42 LS08 Abstracts

IP0 plasticity, whereas a breakdown in traﬃcking appears to be Public Lecture: Reinventing the Sacred: Science, a contributory factor to a number of neurodegenerative dis- Faith and Complexity eases associated with memory loss including Alzheimer’s.

I propose to discuss three topics. Several alternative the- ories and experimental work bear on the origin of molecu- Paul C. Bressloff lar reproduction (here we at least think we know what we University of Utah are talking about). Second, we discuss agency, the capac- Department of Mathematics ity of organisms to act on their own behalf, hence doing bressloff@math.utah.edu (here molecular reproduction causes value to enter the biosphere). Third, I discuss the evolution of the biosphere by Darwinian preadaptations, which, I believe, is partially IP2 beyond natural law. On the first topic I will discuss the Magnetic Resonance Elastography classical view that life must be based on template repli- cated DNA, RNA or their cousins, the RNA world, the Many disease processes such as cancer cause profound membrane-cell first world, my own work on the emergence changes in the mechanical properties of tissues, yet none of collectively autocatalytic sets of organic molecules and of the conventional medical imaging techniques such as polymers, experimental evidence for collectively autocat- CT, MRI, and ultrasound are capable of delineating this alytic sets of DNA and peptide sequences, and our own and property. Magnetic Resonance Elastography (MRE) is an other workers’ evidence that random peptides fold, at least emerging diagnostic imaging technology that uses a special to molten globules, hence may well have catalytic activity. MRI technique to image propagating acoustic shear waves The study of emergent phenomena such as the emergence in tissue. Inversion algorithms are used to process the wave of molecular reproduction in collectively autocatalytic sets images to generate quantitative maps of tissue mechanical is an area of current mathematical research. On the second properties such as stiffness, viscosity, and anisotropy. Sev- topic I will discuss the tentative definition that a minimum eral clinical applications of MRE are now well-established, molecular autonomous agent is a self reproducing molec- while others await the development of more effective inver- ular system that also does at least one thermodynamic sion algorithms. work cycle. Work cycles are necessarily non-equilibrium, Richard L. Ehman so agency is non-equilibrium, and in life links exergonic Department of Radiology and endergonic processes. More, work is the constrained Mayo Clinic release of energy into a few degrees of freedom. But it typi- [email protected] cally takes work to construct those very constraints. Some- thing new enters physics here - propagating organization of process where work constructs constraints on the release IP3 of energy, the resulting work does many things including Title Not Available at Time of Publication constructing more constraints on the release of energy until a cycle of these processes closes on itself and a cell builds Abstract not available at time of publication. a rough copy of itself. We have no theory for propagating organization of process. Moreover, maximal work cycle Claire J. Tomlin efficiency is adiabatic, infinitely slow. Agents would re- University of California, Berkeley produce infinitely slowly. I suggest instead that cells may [email protected] maximize work per unit time hence power per unit fuel. On the third topic I will discuss Darwinian preadaptations in the biosphere, human economy and culture and try to IP4 show that these cannot be prestated, let alone predicted. Modeling and Inference of Transcriptional Regula- Then if a natural law is a compact description of the regu- tory Networks larities of a process, these aspects of evolution appear to be partially beyond natural law, and perhaps are not math- Living systems are manifestations of their underlying com- ematizable. In their place is a ceaseless creativity where, I plex dynamical networks of molecular interactions. A hope, we can find a sharable, fully natural, sacred. paramount problem is to understand how functional cellular behavior and interaction with the cell’s environment Stuart Kauffman is mediated by these complex molecular systems. Recent Director of Institute for Biocomplexity and Informatics advances in measurement technologies allow us to inter- at Santa Fe Institute rogate biological systems and collect massive amounts of skauff[email protected] heterogeneous information under a variety of experimental conditions. Integrating this information and constructing predictive models of system behavior are the central goals IP1 of systems biology. I will discuss our efforts focused on the Protein Trafficking in Neurons inference of models of transcriptional regulatory networks from high-throughput measurement data, integration of Neurons are amongst the largest and most complex cells in multiple sources of evidence, network simulation and vi- biology. Their intricate geometry presents many challenges sualization tools, and the use of such models for gaining for cell function, in particular, the efficient trafficking of insight into the nature of cellular behavior in health and newly synthesized proteins from the soma to distant loca- disease. tions on the axon or dendrites. In this talk I describe recent work on the mathematical modeling and analysis of one Ilya Shmulevich important aspect of protein trafficking, namely, glutamate Institute for Systems Biology receptor transport within dendrites. Glutamate receptors [email protected] mediate the majority of excitatory synaptic transmission in the central nervous system. The regulation of glutamate receptor trafficking is an important mechanism for synaptic LS08 Abstracts 43

IP5 sound Vibrometry Title Not Available at Time of Publication Evaluation of tissue elasticity and viscosity non-invasively Abstract not available at time of publication. and quantitatively has important medical applications. A method is presented to quantify both elasticity and viscos- Kai E. Thomenius ity of a homogeneous tissue by fitting a Voigt dispersion GE Global Research model to the measured shear wave speed at multiple fre- [email protected] quencies. Ultrasound radiation force is used to generate harmonic shear waves of various frequencies in the studied medium. Shear wave speed versus frequency is estimated IP6 from the phase difference detected by pulse echo ultrasound The Mechanics of Tissue Dynamics over a known propagation distance. This method provides a virtual biopsy of tissue elasticity and viscosity one lo- Tissues grow, change shape, and differentiate, function cation at a time. A special pulse sequence is developed to normally or abnormally, get diseased or injured, repair allow a single array transducer to both generate and detect themselves, and sometimes atrophy. This complex suite tissue vibrations. In vitro and in vivo tissue experiments of behaviors is governed by a complex suite of controls. demonstrate the feasibility of this technique. Practical con- Nonetheless, we can identify some general principles at siderations and challenges in possible medical applications work in the dynamics of tissues. Our goal is to understand are also discussed. how a tissues mechanics and biology regulate each other. Our models use a biologically-based continuum framework James F. Greenleaf to track the mechanics, biology, and mechanobiology of the Mayo Clinic component cells, fluids, signaling molecules, and extracel- Rochester, MN lular matrix materials. The presentation will describe our [email protected] modeling approach, reveal some of the general principles we have identified, and discuss some of the questions our Shigao Chen, Matt Urban findings have raised about specific morphogenetic systems. Mayo Clinic College of Medicine [email protected], [email protected] Sharon R. Lubkin North Carolina State University MS1 Department of Biomathematics Constructing Images of Linear and Nonlinear Elas- [email protected] tic and Viscoelastic Tissue Parameters

Recent advances in imaging technology allow remarkably IP7 accurate and detailed measurements of in-vivo tissue de- Title Not Available at Time of Publication formation under different types of loading. For example using ultrasound it is now possible to accurately (less than Abstract not available at time of publication 1% noise) determine the displacement field in the interior of a breast compressed to 10 % strain with a resolution of Jeff Hasty μm Department of Bioengineering about 100 . This type of displacement data contains a University of California, San Diego wealth of information about the macroscopic mechanical [email protected] properties of tissue. These properties are in turn closely connected to the health of the tissue. For example, cancerous tumors are often stiffer than their surroundings, fibrosis IP8 in a liver is associated with a diffuse overall stiffening, and Coercion and the Emergence of Cooperation atherosclerosis literally means the hardening of a blood vessel. In this talk I will describe our efforts to determine the One of the major challenges for the theory of natural se- spatial distribution of the mechanical properties of tissue lection is to explain the evolution of cooperation. Such from the knowledge of its displacement field. This process cooperation exists at many levels, among self-replicating involves the solution of an inverse problem, where an ap- molecules, cells, individuals or societies. Coercion is a ma- propriate mechanical model for tissue response is assumed jor factor promoting the collaboration of competing indi- and the spatial distribution of the material parameters is viduals; policing and sanctioning are widespread in human sought. I will focus on different types of mechanical models and insect societies, and can also be found in other bio- (linear elastic, viscoelastic and non-linear elastic models) logical communities. But sanctioning exploiters is costly. and on efficient techniques for solving the resulting inverse How can such spiteful behaviour emerge? In this talk, a problem. variety of deterministic and stochastic models for the emergence of costly punishment is discussed. Remarkably, the Assad Oberai evolutionary dynamics of finite populations shows such be- Department of Mechanical, Aerospace and Nuclear haviour can emerge much more easily if the joint effort is Engineering optional, rather than compulsory. Rensselaer Polytechnic Institute [email protected] Karl Sigmund University of Vienna International Institute for Applied Systems Analysis MS1 [email protected] Mapping and Characterization of the Electro- Mechanical Wave Propagation in the Left Ventricle in Vivo MS1 Measurement of Mechanical Properties with Ultra- Non-invasive conductivity mapping of the live myocardium 44 LS08 Abstracts

could constitute an invaluable tool for diagnosis of car- by which nutrients are delivered. Accounting for the flow diac abnormalities. Using ECG-gated echocardiography field can alter the relative growth rate downstream, induce to achieve ultra-high frame rates, it is possible to es- a directional influence for cell-to- cell signaling, and give timate and image, in a full 2D-view of the left ventri- differential rates for surface erosion. We present our results cle, otherwise undetectable transient displacements initi- illustrating these effects, and our algorithms for efficiently ated by the electrical activation of the myocardium. This expanding the size of the domain in which the solutions are electromechanically-coupled phenomenon can be assessed computed by means of tiling. through imaging of the resulting wave in the left ventricle beginning at the QRS peak. In this work, we propose to David L. Chopp characterize the properties of this wave and study its po- Northwestern University tential for indirect evaluation of conduction properties of Dept. of Engineering Science and Applied Mathematics the myocardium. [email protected]

Jean Provost, Jianwen Luo Columbia University MS2 [email protected], [email protected] Title Not Available at Time of Publication

Elisa E. Konofagou Current research has determined that that the majority of Department of Biomedical Engineering, Columbia bacteria in nature exist in structured communities termed University,NY biofilms rather than free swimming planktonic bacteria. Department of Radiology, Columbia University, NY, USA Moreover, bacteria within biofilms are highly tolerant to [email protected] typical antimicrobial and antibiotic treatments. These observations, coupled with the negative impacts of the presence of biofilms in medical, industrial and natural settings, MS1 have driven research into the processes that govern the The Statistics of Shear Wave Speed Images Ob- formation, growth and development of biofilms. Because tained from Wave Front Arrival Times biofilms typically form in the presence of an externally driven fluid, the dynamics of the viscoelastic biofilm is in- Elastography is a non-invasive method which measures the herently a fluid dynamics problem. Biofilms are physically mechanical properties of tissue. Often this is accomplished and biologically heterogeneous with a range material prop- by generating a shear wave that propagates in the tissue, erties, making any mathematical treatment both challeng- using ultrasound to measure the interior displacement of ing and engaging. This talk will describe the incremental the shear wave. The goal is to image the speed of the process of extending a classical technique used to solve cou- shear wave. The arrival times of the shear wave front sat- pled flow problems (BIM) to incorporate the growth and isfy the Eikonal equation. In this talk we address how to material properties of the biofilm. The goal of the research find the shear wave speed given the arrival times using the is to provide insight into the mechanisms of bacterial tol- Eikonal equation. Unfortunately, the shear wave speed is erance and the development of more effective methods for inversely proportional to the gradient of the arrival times. removal of the bacteria. When Gaussian noise is added to the arrival times, in high speed regions the noise in the recovered shear wave speed Nick Cogan is often Cauchy like, and this leads to instabilities. These Florida State University high speed regions are usually the most interesting regions. [email protected] We give an alternative level set description using curves of constant arrival time. With the level set description, MS2 we show that when Gaussian noise is added to the arrival times, the noise in the recovered wave speed is also ap- A Reaction-Diffusion Model for Resistance of proximately Gaussian, and that the level set description Biofilms to Antibiotics automatically increases the amount of smoothing in high It is an established fact that biofilm formations are more re- speed regions to avoid instabilities. sistant to antibiotic agents than free swimming suspended Jessica Jones bacteria. Several causes have been proposed in the liter- Rensselaer Polytechnic Institute ature to explain this diminished sussceptibility: diffusive Dept of Mathematical Sciences resistance, slow growth of a portion of the microbial pop- [email protected] ulation, existence of persister cells. Our proposed model is continuous and considers the influence of spatial effects on disinfection processes. It is based on a system of highly Joyce R. McLaughlin nonlinear reaction-diffusion partial differential equations. Rensselaer Polytechnic Inst A substrate controlling biofilm growth (typically oxygen), Dept of Mathematical Sciences an antibiotic, as well as active and inert biomass are con- [email protected] sidered in the prototype version of this model. The diffusivity of biomass inside the biofilm phase takes mainly Daniel Renzi two effects into account: fast diffusivity in areas saturated Georgia Gwinnett College with biomass, and singularity at 0 similar to that in porous Atlanta, Georgia media equation at the interface between biofilm and liquid [email protected] phases. Some aspects of the mathematical analysis (due to singularities existence of solution is far from trivial) as well as some numerical issues are discussed.” MS2 The Importance of Fluid Flow in Biofilm Modeling Laurent Demaret Institute of Biomathematics and Biometry In this talk, we explore biofilm models where the fluid flow Helmholtz Zentrum München, Germany field plays a more important role than simply a mechanism LS08 Abstracts 45

[email protected] Michael McCamy Arizona State University [email protected] MS2 Modelling Flow Dynamics in Biofilms MS3 A continuum modelling approach is used to describe 2- Diffusion-Trapping Model of AMPA Receptor Traf- dimensional biofilm growth within“typical” flow chamber ficking Along a Spiny Dendrite experiments using conservation laws, force balances and viscous flow. The modelling also takes into account the We model AMPA receptor trafficking between multiple role of nutrient and bacterial cell-cell signalling, both im- dendritic spines distributed along a dendrite. Receptors portant factors in the normal development of biofilms. The diffuse laterally within the dendritic membrane between resulting model consists of a highly coupled system of non- soma and spines, and can bind to scaffolding proteins linear partial differential equations with a moving interface. within spines. Surface receptors are exchanged with lo- Numerical solutions will be presented and key results dis- cal intracellular pools both at the soma and spines via cussed. exo/endocytosis. We derive a reaction-diffusion equation for receptor trafficking whose solution determines synaptic John P. Ward receptor numbers along the dendrite, and hence how lateral Loughborough University, UK diffusion contributes to synaptic strength. [email protected] Berton A. Earnshaw Mark Newstead University of Utah Mathematical Sciences [email protected] Loughborough University [email protected] Paul C. Bressloff University of Utah Department of Mathematics MS3 bressloff@math.utah.edu Multiscale Modeling of Neural Subcircuits in the Retina MS3 We mathematically model the subcircuits of the outer plex- A Computer Simulation of Voltage Sensitive Cal- iform layer of the retina. We investigate if feedback ef- cium Ion Channels in Dendritic Spines fects in the cone photoreceptor’s synapse are driven by electrical (ephaptic) or chemical (neurotransmitters, e.g., Transmembrane current through voltage-sensitive calcium GABA) mechanisms. We formulate and analyze a partial ion channels in a dendritic spine is investigated. To simu- differential equation system that includes the horizontal late such ion channels and the resulting spatial distribution cell syncytium and its numerous dendritic spines into cone of concentration and voltage within the dendritic spine, the pedicles, and compare simulation results with spatial en- immersed boundary method with electrodiffusion is applied. hancement data from cat retina for different test regions. For the first step, a one-dimensional model is studied with and without an ion channel governed by a continuous-time Markov process. Finally, a two-dimensional model is in- Steven M. Baer troduced that allows for spatially localized ion channels. Arizona State University Department of Mathematics [email protected] Pilhwa Lee University of Colorado at Boulder [email protected] MS3 A Stage Population Model for Dendritic Spines MS4 We formulate a cable model for the stage transitions be- A Novel Neural Population Model for Investigating tween stubby, mushroom, and thin dendritic spines. In this NREM/REM Sleep Regulation model multiple spine types may coexist simultaneously at points along the dendrite, and the model allows for the In sleep/wake regulatory neuronal populations, microdial- study of population dynamics between spine types. A con- ysis and microinjection experiments suggest that neuro- tinuum formulation is used for tracking the interaction be- transmitter dynamics play an important role in the initia- tween the many activity-dependent spines and for studying tion and maintenance of different behavioral states. How- the impact of their individual and collective dynamics on ever, traditional population firing-rate models have in- the output properties of the dendrite. cluded synaptic coupling terms without explicitly modeling the dynamics of the neurotransmitters acting at Sharon M. Crook these synapses. We investigate the mechanisms govern- Dept of Mathematics and Statistics & School of Life ing NREM/REM sleep regulation using a novel popula- Sciences tion modeling framework to capture the dynamic interplay Arizona State University between population activity and neurotransmitter concen- [email protected] tration.

Steven M. Baer Cecilia Diniz Behn Arizona State University University of Michigan Department of Mathematics Dept of Mathematics [email protected] [email protected] 46 LS08 Abstracts

Victoria Booth the connections. University of Michigan Depts of Mathematics and Anesthesiology Michael Rempe [email protected] The Ohio State University Mathematical Biosciences Institute [email protected] MS4 A Computational Study of the Network Mecha- Janet Best, David H. Terman nisms Mediating Anesthesia-Induced Paradoxical The Ohio State University Excitation Department of Mathematics [email protected], [email protected] The anesthetic propofol paradoxically produces both behavioral and electroencephalographic manifestations of excitation at low doses. We model cortical interneurons and MS4 pyramidal cells using Hodgkin-Huxley-type conductances A Quantitative, Metabolic Theory for Mammalian and track the evolution of network dynamics as we simulate Sleep propofol-induced GABAa-potentiation. Network dynamics that correlate with the introduction of low-dose propo- Sleep time generally decreases with body size across species fol include increased post-inhibitory excitability of low fre- of mammals. In this talk, I will translate different hy- quency spiking neurons and the spontaneous formation of potheses for the function of sleep into simple mathemati- interneuron antisynchrony. These dynamics both depend cal models. These models can be used to predict slopes of on GABAa-induced reduction of the intrinsic membrane allometric curves for sleep. Comparing these predictions M-current. with slopes measured from empirical data supports the hypotheses of cellular repair and/or neural reorganization as Michelle McCarthy the primary function of sleep and helps explain why ele- Department of Mathematics & Center for Biodynamics phants sleep much less than mice. Boston University [email protected] Van Savage Dept. of Systems Biology Emery Brown Harvard Medical School Harvard Medical School / MGH van [email protected] MIT [email protected] MS5 Nancy J. Kopell Modelling the Effect of Amantadine on Influenza Boston University A Viral Dynamics in Vitro Department of Mathematics We show that using a controlled experimental apparatus, [email protected] the hollow fiber system, it is possible to develop accurate yet simple mathematical models of influenza infection in MS4 the presence of drug. The parameter estimates obtained from the experimental data are consistent with those ob- A Mathematical Model of the Sleep/Wake Cycle tained earlier for influenza infection in a human model. We Based on Neurophysiology estimated the maximum efficacy of amantadine in block- ∼ We present a biologically-based mathematical model that ing viral entry to be 74% which is likely due to the rapid accounts for several features of the human sleep/wake cy- emergence of resistance. cle. These features include the timing of sleep and wakeful- Catherine Beauchemin ness under normal and sleep-deprived conditions, ultradian Department of Physics rhythms, and the circadian dependence of several sleep Ryerson University variables such as the total sleep time and sleep-onset rapid [email protected] eye movement sleep (SOREMS). Additionally, if the input from the neurotransmitter orexin is removed, the system exhibits more frequent switching between sleep and James J. McSharry, George L. Drusano wakefulness, consistent with the sleep disorder narcolepsy. Ordway Research Institute The model demonstrates how each of these features de- Albany, NY, USA pend on interactions between a circadian pacemaker and a ?, n/a sleep homeostat and provides a biological basis for the two- process model for sleep regulation (Borbely, 1982; Daan et Jack T. Nguyen, David N. Chernoff, Gregory T. Went al., 1984). The model is based on previous ”flip-flop” mod- Adamas Pharmaceuticals els for sleep/wake (Chou et al. 2001) and REM/NREM (Lu Emeryville, CA, USA et al. 2006) and we explore whether the neuronal com- n/a, n/a, n/a ponents of these flip-flop models, with the addition of a sleep-homeostatic process, are sufficient to account for the Ruy M. Ribeiro, Alan S. Perelson features of the sleep/wake cycle listed above. The model Theoretical Biology and Biophysics is minimal in the sense that, besides the sleep homeostat Los Alamos National Lab and constant cortical drives, the model includes only those n/a, n/a nuclei described in the flip/flop models. However, in order to account for certain features of the ultradian rhythms, we found it necessary to add an additional hypothesis about MS5 Models of Acute Hepatitis B Infection: What LS08 Abstracts 47

Causes Viral Persistence? to prevent spread of virus within the host. This new approach of quantitative analyses of HIV vaccine data should To understand the factors that govern disease progression contribute to a better process of rational vaccine design. in viral hepatitis B infection, we study acute stages of the infection where immune responses play an important role Ruy M. Ribeiro in determining whether the infection is cleared or becomes Theoretical Biology and Biophysics chronic. We develop mathematical models to test the con- Los Alamos National Laboratory tribution and role of various immune responses in viral con- [email protected] trol. We validate the model against experimental data to determine how well it represents the biological system and how useful its predictions are. MS6 Functional Localization of Calcium Machinery Stanca Ciupe Laboratory of Computational Immunology We exploit the recent ability to dynamically monitor cy- Duke University Medical Center tosolic calcium in the construction of a map of receptor and [email protected] channel density. In particular, we 1) Infer from the change in cytosolic dye-buffered calcium fluorescence the affinities Alan S. Perelson and diffusivities of all relevant exogenous and endogenous Los Alamos National Laboratory calcium buffering proteins, and 2) Infer from (1) the con- [email protected] centration of free calcium and so determine the distribution of ryanodine receptors and calcium extrusion pumps. Ruy M. Ribeiro Steven Cox Theoretical Biology and Biophysics Dept. of Computational & Applied Mathematics Los Alamos National Laboratory Rice University [email protected] [email protected]

MS5 MS6 HCV Infection and Hepatocyte Homeostasis Mitochondrial Modulation of Intracellular Ca2+ In recent research, several researchers have proposed that Signaling the distinct response of hepatitis C virus (HCV) viral load In cells expressing highly dynamic Ca2+ signaling behav- to antiviral therapy can be explained by the homeostatic ior, mitochondria can shape the spatiotemporal patterns. proliferation of the target cell proliferation. In this talk, In addition, mitochondria have been shown to act as an in- I’ll present a mathematical analysis of their model of HCV dependent network of Ca2+ oscillators. These phenomena infection in the liver, and how differences in treatment are gaining attention as evidence points to mitochondrial efficacy and other host-dependent parameters alter the dysfunction as a potential factor in diseases such as neu- model’s bifurcation structure. In particular, a mathemati- rodegeneration. I will discuss efforts to model dynamic cal hypothesis explaining triphasic treatment responses will phenomena involving mitochondria, and in particular, de- be presented. polarization waves thought to involve Ca2+ and the mito- Timothy C. Reluga chondrial permeability transition. Departments of Mathematics and Biology Christopher Fall Pennsylvania State University Department of Anatomy and Cell Biology [email protected] University of Illinois [email protected] Harel Dahari Department of Medicine University of Illinois at Chicago MS6 [email protected] The Spatial Distribution of Ca2+ Release Channels Affects Ca2+ Dynamics: Insights into the Origins of Alan S. Perelson Arrhythmias Los Alamos National Laboratory [email protected] Calcium (Ca) is released in cardiac cells through Ca release units (CRUs). The CRUs need to be spatially separated to prevent uncontrolled Ca release. Our large-scale simu- MS5 lations show that subtle (∼ 10%) changes in CRU spacing Analyzing the Kinetics of HIV Vaccines profoundly affect the stability of the Ca control system. We propose that changes in the spatial separation of CRUs un- Human immunodeficiency virus infects over 30 million peo- derlie the high incidence of sudden cardiac death in heart ple worldwide, and this pandemic continues to grow. The diseases that have shortened CRU spacing. most affected regions are some of the poorest in the world. The best intervention strategy to curb this epidemic would Leighton T. Izu be the advent of an effective vaccine. Although this has Institute of Molecular Medicine been difficult to achieve, many experimental studies have University of Kentucky been conducted in the macaque model using a variety of [email protected] approaches. We have been analyzing and modeling the dynamics of virus and the immune response in vaccinated vs. Shawn Means unvaccinated macaques. We have quantified the effects of University of Auckland a vaccine in reducing the depletion of CD4+ T-cells. Our [email protected] studies also suggest that CD8+ T-cells do too little too late 48 LS08 Abstracts

John Shadid computational expense to improve project throughput. Sandia National Laboratories Albuquerque, NM Michela Taufer [email protected] University of Delaware [email protected] Tamas Banyasz University of Kentucky Roger Armen University of Debrecen University of Michigan at Ann Arbor [email protected] [email protected]

Ye Chen-Izu MS7 University of Kentucky [email protected] Coarse-Grained Molecular Models of Protein Com- plexation

MS6 A fundamental mathematical challenge relevant to biomolecular simulation is the quantitative description of Ca2+ Buffer Saturation Allows Facilitation of protein complexation to derive molecular machines that Ca2+ Transients by the Pre-Opening of Remote control biological processes such as cell signaling. We Ca2+ Channels have recently achieved a fundamental result in deriving E. Neher proposed that activity-induced enhancement of an analytical solution for computing the screened electro- neurotransmitter release could be explained by the gradual static interaction between arbitrary numbers of proteins depletion of free endogenous Ca2+ buffers by the incom- of arbitrarily complex charge distributions, assuming they ing Ca2+ influx. Recently we showed that this mechanism are well described by spherical low dielectric cavities in requires whole-terminal saturation of highly mobile buffers a higher dielectric salty medium [I. Lotan and T. Head- with rapid Ca2+ binding kinetics. We will examine im- Gordon (2006). An analytical electrostatic model for salt plication of such global buffer saturation, in particular the screened interactions between multiple proteins J. Comp. ability of remote Ca2+ influx to influence Ca2+ elevation Theo. Chem. 2, 541-555]. By exploiting multipole expan- caused by the subsequent opening of local Ca2+ channels. sion theory for the screened Coulomb potential, we can now describe direct charge-charge interactions and all higher- order cavity polarization correctly at all separation dis- Victor Matveev tances. Recently we have been extending this electrostatic New Jersey Institute of Technology model to new numerical formulations that better describe [email protected] realistic shape of the protein molecules that span solutions from low to high spatial resolutions. While alternative numerical approaches are faced with an inherent trade-off MS7 between spatial resolution and memory and time require- Computational Multi-Scale Modeling in Protein- ments, which limits them to system of few macromolecules, Ligand Docking we believe that our method is efficient and fast to compute even for many macromolecules, including frequent updates In our multi-scale approach to protein-ligand docking, in- of changes in their charge distributions due to induced con- creasingly sophisticated docking models can be constructed formational changes. Ultimately, smooth and systematic along three scales of docking assumptions: (1) represen- increase in spatial resolution back to greater molecular de- tation of the protein and ligand (potential energy func- tail of the dielectric boundaries will be the centerpiece of a tion and flexibility of protein and ligand); (2) represen- multiscale scheme that converges on an atom centered solu- tation of the effect of solvent; and (3) sampling strat- tion [E.-H. Yap, N. Lux Fawzi, and T. Head-Gordon (2007). egy. Computationally expensive docking models may be A coarse-grained a-carbon protein model with anisotropic optimized for accuracy for difficult test cases, but may hydrogen-bonding. Proteins, Struct. Func.. Bioinf. 70, not improve results for simple test cases. It is our goal 626-638]. We believe this will realize wide application in to increase the overall efficiency of docking by consider- modeling complex materials problems including spatial or- ing dynamic adaptations along these multi-scales to con- ganization of protein complexes. sider and evaluate new docking models. Using classifications of protein-ligand complexes based on the flexi- Teresa Head-Gordon bility of protein and ligand, docking models can be dy- Department of Bioengineering namically adapted when more expensive models are re- University of California, Berkeley quired for sufficient accuracy. These classifications can [email protected] be used to start an iterative search for adaptive docking models that optimize accuracy and minimize time to solution. The results of our project are being used to develop MS7 a Dynamically Adaptive Protein-Ligand Docking System Understanding Bionanosystems (BNS) via Multi- (DAPLDS), which would be able to dynamically adapt scaling the Basic Laws of Physics to an appropriate docking model for new protein-ligand complexes or a large series of ligands. Our project Dock- The dynamics of a BNS involves processes across multi- ing@Home (http://docking.cis.udel.edu/) uses the ”volun- ple time and length scales. While it is natural to under- teer computing” paradigm, which uses the Internet to har- stand these systems with the basic equations of molecu- ness the computing power and storage capacity of a vol- lar physics (e.g., the Liouville, Schrodinger, or Poisson- unteers computer resources owned by the general public. Boltzmann equations), the supramillion atom scale of these Given a variety of docking tasks, dynamic scheduling poli- systems presents great challenges to direct molecular dy- cies can selectively devote available resources based on namics and quantum mechanics simulation. We illustrate how a multiscale analysis of the N-atom Liouville equation reveals essential principles of virology, and ultimately LS08 Abstracts 49

yields an algorithm for computer-aided drug and vaccine MS8 design and ways to optimize anticancer drug delivery via Mathematical Data Analysis for MRE nanocapsules. MRE (magnetic resonance elastography) is an instrument Peter J. Ortoleva which is expected to realize doctors’ palpation inside living Indiana University body. It measures waves inside living bodies. It can also be [email protected] applied to many problems in rheology. The mathematical data analysis for MRE is to give an appropriate mathematical model for the waves and a scheme to recover the MS7 viscoelastic properties of the living body. We will propose Analysis of Coarse-Grained Nucleic Acid Free En- a mathematically rigorous data analysis for MRE. ergy Landscapes Gen Nakamura We describe algorithms for analyzing the thermodynamic Hokkaido University and kinetic properties of coarse-grained DNA and RNA Hokkaido, 060-0810, Japan free energy landscapes. The utility of these methods will [email protected] be demonstrated by elucidating the empirical behavior of synthetic nucleic acid systems with metastable states. Yu Jiang Niles A. Pierce Hokkaido University Applied & Computational Mathematics, Bioengineering [email protected] California Institute of Technology [email protected] MS8 Nonlinear Algorithms for High Contrast Tissue MS8 Shear Wave Speed Imaging Multi-Modal Breast Imaging with Ultrasound To- Using an elastodynamica model for shear wave speed imag- mography ing in tissue, we present a nonlinear algorithm that recovers We report and discuss clinical breast imaging results ob- the shear wave speed together with the pressure even in the tained with operator independent ultrasound tomography. presence of high contrast small inclusions. The data can be A series of breast exams are carried out using a recently wave propagation data initiated by a line source or a single upgraded clinical prototype designed and built on the prin- frequency excitation. The talk will include images, stabil- ciples of ultrasound tomography. The in-vivo performance ity and accuracy theorems, and examples of robustness in of the prototype is assessed by imaging patients at the the presence of noise. Karmanos Cancer Institute. Our techniques successfully Ning Zhang demonstrate in-vivo tomographic imaging of breast archi- Inverse Problems Center tecture in both reflection and transmission imaging modes. Rensselaer Polytechnic Institute, Troy, NY 12180 These initial results indicate that operator-independent [email protected] whole-breast imaging and the detection of cancerous breast masses are feasible using ultrasound tomography techniques. This approach has the potential to provide a low MS9 cost, non-invasive, and non-ionizing means of evaluating Flocculating Infectious Bacteria: Smoluchowski breast masses. Future work will concentrate on extending and Sepsis these results to larger trials. Klebsiella pneumoniae and Staphylococcus epidermidis are Neb Duric common causes of intravascular catheter infections, the Karmanos Cancer Institute most important sources of bacteremia. These bloodstream Wayne State University infections dramatically increase the mortality of illnesses [email protected] and often serve as an engine for sepsis. Our current model for the dynamics of the size-structured population of ag- MS8 gregates in a flowing system is based on the Smoluchowski coagulation equations, which we are using to study prop- Motion Estimation Between Successive Sonograms erties of these flocculating bacteria. In this talk, I will Elastography is an imaging modality where the strain of discuss the progress of several investigations into proper- tissues is estimated, when the tissues are subject to an ties of our model equations as well as the comparison with external or internal load. We present an algorithm to esti- data. In particular, I will focus on the derivation of an mate the motion between ultrasound images. The Jacobian alternative fragmentation kernel in laminar flow as well as matrix of the cost function to be minimized is assembled the post-fragmentation aggregate size distribution. rapidly using a finite-element method. A global displace- David M. Bortz ment is retrieved, and spatial regularization allows to have University of Colorado a strain estimate with a small amount of noise. Department of Applied Mathematics Jerome Fehrenbach [email protected] Laboratoire MIP Universite Paul Sabatier Toulouse III John G. Younger [email protected] University of Michigan [email protected] 50 LS08 Abstracts

