email protected] Todd Minehardt Emmanuelle Crépeau Department of Pharmaceutical Chemistry Laboratoire de Mathématiques Appliquées UCSF Université de Versailles Saint-Quentin-en-Yvelines [email protected] [email protected]

Taous-Meriem Laleg CP2 INRIA Rocquencourt Mathematical Model of Steroidogenesis to Pre- [email protected] dict Intracellular Response to Endocrine Disrupt- ing Compounds

CP1 Exposure to endocrine disrupting compounds (EDC) can Deformation of a Circular Rod with Twist and induce adverse effects on reproduction mediated through Bend in Fluids alterations in the enzymes involved in steroidogenesis. We are developing a deterministic model of the intratesticular The overwound or underwound double helix of DNA occurs and intraovarian metabolic network in fish that mediates in DNA transcription, DNA replication, and formation of steroidogenesis. This model allows for an improved under- DNA loops in protein-DNA interactions, which are essen- standing of the source to outcome linkages necessary for tial in biological processes. In particular, the deformation risk assessments with EDCs. This work was reviewed by of circular DNA molecules occurs in many prokaryotic and the U.S. EPA and approved for publication but does not viral DNAs and also occurs in the mitochondria of eukary- necessarily reflect Agency policy. otic cells. We consider an elastic rod in a closed circular configuration with a uniform twist that adds up to an in- Daniel Villeneuve, Gerald Ankley teger number of full turns so that the triad configuration U.S. Environmental Protection Agency is smoothly periodic. Moreover this rod is embedded in [email protected], [email protected] the incompressible viscous fluid. The immersed boundary method is used to study the instability of a circular rod Michael S. Breen, Rory B. Conolly with twist and bend. Without twist, a closed circular rod National Center for Computational Toxicology gives an equilibrium configuration; that is, there is no net U.S. Environmental Protection Agency force or torque and it is stable. But with enough twist, [email protected], [email protected] the circular configuration becomes unstable, and the rod relaxes to a stable coiled configuration. CP2 Sookkyung Lim Combining BrdU-Labeling Experiments and Math- Mathematical Biosciences Institute ematical Modeling to Understand Natural Killer The Ohio State University Cell Development and Homeostasis [email protected] Its unclear which role population dynamics play in the distribution of NK cells over different maturation stages CP1 and in shaping the receptor repertoire. Experimental data The Open Nucleotide Pocket of the Profilin:actin were used to test different mathematical models and to op- X-Ray Structure Is Unstable and Closes in the Ab- timize population dynamical parameters. Similar studies sence of Profilin were performed on spleen cells, in order to elucidate mature NK cell homeostasis. Results will be discussed with respect The open nucleotide pocket conformation of actin in the to understanding the regulation of adaptive immunity and profilin:actinCaATP x-ray structure is hypothesized to be specification of important stages in NK cell selection. a crucial intermediate for nucleotide exchange during actin depolymerization/polymerization. The necessary modifi- Marjet Elemans cation of actin with profilin for crystallization leads to am- Karolinska Institutet biguities in this interpretation. Molecular dynamics simu- MTC lations of the open nucleotide pocket, profilin-free actin [email protected] structure show the structure is actually unstable, and closes. Thus there is currently no thermodynamically sta- Maria Johansson, Eleftheria Rosmaraki ble structure representing the open nucleotide pocket state KI-MTC 44 LS06 Abstracts

[email protected], [email protected] from the lymph node, leading to rapid target elimination.

Ramit Mehr Peter S. Kim Faculty of Life Sciences Stanford University Bar-Ilan University [email protected] [email protected] Peter Lee Stanford University CP2 School of Medicine Large Scale Statistical Parameter Estimation for [email protected] the Dynamic Cardiac Metabolism During Ischemia Doron Levy We propose a Bayesian methodology which integrates, via Stanford University a prior distribution, constraints and prior knowledge into [email protected] the parameter estimation process for a three-compartment dynamic model for the cardiac metabolism. The severely underdetermined parameter estimation problem is then CP2 solved by a combination of optimization methods and sta- Modeling Osteoporosis: Predicting Human tistical sampling techniques. A study of the stability of Biomarker Response to Parathyroid Hormone sensitivity to serve as a basis for model reduction is also proposed. Parathyroid hormone (PTH) is a potent bone forming agent that is used to treat severe osteoporosis. PTH- Rachael S. Hageman mediated signal transduction modulates the natural bone Case Western Reserve University remodeling cycle and achieves net gain in bone mass with Department of Mathematics daily dosing. A mathematical model for the human bone [email protected] remodeling cycle has been developed that predicts the effects of PTH on bone remodeling and related biomark- Daniela Calvetti, Rossana Occhipiniti ers. Model simulations explore the effects on biomarkers Case Western Reserve University, Dept of Mathematics of PTH dosing patterns and variability in PTH pharma- Center for Integrated Metabolic Systems cokinetics. [email protected], [email protected] Laura K. Potter Erkki Somersalo GlaxoSmithKline Helsinki University of Technology Scientific Computing and Mathematical Modeling Laboratory of mathematics [email protected] erkki.somersalo@hut.fi Frank Tobin Scientific Computing & Mathematical modelling CP2 GlaxoSmithKline Germline Codon Usage As An Indicator of Immune [email protected] Selection Dynamics

The genetic code defines the relationship between genotype CP2 and phenotype at the basis of all processes of evolution. Vanguard Neural Crest Cells Colonize the Gut: Based on a network view of the genetic code, in which Mathematical and Experimental Analyses every codon is a node and every edge is a mutation, we studied the enclosed process of selection leading to affinity Neural crest cells (NCC) colonize the embryonic gut. Fail- maturation of immune receptors. We found that different ure of this colonization results in Hirschsprungs Disease germline receptor DNA prime different types of change ap- (HD). A continuum model is developed to replicate NCC propriate to movement in affinity landscapes of differing colonization and predictions are compared with experimen- roughness. tal observations. NCC colonization is driven by vanguard proliferation. Accordingly, we examine the case where van- Uri Hershberg, Mark Shlomchik guard proliferation is artificially suppressed. Both experi- Section of Immunobiology, Department of Laboratory ments and modelling predict that colonization still occurs. Medicine These results explain why genes that influence NCC pop- Yale University School of Medicine ulation size cause HD when mutated. [email protected], [email protected] Michael Mariani, Donald Newgreen The Murdoch Childrens Research Institute CP2 [email protected], [email protected] Regulation Mechanisms in the Immune System Matthew J. Simpson We model interactions among effector and regulatory T Department of Mathematics and Statistics cells during an immune response to two simultaneous tar- The University of Melbourne gets to show that the system discriminates based on target [email protected] behavior and not only TCR affinity. The model affirms the necessity of regulatory cells for self-tolerance, but also Kerry A. Landman shows that low amounts do not hinder, but enhance strong Department of Mathematics amd Statistics responses by inducing T cell contraction and emigration University of Melbourne [email protected] LS06 Abstracts 45

CP2 tiotemporal patterns such as bumps and waves. Modeling Extracellular Matrix Realignment Dur- ing Glioblastoma Invasion in An in Vitro Experi- Carlo R. Laing ment Massey University Auckland The outcome for patients with highly malignant brain tu- [email protected] mors is extremely poor. One factor that makes GBM diﬃ- cult to treat is its high invasiveness. To better understand invasion, we study a 3D assay for tumor spheroid inva- CP3 sion in collagen gel. Previous work indicates that invasive Waves and Noise in Dendrites with Active Spines cells follow directed paths away from the tumor spheroid and we present a model that illustrates how the interac- Dendrites form the major components of neurons and many tions between invasive cells and collagen ﬁbrils can cause are equipped with excitable channels located in spines. directed motility. Computationally we obtain a quasi–analytic solution which can be used to study the neural response to spatio-temporal Andrew M. Stein patterns of synaptic input. We examine the robustness of University of Michigan the wave propagation to both space-time white and corre- University of Michigan lated noise that arise in the cable (eg electrical coupling) [email protected] and spine-heads (eg stochastic gating) through weak and strong approximations.

CP3 Gabriel J. Lord Reduced Models of Networks of Electrically Cou- Heriot-Watt University pled Neurons [email protected]

Neurons in the brain are coupled both chemically Yulia Timofeeva (synapses) and electrically (gap junctions). In networks The University of Nottingham of chemically coupled neurons, the precise details of the [email protected] voltage spikes are often unimportant. It is therefore rea- sonable to model voltage spike shapes either in stereotyp- Steve Coombes ical ways, or even not at all, as in the integrate-and-fire University of Nottingham model. By contrast, the speed at which signals propagate Division of Applied Mathematics, School of Mathematical through networks of electrically coupled neurons can be Scie sensitive to the details of spike shapes. For reduced mod- [email protected] els such as integrate-and-fire models, this raises accuracy issues. We demonstrate these issues computationally, and discuss ways of resolving them. CP3 Neural Timing in Highly Convergent Systems Christoph Borgers, Erin C. Munro Tufts University In order to study how the convergence of many variable [email protected], [email protected] neurons on a single target can sharpen timing information, we investigate the limit as the number of input neurons and the number of incoming spikes required to fire the target CP3 both get large with the ratio fixed. We use asymptotic A Stochastic Model for Neuronal Membrane Po- forms of the density and the standard deviation near the tential and Time-Varying Inputs limit to understand the behavior of octopus cells in the mammalian cochlear nucleus. We propose a stochastic model for the firing activity of a neuronal unit, that is based on a suitable exponential trans- Michael C. Reed formation of a continuous-time stochastic process subject Duke University to random jumps. Such a model includes the decay effect [email protected] of the membrane potential in absence of stimuli, and the occurrence of various types of tyme-varying inputs. An Colleen C. Mitchell analysis of the probability distributions of the membrane University of Iowa potential and of the firing times is performed. Department of Mathematics Antonio Di Crescenzo [email protected] Dipartimento di Matematica e Informatica Universita‘ di Salerno CP3 [email protected] Inverse First Passage Time Methods and Their Ap- plications to Neuronal Modeling CP3 We consider an Ornstein-Uhlenbeck diffusion process Xt “Equation-Free” Modelling of Neural Systems constrained by an unknown absorbing boundary S(t). We T “Equation-free” modeling allows one to compute with the assume known the distribution of the time when the effective equations governing the macroscopic dynamics of process crosses for the first time the boundary. The aim a system even if they cannot be explicitly derived, proof our study is to determine the boundary shape. Two vided that the microscopic dynamics are known. These alternative algorithms are proposed and their features are techniques can be used to do bifurcation analysis of com- discussed. Application of these methods to a classification plex networks of neurons. We demonstrate these ideas for algorithm and to detect non-stationarity in observed data several types of networks, studying steady states and spa- 46 LS06 Abstracts

in a neuroscience context is presented. at multiple levels: within-cell, within-host and within- population (of hosts). We looked at how viruses can op- Laura Sacerdote, Cristina Zucca timally exploit their hosts and how this behaviour may Dept. Mathematics influence the most successful strategy at the between-host, Torino University or epidemiological level. I will present a fairly general way [email protected], [email protected] to consistently combine models of disease process and disease spread with the goal of understanding the net selection pressure on a model virus. The method is illustrated using CP3 two popular models at the within- and between-host levels. Wavelet Analysis of Neurophysiological Signals Daniel Coombs Using wavelet analysis we have studied: (a) movement- University of British Columbia related changes in the local field potentials recorded from [email protected] the subthalamic nucleus of patients with Parkinsons disease, (b) cortical control of hand movement in healthy sub- Michael A. Gilchrist jects from functional MRI time series, and (c) seizure EEG University of Tennessee in kindled epileptic rats. The mathematical framework and Dept. of Ecology & Evolutionary Biology some results of the analysis of these neurophysiological sig- [email protected] nals will be discussed. Moran Weinberger, Jonathan Dostrovsky Colleen Ball Department of Physiology University of British Columbia University of Toronto [email protected] [email protected], [email protected] CP4 Kristine Mosier Department of Radiology The Role of IL-2 in CD4 T Cell Proliferation: In- Indiana University sights from Modeling CFSE Data [email protected] We analyze the data on the dynamics of CFSE-labeled CD4 T cells in vitro at suboptimal concentrations of IL-2 using Michael Kubek several mathematical models. We find that to adequately Department of Anatomy & Cell Biology describe the data, the death rate of divided cells needs to Indiana University increase with the number of divisions cells have undergone. [email protected] Our results suggest that IL-2 regulates expansion of CD4 T cell by increasing dependence of cell death rate on the Harlan Shannon division number, and not by speeding up cell division. Divison of CNS Research Eli Lilly Research Laboratories Dejan Milutinovic [email protected] Theoretical Biology Utrecht University Asok K. Sen [email protected] Professor of Applied Mathematics [email protected] Rob De Boer Division of Theoretical Biology Utrecht University CP3 [email protected] Modeling Excitatory Neurotransmitter Transport Processes Vitaly V. Ganusov Theoretical Biology Synapses in the central nervous system adapt to reflect the Utrecht University history of received action potentials on a molecular level, [email protected] a phenomenon known as synaptic plasticity. Of recent interest is the question of “spill-over”, can neurotransmitters released at one presynaptic terminal escape that cleft and CP4 eventually trigger a response in neighboring synapses? To Influenza A Virus Infection Dynamics and its De- address this question we are coordinating experiments on pendence on Antibody Response the transport systems responsible for mediating the uptake and sequestration of the excitatory neurotransmitter We present a mathematical model of IAV infection in an glutamate (M. Kavanaugh, UM), with the analysis of com- individual, explore the effect of initial viral load and per- putational models. form sensitivity analysis to explore which parameters influence the onset, duration and severity of infection. Im- Emily F. Stone mune memory is modeled by a new variable that quantifies Dept. of Mathematical Sciences the antigenic distance between the virus and the existing The University of Montana antibodies. We find that if antibody response is low or [email protected] nonexistent, chronic disease may develop. Baris Hancioglu CP4 University of Pittsburgh Virus Competition at Multiple Scales Department of Mathematics [email protected] Viruses compete and are subject to natural selection LS06 Abstracts 47

Gilles Clermont viral-cell systems. University of Pittsburgh Department of Critical Care Medicine Hoan Nguyen [email protected] Center for Research in Scientific Computation North Carolina State University David Swigon [email protected] Department of Mathematics University of Pittsburgh jennifer Webster-Cyriaque [email protected] Department of Dental Ecology School of Dentistry, UNC [email protected] CP4 Ebv-Cimmsim: An Agent-Based Model of Epstein ht Banks, Grace M. Kepler Barr Virus Center for Research in Scientific Computation North Carolina State University Epstein Barr virus (EBV) infects more than 90% of all [email protected], [email protected] humans benignly for life but occasionally leads to oncogenic transformation in susceptible individuals. As EBV is a human pathogen, appropriate animal models do not CP4 exist. In this talk, I will present an agent-based model, Continuous Model for the Rock - Scissors - Paper EBV-CImmSim, which simulates both the acute and the Game Between Bacteriocin Producing Bacteria chronic phases of EBV infection. The results of this model correspond qualitatively to data relating to the infected B- In this work, important aspects of bacteriocin produc- cell dynamics derived from patients presenting with acute ing bacteria and their interplay are elucidated. Various infectious mononucleosis (AIM). Furthermore, the model attempts to model the Resistant, Producer and Sensi- suggests that EBV persistence is maintained via exit of la- tive Escherichia coli strains in the so called RSP (Rock- tently infected B cells into the circulation, which acts as Scissors-Paper) game have been made and the question a reservoir for continuous reactivation of the virus. In the arose whether there is a continuous model that admits a absence of this compartment, the infection is cleared. cyclic structure. The observations in experiments showed a cyclic dynamics of these three competing species. This Abdul Salam Jarrah paper gives a possible competitive Lotka-Volterra system Virginia Bioinformatics Institute model and clarifies the underlying dynamics. A continu- Virginia Tech ous, spatially homogeneous competitive model, describing [email protected] the interactions between these bacteria with an exact parameter set for a robust coexistence, is established. Also F. Castiglione statistical effects will be considered. There are medical Istituto Applicazioni del Calcolo applications in eukaryotic organisms such as Malaria and Rome, ITALY infectious diseases. [email protected] Gunter F. Neumann K. Duca Friedrich-Schiller-University, Jena. Virginia Bioinformatics Institute Chair of Bioinformatics Virginia Tech [email protected] [email protected] Stefan Schuster V. Hadinoto, D. Thorley-Lawson Friedrich-Schiller-University Jena Tufts U. Medical School Department of Bioinformatics Boston, MA [email protected] [email protected], [email protected] CP4 R. Laubenbacher Mathematical Modeling of Hhv-6 Immune System Virginia Bioinformatics Institute Dynamics Virginia Tech [email protected] We propose a mathematical model for describing the immune system response to the Human Herpesvirus-6 infection. Our research is focused on the cellular response CP4 of CD4/CD8 T-cells at infection. Starting with a simple A Dynamic Model for Induced Reactivation of La- model that can be applied to clinical data, we estimate tent Virus values of important parameters. The predictions based on this beginning model, and the future work for improve- We report on a deterministic mathematical model to de- ment of it to a realistic model through adapting to new scribe reactivation of latent Kaposi’s Sarcoma-associated experimental data, will be discussed. Herpese Virus (KSHV) in BCBL-1 cell cultures. Model parameters are estimated from properties of uninduced Jeong-Mi Yoon cell cultures undergoing spontaneous reactivation. Addi- Department of Computer & Mathematical Sciences, tional parameters that describe chemically-induced reacti- University of Houston-Downtown vation are determined, by fitting to experimental data and [email protected] standard errors are reported. This model provides good agreement with experimental data and establishes a gen- Mandri Obeyesekere eral framework for modeling of other inducers and latent University of Texas M. D. Anderson Cancer Center 48 LS06 Abstracts

[email protected] Growth We describe several population models exposed to a mild CP5 and long standing infectious disease, i.e. without signifi- Effect of Space and Stochasticity on Two Compet- cant increased natural mortality rate among infected indi- ing Plant System viduals, and providing no immunity/recovery. We modify these models to include non-reproductive groups, and ana- The talk aims in studying the effect of space and stochas- lyze their potential effects on the dynamics of the popula- ticity on two competing plant species, of which one is a su- tion. We are interested in how the non-reproductive class perior competitor and the other, a superior disperser. The may curb the growth of the infected group while keeping system is modeled as a spatially structured Markov process the healthy population at acceptable levels. and is analyzed using systematic perturbation expansion, based on the theory of distributions to account for space Fabio A. Milner and the underlying stochastic differential equations to ac- Purdue University count for stochasticity. Analytical results are compared to Department of Mathematics simulations of the underlying Markov Processes. [email protected]

Otso Ovaskainen Daniel Maxin Department of Biological and Environmental Sciences Purdue University, Mathematics University of Helsinki [email protected] otso.ovaskainen@helsinki.ﬁ

Sandip Banerjee CP5 University of Helsinki Interactions Between Dispersal, Competition and sandip.banerjee@helsinki.fi Landscape Heterogeneity I describe and interpret results obtained from analysing CP5 a set of stochastic, spatially explicit models of population The Impact of External Forcing on Invasion, Ex- dynamics. The analytical method employed a novel math- tinction and Coexistence ematical technique that uses stochastic differential equations. Spatial heterogeneity is generally found to have a External forcing can have a significant impact on ecological positive effect on populations. With regards to both patch and epidemiological systems, not only through resonance size and dispersal scale, an intermediate level is found to be amplification and the generation of subharmonics but also optimal, due to a conflict between minimising endogenous in shifting the thresholds at which a species becomes ex- competition and maximising the benefits of heterogeneity. tinct or invades a community. This threshold phenomenon is clearly of great importance in wildlife management and Ace R. North medical science. Conditions for threshold shift are deter- University of Helsinki mined for many species differential equation systems and ace.north@helsinki.fi their dependence on subharmonic resonance established using Lyapunov exponent analysis. CP5 Jonathan V. Greenman Modelling the Spatio-Temporal Dynamics of Multi- University of Stirling Species Host-Parasitoid Interactions: Aggregated [email protected] Searching, Heterogeneous Patterns and Ecological Implications

CP5 A mathematical model of the spatio-temporal dynamics of Modeling Marine Phage Ecology a two host, two parasitoid system is presented. There is a coupling of the four species through parasitism of both Marine phage infect bacteria, the largest biomass in the hosts by one of the parasitoids. When searching for hosts, ocean, and daily destroy about 25% of the marine bacteria, the parasitoids are observed to aggregate in response to playing an important role in the carbon cycle of the oceans. chemical signalling cues emitted by the host plants dur- Still little is known about phage ecology and population dying host feeding, a phenomenon which is widely reported. namics. From shotgun sequencing, our mathematical mod- We model this aggregative parasitoid behaviour in a multi- els based on a Lander-Waterman algorithm explain about species community using a reaction-diffusion-chemotaxis species diversity and abundance of marine phage. A two model. The spatio-temporal dynamics of our system high- compartment model is developed, and parameters are fit to light behaviour of significant interest. In addition to inva- describe phage/bacteria dynamics. Analysis of the model sive behaviour characterised by travelling waves, we ob- gives stable and oscillatory regimes for this system that serve both quasi-chaotic dynamic heterogeneous spatio- match biological experiments. temporal patterns and a destabilisation of the system to produce quasi-stationary heterogeneous patterns. We show Joseph M. Mahaffy that the destabilisation is due to chemotaxis. The dynam- San Diego State University ical behaviour of our system has significant ecological im- Dept of Mathematical Sciences plications and the concepts of stability and coexistence, mahaff[email protected] biological control and evolution of parasitoid searching behaviour are discussed. CP5 Mark Chaplain, Alexander R. A. Anderson Effects of Non-Reproductive Groups on Population Division of Mathematics University of Dundee LS06 Abstracts 49

[email protected], [email protected] cent experimental studies have highlighted the role of a morphogen (Dpp) in controlling domain growth in the Peter G. Schofield Drosophila wing. We model this phenomenon using a sys- SCRI tem of reaction-diffusion equations with advection. Anal- p.g.schofi[email protected] ysis is carried out using a Lagrangian based approach and results show how uniform growth across the wing may be Stephen F. Hubbard achieved. Division of Applied and Environmental Biology Ruth E. Baker, Philip K. Maini University of Dundee Centre for Mathematical Biology [email protected] University of Oxford [email protected], [email protected] Ian G. Pearce Division of Mathematics, University of Dundee [email protected] CP6 Data Pooling and Robust Dynamic Prediction in Predictive Fermentation Microbiology CP5 Invading Beetles in Nyc: Modeling a Contagion A desirable feature of mechanistic models of bacterial pop- Process with Timing Uncertainty ulation growth is that they describe the interaction between a bacterium and its micro-environment in a frame- We present a model of the spread of a contagious process on work that can be calibrated under relevant experimental a network of nodes that allows the incorporation of uncer- conditions. I present a two-phase modeling approach that tainty about the timing of events. The model is appropriate permits validation the environmental dynamics prior to full for analyzing real-world data on the spread of disease, or model validation. In this talk, I will discuss the approach of an invasive species. We illustrate the model by applying and introduce a model building and database management it to data on the spread of the invasive Asian Longhorned software that facilitates collaboration among multiple re- Beetle among the street trees of New York City. search groups via the internet. Gareth J. Russell Daniel P. Dougherty New Jersey Institute of Technology Lyman Briggs School of Science [email protected] Department of Statistics and Probability, MSU [email protected] Jacqueline Lu New York City Parks [email protected] CP6 Hyperbolic Models for Chemosensitive Movement in Interacting Cell Systems CP5 Nonlinear Dynamics of a Demographically and In the talk, we present two hyperbolic models in interact- Spatially Structured Population under Perturba- ing cell systems. The first model describes chemotactic tion cell movement driven by a diffusive external signal while the second model in addition includes intracellular signal In some situations the management objective of a nuisance transduction mechanism to the cell dynamics. Macroscopic population is to achieve a steady-state equilibrium signif- behavior in biological systems can be explained in terms of icantly below the carrying capacity. Achieving such an microscopic parameters of the hyperbolic models. The con- objective through harvest may be complicated by the pres- ditions for global existence are also investigated in terms ence of stage and spatial structure in the target population. of the properties of signal transduction network . In such cases, optimal harvest strategies must account for differences among classes of individuals in their relative Radek Erban contribution to the population. We consider this hetero- University of Oxford geneity in the dynamics of density-dependent structured Mathematical Institute populations. [email protected]

Evan Cooch, Patrick Sullivan Kyungkeun Kang Cornell University Sungkyunkwan University Department of Natural Resources [email protected] [email protected], [email protected] Angela Stevens Elise Zipkin Max-Planck-Institute for Mathematics in the Sciences Cornell University in Liepzig [email protected] [email protected]

CP6 Hyung Ju Hwang Department of Mathematics, Trinity College Dublin A Mechanism for Morphogen-Controlled Domain [email protected] Growth

Growth is a fundamental aspect of development: it re- CP6 sults from a tightly regulated combination of processes including cell diﬀerentiation, division and movement. Re- Better Triple-Drug Regimen for Hiv: Evaluating 50 LS06 Abstracts

Clinically Feasible Strategies mechanisms involve complex biological networks, which can be analyzed with computational tools such as logi- Current HIV drug therapy, although highly effective, may cal and ODE-based methods ”[ THOMAS, R. and KAUF- cause severe side effects making adherence to the prescribed MAN, M., ”Multistationarity, the basis of cell differentia- regimen difficult. We weigh the positive results of treat- tion and memory. II. Logical analysis of regulatory net- ment, such as higher helper T-cell levels, against such neg- works in terms of feedback circuits.”, Chaos 11, (2001) ative consequences; the appropriate weights can be esti- 180-195.]”,”[ THOMAS, R. and KAUFMAN, M., ”Multi- mated by considering clinical determinants of when to ini- stationarity, the basis of cell differentiation and memory. I. tiate therapy. We then systematically compare clinically Structural conditions of multistationarity and other non- feasible triple-drug strategies based on expected treatment trivial behavior.”, Chaos, 11 (2001) 165-179.]”. We use outcome, including the possibility that therapy will fail due these tools in conjunction with experimental data to iden- to emergent drug resistance. tify morphogens and interpretation mechanisms, which induce bistable behavior in the developing brain ”[Monuki Olga Krakovska ES, Porter FD, Walsh CA. Patterning of the dorsal telen- Department of Applied Mathematics cephalon and cerebral cortex by a roof plate-Lhx2 pathway. The University of Western Ontario Neuron. 2001 Nov 20;32(4):591-604. ]”. We also discuss [email protected] implications for biological phenomena such as robustness.

Lindi M. Wahl Wayne Hayes, Edwin Monuki, Shyam Srinivasan Dept of applied mathematics University of California, Irvine University of Western Ontario [email protected], [email protected], [email protected] [email protected] CP6 CP6 The Role of Wnt Signaling in Colorectal Cancer: a Emergent Bursting in Small Networks of Condi- Theoretical Study tional Square-wave Bursting Cells Wnt signaling regulates gene expression in development, Consider a population of neurons that are all capable of stem cells and colorectal cancer by controlling β-catenin square-wave bursting when given appropriate inputs, but levels. As β-catenin is also a primary component of ad- tuned such that some cells are silent, some are bursting, herens junctions, we developed an ODE model to investi- and some are tonically active. When synaptic coupling is gate how transcription and adhesion interact. Some exper- introduced, how will the population behave? In this talk, imentalists hypothesise that the system is purely compet- I will discuss ways in which synaptic coupling promotes itive, whereas others propose the presence of two forms of emergent bursting in the network. In particular, I will ex- β-catenin. Our model allows us to discriminate between plain a mechanism that can lead to network bursting, even these theories on the basis of their response to specific sys- when none of the cells in the network burst in isolation. I tem perturbations. will use models for conditional respiratory pacemaker cells in the pre-Botzinger complex to illustrate this mechanism. Ingeborg Van Leeuwen University of Nottingham Jonathan E. Rubin Centre for Mathematical Medicine University of Pittsburgh [email protected] Department of Mathematics [email protected] Oliver Jensen Applied Mathematics University of Nottingham CP6 [email protected] Reaction Diffusion and Density Dependent Chemo- taxis John King A system of reaction-diffusion equations with volume filling University of Nottingham chemosensitivity is considered. Questions of existence and School of Mathematical Science uniqueness ansas well as qulitative behaviour of solutions is [email protected] discussed. Applications to morphogenesis and angiogenesis are outlined. Helen Byrne University of Nottingham Brian Sleeman Centre for Mathematical Medicine Leeds University [email protected] England [email protected] CP7 Biological Control Through Intraguild Predation: CP6 a Case Study In Analyzing Morphogen Interpretation Mechanisms in the Developing Brain Rusty crayfish are aggressive invaders of the Great Lakes ecosystem. They interact with indigenous smallmouth bass The mechanism of morphogen interpretation ”[Ashe HL, through intraguild predation. Mature bass are predators Briscoe J. The interpretation of morphogen gradients. De- of rusty crayfish, but predation is gape-limited, the largest velopment. 2006 Feb;133(3):385-94. ]” at the cellular level crayfish escaping predation. These individuals are the most is important in understanding the role of morphogen gra- fecund and compete with juvenile bass, causing a “juvenile dients in cell fate specification, proliferation, and further competitive bottleneck.” We used a stage-structured model signalling cascades. Models of morphogen interpretation to investigate the biological control of rusty crayfish by LS06 Abstracts 51

smallmouth bass and suggest methods for effective control. persal in Homogeneous Environments Mark Lewis We consider a correlated random walk in two dimensions University of Alberta, Canada for simulating the movement of the slug parasitic nema- [email protected] tode P.hermaphrodita in order to quantify its dispersal in homogeneous environments. The correlated random walk Caroline J. Bampfylde leads to anomalous diffusion, more precisely to a fractional Department of Mathematical & Statistical Sciences sub-diffusion equation. The stochastic process associated University of Alberta is characterized by strong memory effects on the level of [email protected] the probability distribution function, i.e., unlike a Markov process, the now-state of the system depends on the entire history of its preparation. CP7 Stochastic Stable Population Growth in Integral Simona M. Hapca Projection Models: Theory and Application SIMBIOS Centre, University of Abertay, Dundee, UK DD1 1HG, Dundee Integral projection models generalize classical matrix pro- [email protected] jection models by allowing individuals to be cross-classified by multiple attributes, discrete or continuous. We show John Crawford, Iain Young that stochastic integral models share the qualitative prop- SIMBIOS Centre, erties of stochastic matrix models that are essential for ap- University of Abertay, Dundee, UK plications: existence of a long-term growth rate, ergodicity [email protected], [email protected] of population structure, and asymptotic lognormality of total population. Case-studies demonstrate model param- eterization from empirical data, and applications in situa- CP7 tions that pose difficulties for conventional matrix models. Effects of Genetic and Phenotypic Diversity on Predator-Prey Cycles Stephen P. Ellner Cornell University We examine characteristics of limit cycles in a simple Dept. of Ecology and evolutionary Biology predator-prey system which allows phenotypic diversity [email protected] and rapid evolution in the prey species. Level of defense against predation and the community composition Mark Rees of the prey species determine whether the system exhibits University of Sheffield short-duration classical predator-prey oscillations, longer Department of Plant and Animal Sciences “evolutionary cycles” or exists at equilibrium. Distinc- m.rees@sheffield.ac.uk tive phenomena resulting from rapid prey evolution include predator-trait cycles in which prey density remains nearly constant while predator density and prey traits cycle. CP7 Diet Selection As An Asynchronous Differential Stephen P. Ellner Foraging Game Cornell University Dept. of Ecology and evolutionary Biology An important issue addressed by Behavioural Ecology is [email protected] that of the evolutionary relevancy of foraging strategies adopted by animals in quest of a patchily distributed re- Laura Jones source, both in terms of diet selection and patch-leaving Cornell University decisions under competition. Solving the corresponding Department of Ecology and Evolutionary Biology asynchronous non-zero sum differential game, which in- [email protected] volves discontinuous state feedback strategies constructed via a regular synthesis technique, requires a careful analysis of the induced discontinuities of the adjoint variables. CP7 Partial preferences arise in several fashions. Modeling Wolf Movement in a Heterogeneous En- vironment Frederic Hamelin CNRS and University of Nice - Sophia Antipolis – I3S The effect of linear features (e.g. roads) on animal move- INRA Sophia Antipolis ment is not well understood. We derive an advection- [email protected] diffusion model with variable coefficients for the mean transit time, which describes the expected time for a wolf to Pierre Bernhard, aj Shaiju interact with environment features, including prey items. CNRS and University of Nice - Sophia Antipolis – I3S This formulation is the adjoint of the forward Kolmogorov [email protected], [email protected] equation. By analyzing the model under various linear feature configurations and densities, we demonstrate the effect eric Wajnberg of linear features on predator-prey interactions. INRA Sophia Antipolis Mark Lewis [email protected] University of Alberta, Canada [email protected] CP7 Modelling P.HERMAPHRODITA Nematode Dis- Hannah Mckenzie, Evelyn Merrill University of Alberta [email protected], [email protected] 52 LS06 Abstracts

CP7 John W. Cain Does Transient Spatiotemporal Chaos Apply to Department of Mathematics Ecological Systems? Virginia Commonwealth University [email protected] A sudden, system-intrinsic collapse of spatiotemporal chaos to regular dynamics is a striking phenomenon; it was sug- Daniel Gauthier gested as a source for species extinction. The Gray-Scott Departments of Physics and Biomedical Engineering system captures fundamental ecological mechanisms like Duke University density dependent species reproduction, food competition, [email protected] species decay, and dispersal. Numerical studies show that the transient time increases exponentially with medium size. The collapse process is robust to noise, but the av- CP8 erage transient lifetime can be influenced drastically. We A Mathematical Model for the Pulsatile Secretion also find that few nonlocal connections in the network can of Gnrh Hormone by Synchronized Gnrh Neurons prevent the collapse phenomenon. Based on recently observed autocrine effects of GnRH on Renate A. Wackerbauer its own release, we develop a mathematical model for pul- University of Alaska Fairbanks satile GnRH release in which GnRH plays the roles of a Department of Physics feedback regulator and a diffusible synchronizing agent. ff[email protected] Results on both the single-cell and population models of GnRH neurons suggest that the positive and negative ef- Sumire Kobayashi fects of GnRH regulation through the G-proteins is suffi- Dartmouth College cient and robust in generating GnRH pulses. Dept of Physics [email protected] Anmar Khadra Department of Mathematics Safia G. Yonker University of British Columbia University of Alaska, Fairbanks [email protected] Physics Department [email protected] Yue-Xian Li University of British Columbia Department of Mathematics CP7 [email protected] Modelling Dispersal in Highly Fragmented Land- scapes CP8 We model dispersal in highly fragmented landscapes as a Traveling Pulses in a One-dimensional Neural Net- correlated random walk incorporating edge-mediated be- work Model with Long-range Horizontal Connec- havior, and employ its diffusion approximation to derive tions closed expressions for various characteristics of the dispersal process, e.g. average time of an individual spending We investigate existence and stability of traveling pulses in current patch i before hitting patch j, conditional that in a one-dimensional neural network with recurrent excita- it will hit patch j before hitting any of the other patches tion. The network model uses non-local integro-differential or dying. Our results can be used to construct individual- equations whose integral kernel represents spatial distribu- based simulation models of movement. tion of synaptic weights. The latter is decomposed into an exponential representing local connections and a set of Otso Ovaskainen, Chaozhi Zheng delta functions representing long-range patchy connections. Department of Biological and Environmental Sciences Solving for pulse solutions of the system, we determine University of Helsinki wave-speeds relation to threshold. Stability is determined otso.ovaskainen@helsinki.fi, chaozhi.zheng@helsinki.fi by zeroes of the associated Evans function. Paul Bressloff, Zachary Kilpatrick CP8 University of Utah Adaptive Control of Abnormal Rhythms in a Patch [email protected], [email protected] of Cardiac Tissue

