## Christine Heitsch : The Combinatorics of RNA Branching

- Mathematical Biology ( 304 Views )Understanding the folding of RNA sequences into three-dimensional structures is one of the fundamental challenges in molecular biology. For example, the branching of an RNA secondary structure is an important molecular characteristic yet difficult to predict correctly, especially for sequences on the scale of viral genomes. However, results from enumerative, probabilistic, analytic, and geometric combinatorics yield insights into RNA structure formation, and suggest new directions in viral capsid assembly.

## Rachel Howard : Monitoring the systemic immune response to cancer therapy

- Mathematical Biology ( 246 Views )Complex interactions occur between tumor and host immune system during cancer development and treatment, and a weak systemic immune response can be prognostic of poor patient outcomes. We strive to not only better understand the dynamic behavior of circulating immune cell populations before and during cancer therapy, but also to monitor these dynamic changes to facilitate real-time prediction of patient outcomes and potentially therapy adaptation. I will provide examples of both theoretical (mathematical) and data-driven (epidemiological) approaches to incorporating established systemic immune markers into clinical decision-making. First, coupling models of local tumor-immune dynamics and systemic T cell trafficking allows us to simulate the evolution of tumor and immune cell populations in anatomically distant sites following local therapy, in turn identifying the optimal treatment target for maximum reduction of global tumor burden. Second, improved understanding of how circulating immune markers vary both within and between individual patients can allow more accurate risk stratification at diagnosis, and personalized prediction of patient response to therapy. The importance of multi-disciplinary collaborations in making predictive and prognostic models clinically relevant will be discussed.

## Suncica Canic : Fluid-composite structure interaction and blood flow

- Mathematical Biology ( 210 Views )Fluid-structure interaction problems with composite structures arise in many applications. One example is the interaction between blood flow and arterial walls. Arterial walls are composed of several layers, each with different mechanical characteristics and thickness. No mathematical results exist so far that analyze existence of solutions to nonlinear, fluid-structure interaction problems in which the structure is composed of several layers. In this talk we will summarize the main difficulties in studying this class of problems, and present a computational scheme based on which a proof of the existence of a weak solution was obtained. Our results reveal a new physical regularizing mechanism in FSI problems: inertia of the thin fluid-structure interface with mass regularizes evolution of FSI solutions. Implications of our theoretical results on modeling the human cardiovascular system will be discussed. This is a joint work with Boris Muha (University of Zagreb, Croatia), Martina Bukac (U of Notre Dame, US) and Roland Glowinski (UH). Numerical results with vascular stents were obtained with S. Deparis and D. Forti (EPFL, Switzerland), and with A. Quaini (UH). Collaboration with medical doctors Dr. S. Little (Methodist Hospital Houston) and Dr. Z. Krajcer (Texas Heart Institute) is also acknowledged.

## John Bush : Biocapillarity

- Mathematical Biology ( 157 Views )We report the results of our integrated experimental and theoretical investigations of biological systems dominated by interfacial effects. Particular attention is given to elucidating natural strategies for water-repellency, walking on water, underwater breathing, and drinking.

## Steven Baer : Multiscale Modeling of Neural Subcircuits and Feedback Mechanisms in the Outer Plexiform Layer of the Retina

- Mathematical Biology ( 143 Views )Visual processing begins in the outer plexiform layer of the retina, where

bipolar, horizontal, and photoreceptor cells interact. In vertebrates, the

onset of dim backgrounds can enhance small spot flicker responses of

retinal horizontal cells. This flicker response is called background-

induced flicker enhancement. The underlying mechanism for the feedback

is unclear but competing hypotheses have been proposed. One is the GABA

hypothesis, which states that the inhibitory neurotransmitter GABA,

released from horizontal cells, mediates the feedback by blocking calcium

channels. Another is the ephaptic hypothesis, which contends that calcium

entry is regulated by changes in the electrical potential within the

intersynaptic space between cones and horizontal cells. In this study, a

continuum spine model of cone-horizontal cell synaptic circuitry is

formulated. The model captures two spatial scales - the scale of an

individual synapse and the scale of the receptive field involving hundreds

to thousands of synapses. We show that the ephaptic mechanism produces

reasonable qualitative agreement with the temporal dynamics exhibited by

flicker enhancement experiments. We find that although GABA produces

enhancement, this mechanism alone is insufficient to reproduce the

experimental results. We view this multiscale continuum approach as a

first step in formulating a multi-layer mathematical model of retinal

circuitry, which would include the other Â?brain nucleiÂ? within the retina:

the inner plexiform layer where bipolar, amacrine, interplexiform, and

ganglion cells interact.

## Rodica Curtu : Mixed-Mode Activity Patterns in Neuronal Networks with Lateral Inhibition

- Mathematical Biology ( 141 Views )Stimulus tuning in a reduced model for neural competition leads to

## Yuan Lou : Finding Evolutionarily Stable Strategies

- Mathematical Biology ( 126 Views )From habitat degradation and climate change to spatial spread of invasive species, dispersal plays a central role in determining how organisms cope with a changing environment. How should organisms disperse Â?optimallyÂ? in heterogeneous environments? I will discuss some recent development on the evolution of dispersal, focusing on evolutionarily stable strategies (ESS) for dispersal.