MS9 clude simple modeling. The most important of these re- Biofilm Control with Probiotics late to compartments that are either hidden (in humans) or whose sampling is destructive (in mice), meaning that Traditionally, probiotics have been used as functional foods individual multicompartmental trajectories can never be (e.g. in dairy products) but recently some interest devel- measured. In this presentation, I’ll provide an overview oped in the potential of this concept for medical purposes, of this important disease, discuss modeling options and e.g. as alternative to antibiotics. Since many bacterial a Monte Carlo strategy for parameter estimation, and, by infections are caused by pathogenic biofilms and some pro- highlighting how key assumptions needed for compartmen- biotics form biofilms as well, one deals with a dual-species tal modeling are violated in reality, lay the groundwork for biofilm system of a pathogen and a probiotic. Modeling the other minisymposium talks on modeling bacterial com- this leads to a system of highly nonlinear partial differen- munities. tial equation which we will study in computational experiments. John G. Younger University of Michigan Hermann J. Eberl [email protected] Dept. Mathematics and Statistics University of Guelph [email protected] MS10 Signal Transduction Model Update via Sensitivity Hassan Khassehkhan Analysis Univ. Guelph [email protected] Sensitivity analysis has traditionally been used to determine important mechanisms of a system and parameters to estimate. However, these traditional applications of sensi- MS9 tivity analysis assume that the model accurately describes Soft Materials Approach to Measuring the Vis- a system. This paper presents a new application of sensi- coelastic Properties of Biofilms tivity analysis for guiding model development. Sensitivity analysis is used to determine which parts of signal trans- We combine methods from computational mathematics duction models should be modified to improve the model and the science of soft matter to determine the viscoelastic predictions of experimental data. properties of biofilms on the micron scale in which structural heterogeneity has been reported. Using image pro- Juergen Hahn, Yunfei Chu, Zuyi Huang cessing coupled with microfluidics we convert confocal mi- Chemical Engineering croscopy images to statistical quantification. These prop- Texas A&M University erties have typically been difficult to characterize by bulk [email protected], [email protected], experimental techniques. These new data support appro- [email protected] priate mathematical modeling approaches to predict properties such as fracture dynamics under shear stresses typi- MS10 cal of the vascular system. Embedding Global Sensitivity Analysis within Danial Hohne Global Optimization to Constrain Parametric and University of Michigan Structural Model Uncertainty Chemical Engineering [email protected] Mathematical modeling of cellular processes requires resolving the appropriate degree of complexity while con- straining relevant structural detail and parameter uncer- David M. Bortz tainty. Active use of sensitivity screening methods for rapid University of Colorado assessment of feasibility and global sensitivity analysis cou- Department of Applied Mathematics pled with global optimization searches for data compati- [email protected] bility can result in model structure alterations, parameter range reduction or experiment design. Models of T cell John G. Younger signaling and cardiac myocyte metabolism will serve to il- University of Michigan lustrate the application of these techniques. [email protected] Ann E. Rundell, Maia Donahue, Jason Bazil Michael Solomon Weldon School of Biomedical Engineering Chemical Engineering Purdue University University of Michigan [email protected], [email protected], [email protected] [email protected]

Gregory Buzzard MS9 Mathematics Department Biomechanics and the Limitations of Compartmen- Purdue University tal Models in Bloodstream Infections [email protected] Bloodstream bacterial infections are common, rapidly progressive, and frequently lethal illnesses. The fundamental MS10 mechanism of bacteremia is organism-wide distribution of Sensitivity Analysis Based Adaptive Search-Space pathogens carried in the blood stream, a process well suited Reduction for Parameter Estimation Applications for compartmental analysis. However, in animal and human disease there are experimental limitations that pre- One of the central aspects in systems biology is the estima- LS08 Abstracts 51

tion of parameters based on experimental data. Due to the rarely known with great accuracy for biochemical reaction high dimensionality of the search space, often encountered networks. In this context any claims which can be made for biochemical models, it is of great interest to reduce the based on reaction network topology are particularly impor- numbers of parameters that need to be estimated. Here, tant. For a broad class of reaction networks it is possible we present a new method that, based on sensitivity analy- to make strong statements in two areas based on network sis, allows to iteratively adapt the search space to the most topology: 1) Claims about the nonexistence of multiple important parameters. equilibria based on sufficient conditions for injectivity of networks, and 2) Claims about the nonexistence of sta- Ulf Liebal, Sylvia Haus, Olaf Wolkenhauer ble periodic orbits, based on sufficient conditions for the Systems Biology & Bioinformatics networks to be monotone systems. Results in these areas University of Rostock will be presented with examples of their application. Tech- [email protected], niques used in the proofs will be outlined. [email protected], [email protected] Murad Banaji Department of Biological Sciences Henning Schmidt University of Essex, United Kingdom Systems Biology & Bioinformatics [email protected] University of Rostock [email protected] MS11 Treatment for Within-Host Virus Dynamics MS10 Analytical Advantages of Canonical Models for the We revisit a standard model describing the infection cycle Assessment of Cellular Responses of a virus in an individual. One example of this model is furnished by HIV, a retrovirus which infects a particu- Nature has not provided us with guidelines for selecting lar class of immune cells, the CD4+ T cells, giving rise to mathematical representations for biological phenomena. In infected T cells that spawn off new virus. However, the dy- relatively simple cases, a possible choice is a model designed namics of other infections such as hepatitis, influenza and from first principles of physics. However, most biological even the malaria parasite P. falciparum can be described systems are too complicated for this approach, leaving as by the same model. We will discuss the effect of periodic alternatives ad hoc and canonical models. Canonical mod- treatment on the system, and give tight bounds for the els are directly based on approximation theory and offer drug efficiencies required to eradicate the infection. We very significant analytical and computational advantages. will also consider the problem of finding optimal treatment I illustrate these advantages with power-law models within schedules that minimize various measures of the burden of Biochemical Systems Theory. the treatment on the patient. Eberhard O. Voit Patrick L. De Leenheer Georgia Institute of Technology University of Florida [email protected] [email protected]fl.edu

MS11 MS11 Product form Stationary Distributions for Com- The Dynamics of Protein Folding and Export from plex Balanced Chemical Reaction Networks the Endoplasmic Reticulum

The dynamics of chemical reaction networks can be mod- One third of proteins are folded and delivered to their re- eled either deterministically or stochastically. The defi- spective pathways from the endoplasmic reticulum (ER). ciency zero theorem for deterministically modeled systems Mutations in ER export, folding and degradation proteins gives conditions under which a unique equilibrium value are the cause for many ER storage (or protein-misfolding) with strictly positive components exists within each stoi- diseases. We have developed a model of protein matura- chiometric compatibility class (linear subset of Euclidean tion, misfolding and export to investigate ER storage dis- space in which trajectories are bounded). The conditions eases. There are currently two prevailing hypotheses in of the theorem actually imply the stronger result that there the field: ER stress can result either from deterioration of exist concentrations for which the network is “complex bal- the protein folding pathways or from deterioration of the anced”. That observation in turn implies that the standard transport proteins responsible of extracting protein from stochastic model for the reaction network has a product the ER. We explore these hypotheses to study the origins form stationary distribution. Examples will be given show- of ER diseases and predict strategies for restoring protein ing the applicability of such results in the analysis of the homeostasis in the ER diseases. dynamics of systems with multiple time-scales. Santiago Schnell David Anderson Indiana University Department of Mathematics School of Informatics University of Wisconsin [email protected] [email protected] MS11 MS11 Multiple Roles of Negative Feedback in Immune Injectivity and Monotonicity in Chemical Reaction Response to Virus Attack Networks Recently developed model of the immune response to in- Details of the kinetics and values of rate constants are fluenza A virus focuses on the control of the infection by the innate and adaptive immunity, represented by interferon- 52 LS08 Abstracts

induced resistance, the removal of infected cells by effector imbalance leads to pathological synchronization of neu- cells, and virus-specific antibodies. Each of the immune ronal activity leading to a seizure. Homeostatic mecha- mechanisms suppresses the virus through a negative feed- nisms in neurons try to keep these forces in balance. Some back loop, with a distinct character and effect. We explore ion channels, such as the hyperpolarizing Ih current, are the effect of the feedback loops on the severity and duration known to change in their density in epileptic animal mod- of the disease. els reflecting these homeostatic changes. To understand the effects of the Ih on the dynamics of the neuron and David Swigon on the network, we have measured phase response curves Department of Mathematics of neurons with and without Ih added to the neuron us- University of Pittsburgh ing electrical knock-in via the dynamic clamp. Ih’s effect [email protected] on the neuron is to shunt excitatory inputs early in the phase. This results in a phase dependent decrease in excitatory synaptic efficacy. The effect predicted on networks MS12 is to increase synchrony. This is a surprising finding, that Information Processing in Dendrites a decrease in excitatory synaptic efficacy could increase synchrony. We hypothesize then that a neuron will mod- Dendrites are the main site for synaptic input to neurons. ulate Ih differently depending on whether it is in a net- They are usually considered as pure post-synaptic elements work with significant recurrent connections or a network that serve as a spatio-temporal filter for the synaptic input receiving synaptic input from another population. We be- to the soma. Here I will discuss how to compute this re- lieve that this explains why Ih is found to be downregu- sponse function for realistic dendritic geometries, and in lated in Hippocampus in one model of epilepsy (Chen and particular address the case when the tree has electrical Soltesz, 2001) while it is upregulated in the Entorhinal cor- resonances associated with the presence of HCN channels I tex (Shah and Johnston, 2004). If homeostatic mechanisms (that underlie the h current). When coupled to an active do not take the network structure into account, an attempt soma I will discuss the consequences of neuronal geometry to dampen synaptic input by increasing Ih could increase and intrinsic membrane resonances in determining output network synchrony making the brain region more prone to spiking patterns. I will further show how this framework seizures. for computing dendritic responses can be extended to cover networks with dendrodendritic junctions. These are promi- Theoden Netoff nent in some brain areas, for example in the olivocerebel- Department of Biomedical Engineering lar system and the olfactory bulb. Here the presence of University of Minnesota gap junctions means that the dendrites of cells function as tnetoff@umn.edu both post and pre-synaptic elements simultaneously. Fi- nally, I will discuss the derivation of STDP like learning John A. White rules in such networks via the maximisation of a given Dept of Biomedical Engineering likelihood function with respect to some set of synaptic Boston University weights. Time permitting I will also address how to model [email protected] active membrane in the dendritic tree in a computationally cheap fashion, and discuss the role of dendritic spikelets in information processing. MS12 Stephen Coombes Correlation and Synchrony Transfer in Integrate- University of Nottingham and-Fire Neurons [email protected] We use perturbation techniques to study how pairs of neurons transfer correlated input currents into correlated MS12 spikes. For spike correlations, or synchrony, over rapid timescales, correlation transfer increases with both spike Adaptive Coding of Visual Information in Neural time variability and rate. We show how this dependence Populations on variability disappears at large observation time scales. Our perception of the environment relies on the capacity We demonstrate that this result persists for a nonlinear of networks neurons to rapidly adapt to changes in en- membrane model and for heterogeneous cell pairs, and un- vironmental stimuli. Examining how brief exposure, or cover strong nonmonotonicities due to refractory effects. adaptation, to a stimulus of fixed structure changes in- This analysis allows us to present consequences for the en- formation processing by neuronal networks is essential for coding of time-varying stimuli. understanding the relationship between sensory coding and Eric Shea-Brown behavior. I will present experimental evidence that shows Department of Applied Mathematics how brief adaptation changes the interneuronal correlation University of Washington structure and the accuracy of population coding in primary [email protected] visual cortex.

Diego Gutnisky Kresimir Josic Department of Neurobiology and Anatomy University of Houston University of Texas, Houston Department of Mathematics [email protected] [email protected]

Brent Doiron MS12 Dept. of Mathematics Multiscale Eﬀects of Ion Channels in Epilepsy Univ. of Pittsburgh [email protected] Seizures are thought to be caused by an imbalance between the excitatory and inhibitory processes in the brain. This LS08 Abstracts 53

Jaime De La Rocha ity, beta-cell function, and gastric emptying from standard Center for Neural Science, NYU meal or oral glucose tolerance tests. [email protected] David C. Polidori Johnson & Johnson Pharmaceutical Research & MS13 Development, LLC Eﬀect of Exercise on Skeletal Muscle and Whole- [email protected] Body Metabolism

Exercise training induces structural, biochemical, physio- MS14 logical, and functional adaptations ranging from the molec- Multi-Scale Modeling of Collagen Gel Mechanics ular to the whole-body levels. The extent of the adaptation depends not only on the characteristics of the training ses- Collagen gels consist of an interacting network of long, thin sion (modality, frequency, intensity, time), but also on the fibers, allowing even very dilute solutions (1-3 mg/ml) to training program duration. To predict the long-term ef- solidify. The critical challenge in understanding the me- fects of exercise training, a multiscale model of metabolism chanics of these gels (and of collagenous tissues engineered has been develop that integrates processes and adaptations from them or native tissues) is to incorporate the network at the cellular, tissue-organ, and organismal level to simu- behavior, which occurs on the micrometer length scale, into late the metabolic response to acute exercise of a normal- the tissue behavior, which occurs on the millimeter length sedentary and an endurance-trained individual. scale. A two-scale scheme has been developed in which the average stress is calculated on a representative network Ranjan Dash at each integration point of a finite-element representation Medical College of Wisconsin of the tissue. The strain from the finite-element model [email protected] is used to generate boundary conditions for each micro- model, which in turn provides the stress for the macro- Jae Kim, Nicola Lai, Marco E. Cabrera scopic scale. Further developments include a biphasic for- Case Western Reserve University mulation to account for interstitial and image-based con- [email protected], [email protected], [email protected] struction of the networks. Victor Barocas MS13 University of Minnesota The Dynamics of Human Body Weight Change [email protected]

We show that the long-term dynamics of human weight change can be captured by a two dimensional autonomous MS14 system and that the generic dynamical behavior can be Multi-Scale Modeling of Blood Vessels Using a divided into two classes. In the first, body composition Fluid-Solid-Growth Framework and mass are determined uniquely at steady state while in the second, the body composition can exist along an Blood vessels adapt and remodel in response to changes invariant manifold of possible states. We use the model in their mechanical and biochemical environment dur- to make predictions and to dispel some commonly held ing development and aging, and with diseases including assumptions about weight change. atherosclerosis, aneurysms, and hypertension to name just a few examples. While computational methods have been Carson C. Chow utilized separately to quantify hemodynamic conditions Laboratory for Biological Modeling and to simulate growth and remodeling processes, there NIDDK, NIH is a pressing need for a unified approach to model vascu- [email protected] lar adaptation and disease in response to biomechanical and biochemical stimuli. This class of Fluid-Solid-Growth (FSG) problems are inherently multi-scale in time since MS13 the biomechanical forces due to the heart beat change on Models of Whole Body Fuel Selection the scale of seconds whereas vascular adaptation can occur over days to weeks and diseases progress over months to Abstract not available at time of publication. years. In addition, FSG problems are multi-scale in space since biomechanical forces and biochemical stimuli, sensed Kevin Hall at a molecular and cellular scale, elicit adaptive and mal- NIDDK, NIH adaptive responses from molecular to organ scales. We [email protected] describe herein a novel computational method to model fluid-solid growth problems and illustrate this method by applying it to simulate the enlargement of a cerebral vas- MS13 cular aneurysm in response to shear and tensile stress. Efficient Methods for Assessing Insulin Sensitivity, Beta-Cell Function, and Gastric Empyting From Alberto Figueroa Meal Tests Stanford University Bioengineering Department Type 2 diabetes is progressive heterogeneous disease char- alberto.fi[email protected] acterized by varying degrees of insulin resistance and decreased beta-cell function. Due to the increasing preva- Seungik Baek lence of diabetes, several new therapeutic approaches are Michigan State University being tested to treat these patients, including behavioral, [email protected] pharmaceutical, and surgical interventions. We present recent advances in the application of mathematical modeling to determine quantitative measures of insulin sensitiv- Charles A. Taylor 54 LS08 Abstracts

Depts. of Mech. Eng., Bioengineering and Surgery MS14 Stanford Univesity Multi-Scale Modeling of Calcium Responses in Re- [email protected] alistic Cell Geometry

Jay D. Humphrey Release of inflammatory mediators by mast cells in type 1 Texas A&M University immediate hypersensitivity allergic reactions relies on the [email protected] antigen-dependent increase in cytosolic calcium. Here we used a series of electron microscopy images to build a 3D reconstruction of a rat tumor mast cell, which then served MS14 as a basis for modeling of IP3-mediated calcium responses. Accurate Coarse-Graining of Red Blood Cell Mod- Local proximity of the endoplasmic reticulum (ER) to both els the plasma membrane and to mitochondria is considered. We found that local ER luminal calcium concentration We develop a systematic coarse-graining procedure for during IP3R transport is markedly affected by nearby or- modeling red blood cells (RBCs) using arguments based ganelles. In addition to compartmental and PDE-based on mean-field theory. The three-dimensional RBC mem- approaches, we describe the first application of stochas- brane model takes into account the bending energy, in- tic reaction-diffusion modeling within a complete 3D cell plane shear energy, and constraints of fixed surface area geometry. These combined approaches help to bridge the and fixed enclosed volume. The sensitivity of the coarse- gap between measured single molecule kinetic constants grained model is investigated and its behavior is validated and overall calcium dynamics. against available experimental data and in Dissipative Par- ticle Dynamics (DPD) simulations of RBCs in microcircu- Bridget Wilson lation. University of New Mexico School of Medicine [email protected] George Karniadakis Brown University George [email protected] MS15 Regularisation and Prior Knowledge in Diffuse Op- tical Tomographic Reconstruction MS14 Multi-Scale Modeling of Chemical-to-Mechanical Optical Tomography in highly scattering media is non- Energy Conversion in Actin-Based Motility linear and severely ill-posed. An increasingly widely used approach for image reconstruction is a parameter estima- In actin-based motility, monomeric actin polymerizes into tion method based on optimisation of a likelihood func- stiff filaments from surface-bound components, which tion. These kinds of problems always require regularisa- crosslink and propel the surface forward. How the chemi- tion which most generally should be interpreted in terms cal energy involved in monomer addition is converted into of Bayesian prior term. In this talk I will describe different mechanical work is critical in understanding cell motility. regularisation techniques incorporating structural and sta- The scientific goal of this project is based on the hypoth- tistical information. An emphasis will be placed on cross- esis that the structural and force-producing properties of construction with an auxiliary image representing a multi- the network are critically dependent on whether working modality approach. filaments remain tethered by end-tracking proteins or remain untethered as required by the conventional Brownian Simon Arridge Ratchet model. The computational goal of the project is University College London to develop and validate a biologically relevant, multi-scale [email protected] model of force generation by actin polymerization. We are designing a computational framework for modeling the mechanical properties of solutions of stiff biopolymers such as MS15 actin, accounting for its resistance to bending and torsion, Inverse Transport From Angularly Averaged Mea- position and orientation dependent chemical functionaliza- surements tion along the molecular backbone, and the coupling of the polymer dynamics to the surrounding solvent. In this talk Inverse transport consists of reconstructing the absorption I will outline the theory underlying the mechanical model and scattering coefficients in a domain from measurement of a stiff polymer and describe some tests of our numer- of the outgoing density of particles at the domain’s bound- ical implmentation. Parallel work developing the means ary. Uniqueness and identification of the coefficients has of modeling the fluid-mitigated hydrodynamic interactions been established in many settings where the source term will also be described. At longer times a quasi-static ap- and the outgoing measurements are allowed to depend on proach can replace the detailed dynamic model and we are both the spatial and directional variables. In practice, how- also developing Monte-Carlo simulations of thermally fluc- ever, the sources and the measured density of particles are tuating filaments. Finally under high load thermal fluctu- often angularly averaged. I will present recent uniqueness ations may be ignored and the classical equilbrium theory and stability results in the latter context for continuous of flexible rods used instead. I will show some preliminary wave (time-independent) and modulated (or equivalently, calculations for individual filaments and simple filament time-dependent) sources. This is based on joint works with networks. Alexandre Jollivet, Ian Langmore, and Francois Monard.

Tony Ladd Guillaume Bal University of Florida Department of Applied Physics & Applied Mathematics [email protected]ﬂ.edu Columbia University [email protected] LS08 Abstracts 55

MS15 MS16 Interferometric Synthetic Aperture Microscopy Boundary Integral Methods Biofilm/Fluid Sys- tems: Growth and Viscous Interactions Methods of computed imaging have historically provided new levels of insight and utility when coupled with estab- Current research has determined that that the majority of lished instrumentation. Examples include the growth of X- bacteria in nature exist in structured communities termed ray projections into modern computed tomography (CT), biofilms rather than free swimming planktonic bacteria. nuclear magnetic resonance spectroscopy into magnetic res- Moreover, bacteria within biofilms are highly tolerant to onance imaging (MRI), and radar ranging into synthetic typical antimicrobial and antibiotic treatments. These ob- aperture radar imaging (SAR). Over the last 16 years, op- servations, coupled with the negative impacts of the pres- tical coherence tomography (OCT) has provided an alter- ence of biofilms in medical, industrial and natural settings, native to physical sectioning and histology that allows for have driven research into the processes that govern the imaging of living samples and even in vivo examination formation, growth and development of biofilms. Because of cell structure and dynamics. Applications range from biofilms typically form in the presence of an externally monitoring the development of engineered tissues to the driven fluid, the dynamics of the viscoelastic biofilm is in- diagnosis of malignancies. The sectional imaging of OCT herently a fluid dynamics problem. Biofilms are physically is achieved by direct visualization of raw data obtained in and biologically heterogeneous with a range material prop- focused optical range finding. As a result, there is, in the erties, making any mathematical treatment both challeng- OCT community, a widely held belief that there exists a ing and engaging. This talk will describe the incremental trade-off between transverse resolution and the thickness process of extending a classical technique used to solve cou- of the volume that may be imaged with a fixed focal plane. pled flow problems (BIM) to incorporate the growth and The extreme manifestation of this effect may be seen in material properties of the biofilm. The goal of the research optical coherence microscopy (OCM) where a single plane is to provide insight into the mechanisms of bacterial toler- is imaged using a highly focused beam to achieve micron ance and the development of more effective techniques for scale resolution, but no sectioning is possible because of the removal of the bacteria. the defocus away from this plane. In this talk I will show that solution of the inverse scattering problem leads to al- Nick Cogan gorithms that provide a three-dimensional reconstruction Department of Mathematics of the object with a spatially invariant point-spread func- Florida State University tion for the system. The spatial resolution is everywhere [email protected] equal to the best resolution in the raw data (in the focal plane). Thus the supposed trade-off between resolution and depth of imaging is eliminated. The resultant recon- MS16 structions show a marked qualitative improvement in all Channel Forming Instabilities in Multiphase Flow regions and moreover are quantitatively meaninful. This Models of True Slime Mold new modality is formally related to SAR and we refer to it as interferometric synthetic aperture microscopy (ISAM). I The true slime mold Physarum polycephalum is a single will present the theoretical analysis, numerical simulations cell organism reaching up to meters in size. The cyto- and experimental results for samples including a tadpole, a plasm shows periodic shuttle streaming through a network human tumor, and a titanium dioxide particle suspension. of tubular structures reaching velocities up to 1 mm/s. When the organism is small (¡ 100 microns) there is no streaming. As it gets larger, flow channels develop and Scott Carney streaming begins. We use a multiphase flow model and University of Illinois discuss instabilities that produce flow channels within the Urbana-Champaign gel. [email protected] Robert D. Guy Mathematics Department MS15 University of California Davis Reflectance Optical Tomography in Layered Tis- [email protected] sues Toshiyuki Nakagaki We will discuss direct and inverse problems for light prop- Research Institute for Electronic Science agation in layered tissues. Light propagation in tissues is Hokkaido University governed by the theory of radiative transport. This the- [email protected] ory takes into account absorption and scattering due to inhomogeneities. A two layer half space is a useful tissue Grady Wright model because it allows one to prescribe different optical Mathematics Department properties in superficial and deep regions of tissues. This Boise State University difference between optical properties is necessary to model [email protected] accurately light propagation through tissues systems comprised of a thin cellular epithelial layer supported by an underlying stroma. We discuss an inverse obstacle scatter- MS16 ing problem in layered tissues with applications to detect- Theory of Swimming Filaments in Viscoelastic Me- ing carcinomas in situ. This theory makes explicit use of dia the fact that tissues scatter light with a sharp peak in the forward direction. Motivated by our desire to understand the biophysical mechanisms underlying the swimming of sperm in the non- Arnold D. Kim Newtonian fluids of the female mammalian reproductive University of California, Merced tract, we examine the swimming of filaments in the non- [email protected] linear viscoelastic upper convected Maxwell model. We 56 LS08 Abstracts

obtain the swimming velocity and hydrodynamic force ex- between parallel calcium detection pathways, driven by cal- erted on an infinitely long cylinder with prescribed beating cium entry through NMDA receptors with distinct subunit pattern. We use these results to examine the swimming compositions. Here we report results and predictions on of a simplified sliding-filament model for a sperm flagel- how such a modular structure can elicit STDP induction, lum. Viscoelasticity tends to decrease swimming speed, derived from biologically detailed simulations of relevant and changes in the beating patterns due to viscoelasticity spatiotemporal dynamics in the MCell environment. can reverse swimming direction. Richard Stoner Thomas R. Powers University of Pittsburgh Brown University Department of Bioengineering Division of Engineering [email protected] Thomas [email protected] Jonathan E. Rubin Henry Fu University of Pittsburgh Brown University Department of Mathematics henry [email protected] [email protected]

Charles Wolgemuth Guoqiang Bi Department of Cell Biology University of Pittsburgh University of Connecticut Health Center Department of Neurobiology [email protected] [email protected]

MS16 MS17 Modeling Yield in a Viscoelastic Network System Protein Synthesis Dependent Consolidation of Synaptic Plasticity Abstract not available at time of publication. Memory lasts a lifetime, yet the physiological substrate of Ke Xu memory, synaptic contacts, are composed of proteins that University of North Carolina at Chapel Hill have much shorter lifetimes. Could the activity dependent [email protected] synthesis of new proteins account for persistence of L-LTP and memory? I will present work, motivated by experimental results, that suggests that a self-sustaining regulation MS17 of the translation phase of protein synthesis can form a AMPA Receptor Trafficking and its Regulation bistable switch that can persistently regulate the on-site During Synaptic Plasticity synthesis of plasticity related proteins. AMPA receptors mediate the majority of fast excitatory Harel Shouval synaptic transmission in the central nervous system, and University of Texas Houston there is growing evidence to suggest that the regulation [email protected] of AMPA receptor trafficking is an important expression mechanism for synaptic plasticity. There are two major mechanisms of AMPA receptor trafficking: exo/endocytic MS17 exchange of surface receptors with intracellular receptor A Model of the Roles of Essential Kinases in the pools, and the lateral diffusion of surface receptors be- Induction and Expression of Late Long-Term Po- tween the dendrite and spines. In this talk we present tentiation a biophysical model of these trafficking mechanisms under basal conditions and during the expression of various forms The induction of late long-term potentiation (L-LTP) in- of synaptic plasticity including LTP/LTD and homestatic volves complex interactions among second messenger cas- scaling. cades. To gain insights into these interactions, a model was developed for L-LTP induction in the CA1 region of Berton A. Earnshaw the hippocampus. The differential equation-based model University of Utah represents actions of protein kinase A (PKA), MAP ki- [email protected] nase (MAPK), and CaM kinase II (CAMKII) and activation of transcription by CaM kinase IV (CAMKIV) and Paul C. Bressloff MAPK. Simulations suggest supralinear stimulus-response University of Utah relationships are essential for translating brief stimuli into Department of Mathematics long-lasting gene activation and synaptic weight increases. bressloff@math.utah.edu The model predicts results of experiments on LLTP induction and expression, and helps clarify similarities between hippocampal LLTP and synaptic strengthening in other MS17 systems. Spatiotemporal Dynamics of Postsynaptic Signal- ing Moleculesin Plasticity Paul D. Smolen Department of Neurobiology and Anatomy, We have shown previously that a model detector system University of Texas Medical School at Houston based on plausible molecular pathways can convert the [email protected] postsynaptic calcium time course into synaptic strength changes consistent with experimental results from spike- timing dependent (STDP) and classical plasticity proto- MS18 cols (LTP/LTD). Recent evidence supports competition Automating Modular Construction of Multiscale LS08 Abstracts 57

Models MS18 VPHOP Hypermodelling Technology: A Peer-to- Success in automating automating the construction of in- Peer Conceptual Architecture for the Modular tegrated models from databases of preconstructured mod- Composition of Multiscale Predictive Models ules (= modular model forms) would allow the extraction of thoroughly validated modules from well-curated databases, The Osteoporotic Virtual Physiological Human (VPHOP) with assurance of clear documentation by acknowledged is a large-scale international project that will run in the pe- experts. Competing modules should similarly be available. riod 2008-2012. The scope is to develop a patient-speciﬁc To pull selected modules into a higher level model requires multiscale modelling technology capable of predicting with common ontologies, complete equations with boundary and high accuracy the absolute risk of bone fracture in osteo- initial conditions. completely deﬁned units, and running porotic patients. The presentation will describe the con- examples. This requires serious collaborative planning, at ceptual architecture of this model of models, a.k.a. hy- the national and international levels. Total success in very permodel, and some of the implementation strategies we general way is unlikely. The problems start with the fact plan to adopt to solve this complex problem. In particular that models stored in databases such as CellML, SBML we shall describe the idea of an agent-based architecture or ours at Physiome.org or others, have not adhered to a that leverages of digital library services for data manage- common ontology. Having multiple synonyms for variable ment to ensure neutrality and easy interoperability, and an and parameter names would help, at some risk of loss of adaptive communication protocol to solve the problem of uniqueness. Suggestions for implementing such capabilities hypermodels combining loosely and tightly coupled mod- is the topic of this discussion. els.

James B. Bassingthwaighte Marco Viceconti U.Washington, Box 35-5061 Istituti Ortopedici Rizzoli Seattle WA 98195-5061 Laboratorio di Tecnologia Medica [email protected] [email protected]

MS18 MS19 Exploiting the Biophysical Semantics of Biosimula- The Impact of Behavioral Changes on the Spread tion Models of Pandemic Inﬂuenza.