Suppressing cardiac arrhythmias via implantable pace- CP8 maker devices is of obvious clinical importance. Stimuli Spatially Explicit Resource Competition Modeling applied by the artiﬁcial pacemaker are constrained in that of Florida Plant Scrub Species they must preempt the stimuli applied by the heart’s natural pacemaker cells. Using a mapping model of paced We simulated demographic consequences of resource com- cardiac dynamics, we analyze a feedback control scheme petitive interactions for two indigenous Florida scrub known as extended time-delay autosynchronization (ET- species in contrasting spatial scenarios. We used data on DAS) which operates successfully under the above con- demography, spatial distribution, and competitive interac- straint. We discuss optimal choice of the feedback gain tions between Ceratiola ericoides, a dominant shrub and and minimization of noise sensitivity. Hypericum cumulicola, an endemic scrub species to pa- rameterize mathematical functions. We assessed the con- Carolyn Berger sequences of alternative spatial conﬁgurations on the per- Department of Physics sistence of the endemic plant as a potential management Duke University [email protected] LS06 Abstracts 53

strategy for the restoration of endangered species. [email protected] Jessica Larson Dept. of Mathematics CP8 University of Central Florida Analysis of the Paradoxical (excitatory) Eﬀect of [email protected] Potassium Currents on Hormone Secretion

Pedro Quintana-Ascencio Lactotrophs are excitable cells. Electrical activity trans- Dept. of Biology lates into calcium entry, provoking secretion of the hor- University of Central Florida mone prolactin. Dopamine inhibits prolactin release by in- [email protected] creasing potassium currents, which hyperpolarize the cells, preventing Ca entry. Surprisingly, low concentrations of David J. Kaup dopamine can increase prolactin secretion. How can an Institute for Training and Simulation & Dept. of increase in inhibitory currents strengthen hormone secre- Mathematics tion? We show how a small increase in fast K+ currents University of Central Florida could convert a spiking pattern into bursting and increase [email protected] Ca2+ influx, increasing prolactin release. Joel Tabak CP8 Dept of Biological Sciences Florida State University Waves of Spreading Cortical Depression [email protected] Waves of spreading cortical depression (SD) occur in experiments on various brain structures in different animals CP8 and have been implicated in classic migraine with aura. Mechanisms that are believed to be important for SD in- Stable and Metastable States in Visual Cortex clude ion diffusion, membrane ionic currents, osmotic ef- A large-scale, biophysically realistic model of turtle visual fects, the spatial buffer mechanism, neurotransmitter sub- cortex is being used to study the spatiotemporal dynam- stances, gap junctions, metabolic pumps, and synaptic con- ics of cortical responses to visual stimuli. This presenta- nections. In this talk, continuum models of SD, consisting tion uses a system of linear non-autonomous ordinary dif- of coupled nonlinear diffusion equations for the ion concen- ferential equations to model the system. The stability of trations, will be described. the system is then studied using the theory of Lyapunov Anisha Panda functions for non-autonomous systems. The analysis indi- Department of Mathematical Sciences cates the system has a single stable fixed point and multiple New Jersey Institute of Technology metastable states. [email protected] Philip Ulinski The University of Chicago, Chicago Huaxiong Huang Department of Organismal Biology and Anatomy Department of Mathematics and Statistics [email protected] York University [email protected] CP9 Robert M. Miura Coupling PDE-Based Intracellular Signaling with Department of Mathematical Sciences Membrane-Bound Monte Carlo Simulations New Jersey Institute of Technology [email protected] Microscopy evidence suggests that the spatial heterogeneity of signaling biomolecules is important in signaling pathways. Yet, most mathematical models assume a uniform CP8 distribution of signaling molecules. The work presented Spatial Patterns Produced by Neural Field Equa- here couples kinetic Monte Carlo simulations, describing tions the spatial heterogeneity of membrane-bound ErbB receptors, with a reaction-diffusion-advection PDE system We study spatially patterned stationary solutions of an governing downstream intracellular signaling. The results integro-differential equation introduced by Wilson and show that spatial heterogeneity is important for ErbB reg- Cowan and proposed by Amari as a model of neural ac- ulation. tivity on a layer of interconnected neurons: Erik Andries ∂u x, t Department of Pathology ( ) −u x, t ω x − y f u y, t dy h. ∂t = ( )+ ( ) ( ( )) + University of New Mexico R [email protected] In particular, we investigate the existence of N-bump stationary solutions, or solutions positive on a region that can be decomposed into a disjoint union of N finite intervals. CP9 Our focus is to extend existing results for the symmetric Modeling and Computation of Signal Transduc- case, establish the linear stability of those solutions, and tion of olfactory Cilia with Non-Uniform CNG and characterize a class of Mexican-hat coupling functions that Cl(Ca) Channels Distributions allow N-bump solutions. Olfactory cilia contain the known components of olfac- J. Angela H. Murdock tory signal transduction, including key aspects, cyclic- University of Memphis nucleotide-gated (CNG) channels and Ca2+-gated Cl- 54 LS06 Abstracts

channels (Cl(Ca)). These two channels produce primary Michel Sorine currents that are induced by signal transduction events INRIA within the cilia of olfactory receptor neuron. We use an- [email protected] alytical and computational methods to study mathematical models of certain aspects of signal transduction in frog Nki Echenim olfactory cilia in conjunction with known experimental re- Inria sults. Predictions on properties of the cilia are desired and, [email protected] in particular, information on the distribution of the CNG and Cl(Ca) channels. We develop two group of mathematical models for two different experiments, one is involving CP9 interplay between CNG and Cl(Ca) channels and other one Multi-Scale Models for Gene Network Engineering is involving the diffusion of Ca2+ into cilia and the resulting electrical activity. All models consisting of two differ- Armed with increasingly fast supercomputers and greater ential equations describing Ca2+ concentration, membrane knowledge of the molecular mechanisms of gene expres- potential and some cases it is analytically solvable. Using sion, it is now practical to numerically simulate complex forward problems with matching experimental data we ob- networks of regulated biological reactions, or gene circuits. tain estimates of spatial distribution of Cl(Ca) channels It is also becoming feasible to calculate the free energy of along the length of a cilium. noncovalent binding of regulatory proteins to specific DNA target sites. We developed a hybrid stochastic-discrete and Dorjsuren Badamdorj stochastic-continuous simulation algorithm, with which we University of Cincinnati obtain an accurate time-evolution of the behavior of com- [email protected] plex gene circuits, including a clear picture on the role of highly dilute, but significant, regulatory proteins. These regulatory proteins are responsible for the non-linear con- CP9 trol used by biological organisms to regulate their most Dynamic Regulation of Interferon-Stat1 Signaling important processes. The network simulations provide insight, which can guide rational engineering of regulatory We developed a detailed kinetic model of the Interferon- proteins and DNA operator sequences using molecular me- Stat1 signal transduction pathway. The model reproduces chanics simulations. In this presentation we examine two the dynamic behavior of the pathway in a quantitative important gene circuits, the bistable switch and the oscilla- manner for wildtype Stat1 and different mutant proteins. tor. We study the role of specific biomolecular interaction We analyzed the control exerted on interferon signaling by phenomena on the dynamics of these gene circuits. Us- the individual reaction and transport steps. The numerical ing models that span multiple time and space scales, from and analytical results show that two little understood pro- atomistic, to molecular, to interaction networks we develop cesses, nuclear dephosphorylation and nucleo-cytoplasmic design principles for high quality bistable switch and oscil- shuttling of unphosphorylated Stat1, control the amplitude lator circuits. and duration of Stat1 activation. Yiannis N. Kaznessis Stephan Beirer Dept. of Chemical Engineering and Materials Science Theoretical Biophysics Department University of Minnesota Humboldt University Berlin, Germany [email protected] [email protected] Howard Salis Thomas Meyer, Uwe Vinkemeier University of Minnesota Abteilung Zelluläre Signalverarbeitung [email protected] Forschungsinstitut für Molekulare Pharmakologie, Berlin [email protected], [email protected] CP9 Thomas Höfer Quasi-Equilibrium Approximation of Biochemical Theoretical Biophysics Department Reaction Networks Humboldt University Berlin, Germany [email protected] We consider a biochemical reaction system in which reactions between various molecular species occur on different time scales. With a graph-theoretical approach, a pertur- CP9 bation method and an invariant theory we eliminate fast Control of Cellular Apoptosis in Ovarian Follicles kinetics and reduce the system on a slow time scale. Under quasi-equilibrium assumption on deterministic description In each ovarian cycle, only a definite number of folli- of models, we explore a reduction method on a slow time cles ovulate, the others degenerate through an apoptosis- scale and present conditions for a complete separation of mediated process. We have designed a multi-scale slow and fast kinetics for the governing equation. On the mathematical model where degeneration results from the stochastic description, we reduce the system on a slow time hormonally-controlled confinement of follicular cells within scale by utilizing a perturbation analysis on Markov pro- a zone of vulnerability towards apoptosis. We study how cesses and quasi-equilibrium approximation on fast sub- the control operates and how to control apoptosis by con- system. We make a connection between quasi-equilibrium sidering the characteristics of the 2D-conservation law de- approximation as applied to deterministic and stochastic scribing the age and maturity structuration of the follicular description. We present an efficient stochastic simulation cell population. algorithm on slow time scale based on analytic results and illustrate the numerical accuracy of the approximation by Frédérique Clément simulating motivating examples. INRIA Rocquencourt [email protected] Chang Hyeong Lee LS06 Abstracts 55

Department of Mathematics, University of Minnesota used the methods of contact network epidemiology to eval- [email protected] uate the efficacy of these strategies across a wide range of viral transmission rates and for two different age-specific mortality distributions. We have found that the optimal CP9 strategy depends critically on the viral transmission level A Dissimilarity Parameterized Approach to the (reproductive rate) of the virus: morbidity-based strate- Embedding Problem in Molecularbiology gies outperform mortality-based strategies for moderately transmissible strains, while the reverse is true for highly We discuss an approach to the embedding problem in struc- transmissible strains. If time permits, I will also discuss tural molecular biology that treats interatomic distances the ramifications of mutating pathogens to the spread of (dissimilarities) as independent variables. Using distance disease. geometry we can steer the set of dissimilarities to one corresponding to the interpoint distances of an actual config- Lauren A. Meyers uration of atoms. Our formulation leads to a large-scale, The University of Texas at Austin bound constrained, nonconvex spectral optimization prob- Section of Integrative Biology lem that seems less plagued by nonmeaningful local mini- [email protected] mizers than coordinate parameterized formulations. More- over, as we discuss, computational costs are tractable. Shweta A. Bansal University of Texas, Austin Michael W. Trosset [email protected] College of William & Mary [email protected] CP10 Robert M. Lewis Pair-Level Approximations to the Spatio-Temporal College of William and Mary Dynamics of Epidemics on Asymmetric Contact [email protected] Networks

Existing pair approximations to the spatio-temporal dy- CP9 namics of epidemics assume that the contact matrix is sym- Stochastic Simulation for Mod- metric. There are circumstances where this is unlikely to be eling Highly-Branched Protein-Protein Interaction true for example transmission between fish farms via river Networks: Attacking Combinatorial Complexity networks or more generally spread by transport links. We extend the formalism to asymmetric networks and compare Automated generation of biochemical reaction networks the results of a naive application of the symmetric model, with rule-based graphic rewriting scheme and ”on-the-fly” of a partially asymmetric model, of our fully asymmetric technique have been used to model and simulate protein- model and of stochastic simulation. protein interactions. However, complex and highly- branched networks, where number of reactions exponen- Kieran Sharkey, Roger G. Bowers tially grows as higher-ordered molecular complexes being The University of Liverpool formed, still remain computationally intractable. We pro- [email protected], [email protected] pose a discrete event simulation method which computes dynamics of a system without pre-generating a biochemical reaction network. This method provides a modeling and CP10 computational technique which greatly reduces the com- Evolution of Metabolic Network Functions binatorial complexity observed in most protein-protein interaction systems and present a viable way to study large From the reaction content of the metabolic networks of molecular systems. over 200 organisms which have been retrieved from the KEGG database, we derive scenarios for networks of com- William Hlavacek mon ancestors as defined in the NCBI taxonomy tree. A Theoretical Biology and Biophysics Group structural analysis using the recently developed technique Los Alamos National Laboratory of network expansion allows to investigate at which stage [email protected] during evolution particular network functions are discovered or lost. We further identify structural features which Jin Yang are responsible for the emergence of these functions. Theoretical Biology and Biophysics Los Alamos National Laboratory Daniel Kahn [email protected] Universite Lyon 1 [email protected]

CP10 Oliver Ebenh¨oh Using Contact Network Models for the Spread and Humboldt University Berlin Control of Inﬂuenza [email protected]

The threat of avian influenza and the 2004-2005 influenza vaccine supply shortage in the United States has sparked CP10 a debate about optimal vaccination strategies to reduce Comparing Evolutionary Markov Processes the burden of morbidity and mortality caused by the influenza virus. I will discuss a comparative analysis of two Molecular evolution is often modeled as a homogeneous, classes of suggested vaccination strategies: mortality-based positive-recurrent, irreducible Markov process. Evolution strategies that target high risk populations and morbidity- is studied using the process’ infinitesimal generator, oth- based that target high prevalence populations. We have erwise known as its “substitution matrix.” Over eighty 56 LS06 Abstracts

substitution matrices have been proposed, but rigorous used for social forces. quantitative comparisons are lacking between them. Us- ing composition and latent-variable analyses, we propose Tom Clarke Hilbert-space and statistical metrics to quantify the “dif- Insitute for Simulation and Training ference” between diﬀerent substitution matrices, and by University of Central Florida implication, diﬀerent evolutionary Markov processes. [email protected]

Andrew D. Fernandes Linda Malone Bioinformatics Program Industrial Engineering and Mangement Systems North Carolina State University University of Central Florida [email protected] [email protected]

William Atchley Linda Walters, John Fauth North Carolina State University Dept. of Biology [email protected] University of Central Florida [email protected], [email protected] CP10 Rex Oleson Optimal Disease Control - the Importance of Eco- Insitute for Simulation and Training nomics and Time-Scales for Control University of Central Florida Using a contact-process model for the spread of crop dis- [email protected] ease over a regional scale, we examine the importance of the time-scale for control with respect to the cost of the epi- David J. Kaup demic. We analytically derive economically optimal treat- Institute for Training and Simulation & Dept. of ment regimes using methods from control theory to show Mathematics that there are significant qualitative differences between University of Central Florida long and short-term control. We also emphasise the im- [email protected] portance of economic constraints by deriving a critical relationship between the epidemiological and economic parameters. CP10 On the Role of Cross-Immunity and Vaccines on Graeme A. Forster, Christopher Gilligan the Survival of Less Fit Flu-Strains University of Cambridge [email protected], [email protected] A pathogen’s route to survival involves various mechanisms including their ability to invade (host’s susceptibility) and their reproductive success within an invaded host (“infec- CP10 tiousness”). The immunological history of an individual of- The Adaptive Dynamics of the Evolution of Host ten plays an important role in reducing host’s susceptibility Resistance to Indirectly Transmitted Micropara- or it helps the host mount a faster immunological response sites de facto reducing infectiousness. The cross-immunity generated by prior infections to influenza A strains from the We use adaptive dynamics and pairwise invadability plots same subtype provide a significant example. In this paper, to examine the evolutionary dynamics of host resistance we study the role of invasion mediated cross-immunity in to microparasitic infection transmitted indirectly via free a population where a precursor related strain (within the stages. We investigate trade-offs between pathogen trans- same subtype) has already become established. An uncer- mission rate and intrinsic growth rate. Adaptive dynam- tainty and sensitivity analysis is carried out on the ability ics distinguishes various evolutionary outcomes associated of the invading strain to survive for given cross-immunity with repellors, attractors or branching points. We find cri- levels. Our findings indicate that it is possible (for relative teria corresponding to these and demonstrate that a major low levels of cross-immunity) to increase the likelihood of factor deciding the evolutionary outcome is whether trade- strain coexistence even in the case when invading strains offs are acceleratingly or deceleratingly costly. are “unfit”, that is, when the basic reproductive number of the invading strain is less than one. The development of Angela E. Giafis, Roger G. Bowers “flu” vaccines that minimally enhance herd cross-immunity The University of Liverpool levels may, by increasing genotype diversity, help facilitate a.e.giafi[email protected], [email protected] the generation and survival of novel “virulent” strains, that is strains that have high levels of reproduction within the host. CP10 Simulations As a Mathematical Tool Miriam Nuno Harvard School of Public Health Simulations based on a collection of physical and social [email protected] action-at-a-distance forces can be used to describe interacting organisms. Examples of these will be given for both Xiaohong Wang a panicking crowd and a classical biological phenomenon: Arizona State University niche partitioning by salamanders along a streambank- Department of Mathematics and Statistics forest floor ecotone. The simulations are found to pro- [email protected] duce realistic salamander behavior, including the non- overlapping territories and interspecific niche partitioning. Furthermore, the simulations validate the functional forms Gerardo Chowell Mathematical Modeling and Analysis Los Alamos National Laboratory LS06 Abstracts 57

[email protected] University of Guelph [email protected] Carlos Castillo-Chavez Department of Mathematics and Arizona State University CP11 [email protected] Estimation and Identiﬁcation of Klebsiella Pneu- moniae Aggregation Dynamics

CP11 The bacterial pathogen Klebsiella pneumoniae is a cause Hepatitis A: The Us and Canada As a Coupled of community- and hospital- acquired lung, urinary tract, Epidemiological System and blood stream infections. A common contaminant of in- dwelling cathethers, it is theorized that a common infection Vaccination against Hepatitis A has been widespread in pathway for this gram-negative organism is via shedding off the US since 1996, and more limited in Canada, though of biofilm colonies. In an effort to better understand bac- few epidemic models of Hepatitis A have been developed. terial proliferation in the host bloodstream, we develop a Evidence suggests correlated epidemics in the two coun- size-structured PDE for the aggregation dynamics of the tries. Here we analyze an epidemic model which treats the bacteria in an agitated suspension. We will present results countries as coupled populations, using dynamical systems of an investigation of the fragmentation properties of the methods, in order to study the impact of vaccination in viscoelastic biofilm emboli. the US, and how disease dynamics in the US affect disease dynamics in Canada. David M. Bortz University of Michigan Raluca Amariei Department of Mathematics University of Guelph [email protected] Department of Mathematics and Statistics [email protected] CP11 Multi-Strain Disease Dynamics Due to Stochastic CP11 and Periodic Forcing Implications of Universal Hepatitis A Vaccina- tion in Canada: Predictions of An Age-Structured We consider the coupled-system dynamics of multi-strain Compartmental Model diseases such as the flu, malaria and dengue fever. When the probability of reinfection to a second strain is weak, Vaccination against Hepatitis A became widespread in the the global coupling between the strains leads to a manifold 1990s, however few transmission models have been devel- of steady endemic states. We show that the manifold is oped. Here we develop an age-structured compartmental globally attracting but that stochastic noise results in mo- model to predict the impact of universal vaccination in tion on the manifold. We then investigate the oscillatory Canada. Peculiarities of HAV transmission such as a co- epidemics that result from seasonal forcing and latentcy hort effect and travel-related incidence are addressed. The periods. model shows that transmissibility has declined by a factor 2.8 over the past century. The model also predicts that Thomas W. Carr vaccinating 4-year-olds achieves the best gains. Southern Methodist University Department of Mathematics Arni Rao [email protected] University of Guelph [email protected] Michael Taylor Department of Mathematics Ba’ Pham Southern Methodist University GlaxoSmithKline Canada [email protected] [email protected] CP11 Murray Krahn University of Toronto Maximum Likelihood Estimation in Nonlinear Dy- [email protected] namical Models of Hiv The study of dynamical models of HIV, based on system of Vladimir Gilca, Bernard Duval nonlinear ordinary differential equations (ODE), has con- Institut national de santé publique Quebec siderably improved the knowledge on the pathogenesis of [email protected], the infection. Complexity of those models leads to great [email protected] difficulties for inference and classical sofwares for nonlinear mixed effects models cannot be used. We develop an al- Maggie Chen gorithm for direct likelihood maximization adapted to the Toronto General Hospital context of ODE. Based on simulated and real data, we [email protected] show that it provides efficient estimations of parameters.

Andrea Tricco Rodolphe Thiebaut GlaxoSmithKline Canada Inserm E0338 [email protected] [email protected]

Chris T. Bauch Daniel Commenges, Jeremie Guedj Department of Mathematics and Statistics INSERM E0338 58 LS06 Abstracts

[email protected], [email protected] outbreaks. Thomas W. Carr CP11 Southern Methodist University Disease Modeling to Assess Outbreak Detection Department of Mathematics and Response [email protected]

Bioterrorism is a serious threat that has become widely rec- Michael Taylor ognized since the anthrax mailings of 2001. In response, Department of Mathematics one national research activity has been the development Southern Methodist University of biosensors and networks thereof. A driving factor be- [email protected] hind biosensor development is the potential to provide early detection of a biological attack, enabling timely treatment. This presentation introduces a disease progression CP12 and treatment model to quantify the potential benefit of Polymer Coating of Biological Surfaces early detection. To date the model has been used to assess responses to inhalation anthrax and smallpox outbreaks. Many drug delivery systems suffer from undesirable interactions with the host immune system. It has been exper- Diane C. Jamrog, Adam Szpiro imentally established that covalent attachment of suitable Lincoln Laboratory polymers to the surface of the drug carrier can reduce such Massachusetts Institute of Technology undesirable interactions. In this talk we present and anal- [email protected], [email protected] yse mathematical and computational models of the polymer coating of biological surfaces. In particular, we apply our models to the coating of virus particles by hydrophilic CP11 polymers (such as pHPMA) which are currently used in Effects of Contact Tracing and Removal on the some gene therapy systems. Spread of New Emerging Diseases Radek Erban This study presents a framework for studying the effects University of Oxford of contact tracing, quarantine and isolation on the spread Mathematical Institute of emerging infectious diseases, using SARS outbreak data [email protected] from Hong Kong as an illustration. We consider three different contact tracing functions and their effects on the dis- Kerry Fisher, Leonard Seymour eases reproduction number, including sensitivity and un- University of Oxford certainty analysis. Tracing and quarantining contacts of Department of Clinical Pharmacology diagnosed cases can reduce transmission greatly, but may kerry.fi[email protected], also be cost-prohibitive on the large scale needed for erad- [email protected] ication. Carlos Castillo-Chavez Jonathan Chapman Department of Mathematics and Mathematical Institute Arizona State University University of Oxford [email protected] [email protected]

Christopher M. Kribs Zaleta CP12 University of Texas at Arlington [email protected] A Penalty Func- tion Method for Distance-Constrained Molecular Dynamics Simulation Maia Martcheva Department of Mathematics MD simulation can be used to study various dynamic prop- University of Florida erties of proteins, but a long sequence of iterations has to be [email protected]fl.edu carried out even for small protein motions due to the small time step (10e-15sec) required. The bonding forces are Anuj Mubayi among those causing fast protein vibrations that require Arizona State University small time steps to integrate, but they may be replaced by [email protected] a set of bond length constraints, to increase the step size and hence the simulation speed. Lagrange multiplier methods have been developed for constrained dynamics simula- CP11 tion. However, the multipliers have to be determined in An Sir Epidemic Model with Partial Temporary every step to satisfy the constraints through the solution Immunity of a nonlinear system of equations. Here we propose a penalty-function method for constrained dynamics by con- The SIR-epidemic model considers that recovered individ- sidering the least action problem with the bond-length con- uals are permanently immune, while the SIS model consid- straints as a constrained optimization problem and defining ers recovered individuals to be immediately re-susceptible. a quadratic penalty function for the constraints. The sim- We study the case of temporary immunity in an SIR based ulation with the penalty function method can be done by model with delayed coupling between the susceptible and using a conventional unconstrained solver such as Verlet, removed classes. We perform a numerical and analytical only with the penalty parameter increased in an appropri- bifurcation analysis of the resulting DDEs and describe ate manner as the simulation proceeds. More specifically, how temporary immunity leads to recurrent outbreaks and we scale the constraints with their force constants when how model parameters affect the severity and period of the forming the penalty terms. The resulting force function LS06 Abstracts 59

can then be viewed as a smooth continuation of the original bution and allows for the identification of different bifur- force field as the penalty parameter increases. The penalty cation events, and thus has clear advantages over direct function method is easy to implement and costs less than a Monte Carlo simulations. We illustrate this analysis on a Lagrange multiplier method, which requires the solution of model thalamocortical (TC) cell subject to two example a nonlinear system of equations in every time step. We im- distributions of excitatory synaptic inputs, in the cases of plemented the penalty function method in CHARMM and constant and rhythmic inhibition. The analysis shows that applied it to protein Bovine Pancreatic Trypsin Inhibitor there is a drastic drop in the likelihood of firing just after (BPTI). We compared the simulation results with Verlet inhibitory onset in the case of rhythmic inhibition, relative and Shake, and found that the penalty function method even to the case of elevated but constant inhibition. This had high correlations with Shake and outperformed Ver- observation provides support for a possible mechanism for let. In particular, the RMSD fluctuations of backbone and the induction of motor symptoms in Parkinson’s disease. non-backbone atoms and the velocity auto correlations of C atoms of the protein calculated by the penalty function Jonathan E. Rubin method agreed well with those by Shake. We describe the University of Pittsburgh penalty function method and its implementation details, Department of Mathematics discuss our results and the issues to be resolved, show the [email protected] advantages as well as the disadvantages of the method, and demonstrate the potential of using the method for general Kresimir Josic constrained molecular dynamics and energy minimization. University of Houston Department of Mathematics Ajith Gunaratne [email protected] Iowa State University Department of Mathematics [email protected] CP12 Support Vector Regression Approach for Predic- Zhijun Wu tion of Relative Lipid Accessibility in Membrane Iowa State University Proteins Dept of Math [email protected] Membrane proteins constitute a significant fraction of a typical proteome and they play a number of critical functions, e.g., enabling signaling and transport through the CP12 membranes. Computational studies of membrane proteins Swelling Dynamics of Weakly Acidic Polyelec- are an important complement of (often facing serious lim- trolyte itations) experimental efforts in that regard. Here we present a novel protocol for prediction of relative lipid ac- The behavior of polyelectrolytes plays an important role cessibility in membrane domains. The new method is based in many biological processes, e.g. vesicle exocytosis. We on a linear, Support Vector Regression-based model that explore a simple model of polyelectrolyte swelling, featur- can be used to efficiently and reliably estimate the param- ing flows that are driven by gradients in electro-chemical eters in the model from a limited number of experimen- potential and that conserve volume. The mean-field po- tally validated examples. The new method will be avail- tentials derive from a statistical thermodynamics model able to the community through the MINNOU web server of Gibbs free energy and include pressure, electro-static (http://minnou.cchmc.org). potential, short-range interaction energies and entropic terms. We explore the interplay of corresponding force Michael Wagner components during swelling. Cincinnati Children’s Research Foundation [email protected] Viktoria Hsu University of Utah Baoqiang Cao Mathematics University of Cincinnati [email protected] [email protected]

CP12 Jarek Meller Children’s Hospital Research Foundation The Firing of an Excitable Neuron in the Presence University of Cincinnati, Cincinnati, OH of Stochastic Trains of Strong Synaptic Inputs [email protected] We consider a fast-slow excitable system subject to a stochastic excitatory input train, and show that under gen- CP12 eral conditions its long term behavior is captured by an irreducible Markov chain. In particular, the firing prob- A Chemical Kinetic Model for RNA Polymerase ability to each input, expected number of response fail- Translocation During Transcriptional Elongation of ures between firings, and distribution of slow variable val- the Nascent Rna Chain ues between firings can be obtained analytically from the A chemical kinetic model of the elongation dynamics of distribution of interexcitation intervals. The approach we RNA polymerase along a DNA strand is introduced. Un- present immediately generalizes to any pair of input trains, like previous models that attempt to explain the motion of excitatory or inhibitory and synaptic or not, with distinct RNA polymerase using internal strain and stresses, we pro- switching frequencies. We also discuss how the method can pose a chemical kinetic model which governs the discrete be extended to other models, such as integrate-and-fire, movement of the RNA polymerase along a DNA tether, that feature a single variable that builds up to a threshold with no consideration given to elastic effects. The model’s where an instantaneous spike and reset occur. The Markov novel feature includes a ’look-ahead’ feature in which nu- chain analysis guarantees the existence of a limiting distri- cleotides bind reversibly to the DNA prior to being incor- 60 LS06 Abstracts

porated covalently into the nascent RNA chain. Results are a natural small parameter for developing a perturbation presented for a random DNA sequence, and also with spe- theory around the infinite-range, mean-field limit. This cific DNA sequences that have been used in single-molecule permits an asymptotically exact calculation of the contri- experiments of the random walk of RNA polymerase along bution of space and stochasticity. I apply this to the eigen- DNA. We also discuss preliminary parameter fitting results values describing approach to equilibrium, showing how the of our model to the experimental data. interaction and dispersal kernels determine the stability of spatially extended populations. Richard Yamada Center for Applied Mathematics Stephen J. Cornell Cornell University Institute of Integrative and Comparative Biology [email protected] University of Leeds [email protected] Charles S. Peskin Courant Institute of Mathematical Sciences Otso Ovaskainen New York University Department of Biological and Environmental Sciences [email protected] University of Helsinki otso.ovaskainen@helsinki.fi CP12 Building Molecular Surfaces Using Surface Tension MS1 Models Conditional Dispersal in Ecological Models

An important tool in the analysis of biological macro- Traditional spatial models in ecology assume that organ- molecules is the solvent-accessible surface, a ”wrapper” isms disperse randomly by simple diffusion or similar pro- for the molecule which defines the boundary between the cesses. In some cases, however, organisms may disperse in the solvent and the molecular interior. These surfaces are response to their surroundings or other organisms. McPeek typically generated geometrically, through the action of a and Holt introduced the term “conditional” to describe rolling probe meant to represent a single water molecule. that type of dispersal. This talk will describe some models We are exploring new, finite-element-based approaches to with conditional dispersal. The models are partial differ- generate surfaces via energy minimization, under the as- ential equations similar to reaction-diffusion equations, but sumption of constant solvent pressure and surface tension. incorporating advection or density dependent diffusion or boundary conditions. Randy Zauhar Department of Chemistry & Bioc Chris Cosner University of the Sciences in Philadelphia University of Miami [email protected] Department of Mathematics [email protected] LiFeng Tian Dept. Chem & Biochem Robert Cantrell University of the Sciences Department of Mathematics [email protected] University of Miami [email protected]

MS1 Yuan Lou Correlation Approaches for Extracting Process In- Ohio State University formation from Spatial Data Department of Mathematics [email protected] Small-scale spatial patterns in ecosystems (e.g. plant species distributions, epidemic patterns) are driven by environmental variation and demographic stochasticity, mod- MS1 ified by movement and spatial interactions among species. Spatial Stochastic Host-symbiont Models Defining these spatial dynamics in terms of spatial correlation functions provides a natural connection to data. Here Optimal foraging and habitat selection theories that are I demonstrate how, given that we know which spatial pro- based on non-spatial, deterministic models predict evolu- cesses are operating, one can invert Fourier-transformed tion towards generalist strategies in fine-grained habitats versions of correlation models to estimate the parameters and towards specialization in coarse-grained habitats. In of spatial processes. addition, coevolutionary processes appear to favor extreme specialization among parasites. We introduce a spatially Ben Bolker explicit, stochastic model that confirms the effect of habi- Department of Zoology tat coarseness on specialization in the absence of coevo- University of Florida, Gainesville lutionary processes. To understand the effects of coevo- [email protected]fl.edu lutionary processes, we introduce feedback between hosts and their symbionts into our spatially explicit, stochastic MS1 model. This is joint work with Nicolas Lanchier, University of Minnesota. Perturbative Approach to Transient Dynamics in Spatial Ecology Claudia Neuhauser University of Minnesota The coexistance or exclusion of interacting species is of [email protected] fundamental importance in ecology. If an individual’s interactions extend beyond its nearest neighbours, there is LS06 Abstracts 61

MS2 Gatsby Unit The Criticality Hypothesis: How Local Cortical [email protected] Networks Might Optimize Information Processing

Several models suggest that neural networks should oper- MS2 ate near a critical point to optimize information transmis- Detecting Weak Ratiometric Signals from Geneti- sion, information storage, computational power, and sta- cally Encoded FRET Indicators bility. To test this, we recorded cortical slices and cultures on 60-channel multielectrode arrays. Networks produced Genetically encoded ratiometric indicators have become an avalanches of neural activity whose sizes were distributed important part of the neural imaging toolkit. Voltage- according to a power law, reminiscent of critical phenom- sensitive and calcium-sensitive indicators have been used ena. Moreover, avalanches occurred in repeating patterns to study neurons as well as other tissues such as the heart that could be used to store information. These data are and liver. We present a simple, new multivariate method consistent with the criticality hypothesis. for teasing out small ratiometric signals from FRET- or Stokes’ shift-based fluorescence data. We will present the John Beggs method and show an application to sensory neurons in ze- Indiana University brafish. Dept. of Physics [email protected] Andrew Sornborger University of Georgia Dept. of Mathematics MS2 [email protected] Reverse-Correlation Techniques and Cortical Ar- chitecture MS3 Reverse-time correlation measurements give the average A Mathematical Model of Tumor Lymphangiogen- orientation dynamics of individual neurons within a highly esis excited visual cortical neuronal network. The resulting orientation tuning curves provide specific information about The lymphatic system provides a much more favorable en- the nature of cortico-cortical connections, in particular, the vironment for tumor invasion and metastasis than does the strength and extent of cortical inhibition. We present a set blood vasculature. As more specific markers for lymphan- of models that uncover and explain the connection between giogenesis are emerging, a modeling of this process is be- the experimentally observed tuning curves and the relevant coming more feasible. In this talk I shall present such a cortical architecture. model, in terms of PDEs for the densities of lymphatic endothelial and cancer cells, concentrations of urikinase, plas- Louis Tao minogen and extracellular matrix, and VEGF-C growth- Department of Mathematical Sciences factor. joint work with Georgios Lolas. New Jersey Institute of Technology [email protected] Avner Friedman Mathematical Biosciences Institute, Ohio State University Michael J. Shelley [email protected] New York University Courant Inst of Math Sciences MS3 [email protected] Modeling the Tumor-vasculature Interaction Sug- gests Time-dense Antiangiogenic Schedulings Gregor Kovacic Rensselaer Polytechnic Inst Clinical inferences can be derived from the simple ODE Dept of Mathematical Sciences model of antiangiogenic therapy proposed by Hahnfeldt [email protected] et al. (1999) and its generalizations. We compared constant continuous-infusion and periodic boli-based thera- David Cai pies, showing by analytical conditions and simulations that Courant institute schedulings which guarantee the same mean drug concen- New York Unvirsity tration may exhibit different efficacy, with the profiles that [email protected] approach the constant one being more effective. This behavior appears to depend on the functional form of the nonlinear tumor-vasculature relationship. MS2 Statistical Modeling of Multi-neuron Responses in Alberto d’Onofrio Primate Retina European Institute of Oncology - Milan, Italy Neural circuits are well known to exhibit correlated spiking alberto.d’[email protected] activity, whose origin and significance is a topic of much current interest. We show that a generalized linear model, Andrea Rocca fit using maximum likelihood, can account for the stimulus- European Institute of Oncology, dependence, history-dependence, and correlation structure Milan, Italy in the spike responses of a group of nearby neurons in pri- [email protected] mate retina. We will discuss implications for the multi- neuronal coding of visual information. Alberto Gandolfi Jonathan W. Pillow Ist. Analisi Sistemi University College London Informatica - CNR, Roma, Italy 62 LS06 Abstracts

gandolﬁ@iasi.cnr.it MS4 Parameter Estimation in PBPK Models

MS3 A physiologically based pharmacokinetic (PBPK) model A New Cancer Drug Regimen Based on the Inter- for TCDD was used as the framework for models of TCDD, play Between Tumor Growth and Angiogenesis - PCB126, PeCDF, and a mixture of these three chemicals. Prediction of a Mathematical Model A goal was to assess how a model developed specifically for TCDD would serve as a general Ah receptor model We mathematically modeled the interplay between key bio- for individual dioxin-like chemicals as well as a mixture of logical, pathological and pharmacological processes under- dioxin-like chemicals. I’ll discuss the mixture model and lying drug-patient interactions, from the molecular level to efforts on variance estimates for the model parameters and that of the whole organism. Simulating a large number predictions. of treatment options, we showed that unlike the recom- mended regimen, applying large doses every three weeks, Michael Easterling the optimal treatment schedule for common anticancer Constella Health Sciences drugs, such as docetaxel and doxorubicin, is one of rela- [email protected] tively small doses, the dosing interval being one week. Levon Arakelyan, Yifat Merbl MS4 Optimata Ltd., Ramat Gan, Israel Development of an Air-Tissue Computational Fluid [email protected], [email protected] Dynamics Model to Describe Extraction of Hydro- gen Sulfide in Rat Nasal Passages Vladimir Vainstein Institute for Medical Biomathematics, Rats exposed to hydrogen sulfide (H2S) develop olfac- Bene Ataroth, Israel tory neuronal loss (ONL). A computational fluid dynamics [email protected] model was developed to simulate H2S uptake in the rat nasal cavity. Wall mass flux was governed by H2S reaction Zvia Agur kinetics in nasal tissue with kinetic parameters estimated from a pharmacokinetic model. Regions with predicted Institute for Medical Biomathematics and Optimata Ltd., H S andBene Ataroth, Israel high 2 flux were associated with sites that develop ONL, [email protected] indicating that airflow patterns play an important role in the distribution of H2S-induced lesions. Yuri Kheifetz Jeffry Schroeter, Melvin Andersen, David Dorman, Julia The Institute for Medical BioMathematics, Israel Kimbell [email protected] CIIT Centers for Health Research [email protected], [email protected], [email protected], [email protected] MS3 Stochastic Geometrical Methods for the Statistical Analysis of Tumor-induced Angiogenesis MS4 One of the Applications of Physiologically Based Tumor-induced angiogenesis may be modelled as a birth- Pharmacokinetic Modeling: Interpretation of and-growth stochastic process, which is composed of Biomonitoring Data branching and subsequent growth of vessel networks. The growth of vessels (and possibly the inhibition of growth, via Physiologically based pharmacokinetic (PBPK) modeling drugs) is coupled with interacting underlying fields, so that has been applied broadly for a wide variety of compounds the geometric structure of vessels becomes spatially hetero- to describe the relationship between external and internal geneous. Here we provide methods of statistical analysis measures of exposure. As a measure of internal exposure, for the estimation of geometric densities that characterize biomonitoring data reveal the presence of chemicals in hu- the morphology of a real system. man populations. To interpret the health implications of such data, however, requires knowledge of dosimetry that Elena Villa can be provided by PBPK modeling. Department of Mathematics and ADAMSS Centre, Universita’ degli Studi di Milano, Milan, Italy Yu-Mei Tan [email protected] CIIT Centers for Health Research [email protected] Alessandra Micheletti Department of Mathematics and ADAMSS Centre, Universita’ degli Studi di Milano, Milano, Italy MS4 [email protected] Modeling Sensory Irritation Response in Rats