## Michael Siegel : Elastic capsules in viscous flow

- Mathematical Biology ( 125 Views )Elastic capsules occur in nature in the form of cells and vesicles and are manufactured for biomedical applications. They are widely modeled but there are few analytical results. In this talk, complex variable techniques are used to derive semi-analytic solutions for the steady-state response and time-dependent evolution of elastic capsules in 2D Stokes flow. The analysis is complemented by spectrally accurate numerical simulations of the time-dependent evolution. One motivation for this work is to provide analytical solutions to help validate the accuracy of numerical methods for elastic membranes in flow. A second motivation is to clarify the steady response of capsules in some canonical flows. Finally, we investigate the formation of finite-time cusp singularities, of which there are only a few examples in interfacial Stokes flow, and where none involve elastic interfaces. This is joint work with Michael Booty and Michael Higley.

## Steve Vogel : Lifes Launchers: The Scaling of Bioballistic Projectiles

- Mathematical Biology ( 117 Views )Biological projectiles range from a 10-micrometer spore to a 1-meter leaping mammal. Pre-launch accelerations scale inversely with length, with that of the smallest projectile approaching a million times gravity. These projectiles follow Borelli's rule, that all jumpers should jump to the same height. Nonetheless, his rationale is wrong on at least two accounts. For one thing, it presumes a muscular engine operating with no energy storage, often far from the case. For another, it ignores drag, critical for small projectiles, which operate in an overwhelmingly drag-dominated rather than gravity- dominated domain and whose optimal trajectories look decidedly unfamiliar. But the rule can be given quite a differentÂ?and more generalÂ?basis. And a simple dimensionless index helps us anticipate best launch angles and path lengths, these latter illustrated with a simple computer simulation.

## Colleen Mitchell : Models of cardiac caveolae reveal a novel mechanism for delayed repolarization and arrhythmia.

- Mathematical Biology ( 115 Views )Recent studies of cholesterol-rich membrane microdomains, called caveolae, reveal that caveolae are reservoirs of recruitable sodium ion channels. Caveolar channels constitute a substantial and previously unrecognized source of sodium current in cardiac cells. In this talk, I will present a family of DE and PDE models to investigate caveolar sodium currents and their contributions to cardiac action potential morphology. We show that the b-agonist-induced opening of caveolae may have substantial impacts on peak overshoot, maximum upstroke velocity, and conduction velocity. Additionally, we show that prolonged action potentials and the formation of potentially arrhythmogenic afterdepolarizations, can arise if caveolae open intermittently throughout the action potential.

## Harsh Jain : A delay differential equation model of cancer chemotherapy, with applications to ovarian carcinoma treatment

- Mathematical Biology ( 114 Views )The use of delay differential equations (DDEs) to study biological phenomena has a long history, when the rate of change of model variables depends their previous history. Today, DDEs occupy a central place in models of infectious disease dynamics, epidemiology, ecology and tumor growth. In this talk, I will present a delayed partial differential equation (PDE) model of tumor growth and treatment. The model accounts for cell cycle arrest and cell death induced by chemotherapy, and explicitly includes intracellular signaling pathways relevant to drug action. The model is simplified to give a 1D hyperbolic PDE, which is further reduced to a nonlinear, non-autonomous DDE by projecting along characteristics. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined. This has clinical implications since it leads to a lower bound for the amount of therapy required to affect a cure. Finally, I will present a clinical application of the model, by applying it to the treatment of ovarian cancers. Two types of drugs are considered Â? platinum-based chemotherapeutic agents that are the current standard of care for most solid tumors, and small molecule cell death inducers that are currently under development. The model is calibrated versus in vitro experimental results, and is then used to predict optimal doses and administration time scheduling for the treatment of a tumor growing in vivo.

## Marty Golubitsky : Homeostasis and Network Invariants

- Mathematical Biology ( 113 Views )We discuss the question: What properties of solutions to coupled cell network systems are invariant under changes of coordinates that preserve network structure? This question was motivated by trying to understand the biological phenomenon of homeostasis in a mathematically satisfactory way. In its simplest mathematical form homeostasis can be described as follows. Given a stable equilibrium $x(lambda)$ of a system that depends on an input parameter $lambda$: When is some coordinate (say $x_j(lambda)$) approximately constant? First, we translate approximately constant to derivative approximately 0. This allows us to search for regions of homeostasis in a model using bifurcation theory like formulas. Second, we claim that there is a sense in which homeostasis can be thought of as a network invariant. This is joint work with Ian Stewart.

## Suzanne Lenhart : Optimal Harvesting in Fishery Models

- Mathematical Biology ( 106 Views )We discuss two types of partial differential equation models of fishery harvesting problems. We consider steady state spatial models and diffusive spatial-temporal models. We characterize the distribution of harvest effort which maximizes the harvest yield, and in the steady state case, also minimizes the cost of the effort. We show numerical results to illustrate various cases. The results inform ongoing debate about the use of reserves (regions where fishing is not allowed), and are increasingly relevant as technology enables enforcement of spatially structured harvest constraints.