Currently, the merging of validated physics-based modules Abstract not available at time of publication. into multiscale (molecules to organisms) and multidomain (chemical kinetics, fluid dynamics, etc.) biosimulation Sara Del Valle models depends on manual, code-level integration meth- Los Alamos National Laboratory ods that scale poorly to the scope of the physiome. Pro- Los Alamos National Laboratory viding computational assistance, or outright automation of [email protected] model merging must rely on: (1) computable knowledge of the biophysical properties and property dependencies that models encode as, respectively, variables and equations, MS19 and (2) a corresponding bioinformatics architecture and Sustained Oscillations via Coherence Resonance tool set that can merge and encode models across disparate Stochastic a Pandemic modeling languages while resolving pervasive curatorial er- rors. Toward these goals, we introduce (1) the Ontology Abstract not available at time of publication. of Physics for Biology (OPB) an ontology of biophysical and systems dynamical knowledge, (2) Semantic Simula- Priscilla Greenwood tion (SemSim) models light-weight ontologies that encode Arizona State University the biophysical semantic content of individual models in [email protected] terms of the OPB and other knowledge resources, and (3) BioSem Builder software that semantically merges Sem- MS19 Sim models and re-encodes the merged models into a variety of biosimulation languages. We anticipate that these The Diffusion Along a Genetic Space of Strains of bioinformatics knowledge resources and tools will greatly Influenza accelerate and facilitate automatic, or semi-automatic com- Abstract not available at time of publication. position of patient- and pathology-specific biosimulation models. Joaquin Rivera Arizona State University Daniel L. Cook [email protected] University of Washington Department of Physiology & Biophysics [email protected] MS19 Antiviral Intervention During Pandemic Influenza: MS18 Prophylaxis and Treatment Coverage Levels Driven by Individual and Societal Interest Distributing and Maintaining Models in CellML Abstract not available at time of publication. Abstract not available at time of publication. Eunha Shim Peter Hunter Yale University University of Auckland [email protected] New Zealand [email protected] 58 LS08 Abstracts

MS20 [email protected] Nonlinear Effects of Signal Transduction in Olfac- tory Sensory Neurons MS20 Using stoichiometric network analysis and bifurcation the- Olfaction as a Model System for Sensory- ory, we identify a calcium-induced negative feedback on Processing Neural Networks the ion channel level that explains experimentally observed fast adaptation and oscillations in the signal transduction The olfactory system is a prominent model for sensory pro- of vertebrate olfactory receptor neurons (ORNs) (Reidl cessing, particularly regarding how groups of nerve cells et al., Biophys.J. 90 (2006)). The characteristic quasi- collectively represent sensory inputs. A nerve cell is tra- onedimensional geometry of the cilia of the ORN leads to ditionally considered the processing unit of the brain, but a description in terms of interacting sensing modules. The recent data suggest that nerve cells may consist of several effect of negative feedback on the dynamics and coopera- processing units. The organized interaction of processing tion of these modules is examined (Gopalakrishnan et al., units results in electrical brain waves. This presentation PRE 76 (2007)). provides an overview of recent experimental findings in the olfactory system. Peter Borowski The University of British Columbia Jens Midtgaard Department of Mathematics University of Copenhagen [email protected] Dept. of Neuroscience and Pharmacology j.midtgaard@mfi.ku.dk Juergen Reidl SAP MS20 [email protected] Analysis of Macroscopic Network Activities

Jens Starke Equation-free techniques allow for systematic investiga- Technical University of Denmark tions of macroscopic neural network activities and their Department of Mathematics dependence on biological parameters such as kinetic pa- [email protected] rameters or the network topology. The considered olfactory bulb network consists of mitral cells which are cou- Martin Zapotocky pled in an inhibitory way via granular cells and is described Max Planck Institute for the Physics of complex systems as spike response model. The investigated phenomena in- [email protected] clude contrast enhancement, hysteresis effects in odorant discrimination and traveling waves which were analyzed Markus Eiswirth with continuation methods and bifurcation analysis. Fritz-Haber-Institute, Berlin [email protected] Jens Starke Technical University of Denmark Department of Mathematics Anke Sensse [email protected] Bayer Technology Services [email protected] Carmen Ellsaesser University of Heidelberg MS20 Interdisciplinary Center for Scientific Computing Axonal Pathfinding and Sorting in the Olfactory [email protected] System

The axonal pathfinding in the olfactory system is an exam- MS21 ple for an extremely precise sorting behavior: all axons of Analyzing Dynamic Crosstalk Among Kinase Path- an odorant receptor of certain type project onto the same ways with Fuzzy Logic site in the olfactory bulb, the glomerulus. This process is described with a mathematical model with attractive and We adapted fuzzy logic to analyze a dataset characteriz- repulsive interactions between the growing axons. Simula- ing the dynamic behavior of kinase pathways governing tions reproduce the observed sorting of the axons. Under apoptosis. Use of fuzzy logic enabled balance of mecha- certain conditions, the convergence into a sorted state can nistic detail and ease of interpretation. Simulations of our also be shown analytically. model recapitulated most features of the data and generated several predictions involving pathway crosstalk and Noemi Hummel regulation. Additionally, we have demonstrated that fuzzy ETH Zuerich logic rules can be produced with empirical data, creating Makroökonomie: Innovation und Politik potential for automated and unbiased modeling with em- [email protected] phasis on conceptual interpretation. Bree B. Aldridge Simon Kokkendorff MIT, Biological Engineering Department Technical University of Denmark Harvard Medical School, Department of Systems Biology Department of Mathematic [email protected] s.l.kokkendorff@mat.dtu.dk Julio Saez-Rodriguez, Jeremy Muhlich Jens Starke Harvard Medical School Technical University of Denmark Department of Systems Biology Department of Mathematics LS08 Abstracts 59

[email protected], jeremy [email protected] MS21 Parameter Estimation for Bursting Neural Models Peter Sorger Department of Systems Biology, Harvard Medical School Parameter estimation for differential equation models is a Biological Engineering Department, MIT challenging problem. This talk will consider parameter es- peter [email protected] timation for an ODE model of respiratory neurons that ”burst”. I’ll discuss an approach which uses geometric fea- Douglas Lauffenburger tures of the differential equation to aid the estimation. In Division of Biological Engineering, Dept. of Chem. Eng. particular, we formulate a geometric definition of bursting MIT based upon multiple time scales in the ODE, and restrict lauff[email protected] to periodic burst solutions in our parameter search. The results suggest possible ways that the neuronal output may be modulated. MS21 Joe Tien Analysis of the Regulators of Caspase Activation Mathematical Biology Research Group by Death Receptor Ligands McMaster University To understand ligand-induced cell death decisions in hu- [email protected] man cells, we combine single-cell and population-based measurements with ODE models of relevant protein sig- MS22 naling networks. We seek a quantitative understanding of what controls the completeness, rapidity and timing of cas- Dynamic Integration of Distributed Biological pase activation. Because these descriptors of caspase dy- Pathway Models Using Cytosolve namics are more biologically relevant than time-dependent One prevailing strategy to model the whole cell is a bot- caspase activity profiles, we used numerical methods based toms up one: first integrate smaller biological pathway on finite differences to analyze their sensitivity to changes models to build larger models of cellular function and then in initial protein concentration and parameter values. link such larger models to produce a computational model Suzanne Gaudet, William Chen, John Burke of the whole cell. The current approach to realize this strat- Department of Systems Biology egy is a monolithic one, where the model integrator manu- Harvard Medical School ally merges the computer source codes of smaller biological suzanne [email protected], pathway models to create one large monolithic computer william [email protected], program containing the merged source codes. The mono- john [email protected] lithic approach is not scalable for integrating the thousands of biological pathway models necessary to model the whole cell. We present Cytosolve, a new method that dynami- Douglas Lauffenburger cally integrates a distributed ensemble of biological path- Division of Biological Engineering, Dept. of Chem. Eng. way models without the need to merge the source codes of MIT the individual biological pathway models. Cytosolve allows lauff[email protected] each biological pathway model to reside at its own location on any computer worldwide, where the authors of each Peter Sorger model can independently maintain and update the models Department of Systems Biology, Harvard Medical School source code. As more biological pathway models develop in Biological Engineering Department, MIT a disparate and decentralized manner, Cytosolve provides peter [email protected] a scalable method to integrate complex models of cellular function, and eventually to model the whole cell. In this talk, we will present the Cytosolve architecture and share MS21 two working examples: (1) integrating the EGFR pathway Elucidating Mechanisms in Genetic Oscillators Via of Kholodenko, and (2) an integrative model of the IFN Inverse Bifurcation Analysis response to viral infection.

Given a plausable ODE model that captures the known V.A. Shiva Ayyadurai, C. Forbes Dewey qualitative dynamics of an oscillatory gene network, one Massachusetts Institute of Technology often would like to derive insights on how the system be- [email protected], [email protected] havior is controlled by the various gene interactions. To address such issues, we formulate inverse problems whereby bifurcation phenotypes are mapped to biochemical mecha- MS22 nisms. For applications ranging from redox oscillations to Merging Cellular Biochemical Models Using circadian rhythm, there is a need to elucidate the mech- Physicochemically Rigorous Rules anisms governing limit cycles solutions and their bifurcations (including period-doubling and Neimark-Sacker). In Simulations of cellular systems are optimally realistic and this talk, we show the mathematical formulations for tack- meaningful only when appropriate physical chemical rules ing such problems and demonstrate the results of inverse are adopted. Since a great deal of information is available bifurcation analysis to a number of oscillator models. regarding the thermodynamic and ion-binding properties of biochemical reactants, it is possible to construct sim- James Lu ulations of biochemical systems that properly incorporate Johann Radon Institute these data. Speciﬁcally, realistic simulations of biochemical for Computational and Applied Mathematics systems require accounting for: (i.) the complex multiple [email protected] equilibria of biochemical species and dynamic buﬀering of ions; and (ii.) the pH and ionic dependence of enzyme kinetics and apparent equilibria and thermodynamic driving 60 LS08 Abstracts

forces for biochemical reactions. Using a formal method MS24 that treats these phenomena, we can develop and validate Origin and Spatiotemporal Organization of Cardiac computational models of systems of unprecedented com- Alternans plexity. In addition, rigorous physical chemical rules facilitate non-ambiguous model integration while reducing Cardiac alternans are period-doubling oscillations of heart uncertainty in parameter estimates and improving the re- activity with a well-established clinical link to sudden liability of model predictions. As an example we will show death. This talk will discuss recent progress made to under- how a model of cardiac energy metabolism that tracks more stand the cellular origin of these oscillations and their com- than 100 species is developed, parameterized, validated, plex spatiotemporal organization at the tissue scale, using and used to generate hypotheses and understand emergent both physiologically detailed and abstract models. The re- phenomena. sults shed light on the fundamental nature of the alternans bifurcation and the complex dynamics of phase-defects un- Daniel A. Beard derlying the formation of an arrhythmogenic substrate. Medical College of Wisconsin Department of Physiology Alain Karma [email protected] Distinguish Professor Northeastern University [email protected] MS22 Robust Large-Scale Individual-Based Modelling in Biology MS24 Purpose and Methods of a Bidomain Reaction- We are interested in the complex (emergent) behaviour of Diffusion Model of the Human Heart large numbers (millions) of interacting entities. The interactions might take place on the same length and time scale The first mathematical heart model consisted of a single or on a hierarchy of length and time scales. The entities dipole source. It is still used. More recent models couple may be physical objects which are constrained to obey the millions of elements, each represented by a detailed mem- laws of physics, and may have complex networks embed- brane model. We pushed this further by making a bido- ded within them. Examples include cell signalling networks main reaction-diffusion model of the human heart with over (molecule level), tissue development, wound healing, and 50 million elements. In this presentation we discuss how the development of malignancy (cell level), and the be- to make such a large bidomain system converge, and what haviour of ant colonies and macro-economic behaviour in are the useful applications of this large and resource-hungry human societies (society level). Our aim is to understand model. behaviour and predict the effect of intervention, in order to design therapeutic interventions or influence social policy. Mark Potse Properly engineered and robust software tools are essential Institut de Génie Biomédical, Université de Montréal if the goal is to use the software to inform clinical and policy Centre de Recherche de lHôpital du Sacré-Cur de decisions. We are developing FLAME (Flexible Large-scale Montréal Agent Modelling Environment, http://flame.ac.uk) to pro- [email protected] vide these robust software tools. The presentation will provide an overview of our approach to modeling complex systems and the aims of the software development team, and MS24 examples of model building using the software, including Spatial Heterogeneity and Atrial Arrhythmias links to physics models and other modeling paradigms (e.g. COPASI). Atrial fibrillation is the most commonly encountered cardiac arrhythmia. The atria express great heterogeneity in Rod Smallwood terms of action potential duration and morphology, which University of Sheffield ,UK can be further amplified by neural modulation. The con- r.smallwood@sheffield.ac.uk sequences of two aspects of this heterogeneity are explored in a computer model. The role of action potential duration gradients in establishing reentry is discussed. Second, ar- MS24 rhythmogenic aspects of acetylcholine release in the sinoa- Numerical Treatment of the Bidomain Equations trial node are explored. in Large Scale Simulations Edward Vigmond In deriving the conductivity tensor of cardiac tissue, we are Associate Professor forced to deal with very large Finite Element matrix sys- University of Calgary tems. To cope with this problem we introduce a conjugate [email protected] gradient method with dual search directions that exploits the structure of the Bidomain equations. The procedure accelerates the rate of convergence, guarantees convergence MS25 to a null residual and allows us to determine the influence Coarse-Grained Modeling and Simulation of Lipid of high resistive barriers on the conductivity tensor. Bilayer Membranes

Jacques Beaumont Lipid molecules consist of a hydrophilic head group and Binghamton University a hydrophobic tail whose competition leads to intriguing Department of Pharmacology phases. These include micelles, bilayered ﬂuidic sheets, or [email protected] enclosed vesicles with rich geometric structures having features over a wide range of length-scales. A fundamental challenge in studying lipid systems is to understand how molecular level interactions lead to observed large-scale phenomena. In this talk we shall discuss a coarse-grained LS08 Abstracts 61

modeling and simulation approach which captures many [email protected] of the features of lipid bilayers. We shall then discuss hydrodynamic phenomena related to bilayer membranes. In particular, the role of thermal fluctuations and the coupling MS25 of membrane deformations and lipid flow. We will also dis- Equilibrium Shapes of Multicomponent Vesicles cuss the role of fluid-like features of the membrane in the dynamic coupling of protein inclusions within a bilayer. Phase separation within a multi-component membrane can lead to the formation of domains with distinct mass concen- Paul J. Atzberger tration. The physical quantities such as bending stiffness University of California-Santa Barbara and surface tension may adjust their values correspond- [email protected] ingly. As a result, shape transformations occur. The classical theory on the equilibrium shapes focus on the compe- Frank Brown tition between the bending energy and the line energy of Department of Chemistry and Biochemistry the phase boundaries. Surface tension, another important University of California Santa Barbara mechanical property at small scales, usually is neglected. fl[email protected] In this talk, we assume surface tension depends on the local mass concentration. We present a group of nontriv- ial equilibrium shapes induced by the competition between MS25 surface energy and the line tension. Our results show that, Investigating Platelet Motion Towards Vessel Walls without bending, this competition gives rises to phenom- in the Presence of Red Blood Cells ena of domain-induced budding for a membrane with fixed surface area and volume. Blood is a heterogeneous medium composed primarily of red blood cells and plasma. Although platelets make up John Lowengrub only one percent of blood by volume, they are highly con- University of California, Irvine centrated near vessel walls in vivo. This phenomenon has Department of Mathematics proven difficult to quantify. We use a lattice Boltzmann- [email protected] immersed boundary method to investigate how shear rate, hematocrit, red cell deformability, as well as platelet size Geoff Cox and shape affect lateral platelet motion. Dept Math, UC Irvine [email protected] Lindsay M. Crowl University of Utah Shuwang Li Graduate Student University of California, Irvine [email protected] [email protected] Aaron L. Fogelson University of Utah MS26 [email protected] Rapid Spontaneous Evolution of Modularity

Biological networks have an inherent simplicity: They are MS25 modular, with a design that can be separated into units Cell Quakes: Microrheology in Active Gels and that perform almost independently. Little is known about Living Cells the evolutionary origin of modularity. We suggest a possible explanation for the origin of modularity in biology. The mechanics of the in vivo cytoskeleton is controlled in We find that evolution under ’modularly varying environ- part by the details of its non-equilibrium steady-state. In ments’ can lead to the spontaneous emergence of modular this “active’ material, molecular motors (e.g. myosin) ex- systems. We further find that varying environments can ert transient contractile stresses on the F-actin filament dramatically speed up evolution compared to evolution un- network. Since microrheology traditionally relies of the der a fixed environment. linear response properties of the soft materials in thermal equilibrium, this departure from equilibrium has profound Nadav Kashtan implications for the interpretation of microrheological data Weizmann Institute from the interior of living cells and in vitro active networks. [email protected] In active networks, such as the in vitro systems of Mizuno et al. [Science 315 (5810) pp. 370-373 (2007).] and in living cells, the underlying theoretical foundation of the interpre- MS26 tation of microrheology – the Fluctuation-Dissipation the- Critical Dynamics in a Living Cell orem – does not apply. New ideas are needed. In this talk, I review microrheology, and then discuss a new theoreti- Cells are dynamical systems of biomolecular interactions cal interpretation of microrheology in active (i.e. molecu- that process information from their environment to mount lar motor driven) networks. I also explore how molecular diverse yet specific responses. A key property of many motor activity can reversibly control the elastic proper- self-organized systems is that of criticality: a state of a sys- ties of these active gels. The cytoskeleton points towards tem in which, on average, perturbations are neither damp- the development of new biomimetic materials whose elas- ened nor amplified, but are propagated over long temporal tic properties can be tuned by controlling the material’s or spatial scales. Criticality enables the coordination of non-equilibrium steady-state. complex macroscopic behaviors that strike an optimal balance between stability and adaptability. Using an approach Alex Levine based on algorithmic information theory and applying it to Department of Physical Chemistry global gene expression data from macrophages, we found University of California Los Angelos that macrophage dynamics are critical, providing the most 62 LS08 Abstracts

compelling evidence to date for this general principle of of STDP that Sjoestroem has measured [2] 2. accounts for dynamics in biological systems. the triplet effects of STDP that Bi-lab has measured [3] 3. accounts for a voltage dependence similar to Artola- Ilya Shmulevich Broecher-Singer (ABS) [4] 4. accounts for the Dudek-and- Institute for Systems Biology Bear experiments [5] 5. and can be formally reduced to the [email protected] Bienenstock-Cooper-Munro (BCM) model [6] if spiking is generated by Poisson processes. References * [1] Pfister and Gerstner, J. Neuroscience, 2006 * [2] Sjoetrom et al., MS26 Neuron, 2001 * [3] Wang et al., Nature Neuroscience 2005 Systems-Level Regulation of Immune Responses * [4] Artola et al., Nature, 1990 and Ngezahaio et al., J. Neuroscience 2000 * [5] Dudek and Bear, J. Neuroscience, The immune response is a complex intertwined network 1993 * [6] Bienenstock, Cooper, Munro, J. Neuroscience, of interactions. We have examined a respiratory infection 1982 model system by synthesizing a network based on existing experimental information and integrating it in dynamic Claudia Clopath models based on Boolean formulation. Our model offers Ecole Polytechnique Federale de Lausanne novel predictions regarding cytokine regulation, key im- Brain-Mind Institute, EPFL mune components and clearance of primary and secondary claudia.clopath@epfl.ch infections; we experimentally validate few of these predictions. The model provides insights into the virulence and Wulfram Gerstner pathogenesis of disease-causing microorganisms and allows Ecole Polytechnique Federale de Lausanne system-level analysis. [email protected]fl.ch Juilee Thakar Pennsylvania State University MS27 Cancer Research Institute/ Irvington Instritute [email protected] Matching a Decision with Response: Learning to Solve the XOR Problem

MS26 Many cognitive tasks require particular responses to specific combinations or pairings of stimuli. Such paired re- Evolution of Complexity sponses require logic equivalent to XOR and formation of Abstract not available at time of publication. neurons responsive to specific stimulus pairs. We generate such neurons from an initially randomly connected network Roy Wilds of spiking neurons. We find spike-timing dependent plas- McGill University ticity tends to over-associate. However, long-term potenti- [email protected] ation of inhibition counters over-association by generating cross-inhibition that is essential for producing specificity and enabling solution of such stimulus-pairing tasks. MS27 Tracking Calcium Dynamics from Voltage Mea- Paul Miller, Mark Bourjaily surements Brandeis University [email protected], [email protected] Using models of calcium dynamics in postsynaptic cellular stimulations by electrophysiological protocols, we show how one can verify and then validate models of those dy- MS27 namical processes. The method, Dynamical Parameter Es- Reinforcement Learning in Populations of Spiking timation, allows single measurements on networks of neu- Neurons. rons to follow dynamical processes and verify and validate models of those processes. Averaging over fluctuations of many individual neurons within a population is a key mechanism for achieving ro- Henry Abarbanel bust information processing in the brain. However, in the University of San Diego context of reinforcement learning, single neuron perfor- [email protected] mance is only loosely related to the population response, so that a global reinforcement signal based on the population response cannot reliably assess the performance of any MS27 single neuron. This results in a degradation of standard Phenomenological Model of Synaptic Plasticity Ex- reinforcement algorithms with increasing population size. periments We suggest a novel, biologically realistic form of synaptic plasticity which overcomes such degradation. Spike-Timing-Dependent Plasticity (STDP) has been described by numerous models, either simple phenomenolog- Robert Urbanczi, Walter Senn ical and biophysical models based on calcium-calmodulin University of Berne dynamics. A challenge for all modeling approaches is to [email protected], [email protected] describe not only one experiment but a broad set of experimental paradigms in a single framework. Here we present a model of STDP that is triggered by presynaptic spike MS28 arrival in combination with postsynaptic voltage and gen- Multiscale Cancer Modeling eralises an earlier model [1]. Action potentials of the postsynaptic neuron lead to voltage peaks, but subthreshold Based on the concept that tumors behave as complex dy- voltage gives also a contribution. This simple phenomeno- namic and self-organizing biosystems, the talk will describe logical model of STDP 1. accounts for the frequency effects the development of a data-driven, agent-based multi-scale LS08 Abstracts 63

and multi-resolution brain cancer model. This algorithm variables. is designed to investigate how changes on the molecular level can percolate across the scales of interest, by impact- Roger D. Kamm ing microscopic behavior as well as multi-cellular patterns. Depts Mechanical Engineering and Biological Engineering This project is part of The Center for the Development of Mass Inst of Tech a Virtual Tumor, CViT [email protected] Tom Deisboeck Massachussetts General Hospital MS28 [email protected] Perturbations in Epithelial Tissue Renewal and Cancer; Modeling Clonal Expansions and Genetic Diversity in Carcinogenesi MS28 PreDiCT: Computational Prediction of Drug Car- Mathematical analysis of a general class of multistage cardiac Toxicity cinogenesis models reveals two basic phases in the age- specific cancer incidence function: a first exponential phase Approximately 50% of the compounds developed by the until the age of about 60 followed by a linear phase af- pharmaceutical industry interfere with the heart (e.g., pro- ter that age. These two phases in the incidence curve re- longing the QT-interval in the ECG). The regulatory agen- flect two phases in the process of carcinogenesis. Paradox- cies either restrict or decline the usage of these compounds ically, the early exponential phase reflects events between for medical treatments. Products have been withdrawn the formation (initiation) of premalignant clones in a tis- from the market due to indications of cardiac toxicity. sue and the clinical detection of a malignant tumor, while However, it is well-known that the QT-interval is not al- the linear phase reflects events leading to initiated cells ways a good metric and only little is known on the rela- that give rise to premalignant lesions as a result of abro- tion between drug properties and arrhythmicity. We will gated growth/differentiation control and/or perturbed tis- present our multi-scale approach to predict the toxicity of sue renewal due to damaging exposures inflicting wound- drugs in the heart - ranging from the ion channel level to ing. This model is consistent with Knudson’s idea that whole organ models. In collaboration with pharmaceuti- renewal tissue, such as the colon, is converted into growing cal industries we will investigate the interaction of various tissue before malignant transformation. The linear phase drug compounds on the main sodium, calcium and potas- of the age-specific incidence curve represents this conver- sium ion channels. The modelling framework then leads to sion, which can be the result of a recessive inactivation of the possibility to examine the relation between the mode a gatekeeper gene that maintains normal tissue architec- of action of the compounds and the arrhythmic events in ture. Modeling Clonal Expansions and Genetic Diversity the whole heart of rabbit and human. in Carcinogenesis Carlo C. Maley Carcinogenesis is a dynamic, multiscale process of clonal evolution in which ge- Martin Fink netic and epigenetic lesions (at the molecular scale) affect Department of Physiology, Anatomy and Genetics the expansion of clones and the accumulation of clonal di- University of Oxford, UK versity (at the organ scale). Most of the details of these martin.fi[email protected] dynamics remain unknown. For example, we do not understand how clones spread within a neoplasm or how clonal diversity changes over time as clones develop genetic insta- MS28 bility and competition drives some clones extinct. These An Agent-Based Markovian Model for Angiogene- problems are important because suppressing clonal expan- sis sions would help to prevent cancer and we have shown that patients with more genetic diversity in their pre-malignant Angiogenesis is the process by which blood vessels form tumors are more likely to progress to cancer. Genetic di- from an endothelial monolayer. Development of angiogen- versity is also likely to be associated with therapeutic resis- esis models is essential to understand the contribution of tance, which is the cause of most cancer deaths. We have various factors (biochemical and biomechanical) involved developed agent based models to explore the dynamics of in the process. Many existing models fail to account for clonal expansions and diversity in neoplasms. We are using cell-cell communication or the response of each cell to var- these models to guide the development of experiments to ious angiogenic factors. Also, a comprehensive analysis measures those dynamics in vivo. of signaling pathways is lacking. This study aims at understanding the response of cell populations, wherein each Georg Luebeck cell is modeled by using Markov process, responding to Fred Hutchinson Cancer Research Center certain global and local conditions. Thus, feedback loops [email protected] (local and global) which are crucial to the biological process are an integral part of the model. The overall model is Carlo Maley stochastic and the probabilities of transition between cell Wistar Institute states (quiescent/ migrating/ dividing/ dying) are based [email protected] on output from the cue-signal-response model. The transition probabilities are functions of the current cell state and the cues added to the system. The direction of transition MS28 (migration/division) depends on matrix properties, which Modeling Clonal Expansions and Genetic Diversity change every time step and affect the cell state in the fol- in Carcinogenesis lowing step. One mathematical challenge is dealing with the different timescales of intra-cellular and inter-cellular Carcinogenesis is a dynamic, multiscale process of clonal interactions. The overarching objective is to obtain a com- evolution in which genetic and epigenetic lesions (at the plete model of angiogenesis as it pertains to a controlled, molecular scale) affect the expansion of clones and the ac- in vitro experimental system with a reduced number of cumulation of clonal diversity (at the organ scale). Most of the details of these dynamics remain unknown. For ex- 64 LS08 Abstracts

ample, we do not understand how clones spread within onance imaging (tMRI) is a cardiac imaging modality de- a neoplasm or how clonal diversity changes over time as veloped to assess region myocardial motion within the LV clones develop genetic instability and competition drives wall. This presentation summarizes the principle of tMRI, some clones extinct. These problems are important be- some of the sensitive motion estimators, including har- cause suppressing clonal expansions would help to prevent monic phase interference, and simple time-reversal model cancer and we have shown that patients with more genetic of left ventricle wall motion used for evaluating the cardiac diversity in their pre-malignant tumors are more likely to performance using tMRI data. progress to cancer. Genetic diversity is also likely to be associated with therapeutic resistance, which is the cause Mehmet Bilgen of most cancer deaths. We have developed agent based Medical University of South Carolina-Charleston models to explore the dynamics of clonal expansions and [email protected] diversity in neoplasms. We are using these models to guide the development of experiments to measures those dynamics in vivo. MS30 Inversion Techniques for Magnetic Resonance Elas- Carlo Maley tography Wistar Institute [email protected] MR elastography can quantitatively and non-invasively measure full vector displacements from propagating acoustic waves in vivo. From these data, inversion algorithms MS29 can calculate biomechanical tissue properties such as stiﬀ- Quiescent Phases and Their Impact on Predator- ness, viscosity, and anisotropy. An overview of inver- Prey Dynamics sion techniques proposed for this data and their relative strengths and weaknesses will be presented. Preliminary Abstract not available at time of publication. studies indicate that the technique has substantial potential as a diagnostic tool. Lydia Bilinsky Arizona State University Armando Maduca [email protected] College of Medicine Mayo Clinic [email protected] MS29 Optimal Control of Lipid Production is Green Al- gae MS30 Reconstructing Tissue Elasticity Using a Lumped Abstract not available at time of publication. Parameter Model

Sarah Hews Lumped parameter system identification can be used to Arizona State University recover accurate mechanical properties of an anomaly in [email protected] soft tissues such as a cancerous region in the brain or breast. The LPSID method competes with, and offers trade-offs to the current technology used in elastography MS29 where these primary advantages are 1) computational effi- The Potential Impact of Disease on the Migratory ciency through exact linear solutions, and 2) the recovery of Structure of a Partially Migratory Bird Population first and second derivative mechanical properties, namely damping and mass. Abstract not available at time of publication. David Manegold Paul Hurtado Dartmouth College Cornell University [email protected] [email protected]

MS30 MS29 Detectability in Magnetic Resonance Elastography Saturation in Predation and Predation-Transmitted Infections MR elastography may detect early stage small cancerous tissue, which is believed to be of35mmdiameter. The Abstract not available at time of publication. detection of this small inclusion is challenging, because the Christopher Kribs Zaleta inclusion is small relative to the typical wavelength (10 30 University of Texas at Arlington mm) of a low frequency excitation. This talk provides a [email protected] theoretical bound of the smallest possible size of the de- tectable inclusion as a function of noise level, contrast ratio of the stiﬀness, and the excitation frequency. MS30 Jeong-Rock Yoon Tagged Magnetic Resonance Imaging for Evaluat- Department of Mathematical Sciences ing Regional Cardiac Function: Data Acquisition Clemson University and Processing Approaches [email protected] Cardiac dysfunction or impaired relaxation/contraction of myocardium is associated with a variety of cardiovascular condition that leads to heart failure. Tagged magnetic res- LS08 Abstracts 65

MS31 Robert D. Guy Optimal Flexibility in Flapping Appendages Mathematics Department University of California Davis When oscillated in a fluid, appendages such as insect wings [email protected] and fish fins can produce large thrust forces while undergoing considerable bending. Can we determine the flexibility which produces maximum thrust and efficiency? We solve MS31 a general model for how flexible surfaces produce vortic- The Lower Reynolds Number Limit of Flapping ity and bend passively in a fluid. We find a series of local Flight thrust optima which are resonant peaks, and can be predicted with a scaling analysis. We discuss extensions to In this talk, the aerodynamic challenges of tiny insect large-amplitude motions, and motions of actual fish fins. flight and the possible morphological and kinematic adaptations insects use to increase lift forces will be discussed. Silas Alben Aerodynamic forces were studied over a range of Reynolds Georgia Institute of Technology numbers using the immersed boundary method to numer- School of Mathematics ically solve the two-dimensional Navier-Stokes equations [email protected] with moving, flexible boundaries. For the smallest insects, flapping flight becomes less efficient as relative lift forces decrease and relative drag forces increase with decreasing MS31 Reynolds number. Simulating Cardiac Fluid-Structure Interaction by the Immersed Boundary Method Laura A. Miller University of North Carolina - Chapel Hill The immersed boundary (IB) method is a framework for Department of Mathematics modeling and simulating problems in which a viscous [email protected] incompressible fluid interacts with an immersed elastic boundary. I shall describe an adaptive IB method that employs Cartesian grid adaptive mesh refinement (AMR) MS32 and present results from the application of this methodol- Mathematical Analysis of Error Regulation in Bi- ogy to a model of the human aortic valve as well as a new ological Systems medical imaging-derived model of the heart and nearby great vessels. We develop a quantivative, stochastic thermodynamic analysis for the error rate of the DNA replication process Boyce E. Griffith inside a living cell. The analysis suggests that a flux-driven Courant Institute of Mathematical Sciences mechanism for the high fidelity according to the theory of New York University “kinetic checkpoints”. It shows how it is coupled to en- griffi[email protected] ergy input from the cell. Though we focus primarily on DNA replication, the model and mechanism are applicable David M. McQueen to other biochemical processes. Courant Institute of Mathematical Sciences New York University Field Cady [email protected] University of Washington fi[email protected] Charles S. Peskin courant institute of mathematical sciences, NYU Hong Qian [email protected] Department of Applied Mathematics University of Washington [email protected] MS31 Grow with the Flow: A Dynamic Tale of Blood MS32 Clot Formation Specificity of Cell Signalling The body heals injured blood vessels and prevents bleeding by clotting the blood. Clots are primarily made of Different cellular signal transduction pathways are often in- blood-borne cells and a fibrous material that is assembled terconnected, so that the potential for undesirable crosstalk at the site of injury in flowing blood. Clot composition and between pathways exists. Nevertheless, signaling networks structure change with local chemistry and fluid dynamics, have evolved that maintain specificity from signal to cel- which in turn alters the flow. To better understand this lular response. In this talk, I will introduce a new frame- fluid-structure coupling, we model the growing clot as a work on specificity for the analysis of networks containing mixed porous material immersed in a dynamic fluid envi- two or more interconnected signaling pathways. Using this ronment. framework, along with existing and new experimental data, I shall study the mating pathway in yeast. Karin Leiderman Mathematics Department Qing Nie University of Utah Department of Mathematics [email protected] University of California, Irvine [email protected] Aaron L. Fogelson University of Utah MS32 [email protected] Some Defining Quantities in Stochastic Gene Tran- 66 LS08 Abstracts

scription University of Notre Dame Department of Mathematics To examine how the environmental signals contribute to [email protected] the regulation and noise of gene transcription, I will present a three states stochastic model. The transition between Yilin Wu these states is characterized by several deﬁning quanti- University of Notre Dame ties, which decompose the stochastic nature of transcrip- [email protected] tion activation into environmental signals, speciﬁc binding of transcription factors with promoter DNA, and the gene promoter stability. Some mathematical results and Yi Jiang questions, along with their biological implications and chal- Los Alamos National Laboratory lenges, will be discussed. [email protected]