Vincenzo Capasso A model describing the decrease in respiration from inhaled Department of Mathematics and ADAMSS Centre, gases that irritate nasal cavity nerves in rats is presented. Universita’ degli studi di Milano, Milan, Italy The model is optimized to describe respiratory response [email protected] data and evaluated through sensitivity analysis. The model predicts data well and reasonably describes the physiological system of sensory irritant response. (This abstract does Daniela Morale not reﬂect EPA policy.) Department of Mathematics and ADAMSS Centre, DepartUniversita’ degli Studi di Milano, Milan, Italy Karen A. Yokley [email protected] University of North Carolina-Chapel Hill LS06 Abstracts 63

Curriculum in Toxicology mathematics courses. We discuss efforts to create a math- [email protected] ematical biology course targeted at biology majors with minimal prerequisites (1 semester of calculus). Course emphasis is in the modeling process, particularly as it relates MS5 to the scientific method. Communication and interpreta- Some Lessons in Math and Biology Education tion is stressed, thereby giving this course a novel aspect to mathematics majors as well. Higher level mathematics are I summarize experiences from a project that coupled math introduced in a way that might motivate biology students and biology undergraduates in field and laboratory re- to take further mathematics courses. search projects. This encouraged the students to jointly develop hypotheses and appropriate experimental systems Brian Walton to address them, in conjunction with development of math- James Madison University ematical models. I’ll also present educational survey re- [email protected] sults of attendees at the 2005 SMB/ESMTB meeting. The survey allows differences to be determined based upon education background of the respondent, their gender and MS6 country of origin. Functional Analysis of Biochemical Signaling Path- ways Mediating the Acute Inflammatory Response Louis J. Gross Departments of Ecology and Mathematics Acute inflammation in the skin is mediated by IL-1 sig- University of Tennessee naling. We have used CellDesigner software to develop [email protected] a detailed, visual representation of this signaling. Func- tional modules are abstracted from the visual representation. Quantitative description of the modules and their key MS5 interactions allows essential behaviors of the IL 1 pathway CoMBiNe- A Computational and Mathematical to be captured while omitting many of the molecule-to- Biology Network molecule interactions depicted in the visual model. (This presentation does not necessarily reflect policies of the I will present an overview of a new project supported by U.S.EPA.) the Shodor Education Foundation to help make integrating mathematics, computation, and biology in the classroom Rory B. Conolly easier. We are developing an electronic resource in coordi- National Center for Computational Toxicology nation with the National Science Digital Library through U.S. Environmental Protection Agency the Shodor Foundation’s CSERD website for easy access to [email protected] basic introduction, interactive activities, laboratory ideas, and references of mathematical and computational topics James n. McDougal in biology. The project will make use of existing materials Boonshoft School of Medicine and provide a searchable, indexed interface to help faculty Wright State University make the discovery and integration of those materials rou- [email protected] tine and seamless.

Eric Marland, Ren´e Salinas MS6 Appalachian State University The Challenge of in Vivo Experiments in Support [email protected], [email protected] of Systems Biology Models

Systems biology models have specific biologically-based MS5 structures and parameters. After structure is decided, a Computational Science Education and Research for large number of diverse parameters must be determined for Undergraduate Biology Majors a model to accurately predict behavior. Theoretically, parameters from intact organisms are more appropriate than From ecology to spread of disease to metabolism, biology parameters from cell lines. Estimation of parameters using offers a wealth of interesting applications for undergrad- an intact in vivo system can bring a wide variety of chal- uates in computational science. Moreover, with a foun- lenges. Examples of various types of model parameters and dation in mathematics and computer science, biology ma- their estimation using in vivo methods will be discussed. jors can perform meaningful interdisciplinary research in internships, graduate school, and post-graduate positions. James n. McDougal This talk covers some of the applications, materials, and Boonshoft School of Medicine opportunities that have evolved through Wofford College’s Wright State University Emphasis in Computational Science. [email protected] Angela B. Shiflet Mathematics and Computer Science MS6 Wofford College Statistical Issues in the Development of Systems shifletab@wofford.edu Biology Models

Abstract not available at press time. MS5 Creating a Mathematical Biology Course for Biol- Chris Portier ogy Majors National Toxicology Program NIEHS In spite of the surge in applications of mathematics in biol- [email protected] ogy, biology majors often take only the minimum number of 64 LS06 Abstracts

MS6 solve two inverse problems: (1) Infer from the change in Application of Functional Genomics Technologies cytosolic calcium Fluorescence the associated membrane to Understand the Topology of Signaling Networks calcium current in space and time, and (2) Infer from the calcium current the nonuniform distribution of all partici- Over the past decade, the focus on genomic sequencing and pating channels. gene discovery has provided a virtual parts list that comprise the molecular machinery of the cell. Today, the focus Steven Cox has shifted towards obtaining a broader understanding of Dept. of Computational & Applied Mathematics gene function and how the various genes are contextually Rice University organized into signaling modules. In this presentation, we [email protected] will discuss the application of high-coverage functional genomic screens together with bioinformatic tools for dissecting cell signaling modules. MS7 Ion Channel Distributions in Olfactory Neurons: Russell S. Thomas Asymptotic Analysis CIIT Centers for Health Research [email protected] Transduction of an odor into an electrical signal to the brain involves the activation of cyclic-nucleotide-gated (CNG) channels in olfactory cilia. An inverse problem is MS7 presented which uses experimental measurements of electri- Modeling and Computation of Signal Transduc- cal activity to determine the distribution of CNG channels tion in Olfactory Cilia with Non-Uniform CNG and along the cilium. The model, which consists of two nonlin- Cl(Ca) Channels Distributions ear partial differential equations, is studied using perturbation techniques. A one-dimensional computer minimiza- Signal transduction in olfactory cilia is produced primar- tion and special delay iteration are used with the perturba- ily by the cyclic-nucleotide-gated (CNG) and Ca2+-gated tion formulas to obtain solutions in the cases of simulated Cl (Cl(Ca)) ion channels.We use analytical and computa- and experimental data. tional methods to study mathematical models in conjunction with known experimental results. We develop differ- Donald A. French ential equation models for two different experiments, one University of Cincinnati involves the interplay between CNG and Cl(Ca) channels [email protected] and the other, the diffusion of Ca2+ into cilia and resulting electrical activity. The Ca2+ concentration and membrane David A. Edwards potential are simulated in our study. We obtain predictions University of Delaware on the distribution of the Cl(Ca) ion channels and place- Newark, DE ment of the channel types in order to optimize the electrical [email protected] signal. Dorjsuren Badamdorj MS7 University of Cincinnati Identification of Ion Channel Distributions in Ol- [email protected] factory

Recent discoveries are revealing that cilia, which are small MS7 hairlike cellular projections, play a fundamental role in Methods to Estimate Distributed Parameters in many diseases. In our lab we have focused on olfactory cilia Neuronal Cable Theory Models and the determination of the distributions of their various ion channel types. Transduction of an odorant molecule Spatially distributed ionic channel densities in a nerve into an electrical signal begins in these olfactory cilia. Our cell determine the type of excitable responses of the cell. research findings suggest that the profile of their channel These densities are typically represented by constant pa- distributions is quite different than the shapes previously rameters, but it is known that channels are non-uniformly considered. This diversity of shapes appears to have a distributed. We will discuss two numerical approaches significant impact on the strength of the transmitted sig- to identifying a non-constant conductance, one being a nal. Although fully experimental procedures (immunocy- marching method based on overspecified boundary data, tochemistry) appear to be feasible for some (but currently the other a pde-constrained optimization method. These not all) of the channel types they are very difficult and will be applied to linear and nonlinear cable models. have not been successful to date. As an alternative, we have formed sets of data which measure the current response due Jonathan Bell to specific ion channels during the diffusion of a ligand into University of Maryland, Baltimore County a cilium. This data, in conjunction with the computational Department of Mathematics solution of an inverse problem arising in our mathematical [email protected] model of this ciliary diffusion process, has led to estimates of ion channel distributions. These inverse problems are ar- MS7 gueably more difficult than, but related to, a well-studied (though apparently not well-understood) class of such in- Channel Localization Via Calcium Imaging verse problems. In this talk we provide an overview of our Calcium, the most important of the second messengers, lo- work on this problem and its context. We also formulate a cally modulates the excitability of nerve and muscle. We particular integral equation problem that arises in the so- exploit the ability to monitor cytosolic calcium, through- lution of the inverse problem and describe some theoretical out intact cells, with sub-millisecond temporal resolution and computational results. and sub-micron spatial resolution in the construction of Donald A. French a map of channel density. In the process we pose and LS06 Abstracts 65

University of Cincinnati caused by hypertumors—tumors growing on a tumor. Hy- [email protected] pertumors arise when a cell strain trades away the ability to secrete tumor angiogenesis factors to gain growth po- Rick Flannery tential. What results is an area of tissue characterized by Department of Cell Biology, Neurobiology, and Anatomy aggressive histology and hypoxia, ultimately causing the University of Cincinnati deﬁnitive ecological collapse of necrosis. Here I elucidate ﬂ[email protected] conditions under which natural selection favors the hypertumor. Chuck Groetsch John D. Nagy Mathematical Sciences Scottsdale Community College University of Cincinnati Arizona State University [email protected] [email protected]

Steve Kleene College of Medicine MS8 University of Cincinnati Introduction to Disease Ecology with a Case Study [email protected] Rabies, the most important viral zoonotic disease world- wide, has been undergoing epidemic expansion along the MS8 eastern seaboard of the United States since the mid-1970s Some Spatial Aspects of Control and Management following an accidental introduction of rabid raccoons from in Disease Ecology a source of endemic infection in the southeastern US. Us- ing data submitted from US States to the Centers for Dis- Recent approaches on spatial spread of wildlife diseases ease Control and Prevention, we have constructed stochas- and infestations provide assessments of control methods. tic simulations of the spatial dynamics of rabies as it has Little work has been done to determine optimal spatio- spread into new geographic region. The simulation was temporal controls, allowing choice of objective functions constructed as an interaction network with nodes of the for economic costs of control and associated disease costs. network defined by township and county centroids. Inter- We describe case studies using a mixture of analytic and action strengths along specific connections were sensitive computational methods to derive optimal spatial controls. to local geographic conditions and parameterized against Linking these methods to geographic information systems reported data on the time and spatial location of detected provides managers and epidemiologists with efficient tools rabid animals. The parameterized model has proven to be a to manage disease spread. valuable model for strategic planning for disease emergence and to direct the development of spatial control strategies. Suzanne M. Lenhart University of Tennessee Les Real Department of Mathematics Dept Biology, Center for Disease Ecology [email protected] Emory University [email protected] Louis J. Gross Departments of Ecology and Mathematics University of Tennessee MS8 [email protected] Case Study of Disease Ecology: Avian Flu Avian Influenza or bird flu has recently been the subject MS8 of much media attention and public interest. Opinions on Host Extinction Dynamics in Epidemiology Models its potential to spawn a global pandemic range from the alarmist to the cautiously skeptical. In this talk deter- We present a SI model formulated through birth and death ministic models are presented for both the temporal tra- processes. This model reveals and corrects errors in similar jectories of the bird flu both in avian as well as human exisitng models. Complete mathematical investigation of populations. Of particular interest is the propensity of an this simple model shows that the host extinction dynamics infection of an avian population to induce a human pan- can happen and the outcomes may depend on the initial demic. conditions. We also present some extensions of this model to structured SI models, including delay differential equa- Paul J. Tian tion SI models. We show that host extinction dynamics is Mathematical Biosciencs Institute ubiquitous to many well formulated epidemiology models. The Ohio State University [email protected] Yang Kuang Arizona State University Department of Mathematics MS9 [email protected] New Multiscale Approaches for Examining the Structure and Dynamics of Membrane Bound Pro- teins MS8 Evolutionary Suicide by Hypertumor: a Novel Hy- Some new approaches for simulating membrane bound pro- pothesis for the Cause of Necrosis in Malignant teins in lipid bilayers will be presented. Specifically, some Neoplasia. aspects of Multiscale Coupling will be elaborated on, where atomistic-level simulations of membrane bound proteins Tumor necrosis is a common feature of malignancy. Re- (such as the influenza A virus M2 proton channel) are di- cent mathematical models suggest that necrosis may be rectly coupled to corresponding field theory-based meso- 66 LS06 Abstracts

scopic bilayer/viscous solvent simulations. The protein is MS9 observed to couple to the long-wavelength stress fields aris- Adaptive Algorithms for the Simulation of Vesicle ing at the mesoscopic level, and small structural changes Membranes are indicated. Abstract not available at press time. Gary Ayton, Gregory Voth Department of Chemistry, University of Utah Jian Zhang [email protected], [email protected] Department of Mathematics Penn State University zhang [email protected] MS9 Boundary Layer Analysis of the Shape of Two- Qiang Du phase Lipid Vesicles Penn State University Department of Mathematics We present approximate analytical solutions of the shape [email protected] equations of giant unilameller vesicles with fluid phase coexistence using a boundary layer calculation. We show that the boundary layer calculation agrees well with the numer- MS10 ical solution for a variety of parameter values. We demon- Individualized Response-guided Monitoring of strate, using the best fit parameter values of our earlier Cancer Therapy: A Simulation-based Approach work, that the shape obtained from the boundary layer calculation matches well with the experimental shapes. The Abstract not available at press time. approximate calculation eliminates the laborious and time consuming iterative task of manually tuning parameters to Dean Bottino obtain a suitable numerical shape. It also facilitates the Novartis Pharmaceuticals determination and influence on shape of material parame- [email protected] ters associated with the resistance to changes in mean and Gaussian curvature and with any distributed or localized spontaneous curvature. MS10 From Tobias Baumgart Tissue Sample to Cancer Prognosis: Data Quan- Department of Chemistry tification and Application for Protein Biomarkers University of Pennsylvania [email protected] Abstract not available at press time.

S. Das Ned Haubein Theoretical and Applied Mechanics, The BioAnalytics Group LLC Cornell University, [email protected] [email protected] MS10 James Jenkins Insights from Data Driven Modeling and Model Cornell University Driven Drug Design [email protected] Abstract not available at press time. MS9 Birgit Schoeberl Forces and Geometry in 3-D Membrane Mechanics Merrimack Pharmaceuticals [email protected] Abstract not available at press time.

William Klug MS11 Mechanical and Aerospace Engineering Numerical Analysis of a Degenerate Biofilm Model University of California, Los Angeles [email protected] Recently, a doubly degenerated diffusion-reaction modelling framework was proposed that is able to describe the formation of spatially heterogeneous biofilm morphologies, MS9 such as cluster-and-channel or ”mushroom” biofilm archi- Simulation of Multicomponent Vesicle Membranes tectures. In this presentation we review the basics of the and Membranes with Open Edges model, its application to mixed culture biofilms, and discuss numerical strategies how to solve it. We will present numerical algorithms to simulate the recent experimental observations of multicomponent vesicle mem- Hermann J. Eberl branes based on a variational phase field approach. The Dept. Mathematics and Statistics approach can also be used to simulate membranes with University of Guelph free edges. The effectiveness of our simulation approach [email protected] will be demonstrated. Xiaoqiang Wang Institute for Mathematics and Applications University of Minnesota [email protected] LS06 Abstracts 67

MS11 the characteristic time scale for calcium channel gating. Thin-ﬁlm Modelling of Bioﬁlm Growth Bori Mazzag Abstract not available at press time. Humboldt State University [email protected] John King University of Nottingham Christopher Tignanelli, Gregory D. Smith School of Mathematical Science College of William and Mary [email protected] [email protected], [email protected]

MS11 MS12 Biofilms and the Plasmid Maintenance Question Calcium Waves as a Signal for Late Long Term Po- tentiation Abstract not available at press time. As a coincidence of synaptic stimulation and back propa- Hal L. Smith gating action potentials, the initiation of calcium waves in Arizona state university dendrites of hippocampal pyramidal cells has been shown [email protected] experimentally. It is also known that calcium is a critical second messenger for gene regulation within the nucleus. MS11 We construct and analyze a model which incorporates an appropriate spatial mechanism of calcium signaling to ac- Drug Delivery in Bacterial Biofilms count for protein production leading to synaptic strength- A continuum modelling approach is used to describe ening indicative of late long term potentiation. biofilm growth based on fluid dynamics and conservation Bradford E. Peercy laws. The modelling considers the role of nutrient and Rice University bacterial cell-cell signalling, both important factors in the [email protected] normal development of biofilms. The model is extended to investigate the effects of an externally applied anti-biotic treatments (that directly kill bacteria) and cell-signalling MS12 targeting drugs. A number of key results are established A Model of the Roles of Essential Kinases in the based on asymptotic and numeric analysis of the model. Induction and Expression of Late Long-Term Po- John P. Ward tentiation Loughborough University, UK The induction of late long-term potentiation (L-LTP) re- [email protected] lies on several key second messengers and kinases. We developed a model representing synaptic actions of protein MS12 kinase A, MAP kinase, and CaM kinase II, and activation of transcription by CaM kinase IV and MAP kinase. The Effect of Luminal Depletion on the Dynamics The model simulates electrical and chemical L-LTP, in- of Ca-regulated Ca Channels hibitor effects, and synaptic tagging. Supralinear stimulus- We analyze how the dynamics of depletion and refilling response relationships are essential to translate brief stim- of a restricted volume of endoplasmic reticulum associated uli into long-lasting synaptic strengthening. The model with an intracellular Ca-regulated Ca channel influences suggests experimental tests and clarifies relationships of it’s stochastic gating and equilibrium properties. We em- hippocampal L-LTP with synaptic strengthening in other phasize numerical solutions of advection-reaction equations organisms. describing probability densities representing cytosolic [Ca] Douglas Baxter and lumenal [Ca] conditioned on the channel’s state. Ex- University of Texas tensions of this approach can give insight into the effect Medical School at Houston of luminal depletion on the characteristics of Ca puffs and [email protected] sparks.

Marco A. Huertas, Gregory D. Smith John H. Byrne College of William and Mary Dept. Neurobiology and Anatomy [email protected], [email protected] Univ Texas-Houston Med School [email protected]

MS12 Paul D. Smolen Analysis of the Effect of Residual Calcium on the Department of Neurobiology and Anatomy, Gating of Calcium-regulated Calcium Channels University of Texas Medical School at Houston [email protected] We study the effect of ‘residual calcium’ on the stochastic gating of several inositol-4,5-triphosphate receptor models coupled to a differential equation describing a dynamic MS13 calcium domain. Using Monte-Carlo simulations, numer- Mathematical Modeling of Cancer Virotherapy ical solution of a system of Fokker-Planck-type equations and analytical methods, we show how the equilibrium open Cancer therapy with replicating viruses may have various probability of such models depends on the time constant outcomes which can be best understood by mathematical for calcium domain formation and collapse compared to modeling. We propose a model which includes most salient features of virotherapy: kinetics of untreated tumor, infec- 68 LS06 Abstracts

tion of tumor cells, replication of viruses, elimination of in- and pharmacodynamic results of TPT in a formal mathe- fected tumor cells and effects of immune response on virus matical framework to design more effective treatment ap- by cytotoxic T-cells. The model is validated by available proaches in pediatric neuroblastoma. data on virotherapy for multiple myeloma in SCID mice. Relevant equilibrium points are evaluated, and by using Carl Panetta simulations we analyze the influence of model parameters Department of Pharmaceutical Sciences on the outcome of the therapy. We also propose a model St. Jude Children’s Research Hospital for virotherapy enhanced by radiation. Viruses engineered [email protected] to express thyroid sodium iodide symporter make infected cells targets for radioactive idodide. The effects of radiation upon administration of radioactive iodide may lead to MS14 elimination of tumor cells, when virotherapy alone is not Mechanics Explains the Structures of Coiled Poly- sufficient. We evaluate various therapeutic scenarios and mers in Bacteria discuss therapy optimization. Abstract not available at press time. David Dingli Program in Evolutionary Dynamics Steven Andrews Harvard University Physical Biosciences Division [email protected] Lawrence Berkeley National Laboratory [email protected] Zeljko Bajzer Mayo Clinic MS14 Biomathematics Resource A Stochastic Immersed Boundary Method Incor- [email protected] porating Fluctuations : Toward Modeling Cell Mi- cromechanics

MS13 The mechanics of many cellular systems involve elastic A Model for Antimitotic Chemotherapy: The Im- structures which interact with a fluid, for example the outer portance of the Proliferation Ratio cell membrane deforms during protrusions generated during motility and cell organelles such as the Golgi Appa- A model for antimitotic chemotherapy is presented which ratus and Mitochondria involve membranes which deform suggests the limits of such therapy and explores the efficacy and bud vesicular and tubular structures during biological of different therapy regimes. The proliferation ratio and so processes. Modeling, analyzing, and simulating the me- the tumor age on therapy commencement will be shown to chanics of such systems presents many mathematical chal- be a key factor in these efficacies. lenges. The immersed boundary method is one modeling Michele Bourdeau approach for such systems, and has been applied to many Risk Management macroscopic biological problems, such as blood flow in the Lehman Brothers heart and lift generation in insect flight. At the length [email protected] scales of cells and cell organelles, thermal fluctuations also become significant and must be taken into account. In this talk we discuss an extension of the immersed bound- MS13 ary method framework which incorporates thermal fluctu- Modeling Gompertzian Tumor Growth through ations through appropriate stochastic forcing terms in the Cell Dynamics fluid equations. This gives a system of stiff SPDE’s for which standard numerical approaches perform poorly. We A model for Gompertzian tumor growth based on cell dy- discuss a novel stochastic numerical method which exploits namics and cell quiescence is presented. The model pre- stochastic calculus to handle stiff features of the equations. dicts that tumors of the same carrying capacity may have We further show how this numerical method can be ap- significantly different proliferation profiles which depend on plied in practice to model the basic microscopic mechanics quiescent cell death rate. The model is applied to specific of polymers, polymer knots, membrane sheets, and vesi- examples of multiple myeloma, parathyroid and testicular cles. We also discuss preliminary work on modeling the tumors. dynamics of cell organelle structures. Frank P. Kozusko Paul Atzberger Department of Mathematics Rensselaer Polytechnic Institute Hampton University [email protected] [email protected] MS14 MS13 T-Cell Receptor Signaling Model Predicts Multiple Optimizing Topotecan Therapy in Pediatric Neu- Activation Levels and Switching Mechanisms roblastoma A properly functioning immune system requires ligand- Topotecan (TPT) has activity in a dose/schedule depen- appropriate T-cell responses. Theoretically, T-cell re- dent manner against neuroblastoma. Mathematical mod- sponses (viral, self, and partial) to antigens are biologically els are described that incorporate the growth of neuroblas- controlled by two parameters: receptor to peptide ratio toma along with the antitumor and toxic effects of TPT. (μ) and specific peptide affinity (κ). An experimentally- In addition, optimal control methods are used to aid in verified mass-action ODE model describing this signaling designing effective treatment strategies. The goal of this process is derived with minimal rate constant fitting. Simu- analysis is to combine the various known pharmacokinetic lations varying μ) and κ suggest existence of multiple quasi- stable states corresponding with appropriate immune re- LS06 Abstracts 69

sponses, implying possible switching mechanisms control- of multiple chemical signals. We present a model for sig- ling T-cell receptor activation. nal integration by mixed clusters of interacting two-state chemoreceptors. Our model results compare favorably to John M. Burke the results obtained by Sourjik and Berg using in vivo flu- Massachusetts Institute of Technology orescence resonance energy transfer (FRET). Importantly, Biological Engineering Division we identify two distinct regimes of behavior, depending [email protected] on the relative energies of the two states of the receptors. In regime I, coupling of receptors leads to high sensitivity, Douglas Lauffenburger while in regime II, coupling of receptors leads to high coop- Division of Biological Engineering, Dept. of Chem. Eng. erativity, i.e. high Hill coefficient. For homogeneous recep- MIT tors, we predict an observable transition between regime lauff[email protected] I and regime II with increasing receptor methylation or amidation. Furthermore, we address the question of adap- Melissa Kemp tation within our model. Biological Engineering Division Massachusetts Institute of Technology Roberts Endres [email protected] Department of Molecular Biology Princeton University [email protected] Lucia Wille Department of Biology Massachusetts Institute of Technology MS15 [email protected] From Signal Transduction to Spatial Pattern For- mation in E. coli Emily Miraldi Department of Chemistry Appropriate responses to signals in the environment are Oberlin College essential for the survival of any organism, and thus so- [email protected] phisticated means of detecting external signals, transduc- ing them into internal signals, and altering behavioral patterns appropriately have evolved. Many organisms use MS14 a random-walk search strategy to search for food when Finding Gene Regulatory Sites: Protein Localiza- the signals are spatially uniform, and bias movement ap- tion propriately when a suitable change in signal is detected. The collective behavior of bacterial populations provides Abstract not available at press time. an example of how cell-level decision-making translates into population-level behavior, and illustrates the math- Samual Isaacson ematical problem of incorporating individual-level behav- Department of Mathematics ior into population-level models. In this talk we focus on The University of Utah the flagellated bacterium E. coli, for which a great deal is [email protected] known about signal detection, transduction and cell-level swimming behavior. We review the biological background MS14 on individual and population-level processes and discuss the velocity-jump approach used for describing population- Stochasticity in Gene Regulatory Networks and level behavior based on individual-level intracellular pro- Cell Signaling Pathways cesses. We also show how aspects of the signal transduc- First a model of a synthetic gene regulatory networks will tion and response enter into the macroscopic equations, be presented. This stochastic model quantitatively cap- and discuss computational issues that arise in the bacte- tured the means and distributions of the expression from rial pattern formation problem. this modular system and accurately predict the in vivo Hans G. Othmer behavior of an expanded network that included positive University of Minnesota feedback. The model also revealed the counterintuitive Department of Mathematics prediction that noise in protein expression levels can in- [email protected] crease upon arrest of cell division, which was confirmed experimentally. Then a stochastic model of the biochemical steps that regulate activation of the MAPK in yeast MS15 signaling pathway will be used to demonstrate the use of Diversity in Bacterial Chemotaxis equation free method to quickly compute the steady state distribution of activated MAPK. The chemotaxis pathways in Escherichia coliand Bacillus subtilisboth regulate the same task, namely excitation and Xiao Wang adaptation to environmental signals. Both pathways em- Department of Statistics and Operations Research ploy orthologous genes that genetically complement be- University of North Carolina at Chapel Hill tween the two species (i.e. can function in the heterologous [email protected] host). Yet how these orthologs contribute to network function in each organism is different due to differences in the MS15 pathway topologies. Bacterial chemotaxis, therefore, provides an excellent system for studying the structure and Modeling Chemotaxis in Escherichia coli: From evolution of biological networks using comparative anal- Single Receptors to Strongly-coupled Clusters ysis. We present mathematical models for the pathways The chemotaxis network in E. coli is remarkable for its regulating chemotaxis in E. coli and B. subtilis. By ana- sensitivity to small relative changes in the concentrations lyzing the two models, we identify a common regulatory 70 LS06 Abstracts

strategy in both organisms. These results demonstrate the Mathematical Modeling and Analysis limitations of pathway inferences based solely on protein Los Alamos National Laboratory homology and indicate the need for a theoretical metric [email protected] to analyze functionally similar pathways. We then demonstrate how comparative analysis can be used to reconstruct Catherine Ammon pathways in species with limited experimental data such as Institute of Social and Preventive Medicine Helicobacter pylori, illustrating the power of comparative Faculty of Medicine, CMU, PoBox 1211, Geneva 4, network analysis as a tool for analyzing, dissecting, and Switzerland reconstructing complex biological networks. [email protected] Chris Rao Department of Chemical Engineering Mac Hyman Univeristy of Ilinois Mathematical Modeling and Analysis [email protected] Los Alamos National Laboratory [email protected]

MS15 Nick Hengartner Modelling Bacterial Chemotaxis: From Molecular Statistical Science Group Interaction to Cellular Behavior Los Alamos National Laboratory [email protected] I will first review some of the recent progress made in modelling various aspects of the bacterial chemotaxis pathway. I will then focus on describing our works on understanding MS16 molecular level cooperativity, which is responsible for large Comparing Rubella Vaccination Strategies in signal amplification sustained in a wide dynamic range in China - Modeling and Simulation bacterial chemotaxis. Computer simulations of a deterministic model are used Yuhai Tu to predict the effect of the changing age distribution in IBM Research China on the dynamics of rubella epidemiology and the [email protected] incidence of congenital rubella syndrome (CRS). In comparing rubella vaccination strategies for China using simulations, our results predict some severe consequences of the MS16 current policy and suggest better alternatives for reducing Epidemiological Approaches in the Study of Social and eliminating the incidence of CRS. Dynamics: Drinking Dynamics at US colleges Herbert Hethcote Abstract not available at press time. University of Iowa [email protected] Carlos Castillo-Chavez Department of Mathematics and Linda Gao Arizona State University North Central College [email protected] [email protected]

MS16 MS16 Estimating the Reproductive Number and the Ef- Disease Emergence in Multi-host, Multi-patch Epi- fect of Hypothetical Interventions for the Spanish demic Models Flu Pandemic in Geneva, Switzerland Most pathogens are capable of infecting multiple hosts. Recurrent outbreaks of the avian H5N1 influenza virus in These multiple hosts provide many avenues for the dis- several regions of the world pose a global pandemic threat. ease to emerge. In this investigation, we formulate and I will present an analysis of historical hospital notification analyze multi-host and multi-patch epidemic models and data of the 1918 influenza pandemic in Geneva, Switzer- determine conditions under which the disease can emerge. land. We estimated the number of secondary cases gen- In particular, SIS and SIR epidemic models are formulated erated by a primary case during its period of infectious- for a pathogen that can infect n different hosts. The basic ness during the first two waves of infection. We then used reproduction number is computed and shown to increase these estimates to evaluate the single and combined effect with n, the number of hosts that can be infected. The of reductions in the overall influenza transmission rate via SIS model for two hosts is studied in detail. Necessary effective isolation strategies in hospitals or via reductions and sufficient conditions are derived for the global stability in the susceptibility of the general population through, for of an endemic equilibrium. Numerical examples illustrate example, increasing hygiene and protective measures (e.g., the dynamics of the two- and three-host epidemic models. increase hand washing, use of face masks), prophylactic an- The models have applications to hantavirus in rodents and tiviral use, and vaccination. Some model parameters are other zoonotic diseases with multiple hosts. estimated by fitting an epidemic model to the data and others are obtained from published literature. We estimated Robert McCormack the reproductive number for the spring wave R1 +1.49 (95 Department of Mathematics and Statistics % CI: 1.45 − 1.53) and the fall wave R2 =3.75 (95 % CI: Texas Tech University 3.57 − 3.93). We found that the implementation of single- [email protected] component interventions is unlikely to achieve containment while control through their combined effect is feasible. Linda Allen Gerardo Chowell Department of mathematics and Statistics LS06 Abstracts 71

Texas Tech University MS17 [email protected] Calcium Signaling Diﬀerentiation in the Maturing Xenopus oocyte: A Modeling Approach

MS16 The calcium signaling apparatus undergoes significant Could Low-efficacy Malaria Vaccines Increase Sec- changes during oocyte maturation. Brief, local simula- ondary Infections in Endemic Areas? tion through caged IP3 or calcium gives rise to sweap- ing and long-lasting intracellular Ca2+ elevations in the Recent breakthroughs in malaria vaccines have given new mature egg, while the reponse in the occyte is local and hope that a safe, effective malaria vaccine may be found. short. To the contrary, Ca2+ puffs, spatially and tempo- The following epidemiological question is addressed: could rally limited release events through single clusters of release the introduction of a low or medium efficacy malaria vac- channels, are shorter in the mature egg. We use mathe- cine lead to an increase in the number of secondary in- matical modeling in conjunction with experimental anal- fections and what characteristics of such a vaccine will ysis (Klaled Machaca, U of Arkansas, Med. Sciences) to have the greatest effect on the outcome? A mathemati- identify changes in the Ca2+ signaling machinery during cal model is developed for a malaria vaccine that is given oocyte maturation consistent with the experimental find- once prior to infection which accounts for separate malaria ings. We hypothesize that incraesed IP3 affinity of the infection events. There is a threshold depending on the IP3 receptors in the mature egg causes the long-lasting relative transmission probability, the recovery rate and the Ca2+ elevation in the mature egg. We further hypothesize acquired immunity rate. If the recovery rate decreases, that clustering of release channel clusters to larger super- then there will always be fewer secondary infections. How- clusters gives rise to the shortening of the Ca2+ puffs in ever, if the recovery rate increases, then there is a “shoul- the mature egg. der” within which the number of secondary infections will decrease. Beyond this, the number of secondary infections Peter Jung will increase unless the transmission probability is suffi- Ohio University ciently lowered. This effect is lessened as the acquired [email protected] immunity rate increases. If the transmission probability is not sufficiently lowered, then vaccinated individuals will always cause more secondary infections than unprotected MS17 individuals. For low efficacy vaccines, this will be corre- Messages Diffuse Faster than Messengers lated to an increase in the overall severity of the disease in endemic areas. Abstract not available at press time. Robert J. Smith John Pearson The University of Illinois at Urbana-Champaign Los Alamos National Laboratory [email protected] Computational Science Methods, (X-8) [email protected]

MS16 Mathematical Models of Tuberculosis Re-infections MS17 and Multiple Strains Stochastic Gating of Instantaneously Coupled Calcium-regulated Calcium Channels The reemerge of tuberculosis (TB), the TB co-infections with HIV and the fast growing of multiple-drug resistant Although there is consensus that calcium puﬀs and sparks tuberculosis (MDR-TB) have brought new challenges for arise from the cooperative action of multiple intracellular controlling and eliminating this old disease. In this talk, calcium channels, the precise relationship between single- the transmission dynamics of tuberculosis is studied by channel kinetics and the collective phenomena of stochas- a mathematical model that incorporates re-infections and tic calcium excitability is not well understood. Here we multiple strains. The model presents several distinct bifur- present and analyze several stochastic automata network cations and multiple stable nontrivial steady states for both models of calcium release sites that include calcium acti- the basic reproductive number less than one and greater vation, calcium inactivation, or both. than one. It shows that a single tipping point cannot totally determine the transmission dynamics and the full Gregory D. Smith picture of the dynamics are determined not only by pa- College of William and Mary rameters but also by the initial data. It also shows that [email protected] MDR-TB can survival independent of drug-sensitive TB. Baojun Song MS18 Montclair State University Beads in Mucus, Generalized Langevin Equations, Department of Mathematical Science and State Space Models [email protected] Abstract not available at press time.