Moxun Tang Dale Kaiser Department of Mathematics Stanford University Michigan State University [email protected] [email protected] MS33 MS32 Oscillations in Biochemical Reaction Networks Robust Cell Polarization An important problem in cell biology is to predict the dy- Cells polarize components to specific locations leading to namics of interactions in biochemical reaction networks. If morphological changes in response to internal and exter- available, realistic mathematical models of oscillatory bio- nal cues. Often, the external cue is a spatial chemical chemical reactions are large systems of differential equa- gradient. Sensing and responding to a chemical gradi- tions with many unknown parameters, making their anal- ent present many challenges including sensitivity, dynamic ysis difficult. Subnetworks of cycles in a bipartite graph range, tracking, and noise. In this talk, I will describe how associated with a biochemical reaction are used to predict we investigated in a systematic fashion the tradeoffs among oscillations. Generalized network conditions for the two these performance objectives. types of oscillations associated with negative and positive cycle will be presented. Ching-Shan Chou Department of Mathematics Maya Mincheva University of California, Irvine Department of Mathematics [email protected] University of Wisconsin-Madison [email protected] Travis Moore Department of Developmental and Cell Biology University of California, Irvine MS33 [email protected] Modeling Electrocortical Activity Through Inte- gral Neural Field Equations

Qing Nie In many regions of mammalian neocortex, synaptic con- Department of Mathematics nectivity patterns follow a laminar arrangement. Recently University of California, Irvine there has been a growing interest in such models with [email protected] delayed due to the speed of action potentials, and new progress has been made in one spatial dimension. In this Tau-Mu Yi study, we address the physiological importance of a model Dept. of Developmental and Cell Biology in two spatial dimensions with axonal delays, and obtain U. of California, Irvine an equivalent PDE model used in several EEG modeling [email protected] studies. LieJune Shiau MS33 University of Houston at Clear Lake Reversals Facilitate Collective Motion of Gliding [email protected] Bacteria Stephen Coombes, Nikola Venkov Myxobacteria move by gliding over surfaces, always retain- University of Nottingham ing contact with the surface. Many other bacteria also [email protected], glide, which does not require flagella. Gliding is partic- [email protected] ularly useful for building such multicellular structures as swarms. Myxobacterial cells are long, thin, flexible rods that tend to glide in the direction of their long axis with Ingo Bojak small deviations. Surprisingly, they reverse their gliding di- Radboud University rection regularly with almost fixed periods; reversal is con- [email protected] trolled by a protein-regulatory network. We will describe a computational model of the network which includes rever- David Liley sals and random noise in the distribution of reversal rates. Swinburne University of Technology The model shows how reversal actually facilitates swarm- [email protected] ing. Carlo R. Laing Mark S. Alber Massey University LS08 Abstracts 67

Auckland MS34 [email protected] Dynamical Evolution of Spatiotemporal Patterns in Mammalian Middle Cortex

MS33 The spatiotemporal structure of brain oscillations are im- Oscillations in NF-kappa B Signalling Pathways portant in understanding neural function. We analyze oscillatory episodes from isotropic preparations from mam- NFκB oscillations were suggested by Hoffmann et.al from malian cortex which display irregular and chaotic spa- electro-mobility shift assays (EMSA) in population stud- tiotemporal wave activity, within which spontaneously ies of IκBα-/- embryonic fibroblasts and simulated in a emerge spiral and plane waves. The evolution of these computational model. A common comment on the source patterns are likely related to activity dependent ion con- of oscillations is the existence of negative feedback loops. centration changes. The use of a principal orthogonal de- However, this is not a sufficient condition. In this paper, we composition and Galerkin projection to show the modal explore the source of oscillations by analyzing the dynam- interactions which underlie such persistent activity will be ical properties of the computational model. We find that discussed. the computational model can be treated as a fast-slow system where the level of total IκB Kinase (IKK) in the model Steven Schiff is treated as a slow variable. Assume the level of total IKK Center for Neural Engineering does not change at all. We can view the level of total IKK Pennsylvania State University as a parameter. Orbits in the true system trace attractors [email protected] in this reduced model. We find that for a some range of the level of NFκB, the reduced system experiences Hopf bifurcation twice while varying the level of total IKK. The MS34 damped oscillations come from the existence of a stable Waves and Synchrony in the Pinto-Ermentrout limit cycle or a stable spiral in the reduced system. Model with Asymmetric Coupling

Yunjiao Wang We investigate the Pinto-Ermentrout integro-diﬀerential The School of Mathematics equation model in the presence of asymmetric coupling. University of Manchester There is a parameter beta that appears in the equation, [email protected] and we focus on values of beta for which the lineariza- tion around the rest state has complex eigenvalues. In David Broomhead this regime we study single pulse and multiple pulse waves, The University of Manchester as well as the formation of synchronous oscillations which Applied Mathematics spread out spatially from a point of stimulus. [email protected] William Troy University of Pittsburgh Caroline Horton Department of Mathematics University of Liverpool [email protected] [email protected]

Douglas Kell MS34 University of Manchester Cortical Wave Dynamics Observed by Voltage- [email protected] Sensitive Dye Imaging

I will start with showing cortical wave dynamics in rat MS34 brain slices and in vivo. Then I will discuss a new method A Coupled Hypercolumn Model Approach to Con- we developed for characterizing spatiotemporal complexity tour Grouping in the Visual Cortex of waves. We analyze angular distribution of spectral energy in the wave patterns, and quantify their complexity We use a coupled hypercolumn model to study how the by the number of propagation modes of the waves. Com- primary visual cortex may accomplish the task of group- pared to empirical orthogonal function (EOF) method, our ing a contour presented in visual space. An initial blip of method is more accurate when dealing with nonstationary attentional firing rate elevation spreads along neurons that waves. contain the contour in their receptive field. Long range horizontal connections between hypercolumns are taken to be Jian-Young Wu modulatory and orientation specific. Under this assump- Georgetown University tion, we can expand solutions to the coupled hypercolumn Physiology and Biophysics model in a small parameter representing the ratio of long [email protected] range to local connection strength. Using perturbation theory we can solve for small order corrections to the homo- Chuan Zhang geneous case. Georgetown University Physiology and Biophysics Department Zachary Kilpatrick [email protected] Department of Mathematics University of Utah [email protected] Xiao-Ying Huang Physiology and Biophysics Department Georgetown University Paul Bressloff [email protected] University of Utah [email protected] Weifeng Xu 68 LS08 Abstracts

Georgetown University developed by our team at Stanford. Array Tomography Physiology and Biophysics Department allows the imaging of molecularly labeled objects in the [email protected] brain tissue using fluorescent microscopy, and registered high-resolution imaging with scanning electron microscopy, enabling an accurate mapping across nano- to micro scale. MS35 Due to the massive amounts of data at multiple scales, mor- Quantitative Analysis of Gut Motion in an Animal phological reconstruction algorithms that are fast, resource Model using Dynamic MRI and 3-D Live-wire Im- efficient, and accurate become necessary. We will present age Segmentation our latest results in large-scale microscopic neuronal circuit data acquisition in the mouse brain using KESM and Array Conventional methods of quantifying segmental and peri- Tomography, and discuss the fast algorithms we developed staltic motion in animal models are highly invasive, in- for tracing and analyzing neuronal morphology. volving the isolation of segments of small intestine either from dead or anesthetized animals. The present study was Yoonsuck Choe undertaken to non-invasively analyze these motions in the Texas A&M University jejunum region of anesthetized rats using dynamic contrast [email protected] enhanced magnetic resonance imaging (MRI), and quantify thses motion using spatiotemporal maps. Dynamic images ( 1000 images at 6 frames per second) of the GE tract were MS35 acquired in vivo using a gradient echo imaging sequence. Model-based Assessment of the Lung by Imaging A semi-automated 2D spatial + time image segmentation algorithm based on 3D live wire and gradient vector flow There has been a growing need for sensitive and objec- snakes was implemented to accurately segment the dynam- tive measures of regional lung status both for detection ically acquired images. A 2D thinning algorithm was ap- of disease and for outcomes analysis. X-ray CT remains plied to the segmented images to compute the medial axis, the imaging modality of choice for comprehensively eval- which was used to compute the spatiotemporal map of the uating the lung. Significant advances are being made in acquired image sequence. The spatiotemporal map, which both temporal and spatial resolution. Scan apertures are is plot of the diameter of the gut along the length of the gut at sub-cardiac cycle time frames, allowing for the imag- with respect to time, is a widely-used and a compact repre- ing of not only anatomy but also ventilation and perfu- sentation of the complex gut motion. The frequency (0.29 sion, providing structure-to-function correlations. We have 0.05 Hz) and period of segmental contraction (3.14 0.14 s) brought together a multi-disciplinary team of investigators and average distance between segmental constrictions (4.56 to develop a model/atlas of the normal human lung based 1.21 mm) were very similar in the jejunum region among upon these new measures. This atlas includes the lungs, different rats, showing little inter-animal variability. The lobes sublobar segments and airway and vascular branch- frequency (0.46 0.01 Hz) and period of peristaltic waves ing structures of the lung and attached to each level of (2.18 0.05 s) correlated well with the frequency (0.5 Hz) this structure will be the normal range of the CT-based and period (2 s) of slow waves which have been described in measures of regional lung physiology including ventilation, previous literature, leading to the conclusion that in vivo perfusion, etc. This model/atlas of the normal human lung short distance peristaltic type contractions are the result provides the comparative basis for detecting and quantitat- of slow waves generated by interstitial cells of cajal. The ing pulmonary pathology. Imaging is serving an important speed of propagation of peristalsis wave (4.34 1.03 mms-1) role in the phenotyping of diseases such as Asthma, COPD was found to be reduced under in-vivo conditions compared in general, as well as other interstial lung pathologies. As to in-vitro speeds. These represent the first quantitative in we are identifying specific differences amongst these pa- vivo results of the small intestine using non-invasive dy- tient populations, there is a growing interest to determine namic MRI approach. In this approach the segments of if computational fluid dynamics can provide insights into the GI tract are not isolated or exteriorized but are in true particular distribution patterns of pathology. In this talk physiological conditions. we will discuss the growing interplay between CFD studies and the phenotyping of lung disease. Amit Ailiani Pennsylvania State University Eric Hoffman [email protected] Iowa State University eric-hoff[email protected]

MS35 High-throughput Imaging using Knife-Edge Scan- MS35 ning Microscope and Array Tomography, and Fast Image-Based Patient-Specific Multi-Scale Model- Algorithms for Multiscale Image Analysis and Re- ing of the Failing Heart construction The most significant recent advance in management of Recent advances in serial-sectioning microscopy have en- heart failure (HF) with a conduction block has come from abled high-throughput imaging of massive volumes of bio- CRT and defibrillator therapy. However, up to 30% of cur- logical microstructure at a very high resolution. One ex- rently eligible patients fail to respond to CRT. Notably, ample is the Knife-Edge Scanning Microscope (KESM) we exact estimation of the percentage of non-responders, or developed at Texas A&M, which is one of the few that of factors predicting non-response, are difficult because of combines serial sectioning and imaging in an integrated different criteria used to define ’response’. Although these process. The KESM is capable of imaging biological tis- factors make it difficult to select optimally select patients sue (about 1 cm3) at 300 nm x 300 nm x 500 nm reso- for CRT, this remains of paramount importance to reduce lution within 100 hours, generating data at a rate of 180 unnecessary implants, procedural risks and healthcare ex- MB/s. The resulting data per organ (e.g., a mouse brain) penses. We propose to develop new computational tools can easily exceed tens of terabytes. Another example is for optimally selecting patients for CRT, then for opti- a complementary microscopy method, Array Tomography, mizing CRT to each individual patient. Having acquired LS08 Abstracts 69

IRB approval, two to five patients with NYHA Class III of the Primary Visual Cortex or IV will be recruited at the San Diego VA Medical Cen- ter. Implementing the strategy outlined above, we will We discuss our large-scale ( 1 million neurons) compu- develop patient-specific computational models of the hu- tational modeling of the primary visual cortex (V1). In man heart from detailed mapping, and test their ability particular, we describe network mechanisms underlying to predict observed short-term functional improvements stochastic, spatiotemporal dynamics associated with spon- after CRT. The clinical procedures that we will perform taneous on-going activity of the V1 and the line-motion include: cardiac contrast CT to obtain ventricular geom- illusion — which is the illusory motion sensation from a etry; electroanatomic mapping of both ventricles to ob- static cue of a flashed stationary square quickly followed tain ventricular activation patterns during native (dyssyn- by a stationary bar. Furthermore, we use a new analy- chronous) ventricular activation and during CRT; cardiac sis of coarse-grained event-chains to demonstrate the fine ultrasound to obtain dynamic ventricular (pseudo-) vol- discriminability of orientation of V1. umes and invasive dynamic pressure measurements during cardiac catheterization. Pressure-volume loops will be ob- David Cai tained during maneuvers to alter preload and afterload. Courant institute Three and six months follow ups will be performed to as- New York Unvirsity sess long-term outcomes, to determine the predictive accu- [email protected] racy of our models, and also to provide an opportunity for the patient-specific models to optimize CRT in a patient- MS37 tailored fashion. Optical Imaging of Tissue Culture Models of Car- Roy Kerckhoffs diac Arrhythmias UCSD Department of Bioengineering Cardiac arrhythmias are associated with the abnormal ini- [email protected] tiation and/or abnormal propagation of the heart rhythm. By carrying out optical imaging of tissue cultures of spontaneously beating heart cells, it is possible to analyze macro- MS36 scopic patterns of excitation with a goal of relating this to Alcohol Drinking Dynamics in Distinct Risk Envi- the cellular and subcellular electrophysiological properties ronments: Application to College Drinking of heart cells. In particular we have been able to observe transitions between rhythms in vitro, that model the nor- Abstract not available at time of publication. mal and pathological rhythms in vivo. Optical imaging of tissue culture offers the benefit of providing a controlled Anu Mubayi enviroment that can be observed over long times, in which Arizona State University it is possible to systematically modify the geometry of the [email protected] culture, the density of the culture, as well as change the physiology by the addition of pharmacological agents. The experimental work is complemented by theoretical studies MS36 of bifurcations and dynamics in mathematical models of Modeling B Cell Dysfunction in HIV Infection excitable, heterogeneous systems. This work points to uni- versal patterns of bifurcations underlying cardiac arrhyth- Abstract not available at time of publication. mias in humans. Loan Nguyen Leon Glass Arizona State University McGill University [email protected] Department of Physiology [email protected] MS36 Nosocomial Infections: The Basic Reproduction MS37 Number Joke! Multiscale Imaging Reveals Robustness and Capac- ities of the Human Respiratory System Abstract not available at time of publication. System engineered organ representations based on multi- Daniel Romero scale imaging provide insight into the evolutionary shaped Cornell University design of the transport networks in terms of modular- [email protected] ity,physical optimality and robustness. We have assembled a consortium of investigators to image, model and simu- MS36 late functional properties of the human respiratory system. MDCT data of nine human lungs and a highly resolved A Mathematical Model of Solid Tumor Regrowth cast, as well as micro-CT and light microscopic imaging Abstract not available at time of publication. was used to investigate dimensions and heterogeneities in geometric branching patterns, gas supply and diffusion ca- Jianjun Paul Tian pacities. We show that the dimensions of airways in these Mathematics Department cases change systematically from area-preserving to area- College of William and Mary increasing,thus they reflect multifractal properties. Air- [email protected] ways are generally larger than predicted by the Hess- Murray law, providing up to four-fold less resistance as well as increase in robustness against perturbations. We MS37 show that resistance in the network topology of airways Multi-Scale Modeling of Spatiotemporal Dynamics mediates a mismatch between anat omically demanded and 70 LS08 Abstracts

predicted oxygen supply, which oﬀers an explanation for work, we provide the mathematical basis for these three dif- the excess diﬀusion capacity of human lungs. Robustness ferent magneto-acoustic imaging approaches and propose and capacities are important cornerstones for the develop- new algorithms for solving the inverse problem for these ment of solutions to improve diagnostics and intervention approaches. This is a joint work with Y. Capdeboscq, H. planning in aging and disease. Kang, and A. Kozhemyak. Andres Kriete Habib Ammari Drexel University Ecole Polytechnique [email protected] [email protected]

Daniel C. Haworth, Robert Kunz Pennsylvania State University MS38 [email protected], [email protected] A Method of Biological Tissues Elasticity Recon- struction Using Magnetic Resonance Elastography Kai Zhao Measurements Monell Chemical Senses Center Magnetic resonance elastography (MRE) is an approach to [email protected] measuring material properties using external vibration in which the internal displacement measurements are made Warren Gefter with magnetic resonance. A variety of simple methods University of Pennsylvania have been designed to recover mechanical properties by [email protected] inverting the displacement data. Currently, the remaining problems with all of these methods are that in general the homogeneous Helmholtz equation is used and therefore it MS37 fails at interfaces between tissues of different properties. Mapping and Modeling Receptor Topography Dur- The purpose of this work is to propose a new method for ing Signal Transduction reconstructing both the location, the shape and the shear modulus of a small anomaly with Lamé parameters differ- The ErbB family of growth factor receptors are widely ent from the background ones using internal displacement expressed by cells of epithelial and mesenchymal lin- measurements. This is a joint with H. Ammari, P.Garapon, eages. EGFR and ErbB2 overexpression can lead to and H. Lee. ligand-independent signaling and is linked to carcinogenesis. We use a combination of high resolution microscopy ap- Hyeonbae Kang proaches to quantitatively evaluate the topography and be- Seoul National University havior of resting and actively signaling ErbB receptors. Im- [email protected] munoelectron microscopy methods capture nanoscale spatial relationships between receptors and their intracellular signaling partners. Live cell imaging approaches, including MS38 single particle tracking of quantum dot probes, monitor dif- SWIFT (SWeep Imaging with Fourier Transform), fusional properties of receptor monomers and dimers and A New Paradigm for Near Simultaneous Transmit provide evidence for cytoskeletal corrals. These data pro- and Receive MR Imaging vide the foundation for our agent-based modeling efforts. Our stochastic modeling framework incorporates impor- SWIFT utilizes RF encoding sampled prior to completion tant spatio-temporal aspects of signaling, including pro- of the RF pulse. Current hardware limits the switching be- tein clustering, protein motion and biochemical reactions tween transmit and receive to the order of 10 micro seconds. within an idealized cellular geometry. We investigate mech- The data handling is inherently different than conventional anisms of receptor dimerization and activation as functions NMR, since the acquired data is the distribution of isochro- of time and receptor conformation, density and spatial dis- mats convolved with the RF pulse shape. The deconvolu- tribution. For example, we have considered the effects of tion is well behaved and the techniques have been found receptor clustering patterns of ErbB family members on to offer increased detection of very short (T2) species, e.g. both hetero- and homo-dimerization rates, using immuno- teeth, plastics and bone. Additionally the simultaneous electron microscopy data. Simulation results suggest that acquisition of excited spins is beneficial for relaxing the B0 partial spatial segregation of ErbB receptors has a pro- homogeneity demands. Theoretical and experimental data found impact on heterodimerization rates. We propose will be discussed. that membrane spatial organization is a significant contributor to the carcinogenesis process. Steen Moeller University of Minnesota Bridget Wilson Center for Magnetic Resonance Research University of New Mexico School of Medicine [email protected] [email protected] MS38 MS38 Conductivity Imaging from the Magnitude of One Mathematical Models and Reconstruction Algo- Current Density Field rithms in Magneto-Acoustic Imaging This talk concerns the problem of Electrical Impedance An acoustic wave can excite a local area of tissue placed Tomography when interior knowledge of the magnitude of in a magnetic field and induce an electrical current. Then the current density field is available. The current density Lorenz force causes a local current density. Some imag- field is generated by maintaining a given potential on the ing modalities, such as the vibration potential imaging boundary and its magnitude can be determined from Mag- and the magneto-acoustic tomography with magnetic in- netic Resonance measurements. Two non-material proper- duction, are based on this physical phenomena. In this ties are related via a problem in the (non-smooth) calculus LS08 Abstracts 71

of variation. The mathematical tools used in the proofs University of Manitoba range from harmonic measure theory to algebraic topology. Department of Mathematics This work is jointly with A. Nachman and A. Timonov. [email protected] Alexandru Tamasan University of Central Florida MS39 [email protected] Paths to Disease Extinction in the Presence of Non- Gaussian Noise

MS39 We investigate stochastic extinction in an epidemic model Modeling Multistrain Interactions: Cross Immu- and the impact of random vaccinations. In the absence nity and Antibody Dependent Enhancement of vaccinations, the extinction rate has an unusual critical exponent that scales with the distance to the bifurcation We investigate the dynamics of a model for multistrain dis- point of disease onset. Analysis shows that a comparatively eases with strain interaction mediated by temporary cross weak Poisson-distributed vaccination leads to an exponen- immunity and antibody dependent enhancement (ADE). tial increase in the extinction rate, with an exponent that ADE increases the infectivity of secondary infections. strongly depends on the vaccination parameters. Numeri- While ADE alone is known to trigger chaotic outbreaks and cal constructions of extinction paths will be presented. desynchronization of the strains, we find that when both ADE and cross immunity are included, stabilization oc- Ira B. Schwartz curs for weak cross immunity. Large cross immunity leads Naval Research Laboratory to large amplitude chaotic outbreaks. Nonlinear Dynamical Systems Section [email protected] Simone Bianco Dept. of Applied Science Mark I. Dykman College of William and Mary Department of Physics and Astronomy [email protected] Michigan State University [email protected] MS39 Vaccinations in Disease Models with Antibody- Alexandra Landsman Dependent Enhancement US Naval Research laboratory Washington, DC 20375 As we increase our resources to fight disease, pathogens [email protected] become more resilient in their means to survive. One example is antibody-dependent enhancement (ADE), a phenomenon in which viral replication is increased rather than MS40 decreased by immune sera. We study the complex dynam- Integration of Mitochondrial ics induced by ADE in multi-strain disease models and in- and Cellular Metabolism with Tissue-Level Sub- vestigate the effects of vaccine campaigns. In particular, strate Transport to Explain Emergent Phenomena we study the consequences of using single-strain vaccines, on Phosphate Metabolite Concentations and ATP which would increase the virulence in other infections. Hydrolysis Potential in the Heart Lora Billings To understand how cardiac ATP and CrP remain sta- Montclair State University ble with changes in work ratea phenomenon that has Dept. of Mathematical Sciences eluded mechanistic explanation for decadesdata from [email protected] 31phosphate-magnetic resonance spectroscopy (31P-MRS) are analyzed to estimate cytoplasmic and mitochondrial Amy Fiorillo phosphate metabolite concentrations in the normal state, Montclair State University during hypoperfusion, and during acute ischemia and re- amyfi[email protected] active hyperemic recovery. Analysis is based on simulating distributed heterogeneous oxygen transport in the myocardium integrated with a detailed model of cardiac en- Ira Schwartz ergy metabolism. It is determined that baseline inorganic Naval Research Laboratory phosphate (Pi) concentration in the canine myocyte cyto- Washington DC plasma variable not accessible to direct noninvasive mea- [email protected] surementis approximately 0.29 mM and increases to 2.3 mM near maximal cardiac work states. This variable is MS39 shown to be crucial in controlling oxidative metabolism in vivo. During acute ischemia (from ligation of the left an- Some Results and Challenges on Modelling HIV terior descending artery) Pi increases to approximately 2.8 Transmission Dynamics mM and ATP consumption in the ischemic tissue is reduced Since its inception in the 1980s, the human immunodefi- to less than half its baseline value before the creatine phos- ciency virus (HIV) continues to inflict major public health phate (CrP) pool is 16% depleted. It is determined from and socio-economic damage globally, particularly in some these experiments that the maximal work rate of the heart of the resource-challenged nations of the world. The talk is an emergent property and is limited not simply by the will focus on some of our recent work on modelling the maximal rate of ATP synthesis, but by the maximal rate transmission dynamics of HIV as well as the evaluation of at which ATP can be synthesized at a potential at which some control strategies. it can be utilized. Abba Gumel Daniel A. Beard Medical College of Wisconsin 72 LS08 Abstracts

Department of Physiology MS40 [email protected] A Multi-Scale Approach Towards Understanding Anitgen Presentation in the Immune Response to Mycobacterium Tuberculosis MS40 Multi-Cell Modeling of Biological Development Us- The immune system and the process of antigen presenta- ing the GGH Model and tion in particular encompass events that occur at multiple CompuCell3DApplications, Technology and Open length and time scales. Despite a wealth of information Problems in the biological literature regarding each of these scales, no single representation synthesizing this information into While bioinformatics tools for the analysis of DNA se- a model of the overall immune response as it depends on quences, reaction kinetics models of biomolecular networks antigen presentation is available. In this talk, I outline an and molecular dynamics simulations of biomolecules, are approach for integrating information over relevant biolog- all widely used, multi-cell modeling of developmental pro- ical and temporal scales to generate such a representation cesses at the tissue scale is still relatively undeveloped. for MHC class II-mediated antigen presentation. In addi- One of the key reasons for this neglect has been the lack tion, I begin to address how such models can be used to of widely-accepted modeling approaches and the computa- answer questions about mechanisms of infection and new tional difficulty of building such models. Now, a growing strategies for treatment and vaccines. community of modelers has settled on the GGH Model, a modeling approach that derives from the familiar Potts Denise E. Kirschner model of statistical mechanics, as a convenient methodol- Univ of Michigan Med School ogy to create sophisticated multi-cell simulations of tissue Dept of Micro/Immuno development, creating a de facto common modeling ap- [email protected] proach. The GGHs use of an Effective Energy and constraints to describe cell behaviors simplifies integration of multiple biological mechanisms, while the availability MS40 of open-source tools like CompuCell3D for building GGH Modeling Multicellularity: from Cell Rheology to models makes developing, validating and sharing such sim- Gastrulation ulations much easier for non-specialists. I will introduce the GGH and the modeling environment CompuCell3D I will present an overview of recent work focused on con- (http://www.compucell3d.org/), then apply the GGH to structing computer models of developmental systems. In modeling somitogenesis in vivo, and to angiogenesis and particular, we have devised an off-lattice algorithm, called vasculogenesis in vitro (see pictures), illustrating some of the Subcellular Element Model, which is able to simulate the questions this type of modeling can address (e.g. er- large numbers (thousands) of deformable cells in three di- ror correction mechanisms in development) and discussing mensions. I will describe the inner workings of the algo- its application to other developmental-biology problems in- rithm, and indicate that the method is capable of modeling cluding tumor growth, gastrulation, and biofilms. I will developmental systems over a wide range of scales - cap- also discuss some of the key mathematical and computa- turing cell visco-elasticity at small scales, and long-ranged tional issues which GGH models and modeling environ- coordinated cell movement at large scales. Modeling of ments still need to address. primitive streak extension in the chick embryo will be discussed as a concrete application. James A. Glazier Indiana University, Biocomplexity Institute Timothy J. Newman Depts. of Physics and Biology, School of Informatics ASU [email protected] Department of Physics [email protected]

MS40 Rod Smallwood From Endothelial Signaling to Tissue Growth in University of Sheffield ,UK Cerebral Aneurysms r.smallwood@sheffield.ac.uk Cerebral aneurysms are a result of growth and adaptation of the arterial wall tissue to a change in fluid shear MS40 stress at the surface of endothelial cells in cerebral arteries. MAPK Signaling in Equations and Embryos In a contribution to the European FP6 aneurIST project (www.cilab.upf.edu/aneurist1/) we are modelling the sig- Exploring the robustness and evolvability of developmen- nal transduction pathways that link changes in shear stress tal signaling mechanisms is essentially impossible without to collagen turnover and smooth muscle activity. Mixture computational modeling approaches. Successful models theory is used to couple the changes in tissue composition, should integrate large amounts of data, test the feasibil- that result from these signalling pathways, to a fibre dis- ity of proposed modes of regulation, and lead to the for- tribution constitutive law model which, in turn, is used in mulation of new mechanisms. I will describe how we are the large deformation mechanics finite element solution of combining imaging, modeling, and molecular genetics tech- wall stress. niques in order to develop and experimentally test multiscale models of the Mitogen Activated Protein Kinase Peter Hunter (MAPK) signaling pathway, a key regulator of develop- University of Auckland ment across species. We are using the terminal patterning New Zealand system in the early Drosophila embryo as the main exper- [email protected] imental model for studying the MAPK-mediated pattern formation. Our imaging results provide the first quantitative measurements of the gradient of MAPK signaling in the early Drosophila embryo and lead to the model where LS08 Abstracts 73

this gradient is controlled by a cascade of diﬀusion-trapping Courant Institute for Mathematical Sciences systems. We tested this model in a combination of mod- New York University eling, imaging, and genetic experiments. We are also ex- [email protected], [email protected] ploring how the gradient of MAPK signaling is interpreted by giving rise to the gradients of biochemical modiﬁca- Jaime De La Rocha tions and subcellular locations of its biochemical targets. Center for Neural Science, NYU Our preliminary data suggest that a substrate competi- [email protected] tion mechanism coordinates the actions of the anterior and terminal patterning systems in the early embryo. I will present the results of genetic and computational tests of MS41 this mechanism. Reliability of Layered Neural Oscillator Networks

Stanislav Shvartsman This talk concerns the reliability of large networks of neu- Department of Chemical Engineering ral oscillators in response to fluctuating stimuli. Reliability Princeton University means that repeated presentations of a stimulus elicit es- [email protected] sentially identical responses regardless of the system’s state at the onset of the stimulus; the degree to which a system is reliable impacts the precision of neural codes based on MS41 temporal patterns of spikes. Under what conditions is a Modules and Roles: Towards a Cartography of network reliable? I will present recent work addressing Complex Biological Networks this question for certain idealized neuronal networks with layers. The problem is studied on two scales: neuronal re- In complex systems, individual components interact with liability, which concerns the repeatability of spike times of each other giving rise to complex networks, which are nei- individual neurons embedded within a network, and pooled- ther totally regular or totally random. Because of the inter- response reliability, which concerns the repeatability of the play between network topology and dynamics, it is crucial total synaptic output from the network. It will be shown to characterize the structure of complex networks. Most that individual embedded neurons can be reliable or un- real world networks display a marked modular structure, reliable depending on network conditions, whereas pooled which means that, rather than being homogeneous in their responses of sufficiently large networks are mostly reliable. connectivity, nodes tend to establish many more connec- I will also discuss the effects of noise; our main finding here tions with a subset of the nodes in the network than with is that some types of noise affect reliability more seriously the remaining nodes. In my talk, I will discuss recent the- than others. oretical and computational developments that enable one to uncover the modular structure of complex networks. I Kevin K. Lin will also discuss how, after identifying network modules, Department of Mathematics one can classify nodes into roles according to their pattern University of Arizona of intra- and inter-module connections. Finally, I will show [email protected] that understanding the modular structure of biochemical networks sheds light onto their evolution, and has potential Eric Shea-Brown applications for the identification of drug targets. Department of Applied Mathematics Roger Guimera University of Washington Northwestern University [email protected] [email protected] Lai-Sang Young Courant Institute of Mathematical Sciences MS41 New York University The Effect of Spatially and Temporally Correlated [email protected] Input on Network Behavior

Recent work shows that spike-to-spike correlations MS41 amongst neurons receiving shared inputs increase as as Optimization of Metabolic Networks a function of the neurons’ firing rates. Thus, if different stimuli evoke different rates, they may also be expected to Cellular metabolism occupies a central role in the processes evoke different levels of correlation: in this sense, rate and that form the basis of life. Yet, the whole-cell behavior of correlation are co-tuned. I will explore the consequences the metabolic system remains widely unexplored because of this co-tuning for the information that populations of large-scale studies require establishing a mathematical and neurons carry about the stimuli. First, the impact of cor- computational approach that goes beyond traditional bio- relation tuning on the Fisher information in the case of a logical research. Using a network-based approach, in this single layer of cells will be considered. Previous work on talk I will discuss intriguing recent results about the func- the subject took into account changes in covariance, but tional behavior of the metabolic system that follow from not correlation. The results of an experimental study that the interplay between network structure and network dy- illustrates how a single cell can read out information en- namics. coded using correlation tuning will be shown Adilson Motter Kresimir Josic Northwestern University University of Houston [email protected] Houston, TX [email protected] MS42 Eric Shea-Brown, Brent Doiron The Role of Feedback in the Formation of Mor- 74 LS08 Abstracts

phogen Territories feng Zhu, Stuart Newman, Mark Alber.)