MS17 John Fricks Dept of Statistics Oscillation Mechanism of Intracellular Calcium Penn State University Dynamics [email protected] Abstract not available at press time. Martin Falcke MS18 Hahn Meitner Institut Cholera Population Dynamics - Inference for Par- [email protected] 72 LS06 Abstracts

tially Observed Systems MS19 Mathematical Models of Cancer A population model for cholera in Bangladesh is investigated as a case study in inferring infectious disease dy- In this talk we will present an overview of recent develop- namics from data. Inference for nonlinear state space mod- ments in the mathematical modelling of cancer growth. We els can be a challenging step in developing stochastic dy- will focus specifically on partial differential equation and namical models appropriate for infectious diseases. This discrete models of tumour-induced angiogenesis (including motivates the introduction of a new method for likelihood blood flow and drug delivery) and cancer cell invasion of based inference, which we call MAPLE (Maximum A Pos- tissue (the role of the urokinase plasminogen activation sys- terori Limit Likelihood Estimation). The MAPLE algo- tem). Mathematical and clinical/therapeutic implications rithm computes a maximum likelihood estimator as the of the model results will be discussed. limit of an average of Bayesian posterior mean estimators. The new methodology has computational advantages and Mark Chaplain a theoretical justification. Division of Mathematics University of Dundee Edward Ionides [email protected] Dept of Statistics University of Michigan [email protected] MS19 Evolutionary Models of Carcinogenesis

MS18 Abstract not available at press time. Stochastic Challenges in Single-molecule Bio- physics Robert Gatenby Department of Radiology Recent advances in nanotechnology allow scientists for the University of Arizona first time to follow a biological process on a single molecule [email protected] basis. These advances also raise many challenging stochastic inference and modeling problems. First, by zooming in on single molecules, recent single-molecule experiments re- MS19 vealed that many classical models derived from oversimpli- Mathematics-driven Experimental Oncology fied assumptions are no longer valid. Second, the stochastic nature of the experimental data and the presence of Abstract not available at press time. latent processes much complicate the inference. In this talk we will use the modeling of subdiffusion phenomenon Vito Quaranta in protein conformational fluctuations and the modeling of Department of Cancer Biology enzyme reaction pathways to illustrate the stochastic chal- Vanderbuilt University lenges in single-molecule biophysics. [email protected] Samuel Kou Dept of Statistics MS19 Harvard University Mathematical Modeling in Clinical Oncology [email protected] Abstract not available at press time.

MS18 Kristin R. Swanson University of Washington Multiscale Approximations to Reaction Networks Dept of Pathology A reaction network is a chemical system involving multiple [email protected] reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov MS20 chain on the number of molecules of each species with reactions as possible transitions of the chain. In many cases Title not available at press time of biological interest some of the chemical species in the Abstract not available at press time. network are present in much greater abundance than others and reaction rate constants can vary over several orders Jeﬀ Hasty of magnitude. We consider approaches to approximation Department of Bioengineering of such models that take the multiscale nature of the sys- University of California, San Diego tem into account. Our primary example is a model of a [email protected] cell’s viral infection for which we apply a combination of averaging and law of large number arguments to show that the “slow” component of the model can be approximated MS20 by a deterministic equation and to characterize the asymp- New Approaches to Studying Stochastic Chemical totic distribution of the “fast” components. The main goal Kinetics in Biochemical Reaction Networks is to illustrate techniques that can be used to reduce the dimensionality of much more complex models. We used various analytic and numerical methods to elucidate complex dynamics in stochastic signal transduction. Lea Popovic We demonstrate that the commonly used linear noise ap- Dept of Mathematics proximation to solving the chemical master equation fails Cornell University when the number of proteins becomes too low. Conse- [email protected] quently, we developed a new analytical approximation to LS06 Abstracts 73

the solution of the master equation, based on the generat- the duration and the level of input growth stimuli. Corre- ing function approach, which works in a much wider range spondingly, the cell cycle entry is governed by a restriction of protein number fluctuations. We show that in a lin- curve (R-curve), at which each point represents the mini- ear signaling pathway, a reaction rate at a node could be mum duration required for growth stimuli at a given level tuned so the node acts either as a noise amplifier or as a to activate E2F expression. Genetic and biochemical mod- noise filter. For more complex cascades, we mapped the the ifications of the R-curve may contribute to development of stochastic chemical kinetics master equation into a quan- cancer and terminal quiescence. tum field theoretical problem, which we solved using the variational principle. Lingchong You Duke University Garegin A. Papoian Department of Biomedical Engineering & Department of Chemistry [email protected] University of North Carolina at Chapel Hill [email protected] MS21 Yueheng Lan Introduce Undergrad Research Presentations 3 and University of North Carolina at Chapel Hill 4 [email protected] Abstract not available at press time.

MS20 Carlos Castillo-Chavez Department of Mathematics and The Role of Population Dynamics in Phenotypic Arizona State University Variability [email protected] A population of genetically identical cells is known to exhibit a substantial phenotypic variability. This variabil- MS21 ity originates from both intrinsic and extrinsic sources. We concentrate on the role of population dynamics as an Introduce 2 Undergrad Research Presentations 5 unavoidable source of variations. A clonal population is and 6 modeled as an ensemble of nearly identical genetic circuits Abstract not available at press time. whose dynamics is altered by the growth and division of cells. The predictions of theoretical analysis is compared Aloysius Helminck with experimental measurements at the single-cell level. North Carolina State University [email protected] Dmitri Volfson Dept of Bioengineering University of California, San Diego MS21 [email protected] Introduce 2 Undergrad Research Presentations 1 and 2 Jeff Hasty Department of Bioengineering Abstract not available at press time. University of California, San Diego [email protected] Charles E. Smith North carolina state univ. Lev S. Tsimring [email protected] Institute for Nonlinear Science University of California San Diego, La Jolla, CA 92093 MS22 [email protected] Validation and Applications of a Non-linear One- dimensional Model of Pulse MS20 We present a non-linear 1D model of blood pressure and Control of Cell Cycle Entry by a Bistable velocity pulse wave propagation in the larger arteries to Myc/Rb/E2F Switch understand the performance of the system in healthy con- The entry of mammalian cell cycle is associated with a dis- ditions and how anatomic variations and cardiovascular tinct time point, the restriction point (R-point), at which pathologies, such as atherosclerosis, affect the pattern of cells are committed to proliferation. Removal of growth pulse waves. We validate our 1D model by comparison factors before the R-point rejects cells back to the quies- against a well-defined laboratory model with 35 arteries. cence. Removal of growth factors after the R-point, how- Our numerical model is able to capture the main wave ever, does not prevent completion of the cell cycle. De- propagation features measured in the experiment. spite its importance in maintaining normal cell physiology, Jordi Alastruey Arimon the molecular nature of the R-point remains elusive due to Dept of Aeronautics lack of integrated understanding of the underlying regula- Imperial College, UK tory network. Here we combined mathematical modeling [email protected] with detailed experimentation in a mammalian cell culture system to gain insight into the R-point control. Our results suggest that the Myc-Rb-E2F pathway functions as a MS22 bistable switch that separates quiescence and proliferation. Sensitivity Analysis and Parameter Estimation for Once turned-on, as characterized by activation of E2F, the switch can trigger S-phase in a digital all-or-none manner. Furthermore, E2F activation is dependant on both 74 LS06 Abstracts

a Model of the Cardiovascular crucial roles in both tumour progression and suppression. In this talk we present a hybrid discrete/continuum math- Abstract not available at press time. ematical model which describes the invasion of host tissue by tumour cells and examines how mutations in cell phe- Ben Fitzpatrick notypic attributes (e.g. P53 mutation, cell-cell adhesion, Department of Mathematics invasiveness) affect both tumour morpholgy and genetic Loyola Marymount University makeup. In the model, we focus on four key variables im- bfi[email protected] plicated in the invasion process, namely, tumour cells, host tissue (extracellular matrix, ECM), matrix-degradative en- MS22 zymes (MDE) associated with the tumour cells and oxygen supplied by the angiogenic network. In particular we will Sensitivity Analysis and Parameter Estimation for discuss the evolutionary implications of tumours growth in a Model of the Cardiovascular either harsh/mild microenvironmental conditions. Abstract not available at press time. Sandy Anderson Franz Kappel University of Dundee Department of Mathematics [email protected] University of Graz [email protected] MS23 Mathematical Modeling of Cellular Signaling: MS22 Lipid Signaling Kinetics Autonomic and Vascular Regulation in Aging Our goal is the construction of a comprehensive mathemat- Human aging is associated with changes in the autonomic ical model for the uridine 5-diphosphate signaling path- control that may affect interactions among multiple organ way in the macrophage, a type of white blood cell. The systems. Regulatory changes in the cardiovascular and mathematical model currently includes a system of nonlin- cerebrovascular systems may have broad impact on cere- ear ODEs that describe the major pathway components, bral perfusion and adaptation to activities of daily living, with an emphasis on the production and degradation of namely to the orthostatic stress. Genetic, environmental diacylglycerol, a cellular second messenger molecule which and behavioral risk factors, however, may have additive plays an important role in initiating various changes in nonlinear effects on systemic regulation that may acceler- cell behavior. Modeling techniques, challenges, and com- ate aging process and functional decline. putational simulations will be presented. (Joint work with H. Alex Brown, Jeffrey Forrester, Mark Byrne and other Vera Novak members of the Brown lab.) Beth Israel Deaconess Medical Center and Harvard Medical School Hannah Callender, Mary Ann Horn [email protected] Department of Mathematics Vanderbilt University [email protected], MS22 [email protected] Blood Flow Changes Caused by Respiratory Me- chanical Effects MS23 Changing pressure in the trunk due to respiration alters Nonlinear Simulation of Tumor Growth pressure for arteries and veins in the chest and stomach region in humans. This talk presents 1D models of the In this talk, I will focus on recent efforts to study solid cardiovascular system and the respiratory pump. These tumor progression. Here we focus on a continuum-scale models serve as tools for understanding the physiology and description and pose the problem in terms of conservation allow variations from normal resting conditions to exer- laws for nutrients, chemical factors and tumor cell popu- cise. We show how to evaluate physiological conditions in lations. We develop a multiscale mixture model that ac- response to CPR. Results raised a spectrum of problems counts for cell-to-cell adhesion. We analyze the equations that require clarification related to the role of pumps, the and develop accurate, adaptive numerical schemes. We re- differences between flows and pressures, and the function late the model to more classical single-phase models and we of valves. demonstrate the predictive capability of the model through comparisons with experimental studies of tumor growth. Johnny Ottesen We then discuss extensions to include the effect of residual Inst for mathematics and physics stress. Roskilde University, DK [email protected] John Lowengrub Department of Mathematics University of California at Irvine MS23 [email protected] A Hybrid Model of Tumour Invasion: Evolution and the Microenvironment MS23 The importance of tumour cell/microenvironment itera- Drug Delivery to Solid Tumors tions is currently of great interest to the biological community. In particular, both the immediate microenvironment Physiological transport barriers limit the distribution of (cell-cell or cell-matrix interactions) and the extended mi- systemically administered chemotherapeutics in solid tu- croenvironment (e.g. vascular bed) are thought to play mors. Intratumoral delivery is a promising technique that can improve the efficacy of existing chemotherapeutics by LS06 Abstracts 75

circumventing physiological barriers. I will present a con- for Low Reynolds Number Spinning Rods tinuum reaction diﬀusion model of intratumoral delivery of paclitaxel loaded microspheres and illustrate how simu- Abstract not available at press time. lations augmented by analytical approximations can help to elucidate the impact of cell pharmacokinetics, tumor Terry Jo Leiterman morphology, microsphere release kinetics and spatial dis- Math tribution on intratumoral drug distribution. UNC Chapel Hill [email protected] Rami Tzafriri Harvard-MIT Biomedical Engineering Center [email protected] MS25 Bio Fluids Experiments: Nanoscale-Macro Scale

MS24 Abstract not available at press time. Wavelets in Medical Sciences-Case Studies Richard McLaughlin Abstract not available at press time. UNC Chapel Hill [email protected] Faouzi Khene Research Institute,KFUPM Dhahran,Saudi Arabia MS25 mfkhene Nanoscale Biological Manipulation Abstract not available at press time. MS24 Richard Superfine Multifractal Analysis of Pollution of Delhi and Physics Bombay UNC Chapel Hill Abstract not available at press time. [email protected] Pamm Manchanda GNDU, Department ofMathematics MS26 Amritsar,India A Novel Algorithm for MALDI-TOF MS Data Pre- [email protected] processing Using Wavelets Mass Spectrometry, especially matrix assisted laser desorp- MS24 tion/ionization (MALDI) time of flight (TOF), is emerging New Fractal Methods for Time Series Analysis as a leading technique in the proteomics revolution. It can be used to find disease-related protein patterns in mixtures Abstract not available at press time. of proteins derived from easily obtained samples. In this paper, a novel algorithm for MALDI-TOF MS data prepro- Fahim Nekka cessing is developed. A MatLab implementation shows the Faculty of Pharmacy& Research Inst.Math preprocessing steps consecutively including step-interval Montreal University,Canada unification, adaptive stationary discrete wavelet denoising, [email protected] baseline correction using splines, normalization, and peak detection, a newly designed peak alignment method using clustering techniques. MS24 Multifractal Analysis of ECG Don Hong Middle Tennessee State University Abstract not available at press time. [email protected] Abul Hasan Siddiqi Mathematical Sciences Department MS26 King Fahd University of Petroleum & Minerals Incorporating Covariates in Survival Analysis Us- [email protected] ing Artificial Neural Networks

In survival analysis, the Cox proportional hazards model MS25 is widely used to incorporate covariates. However, it has Air-Mucus Transport in the Lung strong assumptions and requires knowledge of all covariates under consideration at every failure time. We consider Abstract not available at press time. time-dependent covariates and propose a method based on artiﬁcial neural networks. This method relaxes the as- Roberto Camassa sumptions and allows us to perform inference using the Mathematics observed covariates values. We illustrate its use through University of North Carolina simulations and apply it to a study of lung cancer. [email protected] Yali Liu East Tennessee State University MS25 [email protected] Exact and Asymptotic Hydrodynamics Solutions 76 LS06 Abstracts

MS26 University of Dundee Simulation of Solid Tumor Growth Division of Mathematics [email protected] We develop and check the accuracy a mathematical model for solid tumor growth. The model uses a set of partial dif- Alexander Anderson ferential equations describing the spatio-temperal changes Department of Mathematics in cell concentrations based on reaction-diffusion dynamics University of Dundee and the law of mass conservation. Unlike existing models, [email protected] this model takes into account higher dimensions and arbitrary geometries, and incorporates random mitotic rate and nutrient supply. Furthermore, the model incorporate MS27 the dependence of cell proliferation rate on the growth in- Derivation of the Tumor Control Probability hibiting factors secreted by necrotic cells. The model is (TCP) for Radiation Treatment solved using B-spline collocation method. The results are compared with the published experimental data. The bio- The Tumour Control Probability (TCP) is used as an in- logical and clinical implications are discussed. dicator of the effectiveness of radiation treatment of cancer. Standard TCP models do not include the cell cycle of Zach Sinkala cancer cells. In my talk, I will derive a cell cycle cancer Middle Tennessee State University growth model from physical principles. This model can be [email protected] extended to a nonlinear birth-death process, which then gives an explicit formula for the TCP. This TCP formula is an extension of the model of Zaider and Minerbo (joint MS26 work with A. Dawson). This talk related to G. de Vries’ Stochastic and State Space Models of Carcinogen- talk in the Minisymposium on ”Mathematical Models of esis Interactions in Biological Rythms”. In this lecture, I will summarize the most recent develop- Thomas J. Hillen ment of cancer biology from the past 5-10 years. By artic- University of Alberta ulating these biological studies, I will then propose some Department of Mathematical and Statistical Sciences stochastic and state space models for carcinogenesis. I will [email protected] develop stochastic differential equations for the state variables. Using these stochastic equations as the stochastic system model, I will then propose some state space mod- MS27 els with the stochastic observation model being based on Anti Bcl-2 Therapy Inhibits Tumoral Angiogenesis cancer incidence data available from SEER or other studies. A general Bayesian procedure using multi-level Gibbs Recent experiments show that vascular endothelial growth sampling and predictive inferences to estimate the param- factor (VEGF) is the crucial mediator of downstream eters and to predict the state variables will be developed. events that ultimately lead to enhanced endothelial cell The models and the methods are illustrated by using the survival and increased vascular density within many tu- British physician data and some environmental data. mours. The newly discovered pathway involves up- regulation of the anti-apoptotic protein Bcl-2, which in Waiyuan Tan turn leads to increased production of interleukin-8 (IL-8). University of Memphis The VEGF - Bcl-2 - IL-8 pathway suggests new targets [email protected] for the development of anti-angiogenic strategies. In this talk, I present and validate a mathematical model designed to predict the effect of the therapeutic blockage of VEGF, MS27 IL-8, and Bcl-2 at different stages of tumour progression. Modelling Multi-stage Breast Cancer Develop- ment, Treatment and Recurrence Harsh Jain Department of Mathematics Models of the step-wise development of cancer help in the University of Michigan understanding of how the disease develops and lead to more [email protected] efficient treatment strategies that prevent local recurrence. In breast cancer, about 10-30 percent of patients develop a recurrent tumour within a few years of the primary treat- MS27 ment. We present a model of the multi-stage development Metamodeling the Tumor-immune System Interac- of breast tumours with respect to clonal breast formation, tion examine radiation treatment strategies, and discuss the risks of local recurrence. Tumoral dynamics and antitumor immunotherapies are likely to be influenced by the modalities of interaction be- Jayant Vaidya tween tumor cells and immune system effectors, and by the Department of Surgery and Molecular Oncology inter-effectors interactions. In the framework of the the- University of Dundee ory of competing populations, we study here the influence [email protected] of the proliferation response of effectors to tumor burden, and of cooperation and/or competition between immune Mark Chaplain system effectors, by means of a meta-modeling approach. Division of Mathematics University of Dundee Alberto d’Onofrio [email protected] European Institute of Oncology - Milan, Italy Heiko Enderling alberto.d’[email protected] LS06 Abstracts 77

MS28 the interaction between the gastric mill motor network and Resolving the Bursting Mechanisms in a Two- two identiﬁed descending projection neurons in the crab. compartment Pyloric Dilator Cell Model Using reduced mathematical models, we demonstrate that rhythmic feedback to descending neurons moves the locus The role of electrical coupling between neurons with widely of pattern-generation from a half-center oscillator to an diﬀerent intrinsic properties is not well understood. We excitation-feedback circuit. systematically reduce a multi-compartment conductance- based model of electrically coupled neurons in the crus- Michael Nusbaum tacean pyloric network that exhibits multi-stable modes of Univ. of Pennsylvania School of Medicine oscillation. We determine the low-dimensional organizing [email protected] structure behind its multi-stability in a “critical regime” of the dynamics, and thus study the dependence of the sys- Nickolas Kintos tems selection of network oscillation on initial conditions NJIT and parameters such as the electrical coupling strength. [email protected]

Cristina Soto-Trevino Amit Bose Department of Mathematical Sci Dept of Mathematical Sciences NJIT NJIT [email protected] [email protected]

Farzan Nadim Farzan Nadim NJIT & Rutgers University NJIT & Rutgers University [email protected] [email protected] Robert Clewley Cornell University MS28 Department of Mathematics Exploring a Mammalian Locomotor CPG Network [email protected] via Analysis of Reduced Subnetworks

We examine a detailed conductance-based model of a neu- MS28 ronal network in the neonatal rodent spinal cord that serves Multistability of Half-center Bursting in a Two-cell as a central pattern generator for coordinated locomotion. Inhibitory Network with T-currents Analyzed via The size of the full model precludes detailed analysis; sym- a Poincare Return Map metry and functionality considerations are used to isolate reduced subnetworks that are building blocks or schemat- We explore the dynamics of a network of two type-I model ics of the full network. The phase-response and synchro- neurons endowed with T-currents and coupled by recip- nization properties of the subnetworks illuminate the cor- rocal inhibition. The post-inhibitory rebound due to the responding properties of the larger system. T-current deinactivation allows the network to maintain a stable antiphase (half-center) periodic bursting, whereby Erik Sherwood a burst in one cell causes a rebound burst in the partner Center for Applied Mathematics cell. We show that the existence and stability of bursting Cornell University solutions is captured by a 1D Poincare return map, and [email protected] find that multiple bursting states with different numbers of spikes per burst can be co-stable for a range of parame- John Guckenheimer ter values. Cornell University [email protected] Victor Matveev New Jersey Institute of Technology [email protected] Robert Clewley Cornell University Department of Mathematics Amit Bose [email protected] Dept of Mathematical Sciences NJIT [email protected] MS29 Structural Monotonicity of Chemical Reaction Farzan Nadim Networks NJIT & Rutgers University [email protected] New results linking the structural and dynamical properties of certain chemical reaction networks will be presented. The key idea is to find appropriate coordinates in which MS28 the system is monotone, so that convergence results can The Role of Feedback to Descending Projection be applied to prove that solutions converge. An important Neurons in Rhythmic Motor Pattern Generation feature of our results is that they are independent of the precise form of the reaction kinetics. For instance, we do Pattern-generating networks are generally studied assum- not require that they are of mass action type. The main ing feed-forward architecture from descending projection tools used in the proofs come from graph theory and dy- neurons that initiate, terminate or modify the network out- namical systems theory. This is joint work with David An- put. Yet, in all complex systems, feedback to descending geli (University of Firenze) and Eduardo Sontag (Rutgers inputs is pervasive and mostly not understood. We model 78 LS06 Abstracts

University). marine sediment and begin producing polymer which eventually forms a loose hydrogel. Bacteria are transiently Patrick DeLeenheer attached to this gel by stalks. Bacteria attached to the Department of Mathematics veil rotate their flagella, which produces a small fluid flow University of Florida that draws nutrient rich water across the veil. Meanwhile [email protected]fl.edu bacteria continuously detach and re-attach from the veil. Detached bacteria actively swim and are also advected by the fluid flow, coupling the bacterial concentration to the MS29 fluid flow. The bacteria tend to attach at the boundary Convex and Toric Geometry for the Dynamics of between regions of relatively high and low polymer concen- Reaction Networks tration evidently because of fluid effects. This aggregation is reinforced by the evolving fluid dynamics which tends to The stability problem of complex reaction networks with push bacteria away from voids and towards the edges. Vi- nonlinear kinetics can be addressed by reformulation in sual observation of the veil shows regular hexagonal arrays convex coordinates and by using the properties of cer- or rolls depending on the experimental parameters. We tain algebraic structures defined on the reaction monomi- describe the pattern formation that occurs in this system als. The procedure is exemplified using a Hopf bifurcation, using both analytic and numerical techniques. Boundary showing which features in a network can give rise to chem- Integral Methods will be used to simulate the fluid flow ical oscillations. that is generated by attached bacteria; a reaction-diffusion- Markus Eiswirth advection model will be formulated to describe the translo- Fritz-Haber-Institute, Berlin cation of and nutrient consumption by the attached and [email protected] detached bacteria and the nutrient concentration. We will also use gel mechanics to explore the effects of viscoelastic properties of the veil. These systems will be coupled MS29 together to create a full model for pattern formation in Graph-theoretic Approach to Oscillations in Bio- systems of sulfur-oxidizing bacteria. chemical Networks with Multiple Delays Nick Cogan In chemical modeling, delays represent subsystems of un- Florida State University known intermediates and delay system models capture the [email protected] essential properties of a chemical mechanism when only a few details are available. We use a bipartite graph to rep- MS30 resent the chemical mechanism, and show that if certain subgraphs are present in the graph then the correspond- Flow Through Flowing Structures: A Mulitphase ing delay model can admit oscillations for some values of Model of True Slime Mold the system’s parameters. Our subgraph condition for os- The true slime mold physarum polycephalum is a single cillations generalizes the condition of a negative (feedback) cell organism reaching up to meters in size. The cyto- cycle which is usually used in the biochemical literature. plasm shows periodic shuttle streaming through a network Maya Mincheva of tublar structures reaching velocities up to 1 mm/s. The Department of Chemistry motion is driven by the periodic contraction of an actin- University of Lethbridge, Canada myosin gel and is necessary to transmit chemical signals [email protected] and organize structures over large distances. We present a mechanochemical mulitfluid model of the sol/gel that describes the initiation of streaming. MS29 Toshiyuki Nakagaki What is the Origin of Cell Diversity? Research Institute for Electronic Science Complexity of interactive gene regulation is considered to Hokkaido University be responsible for generating diversity of distinct cell types [email protected] in developmental process. I studied diversity of cell types by analyzing the number of steady states (or attractors) Robert D. Guy of gene activity using network models. The results were Mathematics Department contrary to the previous arguments. Neither gene number University of Utah nor connectivity between genes increases number of steady [email protected] states. Number of loops in gene regulation rather increases number of steady states. MS30 Atsushi Mochizuki Transport Along A Contracting Tube Division of Theoretical Biology National Institute for Basic Biology, Okazaki, Japan In addition to passing kidney stones, the peristaltic con- [email protected] tractions of the ureter also propel urine toward the bladder in boluses. Thus, flow in CDs is very different from flow in a pipe with fixed diameter, because the linear velocity of MS30 the boluses is determined, not by urine flow rates, but by Dynamics of Polymer Veils the velocity of the peristaltic waves, whereas the lengths of the boluses, and thus the contact time with the CD ep- This project focuses on the formation and dynamics of pat- ithelium, vary with urine flow rates. We model solute and terns created by the interaction between swimming bacte- fluid transport along an actively contracting tube as an ria, thin polymeric gels, and fluid motion. Here motile immersed boundary problem, in axisymmetric cylindrical marine bacteria chemotactically aggregate to a layer over coordinates. The model equations embody the principal of LS06 Abstracts 79

mass conservation of solute and water, and represent single- MS31 barrier transport processes. Model solutions are computed The UBM Program at Truman State using a second-order immersed interface-type method. The model can be used to assess the effective tubular transport At Truman, faculty and undergraduates in the biology and properties of the CD undergoing peristalsis. the mathematical sciences are engaged in multi-semester collaborative interdisciplinary research experiences. The Anita T. Layton outcomes of this NSF UBM supported program include fos- Duke University tering sustained cross-disciplinary collaborative relation- Department of Mathematics ships between faculty and preparing our undergraduates [email protected] to work in an interdisciplinary fashion. These ends are achieved through research activities and a year-long program of seminars and workshops. Preliminary assessment MS30 data will be used to illuminate successes The Endothelial Glycocalyx: Flow, Permeability, and Stress Jeffrey Osborn Truman State University Fluid mechanical forces from blood are transmitted across Department of Biology the membrane of endothelial cells via the glycocalyx, a [email protected] dense matrix of membrane-bound macromolecules whose structure is not well understood. Using mathematical mod- Jon Beck els we explore the effect of matrix permeability on flow Truman State University through the matrix and the resulting fluid stresses exerted Department of Computer Science on the matrix. We also use physical models to measure [email protected] flow as a function of the size and spatial distribution of ‘macromolecules’. Michael Kelrick Aaron L. Fogelson Truman State University University of Utah Department of Biology [email protected] [email protected]

Laura A. Miller Jason Miller Department of Mathematics Truman State University University of Utah Department of Mathematics [email protected] [email protected]

Karin Leiderman MS31 Mathematics Department University of Utah Interdisciplinary Training for Undergraduates in [email protected] Biological and Mathematical Sciences at Arizona State University

MS31 The UBM program at ASU intimately combines new cross- disciplinary courses and summer research programs. The The UBM Program at NJIT former are constructed to allow maximal participation The Undergraduate Biology and Mathematics Training among undergraduate cadres, and facilitate life science Program seeks to train undergraduates at the interface of majors to achieve a minor in mathematics, and, likewise, biology and mathematics through a combination of curric- mathematics majors to enrich their education with a minor ular activities and research project based activities. In this in bioscience. Research projects span modeling of ecologi- talk, we will provide an overview of our program describing cal and evolutionary processes through the lens of stoichio- student cohort activities in the Spring, Summer and Fall metric constraints, bio-economics, chemostat theory, and semesters. We will also describe the two main research modeling of visual perception. The program’s holistic ap- projects conducted by the 2005 cohort of students. One proach in mathematical biology training can also vertically project involved quantifying the formation of plant bor- integrate all the relevant components in the ASU education ders, the other focused on determining the location of gap system. The program has already trained 17 students. junctions in neuronal networks. John D. Nagy Jorge Golowasch Scottsdale Community College Division of Biological Sciences Arizona State University New Jersey Institute of Technology [email protected] [email protected] Yang Kuang Farzan Nadim Arizona State University NJIT & Rutgers University Department of Mathematics [email protected] [email protected]

Amitabha K. Bose MS31 New Jersey Inst of Technology REUs on DEEP Problems Department of Mathematical Sciences [email protected] In the past few years, I have the privilege to mentor over a dozen research experiences for undergraduates (REUs) 80 LS06 Abstracts

on problems concerning the dynamics of ecology and evo- MS32 lutionary processes (DEEP). These research experiences Moment Approach for Computing Discrete- have varied in mathematical content (ranging from proving stochastic Biological Systems theorems to empirically testing predictions in mesocosms), group size (ranging from one student in isolation to three It has now been demonstrated that the behavior of low students as part of a larger REU program), duration (from molecular number reaction systems encountered in biolog- one month to two years), final outcomes and degree of in- ical settings frequently requires a discrete-stochastic de- terdisciplinary involvement. In this talk, I will give an scription via the chemical master equation (CME). How- overview of these experiences and share stories of success, ever, solving this differential-difference equation for the failure, and unexpected surprises. probability distributions of most biochemical systems typically presents substantial computational challenges. We Sebastian Schreiber consider an alternative, but equivalent representation of College of William and Mary CME probability in terms of its factorial moments. This [email protected] f-moment approach results in a formulation, which exhibits significant advantages for computing certain CME system properties. MS32 Adaptive Multiscale Stochastic Simulation of Bio- Michael Samoilov chemical Systems Center for Synthetic Biology Lawrence Berkeley National Laboratory Biochemical systems are inherently multiscale and stochas- [email protected] tic. In microscopic systems formed by living cells, the small numbers of reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continu- MS32 ous and deterministic. An analysis tool that respects these Stochastic Modeling of the Eukaryotic Cell Cycle dynamical characteristics is the stochastic simulation algorithm (SSA), a numerical simulation procedure that is Events of the eukaryotic cell cycle (DNA synthesis, mitosis essentially exact for chemical systems that are spatially ho- and cell division) are regulated by a complicated network mogeneous or well stirred. Despite recent improvements, of interacting protein kinases, phosphatases, transcription as a procedure that simulates every reaction event, the SSA factors and proteases. Deterministic models (nonlinear is necessarily inefficient for most realistic problems. There ODEs) have proved very useful in accounting for average are two main reasons for this, both arising from the mul- properties of populations of growing-dividing cells, for un- tiscale nature of the underlying problem: (1) stiffness, i.e. derstanding how the control system works in normal cells the presence of multiple timescales, the fastest of which are (and why it fails when certain genes are mutated), and for stable; and (2) the need to include in the simulation both predicting counterintuitive outcomes of novel experiments. species that are present in relatively small quantities and But deterministic models are insufficient to deal with a should be modeled by a discrete stochastic process, and growing body of experimental results on the variability of species that are present in larger quantities and are more the cell cycle control system within single cells. To account efficiently modeled by a deterministic differential equation for such variability will require a careful accounting of all (or at some scale in between). Discrete stochastic simu- sources of stochastic fluctuations in the control system, in- lation algorithms that can efficiently solve the multiscale cluding molecular noise at the level of gene expression, problem are highly desired. This talk will introduce our re- protein synthesis and degradation, protein-protein inter- cent work in multiscale stochastic simulation methods for actions, and random events in the division process and the biochemical systems. distribution of molecular components to the two daughter cells. I will present some preliminary results on my Yang Cao research group’s attempts, to date, to convert phenomeno- Dept. of Computer Science logical deterministic ODE models into elementary reaction Virginia Tech mechanisms suitable for exact stochastic simulations. [email protected] John J. Tyson Virginia Poly Inst & St Univ MS32 Department of Biology STOCHKIT: Software Tools for Discrete Stochas- [email protected] tic and Multiscale Simulation of Biochemical Sys- tems MS33 Traditional ordi- Mathematical Analysis of Effector Caspase Ampli- nary differential equation-based approaches to simulation fication in the Death Receptor Network in Single- of chemical reacting systems fail to capture the randomness cells inherent in such systems at scales common in intracellular biochemical processes. We present StochKit, an efficient, A proposed mechanism of ligand-induced single-cell rapid extensible stochastic simulation framework that aims to all-or-none death is positive feedback in the apoptotic net- make stochastic simulation accessible to practicing biolo- work. However, this hypothesis is not supported experi- gists and chemists, while remaining open to extension via mentally in HeLa cells. Apoptosis is described by an ex- new stochastic and multiscale algorithms. perimentally verified, mass-action ODE model, which indicates that in single HeLa cells, the mitochondrial death Linda R. Petzold pathway is responsible for rapid, all-or-none apoptosis. As University of California, Santa Barbara a corollary of Singular Perturbation model reduction, a [email protected] threshold parameter is identified that when crossed, ini- LS06 Abstracts 81

tiates fast, all-or-none mitochondrial cell death. Department of Biological Sciences Northern Arizona University Peter Sorger [email protected], [email protected] Department of Biology, Division of Biological Engineering MIT James Faeder [email protected] Theoretical Division Los Alamos National Laboratory Douglas Lauffenburger [email protected] Division of Biological Engineering, Dept. of Chem. Eng. MIT lauff[email protected] MS33 Signal Transduction at Point-blank Range: Brow- John Albeck nian Dynamics Simulations of Receptor-mediated Department of Biology Ras/PI 3-kinase Crosstalk MIT [email protected] We have developed an efficient Brownian dynamics model for stochastic simulation and computational analysis of sig- John M. Burke nal transduction reactions on cell membranes. For a rela- Massachusetts Institute of Technology tively simple system, the collision coupling mechanism, the Biological Engineering Division simulations are in quantitative agreement with continuum [email protected] theory. We have used this validated approach to study the spatial interplay and crosstalk between two receptor- mediated signal transduction pathways, involving activa- MS33 tion of Ras and phosphoinositide (PI) 3-kinase, at the sin- Monotonicity and the Stability of Biochemical Sys- gle molecule level. tems Michael Monine We use the concept of monotone dynamical systems to Department of Chemical & Biomolecular Engineering study certain biochemical networks and predict their long North Carolina State University time behavior. We show that under certain qualitative and [email protected] quantitative conditions, the systems in question present global attractivity towards one or several equilibria. Cru- Jason Haugh cially, the system itself is not necessarily required to be North Carolina State University monotone in some important cases. Some results can be Department of Chemical & Biomolecular Engineering generalized to systems with delays or reaction terms. jason [email protected] German A. Enciso Rutgers University MS34 Department of Mathematics A Model of the Epithelial-Mesenchymal Transition [email protected] (EMT) Regulatory Network

Eduardo Sontag EMT, a fundamental process governing embryonic devel- Rutgers University opment in multicellular organisms, has recently been im- [email protected] plicated in the early stages of cancer metastasis. Dur- ing this transition, epithelial cells lose adhesive properties and acquire a motile mesenchymal phenotype. EMT is di- MS33 rectly correlated with the downregulation of E-cadherin, Rule-based Modeling of Biochemical Networks a protein involved in adherens junctions holding epithelial cells together. Several oncogenic pathways are now known The modular structure of signaling proteins gives rise to to induce E-cadherin downregulation. We will present a complex networks that are challenging to model. The con- model EMT regulatory network involving the TGF-beta, ventional approach to specifying these networks is error- Ras and Wnt signaling pathways. Our computer simu- prone and fraught with hidden assumptions that are dif- lations demonstrate how a reduction in E-cadherin levels ficult to justify. As an alternative, we have developed a correlate with the induction of EMT and, in parallel, how modeling language that allows a rule-based description of the mesenchymal marker, vimentin, is upregulated. signaling biochemistry based on protein modularity. We discuss various approaches to simulating rule-based models Baltazar D. Aguda, Felicia Ng and the insights that can be gained about the underlying Bioinformatics Institute biology. Singapore [email protected], [email protected] Michael Blinov, William Hlavacek, Byron Goldstein Theoretical Biology and Biophysics Group Los Alamos National Laboratory MS34 [email protected], [email protected], [email protected] A Mathematical Model of the G2 to M Transition A mathematical model of the cell cycle transion from G2 G. Matthew Fricke phase into Mitosis has been developed. The purpose of Go Figure Software this model is to ascertain (in collaboration with experimen- matthew@gofigure.org talists) the biochemical mechanisms involved in the DNA damage G2 checkpoint response and to model the effect Richard Posner, Josh Colvin of disruption of checkpoint response pathways on cellular 82 LS06 Abstracts

outcomes. lies on the phase response of circadian gene regulation to dfferent environmental cues, of which light is the most ob- Kevin J. Kesseler vious and important. Dynamic analysis of oscillatory sys- Lineberger Cancer Center tems necessitate the development of methods specific for UNC - Chapel Hill these systems’ attributes, such as the period and phase. [email protected] Investigation of the phase behavior of Drosophila circadian rhythm gives experimentally testable predictions for the control mechanisms of circadian phase and period re- MS34 sponses. Cellular Identity, Microenvironment, and Genomic Integrity Francis J. Doyle Dept. of Chemical Engineering In development, a balance between cellular proliferation, University of California, Santa Barbara differentiation, and death emerges in collective genetic re- [email protected] sponse to naturally varied intrinsic and extrinsic factors. Highthroughput efforts to ”interrogate” systems have led to putative causal relationships, on a molecular level; i.e., MS35 databases of pathways of interacting gene products. Of Incorporating Mechanisms for Fatigue into a Cog- note, it seems that cell-type and experimental-preparation nitive Architecture specificity is of paramount importance. I will present work on top-down modelling that addresses genomic integrity, This research uses outputs from mathematical models that microenvironment, and lineage commitment during neuro- characterize how circadian rhythms and sleep-wake home- genesis. ostasis influence overall human cognitive functioning. The mathematical models are used to represent fatigue by driv- Hugh R. Macmillan ing parameter changes in a cognitive architecture, which Dept. of Mathematical Sciences uses a common set of mechanisms to produce psychologi- Clemson Universtiy cally valid performance predictions across a range of tasks. [email protected] With mechanisms to represent fatigue, quantitative, a priori predictions can be made about the impact of sleep loss in particular tasks. MS34 A Mathematical Model of Haemopoiesis as Exem- Glenn Gunzelmann plified by CD34 Cell Mobilization into the Periph- Air Force Research Laboratory eral Blood AFRL/HEAS [email protected] We propose to simulate the kinetics of haemopoietic cells, including CD34+cells, with a mathematical model consisting of nonlinear, coupled, ordinary differential equa- MS35 tions. This minimal model mimics the known kinetics of Frontiers in Modeling Circadian Rhythms, its In- haemopoietic progenitor cells in the bone marrow and the puts and Outputs CD34+ cells, white blood cells, and platelets from the peripheral blood in the presence of the granulocyte colony- Complementary experimental and modeling efforts have al- stimulating factor. Perturbations within this system, sub- lowed determination of key features of the human circadian jected to granulocyte colony-stimulating factor treatment system and its effects on performance. Limit cycle oscil- and apheresis of peripheral blood progenitor cells (CD34+ lators are used model the 2-dimensional state circadian cells) in healthy individuals, are reproduced. With this system. Current efforts include incorporating the effect model, we make predictions for reducing the length of time of wavelength of light and non-photic effects on the input with neutropenia after high-dose chemotherapy. Results pathway, and circadian control of melatonin rhythms. The based on this model indicate that myelosuppressive treat- use of analysis and modeling of data to understand the ment combined with infusion of CD34+ peripheral blood physiology will be discussed. progenitor cells provides a faster recovery of the haemopoietic system than does treatment with the granulocyte Richard Kronauer colony-stimulating factor alone. Additionally, this model Harvard University predicts that infusion of white blood cells and platelets Brigham and Women’s Hospital can relieve the symptoms of neutropenia and thrombo- [email protected] cytopenia, respectively, without drastically hindering the haemopoietic recovery period after high-dose chemotherapy. MS35 Modeling Individual Differences Mandri Obeyesekere University of Texas M. D. Anderson Cancer Center Reducing or displacing sleep consistently leads to neu- [email protected] robehavioral impairment, although the magnitude of impairment varies considerably among individuals. Sleep- dependent changes in neurobehavioral performance across MS35 time of day and over days have been captured in biomath- Systems Approaches to Understanding Robustness ematical models. However, these models do not deal with and Performance in Circadian Rhythm inter-individual differences. Novel approaches to biomathematical prediction of performance in the face of inter- The regulatory architecture responsible for robust mainte- individual differences, and the physiologic implications nance of 24 hour cycles is analyzed as a control system. thereof, will be discussed. Circadian rhythms possess the ability to entrain their internal phase to that of the environment. This ability re- Hans Van Dongen LS06 Abstracts 83

Sleep and Performance Research Center [email protected] Washington State University Spokane [email protected] Arthur Sherman National Institute of Health Bethesda, MD 20892-5621 MS36 [email protected] Can We Discern Cause-and-effect in Polycystic Ovarian Syndrome (PCOS) and Diabetes? MS36 Soon after PCOS was defined as Amenorrhea associated Improving Clinical Outcomes Through Data Min- with bilateral polycystic ovaries, obesity (up to 50%) and ing androgen excess (up to 80+ %) were recognized as common features. Hormonal studies confirmed both excess an- With the advent of electronic medical records, opportuni- drogen (ovarian and adrenal) and insulin resistance (IR) ties are emerging to apply advance mathematical modeling and/or type 2 diabetes (up to 80+ %). Since effective ther- and data mining methods to improve the quality of health- apies treat either IR or androgen excess, a positive feedback care. Practice management software is being developed to mechanism involving insulin and androgen signaling must suggest the most favorable treatment plans to physicians be central to the causal pathway in PCOS. given the complex array of diagnostic information available. Medical arenas with fee-for-services or where compe- Claude Hughes tition for patients is acute (eg. assisted reproduction) are Quintiles, Inc. particularly interested in modeling approaches to improve Morrisville, NC 27560 results and revenue. [email protected] James Trimarchi Brown University MS36 [email protected] BK Channel Diversity: Consequences for Cellular Excitability MS37 BK channels are expressed in many tissues throughout the Odor Identity and Concentration Coding in a body, where they play diverse roles in the control of cellu- Model Olfactory System lar excitability. This diversity arises from different cellular contexts, as well as alternative splice variants, accessory Using realistic computational model of the locust olfac- subunits, and modulation by circulating steroids on mul- tory system we studied its response properties for different tiple time scales. To capture the diversity and its conse- odor concentrations. A dimension reduction analysis re- quences, we model whole cell excitability using stochastic vealed that projection neurons activities for different odors simulation of a BK channel gating model. diverged quickly in the response space while the activities corresponding to different concentrations of a particu- David McCobb lar odor evolved along neighboring trajectories. Both the Dept. of Neurobiology and Behavior identity and the concentration of odors, therefore, can be Cornell University encoded in the spatiotemporal firing patterns of projection [email protected] neurons activity. Danielle Lyles Maxim Bazhenov Center for Applied Math Salk Institute for Biological Studies Cornell University [email protected] danielle [email protected] MS37 MS36 Dynamic Clustering in a Model of the Insect’s An- Glucose Sensing by Combined Metabolic and Ionic tennal Lobe Oscillations in Pancreatic Islets Abstract not available at press time. Pancreatic beta-cells secrete insulin to maintain blood glucose within a narrow range. We have proposed that se- Alla Borisyuk cretion is mediated by a combination of fast electrical and University of Utah slow metabolic oscillations. The fast and slow oscillations Dept of Mathematics both follow the typical pattern of relaxation oscillators - [email protected] off, oscillating, saturated - but may differ in the thresholds for the transitions. The nine resulting combinations account for most of the oscillatory patterns observed, in- MS37 cluding pure fast and pure slow. Neural Dynamics in the Antennal Lobe: Sensory Coding and Memory Traces in an Insects Brain Krasimira Tsaneva-Atanasova National Institutes of Health I will present a detailed analysis of the neural dynam- Bethesda, MD 20892-5621 ics in the antennal lobe of the honeybee, as recorded [email protected] with calcium-imaging. The analysis yields three important results: 1) the neural dynamics possess odor specific- Richard Bertram attractors; 2) the perceptron provides a realistic model for Department of Mathematics odor recognition and odor discrimination; 3) the sponta- Florida State University neous activity of this network contains memory traces that are stored following the Hebbian learning rule, and they 84 LS06 Abstracts

can be retrieved through a principal component analysis. [email protected] Roberto Fernandez Galan Carnegie Mellon Univeristy MS38 [email protected] Stoichiometric Model that Links Cellular Machin- ery with Global Nutrient Ratios

MS37 Redfield ratios are one of the largest-scale patterns found in Encoding a Temporally Structured Sensory Stim- the Biosphere. First identified by Harvard oceanographer ulus with a Temporally Structured Neural Repre- Alfred Redfield in 1930s, the pattern refers to the remark- sentation able similarity of carbon(C) : Nitrogen (N) : Phosphorus (P) ratios in open ocean and phytoplankton. In particular, Can the temporal structure of a stimulus interfere with Redfield ratios state that for every P atom there are about the spatio-temporal structure of the neural representation? 16 N atoms in both oceanic water and phytoplankton. Due We investigated this in the locust olfactory system. When to the importance of Redfield ratio to biogeochemical cy- odors were presented in trains of nearly overlapping pulses, cles, carbon balance and, hence, global climate, numerous responses of first-order interneurons changed reliably and attempts have been made to explain it. Here, we derive often greatly with pulse position, as responses to one pulse Redfield ratios by linking molecular processes on cell level interfered with subsequent responses. However, ensem- with competition among species and global nutrient feed- ble based spatio-temporal coding could disambiguate these backs. First, we show that N:P=16 can stem from fun- patterns, providing an invariant response to the stimulus damental molecular constants such as N content in amino in second-order interneurons. acids, and N and P content in nucleotides to manifest itself in a biochemically optimal RNA:Protein ratio. Next, we Mark Stopfer incorporate this biochemical optimum into the ODE model NIH/NICHD of competition between phytoplankton species to show how [email protected] the pattern found on molecular scale can propagate itself to global Redfield ratio. The necessary condition for this to happen is nutrient feedbacks that indeed exist in oceans. MS38 Effect of Antibiotic on Heterogeneous Bacterial Simon Levin Populations Ecology and Evolutionary Biology Princeton University We consider a mathematical model of two microbial strains [email protected] competing for a common nutrient while exposed to periodic dosing of an antibiotic or growth inhibitor. One strain is James Elser assumed to be more resistant to the drug but slower grow- Arizona State University ing than its competitor. The focus of our work is on ob- [email protected] taining sufficient conditions for successful drug treatment, i.e., eradication of the bacteria, and on finding conditions implying persistence of one or more of the strains. This Irakli Loladze amounts to a stability analysis of the periodic solutions of Department of Mathematics the model. University of Nebraska - Lincoln [email protected] Mudassar Imran Arizona State University [email protected] MS38 A Resource-based Model of Microbial Quiescence

MS38 The implications of microbial quiescence are analyzed Competition for Multiple Resources through a model that involves ”wake-up” and ”sleep” rates for cell transition between a quiescent and an active state. We discuss a standard chemostat model of three species These rates depend on resource levels, turning on and oﬀ at competing for three essential resources. We show that thresholds which may not coincide. The population is ei- the model can have at least two limit cycles, or an un- ther washed out or a single ”survival” steady state exists. stable limit cycle. The results suggest that this standard Proportional nutrient enrichment is used to analytically model can exhibit both equilibrium dynamics and non- and numerically explore the steady state bifurcating from equilibrium dynamics for a given set of parameter values. the washout state. (Joint work with Hal L. Smith and Steven M. Baer) Hal L. Smith Steven Baer Arizona state university Department of Mathematics and Statistics [email protected] Arizona State University [email protected] Tufail M. Malik Department of Mathematics and Statistics Hal L. Smith Arizona State University Arizona state university [email protected] [email protected] MS39 Bingtuan Li Department of Mathematics Mechanisms of Chromosome Segregation in Bud- University of Louisville LS06 Abstracts 85

ding Yeast University of Minnesota Department of Biomedical Engineering We have used quantitative fluorescence microscopy to [email protected] count the number of proteins that comprise the microtubule binding site at the kinetochore. These measurements represent the minimal molecular requirements for MS40 assembling one kinetochore-MT attachment. We propose Modeling Shear Wave Propagation in Biotissue: that the core centromere nucleosome (120 bp wrapped An Internal Variable Approach to Dissipation around a Cse4 containing nucleosome) and flanking chro- matin adopts a cruciform configuration in metaphase. This In this presentation, we examine the propagation of dis- establishes the geometry for the microtubule attachment turbances consisting primarily of shear waves through bi- site. otissue. We develop a model based on specific physical geometries in polar coordinates, using the well known equa- Kerry Bloom tions of motion and a set of constitutive equations based on University of North Carolina the internal variable method outlined in [H.T Banks, J.H. kerry [email protected] Barnes, A.Eberhardt, H.Tran, and S.Wynne,Modeling and computation of propagating waves from coronary stenoses, Computational and Applied Mathematics,Vol 21, N.3, 2002 MS39 ]. Computational results first for a viscoelastic homoge- Modeling Polymer Dynamics in Bacterial Cell Di- neous medium are presented and compared to previous vision findings. We then consider a more complex geometry by introducing heterogeneities into the medium. The resulting In order to correctly divide into two daughter cells, E. coli simulations are discussed. uses a remarkable dynamic process whereby it alternately assembles and disassembles a linear polymer at each of its Nicholas Luke, Shannon Wynne, H.T. Banks ends which suppresses the formation of the division ring North Carolina State University everywhere but at the midpoint of the cell. By model- CRSC ing this process, we replicate much of the experimentally [email protected], [email protected], [email protected] observed behaviour and thereby generate a set of mechanistic constraints and experimentally testable quantitative predictions. MS40 Multiphasic Models for Chondron Deformation un- Eric N. Cytrynbaum der Micropipette Aspiration University of British Columbia Department of Mathematics The chondron of articular cartilage consists of a cell and its [email protected] encapsulating pericellular matrix (PCM). Previous application of a single phase layered elastic contact solution for micropipette aspiration demonstrated a considerable de- MS39 crease in apparent PCM stiffness of isolated human chon- FtsZ Self-Assembly Dynamics and Bacterial Cell drons with osteoarthritis. We extend this layered elastic Division solution by treating the chondron as a multiphasic (solid- fluid, or solid-fluid-ion) material to quantify the relative FtsZ, a bacterial tubulin homolog, forms a ring that con- contributions of collagen and proteoglycan fixed charge stricts to divide the cell. The ring is constructed from density to apparent PCM stiffness. single-stranded protofilaments, which have been visualized by EM in vitro. Protofilaments are turning over very Mansoor A. Haider rapidly, with a half time of 8 sec both in vitro and in vivo. North Carolina State University The protofilaments transit from a straight to a curved con- Department of Mathematics formation, and we propose that this is the basis for the m [email protected] constriction force. Harold Erickson Farshid Guilak Duke University Duke University Medical Center [email protected] [email protected]

Brandy A. Benedict MS39 North Carolina State University Modeling the Stochastic Mechanics of the Budding [email protected] Yeast Mitotic Spindle

Proper segregation of chromosomes is one of the most fun- MS40 damental cellular processes. The physical movement and Modeling Auricular Chondrocytes for Lining of separation that occurs during each round of division in eu- Vascular Stents karyotes is mediated largely by microtubules in a complex known as the mitotic spindle. We have developed stochas- Stents are tube-like meshes used in the treatment of coro- tic models for microtubule assembly that describe the phys- nary artery diseases. They serve to prop the diseased arter- ical and chemical forces that influence the dynamics. We ies open and to secure normal blood flow. Although stents have focussed our modeling efforts on budding yeast, behave revolutionized the treatement of coronary artery dis- cause it has the simplest mitotic spindle and therefore is eases, there are various clinical complications in patient likely the most tractable. follow-ups.The major one is re-stenosis or re-narrowing of coronary arteries which might lead to a heart attack. Re- David J. Odde stenosis is largely related to the development of scar tissue 86 LS06 Abstracts

(neo-intimal hyperplasia) that occurs within an artery af- Lori Setton ter it has been treated with a foreign device with poor bio- Dept. of Biomedical Engineering compatibility. To improve the biocompatibility of stents, Duke University a team of cardiologists around Dr. Rosenstrauch at the [email protected] Texas Heart Institute is investigating the use of genetically engineered auricular chondrocytes for lining a stent. Stents lined with geneticaly engineered chondrocytes might lower MS41 the re-stenosis reates and provide a long-lasting biocompat- How and Why Cells Make Networks within the Pi- ible prothesis. The speaker will talk about a mathematical tuitary Gland model describing the growth of auricular chondrocytes on a stent in the novel environment: exposed to controlled flow Pituitary cells that secrete growth hormone (GH) are dis- conditions for enhanced growth. tributed according to a 3D-network. The architecture of this network is robust across lifespan and displays modular- Suncica Canic ity correlated with pituitary GH content and body growth. Department of Mathematics Importantly, this anatomical network supports functional University of Houston connectivity revealed by spatially stereotyped motifs of [email protected] cell synchronization after stimulation by GH-releasing hormone. This type of network may be a critical determinant for coordinated secretory pulses by the pituitary gland and MS40 other endocrine tissues. Modeling Scanning Microphotolysis to Measure Molecular Diffusion in Articular Cartilage Patrice Mollard CNRS UMR5203 INSERM U661 Diffusion is the primary mode of transport of solutes University Montpellier1&2 through articular cartilage. We developed a mathemati- [email protected] cal model of scanning microphotolysis (SCAMP) to measure macromolecular diffusion in subcellular-size volumes Xavier Bonnefont of cartilage. SCAMP is a rapid, single-line photobleach- CNRS UMR5203 INSERM U661 ing procedure that accounts for out-of-plane bleaching at Universities Montpellier1&2 high magnification. Data was analyzed by best-fit compar- [email protected] ison to simulations generated using alternating direction implicit discretization of the diffusion-reaction equation in conjunction with the 3-D bleaching (excitation) and point- MS41 spread (detection) profiles. A Model for the Switch Between the Pulse and Surge Pattern of GnRH Secretion Farshid Guilak, Susan Christensen, Holly Leddy Duke University Medical Center We propose a mathematical model allowing for the alter- [email protected], [email protected], [email protected] nating pulse and surge pattern of GnRH (Gonadotropin Releasing Hormone) secretion. The model is based on the coupling between two FitzHugh-Nagumo systems running MS40 on different time scales. The analysis of the slow/fast dy- Biphasic Modeling and Optimization of Mouse namics allows to explain different secretion patterns (slow Cartilage in Compression for Material Property oscillations, fast oscillations and periodical surge). Spec- Determinations ifications on the parameter values are derived from physiological knowledge in terms of amplitude, frequency and Cartilage mechanical properties are important measures of plateau length of oscillations. tissue function. Mouse models of cartilage degeneration are important for studying a role for genetic background in this Frédérique Clément process. A micro-indentation testing system was used to INRIA Rocquencourt determine the compressive and biphasic mechanical prop- [email protected] erties of cartilage in the small joints of the mouse. A nonlinear optimization program employing a genetic algorithm for parameter estimation, combined with a biphasic finite MS41 element model of the micro-indentation test, was developed An Electrophysiological Approach to Gathering to obtain the biphasic, compressive material properties of Data Needed to Model the Gonadotropin-releasing articular cartilage. Hormone Neural Network

Farshid Guilak Gonadotropin-releasing hormone (GnRH) secreting neu- Duke University Medical Center rons form the ﬁnal common pathway for the central regula- [email protected] tion of fertility. This is accomplished by releasing GnRH in a frequency-modulated pattern to code downstream repro- Li Cao ductive activity. We use electrophysiological approaches to Department of Biomedical Engineering understand how individual GnRH neurons initiate, main- Duke University tain and terminate action potential ﬁring, how these cells [email protected] coordinate activity to produce distinct hormone pulses and how this activity is modulated by homeostatic and non- Inchan Youn homeostatic feedback. Department of Surgery Duke University Suzanne Moenter [email protected] Division of Endocrinology and Metabolism University of Virginia LS06 Abstracts 87

[email protected] Department of Mathematics [email protected]

MS41 Thomas Scammell Catastrophe Theory Model of Hyperthyroidism Department of Neurology Beth Israel Deaconess Medical Center Abstract not available at press time. [email protected] Sir Christopher Zeeman Warwick Mathematics Institute Cecilia Diniz Behn [email protected] Dept of Mathematics Boston University [email protected] MS42 Progress in Sleep Studies and Modeling MS42 Recent studies at the molecular, cellular, and systems level The Function of Sleep for Learning and Memory offer several candidate mechanisms by which sleep states may enhance learning, thereby serving an important cog- Experimental recordings show that hippocampal cells fire nitive function. We will outline the scope of these hypoth- in the same manner during REM sleep as during waking esized effects and some approaches to modeling them. We learning, supporting a strengthening of LTP, the building will also describe efforts to understand the dynamics of block for learning. Once the memory is consolidated, re- sleep-wake cyclicity, focusing on modeling and quantita- activation firing during REM reverses in a manner that tive analysis, especially dynamical systems and stochastic supports depotentiation, or weakening of those hippocam- modeling approaches. pal synapses encoding the memory. This finding is consistent with the idea that the hippocampus is an assembly Janet A. Best warehouse rather than permanent repository of complex Mathematical Biosciences Institute associative memories. Ohio State University [email protected] Gina Poe University of Michigan Dept of Anesthesiology MS42 [email protected] Modeling Learning and Forgetting in REM Sleep

In a computational modeling study, we investigate the re- MS43 versal of hippocampal cell activity in REM sleep from a fir- Support-vector Regression Approach for Predic- ing pattern that promotes synaptic strengthening (or learn- tion of Relative Lipid Accessibility in Membrane ing) to a pattern more consistent with synaptic weakening Proteins (or forgetting) during the course of memory consolidation. Numerical simulations using a biophysically accurate neu- Computational prediction of relative solvent accessibility ron model support our hypothesis that changes in the rel- for amino acid residues in soluble proteins plays an im- ative strengths or efficacies of the two synaptic pathways portant role in folding simulations, protein structure pre- targeting hippocampal cells cause this reversal. diction and functional annotations. Here, we present a novel protocol for prediction of relative lipid accessibility Victoria Booth in membrane domains. The new method is based on a University of Michigan linear, Support Vector Regression-based model that can Depts of Mathematics and Anesthesiology be used to efficiently and reliably estimate the parame- [email protected] ters in the model from a limited number of experimentally validated examples. The new method will be available to the community through the MINNOU web server MS42 (http://minnou.cchmc.org). Network Dynamics and Mechanisms of Transition in the Mouse Sleep-Wake Network Michael Wagner Cincinnati Children’s Research Foundation Behavioral states (wake, NREM sleep, and REM sleep) [email protected] and transitions between them are regulated by a network of neurons in the brainstem and hypothalamus. We Jarek Meller model network dynamics with a system of coupled Morris- Children’s Hospital Research Foundation Lecar-type relaxation oscillators. The fast-slow nature of University of Cincinnati, Cincinnati, OH the equations captures network behavior on multiple time [email protected] scales. We study mechanisms of transition in reduced models obtained using combinations of fast-slow and dominant scale techniques. We also discuss canard-like behavior in MS43 the equations. A Prototype of the Human-virus Interactome Re- source Emery Brown Harvard Univ/ MIT The large amounts of information generated by research [email protected] in systems biology makes it necessary for biologists to employ literature mining tools in their work. We describe the Nancy J. Kopell prototype of a digital library containing interactions be- Boston University tween human and viral proteins, which provides virologists 88 LS06 Abstracts

a tool to rapidly identify protein interactions responsible tational results are promising. for infection. The data is obtained by text mining the literature and searching proteomic databases, and needs to Rachana Jain be updated frequently. Biomedical Engineering University of Cincinnati Kurt Maly [email protected] Department of Computer Science Old Dominion University Michael Wagner [email protected] Cincinnati Children’s Research Foundation [email protected] Alex Pothen Old Dominion University Dept of Computer Science MS44 [email protected] A Stochastic Model of the Tubuloglomerular Feed- back Mechanism in a Rat Nephron M Zubair Department of Computer Science Experimental studies have demonstrated the presence of Old Dominion University self-sustained oscillations in proximal tubular pressure in [email protected] the nephrons of rats. The oscillations are regular in nor- motensive Sprague-Dawley rats, and highly irregular in spontaneously hypertensive rats. A dynamic model of Chris Osgood the renal autoregulation has been extended to include a Department of Biological Sciences stochastic differential equations model of one of the main Old Dominion University parameters that determines feedback gain. The model re- [email protected] produces fluctuations and irregularities in both period and amplitude that the former deterministic models failed to John Semmes describe. This approach assumes that the gain exhibits Molecular and Cell Biology spontaneous erratic variations, which can be explained by Eastern Virginia Medical School a variety of influences, which change over time (blood pres- [email protected] sure, hormone levels etc). Estimation of key parameters of the model reveals important differences in the autoregulation mechanisms between the two strains of rats. This MS43 insight was achieved by directly modeling the dynamic fea- A Two-level Architecture for Proteomic Networks tures of the feedback gain, normally modeled with a constant that is not capable of capturing time variations. We describe an approach to clustering protein-protein interaction networks in order to identify functional modules. Niels-Henrik Holstein-Rathlou Our algorithm accounts for the small-world nature of the Department of Medical Physiology network by dissecting the protein interaction network into University of Copenhagen a global subnetwork of hub proteins (connected to several niels@mfi.ku.dk clusters), and a local network consisting of cluster proteins. Emad Ramadan Kay-Pong Yip Department of Computer Science University of South Florida Old Dominion University [email protected] [email protected] Susanne Ditlevsen Alex Pothen University of Copenhagen Old Dominion University Department of Biostatistics Dept of Computer Science [email protected] [email protected] Donald Marsh Chris Osgood Brown University Department of Biological Sciences Donald [email protected] Old Dominion University [email protected] MS44 Theoretical Effects of Convection and Epithelial MS43 NO Production on NO Distribution in the Renal Peptide Mass Fingerprinting Via Machine Learn- Medullary Microcirculation ing: New Algorithms and Applications The objective of this study is to develop a three- Peptide Mass Fingerprinting is a process by which the iden- dimensional mathematical model of nitric oxide (NO) tity of a protein is determined by measuring the masses of transport in the renal medulla in order to investigate how its tryptic peptides (its fingerprint) via mass spectrome- NO affects blood distribution in the medulla. Using a one- try. The process requires a database search, whereby the unit model, that is, a single vasa recta embedded in intersti- experimentally determined spectrum is compared against tium and surrounded by nephron loops, we have found that theoretical spectra, which requires an appropriate metric. convection (i.e., blood flow per se) has negligible effects on We propose new algorithms to design metrics to increase NO concentration in pericytes, i.e., the smooth muscle- the specificity and sensitivity of the process. Early compu- like cells that impart contractile properties to descending vasa recta (DVR). However, the shear stress-mediated ef- LS06 Abstracts 89

fects of blood flow on NO generation rates, and therefore Department of Mathematics on NO concentrations, are predicted to be significant. We [email protected] are expanding the model to include all vessels and tubular segments based on one vascular bundle and surrounding Harold Layton tubules, to examine whether the heterogeneous structure DUKE UNIVERSITY of the medulla and the tubular production of NO result in [email protected] NO concentration differences between short and long vasa recta, respectively, thereby affecting blood flow distribution between the outer medullary vascular bundles and the MS44 peripheral capillaries. Nephron Initiated Interactions in a Renal Vascular Network Aurelie Edwards Tufts University Blood flow to single nephrons is governed by two nonlinear [email protected] regulators that operate in each nephron, and by nonlinear interactions between the two. One mechanism, tubuloglomerular feedback (TGF), senses NaCl concentration MS44 in tubular fluid, and the other senses intravascular pres- Dynamics in Coupled Nephrons may Contribute to sure. Both mechanisms are nonlinear, and each generates Irregular Flow Oscillations in Spontaneously Hy- a characteristic limit cycle oscillation. The two oscillations pertensive Rats interact in each nephron. In addition, TGF initiates a signal that is propagated retrograde down the nephron’s We used a bifurcation analysis of a mathematical model afferent arteriole, and the excitation spreads to adjacent of two nephrons, coupled through their tubuloglomerular nephrons, inducing synchronization of the TGF oscilla- feedback (TGF) systems, to investigate the role of cou- tions. Approximately 20 nephrons derive their blood sup- pling in the emergence of irregular tubular flow oscilla- plies from a single cortical radial artery, and all are within tions in spontaneously hypertensive rats (SHR). We an- range of signal propagation from each of the others. We alyzed a characteristic equation for a model of coupled have modeled this interaction, and have also included jux- nephrons having NaCl backleak; that characteristic equa- tamedullary nephrons, whose longer length produces TGF tion revealed a number of parameter regions having the oscillations with longer periods than those of the cortical potential for differing stable dynamic states. Numerical nephrons. There are two initial conclusions: 1) increasing simulations using the full model equations exhibit a num- coupling strength increases the amplitude of the TGF oscil- ber of differing dynamic behaviors in these regions. Some lation in individual nephrons, and 2) although the activity behaviors show marked irregularity and exhibit a degree of the longer nephrons can influence even the most distant of spectral complexity that is consistent with physiologic cortical nephrons, the entire nephron ensemble does not be- experiments in SHR. come fully synchronized at a single frequency at any level Anita T. Layton of coupling strength. The cortical nephrons can become Duke University syncrhonized at a single frequency even at fairly low cou- Department of Mathematics pling strength, and the juxtamedullary nephrons can be- [email protected] come synchronized at high coupling strength, and the two groups show evidence of interaction, but a single frequency is not achieved. Supported by NIH Grant EB003508. Leon Moore SUNY at Stony Brook Donald Marsh [email protected] Brown University Donald [email protected] Harold Layton DUKE UNIVERSITY [email protected] MS44 A Mathematical Model of Distal Convoluted Tubule (DCT): Determinants of Potassium Secre- MS44 tion Estimation of Parameters for Maximum Urine Concentrating Capability in a Mathematical Model This simulation of rat DCT includes luminal and peritubu- of the Rat Inner Medulla lar cell membrane transporters responsible for Na reabsorp- tion in exchange for K secretion. Early tubule conditions A nonlinear optimization technique was used to estimate are conducive to maximal K fluxes, while late conditions re- parameter sets that maximize the ratio of the urine osmo- quire K transport against an electrochemical gradient; the lality to the total NaCl active transport rate in a mathe- model identifies the transporters that optimize K secretion matical model of the urine concentrating mechanism. The under each condition. Tubule inlet volume flow and Na parameters were allowed to vary within ranges suggested by concentration both enhance K secretion; the model tubule physiologic experiments. A set of parameters that yielded identifies the relative importance of each factor. results close to reported experimental values was identified. Research supported by NIH grants DK-42091 and Alan M. Weinstein S06GM08102, and NSF grant DMS-0340654. Cornell University [email protected] Mariano Marcano University of Puerto Rico [email protected] MS45 Modeling Influenza Vaccination Using Minority Anita T. Layton Duke University 90 LS06 Abstracts

Games theory.