We consider a gene regulatory network that utilizes auto- Yong-Tao Zhang activation and cross-inhibition to establish and maintain Department of Mathematics stable boundaries of gene expression. We find that in University of Notre Dame the presence of a general activator, neither auto-activation, [email protected] nor cross-inhibition alone are sufficient to maintain stable sharp boundaries of morphogen production. The minimal requirements for a self-organizing system are a coupled sys- MS43 tem of two morphogens in-which the auto-activation and Stimulus Competition Via Transition From Syn- cross-inhibition have Hill coefficients strictly greater than chrony to Asynchrony one. In networks of excitatory and inhibitory neurons, one can David Iron often find a parameter regime of synchronous, oscillatory Dalhousie University, Canada activity immediately adjacent to a regime in which the in- [email protected] hibitory cells are active asynchronously, and the excitatory cells are suppressed altogether. We describe how to compute the boundary between the two regimes, which we call MS42 the suppression boundary, and show computations illus- Germline Stem Cell Competition trating the often abrupt transition from one regime to the other. We also show computational simulations suggesting In the ovarian niche of drosophila, there are two to three that experimentally observed phenomena concerning com- germline stem cells. They compete each other for occu- petition among visual stimuli and the attentional biasing pancy. The experiment data show cadherin serve as a sig- of this competition may arise from toggling between the nal molecule to play an important role in this process. We two regimes. use mathematical model to study the competition within the niche and the maintenance of the niche. Christoph Borgers Tufts University Jianjun Paul Tian Department of Mathematics Mathematics Department [email protected] College of William and Mary [email protected] Steven Epstein Boston University MS42 [email protected] Genetic Instability and Cancer Growth Nancy Kopell Carcinogenesis (cancer generation) relies on a sequence of Boston University mutations that transforms cells, leading to their unchecked Department of Mathematics growth. An important phenomenon in cancer is genetic in- [email protected] stability, or an increased rate of mutations. We investigate an optimal control model of carcinogenesis which includes cell division, death and mutations, and ask the following MS43 question: what (time dependent) mutation rate leads to Applications of Kinetic Theory to Neuronal Net- most rapid cancer growth? We obtain the optimal muta- work Dynamics tion rate for the fastest time to cancer for different relations between mutation rate and the death rate of cells. Using kinetic theory is a common coarse-graining technique for integrate-and-fire neuronal networks. After revieweing Frederic Y. Wan the basics of this theory, this talk will concentrate on the ki- University of California, Irvine netic theory for networks with fast and slow conductances [email protected] driven by the same spike trains, and the Fokker-Planck limit of the kinetic equations. In the former, correlations Alexander Sadovsky, Natalia Komarova due to the two types of conductances sharing some of the Department of Mathematics same input spikes will be discussed. In the latter, neu- University of California, Irvine ronal gain curves will be presented, and the limit of small [email protected], [email protected] fluctuations will be described. Gregor Kovacic MS42 Rensselaer Polytechnic Inst Dept of Mathematical Sciences Application of Discontinuous Galerkin Methods for [email protected] Reaction-Diffusion Systems in Developmental Biol- ogy David Cai Reaction-diffusion systems in modeling of regulatory net- Courant institute work and tissue growth in developmental biology are usu- New York Unvirsity ally highly stiff. They are typically considered on complex [email protected] domains. We overcome computational challenges by combining discontinuous Galerkin methods with Strang opera- Aaditya Rangan tor splitting, on triangular meshes. Numerical solutions of Courant Institute of Mathematical Sciences the Schnakenberg model, and a system of skeletal pattern New York University formation, are presented to demonstrate effects of domain [email protected] geometries on the resulting patterns. (joint work with Jian- LS08 Abstracts 75

MS43 equations for the local rods concentration and orientation. Coding in Neuronal Networks, Event-Chains, and Above certain critical density of rods the model exhibits Functional Connectivity spontaneous orientational phase transition and the onset of large-scale coherence. We demonstrate that this orien- Networks of neurons respond to different stimuli in dif- tational transition leads to the formation of vortices, asters, ferent ways, namely, distinct inputs generate reproducibly and bundles seen in recent experiment distinct activity profiles within the network. The talk will discuss certain coding properties of these systems, and il- Igor Aranson lustrate these properties with numerical examples. Argonne National Laboratory Materials Science Division Aaditya Rangan [email protected] Courant Institute of Mathematical Sciences New York University [email protected] MS44 Computational Methods for Understanding Flow Kinematics in Blood Vessels MS43 Predictability of Network Dynamics of Hodgkin- Transport mechanisms, such as recirculation and stagna- Huxley Neurons tion, are thought to play important roles in disease progression and clot formation in blood vessels; however these The reliability and predictability of neuronal network dy- mechanisms are not well understood. This is in part due namics is a central question in neuroscience. Here, we to the challenging nature of characterizing unsteady fluid address the theoretical issue of predictability of pulsed- transport. We utilize the computation of Lagrangian co- coupled Hodgkin-Huxley (HH) neuronal network dynam- herent structures to better understand transport mecha- ics. When the interaction of any two neurons in the net- nisms occurring in realistic vascular flow models and dis- work is modeled by a spike that is initiated by the event cuss possible biological significance of these results. when the voltage of one of the neurons passes through a sharp threshold, the dynamics does not belong to the class Shawn Shadden of smooth dynamical systems. For this non-smooth dy- Cardiovascular Biomechanics Research Laboratory namical system, we propose a pseudo-Lyapunov exponent Stanford University (PLE) that captures the long-time predictability of HH [email protected] neuronal networks. We show that the numerical convergence of Runge-Kutta (RK) methods for evolving the HH networks is related to the pseudo-Lyapnov exponent. The MS44 non-convergence of the RK method is correlated with the Multiscale Simulation for Bioimaging Informatics positivity of the PLE. Furthermore, we show that, even of Cells when individual neuronal dynamics can be reliable, the network of these reliable neurons can become chaotic, and Multiscale simulation is emerging as a new scientific field. their long-time dynamics can become unpredictable. The idea of multiscale modeling is straightforward: one computes information at a smaller (finer) scale and passes Yi Sun it to a model at a larger (coarser) scale by leaving out New York University degrees of freedom as one moves from finer to coarser Courant Institute scales. The obvious goal of multiscale modeling is to pre- [email protected] dict macroscopic behavior from first principles (bottom-up approach). However, the emerging fields of biotechnology David Cai impose new challenges and opportunities. For example, the Courant institute ability to predict and control phenomena with resolution New York Unvirsity approaching molecular scale while manipulating macro- [email protected] scopic scale variables can only be realized via multiscale simulation (top-down approach). In this talk, recent developments on coarse-grained Monte Carlo simulations will be MS44 discussed. Examples will be presented from the epidermal Multiscale Description of Self-Organization of Mi- growth factor receptor (EGFR) spatiotemporal dynamics crotubules Interacting with Molecular Motors and on the surface of plasma membranes of mammalian cells. Crosslinks The focus will be on diffusion (short times) and reaction (long times) leading to spatial self-organization of EGFR, A central question in biology concerns the origin of highly- whose signaling disregulation is implicated in a number of organized self-assembled macroscopic structures from ini- cancers. Our work demonstrates that plasma membrane tially disordered states. The mixture of long and rigid heterogeneity is central to signal transduction, especially microtubules and dynamic molecular motors constitutes for cancerous cells, and provides a means to bridge the a unique well-controlled system where the fundamentals length and time scale gap between various experimental of self-assembly process can be studied in a great detail. techniques. In vitro experiments on self-assembly of motors and microtubules in quasi-two-dimensional geometry revealed a Dion Vlachos variety of spontaneous large-scale patterns: ray-like asters, University of Delaware rotating vortices and filament bundles. Motivated by these [email protected] experiments, we derive from microscopic interaction rules a model describing spatio-temporal organization of an array MS44 of microtubules interacting with dynamic molecular motors and static cross-links. Starting from a generic stochastic A Multiscale Model of Thrombus Development microscopic model of inelastic polar rods, we obtain a set of A multiscale model for studying formation of thrombus in 76 LS08 Abstracts

a blood vessel will be presented. This computational model standing. involves components for modeling viscous, incompressible blood plasma; non-activated and activated platelets; blood David Finch cells; activating chemicals; fibrinogen; the vessel walls Oregon State University and their interactions. The macro scale dynamics of the fi[email protected] blood flow is described by the continuum Navier-Stokes equations. The micro scale interactions between activated platelets, platelets and fibrin(ogen) and platelets and the MS45 vessel wall are described through a stochastic discrete Cel- Image Reconstruction in Optical Tomography II lular Potts Model (CPM). Newly developed computational methods will be described for overcoming the difficulties The inverse problem of optical tomography is to recon- posed by the coupling of events occurring at distinct spa- struct the optical properties of a highly-scattering medium tial and temporal scales; by the non-linearity of the cou- from boundary measurements. I will review recent work pled governing equations; and by the geometry of the blood on associated inverse scattering problems for the radiative vessel. Simulation results predicted the development of an transport equation. Our results will be illustrated by nu- inhomogeneous internal structure of the thrombus and ver- merical simulations and experiments in model systems. tex blood flow behind the thrombus which were confirmed John Schotland by the preliminary experimental data. University of Pennsylvania Zhiliang Xu [email protected] Department of Mathematics University of Notre Dame MS45 [email protected] Image Reconstruction in Optical Tomography I

Nan Chen The inverse problem of optical tomography is to recon- University of Notre Dame struct the optical properties of a highly-scattering medium [email protected] from boundary measurements. I will review recent work on associated inverse scattering problems for the radiative Malgorzata Kamocka, Elliot Rosen transport equation. Our results will be illustrated by nu- Indiana University School of Medicine merical simulations and experiments in model systems. [email protected], [email protected] John Schotland Mark S. Alber Department of Bioengineering University of Notre Dame University of Pennsylvania Department of Mathematics [email protected] [email protected] MS46 MS45 Taylor Dispersion of Nano-Particles in Compliant Sound and Light Show Structure: Mathematics of Arterioles Thermoacoustic Tomography II A nanovector is a hollow or solid structure, with diameter Photoacoustic and thermoacoustic tomography are devel- in the 1-1000 nm range, which can be filled with anticancer oping imaging technologies for biology and medicine. Via drugs and detection agents. These nanovectors must reach the thermoelastic effect, an imposed radiation field gen- with their payloads sites of inflammation, cancer lesions, erates a pressure wave in the interior of a body which is and tumors via convective and diffusive transport throught then measured in the exterior. Associated inverse prob- the vasculature. In arterioles and capillaries the flow condi- lems are to determine the absorption coefficient or the tions are those of Taylor dispersion when convective trans- optical/acoustic properties of the medium. There has port competes with molecular diffusion. In this flow regime been substantial progress recently on several aspects of the G.I. Taylor derived effective equations that hold in tubes mathematics, and this talk will survey our current under- with FIXED walls, which can be used to describe effective standing. diffusion of nano-particles in tubes with fixed walls. The resulting effective equations are of parabolic type. In this talk David Finch we present the results related to the study of Taylor dis- Oregon State University persion in COMPLIANT tubes such as those of arterioles. fi[email protected] We found a surprizing result: effective equations describing concentration of nano-particles in compliant arterioles are of hyhperbolic type. This means, in particular, that sharp MS45 fronts in nanoparticle concentration may arise due to the Sound and Light Show Structure: Mathematics of motion of the vessel walls! In particular, we found that in Thermoacoustic Tomography I arterioles with porous vessel walls, such as those associated with neighbouring pathologies, the initial-boundary value Photoacoustic and thermoacoustic tomography are devel- problem is not well-posed (Goursat problem). This means oping imaging technologies for biology and medicine. Via that injecting nano-particles near the location of the tu- the thermoelastic effect, an imposed radiation field gen- mor will give rise to the instabilities in the concentration erates a pressure wave in the interior of a body which is distribution, not recommended for optimal drug delivery. then measured in the exterior. Associated inverse prob- Instead, nano-particles should be administered upstream lems are to determine the absorption coefficient or the from the location of the tumor, as is typically performed optical/acoustic properties of the medium. There has in intravascular cancer drug delivery. been substantial progress recently on several aspects of the mathematics, and this talk will survey our current under- Suncica Canic LS08 Abstracts 77

Department of Mathematics MS46 University of Houston Modeling Viscoelasticity of the Arterial Wall [email protected] The mechanics of the arterial wall is complex, due to its Giovanna Guidoboni material structure and load conditions, which influences University of Houston hemodynamic properties as well as the growth and remod- Department of Mathematics eling of the arterial network. In this study we analyze [email protected] how elastic and viscoelastic wall properties differ across the large arteries and show how a viscoelastic model can Andro Mikelic be used to predict flow in the circle of Willis. Experimental University of Lyon 1, France data will be used to validate the model. [email protected] Mette S. Olufsen Department of Mathematics Fabien Marpeau North Carolina State University University of Houston [email protected] [email protected] Daniela Valdez MS46 Department of Mathematics [email protected] A Kinematically Coupled Scheme for Fluid- Structure Interaction in Blood Flow MS47 We will present a novel numerical strategy to solve the fluid-structure interaction in blood flow. The main dif- A Mathematical Model of Collagen Lattice Con- ficulty of the problem lies in the strong interfacial cou- traction pling due to the fact that the ratio between the densities A mathematical model of fibroblast-collagen interaction is of the blood and the arterial wall is roughly equal to one. proposed which reproduces qualitative features of fibrob- Traditionally, implicit schemes are employed to solve this last populated collagen lattice contraction. The model sug- strongly nonlinear problem. The novel algorithm that we gests two mechanisms for collagen contraction: collagen will present is partitioned, has a modular architecture and, aggregates due to tension lines formed by the moving cells in contrast with other partitioned schemes, is stable in the and collagen aggregates due to wrinkling of the collagen blood flow regime. lattice. Giovanna Guidoboni John Dallon University of Houston Brigham Young University Department of Mathematics [email protected] [email protected]

Suncica Canic MS47 Department of Mathematics Kinetic Model for Lamellipodal Actin-Integrin University of Houston Clutch Dynamics [email protected] In migrating cells, with especial prominence in lamellipo- Roland Glowinski dial protrusions at the cell front, highly dynamic con- University of Houston nections are formed between the actin cytoskeleton and [email protected] the extracellular matrix through linkages of integrin adhesion receptors to actin filaments via complexes of cytosolic connector proteins. Myosin-mediated contractile forces MS46 strongly influence the dynamic behavior of these adhesion Simulations of Blood Flow in a Compliant Vessel complexes, apparently in two counter-acting ways: nega- by the Immersed Boundary Method tively as the cell-generated forces enhance complex dissoci- ation, and at the same time positively as force-induced sig- We introduce a two-dimensional mathematical model naling can lead to strengthening of the linkage complexes. which describes the interaction of blood flow with the aor- We obtained ranges of parameter value sets yielding behav- tic wall by the immersed boundary method. The mathe- ior consistent with that observed experimentally for 3T3 matical model is validated by comparing with well-known cells and for CHO cells, respectively. Model simulations solutions of the viscous incompressible Navier-Stokes equa- are able to produce results for the effects of paxillin mu- tions in arteries. The hysteresis behavior in the pressure- tations on the turnover rate of actin/integrin linkages in diameter relation is observed when the viscoelastic material CHO cells, which are consistent with recent literature re- property of the arterial wall is taken into consideration. ports. Overall, although this current model is quite simple it provides a useful foundation for more detailed models Sookkyung Lim extending upon it. Department of Mathematical Sciences University of Cincinnati Alice MacDonald [email protected] Massachusetts Institute of Technology lauff[email protected]

MS47 An Elastic Continuum Model of Enterocyte Layer 78 LS08 Abstracts

Migration Priscilla Greenwood Arizona State University We have developed a mathematical model of migration of [email protected] enterocytes during experimental necrotizing enterocolitis, which is based on a novel assumption of elastic deforma- Paul Gruenewald tion of the cell layer and incorporates the following effects Prevention Research Center (i) mobility promoting force due to lamellipod formation, [email protected] (ii) mobility impeding adhesion to the cell matrix, and (iii) enterocyte proliferation. We have recently extended the model to two-dimensions and using balance equations Dennis Gorman of continuum mechanics we obtained a second order PDE TexasA&MUniversity model with moving boundary. The models allows us to [email protected] predict the time-dependent geometry of the wound edge. Eunok Jung David Swigon Konkuk University Department of Mathematics Department of Mathematics University of Pittsburgh [email protected] [email protected] Sunmi Lee Konkuk University, Korea MS47 [email protected] A Finite Element Model for Wound Healing with Coupling Wound Contraction and Neo- Anuj Mubayi Vascularization Arizona State University Wound healing proceeds by a number of (partially) over- [email protected] lapping steps: bleeding, blood clotting, removal of con- taminants and bacteria, wound closure by cell mitosis and Xiaohong Wang migration towards the wound center, repair of the vascular Arizona State University network, and wound contraction along lines of equal ten- Department of Mathematics and Statistics sion. We consider a model due to Adam [1] for the closure [email protected] of a wound. The model is based on an epidermal growth factor that stimulates cell proliferation. Consequently, cell Fabio A. Sanchez division, and hence also wound closure, takes place only Cornell University if the epidermal growth factor exceeds a threshold value. [email protected] The production of the growth factor is restricted to a strip of the tissue surrounding the wound, the so-called active layer. We assume that healing at a certain location of MS48 the wound edge takes place if and only if the growth fac- Impact of Vaccination and Screening of Chlamydia tor concentration is not below a threshold concentrationc ˆ. Trachomatis: A Mathematical Modeling Approach Furthermore, the rate of closure is assumed to depend on the local curvature of the wound edge. The model predicts Chlamydia trachomatisis the most frequently reported sex- no migration of the wound edge locally whenever the lo- ually transmitted disease in the United States, with an es- cal growth factor concentration is less than the threshold timated 2.8 million Americans infected per year. The U.S. valuec ˆ. This implies the existence of a waiting time before Preventive Services Task Force (USPSTF) recommends wound closure sets in. screening for Chlamydia infection for all sexually active non-pregnant young women aged 24 or younger and for Fred Vermolen older non-pregnant women who are at increased risk. Cur- Delft University of Technology rently, researchers are also investigating potential vaccines [email protected] for Chlamydia. Two mathematical models are formed to investigate the dynamic of the Chlamydia transmission. In a simple model, equilibriums and basic reproduction num- MS48 ber R0 are analyzed, as well as the uncertainty and sensi- The Dynamics and Control of Drinking: A Prelim- tivity of R0 with respect to various parameters. In a model inary Study of the Role of Dispersal, Relapse and with age structure, the transmission dynamic in the United Social Dynamics State population and the effectiveness of various screening and vaccination strategies were investigated with numer- We introduce simple mathematical models in the study of ical solutions of the model. The results of the analysis the dynamics of drinking on homogeneous and heteroge- and simulation of the models expand our understanding of neous mixing communities. The emphasis is on the role the disease transmission and effectiveness of various inter- of relapse, mixing and dispersal on the dynamics and con- vention strategies, develop more questions concerning the trol of drinking behaviors at the population level. Tools infection and transmission dynamic, as well as highlight from population dynamics and control theory are used to the need for particular data for future field studies. identify and highlight challenges and opportunities at the interface of the life, mathematical and social sciences. Linda Gao, Christina Lorenzo, Dorothy Tran, Luke Eichelberger, Christine Muganda Carlos Castillo-Chavez North Central College Arizona State University and [email protected], [email protected], Department of Mathematics [email protected], [email protected], [email protected] [email protected] LS08 Abstracts 79

MS48 [email protected] Evaluation of Hypothetical Mechanisms for the Changing Epidemiology of Pertussis Through Out Kathrin Henschel the Developed World by Analysis of Natural Ex- Freiburger Zentrum für Datenanalyse und Modellbildung periments in Sweden (FDM) [email protected] In Sweden, county health officers included pertussis in their tjnstelkarrapporten early in the 20th Century, and labora- Bjoern Schelter tories began reporting culture-confirmed cases during the Center for Data Analysis and Modeling 1980s. Whole-cell pertussis vaccine was administered to University of Freiburg, Germany Swedish infants from 1953 to 79, as have acellular vaccines [email protected] (aP) since 1996. Pertussis became endemic among young children during the intervening 17 years, permitting several aP efficacy trials. Clinical and laboratory reporting MS49 have been mandatory since 1997. This tradition of report- Synchronization in Oscillatory Networks ing, together with pertussis resurgence during the hiatus in vaccination, enabled colleagues at the Swedish Institute Recent research has revealed a rich and complicated net- for Infectious Disease Control to enhance routine passive work topology in the cortical connectivity of mammalian surveillance, in which clinical course and vaccination sta- brains. A challenging task is to understand the implica- tus may be incomplete or lacking, and to ensure that sera tions of such network structures on the functional organi- from the 1997 national cross-sectional survey were tested zation of the brain activities. This is studied here basing on for IgG antibodies against pertussis toxin. They have fol- dynamical complex networks. We investigate synchroniza- lowed trial cohorts as well as children born since 1996, pri- tion dynamics on the cortico-cortical network by modelling marily to investigate long-term effectiveness of aP vaccines each node (cortical area) of the network with a sub-network counties use one- to three-component products but also to of interacting excitable neurons. We find that the network study the possible need for booster doses. As 98+ percent displays clustered synchronization behaviour and the dy- of infants have been vaccinated at 3, 5, and 12 months of namical clusters coincide with the topological community age since the hiatus, incidence has decreased an order of structures observed in the anatomical network. Our results magnitude. But pertussis has not been eliminated. And provide insights into the relationship between the global Sweden now resembles other developed countries: reported organization and the functional specialization of the brain cases occur mostly among older children and adults, with cortex. These modelling results will be compared with the infants still at greatest risk of severe disease. The first networks reconstructed from single EEGs measured during natural experiment permits evaluation of four hypothet- the performance of simple cognitive tasks. We compare dif- ical explanations for the changing epidemiology: surveil- ferent reconstruction methods based on partial phase co- lance artifact, selection of vaccine-resistant antigenic vari- herence, symbolic dynamics and recurrence. ants, waning of increasingly vaccine-induced immunity absent boosting, and reduced transmission. By 2004, waning Juergen Kurths was apparent among vaccinated cohorts, as one hypothesis Dept. of Physics predicts. Accordingly, vaccinated children were offered aP University of Potsdam with their DT boosters on attaining 10 years of age during [email protected] fall of 2005, with boosters at 4-6 years beginning in 2007 and 14-16 years planned in 2017. We will estimate parameters of a mathematical model of our hypothesis from MS49 observations through 2000, identify deficiencies, if any, by Reconstructing Topology of Sparse Dynamical Net- comparing predictions to subsequent observations, remedy works them, and use the validated model to ascertain the optimal number and timing of booster doses. The second natu- Methods are proposed for reconstructing the topology of ral experiment may permit county-level modeling with aP a general dynamical network, given observations of node product-specific parameters. dynamics. We focus on networks where connections are sparse and data is limited. We find that for inferring net- John W. Glasser work connections, true positive rates are optimized by us- Centers for Disease Control and Prevention ing so-called compressed sensing techniques now common [email protected] in signal processing. Tim Sauer MS49 Department of Mathematics Interaction Structures in Networks of Neurons George Mason University [email protected] Revealing interaction structures in networks of neurons is a major task in understanding information processing in Domenico Napoletani the brain. We propose a methodology to analyze multi- Dept. of Mathematics variate neuronal activity being capable of differentiating George Mason University direct and indirect connections. Furthermore, the chal- [email protected] lenge to determine the direction of information flow is addressed. Particular emphasis is laid on the detection of the possibly time-varying interaction structure. The presented MS49 methodology is applied to animal and human data. Kalman Filter Control of a Model of Spatiotempo- ral Cortical Dynamics Jens Timmer University of Freiburg Recent advances in Kalman filtering to estimate system Department of Physics state and parameters in nonlinear systems has offered the 80 LS08 Abstracts

potential to apply such approaches to spatiotemporal non- features and the amplification or attenuation of distributed linear systems. We here adapt the nonlinear method of input signals in dynamical systems. I will furthermore unscented Kalman filtering to observe the state and es- present topics of biological pathway analysis that would timate parameters in a computational spatiotemporal ex- benefit from the help of statisticians. citable system that serves as a model of cerebral cortex, to track spiral wave dynamics, and to use an observer system Eberhard O. Voit to calculate control signals through electrical fields. Georgia Institute of Technology [email protected] Steven J. Schiff Penn State University sschiff@psu.edu MS50 A Model for Cross-Species Co-Expression Analysis: An Application to Aging Transcription Programs MS50 Integrating Numerical and Statistical Tools: To- Systems biology is a relatively new integrative discipline wards Understanding Brain Energetics that focuses on the systematic study of complex interactions in biological systems, thus using a new perspective The debate over the primary fuel supporting the energetic (integration instead of reduction) to study them. Compar- needs of neuronal activity has been continuing for more ative analysis is a fundamental tool in systems biology. The than a decade, leading the experts to agree on the need focus of comparison is to identify either conservation or dif- for a mathematical model capable of offering a key to the ferences. For examples, conservation of expression values sparse and indirect data. In this talk we show how by in- among species often indicates the functional importance troducing a statistical framework it possible to design a of a gene, while differences of gene expression are critical detailed yet tractable computational model of brain en- markers of cell types. A work-in-progress project on com- ergy metabolism, in spite of the few data points available. parative analysis of gene expression will be reported in this The use of statistical tools can be extended to account for talk. It aims to develop a probabilistic model for identifica- the variability of the model predictions, hence to quantify tion of co-expressed genes that are conserved across species. the reliability of the computed estimates. Finally posit a Different from previous clustering efforts, the goal here is new hypothesis of brain energy metabolism suggested by to simultaneously 1) cluster genes in each species and 2) ar- the models predictions and show how it independently val- range as many orthologous genes into conserved clusters as idates published experimental data. possible. Our current treatment combines a finite mixture model for modeling gene expression in each species and a Daniela Calvetti logistic regression model to the counts of genes in corre- Case Western Reserve University, Dept of Mathematics sponding clusters across species. Results in synthetic data Center for Integrated Metabolic Systems show that this model outperforms the k-means clustering [email protected] performed in each species, even by traditional measures. Appling this model to an analysis of human and fruit fly aging data, we find that dietary restriction, the practice MS50 of limiting dietary energy intake, strongly influences three Predictive Models that Infer Structure and Depen- conserved gene clusters. This result offers an interpretation dencies: Modeling Tumor Progression at molecular level to the repeated observations of correlation between dietary restriction and increase life span in A modeling framework that allows for predictive models various species. It pinpoints the core regulatory pathways that simultaneously infer the geometry and statistical de- that are modulated by food intake throughout the evolu- pendencies explanatory variables in high-dimensional (ge- tion of at least 600 million years. Work in collaboration nomic) data is developed. This is then applied to the prob- with Jun Cai, Zhewen Fan and John Marden. lem of modeling tumor progression. The talk will touch on manifold learning, dimension reduction, and inference of Sheng Zhong graphical models. University of Illinois at Urbana Champaign [email protected] Sayan Mukherjee Duke University [email protected] MS51 Intracellular Mechanisms of Regulation of Muscle MS50 Metabolism During Exercise Current and Future Roles of Statistics in Dynami- Skeletal muscle can maintain intracellular [ATP] constant cal Biological Pathway Analysis during the transition from rest to exercise, while reaction rates may increase significantly. Among the key regula- Computational biology contains distinctly different subspe- tory factors, the dynamics of cytosolic and mitochondrial cialties. While statistics has played a crucial role in as- NADH and NAD+ during exercise have not been char- pects of structure and function prediction, molecular sim- acterized. To determine the extent of regulation exerted ulations, and the analysis of static networks, it is not typi- by these intracellular metabolic signals on skeletal muscle cally associated with, or applied to, dynamic pathway anal- metabolism at the onset of exercise, a computational model yses, which are seen as firmly embedded in the field of dif- was developed. In this model, transport and metabolic ferential equations. Well-known long-term exceptions have fluxes in distinct capillary, cytosolic, and mitochondrial included Kolmogorov differential equations, which result domains are integrated. We hypothesized that during the from stochastic processes, and Monte Carlo simulations. transition from rest to exercise (60% VO2max), the dy- In this presentation I will discuss a few less typical top- namics of lactate concentration [Lac] in exercising muscle ics where biological pathway analysis and statistics meet. is independent of mitochondrial redox state. We tested From among topics that have been addressed in the past I this hypothesis by simulating the metabolic responses of will discuss the dynamics of populations with distributed LS08 Abstracts 81

skeletal muscle to exercise, while altering the transport [email protected] rate of reducing equivalents from cytosol to mitochondria and muscle glycogen content. Simulation with optimal parameter estimates showed good agreement with experimen- MS51 tal data from muscle biopsies in human subjects. Com- Multiscale Simulation of Gas Flow in Subject- pared with the optimal values, a 20% increase (decrease) Specific Models of the Human Lung in NADH transport coefficient led to an 85% decrease (7- fold increase) in cytosolic redox state, and ∼ 50% decrease This presentation describes a comprehensive computa- (∼ 85% increase) in muscle [Lac]. Doubling (halving) tional fluid dynamics (CFD) framework for pulmonary gas glycogen concentration resulted in a 30% increase (20% flow that utilizes multidetector-row computed tomography decrease) in cytosolic redox state, and ∼ 10% increase (MDCT)-based subject-specific airway geometries, spans (∼ 25% decrease) in [Lac]. In both cases, mitochondrial multiple scales, and employs a data-driven approach to redox states had minor changes. In conclusion, simulations simulate flow in a breathing lung. The framework is based suggest that the regulation of lactate production at the on- upon MDCT imaging, geometric modeling of airway trees, set of exercise (∼ 60% VO2max) is primarily dependent on three-dimensional (3D) and one-dimensional (1D) coupled the dynamics of cytosolic redox state and independent of mesh generation, 3D and 1D CFD methods, image-based mitochondrial redox state. physiological boundary conditions, and a novel moving mesh technique. At a local level, the fluid-structure in- Marco E. Cabrera teraction and acinar flow simulations are employed for re- Case Western Reserve University gional wall-shear stress in compliant airways and mixing [email protected] in alveolar sacs. Some applications of the multiscale technique will be presented MS51 Ching-Long Lin Modeling the Cardiovascular Closed-Loop Baro- University of Iowa Reflex [email protected]

In cardiac physiology, a strong interconnection exists between all scales: normal function at a given level (e.g. tis- MS52 sue) depends on the underlying synergy of sublevels (my- Quantitative Reconstruction in PhotoAcoustic To- ocytes) but also on higher levels, when considering feed- mography back mechanisms. Hence, we propose a comprehensive model of the cardiovascular system that includes a finite PhotoAcoustic Tomography (PAT) uses light to create element model of ventricular mechanics with passive and sound sources (by heat generated on optical absorption) active material properties, the circulation, and the baro- and image reconstruction consists of an inverse acoustic reflex which feeds back to heart rate and beta-adrenergic source reconstruction, which can be done using conven- stimulation of the cardiac myocytes tional ultrasound methods. In order to quantify the optical properties underlying the sound generation it is necessary Roy Kerckhoffs to couple models for optical and acoustic propagation. In UCSD this talk I present some of our recent work on this prob- Department of Bioengineering lem, utilising a non-linear alogorithm for recovering optical [email protected] absorption coefficient.

Simon Arridge, Ben Cox, Paul Beard MS51 University College London Geometric and Fluid Flow Coupling Between [email protected], [email protected], Macro and Micro Scales in Respiration Simulation [email protected]

We present several components of a semi-automated subject-specific end-to-end medical image through CFD MS52 analysis capability for the human respiratory system. The Conductivity Imaging Using Electrical Impedance particular model components emphasized here are related Tomography and Elastic Deformation to the macro-through-micro scale coupling of geometry and flow physics. Specifically, in the area of geometric mod- Electrical impedance tomography (EIT) is an imaging tech- eling, four elements are summarized: i) semi-automated nique that uses Cauchy data to reconstruct the conductiv- processing of medical image data to derive upper airway ity in a domain. On the practical point of view the task is and lobe geometries, ii) partitioning and truncation algo- difficult. A new imaging technique that combines bound- rithms, iii) automated unstructured 3D gridding of the tra- ary electrical measurements and elastic deformation inside chea through generation 5-8, and iv) interfacing this upper the domain is under investigation (Ammari et al., to ap- bronchi and lobe geometry with a volume filling algorithm pear). A small spherical deformation is induced by ultra- for the subresolved bronchi. In the area of flow model- sound around a point x in the domain. Using asymptotic ing, algorithm components related to 3D through quasi-1D estimates, the electrical power in a small domain around transition, loss modeling, and boundary conditions are pre- the point x is recovered from the variation of the bound- sented. Particular emphasis here is placed on the issues and ary measures. This modality provides more information models related to interfacing the macro and micro scales. than classical EIT, since measures are available inside the The overall model is demonstrated through application to domain and not only on the boundary. An algorithm is pro- unsteady respiration simulation of a live subject. posed to reconstruct the conductivity, assuming the measured data is the energy density at each point of the do- Robert Kunz main. The cost-function is the L2 distance between the Applied Research Laboratory measured and the predicted energy density. The direct Pennsylvania State University and adjoint derivatives of the energy density with respect 82 LS08 Abstracts

to the conductivity distribution are calculated. The recon- cepts. struction algorithm uses a multigrid approach: at a coarse level the Jacobian of the cost function is assembled. At a Martin Fink fine level a matrix-free Gauss-Newton optimization is im- Department of Physiology, Anatomy and Genetics plemented, using direct and adjoint differentiation. We University of Oxford, UK also present numerical results on synthetical data in 2D martin.fi[email protected] and 3D. Jerry J Batzel Jerome Fehrenbach University of Graz Laboratoire MIP [email protected] Universite Paul Sabatier Toulouse III [email protected] MS53 Development of a Comprehensive Cardiopul- MS52 monary Model Modelling of Wave Equations Obeying Frequency Dependent Attenuation Laws for Thermoacoustic We developed a comprehensive cardiopulmonary model Tomography that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with It is reasonable that the resolution in Computed Ther- their short-term regulatory mechanisms. The model in- moacoustic Tomography can be improved by taking the cludes the systemic and pulmonary circulation, lung me- attenuation of the pressure waves inside the tissue into ac- chanics, gas exchange and metabolism, and the action count. Loosely spoken the classical attenuation law states of several regulatory factors (baroreflex, chemoreflex, pul- that a frequency component of a pressure wave is expo- monary mechanoreceptors, local peripheral control). It can nentially damped with an exponent that is proportional to represent a valid tool for clinical practice and medical re- some fractional power γ of the absolute value of the fre- search, providing an alternative way to experience-based quency and to the distance from the origin. For some frac- clinical decisions. tional powers γ the solutions of the common models have causality problems which indicate the incompleteness of Massimo Giannessi, Antonio Albanese, Elisa Magosso these models. In this talk we discuss these causality prob- Department of Electronics, Computer Science and lems and present a new class of pressure wave equations Systems obeying frequency dependent attenuation that guarantees University of Bologna, Italy causal solutions. [email protected], [email protected], [email protected] Richard Kowar Department of Computer Science Nicolas Chbat University of Innsbruck Philips Research North America [email protected] Briarcliff Manor, NY, USA [email protected] MS52 Thermoacustic Tomography with Integrating Mauro Ursino Transducers Department of Electronics, Computer Science and SYstems Thermoacoustic imaging is a promising new modality for University of Bologna, Italy nondestructive evaluation. So far mainly point measure- [email protected] ment data for thermoacoustic imaging are used. In this talk we review using setups with large detectors. Imaging algorithm based on the Radon transform are presented to MS53 cope with the measurements produced by the large detec- Subset Selection and Reduced-Order Parameter tors. We present numerical simulations for simulated and Estimation real data. Large-scale physiological models have become common- Otmar Scherzer place in medicine and engineering. Identifying model pa- University Innsbruck rameters from experimental data is a challenging task, [email protected] however, as the high level of modeling detail usually stands in contrast to relatively few data streams available for identification. We present a subset-selection approach to assess MS53 which parameters of a given model are the ones to tune in Cardiovascular Control: The Importance of the order robustly to match the model to a particular set of Pulse Pressure experimental signals.

Low pulse pressure (i.e., the diﬀerence between systolic Thomas Heldt, George Verghese and diastolic pressure) has been shown to be an indepen- Laboratory for Electromagnetic and Electronic Systems dent predictor of mortality in heart failure patients. How- Massachusetts Institute of Technology ever, underlying mechanisms have not been discussed in [email protected], [email protected] detail. Applying a pulsatile and a non-pulsatile mathematical model of the cardiovascular system we investigate the information content of the pulse pressure and its role MS53 in the cardiovascular control loop during orthostatic stress Modelling Feedback Mechanisms Regulating the based on experimental data. Sensitivities to physiological parameters provide a quantiﬁcation of the developed con- LS08 Abstracts 83

Cardiovascular System Spread of Disease

The overall function of the baroreceptor feedback mech- In this joint work with Hsieh and van den Driessche, we anism is known. However, the underlying bio-chemical propose a multi-patch model to study the impact of travel mechanistic processes are not fully understood and they are on the spatial spread of disease between patches with dif- not easily investigated in-vivo. By a methodology called ferent level of disease prevalence. The basic reproduction the mathematical microscope a mathematical model is de- number for each patch in isolation is obtained along with veloped making the invisible visible and the inaccessible ac- the basic reproduction number of the system of patches. cessible, via an in silico investigation of the feedback mech- Inequalities describing the relationship between these num- anisms. In this talk, I will illustrate how to access inacces- bers are also given. For a two-patch model with one high sible features of the barorecepter feedback chain regulating prevalence patch and one low prevalence patch, results per- heart rate. taining to the dependence of the basic reproduction number on the travel rates between the two patches are obtained. Johnny Ottesen For parameter values relevant for inﬂuenza, these results Roskilde University show that, while banning travel of infectives from the low Department of Mathematics to the high prevalence patch always contributes to disease [email protected] control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely af- Mette S. Olufsen fect the containment of the outbreak under certain ranges Department of Mathematics of parameter values. Moreover, banning all travel of in- North Carolina State University fected individuals from the high to the low prevalence patch [email protected] could result in the low prevalence patch becoming disease- free, while the high prevalence patch becomes even more Hien T. Tran disease-prevalent, with the resulting number of infectives in North Carolina State Univ this patch alone exceeding the combined number of infec- Department of Mathematics tives in both patches without border control. Under the set [email protected] of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between MS54 patches. Modeling the Eﬀects of Latently Infected Cell Ac- tivation on Low-Level Viral Persistence, Slow De- Lin Wang cay of the Latent Reservoir, and Intermittent Viral University of New Brunswick Blips in HIV-Infected Patients Under Drug Treat- [email protected] ment

Current HAART regimens cannot eradicate HIV-1 from MS54 infected individuals. Although the potent combination an- The Role of Schistosome Mating Structures in the tiretroviral therapy is usually able to suppress plasma viral Maintenance of Resistant Strains loads to below the limit of detection of conventional clinical assays, a low level of viremia can be detected to persist The effects of drug treatment of human hosts upon a pop- in plasma by more sensitive assays. Moreover, a number of ulation of schistosome parasites depend upon a variety of patients experience transient episodes of viremia above the factors. Previous models have shown that multiple strains detection limit, termed HIV-1 blips, even with highly sup- of drug-resistant parasites are likely to be favored as the pressive therapy for many years. A major known obstacle treatment rate increases. However, such models have ne- to viral eradication is the persistence of the latent reser- glected to account for the complex nature of schistosome voir for HIV-1 in resting memory CD4+ T cells. These mating biology. To more accurately account for the biology cells decay slowly, with a half-life up to 44 months, but of these parasites, a simple mating structure is included in are ready to produce new virus when they encounter their a multi-strain schistosome model, with parasites under the relevant antigens and are reactivated. The mechanisms un- influence of drug treatment of their human hosts. Para- derlying low viral load persistence, slow decay of the latent sites are assumed to pay a cost for drug resistance in terms reservoir, and intermittent viral blips are not fully char- of reduced reproduction and transmission. The dynam- acterized. The quantitative contributions of residual viral ics of the parasite population are described by system of replication to the viral and latent reservoir persistence re- homogeneous differential equations with and without time main unclear. In this talk, I will address these issues by delays, and the existence and stability of the exponential developing a mathematical model that considers latently solutions for the systems are used to infer the impact of infected cell activation in response to stochastic antigenic drug treatment on the maintenance of schistosome genetic stimulation. The model provides a quantitative and in- diversity. tegrated prospective into the dynamics of virus and the Dashun Xu latent reservoir in the setting of HAART and may have Southern Illinois University significant treatment implications in clinical practice. [email protected] Libin Rong Los Alamos National Laboratory MS54 [email protected] Modeling, Surveillance, Prediction and Control of West Nile Virus in Ontario MS54 In this project, we marry the mathematical modelling to Impact of Travel Between Patches for Spatial surveillance data from South Ontario to show that the non crow family birds which are susceptible to West Nile virus 84 LS08 Abstracts

are one of the key factors to make the virus become an Guang Qiang Dong, Vandit Sardana, Tharsan endemic disease and the density of dead crow is not an Velauthapillai accurate indicator for the virus after the virus sustain in a University of Toronto Mississauga region, while the density of mosquito in an area can give Dept of Chemical and Physical Sciences us the signal of the risk level of the virus. [email protected], [email protected], [email protected] Huaiping Zhu York University Mathematics and Statistics MS55 [email protected] Modeling Drosophila Development at the Molecu- lar, Promoter, and Pattern-Formation Levels

MS55 The segmentation network of Drosophila melanogaster is Systems Identification and Functional Analysis of well-known for its role in embryo patterning. We present Genetic Switching Networks modeling efforts and methodological advances that improve our understanding of this system at three different lev- Developing a quantitative understanding of switching be- els: at the phenomenological level of pattern formation, haviour in genetic networks is a challenging and multi- at a level relating phenomenological regulatory parameters faceted problem. This talk focuses on two aspects of this to promoter sequence composition, and at the individual problem the generation of unbiased network models from molecule level, where we estimate absolute protein copy experimental observations and the computational analysis numbers and noise based on fluctuations of fluorescence in of network models to gain insights into the network design expression images. features. I will present our efforts to development of a systematic gene perturbation algorithm (SGPA) that can be Theodore Perkins used to infer causalities within genetic networks by com- McGill University bining high-throughput characterization of network input- School of Computer Science output relationships and systems identification methods. [email protected] Additionally, I will discuss our work on using computational tools to develop new insights into the organization of genes within the embryonic stem cell switch and how MS55 different network features contribute to the functional ro- Quantifying and Predicting Gene Regulation in bustness of this switch. Single Cells

Mads Kaern The quantitative relation between transcription factor con- University of Ottawa centrations and the rate of protein production from down- Ottawa Institute of Systems Biology stream genes is central to the function of genetic networks. [email protected] I will describe a technique to measure this relation, the gene regulation function, in individual living cells. The gene regulation function is often a sigmoidal function, and MS55 I will show that, by interpreting genetic networks as in- Time Evolution of Gene Expression Distributions ference modules, we can make predictions about why this in Bacterial Populations sigmoidal function has different characteristics for different genetic networks. Our results should provide a basis We use a highly simplified construct to express a fluorescent for both understanding cellular decision-making and for protein from plasmids in bacterial cells, and observe the designing synthetic genetic circuits. distribution of gene expression levels across the population in this case. We disturb the population in two ways: by Peter Swain diluting it into fresh medium after a period of growth, and Center for Nonlinear Dynamics by using a cell-sorter to select out the brightest 10 percent McGill of the population. The distribution of protein expression [email protected] levels is tracked over six to twelve hours, and I will discuss the resulting dynamics in the two cases. The diluted population shows a transient response in both mean and MS56 variance, and never settles to a simple steady state: val- Inferring Effective Connectivity in Networks of ues continue changing for the full twelve hours observed. Spiking Neurons Recorded with Hundreds of Elec- The sorted population shows different behaviours in two trodes plasmid types: a tightly regulated (medium-copy) plasmid relaxes rapidly back to the initial distribution; while an To probe effective connectivity in cortical slice networks, unregulated (high-copy) plasmid takes many hours to re- we recorded spontaneous activity with a 512 electrode ar- turn to the original state. We have had some preliminary ray for periods > 1 hr in five cultured networks. We used success at modelling these effects. transfer entropy to infer effective connections between neurons. Transfer entropy correctly identified true connections David R. McMillen in simple model networks. The resulting networks from University of Toronto Mississauga the data displayed large fluctuations in topology around a Dept. of Chemical and Physical Sciences small but highly connected central core. [email protected] John M. Beggs Sangram Bagh Indiana University Dept of Chemical and Physical Sciences Dept. of Physics University of Toronto Mississauga [email protected] [email protected] LS08 Abstracts 85

MS56 Columbia University Analyzing Brain Networks with Granger Causality [email protected]

Multielectrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis MS57 provides the basic framework for analyzing the patterns of How in Vivo Conditions Affect Burst Firing Found neural interactions in these data. It has long been recog- in Vitro in Electrosensory Pyramidal Cells. nized that neural interactions are directional. Being able to assess the directionality of neuronal interactions is thus The intrinsic mechanisms underlying burst generation in a highly desired capability for understanding the coopera- vitro are generally well understood. However, how these tive nature of neural processing. Research over the last few mechanisms are implemented under in vivo conditions is years has shown that Granger causality is a key technique still not clear. ELL pyramidal cells have a well defined to furnish this capability. In this talk, I will discuss the con- burst mechanism in vitro but in vivo data shows a very cept of Granger causality and present results from applica- different burst mechanism. This talk will explore, through tions of this technique to multichannel local field potential a combination of experimental and modeling approaches, recordings from monkeys performing cognitive tasks. how the conditions found in vivo affect a well characterized burst mechanism found in vitro. Mingzhou Ding Department of Biomedical Engineering Maurice Chacron University of Florida Department of Physiology and Center for Nonlinear [email protected]fl.edu Dynamics McGill University [email protected] MS56 Estimating Neuronal Network Connectivity De- Natalia Toporikova spite Hidden Nodes Dept. of Physiology McGill University Determining the connectivity structure of neuronal net- [email protected] works from measurements of spike times is hindered by one’s inability to simultaneously measure the activity of all neurons. Many unmeasured neurons could be interact- MS57 ing with the small set of measured neurons and corrupt- Bursts and the Detection of Transient Electrosen- ing estimates of connectivity in unknown ways. For ex- sory Signals. ample, a common connection from an unmeasured neuron could introduce correlations among two measured neurons, Electric fish rely on their electro-sense to localize preys and which might lead one to erroneously infer a connection be- communicate with one another. We show that in different tween the measured neurons. We present a model-based hindbrain regions, bursts encode different behaviourally approach to control for such effects of unmeasured neu- relevant signals. In particular synchronized bursting is trig- rons. We demonstrate the promise of this approach via gered by transient communication signals in a region of the simulations of small networks of neurons driven by a visual hindbrain believed to be important for communication. We stimulus. argue that bursting in electric fish, as in other systems, is a conspicuous neural code signalling the occurrence of tran- Duane Nykamp sient and behaviourally relevant sensory events. University of Minnesota School of Mathematics Gary Marsat [email protected] University of Ottawa [email protected]

MS56 Leonard Maler Modeling and Decoding Multineuronal Responses Cellular and Molecular Medicine in the Primate Retina University of Ottawa [email protected] A key challenge in neuroscience is to understand how large networks of neurons collectively encode information. It has recently become possible to record simultaneously from MS57 complete mosaics of 100 ON and OFF parasol cells over Bugs, Bats and Bursts: Behaviorally Relevant a 4x8 degree region of peripheral retina, providing the op- Bursting in an Insect Auditory System portunity to better understand the message the eye sends the brain. We present a new generalized linear multivari- Bursts of action potentials have been proposed, in many ate point process model of the visual response properties systems, to detect salient stimulus features but have rarely of networks of these retinal ganglion cells. We discuss been shown to influence behavior. Spike bursts of an identi- model fitting and validation (challenging due to the high fied auditory interneuron of crickets accurately detect large dimensionality of the data, but computationally tractable increases in stimulus amplitude and sound location whereas due to the concavity of the loglikelihood), demonstrate the non-burst spikes do so poorly. Comparison of spike trains model’s accuracy in predicting retinal responses to novel vi- and behavioral responses shows that only bursts elicit be- sual stimuli, and describe Bayesian techniques for decoding havioral responses, thus demonstrating that bursts are in- the network responses. With J. Pillow, E. J. Chichilnisky, deed behaviorally relevant. E. Simoncelli, and J. Shlens. Gerald Pollack Liam Paninski Dept of Biology Statistics Department McGill University 86 LS08 Abstracts

[email protected] an overlapping region by communicating state information at the sub-domain boundaries. Imposition of boundary Gary Marsat conditions in the MD and DPD systems involves particle University of Ottawa insertion and deletion, specular wall reflection and body [email protected] force terms. The latter includes a boundary pressure force in order to minimize near-boundary density fluctuations, Patrick Sabourin and an adaptive shear force which enforces the tangential Dept. of Biology velocity component of boundary conditions. The triple- McGill University decker algorithm is verified for prototype flows, including [email protected] simple and multi-layer fluids (Couette, Poiseuille, and lid- driven cavity), using highly accurate reference solutions. A zero-thickness interface is also possible if it is aligned with MS57 the flow streamlines. The Role of Thalamus in Cortical Function: Not Dmitry Fedosov, George Karniadakis Just a Simple Relay Brown University For thalamic relay cells, the recent history of membrane [email protected], [email protected] voltage determines which of two firing modes, tonic or burst, prevails. Burst firing occurs when the cell is rel- MS58 atively hyperpolarized, and tonic firing, when relatively depolarized. These modes have significant consequences Multiscale Simulation of the Musculoskeletal Sys- for the thalamocortical relay. We have begun studies of tem using Surrogate Models of Tissue Behavior another cell showing burst firing, the layer 5 corticothala- The primary tools of computational biomechanics include mic cell, and the consequences of bursting are similar in multi-body dynamics at the body level and finite element these thalamic and cortical cells. methods at the organ level. The multi-body technique Murray Sherman lacks the complexity to accurately capture tissue behavior Department of Neurobiology and finite element models are typically too computation- University of Chicago ally intensive for body level simulations. Presented here [email protected] is the use of computationally efficient surrogate models of tissue within a multi-body framework. The input-output relations of the surrogate models are derived from finite MS58 element solutions. Control of Macro-Scale Mixing and Transport in Trent Guess the Small Intestine: A Lattice-Boltzmann Model University of Missouri Kansas City The primary function of the small intestine is the absorp- [email protected] tion of nutrients through the epithelial surface into the blood stream. Two basic motility patterns are responsible MS58 for the transport: peristaltic contractions for axial transport, and repetitive segmental contractions of short sec- Understanding the Functionality of Myosins, the tions of the gut for radial transport. We evaluate the rela- Motive Forces of Living Systems tive contributions of peristaltic and segmental contractions Molecular motors play crucial roles in diverse biological to the absorption process using a two-dimensional model of processes ranging from gene replication to muscle contrac- flow and mixing of passive scalar using a lattice-Boltzmann tion to cell division. They convert chemical energy such model of small intestine motility with second-order moving as ATP hydrolysis into mechanical work. Myosins belong boundary conditions for velocity and scalar. Mixes of seg- to one important family of molecular motors moving on mental and peristaltic contractions are parameterized with actin filaments and performing various mechanical func- magnetic resonance imaging (MRI) data from the rat in- tions within living cells. Recent studies have shown that testine and nutrient uptake was quantified as surface scalar myosin VI is correlated with ovarian and prostate cancers, flux. We find that any level of peristaltic contribution but the detailed molecular mechanism remains unknown. degrades uptake, explaining radiologic observations where We describe work focused on understanding myosin VI, peristalsis is absent during the initial digestive period and the effect of molecular mutations and its similarity to appears only periodically later to transport chyme. other myosins, which have been extensively studied. We Gino Banco have used computational approaches to guide the design Pennsylvania State University of chimeric myosins and predict the step size and the di- [email protected] rectionality of each designed myosin. We then expressed these molecules and used in vitro motility assays to test their dynamic behavior. One remarkable difference be- MS58 tween myosin VI and other myosins is that it moves in the Triple-Decker: Interfacing Atomistic-Mesoscopic- reverse direction as compared to other myosins. We were Continuum Flow Regimes in Biological Fluids able to engineer myosins moving toward the opposite ends of actin filaments with a change of only 18 amino acids. Multiscale flow phenomena in microfluidic and biomedical applications require the use of heterogeneous modeling ap- Jung-Chi Liao proaches. We present a hybrid method based on coupling Stanford University the Molecular Dynamics (MD) method, the Dissipative [email protected] Particle Dynamics (DPD) method, and the incompressible Navier-Stokes (NS) equations. MD, DPD, and NS are formulated in separate sub-domains and are coupled via LS08 Abstracts 87

MS58 European Union funded projects. Microstructure and Composition Based Constitu- tive Relationships for Meniscus/Cartilage Nicolas Smith University of Oxford Objectives: To develop stress-strain relationship for mod- [email protected] elling the deformation behavior of soft tissues, such as knee meniscus and cartilage, based upon their microstructure and composition. Methods: The knee meniscus and car- MS58 tilage is considered to be composed of hydrated collagen A Multiscale Lattice-Boltzmann Model of Macro- fiber network, hydrated proteoglycan (PG) gel and free to-Micro Scale Couplings in the Small Intestine water. Consequently, we seek constitutive relationships of the type used in fluid saturated porous medium. The effec- Nutrient and pharmaceutical absorption in the small intes- tive stress in this poroelastic constitutive law is obtained tine involve coupled multiscale transport and mixing pro- from a simple volume average of the stress on the non- fib- cesses that span several orders of magnitude. We have hy- rillar PG gel and the stress on the fibrillar network. The pothesized that muscle-induced villi motions generate and stress on the non- fibrillar PG gel is estimated using a mod- control a ”micro-mixing layer” that couples with macro- ified neo-Hookean model. The stress tensor of the fibrillar scale mixing to enhance molecular transport to and from network is obtained by considering the fiber orientations the epithelium. To test this hypothesis, we developed a 2- and fiber loading condition. The fiber network is consid- D numerical method based on a multigrid strategy within ered to be under pre-tension that results from the swelling the lattice-Boltzmann framework. Emphasis is placed on pressure caused by the PG gel hydration under a given ion the treatment of moving boundaries with arbitrary curva- concentration. At present, the pre-tension stress is esti- tures for flow and scalar. We model a macro-scale cavity mated using the Donnan osmotic pressure model. Finally, flow with microscale finger-like ”villi” in pendular motion we make the kinematic assumption that the strain in the on the lower surface and evaluate the coupling between non- fibrillar PG gel and the fibrillar network are the same. macro and micro-scale fluid motions, scalar mixing, and The resultant stress-strain relationship is used to perform uptake of passive scalar at the villi surface. Results show parametric study of overall tissue behavior under various that the moving villi can be effective mixers at the micro loading conditions. Using this approach we are able to ob- scale, especially when groups of villi move in a coordinated tain closed form expressions for overall stress-strain behav- out-of-phase fashion. A time-evolving series of flow recir- ior under uniaxial compression and tension. For multiax- culation eddies are generated over the villi, which form a ial loading cases, the stress-strain behaviors are evaluated micro mixing layer. These eddies increase the transport of numerically. Results: Stress-strain behavior under strain scalar from the macro eddy to the surface of villi by ad- controlled uniaxial compression is found to be significantly vection. Higher frequency of villi motions enhances scalar affected by the fiber content, fiber network pre-tension and absorption. This enhancement of absorption is lower with fiber stiffness. For large pre-tension, the overall behavior smaller villous length. can show softening at intermediate strain-levels. For small Yanxing Wang pre-tension and fiber stiffness, the overall behavior is dom- Pennsylvania State University inated by the non-fibrillar part. [email protected] Anil Misra The University of Kansas PP1 [email protected] Monolithically Coupled Fluid-Structure Interac- tion for Blood Flow in Arteries MS58 We develop a scalable parallel finite element solver for euHeartL: Multi-Scale Computational Models of the simulation of blood flow in compliant arteries. Mono- the Heart lithic coupling of the incompressible Navier-Stokes equa- Mathematical models of the heart are arguably some of tions with a linear elastic structure model for the artery the most advanced examples of integrating multiple data walls ensures stability, and an unstructured dynamic mesh sets into a consistent biophysical framework for quanti- in the arbitrary Lagrangian-Eulerian frame allows for com- tative prediction of function. The philosophy underpin- plicated geometry and large grid deformation. The result- ning a large number of these models is one of providing ing algorithm features good parallel performance and scal- a framework within which to encapsulate physiological un- ability and is robust to changes in timestep, Reynolds num- derstanding. That this is now becoming a reality is demon- ber, and other physical parameters. strated by the increasing number of studies which now Andrew T. Barker use or extend previously developed modelling frameworks. Department of Applied Mathematics Such component reuse and knowledge capture within mod- University of Colorado, Boulder elling frameworks is an enormously powerful feature of [email protected] Systems Biology approaches. Component reuse is also a central philosophy within exciting global initiatives such as the Physiome and Virtual Physiological Human (VPH) Xiao-Chuan Cai Projects which aim to develop integrated multi-scale mod- University of Colorado, Boulder els of physiological systems. We argue that the application Dept. of Computer Science of model reuse requires methods for analysing model struc- [email protected] ture to maintain transparent links with experimental and clinical data. To meet this need we propose tools for the PP1 analysis of cardiac models. We argue that these approaches are important for providing the confidence in model results Bifurcation Theory for a Model of the Oculomotor which will in turn enable the translation of research into clinical environments to meet the objectives of several new 88 LS08 Abstracts

Neural Integrator ual drug pharmacokinetic. An improved drug-drug interaction prediction method based on a three-level hier- The oculomotor neural integrator converts sensory signals archical Bayesian meta-analysis model uses Monte Carlo proportional to eye velocity into eye position commands. Markov chain (MCMC) pharmacokinetic parameter esti- We analyze neural network models of the integrator. Our mation procedure. Underlying the present one is a fast analysis shows that, to function normally, the system must integration method of the stiff pharmacokinetic equations. operate in a region where small perturbations can push it We report the establishment of the existence-uniqueness of into regions of instability or oscillation. Our model will also the solution and the interaction between the MCMC pro- simulate a class of eye movement disorders known as ”con- cedure and the numerical integration scheme. genital nystagmus”. Both normal and abnormal behavior depend crucially on the non-normality of the system. Bruno Bieth Department of Mathematical Sciences Andrea K. Barreiro, Jared Bronksi Indiana University - Purdue University Indianapolis Department of Mathematics [email protected] University of Illinois at Urbana-Champaign [email protected], [email protected] Raymond C.Y. Chin Indiana University - Purdue University Indianapolis Thomas Anastasio [email protected] Molecular and Integrative Physiology University of Illinois at Urbana-Champaign Lang Li [email protected] Division of Biostatistics, Department of Medicine Indiana University PP1 [email protected] IMAG: Multi-Scale Modeling of the Heart in Metabolic Syndrome and Cardiovascular Disease PP1 Our work to date on this project has focused on captur- Finding Biological Signals in Inhomogeneous Se- ing the physiological state of the heartspecifically the in- quences by a Gibbs Sampler Algorithm tegrated components of energy metabolism, electrophysiol- We present a new version of the Gibbs sampler algorithm, ogy, and coronary transportin a computer model at the ap- which helps identify sequence motifs of biological interest. propriate level of detail upon which metabolic dysfunction Detection of branch point site motifs can improve identifi- in cardiovascular disease can be naturally imposed. Several cation of intron borders in eukaryotic genes. The new al- important outcomes have emerged from our analysis of the gorithm utilizes inhomogeneous background Markov mod- physiological system. The first concerns the mechanism of els to better incorporate available sequence information. maintaining metabolic stability in the heart in response to Tests show improved performance of the new Gibbs sam- changes in work rate. The mechanism of metabolic control pler when applied to inhomogeneous sequences. We use has eluded explanation for three decades because it has the new algorithm to examine branch point sites in fungal been assumed that the substrates for oxidative phosphory- intron sequences. lation (ADP and Pi) do not vary enough for feedback to significantly contribute to metabolic control in vivo. How- Marc Bruce ever, by analyzing data from 31phosphate-magnetic res- Georgia Institute of Technology onance spectroscopy (31P-MRS) we have determined that School of Chemistry & Biochemistry feedback-driven control is sufficient to explain the observed [email protected] data. Our detailed mechanistic model of integrated oxygen transport and oxidative metabolism not only explains the Alexandre Lomsadze, Mark Borodovsky observed data, but also predicts that the maximal work Georgia Institute of Technology rate of the heart is an emergent property and is limited not Wallace H. Coulter Department of Biomedical simply by the maximal rate of ATP synthesis, but by the Engineering maximal rate at which ATP can be synthesized at a poten- [email protected], [email protected] tial at which it can be utilized. Novel predictions associated with this finding are validated based on independent data obtain 31P-MRS data obtained during acute ischemia and PP1 recovery. In sum, our mass-, charge-, and energy-balanced Migration and Mixing Between Populations in Dis- model of oxygen transport and energy metabolism in the ease Models heart provides a unique and deeply validated platform for further investigations into roles of metabolism and mito- In the field of epidemiology, models depend on how a popu- chondrial function and dysfunction in cardiac health and lation can be broken down into groups of people that carry disease. similar traits that are important to the disease. Modeling how these groups interact is fundamental to capturing how Daniel A. Beard a disease spreads in and between populations. We study Medical College of Wisconsin how migration and other mixing effects in an SIR model Department of Physiology can induce an epidemic or how these can be controlled to [email protected] curb an oncoming outbreak.