Seasonal epidemics of influenza remain a major global Alison Galvani health concern and a pandemic of influenza is expected Department of Epidemiology and Public Health imminently. One of the national health objectives of the Yale University School of Medicine United States is to increase the influenza vaccination cov- [email protected] erage in order to prevent or substantially reduce influenza epidemics. Vaccination is voluntary and the vaccine is effective for one season only; thus an individual needs to MS45 decide every year whether to vaccinate or not. Gener- Controlling Influenza Epidemics via Public Health ally, individuals are selfish as their sole interest is to avoid Vaccination Incentives getting infected, preferably without having to vaccinate. Here we address the question of whether selfish individu- Using a Minority Game model that describes the adaptive als can adapt their vaccination behavior to prevent severe dynamics of vaccination coverage for influenza in a pop- influenza epidemics or whether public health programs are ulation of non-communicating selfish individuals, we ask necessary. Inspired by Minority Games, we construct an if certain public health incentives could be used to help individual-level model and we analyze the adaptive dynam- prevent influenza epidemics. Specifically, we evaluate the ics of vaccination behavior for influenza in a population of potential effects of the two following incentives: 1) If the non-communicating selfish individuals. We find that most head of the family pays to get vaccinated then their fam- of the time influenza epidemics cannot be prevented by ily gets vaccinated for free; 2) If an individual pays to get vaccination, and occasionally severe epidemics occur even vaccinated then that individual will get free vaccinations without the introduction of pandemic strains. for a certain number of successive years. Vaccinating families would increase: the average prevalence, the variability Sally Blower in prevalence and the frequency of epidemics. However, Semel Institute of Neuroschience and Human Behavior we show that certain public health incentives that offer UCLA free vaccination could ameliorate influenza epidemics. We [email protected] show that it is possible to construct public health incentives that help the vaccination coverage to remain very close to Raffaele Vardavas, Romulus Breban the critical vaccination coverage with only small variability. Semel Institute for Neuroscience and Human Behavior We discuss public health implications. UCLA [email protected], [email protected] Sally Blower Semel Institute of Neuroschience and Human Behavior UCLA MS45 [email protected] Game Theory and the Developing World Raffaele Vardavas The principles of social justice and health as a human right Semel Institute for Neuroscience and Human Behavior in the developing world have been advocated as the main UCLA justification for health assistance from rich to poor coun- [email protected] tries. While we do not disagree with this, we argue that a strategy that emphasizes the shared benefit to rich and Romulus Breban poor countries would facilitate this process. We propose Semel Institute of Neuroschience and Human Behavior that the accomplishment of these challenging tasks should UCLA be viewed from the perspective of game theory, where the [email protected] interests of the parties (in this case rich and poor countries) overlap. As the world becomes increasingly integrated with globalization, economic development in resource-poor MS46 countries will increase the opportunities for richer countries Walking on Water to profit from investment in the developing world. Global health has political and international security implications We present the results of a combined experimental and for the developed world, as well. theoretical investigation of the hydrodynamics of water- walking creatures. We enumerate the many styles of hydro- Carlos Franco-Paredes dynamic propulsion at the free surface, and the resulting Division of Infectious Diseases distinctions form the basis of a dynamic classification of Emory University School of Medicine all water-walkers. We consider creatures spanning a broad [email protected] range of scales, from millimetric insects reliant on surface tension, to tail-walking dolphins. Accompanying adven- tures in biorobotics are described. MS45 Modeling Social Conflicts of Public Health David Hu Courant Institute, NYU Public health strategies that are optimal for the community [email protected] are not necessarily optimal for the individual. For example, if most of the community is vaccinated, it can be best for John Bush an individual to refuse vaccination. This way they receive Department of Mathematics the benefits of reduced disease prevalence while avoiding Massachusetts Institute of Technology anticipated adverse effects of the vaccine. Such conflicts [email protected] can undermine public health programs, and their mathematical analysis involves an interesting application of game LS06 Abstracts 91

MS46 mechanism. Here we discuss alternate ways of achieving ro- The Role of Bristled Wings in Tiny Insect Flight bust temperature compensation and explore the idea that evolution has optimized the interaction of several feedback The smallest flying insects often use ’clap and fling’ to aug- loops to produce an oscillator whose period is tightly reg- ment lift forces generated during flight. There is, however, ulated. an aerodynamic cost for this behavior. For low Reynolds number flight, very large drag forces are generated during Emery Conrad clap and fling. Another feature common to most tiny flying Virginia Polytechnic Institute and State University insects is wing ciliation. Using a porous media version of [email protected] the immersed boundary method, the effect of wing ciliation (i.e. wing bristles) on flight aerodynamics will be explored. MS47 Laura A. Miller Controlling the Period of Intracellular Clocks Department of Mathematics University of Utah The basic function of circadian ( 24-hour) clocks within [email protected] cells is to provide 24-hour timing of biological events. The period of the clocks is affected by genetic mutations, but is remarkably robust to changes in temperature. Several MS46 mathematical models and techniques will be presented to Computational Simulation of Metachronal Waves determine the period of cellular circadian clocks. These in Cilia mathematical theories of period regulations will be validated against experimental data. A simulation of the formation of metachronal waves in carpets of pulmonary cilia is presented. The cilia move Daniel Forger in a two-layer fluid model. The fluid layer adjacent to University of Michagan the cilia base is purely viscous while the tips of the cilia [email protected] move through a viscoelastic fluid. An overlapping fixed- moving grid formulation is employed to capture the effect of the cilia on the surrounding fluid. The 9+2 internal MS47 microtubule structure of an individual cilium is modeled Modeling Circadian Rhythms: Deterministic and using large-deflection, curved, finite-element beams. Real- Stochastic Approaches istic models of the forces exerted by dynein molecules are extracted from measurements of observed cilia shapes. The In most organisms the detailed molecular mechanism of possibility of formation of metachronal waves under differ- the circadian clock involves interlocked positive and neg- ent assumptions of boundary conditions is investigated and ative feedback loops. We studied deterministic models of shown to be dependent on the surrounding geometry. increasing complexity for the occurrence of autonomous circadian oscillations, for their entrainment by light-dark Sorin M. Mitran cycles, and their phase shifting by light pulses. Stochas- Dept. of Mathematics, Applied Math Prog. tic versions of these models indicate that the robustness University of North Carolina of circadian rhythms with respect to molecular noise is af- [email protected] fected upon entrainment by light-dark cycles, by the cooperativity in repression, the proximity from a bifurcation point, the rate of association of the inhibitory protein to MS46 the promoter of the clock gene, and the coupling between A Model of Force Generation in Motile Cells oscillating cells.

Directed migration of amoeboid cells is involved in pro- Didier Gonze cesses such as embryonic development, wound healing, and Unité de Chronobiologie Théorique, Université Libre de the metastasis of cancer. Migration entails force generation Bruxe within cells, and understanding how this force generation [email protected] is controlled in space and time to produce cellular motility is a major challenge. I present a continuum model of cell motility in which the active deformation of the cell re- MS47 sults from spatially-controlled remodeling of the cytoskele- System Biology Reveals an Opposite Role for Tau ton, and force is transmitted to the substrate via controlled in Circadian Rhythms adhesion sites. The passive cellular response is viscoelastic. Finite element simulations of this model reproduce cell Circadian rhythms are stable 24 hour physiologic cycles traction patterns that are observed experimentally. regulated by negative feedback loops. The tau mutation in casein kinase I (CKI?tau) causes a four hour shorting Magdalena A. Stolarska of rhythms and a decrease of kinase activity in vitro. It University of Minnesota - Mathematics is difficult to reconcile this loss of function with the cur- [email protected] rent model of circadian clock function. The Forger-Peskin model, a detailed quantitative model of the mammalian circadian clock, predicts the opposite, that CKI?tau must be MS47 a gain of function mutation. We have verified this counter- Mechanistic Temperature Compensation of the intuitive modeling prediction and find that CKI?tau pro- Circadian Clock duces a gain of function in cells These findings experimentally validate the systems biology approach and provide a One of the key features of the molecular mechanism un- remarkable example of how a specific mutation can be both derlying the circadian clock is its ability to robustly com- a loss and a gain of function depending on the substrate. pensate for changes in temperature over a range of 10 C or more, a feature that isnt typical of models of the clock David Virshup 92 LS06 Abstracts

Huntsman Cancer Institute and support mathematical and computational biology. University of Utah [email protected] Eric Marland, René Salinas Appalachian State University [email protected], [email protected] MS48 Problem-Based Learning: A Way to Motivate Un- dergraduates at the Math/Bio Interface MS49 Mitigating Immunodominance in Multi-Epitope Mathematics and statistics are essential to properly de- Tumor Vaccines by Polytopic Vaccination scribe dynamical phenomena, to construct experimental plans, and to predict general rules in the life sciences. The refractory nature of cancer to many standard thera- With this in mind, I teach a course in France taken by pies has led to substantial efforts to achieve immune con- more than 800 students annually. Students are divided trol. We describe a theory that elucidates the mechanism into small groups and special interactive exercises are built by which polytopic, or multi-site, vaccination mitigates im- to introduce them to the modeling process. I will present munodominance in therapeutic T-cell vaccines for cancer. some of the activities we have developed and how students By inducing a T-cell response to each cancer-associated epi- motivation has increased significantly. tope in a distinct lymph node, vaccine efficacy is increased and immunodominance is reduced. Our approach captures Sandrine Charles the dynamic characteristics between the T-cell receptors Université Claude Bernard Lyon 1 and tumor. Laboratory of Biometry and Evolutive Biology [email protected] Michael Deem Rice Unversity Dept. of Biomedical Eng. MS48 [email protected] The State of Mathematical Biology Training in the UK MS49 With researchers across the world showing a growing inter- Prediction of Treatment Outcome for Laser est in the education of mathematical biologists, in this talk Surgery of Prostate Cancer I examine and compare the training offered by institutions across the UK. In particular, I will discuss the mathemat- Temperature is usually used as the control variable in laser ical biology education at the undergraduate and postgrad- therapy, it is however not an effective measure of treatment uate level in both mathematics and biology departments. outcomes. We proposed models that predict cell damage I will look at the final career destination of these students and heat shock protein in the prostate tumor to charac- and investigate how the training prepares students for a terize effectiveness of the treatment and likelihood of can- career in mathematical biology research. cer recurrence. These models can optimize the therapy outcome by mitigating tumor recurrence and resistance to Christina Cobbold follow-up chemotherapy and radiation therapy due to HSP Department of Mathematics expression and insufficient injury. University of Glasgow [email protected] Yusheng Feng The University of Texas at Ausitn [email protected] MS48 Computational Tools for a Two-Course Calculus Jon Bass, M. Nichole Rylander, Kenneth Diller, J. Sequence for Biology Majors Tinsley Oden University of Texas at Austin The Department of Mathematics at Benedictine Univer- [email protected], [email protected], sity has begun to offer a rigorous two-semester calculus [email protected], [email protected] sequence for biology students. Two important course goals are the integration of mathematical and biological reasoning through the understanding of biological models and MS49 the development of skills to use appropriate computational Protein Wrapping as a Selectivity Switch in the software to analyze and solve biological problems. We dis- Pharmacological Oncokinome cuss how and why we use Excel, Derive, Berkeley Madonna, and MATLAB to achieve these goals. Kinases are central targets for drug-based treatments of cancer. Progress in drug development faces challenges due Timothy D. Comar to undesirable cross-reactivity and difficulties in modulat- Benedictine University ing selectivity. We present a structure-based predictor of [email protected] cross reactivity and validate it against affinity fingerprinting of the kinases and our own drug re-design geared at sharpening the inhibitory impact. The predictor compares MS48 patterns of packing defects and introduces a packing dis- BIO SIGMAA tance between kinases shown to be equivalent to the pharmacological distance. A new special interest group in the MAA. This talk will discuss the new SIGMAA, its direction, and a few upcom- Ariel Fernandes ing inaugural events. We will also have an open discussion Rice University on how the new SIGMAA can work with SMB to promote [email protected] LS06 Abstracts 93

MS49 MS50 Mathematical Modeling of Angiogenesis in Cancer Identifying Functional Constraints on the Quanti- Research tative Evolutionary Design of a Metabolic Circuit

Angiogenesis is critical for tumor growth. To understand We address the following questions for the well- mechanisms of angiogenesis, we have developed a mathe- characterized coupled redox cycles of NADPH and glu- matical model to simulate two-dimensional angiogenesis in tathione in human erythrocytes. Suppose that network the cornea, a commonly used tissue for testing efficacies topology and kinetic mechanisms are conserved, that muta- of angiogenic and antiangiogenic agents. One of the ad- tions can alter the values of any enzyme kinetic parameter vantages of the model is that results from numerical simu- over broad ranges, but only circuits that fulfill the perfor- lations can be compared directly with experimental data. mance specifications of the wild type are selected. Do the Specifically, the dose responses to bFGF, an angiogenic selected circuits share a well-defined design? What specific factor, predicted by the model are consistent with experi- functional requirements evolutionarily constrain the values mental observations. of each parameter? Fan Yuan Armindo J. Salvador Dept. of Bioengineering Centre for Neuroscience and Cell Biology Duke University The University of Coimbra [email protected] [email protected]

Michael Savageau MS50 Department of Biomedical Engineering Randomized Approximation Algorithms for Set The University of California, Davis Multicover Problems with Applications to Reverse [email protected] Engineering of Protein and Gene Networks

In this paper we investigate the computational complexi- MS50 ties of a combinatorial problem that arises in the reverse The Apparent First-order Kinetics of the Substrate engineering of protein and gene networks. Our contribu- Disappearance in Enzyme Digestion: A Theoretical tions are as follows: Investigation • We abstract a combinatorial version of the problem and observe that this is “equivalent” to the set multi- We theoretically investigate the kinetics for protein diges- cover problem when the “coverage” factor k is a function by mathematically formulating rate equations for two tion of the number of elements n of the universe. An proposed mechanisms namely the one by one and zipper important special case for our application is the case mechanisms. Our analysis shows that the kinetics of di- in which k = n − 1. gestion follows apparent ﬁrst-order kinetics irrespective of • the mechanism for low initial substrate concentration with We observe that the standard greedy algorithm pro- respect to the initial enzyme concentration. Also our reduces an approximation ratio of Ω(log n)evenifk is k n − c c> sults suggest new experimental protocol that could reveal “large”, i.e., = for some constant 0. information on the mechanism of digestion. • Let 1

drugs initially tested in human subjects, only 8 percent pany. Using simulation-based design optimization (SBDO) eventually make it to the bedside. The primary cause of methods, information gained from Clinical Trial Simulation drug failure in the clinic is the selection of an inappropri- (CTS) is expanded to not only identify the best design but ate dose and schedule. Modeling mathematically describes also the robustness of the design. Thus, more than one what the body does to administered drug (Pharmacoki- design is proposed that will provide a successful trial out- netics) and what the drug does to the body (Pharmacody- come. namics) to guide and provide rational/quantitative basis for dose regimen selection throughout drug development. Jonathan Monteleone DOV Pharmaceutical, Inc Nelson L. Jumbe Somerset, NJ Genentech Inc [email protected] [email protected] MS52 MS51 Interaction of Biological rhythms : Its Relevance, Case Studies of Innovative Problem Solving in by Means of Examples, for Physiology Therapeutic Protein Development Abstract not available at press time. Therapeutic proteins (MW ¿1000 Da), have unique pharmacokinetic (PK) and pharmacodynamic (PD) properties Jacques Belair compared to small molecules. Different approaches cur- University of Montreal rently being applied for the optimization of dosing in clin- Department of Mathematics ical development of therapeutic proteins include, (i) mech- [email protected] anistic PK/PD modeling to predict drug effects; (ii) nonlinear mixed effect modeling to assess variability and identify covariate effect on drug disposition; and (iii) using MS52 Monte Carlo simulation to guide strategic decision mak- Chronotherapy Strategies in Cancer: It’s About ing on fixed dosing-vs.-weight-based dosing for monoclonal Time antibodies. Cancer chemotherapy causes major cytotoxic stress on nor- Jian-Feng Lu, Amita Joshi, Bert Lum, Sara mal tissues. Chronotherapy takes advantage of the exis- Kenkare-Mitra tence of optimal treatment times; fast renewing tissues, Genentech, Inc both normal and tumoral, display a circadian rhythmicity SSF, CA in drug susceptibility. With a cell cycle model, we devise [email protected], [email protected], the best strategies for colorectal cancer treatment, taking [email protected], [email protected] into account toxicity on the hematopoietic system. We show how the best schedule depends on the interplay be- Nelson L. Jumbe tween the cell cycle kinetics, the circadian amplitude of Genentech Inc drug susceptibility and the treatment itself. [email protected] Samuel Bernard, Branka Cajavec, Hanspeter Herzel Humboldt University MS51 Berlin Germany [email protected], [email protected] Quantitative Structure-Pharmacokinetic Relation- berlin.de, [email protected] ships (QSPKR) using Bayesian Neural Networks

Where the number of molecular descriptors is typically MS52 greater than the number of tested compounds, Bayesian neural networks may provide predicted time-series data Effect of Noise on Cardiac Arrhythmias Associated that allow for PK modeling, data characterization, and pri- with Long-QT Syndrome mary parameter estimation, without the significant limita- Early afterdepolarizations (EADs) can induce cardiac ar- tions that accompany most other methods of in silico mod- rhythmias. In a mathematical model of ventricular cells, eling. Such capabilities hold the promise of reducing the we show that fluctuations generated by additive Gaussian failure rate of compounds in development, while providing white current noise or the stochastic opening and closing key insights into the molecular, physiological, and pharma- of ionic channels influence the genesis of EADs. Prolonged cological factors controlling drug dose-exposure-response repolarization was simulated by partially blocking a potas- relationships. sium current (IKs). The stochastic fluctuations induced Donald E. Mager EADs with patterns that depend on the noise amplitude. SUNY Buffalo The relevance to arrhythmias in patients with Long-QT Buffalo, NY syndrome will be discussed. dmager@buffalo.edu Michael Guevara McGill University MS51 Montreal Quebec Canada [email protected] Improving Clinical Trial Designs using Clinical Trial Simulation (CTS) Claudia Lerma The failure of a clinical trial to provide successful outcomes McGill Uiversity is a significant problem in drug development because failed Montreal Quebec Canada trials must be repeated at a considerable expense to a com- [email protected] LS06 Abstracts 95

Trine Krogh-Madsen Modeling McGill University [email protected] Directed migration of eukaryotic cells often relies on their ability to distinguish receptor-mediated signaling at dif- Leon Glass ferent subcellular locations, a phenomenon known as spa- McGill University tial sensing. We have analyzed, using mathematical mod- Department of Physiology els and live-cell imaging experiments, the sensitivity of [email protected] platelet-derived growth factor (PDGF) gradient sensing in fibroblasts. We demonstrate that PDGF detection is governed by mechanisms that are fundamentally distinct from MS52 those characterized in other chemotactic cells, with impli- Interactions of the Cell Cycle and Radiation Treat- cations for fibroblast chemotaxis during wound invasion. ment of Cancer Jason Haugh The determination of cancer treatment schedules with ra- North Carolina State University diotherapy is highly dependent on mathematical models of Department of Chemical & Biomolecular Engineering proliferation and the effect of radiation on cells. Although jason [email protected] much is known about the cell cycle, few models used in the study of radiotherapy take the cell cycle into account. MS53 We construct a model describing the dynamics of proliferating cells (highly sensitive to radiotherapy) and resting Intracellular Gradients and Microtubule Chemo- cells (less sensitive to radiotherapy), and examine the sig- taxis nificance of the cell cycle and its regulation on the effec- Microtubules are linear filaments of the intracellular cy- tiveness of radiotherapy. We find that the subpopulation toskeleton that serve to organize cytoplasmic components. of resting cells may contribute to failure in radiotherapy. A major question in understanding cytoplasmic organiza- This presentation relates to the talk given by T. Hillen tion is how the self-assembly of microtubules is controlled in the minisymposium ”Mathematical Modeling of Cancer spatially and temporally. We have found that intracellular Treatment”. chemical gradients could potentially play a significant role Ozden Yurtseven in microtubule organization and would be affected by the University of Alberta size and shape of the cell itself. Edmonton Alberta David J. Odde [email protected] University of Minnesota Department of Biomedical Engineering Gerda de Vries [email protected] University of Alberta Department of Mathematical & Statistical Sciences [email protected] MS53 Dynamics of Cell Adhesion: Mass-action Kinetics Thomas J. Hillen in the Presence of Long-range Interactions University of Alberta Department of Mathematical and Statistical Sciences A model is presented that explains why focal adhesions in [email protected] stationary or slowly moving cells tend to concentrate at cell periphery in high curvature regions. According to the theory, adhesions move in the direction opposite to contractile MS53 forces exerted on them by stress fibers. This translocation Finding the Center - How to Solve Simple Geome- to the periphery occurs by treadmilling with the speed pro- try Problems at the Cellular Scale portional to the diffusion coefficient of integrins, the key surface receptors mediating adhesion assembly. Fragments of fish pigment cells can form and center aggregates of pigment granules by dynein-motor-driven trans- Boris M. Slepchenko port along a self-organized radial array of microtubules University of Connecticut Health Center (MTs). I will present a quantitative model that de- Center for Cell Analysis and Modeling scribes pigment aggregation, MT-aster self-organization [email protected] and the subsequent centering of both structures. I will present analysis and simulations of a set of partial integro- differential equations describing the coupled granule-MT MS54 interaction that successfully explains much of the observed Biocalculus in the Community College: Transfer, beahviour and sheds light on role of polymer dynamics and Workforce, and Continuing Education polymer-motor interactions in cytoskeletal organization. A majority of students who successfully complete under- Eric N. Cytrynbaum graduate life science degrees fulfill their math requirements University of British Columbia at community colleges. To fully implement the national re- Department of Mathematics forms called for in recent reports, two-year colleges must be [email protected] included. In this talk, a successful biocalculus course developed for the community college population will be detailed. The course audience includes those going directly into in- MS53 dustry, those transferring to baccalaureate programs, and A Divergent Mechanism of Spatial Gradient Sens- those already in research working to obtain a quantitative ing Revealed through Quantitative Imaging and 96 LS06 Abstracts

perspective. that diﬀer drastically in size, structure, and content. Mike Martin Sebastian Schreiber Johnson County Community College College of William and Mary [email protected] [email protected]

MS54 MS55 Biocalculus: Reflecting the Needs of the Students The Evolution of Defence Portfolios in Integro- difference Models of There are three basic paths to teaching calculus to students of biology. The first is the course that emphasizes the stan- Some organisms maintain a battery of defensive strategies dard calculus topics and minimizes the special background against their exploiters, while others fail to employ a de- and interests of the students. The second is the course fence that seems obvious. We investigate the evolution of that emphasizes those aspects of calculus that mathemati- defence portfolios in a discrete-time model with a mutation cians have found useful when doing biomathematics. The kernel, resulting in a system of integro-difference equations. third is the course that emphasizes the needs of the stu- We introduce the concept of strategy-blocking, where one dents and minimizes some standard topics usually found in strategy prevents the appearance of another that would a calculus course. Here, the third path is described through be adaptive in its absence, and discuss why reed warblers examples and test material developed over 25 years at Mar- reject cuckoo eggs but not cuckoo chicks. quette University. In general, spreadsheets replace algebra, and data is the primary object of study, instead of func- Nicholas Britton tion and equation. This approach allows the development Department of Mathematical Sciences of all standard results while also providing a clear path to University of Bath courses in statistics. [email protected] Stephen J. Merrill Marquette University MS55 Dept of Math, Stats & Comp Sci Adaptive Speciation: Theory and Evolutionary Ex- [email protected] periments Understanding the origin of diversity is a fundamental MS54 problem in biology. According to traditional evolution- Calculus and Beyond ary theory, the process of diversification is a by-product of geographical separation. However, I will show that diversi- Calculus is an important tool for the biological sciences, fication as an adaptive response to biological interactions is and the development of targeted textbooks is a key ingre- also a plausible evolutionary process. I will describe mod- dient to motivating freshmen biology majors and demon- els for evolutionary branching based on the mathematical strate to them the importance of acquiring the means to framework of adaptive dynamics as well as ongoing efforts express biological processes in a formal and precise lan- to test our theory in evolving Escherichia coli populations. guage. Beyond calculus, modeling, stochastic processes, and statistical tools are important quantitative skills every Michael Doebeli biology student must acquire. This talk will present efforts Departments of Mathematics and Zoology in this direction by the author. UBC [email protected] Claudia Neuhauser University of Minnesota [email protected] MS55 The Evolution of Microbial Diversity in Spatially Homogeneous Environments Containing a Single MS54 Resource Biocalculus and Beyond: Getting Biology Majors at William and Mary Hooked on Mathematics and According to the competitive exclusion principle a simple Reeling Them In habitat, defined to be a spatially homogeneous environment that contains a single resource, can only ever support Like many campuses throughout the United States, one competitor. Contrary to this theoretical prediction a William and Mary has bought hook, line, and sinker into number of laboratory experiments of microbial evolution building curricular bridges between mathematics and biol- have found that diversity can evolve in simple habitats. ogy. As part of this initiative, I developed a two semester Using a system of non-local PDEs we test a hypothesis calculus sequence for the life sciences whose goals include that biochemical trade-offs of microbial metabolism play substitutability for the regular calculus sequence and in- an important role in the evolution of microbial diversity troducing biology majors to the excitement of modeling. I will share some of my harrowing tales of trying to navigate Ivana Gudelj between this interdisciplinary Sylla and Charybdis and my Department of Mathematical Sciences successes and failures of enticing students into higher level University of Bath mathematics courses. These higher level courses, in addi- [email protected] tion to the regular mathematical fare, include several at the interface of mathematics and biology. I will compare and contrast my experiences in teaching two of these courses, a MS55 sophomore introduction to mathematical biology and a ju- Evolution of Developmental Timing – Warming nior/senior co-taught seminar on metapopulation ecology, LS06 Abstracts 97

Climate and Phenological Change MS56 Design Principles for Phase Splitting Behavior of Cold blooded organisms develop nonlinearly with respect Coupled Cellular Oscillators to temperatures; with seasonal swings tend synchronizing developmental timing and conveying higher ﬁtness. Hamsters housed in constant light exhibit a phenomenon Persistence of species depends on whether adaptation of known as splitting, in which an animal’s single daily bout phenology can track rates of climate change. Our ap- of locomotor activity dissociates into two components that proach couples existing models of phenology and quantita- are about 12hr apart. Recent data show that this phe- tive genetic theory to predict how phenological parameters nomenon is due to reorganization of the cellular oscillators may evolve. Evolutionary trajectories are characterized in the SCN with its right and left halves oscillating in an- by rapid changes to create synchrony, followed by gradual tiphase. To better understand the splitting, we have ap- adaptation to parameters with marginal dynamic proper- plied mathematical reasoning to infer the essential design ties. principles of this phenomenon James Powell Premananda Indic Department of Mathematics and Statistics Department of Neurology Utah State University University of Massachusetts Medical School [email protected] [email protected]

Christina Cobbold Department of Mathematics MS56 University of Glasgow Suprachiasmatic Nucleus: A Primer for Mathe- [email protected] maticians The suprachiasmatic nucleus (SCN) in the anterior hy- MS56 pothalamus is a paired nucleus straddling the midline and Gates and Oscillators: A Network Model of the composed of 16,000 heterogeneous, densely-packed neu- Mammalian Circadian Clock rons. A wealth of data indicates that it is the site of the master circadian clock in mammals. Now we need to under- The mammalian circadian clock, in the suprachiasmatic stand how multiple single-cell circadian oscillators within nucleus has at least two anatomically and functionally dis- the SCN synchronize to each other and the environmen- tinct cellular constituents. Some cells respond rapidly upon tal light schedule to create an integrated tissue pacemaker receipt of direct retinal input but are not electrically rhyth- with coherent molecular and electrical rhythmicity mic while others have endogenous molecular oscillations, but do not immediately respond to photic input. Us- William Schwartz ing these two phenotypes, we have modeled maintenance Department of Neurology of phase coherence among autonomous cellular oscillators, University of Massachusetts Medical School showing that a common mechanism can account for both [email protected] free-running rhythms and entrainment. Nicholas Foley, Rae Silver MS57 Columbia University Cyton Theory: A Framework for Evaluating the [email protected], [email protected] Cellular Calculus of Signal Integration

Michael Antle How receptor-mediated signals are integrated simultane- Department of Psychology, University of Calgary ously by lymphocytes to control rates of both growth and Hotchkiss Brain Institute, University of Calgary death is a complex problem. We are developing a model of [email protected] the lymphocyte built on an internal mechanical unit called the cyton and show how it can explain and resolve signal integration problems using a cellular calculus. The devel- MS56 opment of a numerical solver allows the interplay between Synchrony Among Daily Oscillators in the Brain proliferation and survival to be extracted from CFSE and BrDU incorporation data. Speciﬁc brain areas act as circadian pacemakers required for daily rhythms in behavior and physiology. In vivo and Marian Turner in vitro, multiple circadian oscillators synchronize to each The alter and Eliza Hall Institute of Medical Research other to sustain near 24-h rhythms. Using long-duration [email protected] recording methods, we have begun to study signals required for coordinated activity. We ﬁnd that a neuropep- Carel van Gend tide (vasoactive intestinal polypeptide) plays a critical role Bioinformatics and Computational Biochemistry Group in entrainment among neurons within one pacemaker, the European Media Laboratory suprachiasmatic nucleus, which regulates daily rhythms in [email protected] locomotion. Philip D. Hodgkin Erik Herzog NHMRC Principal Research Fellow Department of Biology Walter and Eliza Hall Institute for Medical Research Washington University [email protected] [email protected] Edwin Hawkins The Walter and Eliza Hall Institute of Medical Research [email protected] 98 LS06 Abstracts

MS57 MS57 The Impact of Affinity on Proliferation and Death Quantifying Cell Turnover Using CFSE Data in the Immune Response The CFSE dilution assay is used to estimate the param- High affinity B-lymphocytes are critical for protection from eters determining cell division and death in vitro/in vivo. extracellular pathogens, such as bacteria and parasites. To For homogeneous cell populations, we consider the “Smith- understand the basis for positive selection of these cells, we Martin” model of cell turnover and analyze different tech- have investigated transgenic mice expressing B cell recep- niques for estimating its parameters. The CFSE data alone tors of varying affinity. Proliferation and death rates are allows to estimate only the duration of the division phase, estimated through a model-based analysis of time-series la- and in some cases the average division time can be deter- beling data (e.g., BrdU and Casp). These methods have mined using Gett-Hodgkin method. Additional measure- enabled us to elucidate how B cell fate is governed by its ments are required to estimate all model parameters. ability to bind antigen. Sergei S. Pilyugin Ashraf Khalil Department of Mathematics Department of Laboratory Medicine University of Florida Yale University School of Medicine [email protected]fl.edu [email protected] Vitaly V. Ganusov Uri Hershberg, Mark Shlomchik Theoretical Biology Section of Immunobiology, Department of Laboratory Utrecht University Medicine [email protected] Yale University School of Medicine [email protected], [email protected] Kaja Murali-Krishna Department of Immunology Shannon M. Anderson University of Washington Section of Immunobiology [email protected] Yale University School of Medicine [email protected] Rafi Ahmed Microbiology and Immunology Ann M. Haberman Emory University Department of Laboratory Medicine [email protected] Yale University School of Medicine [email protected] Rustom Antia Department of Biology Steven H. Kleinstein Emory University Departement of Computer Science [email protected] Princeton University [email protected] Rob De Boer Division of Theoretical Biology Yoram Louzoun Utrecht University Department of mathematics [email protected] Bar Ilan University [email protected] MS58 Optimum Scheduling of Countermeasures MS57 Elucidating Lymphocyte Development Using BrdU The use of mathematical models to automatically gener- Labeling ate optimal circadian adjustment schedules (CAS) includes computational challenges. CAS are necessary for individ- Immune responses involve many cell types, including B, T uals working night shifts or traveling rapidly across time and NK lymphocytes expressing a diversity of receptors for zones. CAS are used by NASA to help shuttle crew adapt foreign antigens and self-molecules. The dynamics of im- to shifts in the sleep wake cycle. An iterative technique mune cell repertoires, in particular their development, are developed to design CAS will be presented and compared highly complex and non-linear. Understanding the popu- to other methods, including model based predictive control lation dynamics which underlie lymphocyte development and the calculus of variation. is essential for elucidating the causes of various immune dysfunctions and cancers. The results of our studies com- Dennis Dean II bining combine modeling with BrdU data to address this Division of Sleep Medicine issue will be reported. Brigham and Women’s Hospital [email protected] Ramit Mehr, Gitit Shahaf Faculty of Life Sciences Elizabeth B. Klerman Bar-Ilan University Brigam and Women’s Hospital [email protected], [email protected] Harvard Medical School ebklerman@rics. bwh. harvard. edu

Daniel B. Forger III University of Michigan [email protected] LS06 Abstracts 99

MS58 Duke University The Use of Biomathematical Models Within Oper- [email protected] ational Fatigue Risk Management Systems

Biomathematical models of work-related fatigue are be- MS59 coming widely used in industrial, emergency response, and Modeling Immunity in the Lung to Bacterial and military operations. The inputs available for modeling Viral Pathogens vary in these diﬀerent settings, as does the information required by managers and commanders for decision-making. Abstract not available at press time. In addition, biomathematical models are being rapidly integrated into broader systems of operational risk manage- Simeone Marino ment. The practical components, considerations and com- Dept of Micro/Immuno plexities of diﬀerent fatigue risk management systems will University of Michigan be detailed. [email protected] Adam Fletcher Denise E. Kirschner Department of Behavioral Biology Univ of Michigan Med School Walter Reed Army Institute of Research Dept of Micro/Immuno [email protected] [email protected]

Katie J. Kandelaars Centre for Sleep Research, The University of South MS59 Australia : Parameter Identifiability and Statistical Inverse [email protected] Problems in Abstract not available at press time. MS58 Hulin Wu Applications of a Fatigue Model for Predicting University of Rochester and Managing the Consequences of Fatigue in the Department of Biostatistics and Computational Biology Transportation Industry [email protected] Abstract not available at press time. Steve Hursh MS60 Istitutes for Behavior Resources and Models for Directed Cell Movement in Fibre Net- Science Applications International Corporation works [email protected] Mesenchymal motion is a form of cellular movement that occurs in three-dimensions through tissues formed from fi- MS58 bre networks, for example the invasion of tumor metas- Identifying Two-process Performance Models using tases through collagen networks. The movement of cells is Limited Data guided by the directionality of the network and in addition, the network is degraded by proteases. I derive mathemat- Abstract not available at press time. ical models for mesenchymal motion in a timely varying network tissue. The models are based on transport equa- Peter Thompson tions and their drift-diffusion limits. It turns out that the Systems Technology, Inc. mean drift velocity is given by the mean orientation of the [email protected] tissue and the diffusion tensor is given by the variance- [email protected] covariance matrix of the tissue orientations. I will discuss relations to existing models and future applications. MS59 Thomas J. Hillen Stocastic Modeling of Experiments on Virus- University of Alberta stimulated Interferon Beta Induction in Single Hu- Department of Mathematical and Statistical Sciences man Dendritic Cells [email protected]

Abstract not available at press time. MS60 Jay Jayaprakash In Silico Mathematical Model of the Atherogenesis, Dept. of Physics and its Stability Analyzes Ohio State University [email protected] We construct a mathematical model of the early formation of an atherosclerotic lesion based on a simplification of Russell Ross paradigm. Study centres on the interplay MS59 between chemical and cellular species we employ a model Microsimulation Modeling of Spatial Reorganiza- of chemotaxis first given by E. F. Keller and Lee Segel and tion in Immunity present our model as a coupled system of non-linear reaction diffusion equations. We perform numerical simulations Abstract not available at press time. demonstrating that our model captures certain observed features of CVD. Tom Kepler Dept of Biostats and Bioinf Jay R. Walton 100 LS06 Abstracts

Department of Mathematics distinct phases to accomplish hypertrophy and hyperplasia Texas A&M in which they exhibit differing mechanical (stress/strain) [email protected] and transport (diffusion) processes. We describe a modeling frame for capturing these effects and discuss analytical Laura Ritter and simulation results for an example model. TexasA&MUniversity [email protected] Jay R. Walton Department of Mathematics Texas A&M Akif Ibragimov [email protected] Department of Mathematics and Statistics. Texas Tech University [email protected] Akif Ibragimov Department of Mathematics and Statistics. Texas Tech University Catherine McNeal [email protected] Department of Internal Medicine, Division of Cardiology Scott & White, Temple, TX 76508, USA [email protected] PP1 Transmembrane Protein Structure Determination MS60 Using Solid State NMR Chemotaxis Models and their Application to An- Nuclear Magnetic Resonance (NMR) is a technique for the giogenesis study of molecular structures. Solid state NMR (ssNMR) uses orientational constraints to build an atomic model of In the current talk the author will present some recent work the molecule, and has been successful in determining the on chemotaxis models and their application to angiogene- structures of membrane proteins such as ion channels. We sis, and possibly morphogenesis. discuss mathematical problems that arise when building a Brian Sleeman model with ssNMR data. As an illustration, we build a Leeds University model of the M2 transmembrane protein that is a proton England channel in the Influenza A Virus. [email protected] Richard Bertram Department of Mathematics MS60 Florida State University [email protected] Modeling the Role of Environmental Cues during Angiogenesis Jack Quine Angiogenesis is the growth of new capillaries and blood Department of Mathematics, Florida State University vessels from the existing vascular network. It is important [email protected] for wound healing and is a means by which tumors become vascularized. During angiogenesis endothelial cells prolif- Srisairam Achuthan erate and migrate to form new capillaries, a process that is Dept. of Mathematics, Florida State University orchestrated by environmental cues such a growth factors. [email protected] Approaches for modeling the role of environmental cues during angiogenesis will presented, along with numerical Tom Asbury methods that preserve fundamental features (eg. mass) of Institute of Molecular Biology (IMB), the biological system. Florida State University [email protected] Howard Levine Iowa State University [email protected] Jun Hu NIDDK, NIH [email protected] Michael Smiley Iowa State University Department of Mathematics Tim Cross [email protected] Dept. of Chemistry & NHMFL Florida State University [email protected] MS60 Traveling Wave Phenomena for System Modeling PP1 Hypertrophy and Hyperplasia in Soft Tissue Compound Selection in Toxicological Studies Using The growth of soft tissue in vivo often involves a com- Principal Component Analysis. plex interplay between various biochemical, genetic and mechanical processes. An important example of this inter- Several basic schemes and methods using simple statistics play is provided by growth and remodeling of the smooth and Principal component analysis are used in compound se- muscle cells (SMCs) within the medial layer of a large di- lection for toxicological studies. To illustrate the method, 5 ameter human artery. Growth of SMCs is accomplished biophysical properties are used for 71 compounds relevant via two different processes: growth in size of individual for hydrocarbon disposition and toxicity. A comparison be- cells (hypertrophy) and growth in the number of cells (hy- tween (1) a sample using the simple statistics and assess- perplasia). Through genetic expression, SMCs enter into ment by principal component analysis, and (2) sampling LS06 Abstracts 101

based on uniformity in the space of the ﬁrst few principal Dept. of Chemistry and BiochemiNIDDK, Nat. Inst. of components is examined. Health Bethesda MD Charles Smith, Gyoungjin Ahn, Jim Riviere [email protected] Biomathematics(Dept. of Statistics) N.C. State University Srisairam Achuthan [email protected], [email protected], Dept. of Mathematics, Florida State University jim [email protected] [email protected]