David Burger PP1 Montclair State University Analysis of a Drug-Drug Interaction Problem from [email protected] Pharmacokinetic

A two drug interaction is usually predicted by individ- Lora Billings Montclair State University LS08 Abstracts 89

Dept. of Mathematical Sciences Massachusetts Institute of Technology [email protected] [email protected]

Ulrik Nielsen PP1 Merrimack Pharmaceuticals Computational Modeling and Simulation Lead to Cambridge, MA the Development of MM-121, a Human Mono- [email protected] clonal Antibody ErbB3 Antagonist

The epidermal growth factor receptor and ErbB2 have been PP1 heavily targeted by therapeutic agents, with some success. IMAG: Time Course of Metabolic Adaptations Understanding the relative importance of the ErbB recep- during Loading and Unloading tors for inducing activation of downstream signaling cas- cades is complicated for a number of reasons: the ErbB re- Skeletal muscle can maintain intracellular [ATP] constant ceptors homo and heterodimerize to become activated, are during the transition from rest to exercise, while reaction expressed to differing degrees in different cancer types, and rates may increase significantly. Among the key regula- undergo ligand-specific trafficking. Hence, we have taken a tory factors, the dynamics of cytosolic and mitochondrial systems approach to the problem and developed a compu- NADH and NAD+ during exercise have not been char- tational model of the ErbB signaling network for the pur- acterized. To determine the extent of regulation exerted pose of developing more efficacious ErbB targeted thera- by these intracellular metabolic signals on skeletal muscle peutics. The computational model describes the dynamics metabolism at the onset of exercise, a computational model of all four ErbB receptors in response to ligands that bind was developed. In this model, transport and metabolic to EGFR (Betacellulin) or ErbB3 (Heregulin). Ligand- fluxes in distinct capillary, cytosolic, and mitochondrial induced dimerization, receptor internalization, degradation domains are integrated. We hypothesized that during the and downstream signaling of the PI3K-Akt cascade are in- transition from rest to exercise (60% VO2max), the dy- cluded. To train the model the activation status of all namics of lactate concentration [Lac] in exercising muscle ErbB receptors and pAkt, an important regulator of cell is independent of mitochondrial redox state. We tested proliferation and survival, were measured after stimulation this hypothesis by simulating the metabolic responses of with each ligand in ADRr cells: 12 time points ranging skeletal muscle to exercise, while altering the transport up to 2 hours post stimulation and 8 ligand concentra- rate of reducing equivalents from cytosol to mitochondria tions spanning three orders of magnitude. This dataset and muscle glycogen content. Simulation with optimal pa- constrained the dynamic behavior of the model for param- rameter estimates showed good agreement with experimen- eter estimation and the model was then tested using DU145 tal data from muscle biopsies in human subjects. Com- and ACHN cell lines. Sensitivity analysis was performed pared with the optimal values, a 20% increase (decrease) of the system to determine the key proteins in the net- in NADH transport coefficient led to an 85% decrease (7- work for activating pAkt over a diverse range of heteroge- fold increase) in cytosolic redox state, and ∼ 50% decrease neous ErbB receptor profiles. ErbB3 was found to be an (∼ 85% increase) in muscle [Lac]. Doubling (halving) ultra-sensitive inhibition point in response to either Beta- glycogen concentration resulted in a 30% increase (20% cellulin or Heregulin. This prediction was verified by de- decrease) in cytosolic redox state, and ∼ 10% increase veloping and testing a novel anti-ErbB3 antibody, MM121, (∼ 25% decrease) in [Lac]. In both cases, mitochondrial in cell based assays. MM-121 was also found to be more redox states had minor changes. In conclusion, simulations effective at inhibiting Heregulin-induced pErbB3 and pAkt suggest that the regulation of lactate production at the on- than other therapeutic agents targeting the ErbB pathway set of exercise (∼ 60% VO2max) is primarily dependent on further supporting the findings. The kinetic parameters the dynamics of cytosolic redox state and independent of of MM-121 were also used to build an in silico version of mitochondrial redox state. the inhibitor. The model was then used to predict the IC50 values of pAkt and pErbB3 in response to MM121 in Marco E. Cabrera a number of cell lines stimulated with Heregulin or Beta- Case Western Reserve University cellulin and these predictions were experimentally verified. [email protected] These in vitro findings were further validated in vivo using multiple xenograft models. In summary, we describe 1) how a systems approach to drug discovery has suggested a PP1 potentially better mechanism of inhibiting the ErbB path- A Novel Method for Error Regulation in Biological way and 2) the ability of our computational model to ac- Systems curately simulate the effect of an anti-ErbB3 monoclonal antibody on signaling in a variety of cancer cell type. We propose a novel, versatile way for cells to regulate the error rates of biochemical reactions. This mechanism pro- Birgit Schoeberl, Emily Pace, Jonathan Fitzgerald, Brian vides a thermodynamic basis for the theory of “kinetic Harms, Kip West, Aparna Kumar, Art J Kudla checkpoints” and shows how it is coupled to energy input Merrimack Pharmaceuticals from the cell. Though we focus primarily on DNA repli- Cambridge, MA cation, our model and mechanism are applicable to a wide [email protected], range of biochemical processes, including actin binding and [email protected], motor proteins. jfi[email protected], [email protected], Field Cady, Hong Qian [email protected], Department of Applied Mathematics [email protected], University of Washington [email protected] fi[email protected], [email protected]

John Burke Harvard Medical School 90 LS08 Abstracts

PP1 Department of Mathematics Singular Limits of Reaction Diﬀusion Equations of National Taiwan Normal University,Taipei, Taiwan Fisher Type in An Inﬁnite Cylinder. [email protected]

The limit of a scaled reaction diffusion equation of monos- LiFen Chen table type on an infinite cylinder is analyzed. The equation Institute of Brain Science, National Yang-Ming University is scaled with two small parameters. The scaling provides Tapipei, Taiwan the equation with a large and small diffusion coefficients [email protected] in the cross sectional and longitudinal coordinates of the cylinder respectively. The reaction term of this equation JenChuen Hsieh has two equilibrium states, one stable and the other un- Institute of Brain Science, National Yang-Ming stable. We show that the solutions of the scaled equation University, converge locally uniformly to piecewise constant function Taipei, Taiwan that attains the equilibrium of the equation, as the param- [email protected] eters approach zero. Fernando Carreon ChangYuan Cheng Arizona State University Department of Applied Mathematics [email protected] National Pingtung University of Education [email protected]

PP1 Recurrence of Epidemic Human Inﬂuenza: Insights PP1 From Simple Models The Dynamics of Macrophage Activation

Abstract not available at time of publication. The ability of an individual macrophage to change its activation state is an unresolved immunological question with Bernard Cazelle enormous significance. The proper activation state de- CNRS, France termines if the host will effectively eliminate pathogens [email protected] and appropriately heal wounded tissue. Our ode model describes the signaling cascade and associated substrate- enzyme dynamics of competing activation states within an PP1 individual macrophage and demonstrates that individual Complex Temporal Patterns of Spontaneous Ini- macrophages can switch their activation state under cer- tiation and Termination of Reentry in a Loop of tain environmental conditions. Cardiac Tissue Lauren M. Childs A model is developed consisting of a discrete loop of cardiac Cornell University cells that circulates action potentials as well as a pacing [email protected] mechanisms. The dynamics of circulating pulses and the pacer’s action are regulated by threshold relations. Pat- Steven Strogatz terns of spontaneous initiations and terminations of reen- Theoretical and Applied Mechanics try generated by this system are studied. These patterns Cornell University can be regular or irregular; causes of irregularities are iden- [email protected] tified as threshold bistability of reentrant circulation and phase-resetting interactions with the pacer. Matthias Hesse David Chan Cornell University Dept. of Mathematics [email protected] Virginia Commonwealth University [email protected] PP1 IMAG: Multi-Scale Imaging, Analysis, and Inte- PP1 gration of Brain Networks The Difference of Synchronization Between Bipo- The mammalian nervous system exhibits intricate struc- lar Patients and Normal Subjects in the Prefrontal tural (anatomical) organization at multiple scales, subsum- Cortex ing specific functional roles. In this project, we investi- Bipolar Disorder (BD) is a severe mental disorder char- gated such structural organizations and their relationships acterized by recurrent episodes of alternating elated and in the mouse brain at three levels of detail: nanoscale depressed mood states interposed by remission periods. (tens of nanometers), microscale (several micrometers), We recruited ten normal controls and ten patients with and macroscale (hundreds of micrometers up to several mil- bipolar I disorder during euthymic phase (five males and limeters). The use of innovative volume microscopy tech- five females, mean age=32.5 +10.3 y/o, range=21:53). For niques has played a key role in this respect. We employed each subject, 2-minutes eye-closed resting MEG data of 1 data from the Serial Block-Face Scanning Electron Mi- kHz sampling rate were recorded with a whole-head 306- croscopy (nanoscale), Array Tomography (nanoscale and channel neuromagnetometer (Vectorview; Elekta- Neuro- microscale), Knife-Edge Scanning Microscopy (KESM, mi- mag, Helsinki, Finland ). We observed increased delta syn- croscale), and Magnetic Resonance Microscopy (MRM, chronization, decreased alpha and beta synchronization in macroscale) to obtain an accurate structural reconstruc- the frontal regions of bipolar patient. tion of mouse brain circuits and analyze their functions. A major part of the project focused on developing the mi- Shyanshiou Chen croscopy techniques (KESM and Array Tomography) and LS08 Abstracts 91

fully automating them, and another part focused on effi- and infection in order to explore this hypothesis. We as- cient 3D reconstruction algorithms, structural analysis al- sess the effect of varying the reticulocyte replacement rate gorithms, and data organization and dissemination meth- and preference of the parasite for reticulocytes on four key ods for data and model sharing. We expect our extensive outcome measures assessing anemia and parasitemia. For data and dissemination framework to enable major discov- a given level of parasite preference for reticulocytes we un- eries, both by us and other neuroscience researchers. cover an optimal erythropoietic response which minimizes disease severity. Increasing red blood cell production much Yoonsuck Choe above this optimum confers no benefit to the patient, and Texas A&M University in fact can increase the degree of anemia and parasitemia. [email protected] These conclusions are consistent with epidemiological studies demonstrating that both iron deficiency and anemia are protective against severe malaria, whilst iron supplementa- PP1 tion in malaria endemic regions is with an increased num- Monte Carlo Simulations of the Signaling Scaffold ber of malaria related adverse effects. Thus, suppression Formation Linking ErbB1 and Ras of red blood cell production, rather than being an unfortu- nate side effect of inflammation, may be a host protective Experimental evidence reveals heterogeneities of protein effect against severe malarial anemia. clustering within the cell membrane. Two proteins observed in these clusters are ErbB1 and Ras which are key Deborah Cromer regulators of the MAPK pathway and often dysregulated Imperial College in many cancers. When ErbB1 becomes activated pro- Department of Mathematics teins within the cytsol are recruited to the membrane es- [email protected] tablishing a signaling scaffold which leads to the guanine nucleotide exchange from Ras-GDP to Ras-GTP. Interest- Jaroslav Stark ingly both ErbB1 which is a transmembrane protein and Imperial College Ras which is tethered to the cytosolic membrane are seen [email protected] clustered. Although much work has been done to model these proteins very little work has been done to understand the spatial establishment of this signaling scaffold. Miles Davenport Here we have developed a lattice based frame work using University of New South Wales a spatial Monte Carlo algorithm which couples two lattice [email protected] based models with a non-spatial stochastic model. This provides a pseudo 3D framework for understanding forma- PP1 tion of a signaling scaffold. Partial Phase Synchronization of Neural Popula- Michelle N. Costa tions Due to Random Poisson Inputs Department of Chemical and Nuclear Engineering University of New Mexico We show that populations of identical uncoupled neurons [email protected] exhibit partial phase synchronization when stimulated with independent, random unidirectional current spikes with interspike time intervals drawn from a Poisson distribution. Dion Vlachos We derive how the extent of the partial phase synchro- Department of Chemical Engineering nization depends on the magnitude and mean interspike University of Delaware Newark, DE frequency of the stimulus. The degree of partial phase [email protected] synchrony is shown to influence the response of the population to stimulation, which we illustrate using first spike Jeremy Edwards time histograms. Molecular Genetic s & Microbiology and Chemical Engg. University of New Mexico Per Danzl, Robert Hansen [email protected] University of California, Santa Barbara Department of Mechanical Engineering [email protected], [email protected] PP1 Low Red Cell Production May Protect Against Se- Guillaume Bonnet vere Anemia During a Malaria Infection Insights University of California, Santa Barbara From Modeling. Department of Statistics and Applied Probability [email protected] The malaria parasite causes lysis of red blood cells, resulting in anemia, a major cause of mortality and morbid- ity. Intuitively, one would expect the production of red Jeff Moehlis blood cells to increase in order to compensate for this loss. Dept. of Mechanical Engineering However, it has been observed that this response is weaker University of California – Santa Barbara than would be expected. Furthermore iron supplementa- [email protected] tion for iron deficient children in malaria endemic regions can paradoxically adversely affect the clinical outcome of PP1 malaria infection. A possible explanation may lie in the preference that some malaria parasites show for infecting Some Bifurcation Conditions via Stoichiometric immature red blood cells (reticulocytes). In the presence Network Analysis of a parasite preference for immature red cells, a rise in red Using notions from stoichiometric network analysis (SNA) cell production can fuel the fire of infection by increasing and algebraic geometry, we will present some sufficient con- the availability of the parasites preferred target cell. We ditions for polynomial chemical reaction networks to dis- present a mathematical model of red blood cell production 92 LS08 Abstracts

play specific bifurcations that are often associated with between cell internal restructuring and its consequences on model oscillations and multistationarity. Advantage of cell shape and movement. SNA is that it can successfully deal with two common modeling issues in systems biology: parameter uncertainty and Graziela Grise, Michael Meyer-Hermann network size. Frankfurt Institute for Advanced Studies grise@fias.uni-frankfurt.de, Mirela Domijan, Markus Kirkilionis m.meyer-hermann@fias.uni-frankfurt.de Mathematics Institute University of Warwick [email protected], [email protected] PP1 IMAG: Dynamic Simulation of Joints Using Multi- Scale Modeling PP1 Models of Drug Therapy During Hepatitis Delta Dynamic loading of the knee plays a significant role in the Virus Infection development and progression of tissue wear disease and injury. Dynamic rigid-body models provide insight into Hepatitis Delta Virus (HDV) is a subviral satellite that body-level biomechanics and their computational efficiency replicates only with assistance from Hepatitis B Virus facilitates dynamic simulation of neuromusculoskeletal sys- (HBV). Its close relationship with HBV makes it difficult tems. A major limitation of rigid-body models is their to target with virus-specific therapeutic treatments, and simplistic (or non-existent) representation of tissue-level complicates any effort to model its interaction with the structures. This limitation prevents holistic computational host hepatocyte population. We use the results of HBV approaches to investigating the complex interactions of drug trials in HDV patients to develop and refine a model knee structures and tissues, a limitation that hinders our of this viral system, and evaluate the likely efficacy of dif- understanding of the underlying mechanisms of knee in- fering antiviral strategies. jury and disease. This grant supports development of surrogate models, such as neural networks, that reproduce Jonathan Forde the dynamic behavior of menisci-tibio-femoral articulations Hobart and William Smith Colleges within the rigid body framework. These surrogates learn [email protected] from finite element method solutions and are validated using a dynamic knee loading machine. PP1 Trent Guess Cell Metabolism, Parkinson’s Disease and Therapy University of Missouri Kansas City [email protected] Parkinson’s patients who are being treated with levodopa (L-Dopa) have significant elevations of plasma homocysteine, probably due to an alteration of homocysteine PP1 metabolism secondary to catechol-O-methyltransferase A Quasi Newton Method for Constrained Molecu- (COMT) mediated metabolism of L-Dopa. It has also been lar Dynamics Simulation stated that the extend to which homocycteine is elevated above normal is dependent upon the B-vitamin status, as MD simulation can be used to study various dynamic prop- plasma homocycteine is inversely correlated with folate and erties of proteins, but a long sequence of iterations has to be vitamin B12 in L-Dopa treated patients. To better under- carried out even for small protein motions due to the small stand the impact of the L-Dopa treatment on the health of time step (10e-15sec) required. The bonding forces are the Parkinson’s patients we develop a mathematical model among those causing fast protein vibrations that require for the methionine, folate and dopamine metabolism. The small time steps to integrate, but they may be replaced by ODE model reproduces the observed effects of L-Dopa a set of bond length constraints, to increase the step size treatment on cell metabolism, under both normal and folic and hence the simulation speed. Lagrange multiplier meth- acid/B-vitamin deficient conditions. These results suggest ods have been developed for constrained dynamics simula- that cost-efficient computational experiments based on our tion. However, the multipliers have to be determined in model can be used to further explore the complex metabolic every step to satisfy the constraints through the solution pathways relevant to Parkinson’s disease. of a nonlinear system of equations. The Newton method is used in molecular dynamic simulation to solve such con- Paula Grajdeanu strained problems. But, this process is computationally ex- Mathematical Biosciences Institute pensive since Newton method is required to calculate Hes- [email protected] sian matrix every step. Alternatively, the penalty function method is easy to implement and costs less than a Lagrange multiplier method, which requires the solution of a nonlin- PP1 ear system of equations in every step. Here we propose Simulating Cell Internal Structure Using Delaunay a Quasi-Newton method for constrained dynamics. The Technique simulation with the Quasi-Newton Method can be done by using approximation to Hessian matrix. The Quasi New- We develop an agent-based model for a cell where the ton method is easily implement on Newton method and cell is modeled as a set of discrete interacting particles. costs less than a Lagrange multiplier method, which re- We use a Delaunay triangulation [Meyer-Hermann, M.: quires the solution of a nonlinear system of equations in Delaunay-Object-Dynamics: Cell mechanics with a 3D ki- every step. We implemented the Quasi Newton method netic and dynamic weighted Delaunay-triangulation. Curr. in CHARMM and applied it to protein Bovine Pancreatic Top. Dev. Biol., 81 (2007) 373-399] to obtain the neighbor- Trypsin Inhibitor (BPTI). We compared the simulation re- hood relations between the sub-cellular particles, and a set sults with Verlet, Shake and Penalty function. We describe of interaction potentials to differentiate the types of parti- the Quasi Newton method and its implementation details, cles and define their role inside the cell. We believe that discuss our results and the issues to be resolved, show the the model can help us to better understand the relations LS08 Abstracts 93

advantages as well as the disadvantages of the method, and Univeristy of North Carolina at Chapel Hill demonstrate the potential of using the method for general [email protected] constrained molecular dynamics and energy minimization. Ajith Gunaratne PP1 FloridaA&MUniversity Be Still My Beating Heart: Cardiovascular Model- Department of Mathematics ing of Mammalian Hibernation [email protected] Hibernating mammals are able to survive extreme physio- Zhijun Wu logical changes as their core body temperature falls to as Iowa State University low as -3 C. The heart rate can fall from 300 beats per Dept of Math minute to as low as 2 bpm, and respiration and oxygen [email protected] consumption plummet as well. A simple model of the cardiovascular system of a typical mammalian hibernator will be presented. PP1 Network Activity Coupled By Gap Junctions Marshall Hampton University of Minnesota, Duluth We study the network activity of excitable cells coupled by [email protected] gap junctions. We investigate how the voltage response of two gap junctionally coupled cables depends on cable diameter. Specifically, we show that there exists an optimal PP1 diameter for which the signal can be transmitted most ef- Simulation of the Reaction-Diffusion Master Equa- fectively and the propagation time also can be minimized tion on Unstructured Meshes in Molecular Cell Bi- at the optimal diameter. We find that diameter regulation ology allows neurons to selectively transmit action potentials in gap junctionally connected networks. We generate trajectories of the reaction-diffusion master equation on a triangulated, unstructured mesh. The dis- Joon Ha crete, stochastic treatment is very computationally de- Department of mathematical sciences, manding, but necessary when the number of molecules is New Jersey Institute of Technology small, as is the case in many models from molecular cell [email protected] biology. Using ideas from a hybrid method for the chemical master equation, we can simulate some species deter- Amitabha Bose ministically in some regions in space, and stochastically in New Jersey Inst of Technology others, reducing the work substantially in two biological Department of Mathematical Sciences examples. [email protected] Andreas Hellander Division of Scientific Computing Farzan Nadim Department of Information Technology, Uppsala NJIT & Rutgers University University [email protected] [email protected]

Jorge Golowasch Per L¨otstedt, Lars Ferm, Stefan Engblom Dept of math sciences at NJIT and Division of Scientiﬁc Computing Dept of biological sciences at Rutgers-Newark Uppsala University [email protected] [email protected], [email protected], [email protected]

PP1 PP1 Structural Dynamics of Tree Trunks and the Eﬀects Locally Dispersing Populations on Dynamic Spa- of Carbon Dioxide Levels on the Natural Frequency tiotemporally Structured Heterogeneous Land- of Trees. scapes

Studies suggest plants often uproot or snap when forced at Previous models have shown two opposite results: static their natural frequencies by winds or waves because me- spatially clustered habitat heterogeneity increases equi- chanical stresses along the root-shoot system are greatest librium density of locally-dispersing populations, while during resonance. CO2 exposure may alter plants’ natural spatially correlated disturbances simultaneously affecting frequencies. Nonlinear changes in elastic modulus of plant many contiguous sites reduces equilibrium density. Here, stems are investigated. A forced Duffing oscillator model both effects are combined within one model on dynamic is used to study effects of nonlinear stiffness on resonant landscapes with specified spatial and temporal autocorre- behavior. Model results are compared to experimental me- lations, via large-scale disturbances leaving sites temporar- chanical measurements at various levels of CO2 exposure. ily unsuitable. Depending on relative rates of landscape versus population dynamics, increasing the spatial scale of disturbances may help or hinder the population. Laura Miller University of North Carolina David E. Hiebeler Department of Mathematics Dept of Mathematics and Statistics [email protected] University of Maine [email protected] Christina L. Hamlet 94 LS08 Abstracts

Jennifer Houle Boston University Dept of Mathematics and Statistics, and Honors College Department of Mathematics University of Maine [email protected] [email protected] PP1 PP1 Modeling the Flow Cytometric Measurement of the A Phase Space Approximation Method for the Ef- Coverage of Bacteria ficient Solution of Cardiac Membrane Models Surface coverage by host proteins is the beach head of The reaction-diffusion system characterizing cardiac elec- host defense against invasive bacteria. We propose a low- trical behavior requires the solution of a large number dimensional ODE model to characterize the dynamics of of nonlinear equations describing cell membrane behav- surface opsonization of the bacteria. The extent of cover- ior. We have developed a method to reduce the compu- age by fluorescently labeled proteins can be measured using tational effort. Our method dynamically enumerates the a flow cytometer, providing a distribution of size and fluo- phase space of the membrane equations and uses the re- rescence values. We present efforts with model identifica- vealed geometry to reduce the total number of computation and parameter estimation in the presence of Gaussian tions. In this presentation we will describe the method and noise in the observations. show its application to problems in cardiac electrophysiol- ogy. Lisa A. Kalenkiewicz, John G. Younger University of Michigan Jagir R. Hussan [email protected], [email protected] Auckland Bioengineering Institute, University of Auckland David M. Bortz [email protected] University of Colorado-Boulder [email protected] Mark Trew Auckland Bioengineering Institute University of Auckland PP1 [email protected] IMAG: Multi-Scale Analysis of Cellular Force Transmission and Biochemical Activation Peter Hunter University of Auckland Mechanical force plays an important role in numerous cel- New Zealand lular processes such as migration, adhesion and apopto- [email protected] sis. The dynamic framework of the cytoskeleton provides a cell with structural integrity and transmits the physical cues to the targets that respond to the external force. PP1 We have studied the structure and mechanical properties NMDA Receptor Antagonist Induced Rhythm of the cytoskeleton using computational models and ex- Switches in the Entorhinal Cortex perimental measurements. In the computational studies, we have developed a rigorous three-dimensional computa- The medial entorhinal cortex participates in theta (4- tional model of the cytoskeleton based on Brownian dy- 12Hz), beta (15-25Hz), and gamma (30-80Hz) frequency namics and used it to investigate cytoskeletal morphology rhythms. Recent findings from slice preparations have and rheology. Through a parametric study, we found that shown that NMDAR antagonists cause a decrease in the morphological properties of the cytoskeleton are effec- gamma activity in the presence of kainate and an increase tively captured by a relatively small number of parame- in gamma in its absence. We investigate the mechanisms ters. The developed model demonstrates how the actin for these results and interactions of the different frequency cytoskeleton responds to external force exhibiting power- bands with a model consisting of populations of pyramidal law rheology, strain-stiffening, and stress relaxation. In cells, fast-spiking interneurons, theta-producing interneu- the experiments, interactions between actin filaments and rons, and stellate cells. actin binding proteins (ABPs) were probed at both molecular and network scales using optical tweezers. Unbind- Jozsi Z. Jalics ing and unfolding force of ABPs were measured by pulling Department of Mathematics and Statistics one of actin filaments in the ABP/F-actin complex. Me- Youngstown State Univeristy chanical deformation of an actin network cross-linked with [email protected] ABPs under external shear was visualized by confocal microscopy and the network elasticity was characterized by Tilman Kispersky both passive and active methods using optical tweezers. Program in Neuroscience and Dept. of Biomedical We have also developed a two-dimensional coarse-grained Engineering membrane/cortex model with dynamic protein associations Boston University for human erythrocytes or other cell types to elucidate the [email protected] roles of shear stress, specific chemical agents, and thermal fluctuations in cortex remodeling. The human erythrocyte Mark Cunningham, Steve Middleton, Miles Whittington demonstrates extraordinary ability to undergo reversible University of Newcastle large deformations and fluidity. Such mechanical responses [email protected], cannot be consistently rationalized on the basis of fixed [email protected], connectivity of the spectrin network tethered to the phos- [email protected] pholipid membrane. In this study, we have demonstrated a clear solid-to-fluid transition depending on the metabolic energy influx. The solid networks plastic deformation also Nancy J. Kopell manifests creep and yield regimes depending on the strain LS08 Abstracts 95

rate. This cytoskeletal dynamics model offers a means at the leading edge. to resolve long-standing questions regarding the reference state used in red blood cell elasticity theory for determining Zachary Kilpatrick the equilibrium shape and deformation response. Department of Mathematics University of Utah Roger D. Kamm [email protected] Depts Mechanical Engineering and Biological Engineering Mass Inst of Tech Paul Bressloff [email protected] University of Utah [email protected] PP1 Stefanos Folias A Low-Dimensional, Morphologically Accurate, Boston University Quasi-Active Integrate-and-Fire Model [email protected] Realistic compartmental models of active neurons yield nonlinear dynamical systems with thousands of equations. PP1 We linearize such systems and build their balanced trunca- tions where B permits synaptic input into each compart- IMAG: A Multi-Scale Approach for Understanding ment and C observes only the soma potential. Using true Antigen Presentation in Immunity morphologies with a broad class of synaptic inputs, we find The immune system and the process of antigen presenta- that the full quasi-active somatic dynamics can be approx- tion in particular encompass events that occur at multiple imated to nearly 10 digits by reduced systems of dimension length and time scales. Despite a wealth of information two orders of magnitude smaller. in the biological literature regarding each of these scales, Anthony Kellems, Derrick Roos no single representation synthesizing this information into Rice University a model of the overall immune response as it depends on [email protected], [email protected] antigen presentation is available. In the work supported by this grant, we outline an approach for integrating information over relevant biological and temporal scales to Nan Xiao generate such a representation for MHC class II-mediated Stanford University antigen presentation. In addition, we begin to address how [email protected] such models can be used to answer questions about mechanisms of infection and new strategies for treatment and Steven Cox vaccines. Rice University [email protected] Denise E. Kirschner Univ of Michigan Med School Dept of Micro/Immuno PP1 [email protected] Stable Identification of Lame Parameters in Linear Elasticity PP1 This talk will focus on the problem of identifying Lamé T Cell Differentiation and Aging parameters in linear elasticity. This inverse problem has found interesting applications in elasticity imaging (in lo- We report on the derivation and analysis of a model for cating cancerous tissues, and other abnormalities). The tracking the distribution of T cell populations as a func- main emphasis of the talk will be on a comparison of the tion of antigen experience gained through interactions with numerical efficiency of various methods that can be used dendritic cells in lymph nodes during the activation phase to solve the inverse elasticity problem. Adaptive finite el- of an immune response. This model is motivated by the ement methods will be used. heterogeneity of specific T cell lineages which have been observed from early stages in an immune response with Akhtar A. Khan different characteristics including the capacity to become Northern Michigan University short lived effector cells or memory cells. Linear reaction- [email protected] hyperbolic systems of partial differential equations in one space dimension arise in the model formulation similar to models developed for describing axonal transport in nerve PP1 cells. We derive a closed form approximate solution for an Traveling Pulses and Wave Propagation Failure in initial-boundary value problem of such a system. The ap- Inhomogeneous Neural Media proximate solution obtained is a translating solution of a heat equation. We use averaging and homogenization theory to study traveling pulses in an inhomogeneous neural network. Spa- Brynja Kohler tially periodic modulations of homogeneous synaptic con- Utah State University nections reduces the speed of the pulse. For large am- [email protected] plitude modulations, the pulse becomes a multibump solution, where individual bumps are nonpropagating and James P. Keener transient, and propagation corresponds to the appearance University of Utah (disappearance) of bumps at the leading (trailing) edge. [email protected] Wave propagation failure occurs when bumps cease to form 96 LS08 Abstracts

PP1 Repair Stochastic Optimization of the Transition Path- ways Between Protein Conformations A migrating cell is regulated by a complex network of signaling molecules that act on dynamic mechanical struc- Protein structures often reveal distinct conformational tures known as the cytoskeleton. Utilizing biological and states with different functional roles, but the connecting computational tools, we have examined in parallel the ac- pathways of conformational change have to be explored by tivity of signaling molecules with local changes in cytoskele- computational modeling. We use the trajectory swarm ap- ton dynamics in edge cells undergoing wound repair. By proach to compute the dynamics of protein conformations combining high-resolution speckle microscopy with data in discrete intermediate states. Based on these data we analysis programs that examine multivariate behavior, we perform computational interpolation between the states, have gained new insights into complex mechanical pro- and use Markov process machinery to optimize the overall cesses that govern cell motility. probability of the pathway. The resultant path is compared to the output of the string method for several sample sys- James Lim tems. The Scripps Research Institute [email protected] Dmitry A. Kondrashov University of Chicago [email protected] PP1 IMAG: Multi-Scale Simulation of Gas Flow Distri- bution in the Human Lung PP1 Modeling β Amyloid Clearance in Alzheimers Dis- This poster describes the methodologies and technologies ease developed for multi-scale simulations of subject-specific pulmonary air flow. Variation in individual airway geom- Alzheimers disease (AD) is one of the most prevalent neu- etry makes subject-specific models essential for the study rodegenerative disorders affecting elderly populations to- of pulmonary air flow and drug delivery. Recent evidence day. The increased concentration of amyloid β protein is also suggests that early exposure to environmental pollu- thought to be an important contributor to AD pathogen- tants has chronic, adverse effects on lung development in esis. A mathematical model of amyloid β production and children from the age of 10 to 18 years. Thus, the capability clearance both by intracellular and extracellular mecha- of predicting air flow and particle deposition in the subject- nisms has been developed to study what clearance mecha- specific human lungs is essential in understanding the cor- nisms and rate constants may play a role in the pathogen- relation between structure and function, and for assessing esis of AD and the onset of plaque formation. individual differences in vulnerability to airborne pollu- tants. This project aims to develop a comprehensive com- Christina R. Kyrtsos, Sameer Shah putational fluid dynamics (CFD) model for pulmonary flow Dept. of Bioengineering that utilizes subject-specific airway geometries, spans spa- University of Maryland tial scales from the largest bronchial airways to alveolar sac, [email protected], [email protected] and employs a Computed Tomography (CT) data-driven, multistage approach to provide accurate predictions of regional ventilation and gas transport through the entire PP1 moving airway tree. This effort brings together expertise Global Bifurcations and the Appearance of a One- in medical imaging, geometric modeling, high-performance Dimensional Spiral Wave in Excitable Media computing, and physiology and medicine. The potential applications of the model include optimizing pharmaceu- Excitable media can support a “fast” stable traveling pulse, tical aerosol drug delivery, advancing xenon or helium en- which appears through a saddle-node bifurcation accom- hanced CT/MRI imaging, and predicting subject-specific panied by a “slow” unstable traveling pulse. Furthermore, regional ventilation for diagnosis of patterns related to the uniform rest state is stable. We provide numerical evi- pathologic changes in airway geometry and parenchyma. dence that, near the saddle-node bifurcation, the threshold between the rest state and fast pulse consists of the stable Ching-Long Lin manifold of the slow pulse. However, further away from the University of Iowa saddle-node bifurcation, the threshold involves an unstable [email protected] periodic solution sometimes referred to as a 1D spiral wave. PP1 Timothy Lewis Integrating Factor Methods for High Spatial Di- University of California, Davis mensions [email protected] The dominant cost for integration factor (IF) or expo- Eric N. Cytrynbaum nential time differencing (ETD) methods is the repeated University of British Columbia vector-matrix multiplications involving exponentials of dis- Department of Mathematics cretization matrices of differential operators. Although the [email protected] standard discretization matrices usually are sparse, their exponentials are not, unless the discretization matrices are diagonal. For example, a two-dimensional system of PP1 N × N spatial points, the exponential matrix is of a size N 2 × N 2, and the cost of vector-matrix multiplication is of Deciphering Cell Migration Mechanics: Novel Ap- 4 proaches to Understanding Chemical Signaling and order N . The storage and computations associated with Morphological Responses During Epithelial Wound such vector-matrix multiplication are usually prohibitive even for moderate size of N. In this paper, we introduce LS08 Abstracts 97

a compact representation of the discretization of the dif- protein kinase cascade. ferential operators for the IF and ETD methods in both two and three dimensions. In the approach, both required Shev Macnamara memory and computational cost are magnitudely reduced The Institute for Molecular Biosciences for both IF and ETD methods. For the case of the two- The University Of Queensland dimensional system, the required storage is reduced to an [email protected] order of N × N, and the computational cost is reduced to an order of N 3. The improvement on three-dimensional Alberto Bersani systems is even more significant. In this paper, we analyze Department of MAthematical Methods and Models and apply this technique to a class of semi-implicit inte- La Sapienza University gration factor method recently developed for stiff reaction- [email protected] diffusion equations. Direct simulations on test equations along with applications to a morphogen system in two di- Kevin Burrage mensions and an intra-cellular signaling system in three COMLAB, Oxford University, and dimensions demonstrate an excellent efficiency of the new Institute for Molecular Bioscience, University of approach. Queensland [email protected] Xinfeng Liu University of California at Irvine [email protected] Roger Sidje University of Minnesota [email protected], Qing Nie Department of Mathematics University of California, Irvine PP1 [email protected] Estimating Underlying Biological Dynamics From Sequence Data Using Graph Theoretic Measures of Fred Wan Clonal Trees University of California, Irvine [email protected] Mutating birth-death processes (MBDP) are a fundamental component of biology at many different time scales, Yongtao Zhang ranging from evolution of species, through epidemiological University of Notre Dame evolution of bacteria and other pathogens, to within-host [email protected] mutation of viruses such as HIV. A special case is somatic hypermutation of B cells, which is a main focus of this paper. However, the methods that we develop can be ap- PP1 plied to many MBDP. Despite the significance of mutating Spike Train Statistics and Dynamics with Synaptic birth-death processes, methods to estimate the underly- Input from Any Renewal Process ing parameters from available data are lacking in many cases. We consider systems with constant mutation rate In the population density approach to neural network mod- over time and between populations and with discrete gener- eling, a common simplifying assumption is that the arrival ations. The basic biological parameters of the MBDP that times of input events are governed by a Poisson process. we study are the mutation rate, the frequency of lethal mu- This model does not capture temporal correlations in the tations, and the rate and type of selection. We use graph input. We formally extend these methods to allow in- theory measures (further denoted as tree shapes) on genetic puts from any temporally modulating renewal process. We trees to estimates these parameters. Individual trees typi- study how the regularity of the inputs affect the output cally cannot provide information on the underlying dynam- statistics (i.e., spike rate, interspike interval distribution, ics, because of the significant under-sampling. However, by autocorrelation, and coefficient of variation). This is work looking at the collective properties of a set of trees from with Dan Tranchina. the same generative process, maximum likelihood methods can be used to compute the most probable set of biological Cheng Ly parameters. The ML estimates are based on a compar- University of Pittsburgh ison between the expected joint distribution of multiple Department of Mathematics tree shapes based one numerical simulations or analytical [email protected] formulae, and the observed tree shapes. We use synthetic data sets to measure the precision of the maximum likelihood estimates for different numbers of trees, and show PP1 that our methods work even with realistic amounts of ex- The Total Quasi-Steady-State Approximation for perimental data. the Mitogen-Activated-Protein Kinase Cascade Reuma Magori-Cohen The total quasi-steady-state approximation (tQSSA) for Bar Ilan University, Israel Michaelis-Menten enzyme kinetics involves a simple change [email protected] of variable in the conventional QSSA and has the benefit of being valid over a wider parameter range, and more compli- Steven Kleinstein cated networks of coupled enzymatic reactions have been Yale University School of Medicine treated (Ciliberto et al., PLoS Computational Biology, [email protected] 2007). We generalize the tQSSA to discrete and stochastic models of biochemical kinetics, via the chemical master equation, with application to the mitogen-activated- Yoram Louzoun Department of mathematics Bar Ilan University 98 LS08 Abstracts