PP1 Jun Hu NIDDK, NIH Bacteria-Phage Co-Evolution As a Cause of Bacte- [email protected] rial Diversity

Parasites are believed to play a significant role in host di- Tim Cross versification, and there is an increasing body of experi- Dept. of Chemistry & NHMFL mental evidence supporting this hypothesis. In particular, Florida State University experimental studies of bacterial evolution in spatially ho- [email protected] mogeneous environments have shown that the introduction of a bacterial parasite (phage) into the system significantly increases bacterial diversity. We use systems of non-local PP1 PDEs describing bacteria-phage co-evolution in order to Pipath: An Optimized Algorithm for Generating identify ecological mechanisms that could be responsible Alpha-Helical Structures from Pisema Data for this increase in diversity. Solid-state NMR PISEMA experiments generate orienta- Sinan S. Arkin tion constraints which can be used to dervice a membrane Department of Mathematics protein’s atomic structure. We present here a new algo- Imperial College London rithm PIPATH that finds the most α-helical structure in [email protected] agreement with the PISEMA data. PIPATH uses techniques from graph theory to find an optimal assignment Ivana Gudelj and structure. The structure generated is typically quite Department of Mathematical Sciences close to the target structure and is a useful initial model University of Bath for subsequent refinement. [email protected] Richard Bertram Department of Mathematics Robert Beardmore Florida State University Department of Mathematics [email protected] Imperial College London [email protected] Jack Quine Department of Mathematics, Florida State University PP1 [email protected] Pipath: An Algorithm For Generating α-Helical Atomic Structures From Solid-State Nmr Data Srisairam Achuthan Dept. of Mathematics, Florida State University Solid-state NMR PISEMA experiments generate orienta- [email protected] tion constraints which can be used to determine a membrane protein’s atomic structure. We present a new al- Tom Asbury gorithm, PIPATH, that finds the most α-helical structure Institute of Molecular Biology (IMB), in agreement with the PISEMA data. PIPATH uses tech- Florida State University niques from graph theory to find an optimal assignment [email protected] and structure. The structure generated is typically quite close to the target structure and is a useful initial model Jun Hu for subsequent refinement NIDDK, NIH Richard Bertram [email protected] Department of Mathematics Florida State University Tim Cross [email protected] Dept. of Chemistry & NHMFL Florida State University Jack Quine [email protected] Department of Mathematics, Florida State University [email protected] PP1 Computational Study of Spatial Localization Ef- Thomas M. Asbury fects on Signaling Cascades Dynamics Institute of Molecular Biophysics Florida State University Transport phenomena and protein localization details are [email protected] often left aside in the design of quantitative models of cellular signaling pathways. However, there is increasing exper- micheal Chapman imental evidence showing that complex intracellular traffic 102 LS06 Abstracts

and differential spatial localization of members of a sig- objective is to characterize the alternative polyadenylation naling cascade occur in response to many signals. Models by mathematical modeling. neglecting these processes could miss significant features and lead to an incomplete understanding of the live sys- Bin Tian tem. In this study we used computer models to analyze Department of Biochemistry how spatial localization could affect the behavior in Sac- University of Medicine & Dentistry of New Jersey charomyces cerevisiae signaling pathways, with special em- [email protected] phasis put on the effects on stimuli response’s dynamics. The models show that spatial localization and transport Robert Miura rates could play a determinant role controlling signaling Department of Mathematical Sciences response profiles. New Jersey Institute of Technology [email protected] Marcelo Behar University of North Carolina Yiming Cheng [email protected] New Jersey Institute of Technology [email protected] PP1 Extravascular Burden of Carbon Monoxide (CO) PP1 During CO Exposure and Washout A System Equivalence Related To Dulac’s Exten- The extent of extravascular uptake of CO in CO poison- sion of Bendixson’s Negative Theorem For Planar ing has been debated. We developed a model of CO uptake Dynamical Systems and distribution which includes diffusion of CO from blood Bendixson’s Theorem [1] is useful in proving non-existence into tissues and binding of CO to myoglobin. After vali- of periodic orbits for planar systems dation against data from both short and long-term human CO exposures, additional experimental studies were simu- dx dy F x, y , G x, y lated and extravascular distributions of CO predicted. Ex- dt = ( ) dt = ( ) (1) travascular CO levels can change independently of blood carboxyhemoglobin level, and can transiently rise during in simply connected domain D, where F, G are continu- oxygen therapy. ously differentiable. From the work of Dulac [2] one sus- pects that system (1) has periodic solutions if and only if Eugene Bruce, Kinnera Erupaka, Margaret Bruce the more general system University of Kentucky [email protected], [email protected], [email protected] dx dy B x, y F x, y , B x, y G x, y dτ = ( ) ( ) dτ = ( ) ( ) (2)

PP1 does, which makes subcase (1) more tractable, when suit- The High-Throughput Development of High Affin- able non-zero B(x, y) which are can be found. Thus, ity Nucleic Acid Molecules for Targets: Complex Bendixson’s Theorem can be applied to system (2), where Selex: A Mathematical Model and Computer Sim- otherwise it is unfruitful in establishing non-existence of ulation Study periodic solutions for system (1). The object of this note is to give a simple proof justifying this Dulac-related pos- SELEX (Systematic Evolution of Ligands by EXponential) tulate of the equivalence of systems (1) and (2). is an experimental protocol to enrich target-binding ligands from a highly complex nucleic acid library by iterative ex- Charlie H. Cooke traction and amplification of target-bound ligands. In this Old Dominion University talk, we present mathematical model and computer algo- Department of Mathematics rithm for simulating SELEX experiments against complex [email protected] target mixtures (the complex SELEX). We also present simulation results such as the discovery of optimal experimental conditions under which the target-binding ligands PP1 are developed in high efficiency. Mathematical Modelling of Take-All Decline in Winter Wheat Chi-Kan Chen Applied Math Department Take-all disease of wheat is caused by the soil-borne fun- National Chung-Hsing University, Taiwan gus Gaeumannomyces graminis var. tritici (Ggt), which [email protected] infects the roots, crown, and basal stem of plants. The highest risk of take-all occurs when wheat is planted in consecutive years. Disease severity and yield loss can be PP1 substantial in second, third, and fourth wheat crops, with Prediction of Polyadenylation Sites of Mrna Using the worst take-all usually occurring in the third consecu- Support Vector Machine tive crop. Take-all becomes less severe, and yields usually increase, with the fifth or sixth successive wheat crop. It Messenger RNA polyadenylation is important in cellular is postulated that this occurs because of a natural increase processes, such as mRNA stability. Many human and in soil microorganisms antagonistic to the pathogen–a phe- mouse genes have multiple polyadenylation sites (poly(A) nomenon known as ”take-all decline,” which persists only sites) that lead to different functional transcripts. Biased so long as wheat is grown continuously. Using mathemati- alternative polyadenylation in human tissue suggests that cal modelling we test hypotheses about the mode of action the coordinates of similar poly(A) sites can be regulated. of the antagonist microorganisms. In this poster, the Support Vector Machine is used to predict the poly(A) sites based on the gene sequence. Our Nik J. Cunniffe LS06 Abstracts 103

Department of Plant Sciences Cornell University University of Cambridge [email protected] [email protected] Laura Jones Cornell University PP1 Department of Ecology and Evolutionary Biology Modeling Plasma Membrane Recruitment of Cy- [email protected] tosolic Signaling Proteins

We visualize the stimulated translocation of cytosolic sig- PP1 naling proteins to the plasma membrane in live B lym- The Combined Effect of Synaptic and Cellular Res- phocytes with multicolor confocal fluorescence microscopy. onance We use previously developed image processing algorithms to systematically quantify the time course of recruitment We derive a mathematical theory to explain the subthresh- and the spatial colocalization of signaling proteins with old behavior of a resonant cell when it is stimulated by crosslinked receptor. We describe these events with a a presynaptic cell via a resonant synapse. We demon- reaction-diffusion model and estimate relevant kinetic pa- strate how a cell combines the information contained in rameters for the translocation and the spatially localized the frequency dependant synaptic response with its own interaction between signaling proteins and crosslinked re- frequency dependant behavior. Our results show that the ceptor complexes. maximal response in the postsynaptic cell occurs at a frequency located between the preferred frequencies of the Raibatak Das synapse and cell. We show how one can tune the location University of British Columbia of the maximal response by changing the steepness of the Department of Mathematics synaptic response - frequency profile. [email protected] Amitabha K. Bose Daniel Coombs New Jersey Inst of Technology University of British Columbia Department of Mathematical Sciences [email protected] [email protected]

Farzan Nadim PP1 NJIT & Rutgers University A Secondary Mechanism for Cardiac Excitation [email protected] Propagation

It is well known that cardiac action potential propagation Jonathan Drover is possible due to intracellular coupling by gap junction New Jersey Institute of Technology channels. However, recent studies involving gap junction [email protected] deficient myocytes illustrate a complicated relationship between propagation velocity and the degree of gap junctional Vahid Tohidi coupling. This suggests that there might be a secondary Rutgers - Newark mechanism to ensure propagation success. Here, we ex- Dept of Biological Sciences plore a mechanism in which propagation is supported via [email protected] negative electric potentials in the narrow junctional cleft spaces between neighboring cells. PP1 Elizabeth Doman Modeling Immunological Synapse Formation and University of Utah Repolarization [email protected] T cells form an immunological synapse (IS) with antigen presenting cells (APC) bearing appropriate antigenic stim- PP1 uli. Experiments have shown that the IS can repolarize Rapid Evolution and Predator-Prey Dynamics to another APC having a higher antigenic load. We will with Variable Costs of Defense present FRAP experiments and extract the relevant biophysical parameters governing important processes of re- Predation may be a selective pressure that drives adap- ceptor diffusion and binding. Mechanisms of IS formation tation. We investigate the effects of genetic variability in and repolarization are discussed in the context of these pa- predator search efficiency and anti-predator defense on the rameter estimates. stability of a predator-prey system. In particular, we examine the impact of varied versus fixed costs of defense Daniel Coombs, Omer Dushek on population dynamics. We assume that the trade-off for University of British Columbia investment in defense is a decrease in fecundity and that, [email protected], [email protected] at low prey density, defense is without cost.

Stephen P. Ellner PP1 Cornell University A Diffusive Model of Ampa Receptor Trafficking in Dept. of Ecology and evolutionary Biology the Postsynaptic Membrane [email protected] AMPA receptor diffusion in the postsynaptic membrane is Rebecca Dore an essential mechanism for maintaining steady-state con- Department of Ecology and Evolutionary Biology centrations and affecting changes in AMPA receptor number during LTP/LTD. We propose a model of AMPA re- 104 LS06 Abstracts

ceptor trafficking that includes diffusion. We find that dif- [email protected], fusion is critical in maintaining constituitive receptor recy- [email protected] cling and a characteristic steady-state concentration profile. Our model provides the rate of relaxation to new steady-states set by the induction of LTP/LTD, which PP1 could be used for testing the model’s validity. Mathematical Improbability of Using Animals As Cams for Toxicology and Medical Research Berton A. Earnshaw, Paul Bressloff University of Utah Because of differences in gene regulation, gene networks [email protected], [email protected] and molecular mechanisms that have been revealed by evolutionary biology and molecular biology we now understand why even two very similar complex biological systems PP1 may respond differently to the same stimuli, and hence why Modeling and Simulation of Circadian Rhythm of one such complex system (for example, inbred strains of ro- Cyanobacteria by Phosphorylation of the Proteins dents) cannot reliably predict response for a different complex system (for example, humans). Current biomedical We are interested in the mechanism of circadian rhythm research is studying disease and drug response at the level of Cyanobacteria. We make a model by use of phosphory- where known differences between complex systems become lation of Kai C, which is surpressed or accelerated by Kai manifest, hence using nonhuman animals as causal analog- A and Kai B. By use of it, we investigate some important ical models for human disease and drug testing is a scien- properties of it theoretically. tifically invalid paradigm. This has profound implications for using animals in toxicology testing and as models for Isamu Ohnishi human disease. Hiroshima University isamu [email protected] Ray Greek Americans For Medical Advancement Kazumi Ebisu, Tatsuo Shibata [email protected] Dept. of Math. and Life Sci., Hiroshima University Niall Shanks [email protected], Wichita State University [email protected] [email protected]

PP1 PP1 The Role of Gap Junctions in a Neural Field Model Household Epidemiological Models With Clustered Resistant Individuals Recent research has shown a high density of gap junctions in areas of the brain that experience epileptic events. Gap The spatial structure of a population can have profound junctions allow direct electrical connections between neu- effects on the spread of epidemics. We are studying mod- rons and cause a diffusive-type effect on neuronal voltage els of populations partitioned into households, where infec- between surrounding cells. We extend an Amari-type neu- tion attempts occur both within and between households. ral field model by including a diffusion-like term to model Fixed spatially clustered resistant individuals are intro- gap junctions and investigate how this changes the dynam- duced into the population, which may actually increase the ics of spatially localised solutions. Numerical work shows rate of spread of an epidemic, although this may then be families of solutions are destroyed as the strength of the counteracted by clustering of infectious individuals within term modelling gap junctions increases. By placing restric- households as well, depending on their mobility. tive assumptions upon the firing rate function, analytical solutions are explored. Amanda Criner, David E. Hiebeler Dept of Mathematics and Statistics Amanda J. Elvin University of Maine Massey University amanda [email protected], [email protected] [email protected]

PP1 PP1 Ubm at Murray State University: Biomaps Multi-Host and Multi-Patch Models of Zoonotic Diseases The poster will provide insight into the format of the Bi- ology and Mathematics of Population Studies (BioMaPS) Abstract not available at press time. program started in January 2006. The mathematics and biology students work in teams with all involved in labora- Robert K. McCormack tory experience and mathematical modeling studies. Re- Department of mathematics and Statistics search questions, schedule of the program, successes and Texas Tech University challenges will be addressed. [email protected]

K. Renee Fister, Maeve L. McCarthy, Nicole Gerlanc, Chris Mecklin, Terry Derting, Howard Whiteman PP1 Murray State University Predator-Prey Equations with Prey Taxis: Discon- renee.fi[email protected], tinuous Travelling Waves [email protected], [email protected], Diffusion processes have been widely used to incorporate [email protected], spatial effects into predator–prey models. However, obser- LS06 Abstracts 105

vations report that predators tend to move towards prey. sleeves were reported few decades ago. However, the clini- Here we consider prey taxis as a primary spatial processes. cal significance of pulmonary vein was not found until re- Without diffusion process we show analytically that dis- cently. In patients with atrial fibrillation, it was found continuous wave solutions occur due to the singular bar- that ectopic foci existed in the pulmonary veins. There- rier. Introduced diffusion process is shown to make these fore, electrophysiological studies on pulmonary veins have discontinuous solutions smoothly. Fractional step meth- drawn a lot of attention recently. For example, in the ex- ods are used to demonstrate the nature of discontinuous periments of dogs and rabbits, besides the fast response travelling wave solutions. type of action potential, various pacemaker-like automatic- ities and triggered activities, e.g., early afterdepolariza- Thomas J. Hillen tions (EAD), delayed afterdepolarizations (DAD), have University of Alberta been demonstrated in the pulmonary veins sleeves under Department of Mathematical and Statistical Sciences physiological or pathophysiological situations (see [Hocini [email protected] et al., 2002], [Ehrlich et al., 2003], [Hojo et al., 2003], [Wang et al., 2003, 2005], [Po et al., 2005], [Chen et al., Mark Lewis 2000, 2001, 2002-a, 2002-b, 2002-c, 2003-a, 2003-b, 2003- University of Alberta, Canada c, 2004-a, 2004-b]). In this study, we have developed a [email protected] mathematical model which fits well the experiments for the canine PV. Using this model, we have successfully re- Jungmin Lee produced the experimentally observed frequency responses, university of alberta ischemia/hyperkalemia phenomena, pacemaker-like auto- [email protected] maticities, and triggered activities of PV sleeves. Also, as in the experimental results of [Po et al., 2005], our model APD restitution curve, an important index for the breakup PP1 of reentry, was very flat, which supports the hypothesis Kinetic Analysis of the Mechanism of the Cell Di- that reentrant PV tachycardia is a potential mechanism in vision Cycle in Caulobacter Crescentus initiating atrial fibrillation.

Progress in understanding cell cycle regulation in bacteria Juan-Ming Yuan, Chu-Pin Lo has lagged behind eukaryotes. Recently, however, the dis- Department of Applied Mathematics covery of two master regulator proteins, CtrA and GcrA Providence University in Caulobacter crescentus, allows us to propose a realis- [email protected], [email protected] tic molecular mechanism for cell cycle control in this bacterium. The mechanism is cast in a quantitative model Tzyy-Leng Horng revealing the temporal dynamics of the genes and proteins Department of Applied Mathematics, Feng Chia regulating the cell cycle in Caulobacter wild type cells as University, well as in several mutants. Taichung, Taiwan [email protected] John J. Tyson Virginia Poly Inst & St Univ Hsiang-Ning Luk Department of Biology Department of Anesthesiology, Taichung Veterans General [email protected] Hospital, Taichung, Taiwan [email protected] Shenghua Li Department of Biological Sciences Tsu-Juey Wu Virginia Polytechnic Institute and State University Cardiovascular Center, Taichung Veterans General [email protected] Hospital, Taichung, Taiwan Bruno Sobral [email protected] Virginia Bioinformatics Institute Virginia Polytechnic Institute and State University Hui-Chun Tien [email protected] Department of Applied Mathematics, Providence University, Paul Brazhnik Taichung, Taiwan Virginia Polytechnic Institute and State University [email protected] [email protected]

PP1 PP1 Maximizing Cell Free Ethanol Production A Realistic Mathematical Model of the Canine Pul- monary Veins Sleeves Ethanol production by yeast is limited by the toxic eﬀect of ethanol on the yeast and other factors. Removing the Pulmonary veins (PV) are the great vessels connected be- microorganisms from the ethanol production process (cell tween lung and left atrium and transport oxygenated blood free) has a number of advantages including greater process to the heart. There are 4 pulmonary veins in human be- ﬂexibility, more freedom to manipulate enzymes, and the ings. At the intersection between pulmonary veins and ability to easily optimize the production process by altering left atrium, there is a short segment covered with stri- enzyme levels. Models of the twelve enzymatic reactions ated cardiac muscle and called pulmonary vein sleeve. Due involved in the production of ethanol from glucose indicate to the complex intermingled muscle bundles, pulmonary the potential to increase ethanol production. vein sleeves display characteristic electrical behavior. The cellular electrophysiological properties of pulmonary vein Eric Marland, Andrew Madison 106 LS06 Abstracts

Appalachian State University PP1 [email protected], [email protected] Diffusion of High Energy Metabolites in Mdck Cells and Myocytes Eric Allain Department of Chemistry Effective diffusion of high energy metabolites in cells is dif- Appalachian State University ficult to quantify. We describe mathematical models that [email protected] use data for various experimental conditions (e.g., control, stress) to assess diffusion barriers and cell function require- Diana Dardugno, René Salinas ments. We test the hypothesis that local changes modulate Appalachian State University function without significant changes in global cytosolic con- [email protected], [email protected] centrations of ATP, ADP and inorganic phosphate. The model is described by a diffusion equation in two space dimensions and time; namely, C = ·DC+S, where C, D PP1 and S are vectors of concentrations, diffusion coefficients, Multistability in a Two-Cell Inhibitory Network and sources and sinks, respectively. with Synaptic Facilitation and T-Currents Raymond Mejia We explore the dynamics of two type-I neurons with T- Laboratory of Cardiac Energetics like currents coupled by reciprocal inhibition.This net- NHLBI, NIH work exhibits low-frequency tonic firing and chaotic fir- [email protected] ing states, and transitions to antiphase bursting at sufficient coupling strength, due to deinactivation of the T- Ronald Lynch currents. We show that synaptic facilitation promotes Departments of Physiology and Pharmacology bistability between bursting and tonic activity states, and University of Arizona may regularize chaotic firing. In addition, we analyze the [email protected] multi-stability between distinct bursting states using a one- dimensional Poincare map. PP1 Amitabha K. Bose Analysis of a Simple Model of Circadian Rhythm New Jersey Inst of Technology of Arabidopsis Thaliana Department of Mathematical Sciences [email protected] We are basically interested in circadian rhythm of Ara- bidopsis thaliana. We consider about a simple model equa- Farzan Nadim tion of two main components of mRNA’s and its productive NJIT & Rutgers University proteins. Under some simple conditions, it has a periodic [email protected] solution. We investigate properties of the system by use of the numerical simulation and stability analysis. Victor Matveev Isamu Ohnishi Dept. of Mathematical Sciences Hiroshima University New Jersey Institute of Technology isamu [email protected] [email protected] Kazumi Ebisu PP1 Dept. of Math. and Life Sci., Hiroshima University Stochastic Modeling of Periodic Mass Antibiotic [email protected] Treatments for Blinding Trachoma

We develop a stochastic mathematical model to simu- PP1 late ocular chlamydial infection in communities undergoing biannual mass antibiotic treatments. Model param- Perspectives on the Drift-Paradox Problem eters were fit using maximum likelihood estimation and Plankton are often considered passive tracers, but indi- data collected by our group from approximately 5000 chil- vidual plankton behavior may dominate at smaller scales. dren in Ethiopia. Simulations show infection is eliminated Using a hydrodynamic model to create various flows in in more villages with each subsequent treatment. However, an idealized channel with and without rooted plants, we in villages that still harbor infection, it returns to the same, model plankton behavior with an individual-based model quasi-stationary distribution. Overall, local elimination is and explore the extent to which vertical migration can af- feasible; subsequent Ethiopian data confirm these results. fect biological residence time in the channel. We gain ad- Kathryn J. Maxey ditional insight into simulation results by studying a two- F.I. Proctor Foundation dimensional advection-diffusion equation representing the University of California San Francisco system. [email protected] Stephen P. Ellner Cornell University Dr. Tom Lietman Dept. of Ecology and evolutionary Biology F.I. Proctor Foundation [email protected] University of California, San Francisco [email protected] Virginia B. Pasour Cornell University, Center for Applied Mathematics [email protected] LS06 Abstracts 107

Todd Cowen CAFO workers in the community, an influenza epidemic is Cornell University, Civil and Environmental Engineering amplified significantly when the infectivity of the virus is [email protected] low, so that the basic reproduction number in humans is just above 1. PP1 Roberto A. Saenz Random Networks Applied to Axon Growth University of Iowa Dept of Mathematics Many biological situations involve nanoscale fibers having [email protected] directions and shapes that appear random. We propose and study models at the microscale (fiber growth) and at Herbert Hethcote the macroscale (network scale) for the probability distri- University of Iowa bution of position and direction for curves in space. The [email protected] model is applied in two space dimensions, where the direction variable is an angle. Simulations are performed Greg Gray to apply the theory to axonal growth, and the results are Center for Emerging Infectious Diseases compared to data. University of Iowa Donald A. Drew [email protected] Rensselaer Polytech Institute Dept of Mathematical Sciences PP1 [email protected] The Throughput of the Transitional 3 B Cell Pool Accounts for Losses Between Transitional and Ma- Yanthe E. Pearson ture B Cells Rensselaer Polytechnic Institute [email protected] Our study aimed to examine the hypothesis that the transitional 3 (T3) peripheral B lymphocytes subset contains cells undergoing negative selection derived from both the PP1 emerging and mature B cells pools. To address these issues, A Dynamic Mechanism for Episodic Bursting we used mathematical models of population dynamics, and fit it to existing in vivo BrdU labeling data. We suggest Episodic bursting is a behavior found in pancreatic beta- that the throughput of the T3 B cells pool can account for cells as well as in hypothalamic GnRH neurons. One mech- most of the losses in B cells maturation. anism that has been proposed for beta-cells is based upon oscillations in glycolysis. Here we describe an alterna- David Allman tive method for episodic bursting based on the interaction Pathology and Laboratory Medicine, University of of two activity-dependant slow variables. The dynamics Pennsylvani of this episodic bursting mechanism can be understood [email protected] though an analysis of the fast subsystem, and its modulation by one or the other slow variable. Gitit Shahaf, Ramit Mehr Richard Bertram Faculty of Life Sciences Department of Mathematics Bar-Ilan University Florida State University [email protected], [email protected] [email protected] Michael Cancro Joseph A. Rhoads Pathology and Laboratory Medicine, University of Florida State University Pennsylvani Department of Mathematics [email protected] [email protected] PP1 PP1 A Model for Auxin Response in Arabidopsis Confined Animal Feeding Operations As Amplifiers Auxin is a ubiquitous plant hormone, involved during of Influenza nearly all growth stages and processes. Recently reported A pandemic could occur if a strain of influenza such as the results have elucidated the intracellular interactions that H5N1 avian influenza virus evolves so that it is transmis- underlie observed responses to auxin. We have developed sible among humans. Domestic species such as poultry or a differential equation model for auxin response in leaf cells swine could serve as local amplifiers for such a new strain of of Arabidopsis thaliana. Simulation runs produce concen- influenza. This amplification could be particularly strong tration profiles consistent with experimental results. The if the transmission among the birds or pigs is high because modelled cells can be coupled by auxin transport terms to they have very close contacts with each other in confined allow simulations of canalization in a field of cells. animal feeding operations (CAFOs). CAFO-workers form Marc R. Roussel a bridging population between the CAFO species and the University of Lethbridge, Canada general population. In order to assess the magnitude of Department of Chemistry this amplification, we formulate and analyze a mathemat- [email protected] ical model for the transmission dynamics of a novel influenza virus with three sequentially linked populations: the CAFO species, the CAFO workers and the rest of the Martin J. Slingerland local population. We show that for a given percentage of University of Lethbridge 108 LS06 Abstracts

[email protected] near DNA sequences through unequal crossover, gene con- version, etc. and orthogonalization through translocation and duplication can exist and speed up evolution as in PP1 the brain it is caused by Hebb rule and mutual inhibition Probability Density Approaches to Modeling Local by inhibitory cells building hierarchical knowledge struc- and Global Intracellular Calcium Dynamics tures with common characters. Here how wide range of components like not only gap genes, pair rule genes and Deterministic ODE models of intracellular calcium (Ca) segment polarity genes in Drosophila but also alpha helix, dynamics traditionally neglect the stochastic gating of Ca beta sheet, domains, motifs and modules can be concerned channels and important aspects of local Ca signaling. Here with memory compression is shown. we present a novel probability density approach to modeling Ca dynamics in cells that involves coupling ODEs for Mitsuo Takase, Michiko Takase the bulk cytosolic and ER [Ca] to advection-reaction equa- LINFOPS Inc. tions for the probability density of the [Ca] in cytosolic and [email protected], [email protected] lumenal domains associated with each channel and conditioned on channel state. PP1 Blair Williams, Marco A. Huertas, Gregory D. Smith A Spiny Branched Dendritic Tree and its Spatio- College of William and Mary temporal Filtering Properties [email protected], [email protected], [email protected] The dendrites of many nerve cells are complex branching structures that receive and process thousands of synaptic PP1 inputs from other neurons. Dendritic spines can be present A Model for the Actin Polymer Brownian Ratchet in large densities on the dendrites. They are equipped with excitable channels and loci for receiving excitatory Actin forms the cytoskeleton polymer allowing cells to synaptic input. Here we introduce a mathematical model maintain their shape and plays a role in motility. We ex- of a branched dendritic tree based upon a generalisation of tend models for polymer growth and decay in response to the analytically tractable Spike-Diffuse-Spike model. The diffusion of monomers in the cytoplasm. The model inactive membrane dynamics of spines are modelled by an cludes the interaction of the cell membrane with the lead- integrate-and-fire process. The spines are assumed to be ing edge of polymer growth, providing a model for the discretely distributed along a passive branched dendritic Brownian Ratchet. We also discuss the distribution of actin structure. We obtain a quasi-analytical solution using chain length consistent with the distribution of barbed and the sum-over-paths approach formulated by Abbott et al. pointed ends. (Biol. Cybern., 1991, vol.66, pp. 49-60). The model supports saltatory travelling wave propagation and wave scat- Donald A. Drew tering amongst branched dendritic trees. It is ideally suited Rensselaer Polytech Institute for the study of spatio-temporal filtering properties and Dept of Mathematical Sciences neural responses to different patterns of synaptic input. [email protected] Gabriel J. Lord Csilla Szabo Heriot-Watt University Rensselaer Polytechnic Institute [email protected] [email protected] Stephen Coombes University of Nottingham PP1 [email protected] Cancer Growth Model by Ecology with Mass Ad- vantage, Stability and Complete Deletion Condi- Yulia Timofeeva tions Using Mass Shape Information The University of Nottingham This cancer growth model consists of the proliferation rate [email protected] + − λ of cancer cells and with a weaker inhibition rate λin in λ− a cancer mass than out outside it by like immune. This PP1 means mass advantage. λ+ −λ− > 1 λ+ −λ− < 1 Results in out Bursting Without a Slow Variable in a Lactotroph λ+ (1)A higher gives more irregular mass shapes although Model. λ+ can not be easily evaluated because of other nonlinear effects. (2)The situation means the existence of stability We describe a model of the pituitary lactotroph. Low con- not to make a small mass. (3)The conditions to initiate a centration of dopamine activates an A-type K+ current. cancer mass and its complete deletion can be calculated. In the model this converts continuous spiking into a bursting pattern. Even though inactivation of this current is Mitsuo Takase necessary for bursting it is not a slow process. LINFOPS Inc. [email protected] Richard Bertram Department of Mathematics Florida State University PP1 [email protected] How Deeply Memory Compression Can Be Con- cerned with the Knowledge Structure in Genes Natalia Toporikova Like Hierarchical Neural Networks Department of Mathematics, Florida State University In genes memory compression caused by the mixing of [email protected] LS06 Abstracts 109

Joel Tabak, Marc Freeman deregulation in cancer cells in comparison with normal Dept of Biological Sciences ones. Florida State University [email protected], [email protected] Alejandra C. Ventura Int. Med.-Hematology/Oncology Medical School, University of Michigan PP1 [email protected] Multiscale Modeling to Combat Colorectal Cancer

The Integrative Biology consortium brings together com- PP1 puter scientists, modelers and experimentalists to build a Synchronization of Circadian Oscillators virtual tumour. We focus on colorectal cancer because of its social impact and the biological information available. Living beings adjust to the environment via synchro- The model, a hybrid cellular automaton, integrates pro- nization of their biological clocks to external drives like cesses at the subcellular, cellular and tissue levels. This the light-dark cycle and food availability patterns. Ex- multiscale approach enables us to investigate interactions perimental entrainment patterns in activity recordings of between such processes, to combine single-level experimen- house mice under light- and food- restriction are analyzed. tal data, and to test the system’s overall response to dif- Generic nonlinear entrainment behavior like phase locking, ferent treatments. phase slipping, or free running behavior are found in this http://www.integrativebiology.ox.ac.uk/ real biological circadian system. A model of coupled Van der Pol oscillators gives insight into the interaction of light- Jonathan Chapman and food- entrainable biological clocks in these mice. Mathematical Institute University of Oxford Jon Klaas [email protected] University of Alaska Fairbanks Dept of Physics Helen Byrne [email protected] University of Nottingham Centre for Mathematical Medicine Abel Bult-Ito [email protected] University of Alaska Fairbanks Dept of Biology Philip K. Maini ﬀ[email protected] Centre for Mathematical Biology University of Oxford Renate A. Wackerbauer [email protected] University of Alaska Fairbanks Department of Physics John King ﬀ[email protected] University of Nottingham School of Mathematical Science PP1 [email protected] Graphical Causal Reasoning Tool for Systems Bi- ology: C-Map Oliver Jensen Applied Mathematics Abstract available on-site at the conference. Supported University of Nottingham by NIH Cell Migration Consortium GM64346 (KJ) and [email protected] GM073180 (TE, KJ, GW)

Carina Edwards Gabriel Weinreb University of Oxford University of North Carolina at Chapel Hill Mathematical Institute [email protected] [email protected] PP1 Ingeborg Van Leeuwen University of Nottingham Reciprocity Relations Between Stokes Flows of Vis- Centre for Mathematical Medicine cous and Viscoelastic Fluids [email protected] Linear response theory of thermal fluctuations or driven motion of tracers provides a basis for exploring viscous, PP1 elastic and compressible properties of condensed matter. Mathematical Modeling of Cancer Progression: Applications range from atomic physics where the methods Understanding the Role of the RhoC Gtpase on-off were first developed, to recent applications in microrheol- Switch in Aggressive Phenotypes of Breast Cancer ogy. The emphasis here is on hydrodynamics and defor- mations of incompressible viscoelastic materials for vari- The most damaging change during cancer progression is ous geometries and driving conditions, as determined from the growth of metastases. RhoC GTPase was found to be known viscous behavior by straightforward prescriptions, crucial in that process in different cancers, particularly, in called reciprocity relations. Linear response theory can a highly aggressive form of breast cancer. RhoC is a molec- be formulated to yield an explicit correspondence in the ular switch cycling between inactive (GDP-bound) and ac- governing equations of Stokes flow between a viscous fluid tive (GTP-bound) states, tightly regulated by several reg- and any linear viscoelastic material, valid for an arbitrary ulatory proteins. We have developed a dual mathematical- prescribed source: of force, flow, displacement or stress; experimental approach to understand this cycle and its local or nonlocal; steady or oscillatory. Upon specification 110 LS06 Abstracts

of the geometry and source, non-inertial and inertial vis- PP1 cous Stokes solutions (known as Stokes singularities) trans- Pet: Parameter Estimation Toolkit fer to exact solutions for linear viscoelastic fluids. Reci- procity relations inform elasticity-induced contrasts in flow PET provides computational biologists with a graphical or displacement fields for prescribed forces or stresses; con- user interface for performing simulations and estimating versely, one may infer sources necessary to achieve identical parameters of mathematical models of reaction networks responses in viscous and viscoelastic materials. Two spe- describing gene, protein and metabolic interactions. PET cial Stokes singularities form the basis of microrheology is designed 1) to manage the potentially complicated rela- experiments and their interpretation: a prescribed veloc- tionships between a model and simulations of a large col- ity on a translating sphere and a stationary point source lection of experimental observations, 2) to assist the user of force. We revisit and amplify these examples as an il- in manual exploration of parameter space, and 3) to pro- lustration of the reciprocity relations, focusing on measur- vide support for automatic parameter estimation based on able non-inertial and inertial features. Next, we illustrate both global and local optimization algorithms. the generality in source type and geometry of this correspondence principle by analyzing the linear response for a John J. Tyson nonlocal, planar source of unsteady stress. Virginia Poly Inst & St Univ Department of Biology Ke Xu [email protected] University of North Carolina at Chapel Hill [email protected] Jason Zwolak Virginia Tech [email protected] PP1 Modeling Pattern Formation in Proteus Mirabilis Tom Panning Colonies Virginia Polytechnic Institute and State University When inoculated on a hard medium, a colony of the bac- [email protected] terium Proteus mirabilis can form concentric ring patterns of cell density. These patterns have been described as the Layne Watson result of periodic colony expansion due to collective move- Departments of Mathematics and Computer Science ment of swarmer cells differentiated from short-rod swim- Virginia Tech mer cells. However, recent experiments show that swimmer [email protected] cells can stream inward towards the center of the colony and suggest intercellular communication between cells. We develop a new model incorporating chemotaxis of swim- PP2 mers, and we present preliminary results on modeling ra- Modeling Aspects of Wound Closure: The Effects dial spoke-like patterns. of Tgf-β and Wound Geometry Chuan Xue Several aspects of dermal wound healing such as the role of University of Minnesota transforming growth factor beta (TGF-β) and the effects of [email protected] wound geometry are still not completely understood. Using a diffusion equation and a linear parameter, we reproduce some of the known features of the temporal evolution of the PP1 concentration of TGF-β and predict how the concentration Dual feedback mechanisms for p53 response to of TGF-β and the geometry of a wound influence the time DNA damage required for healing.

Recent experiments indicate that p53 responds to DNA Anthony Y. Aidoo, Kim Ward damage by series of pulses of constant amplitude and pe- Eastern Connecticut State University riod. The mechanism and function of these pulses are not [email protected], [email protected] yet fully understood. We explore the pulse-generating potentials of several dual-feedback schemes (containing posi- Joseph Manthey tive and negative feedback loops) and propose a mechanism Saint Joseph College whereby p53 pulses might coordinate cell cycle arrest and [email protected] apoptosis after DNA damages. John J. Tyson PP2 Virginia Poly Inst & St Univ Nonequilbrium Ising Bloch Transition in Forced Department of Biology Nonlocally Coupled Oscillators [email protected] We study phase and amplitude models for 2:1 resonant os- Paul Brazhnik cillators with nonlocal coupling and show that Ising-Bloch Virginia Polytechnic Institute and State University transition is dimmed by a regime with drifting frontal os- [email protected] cillators causing ﬂuctuations of propagation direction. We show that strong nonvariational eﬀects leading to pattern Tongli Zhang formation impede the oscillators drifting and enforce tran- Virginia Polytechnic Institute & State University sition to a Bloch front [email protected] Dorjsuren Battogtokh tokyo university [email protected] LS06 Abstracts 111

PP2 terneurons based on the work of Wang and Buzsaki [J. How Do the Basic Reproduction Ratio (R0) and Neurosci. 16:6402-6413, 1996]. We construct a phase Basic Depression Ratio (D0) Determine the Dy- model representation of the network, and show that this namics of a System with Many Host and Many model can give reasonably accurate quantitative informa- Directly Transmitted Pathogen Strains? tion, such as the size of basins of attraction and the maximum heterogeneity permissible in the inherent frequencies For an individual host strain, the pathogen strain with of the neurons before synchrony is lost. We show that pre- maximum R0 out-competes all others and survives alone dictions of existence and stability of phase-locked solutions with the host at a point equilibrium. For an individual from the two cell network carry over to N-cell networks, pathogen strain, the host strain with minimum D0 behaves either exactly or in the limit of large N. similarly. With many host and pathogen strains how do these criteria interact and is multi-strain co-existence pos- Hojjat Bazazzi sible? Furthermore, can stable cycles occur? We answer Bioengineering these questions using a combination of algebraic and nu- University of Maryland merical studies. [email protected]

Rachel E. Bennett Jeff Chadwick University of Liverpool Applied Mathematics [email protected] University of Waterloo [email protected] Roger G. Bowers The University of Liverpool Sue Ann Campbell [email protected] Department of Applied Mathematics University of Waterloo, Waterloo Ontario, Canada [email protected] PP2 The Evolution of Parasites in Spatially Structure Host Populations: An Approximate Analytical Ap- PP2 proach Using Integral Projection Models to Explore Evo- lution in Complex Environments: Soay Sheep As a We use approximation techniques and simulation to exam- Case Study ine the evolution of parasites in spatially structured populations. Trade-off shapes have important implications to The selection pressures an organism experiences over its the evolutionary outcome and we demonstrate that there is lifetime vary as a consequence of changes in its environ- an ES non-maximal dispersal rate. When parasite disper- ment (both biotic and abiotic) and its own physiology. In- sal and life-history evolves, we find that transmission and corporating these complexities into models is necessary in virulence are maximised. We contrast the results of the ap- order to make accurate predictions about the life history proximations and simulations and highlight the problems decisions an organism makes. Using the long term indi- that small selection gradients in spatially explicit popula- vidually structured Soay Sheep dataset; we show how the tions may cause. recently developed integral projection model may be used to develop such life history analyses. Mike Boots Sheffeld University Dylan Childs m.boots@sheffield.ac.uk Sheffeld University d.childs@sheffield.ac.uk PP2 Modeling Bacterial Populations Undergoing Acid PP2 Stress Phase-LikeTransition in Escaping Behaviors of Prey Flock Induced by a Predator’s Attack Recent outbreaks of acid resistant bacterial pathogens have raised safety concerns about a wide variety of acidified food A prey flock escaping from a predator was investigated products. A model was developed to aid in understanding by using molecular dynamics (MD) simulations in a two- acid sensitivity of bacterial cells within a bacterial cell cul- dimensional model. A phase-like transition was observed ture. Culture growth generating subpopulations of cells at a critical attack angle in the state of the flock moving in with varying acid resistance was simulated using Matlab response to predator’s attack. Contribution of the variables software. Data from the model may be used to develop such as attack speed and angle of the predator was further methods that ensure the safe production of a variety of discussed with regard to tactics for efficient prey capture acid and acidified foods. in the prey-predator relationships.

Fred Breidt Tae-Soo Chon USDA/ARS Div. of Biological Sciences North Carolina State University Pusan National University, Busan (Pusan), Republic of [email protected] Korea [email protected] PP2 Sang Hee Lee Synchronization and Multistability: Predictions Department of Entomology and Nematology from Phase Models University of Florida, Ft. Lauderdale We consider a model for a network of hippocampal in- [email protected] 112 LS06 Abstracts

PP2 calculus students. Determining Environmental Conditions for the Successful in-Vitro Maturation of Mammalian Timothy D. Comar Oocytes Benedictine University [email protected] Harvesting of immature oocytes (eggs) and successful maturation in the laboratory would be a significant break- through in the field of assisted reproduction. Success is PP2 believed to depend on the ability to mimic the nutritional Mathematical Models of Glucose, Insulin and Free environment that pertains within the body in the ovarian Fatty Acid Metabolism in Juveniles Having Irreg- follicle surrounding the oocyte, which is difficult to deter- ular Exercise Regimens mine experimentally. We describe mathematical modelling using experimental data that is aimed at increasing our Hepatic glucose regulation has been notoriously difficult understanding of the in-vivo and in-vitro oocyte environ- to study in vivo due to the liver’s role in hundreds of si- ments. multaneous metabolic processes. A theoretical mathematical model is proposed examining insulin secretion, insulin Yvonne Stokes sensitivity, endogenous glucose, free fatty acids and aero- School of Mathematical Sciences bic exercise in the early development of visceral adiposity. The University of Adelaide Employing deterministic, dynamic and stochastic elements, [email protected] the model elucidates metabolic syndrome pathogenesis lon- gitudinally. Model results are validated using U.S. juvenile Michelle Lane and adult obesity and diabetes prevalence results. Department of Obstetrics and Gynaecology Charles H. Darby The University of Adelaide North Carolina State University [email protected] [email protected]

Alys Clark, Stephen Cox Jim Riviere School of Mathematical Sciences Biomathematics(Dept. of Statistics) The University of Adelaide N.C. State University [email protected], [email protected] jim [email protected]

Jeremy Thompson Charles E. Smith Department of Obstetrics and Gynaecology North carolina state univ. The University of Adelaide [email protected] [email protected]

PP2 PP2 Net Reproductive Value and Graph Reduction Patterns on Growing Square Domains Via Mode with Applications to Control of Invasive Species Interactions Matrix models are widely used tool for demographic anal- We consider reaction-diffusion systems on growing square ysis of age and stage structured biological populations. domains with Neumann boundary conditions (NBC). We Dynamic properties of the model can be summarized by study transitions between two types of squares and tran- the net reproductive value (R0). Here we introduce a new sitions between squares and stripes using mode interac- R D T 2 method to calculate and analyze 0 directly from the life tions for bifurcation problems with 4 + symmetry (hid- cycle graph. We show, with examples, how our method of den symmetries) and the symmetry constraint imposed by analysis of the R0 can be used in the design of strategies NBC. We obtained surprising results: the transition from for invasive species and conservation. squares to stripes in NBC can go through time periodic states, and there are differences between periodic bound- Tomas De-Camino-Beck ary conditions and NBC problems. University of Alberta [email protected] Martin Golubitsky, Adela Comanici University of Houston [email protected], [email protected] Mark Lewis University of Alberta, Canada [email protected] PP2 Biocalculus: Interdisciplinary Course Development PP2 and Validation The Effect of Life-Stage Breakdown on Basins of Benedictine University now offers a two-semester calculus Attraction sequence for majors in the biological sciences. A new text- book and lab manual for this course is currently being de- A stage-structured model of two competing species has veloped by a team of mathematicians and biologists from been shown to exhibit multiple attractors for a variety Benedictine University. We will discuss the content choices of parameter values. Previous work has been done on and how this interdisciplinary team functions. We will computing the basins of attraction using initial conditions also present preliminary data indicating that the biocal- where only the oldest life-stage of each species is present. culus students demonstrate at least the same conceptual Here we consider the impact on these basins of attraction of understanding and computational skills as the traditional splitting the initial conditions between multiple life-stages, LS06 Abstracts 113

while keeping the total population size ﬁxed. [email protected]

Jeﬀ Edmunds Raluca Eftimie University of Mary Washington University of Alberta, Edmonton, Canada [email protected] [email protected]

PP2 Gerda de Vries Biomechanical Modelling of Colonic Crypt Fission University of Alberta Department of Mathematical & Statistical Sciences Colorectal cancer is initiated by unregulated cell division in [email protected] the epithelium of the small pits (crypts) that line the colon. The crypt then deforms and divides a number of times leading to a polyp or adenoma. We examine the initiation PP2 of crypt fission using a biomechanical model incorporating Towards a General Stability Theory of Population both intercellular forces and the forces generated by cell Dynamical Models attachment to and movement along the basal lamina. We propose a generalized model for foodchains of arbitrary Carina Edwards length and foodwebs to study the stability properties of the University of Oxford equilibrium state where all species coexist. Sudden changes Mathematical Institute in the dynamics (bifurcations) can occur when parameters [email protected] are varied. The main advantage of the generalized model is that its stability can be analysed without specifying the Jonathan Chapman interaction functions between species. We discuss the im- Mathematical Institute pact of the specific shape of the functional response on the University of Oxford stability properties. [email protected] Wolfgang Ebenhoeh ICBM, University of Oldenburg, Germany PP2 [email protected] Do Albatrosses Really Perform Levy Flights When Foraging? Thilo Gross Fachbreich Physik We examine the hypothesis that wandering albatrosses Universität Potsdam (Diomedea exulans) undergo Lévy flights when searching [email protected] for food. Lévy flights are random walks whose step lengths come from probability distributions that have infinite vari- Ulrike Feudel ance. Lévy flights have no typical scale, and so have been University of Oldenburg interpreted as comprising an efficient foraging strategy. We ICBM, Theoretical Physics/Complex Systems re-analyse the original temporal flying/floating data that [email protected] were used to infer Lévy flights, and use state-space models to examine recent spatio-temporal data from satellite- tracked birds. PP2 Predicting Protein Production from Codon Usage Nick Watkins, Mervyn Freeman, Richard Phillips, Patterns: Merging Population Genetics & Protein Andrew M. Edwards Translation British Antarctic Survey [email protected], [email protected], [email protected], I demonstrate how the pattern of codon usage within a gene [email protected] can be used to predict protein production rates. Using a population genetics model, I formalize the relationship between the adaptation of a sequence to nonsense errors, PP2 its expression level, and its probability of fixation. I vali- A Hyperbolic Model for Animal Group Formation date the approach using several hundred yeast genes. My and Activity Patterns predictions are probabilistic in nature and coincide with independently measured values. The social interactions between organisms that form groups are governed by three types of forces: attraction, Michael A. Gilchrist repulsion and alignment. I will present a nonlocal hyper- University of Tennessee bolic model that takes into consideration all these social Dept. of Ecology & Evolutionary Biology forces to study group formation. Linear analysis and nu- [email protected] merical simulations are used to explore the behavior of the model, and reveal a wide range of spatial patterns. These patterns can be related to the daily activities of animal PP2 groups, such as foraging and traveling. Effect of Spatial Inhomogeneities on the Tubu- loglomerular Feedback System Frithjof Lutscher University of Ottawa We use a simple mathematical model of rat thick ascend- fl[email protected] ing limb (TAL) to investigate the effects of tubular non- constant transport rate of chloride and inner radius on Mark Lewis TGF-mediated oscillations. Mathematical models have in- University of Alberta, Canada dicated that these regular oscillations arise from a bifurcation: if feedback loop gain is sufficiently large and if the 114 LS06 Abstracts

delay in TGF signal transmission is sufficiently long, then host a level of protection through reduced transmission of the stable state of the system is a regular oscillation and the HTP. The model raises questions about persistence of not a time-independent steady state. In addition, exper- diseases through interactions with others, and also the sta- iments have shown that the TGF system in hypertensive bilising effects of VTPs on dynamical systems in a biolog- rats may exhibit irregular oscillations. These oscillations ical control context. appear to have characteristic of deterministic chaos. The mathematical model previously devised by the group has Ed Jones predicted that irregular oscillations may arise from cou- Sheffield University pling of nephrons with sufficiently different bifurcation pa- bop03eoj@sheffield.ac.uk rameters. As a consequence of the new mathematical results, TAL inhomogeneities may have an remarkable impact on the TGF-mediated oscillations. In particular ir- PP2 regular oscillations resembling those reported by experi- A Function to Predict Sleep and Wake Patterns mentalists, may arise from a bifurcation, not necessarily Using Social and Circadian Factors through nephrons coupling. This research was supported in part by NIH grant DK-42091, and by National Science Recent literature suggests bio-mathematical models of Foundation under Agreement No. 0112050. Co-authors: work-related fatigue could be improved by accounting for Leon Moore, Harold Layton social factors impacting on sleep and recovery. Currently, accuracy of existing models in operational environments Paula Grajdeanu is limited in certain applications. An alternate model ac- Mathematical Biosciences Institute counting for such factors has been developed. Initial vali- [email protected] dations have been performed using operational data. Pa- rameter stability has also been investigated using Monte Carlo simulation analysis. The development and initial PP2 validations of this model will be discussed. Mathematical Modeling of Plastron Respiration in Ticks (Acari: Ixodidae) Jillian Dorrian Centre for Sleep Research Ticks are blood-feeding arthropods that are well known University of South Australia for their survivability. Although ticks are terrestrial or- [email protected] ganisms, they can survive extended periods of submergence under water as for example after heavy rainfall or flooding. Adam Fletcher A plastron is a physical gill consisting of a thin layer of air Department of Behavioral Biology trapped by hydrophobic hairs or other cuticular projec- Walter Reed Army Institute of Research tions. Hence a plastron is an alternate respiration system [email protected] that can absorb oxygen from water. The complex spiracular plates of ticks have been postulated to serve as plas- Katie J. Kandelaars trons but until now, this has not been verified. In this Centre for Sleep Research, The University of South study, we confirm the existence of plastron respiration in Australia the dog tick Dermacentor variabilis. Adult dog ticks can [email protected] survive submergence in water for over two weeks. Wetting the spiracular plate with alcohol, thereby debilitating any potential plastron function lowered survival to less than PP2 three days. Biomathematical studies currently in progress Einstein Relation Approach to Protein Folding Dy- are modeling the efficiency of the spiracular plate as a plas- namics tron. We have developed a mathematical model to predict survivability of submerged ticks under water. This model We propose a protein folding simulation approach based requires determination of a suite of physical and biologi- on energy type partition and Einstein Relations for con- cal parameters including volume of the air film contained strained movements as the important key for understand- within the spiracular plate, the plastron air/water inter- ing of protein shape change dynamics. Lagrange methods face area and the oxygen consumption and biomass of the ensure that the simultaneous minimization of two or more submerged tick. It is hoped that this model can be success- energy forms is describable in terms of the free energies, fully used in the future to predict underwater survivabil- gradients or forces. Interesting point is that a structural ity of other species of ticks which show both interspecific free energy gradient exactly balances an electrical ensemble and intergeneric morphological variation in spiracular plate gradient leading to an infinite mobility. structure. This study provides the first example of plastron respiration in the Ixodidae. Yeona Kang Dept. of Applied mathematics and Statistics Matt Heimann, Bach Q. Ha Stonybrook University Truman State University [email protected] [email protected], [email protected] Charles Fortmann StonyBrook University at New york PP2 Applied mathematics and Statistics Ecological Interference and the Persistence of Ver- [email protected] tically Transmitted Parasites

A model that allows a virulent vertically transmitted para- PP2 site (VTP) to be maintained in a system containing a host A Reduced Diﬀerential Model for Cardiac Action and a horizontally transmitted parasite (HTP) is analysed. The method of persistence relies on the VTP oﬀering the LS06 Abstracts 115

Potentials [email protected]

A differential model for cardiac action potentials with only ten state variables is proposed for 0D or 3D electromechan- PP2 ical simulations of the heart. Three variables describe the Graph-theoretic Models of the Human Hsp70 AT- membrane potential, the main ionic currents and two oth- Pase Domain ers, the Na+/Ca2+ exchangers and Na+/K+ pumps. The remaining seven variables describe the subcellular Ca2+ In this work we represent the Human Hsp70 ATPase do- dynamics. Simulations of action potentials of pacemaker, main by mathematical graphs. Graphical invariants are atrial, ventricular and Purkinje fiber cells are similar to calculated for each model generating corresponding numer- those obtained with more complex models. ical data. The graph-theoretic models coupled with data mining tools inherently combine primary sequential infor- Sorine Michel mation, structural information and amino acid motif recog- INRIA nition. Previous work by the author shows that graphical FRANCE invariants such as those associated with efficient computer [email protected] network designs can also be indicative of protein and nucleic acid structures. These findings initiate a similar study Djabella Karima of the HSp70 molecular chaperone. INRIA Rocquencourt. BP 105. 78153 Le Chesnay Cedex France Celia McIntosh [email protected] Biological Sciences East Tennessee State University [email protected] PP2 Network Environ Analysis Daniel Lamb Mathematics Network environ analysis (NEA) uses network representa- East Tennessee State University tion of ecological systems to identify and quantify impor- [email protected] tant ecosystem properties such as dominance of indirect effects, network amplification, network homogenization and Rhydon Jackson network synergism. These properties provide new insights Information and Computer Science into system level behavior of ecological networks. Using East Tennessee State University NEA, objects can be studied as part of a connected sys- [email protected] tem which is a fundamentally different way of investigating ecosystems. This gives a quantitative foundation to the widely held perception of the interconnectedness of nature. Debra J. Knisley East Tennessee State University Caner Kazanci [email protected] Department of Mathematics and Faculty of Engineering University of Georgia [email protected] PP2 Does Cannibalism Stabilize a Population?

Bernard Patten, Stuart Whipple Cannibalism occurs in a variety of taxa in nature. Forms of Institute of Ecology cannibalism can include consumption of eggs by larvae or University of Georgia adults and predation on smaller individuals by larger ones. [email protected], [email protected] Sometimes cannibalism occurs without discrimination of kin. Whatever competitive advantage this confers must PP2 be visible at the population level. We consider settings in which cannibalism is beneficial to a population. Mathematical Modeling of Tumor Spheroid Growth Glenn W. Ledder University of Nebraska Multicellular tumor spheroids are made of three layers with Dept of Mathematics different mechanical properties, i.e. proliferating outer [email protected] layer, quiescent middle zone, and necrotic zone. Helm- linger et al (1997)’s experiment showed that tumor growth can be regulated by stress and that mechanical proper- PP2 ties of the outer gel, such as stiffness, can inhibit tumor Dynamics of a Multistage Circadian System growth in vitro. Using the cell-based model on the proliferating zone, continuum model on other regions, and Tissues throughout the body exhibit circadian rhythms, reaction-diffusion model for nutrients on whole domain, I forming a multi-oscillatory system whose disruption results investigate the stress effect on tumor growth. in jet lag. Our simulations of a multistage circadian system reveal the flexibility and stability inherent in a multistage Yangjin Kim system, as well as potential pitfalls. The modeling predicts School of Mathematics that jet lag is most severe following an eastward change of University of Minnesota 5-8 time zones due to prolonged desynchrony of the system [email protected] caused by the antidromic reentrainment of some but not all components. Hans G. Othmer University of Minnesota Hava Siegelmann Department of Mathematics University of Massachusetts Amherst 116 LS06 Abstracts

[email protected] St. Olaf College [email protected] Tanya Leise Amherst College Alan M. Hastings [email protected] UC Davis [email protected] PP2 Networks of Three-Identical Coupled Systems PP2 Modeling Functional Consequences of Amino Acid We consider networks of three-identical coupled systems of Replacements in Proteins ODE’s, where which system has at most two couplings. We show that there are 34 distinct networks of three-identical A computational mutagenesis methodology based on data systems, at most double coupled, as opposed to only two obtained from a multibody statistical contact potential such two-identical coupled systems of ODE’s. We also show generates both scalar residual score and vector residual that, remarkably, transitions from a synchonous equilib- proﬁle characterizations for every single-site mutant of a rium that can occur are determined by the coupling struc- protein. With a focus on mutants for which experimen- ture of the network. tal activity data is available, the residual scores enable a clear elucidation of the structure-function relationship in a Martin Golubitsky protein. Additionally, the residual proﬁles lead to accurate University of Houston inferential models of mutant protein biochemical activity [email protected] relative to wild type.

Maria Leite Majid Masso, Iosif Vaisman Purdue University George Mason University Department of Mathematics [email protected], [email protected] [email protected] PP2 PP2 A Note on Science, Mathematics, and Applied Invasions, Range Limits, and Coexistence in Rivers Mathematics

Spatial patterns of community composition and species re- Science is that human activity devoted to the search for placement in rivers emerge from complex interplays of hy- the very explanation for (i.e., for the truth about) some drological, geochemical, biological, and ecological factors. particular naturally occurring phenomenon. The Scien- While these processes are well understood locally, a mecha- tific Method is a six-stage model-building process, one nistic basis for large-scale emerging patterns is lacking. We which mimes the biological process by which first genetic, study invasion speeds, range limits, and spatially-mediated then neuronal, systems have been used to construct intra- coexistence in reaction-advection-diffusion equations for corporeal models for ensuring survival. We investigate two competitors in heterogeneous environments. We show whether mathematics (pure; then applied) is either nec- that emergent patterns have plausible spatial scales, given essary or sufficient for Science, but must answer negatively parameter estimates for certain algae (periphyton). each question. Frithjof Lutscher G Arthur Mihram, Danielle Mihram University of Ottawa Univ of Southern California fl[email protected] , [email protected]

Edward McCauley PP2 University of Calgary [email protected] Linked Selected and Neutral Loci in a Heteroge- neous Environment

Mark Lewis We analyze a system of ODEs modeling allele frequencies University of Alberta, Canada at two linked genomic loci, one selected and one neutral, [email protected] in an environment consisting of two habitats with divergent selection. We use geometric singular perturbation theory and formal expansions to describe the dynamics and PP2 asymptotic behavior of the system. One conclusion is that Protecting Mobile Fish: Results from Diffusion marker-selected locus associations will not generally per- Models sist long enough to allow inference of dynamics and recent history at the selected locus from the state of the marker Persistence of fish populations is a key goal of many marine locus. protected areas. I introduce a PDE model of a population which has all ages of fish moving and which has a partially Bryan Wood protected habitat. The minimum reserve size necessary for Georgetown University species to persist is found for a variety of parameters and [email protected] boundary conditions (including periodic). These results are compared to models where only the juveniles disperse. Judith R. Miller Urmila Malvadkar Georgetown University Department of Mathematics, Statistics, and Computer Department of Mathematics Science [email protected] LS06 Abstracts 117

PP2 technique called the Discrete Wavelet Transform is em- Chemotaxis in Fluid Flows ployed to capture only the relevant features of the sensor array dynamics. Three families of wavelets are evaluated We study the distribution of microorganisms represented using three statistical and neural network classifiers (K- as self-propelled particles, in a fluid medium. The particles nearest neighbor, backpropagation, and RBF neural net- are transported by the flow and, in addition, they swim in works) for three odor samples (bacteria , coffee and co- the direction of the gradient of an external (chemical) field. las). The experimental results show promising classifica- We show that the combined effect of chaotic mixing and tion improvements when compared to conventional steady- chemotaxis leads to aggregation of particles on a complex state classification. Thus, higher classification accuracy manifold. We discuss the properties of the aggregates and and speed are obtained by using transient-feature compres- efficiency of chemotaxis in flows with fluctuating chemical sion with Wavelet decomposition. concentrations. Ekachai Phaisangittisagul Zoltan Neufeld North Carolina State University University College Dublin Ake [email protected] [email protected] PP2 PP2 A New Approache to Identify Binding Sites Three New R’s: Random Walks, Riordan Arrays, and RNA We have developed a novel approach to identify protein binding sites by analyzing triangulated protein surface rep- We use an algebraic and combinatorial technique to count resentation. Atom-atom interactions are derived based on two classes of random walks. It is interesting that cer- interactions of neighboring surface elements using line-of- tain subsets of the walks are counted by the numbers sight intersection test. Atoms are, then, converted into 1,1,1,2,4,8,17,37, .... These numbers are commonly called nodes in a edge-weighted graph. The nodes are further an- the RNA numbers and they also count RNA secondary alyzed using a cluster algorithm. Current implementation structures of a specified length. A bijection is constructed can identify the ion binding site of calix-4-arene and the between the set of RNA structures of a given length and a nucleotide binding site of human Ras. subset of random walks of a given length and height. Randy Zauhar Asamoah Nkwanta Department of Chemistry & Bioc Morgan State University University of the Sciences in Philadelphia [email protected] [email protected]

Michael Bruist PP2 Department of Chemistry & Biochemistry Inferring Causal Subnetworks Using Point Process University of the Sciences in Philadelphia Models [email protected] If one could measure simultaneously and individually the spiking activity of all neurons in a neural network, fitting a Niny Rao network model to the data might reveal causal connections Department of Chemistry & Bioc among the neurons. However, connections from unmea- Univeristy of the Sciences in Philadelphia sured neurons could create the illusion of causal influence [email protected] among the measured neurons. We have developed a framework that addresses effects from unmeasured neurons in PP2 order to reveal causal influence among the measured neurons. The approach exploits predictions from a point pro- Intra-Genomic Conflict and Evolution of Gene Si- cess model of the relationship between neuron spikes and lencing external variables such as a stimulus. The resulting anal- Using a model of early genome evolution, we investigate ysis can be potentially applied to a large range of exper- the hypothesis that gene silencing originally evolved as a iments where the spikes of multiple neurons are recorded mechanism to protect genomes from transposable elements simultaneously. (TEs). We show that pressure from TE replication creates Duane Nykamp weak selection in favor of TE silencers and we explore vari- University of Minnesota ous aspects of the selective dynamics. We show that cycles School of Mathematics of TE activity readily develop if TEs occasionally escape [email protected] from silencing, due to an “arms race” between TEs and TE silencers.

PP2 John McDonald School of Biology On Using Wavelets for Transient Feature Selection Georgia Institute of Technology in Odor Detection [email protected] The performance of electronic olfaction devices is highly dependent on the quality of input signals that represent Paul Schliekelman the sensors response. These units collect information about Department of Statistics the odors they are assessing using an array of 15 or more University of Georgia gas sensors. Consequently, these devices have a high- [email protected] dimensional input feature space which makes odor clas- siﬁcation diﬃcult. Here a multiresolutional approximation 118 LS06 Abstracts

PP2 model will aid in enhancing safety for acidified food pro- Single-Occupancy Binding In Simple Bounded and duction. Unbounded Systems Althea M. Smith The number of substrate molecules that can bind to the North Carolina State University active site of an enzyme at one time is constrained. This [email protected] poster presents boundary conditions corresponding to the constraint of single occupancy binding. Two simple mod- Fred Breidt els of substrate molecules diffusing to a single occupancy USDA/ARS site are considered. When the diffusive time scale is much North Carolina State University shorter than the time scale for entering the single occu- [email protected] pancy site, the dynamics of binding are accurately described by simple approximations. Sharon R. Lubkin North Carolina State Univ Mark F. Schumaker Department of Biomathematics Department of Mathematics [email protected] Washington State University [email protected] PP2 PP2 Reverse Correlation and Network Architecture Haart and the Epidemic of Hiv+ End Stage Renal Reverse-time Correlation (RTC) measurements gives the Disease average response dynamics of individual neurons within a recurrent neuronal network. The resulting RTC function The number of patients with HIV infection and end stage provides specific information about the nature of the recur- renal disease (ESRD) continues to rise. To assess the im- rent network connections, and in particular, the strength of pact of antiretroviral therapy on the progression of patients inhibition. We present a set of models that uncover and ex- with AIDS to the development of end stage renal disease, plain the connection between RTC functions and network we developed a mathematical model of HIV infection in architecture. the ESRD population using available population data. The model was then used to evaluate recent data and to project Louis Tao the prevalence of HIV ESRD through 2020. Department of Mathematical Sciences New Jersey Institute of Technology Elissa J. Schwartz [email protected] Department of Mathematics Harvey Mudd College [email protected] PP2 Distributed and Parallel Algorithms in the Life Sci- Lynda Szczech ences Division of Nephrology Duke University Medical Center This presentation discusses the mathematical framework [email protected] to allow distributed or parallel simulation of biological systems. Both stocastic and deterministic cases are outlined. Michael Ross It is expected that large-scale/ high detail computational Division of Nephrology simulation of cells, tissues and organs of the human body Mount Sinai Medical Center will speed up the development of new medical devices and [email protected] treatment protocols. The lung-heart system is used as an example of how distributed/parallel simulation algorithms Mary Klotman can be successfully deployed. Division of Infectious Diseases Yosef G. Tirat-Gefen Mount Sinai Medical Center Senior Member IEEE Computer Society [email protected] and IEEE Engineering in Medicine and Biology Society [email protected] Jonathan Winston, Paul Klotman Division of Nephrology Mount Sinai Medical Center PP2 [email protected], [email protected] A Computational Model for Motor Pattern Switch- ing Between Taste-Induced Ingestion and Rejection Oromotor Behaviors PP2 Mechanistic Model of Escherichia Coli Cell Death We present a computational model for activity patterns under Acidic Conditions similar to taste-induced ingestion (licking) and rejection (gaping) generated in the brainstem. Single-compartment, By processing acidified vegetable products, e.g. pickles, conductance-based models are used for individual neurons; there is risk of contamination by microbial pathogen such cells within the network are coupled through mutual inhi- as Escherichia coli. We have developed a mechanistic bition. Using geometric dynamical systems methods, we mathematical model which can be used to understand the describe conditions under which a single network config- mechanism behind the killing of these deadly bacteria. Our uration can produce both activity patterns. The analysis model predicts that killing of E. coli is due to the low lev- predicts that prolonged inhibition of some neurons may be els of intracellular pH. The continued development of this LS06 Abstracts 119

an important component responsible for this switch. transmissibility and extinction thresholds, when recover is included. We then extend the reproduction processes of David Terman hosts and infection to include proportions of global inter- Dept. of Math/MBI actions. Thus, providing intermediate structures between Ohio State University the local and mean-field. The evolutionary dynamics of [email protected] host-parasite interactions within this intermediate case is then discussed. Joseph Travers Dept. of Oral Biology Steven D. Webb Ohio State University Sheffield University [email protected] S.D.Webb@Sheffield.ac.uk

Sharmila Venugopal PP2 Neuroscience Graduate Program Ohio State University A Mathematical Model of U Wave in Electrocar- [email protected] diogram U wave was first observed by Einthoven and defined as PP2 the waveform occurred immediately after T wave and before P wave. With more clinic implications, U wave can Numerical Simulation Methods for Tissue Morpho- be observed in various pathological conditions, such as hy- genesis pokalemia, cardiac ischemia etc. Interestingly, the origin Morphogenesis is concerned with shape formations of tis- of the U wave in ECG is still not certain. Previously, we sues, organs and bodies and is of fundamental importance demonstrated volatile anesthetics could suppress delayed to developmental biology and tissue engineering research. after depolarizations and triggered activity in canine ven- To study the mechanisms of epithelial-mesenchymal tissue tricular preparations. Recently, we have documented that interactions (e.g. branching morphogenesis) in terms of ge- volatile anesthetics reversibly suppress U wave in clinical ometry and mechanical force, a two-phase Newtonian fluid patients. A mathematical model of U wave will be pre- model is proposed and solved numerically using the im- sented. mersed interface method (IIM). Jump conditions are nec- J.-J Cao essary to employ the second-order accurate finite differ- Dept. of Applied Math. ence scheme in the immersed interface method. Interfa- Providence University cial jump conditions for kinematic variables (velocity and [email protected] pressure) are derived for the case where the two phases may have unequal viscosity coefficients. Our results of the jump conditions match well with existing results in the Hsiang-Ning Luk literature where the viscosity coefficients are equal across Department of Anesthesiology, Taichung Veterans General the interface. I will illustrate the local Cartesian coordi- Hospital, Taichung, Taiwan nates transformation techniques used in the derivations of [email protected] both the jump conditions for the fluid equations and the finite difference scheme for the IIM. The interface between Chu-Pin Lo the two phases is chosen to be represented implicitly using Department of Applied Mathematics zero level sets. The implementation of the two-phase fluid Providence University solver in both 2D and 3D geometry coupled with the level [email protected] set method for moving interface problems is not trivial. I will show some preliminary simulation results for modeling H.-C. Tien tissue morphogenesis using our efficient numerical solver. Dept. of Applied Math. Providence University Zhilin Li [email protected] Department of Mathematics North Carolina State University Juan-Ming Yuan [email protected] Department of Applied Mathematics Providence University Xiaohai Wan [email protected] North Carolina State University [email protected] PP2 Sharon R. Lubkin Computer Modeling of Perlecan Regulation on North Carolina State Univ Growth Factor Binding to Vascular Surface Department of Biomathematics [email protected] Certain molecules in blood circulation such as perlecan/heparan sulfate play an important role in regulating cancer growth and cardiovascular disease development, the PP2 real mechanism, however, is still under investigation. We When Does Spatial Structure Matter? Sir Models propose a convection-diffusion-reaction model for simulat- Between the Local and Mean Field ing the process of perlecan regulation. An explicit-implicit splitting technique is applied to solve the coupled nonlin- We extend pair-wise spatial SI models to elucidate the ef- ear system of equations, where the chemical reaction is fects of recovery and waning immunity. We demonstrate a handled by the explicit Runge-Kutta method, while the loss of limit cycle behaviour, and an increase in the critical 120 LS06 Abstracts

convection-diﬀusion process is treated implicitly. Wensheng Shen, Jun Zhang University of Kentucky Department of Computer Science [email protected], [email protected]