[email protected] [email protected]

Christina Bjerk´en PP1 Materials Sceince Transitions Between Bursting and Spiking in Con- Malmo University ditional Respiratory Pacemaker Networks With [email protected] Excitatory Synaptic Coupling

In mammals, the respiratory rhythm is maintained under a Anders Heyden wide range of conditions, depending on age, metabolic de- School of Technology mand, and environmental factors. This rhythm is driven Malmo University by a pacemaker system in the brainstem. Hence, a cen- [email protected] tral question is, how does this pacemaker system generate such robust, adaptable rhythms? In this work, we focus on Per St˚ahle a component of the respiratory pacemaker system called Materials Sceince the pre-Botzinger complex (pBC), a collection of neurons Malmo University that can exhibit bursts of activity under appropriate con- [email protected] ditions and that are coupled with synaptic excitation. We derive a map representation for small model networks of synaptically coupled pBC cells and use this to determine PP1 conditions on parameters for the transition between spiking Regression and Path Analysis for Wheat Charac- and bursting activity in the network and for the instability terizes in Dry Land Condition of spike synchrony. These results help show how synaptic coupling promotes bursting in a network of conditional In this study , effect of different density ( 250, 300, 400 oscillators such as may be relevant in driving respiration. and 450 seed per m2 and 3 row space : 15 ,25 ,40 cm ) of wheat ( Kohdasht cultivar) on some morphological, physi- Evandro Manica ological and biochemical properties in dry land farming by University of Pittsburgh use regression and path analysis evaluated. The experi- Department of Mathematics ment was arranged as randomized complete block design. [email protected] The results of path analysis and regression showed leaf area, stem length , seed per spike , protein accumulation Georgi S. Medvedev , water-soluble carbohydrates were effected and decreased Drexel University by increase in density. Multiple regression and path anal- Department of Mathematics ysis indicated that maximum yield showed in 400 seed per [email protected] m2 . The coefficient of correlation between harvest index and density was negative and significant and correlation between root and shoot dry weight was positive. Therefore Jonathan E. Rubin on basis of this data and compare with normal condition we University of Pittsburgh can conclude this cultivar in dry land farming is sensitive Department of Mathematics cultivar [email protected] Omid Massoudifar Agriculture eng. and adviser PP1 [email protected] A Combined Model for Biofilm Development and Biocorrosion PP1 We propose a combined model investigating the interplay IMAG: Multi-Scale Modeling of the Mouse Heart: between a growing biofilm on a metallic surface and en- From Genotype to Phenotype vironmental suported stress corrosion. The biofilm model incorporates both substrate diffusion, bacteria metabolism The goal of this project is to develop mechanistic multi- and biofilm development, making it possible to estimate scale models that can predict the electromechanical func- the pH at the metallic surface. The biocorrosion model is tion of the failing heart in genetically engineered mouse based on strain driven dissolution. The final model iterates models with defects in genes responsible for the regulation between biofilm development that changes the pH at the of cardiac contraction. We have studied several different surface and biocorrosion that changes the geometry of the mouse models and are currently focusing on mice harbor- substratum. ing mutations in MLC2v which render the regulatory light chain of myosin non-phosphorylatable. The multi-scale Alma Masic models span the following scales protein states in the regu- Applied Mathematics latory unit, regulatory network, whole cell, multi-cellular, Malmo University tissue, whole organ, and circulatory system. This poster [email protected] will show new results especially in relation to: Markov model of the regulation of thin filament activation and the Ulf Heijman role of cooperative interactions between adjacent regula- Materials Sceince tory units; Whole cell systems models of the myocyte ex- Malmo University citation contraction coupling; Microstructural modeling of [email protected] murine ventricular myocardium fiber and sheet architecture; Whole organ continuum modeling of ventricular elec- Niels Overgaard tromechanics and the influence of regional heterogeneities Applied Mathematics in protein expression. Much of this work uses the multi- Malmo University scale modeling package Continuity, developed with support LS08 Abstracts 99

of a MSM grant from NSF and the National Biomedical ral structural transitions. Computation Resource, an NIH P41 grant. Yinglong Miao, Peter Ortoleva Andrew D. McCulloch Indiana University Department of Bioengineering [email protected], [email protected] University of California San Diego [email protected] PP1 Stuart Campbell Equilibrium Configurations for a Territorial Model UCSD Bioengineering [email protected] We consider a territorial model based on Voronoi tessella- tions. For rectangular domains and for small population sizes, we show that there can be distinct coexisting sta- Roy Kerckhoffs ble equilibrium configurations, including the possibility of UCSD stable equilibria that are not related by symmetry. By Department of Bioengineering treating the aspect ratio of the rectangle as a bifurcation [email protected] parameter, we numerically explore how stable and unstable equilibrium configurations are related to each other. Anushka Michailova Department of Bioengineering Jeff Moehlis University of California San Diego Dept. of Mechanical Engineering [email protected] University of California – Santa Barbara [email protected]

PP1 Ronald Votel Quantitative Inference of Cellular Parameters from Dept Aeronautics & Astronautics Microfluidic Cell Culture Systems Stanford University [email protected] Measurements in microfluidic cell culture systems can yield quantitative information on cellular biophysical parameters in a more physiological environment. We demonstrate the David A. Barton application of a mathematical nutrient transport model in University of Bristol, U.K. inferring cellular oxygen uptake rates from the measure- [email protected] ments of oxygen concentrations in an oxygen permeable poly(dimethylsiloxane) micro-bioreactor. Our results are PP1 significant for the development of novel assays to quantitatively characterize cell response, and for the design, and New Relationships Between the Parameters of Non optimization of efficient in-vitro systems for tissue engi- Linear Dynamics Methods and Their Application neering. to the Analysis of Physiological Time Series. Khamir Mehta Power spectra, detrended fluctuation analysis and Higuchis Department of Chemical Engineering fractal dimension are some non linear dynamics method- University of Michigan ologies to analyze physiological time series. There are rela- [email protected] tionships between the parameters of these techniques. We test here the validity of these relationships analyzing thousands of time series we previously generated with certain Geeta Mehta, Shuichi Takayama spectral exponent, we find the validity intervals and we Department of Biomedical Engineering propose more general relationships. We apply our results [email protected], [email protected] to analyze heartbeat intervals and other physiological time series. Jennifer Linderman Department of Biomedical Engineering Alejandro Muñoz-Diosdado Department of Chemical Engineering Mathematics Deparment, Unidad Profesional [email protected] Interdisciplinaria de Biotecnologia, IPN, MEXICO [email protected] PP1 All-Atom Multiscale Analysis (ama) Theory and Gonzalo Gálvez-Coyt Application to Virology Mathematics Department, UPIBI-IPN, MEXICO [email protected] Viruses and other bionanosystems undergo structural processes across multiple time and length scales. We introduce order parameters generated with orthogonal polynomials PP1 to capture their slowly-varying nanoscale dynamics and Noise-Driven Oscillation Regularity with Multi- derive a stochastic (Fokker-Planck or Smoluchowski) equa- ple Timescale Adaptation: Insights from the Pre- tion for the order parameters through a multiscale analysis Bötzinger Complex of the N-atom Liouville equation. The AMA theory justi- fies a Molecular Dynamics/Order Parameter eXtrapolation We investigate oscillation regularity of a noise-driven ex- (MD/OPX) approach for simulating large bionanosystems. citable system with a slow after–hyperpolarizing adapta- It greatly accelerates MD code and is demonstrated on vi- tion current (AHP) comprised of multiple exponential relaxation timescales. We show that for sufficiently separated slow and fast AHP timescales (biphasic decay) there 100 LS08 Abstracts

is a peak in oscillation irregularity (maximal incoherence) plexes depends linearly on the concentration of upstream for intermediate input currents I, with relatively coherent products. The model also predicts that receptor dimeriza- oscillations occurring for small and large currents. An ana- tion is not required for steroid gene regulation and suggests lytic formulation of the system as a stochastic escape prob- that steps both before and after the concentrating-limiting lem establishes that the underlying mechanism is distinct step are crucial in regulating the ultimate amount of gene from standard forms of coherence resonance. Our results expression. Applying the model to the cofactor ubiquitin- are used to explain recent data concerning variations in the conjugating enzyme 9 (Ubc9) suggests that at least two oscillation regularity of the Pre B¨otzinger Complex, which catalytic steps are necessary to explain the ability of Ubc9 is a population of neurons responsible for generating the to modulate gene expression. mammalian inspiratory breathing rhythm. Karen Ong, S. Stoney Simons William H. Nesse NIDDK/NIH University of Utah [email protected], [email protected] [email protected] Carson C. Chow Christopher Dell Negro Laboratory for Biological Modeling College of William and Mary NIDDK, NIH [email protected] [email protected]

Paul C. Bressloﬀ University of Utah PP1 Department of Mathematics IMAG: Bifurcation and Self-Organized Cellular bressloﬀ@math.utah.edu Structure and Dynamics: Intercellular Genomics of Subsurface Microbial Colonies

PP1 Key steps in the bacterial life cycle are modeled using Exact Solutions in Population Dynamics: Logistic complementary approaches. A Langevin model is used to Equation with Periodic Harvesting and a Model discover the forces for chromosome segregation following from Epidemiology replication. The dynamics of E. Coli chromosome segregation is simulated with an energy-driven string model. We transform a logistic equation with periodic harvesting The results demonstrate the possibility of self-organized into a classic Mathieu equation. The latter is known to chromosome segregation that does not involve cytoskele- have exact solutions (eigenfunctions) for certain values of tal guidance or an advanced apparatus in E. Coli. A parameters. We give explicit expressions for correspond- 3-D reaction-diffusion model is used to uncover dynami- ing solutions of the original problem in terms of special cal attractors accompanying cell division. Simulated nor- functions. We also introduce a new version of the classic mal and abnormal patterns of intracellular Min protein Taylor method for nonlinear, non-polynomial ODEs and distribution and consequent cell division irregularities are demonstrate its application to a Kermack McKendric epi- predicted. The model accounts for Min protein adsorp- demic model. Possible applications of the classic methods tion/desorption at the membrane, reaction and transport to other population dynamics models will be discussed. along the surface and in the interior of E. Coli. A novel reaction network, involving the role of Min protein dimers Lydia S. Novozhilova, Matthew Buchta and other complexes, is introduced and cast as chemical Western Connecticut State University reactions and associated rate laws. A third model coupling [email protected], [email protected] metabolic reactions and the membrane potential is used to predict the properties of bacterial fuel cells and to serve as a computer-aided tool for optimizing current output. PP1 Bifurcation theory is used to understand mechanisms of A General Model for Steroid Receptor-Mediated stem cell differentiation/proliferation and cancer using an Gene Expression extensive database of transcriptional, translational, post- translational processes in human cells, and concepts of self- Steroid hormones are important in regulating develop- organization and symmetry-breaking instability. Implica- ment, differentiation, and homeostasis in a concentration- tions for energy, environment and health will be discussed. dependent manner. Experimentally, it has been found that the gene activity (Amax) induced by steroids precisely fol- Peter J. Ortoleva lows a Michaelis-Menten (MM) curve. The classic explana- Indiana University tion was that receptor-steroid binding was the rate-limiting [email protected] step in steroid receptor-mediated gene expression. How- ever, this was refuted when it was found that various co- factors affect the sensitivity (EC50) as well as the Amax for PP1 the same receptor-steroid pair. Considering a mass-action Mitochondrial Calcium Trafficking: Sequestrator, model of transcription that involves the building of increas- Excitability, Oscillations, Waves and Untimely ingly large complexes of transcription factors and associ- Demise ated proteins, we derive the most general form of the equilibrium concentrations and mass-conservation equations In the study of calcium waves, the endoplasmic rheticulum that preserve MM kinetics between the steroid concentra- (ER) and its IP3 mediated calcium induced calcium release tion and final product. The form dictates that individual (CICR) mechanism has dominated the spotlight. However, reactions in the steps leading to transcription dissociate more than the ER can display this type of excitability. from downstream reactions, implying that complexes are The oft-times overlooked (in regards to signaling) mito- weakly bound and only exist transiently. The model pre- chondria also exhibit CICR via the permeability transition dicts that there exists a final rate- or concentration-limiting pore (PTP). We extend the well-known Fall-Keizer math- step beyond which the concentration of downstream com- ematical model for the calcium dynamics between the ER, LS08 Abstracts 101

the cytosol, and the mitochrondria to include dynamics University of Pittsburgh due to the PTP. Three key components come into play: [email protected] non-steadystate mitochrondrial proton concentration, the permeability transition pore, and a weak-acid term that is David Swigon essential for robust mitochondrial homeostasis. We show Department of Mathematics that, with these simple additions, the model exhibits mi- University of Pittsburgh tochondrial CICR (mCICR). Furthermore, we extend the [email protected] model from a single point to a spatially extended system and ﬁnd traveling waves of both calcium and potential, Bard Ermentrout as found by Ichas et al. in 1997. In addition, the model University of Pittsburgh also captures the pore “popping” event whereby the pore Department of Mathematics opens to and remains in a high-conductance state, which [email protected] ultimately leads to apoptosis (or oncosis) due to calcium cytotoxicity. Ted Ross, Franklin Toapanta Andrew M. Oster University of Pittsburgh Mathematical Biosciences Institute Department of Medicine The Ohio State University [email protected], [email protected] [email protected] Gilles Clermont Balbir Thomas, David Terman University of Pittsburgh Ohio State University Critical Care Medicine [email protected], [email protected] [email protected]

Christopher Fall PP1 Department of Anatomy and Cell Biology University of Illinois Bifurcation and Self-Organized Intra-Bacterial [email protected] Structure Key steps in the bacterial life cycle are modeled using com- PP1 plementary approaches. A Langevin model is used to discover the arriving forces for chromosome segregation fol- IMAG: All-atom Multiscale Analysis (AMA) The- lowing replication. A 3-D reaction-diffusion model is used ory and Application to Virology to uncover dynamical attractions accompanying the divid- Viruses and other bionanosystems undergo structural pro- ing of the division plane. A third model coupling metabolic cesses across multiple time and length scales. We introduce reactions and the membrane potential is used to predict order parameters generated with orthogonal polynomials the properties of bacterial fuel cells and to serve as a to capture their slowly-varying nanoscale dynamics and computer-aided tool for optimizing current output. Bifur- derive a stochastic (Fokker-Planck or Smoluchowski) equa- cation theory is used to understand mechanism of stem cell tion for the order parameters through a multiscale analysis differentiation/proliferation and cancer using an extensive of the N-atom Liouville equation. The AMA theory justi- database of transcriptional, translation, post-translational fies a Molecular Dynamics/Order Parameter eXtrapolation processes in human cells2, and concepts of self-organization (MD/OPX) approach for simulating large bionanosystems. and symmetry-breaking instability. It greatly accelerates MD code and is demonstrated on vi- Kun Qu, Peter J. Ortoleva ral structural transitions Indiana University Stephen Pankavich [email protected], [email protected] Department of Mathematics Indiana University PP1 [email protected] A Coalescent Theory Analysis of the Population Structure Statistic Fst Yinglong Miao, Zeina Shreif, Peter J. Ortoleva Indiana University Populations are often divided into subpopulations. Fst is [email protected], [email protected], a statistic used to experimentally test for population sub- [email protected] division. We consider a stochastic model of evolution for subdivided populations. We analyze Fst under different scaling limits for parameters of this model. We show that PP1 the distribution of Fst depends on mutation rate. Our re- Immune Response to Influenza A sults are the first to characterize the distribution of Fst and demonstrate its dependence on mutation rate. We use a In mammals, Influenza A virus first triggers innate immu- coalescent approach to derive our results. nity and then adaptive immunity. This project seeks to model the immune response, and identify methods of pre- Sivan Rottenstreich venting lung failure and improving recovery. The model ex- Georgetown University pands upon existing models of adaptive immune response, [email protected] adding an innate immune response; it is then calibrated to a greatly expanded data set. Mathematical techniques explore solutions to the inverse problem and address un- PP1 certainties in data in a fully stochastic framework. Nasal Airflow Distribution in Human Subjects

Ian Price Diﬀerences in nasal anatomy among human subjects may 102 LS08 Abstracts

cause significant differences in respiratory airflow patterns time-lapse experiments. and subsequent dosimetry of inhaled gases and particles in the respiratory tract. This study used computational Matthew J. Simpson fluid dynamics (CFD) to study inter-individual differences Department of Mathematics and Statistics in nasal airflow. Steady-state inspiratory laminar airflow at The University of Melbourne 15 L/min was calculated using commercial CFD software. [email protected] Streamline patterns, velocity and helicity were compared. Kerry A. Landman Rebecca Segal Department of Mathematics amd Statistics Virginia Commonwealth University University of Melbourne Department of Mathematics and Applied Mathematics [email protected] [email protected] Barry Hughes PP1 Department of Mathematics and Statistics The University of Melbourne Modelling Isolation Strategy for Controlling Tu- [email protected] berculosis

In the aim to reduce the incidence of the tuberculosis, we PP1 develop a mathematical model incorporating isolation of smear positive pulmonary tuberculosis individuals to ex- On the Population Dynamics Problem With Child plore the potential of such intervention to control tubercu- Care losis on global scale. The dynamic of the model is governed Many species of animals produce a small number of off- by ordinary differential equations; we therefore present the springs and take care of them. This phenomenon is natu- analysis of the disease free equilibrium and the endemic ral for many species of mammals and birds and forms the equilibrium and give conditions for local and global stabil- main difference between the behavior of a population tak- ity of these points. ing child care and that of a population without maternal Schehrazad S. Selmane (or parental) duties. Mammals and birds feed, warm, and University of Sciences and Technology of algiers defend their young offsprings from enemies. If one of these [email protected] native duties is not realized, young offsprings die, and the population vanishes. For many species of mammals only females take care of their young offsprings. Some species of PP1 mammals and birds care of their offsprings in couples. In Epidemics on Adaptive Networks: The Effects of last years, to describe the population dynamics with child Seasonal Forcing care some models were proposed and examined [?],[?],[?]. The existence and uniqueness theorem, separable solutions, During an epidemic, individuals may modify their behav- and the asymptotic behavior of the solution with the initial ior to avoid exposure to the disease. We consider an SIRS distribution of the general type to a one-sex age-structured model in which the contact network rewires so that non- population dynamics model [?] will be discussed taking into infected individuals avoid contact with infectives. In the account a discrete set of offsprings, their care, and envi- absence of any periodic forcing, mean field bifurcation anal- ronmental pressure. All individuals have pre-reproductive, ysis reveals a homoclinic orbit. We include a seasonally reproductive and post-reproductive age intervals. Individ- varying spreading rate and explore the interaction between uals of pre-reproductive age are divided into young (under the intrinsic dynamics and the forcing in both mean field maternal care) and juvenile (who can live without maternal and the full stochastic network. care but cannot reproduce offsprings) groups. Individuals of reproductive age are divided into the single and taking Leah Shaw child care classes. The model consists of integro-partial dif- College of William and Mary ferential equations subject to conditions of integral type. Dept. of Applied Science The number of these equations depends on the biologically [email protected] possible maximal newborns number of the same generation produced by an individual. Both non-dispersing and mi- Ira B. Schwartz grating population cases will be considered an numerical Naval Research Laboratory results will be exhibited. Nonlinear Dynamical Systems Section [email protected] Vladas Skakauskas Vilnius University, Lithuania [email protected] PP1 Distinguishing Between Directed and Undirected PP1 Cell Motility Within An Invading Cell Population The Effect of Diffusion on Calcium Oscillations Cell invasion is central to several biological systems including developmental morphogenesis and disease progres- Ordinary differential equation models are widely used to sion. The details of whether cell motility is directed or study IP3-mediated calcium oscillations. There, a cell is undirected within the invasive population of cells can- taken as a well-mixed compartment, but experiments often not be determined using continuum models that focus on show spatial inhomogeneity in intracellular [Ca]. Using a population-level data. This is a major impediment lim- spatially extended model, we study how diffusion affects iting our ability to interpret experimental data. We over- calcium release. It lowers the [Ca] at a particular release come this difficulty using individual-level data and discrete site while increasing the concentration at neighboring sites. models. This approach can be used to interpret and design Varying the diffusion coefficient can significantly change LS08 Abstracts 103

the critical IP3-level for oscillation onset. Politecnico of Torino, Italy Department of Mathematics Nessy Tania [email protected] Department of Mathematics University of Utah [email protected] PP1 Optimal Control of the Keller-Segel Chemotaxis James P. Keener Model University of Utah [email protected] This talk proposes and analyzes an optimal control problem associated to the Keller-Segel chemotaxis model which describes the movement of an organism / group of cells to- PP1 ward or away from a chemical or sensory stimulus. The IMAG: DAPLDS: convective part of this convection-diffusion system is of A Dynamically Adaptive Protein-Ligand Docking mixed hyperbolic-elliptic type, which may cause severe in- System Based on Multi-Scale Modeling stabilities when solved by straightforward numerical methods. The optimal solution is obtained by the use of a The DAPLDS project, aims to build a computational en- gradient type algorithm, involving discontinuous Galerkin vironment to assist scientists in understanding the atomic methods and Runge-Kutta methods for the fully discrete details of protein-ligand interactions. High-throughput, optimality system. protein-ligand docking simulations are performed on a computational environment that deploys a large number of Catalin Trenchea volunteer computers (donated compute cycles) connected University of Pittsburgh to the Internet. The scales proposed in DAPLDS are not [email protected] the traditional scales currently used in the life sciences. We deal with computational rather than experimental multi- Yekaterina Epshteyn scales. Our multi-scale approach comprises three spanning Carnegie Mellon University scales (dimensions) of docking assumptions: protein-ligand [email protected] representation, solvent representation, and sampling strategy. Within a scale, different scale values require different Beatrice Riviere models and different algorithms to represent the models.In University of Pittsburgh such a scenario, the two most critical challenges in dealing Department of Mathematics with multiple scales computationally are: (1) the ability to [email protected] model biological systems with algorithms that dynamically adapt to the most appropriate value of each scale and (2) the ability to assure that the algorithms can, indeed, be PP1 executed in the required amount of time using large num- Frequency Response Functions for Cortical Micro- bers of distributed volunteer computing systems. The lat- circuits ter point refers to having the necessary computational resources (CPU cycles, memory, network, etc.). The nature Visual cortex contains groups of neurons that form excita- of these challenges requires collaboration among compu- tory and inhibitory feedforward and feedback circuits. It tational biophysicists, computational scientists, computer is now common to view these neurons as forming ”micro- scientists, and system architects. These challenges and our circuits” within the cortex. This study uses a model of main achievements are presented in this poster. the microcircuits of visual cortex that consists of a family of linear, non-autonomous ordinary differential equations. Michela Taufer Methods from control theory are then used to character- University of Delaware ize the frequency response of the circuit and each of its [email protected] components. Philip Ulinski PP1 The University of Chicago, Chicago Reduction Properties and Synchronization in Department of Organismal Biology and Anatomy Lotka-Volterra Systems with Adaptive Competi- [email protected] tion

A general N-species Lotka-Volterra system is considered PP1 for which, in absence of interactions, each species is gov- Cgmd Simulation Method for the Interaction Be- erned by a logistic equation. Interactions take place in the tween Influenza Ha-Fusion Peptides and a Lipid Bi- form of competition, which also includes adaptive abilities layer Membrane through a (short term) memory effect. As a consequence the dynamics of the model is governed by a system of NxN Fusion of viral enveloped and cellular membranes is a cru- nonlinear ordinary differential equations. The existence of cial step for any successful viral infections. We use a classes of invariant subspaces, related to symmetries, al- Coarse-Grained Molecular Dynamics (CGMD) simulation lows the introduction of reduced models, where N appears method to study the interaction between influenza hemag- as a parameter, which give full account of existence and glutinin(HA) fusion peptides and a phospholipid bilayer stability for the equilibria. Reduced models are found ef- membrane. With CGMD, we have been able to simulate fective also in describing time-dependent regimes, both in a relatively large piece of membrane for a sufficiently long the form of periodic oscillations and chaotic behavior and time period and with more than one peptide embedded with remarkable properties of synchronization. in the membrane, which is necessary for the detail understanding of the fusion process. We obtained the kinked- Claudio Tebaldi shaped conformation of the peptide with the kink at the 104 LS08 Abstracts

level of phosphate group, consistent with NMR study. The usual topographic distributions for receptors and associ- N-terminal segment of the peptide inserts more deeply into ated signaling molecules. For example, Heregulin leads to the membrane bilayer, compared to the C-terminal seg- dramatic clusters surrounded by PI 3-kinase. Other dock- ment. The presence of fusion peptides inside a membrane ing proteins, Shc and STAT5, respond differently to recep- may cause instability to the bilayer thickness. We also tor activation. Levels of Shc at the membrane increase present the effect of the peptide-membrane interaction on 2-5 fold with EGF while preassociated STAT5 becomes other important properties such as helix tilt angle, order strongly phosphorylated. These data suggest that the dis- parameters for one and multiple peptides. tinct topography of receptors and their docking partners modulates signaling activities. We are using several math- Naveen K. Vaidya ematical modeling approaches to evaluate these data and to Department of Mathematics and Statistics, York build predictive models of signal transduction during car- Universtity cinogenesis and response to therapy. We report on novel Toronto, Canada use of Markov Random Field modeling to simulate relative [email protected] locations of receptors and signaling molecules, revealing hidden states or associations. We also report on results Huaxiong Huang using an agent-based, stochastic model designed to simu- York University, Canada late receptor diffusion, clustering, dimerization and signal Department of Mathematics and Statistics propagation in a spatially realistic manner [email protected] Bridget Wilson Shu Takagi University of New Mexico School of Medicine Department of Mechanical Engineering, University of [email protected] Tokyo Tokyo, Japan PP1 [email protected] A Systematic Model of Bacterial Chemotaxis: from Signal Transduction to Cell Motility in Escherichia PP1 Coli Shape Transformations to Sickling in the Red Cell The movement of bacteria in response to environmental We intend to find a transformation that will take the bi- changes of specific metabolites and signaling molecules is concave shape of the red blood cell and map it into the called bacterial chemotaxis. Chemotaxis in Escherichia coli parabolic-type sickle cell shape. Red blood cells change (E. coli) is a best studied system. The authors will present their shapes due to reorganization of their hemoglobin and a systematic model of E. coli chemotaxis that can capture usually this shape change is not reversible in sickle cell many features of the system and reproduce a full range anemia. We would presume that such a shape change will of experimental data from signaling (high sensitivity, wide preserve volume and exhibit no tearing or stretching of the dynamic range, excitation, perfect adaptation, and robust- cell wall. This idea has been presented in the classic paper ness) to motor behavior and cellular motility. of Y.C.B. Fung and P. Tong concerning the sphering of the Xiangrong Xin normal red blood cell. Department of Biomedical Engineering & School of H. Westcott Vayo Mathematics University of Toledo University of Minnesota-Twin Cities [email protected] [email protected] David J. Odde PP1 University of Minnesota IMAG: Mapping and Modeling ErbB Receptor Department of Biomedical Engineering Membrane Topography [email protected]

Our goal is to understand the topographical regulation of Hans G. Othmer ErbB signaling in breast and endometrial cancers, where University of Minnesota amplification of ErbB1 (the EGFR) or ErbB2 genes is as- Department of Mathematics sociated with poor outcome. Specifically, we propose: 1) to [email protected] map the topography of ErbB receptors and their associated signaling molecules using innovative electron microscopy techniques; 2) to apply rigorous biochemical and statisti- PP1 cal analyses to establish quantities of signaling molecules, A Fluid-Structure Interaction Computation of Cel- their distributions and their relationships; and 3) to use lular Blebbing these spatial and quantitative data as a framework for multiscale simulations of the signaling process. In work that is Eukaryotic cells are composed of cytoplasm, a cytoskele- now in press, we report on first electron microscopy images ton and a plasma membrane. Blebs are protrusions of the mapping distributions of ErbB receptors on SKBR3 breast membrane formed when the membrane separates from the cancer cell membranes. We found the most abundant re- underlying actin filament network, and is pushed outward ceptor, ErbB2, is phosphorylated, clustered and active. Ki- by pressure-driven cytoplasm. We present a mathematical nase inhibitors ablate ErbB2 phosphorylation without dis- model to probe this phenomenon. This model includes the persing clusters. Modest coclustering of ErbB2 and EGFR, motion of the actin filaments and the membrane (modeled even after EGF treatment, suggests that both are predom- by elasticity equations), the cytoplasm (modeled by the inantly involved in homointeractions. This observation, unsteady Stokes equation), and the interactions of these in particular, suggests that previous mathematical models overestimate heterodimerzation. We also show some LS08 Abstracts 105

structures. sists of a number of observations that by themselves are relatively inaccurate, is reflected in the refinement of den- Jennifer J. Young sity functions through accumulated low-accuracy measure- University of North Carolina - Chapel Hill ments in the proposed theoretical framework. We outline [email protected] possible steps towards translating this hybrid approach to the bedside, to supplement todays evidence-based medicine Sorin M. Mitran with a quantitatively founded model-based medicine com- Dept. of Mathematics, Applied Math Prog. bining dynamical systems with statistical techniques, to University of North Carolina integrate mechanistic knowledge with patient-specific and [email protected] population-level information. Sven Zenker PP1 University of Pittsburgh From Inverse Problems in Mathematical Physiol- [email protected] ogy to Quantitative Differential Diagnoses Jonathan E. Rubin BACKGROUND : The improved capacity to acquire quan- University of Pittsburgh titative data in a clinical setting has generally failed to im- Department of Mathematics prove outcomes in acutely ill patients, suggesting a need [email protected] for advances in computer supported data interpretation and decision making. Mathematical models as quantita- Gilles Clermont tive descriptions of physiological mechanisms could help to University of Pittsburgh improve this situation by augmenting the interpretation of Critical Care Medicine quantitative, patient-specific information, and could even- [email protected] tually be used to improve therapy by predicting future de- velopements and effects of interventions. An obstacle to achieving this aim lies in the fact that realistic mathemat- PP1 ical models of pathophysiology are complex and nonlinear, Geometric and Analytic Analysis of the Role of the which may prevent the identification of unique parameters A-Current on the Transient and Long-Term Behav- and states of the model that best represent available data; ior of a Neuron Receiving Inhibitory Input that is, the inverse problem of parameter identificaton is usually ill posed, limiting the usefulness of classical param- The transient potassium (A-) current plays a critical role eter estimation techniques such as nonlinear least squares. in determining the post-inhibitory rebound activity phase METHODOLOGY/PRINCIPAL FINDINGS: Hypothesiz- of neurons receiving rhythmic inhibition. We use geometric ing that the non-uniqueness of the solution to the inverse dynamics to analyze how the A-current parameters deter- problem may in fact reflect useful information, we imple- mine the transient behavior of such a neuron. We then de- mented a simplified simulation of a common differential rive iterative equations to predict the long term behavior. diagnostic process (based on hypotension observed in an Our analysis shows that the interaction of the A-current acute care setting), using a combination of a mathematical and other intrinsic parameters, such as the h-current, can model of the cardiovascular system, a stochastic measure- lead to distinct periodic or chaotic solutions. Support: NSF ment model, and Bayesian inference techniques to quantify 0615168 (AB); NIH MH-60605 (FN). parameter and state uncertainty. We used Monte Carlo integration to generate prior densities for model parame- Yu Zhang ters and states, and we approximated the posterior densi- Department of Mathematical Sciences ties on a uniformly spaced grid. For subsequent inference New Jersey Institute of Technology steps, these were smoothed using standard kernel density [email protected] estimation techniques. The output of this procedure was a probability density function on the space of model pa- Amitabha Bose rameters and initial conditions for a particular simulated New Jersey Inst of Technology patient, based on prior population information together Department of Mathematical Sciences with patient-specific clinical observations. We show that [email protected] even from unimodal, uninformative priors, multi-modal posterior probability density functions arise naturally. The Farzan Nadim peaks of these densities correspond to clinically relevant Department of Mathematical Sciences differential diagnoses and can, in the simplified simula- New Jersey Institute of Technology tion setting, be constrained to a single diagnosis by assim- [email protected] ilating additional observations from dynamical interventions (e.g., fluid challenge). By modifying parameters of the stochastic measurement model, we also illustrate how several inaccurate observations, while essentially useless on their own, can cumulatively serve to discriminate between possible hypotheses about physiological state, represented by peaks in the posterior densities obtained. CON- CLUSIONS/SIGNIFICANCE: We conclude that the ill- posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. The discriminatory power of the physical examination performed by a physician, which con-