## Sorin Mitran : Information Theoretic Projection of Cytoskeleton Dynamics onto Surrogate Cellular Motility Models

- Mathematical Biology ( 106 Views )Cellular motility arises from the interaction of numerous components: actin filaments, ligands, adhesion complexes to name a few. Each individual component exhibits stochastic behavior, yet overall cooperative behavior is observed, and leads to motility. Linking overall cellular motion to the stochastic behavior of its components is a remarkable mathematical challenge. This talk introduces a method to cyclically extract surrogate motility models from detailed stochastic simulation of the components. The starting point is a sampling of the detailed cytoskeleton dynamics over a short time interval. This detailed information is repeatedly projected onto a lower dimensional statistical manifold to obtain a coarse-grained model of the cytoskeleton, from which a surrogate cell model is obtained. The projection operation corresponds to transport along the geodesics of embedded statistical manifolds. The surrogate model is advanced over a larger time interval and then used to recreate the detailed microscopic cytoskeleton state needed to start the next cycle. The procedure is applied to study the behavior of Listeria monocytogenes bacterium and inert models of the motility behavior of this bacterium

## Daniel Forger : A mechanism for robust daily timekeeping

- Mathematical Biology ( 106 Views )Circadian clocks persist with a constant period (~24-hour) even after a significant change of the expression level of clock genes. To study the biochemical mechanisms of timekeeping, we develop the most accurate mathematical model of mammalian intracellular timekeeping, as well as a simplified model amenable to mathematical analysis. This modeling work raises interesting questions about existence and uniqueness of models given knowledge of their solutions. Although much is known about cellular circadian timekeeping, little is known about how these rhythms are sustained with a constant period. Here, we show how a universal motif of circadian timekeeping, where repressors bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. Furthermore, we find that, even in the presence of large changes in gene expression levels, an additional slow negative feedback loop keeps this stoichiometry in balance and maintains oscillations with a fixed period. These results explain why the network structure found naturally in circadian clocks can generate ~24-hour oscillations in many conditions.

## Guowei Wei : Multiscale multiphysics and multidomain models for biomolecules

- Mathematical Biology ( 106 Views )A major feature of biological sciences in the 21st Century is their transition from phenomenological and descriptive disciplines to quantitative and predictive ones. However, the emergence of complexity in self-organizing biological systems poses fabulous challenges to their quantitative description because of the excessively high dimensionality. A crucial question is how to reduce the number of degrees of freedom, while preserving the fundamental physics in complex biological systems. We discuss a multiscale multiphysics and multidomain paradigm for biomolecular systems. We describe macromolecular system, such as protein, DNA, ion channel, membrane, molecular motors etc., by a number of approaches, including macroscopic electrostatics and elasticity and/or microscopic molecular mechanics and quantum mechanics; while treating the aqueous environment as a dielectric continuum or electrolytic fluids. We use differential geometry theory of surfaces to couple various microscopic and macroscopic domains on an equal footing. Based on the variational principle, we derive the coupled Poisson-Boltzmann, Nernst-Planck, Kohn-Sham, Laplace-Beltrami, Newton, elasticity and/or Navier-Stokes equations for the structure, function, dynamics and transport of protein, protein-ligand binding and ion-channel systems.

## Ned Wingreen : Why are chemotaxis receptors clustered but other receptors arenÂ?t?

- Mathematical Biology ( 106 Views )The chemotaxis network of bacteria such as E. coli is remarkable for its sensitivity to minute relative changes in chemical concentrations in the environment. Indeed, E. coli cells can detect concentration changes corresponding to only ~3 molecules in the volume of a cell. Much of this acute sensitivity can be traced to the collective behavior of teams of chemoreceptors on the cell surface. Instead of receptors switching individually between active and inactive configurations, teams of 6-20 receptors switch on and off, and bind or unbind ligand, collectively. Similar to the binding and unbinding of oxygen molecules by tetramers of hemoglobin, the result is a sigmoidal binding curve. Coupled with a system for adaptation that tunes the operating point to the steep region of this sigmoidal curve, the advantage for chemotaxis is gain Â? i.e., small relative changes in chemical concentrations are transduced into large relative changes in signaling activity (specifically, the rate of phosphorylation of the response regulator CheY). Â However, something is troubling about this simple explanation: in addition to providing gain, the coupling of receptors into teams also increases noise, and the net result is a decrease in the signal-to-noise ratio of the network. Why then are chemoreceptors observed to form cooperative teams? We present a novel hypothesis that the run-and-tumble chemotactic strategy of bacteria leads to a Â?noise thresholdÂ?, below which noise does not significantly decrease chemotactic velocity, but above which noise dramatically decreases this velocity.

## Jonathan E. Rubin : Respiratory rhythm generation: Does it take bursts to make bursts?

- Mathematical Biology ( 104 Views )Certain neurons can, in isolation, generate a bursting rhythm, in which phases of active spiking alternative repetitively with phases of quiescence. This behavior is itself mathematically interesting, and neurons with this capability have been found in the mammalian respiratory brain stem, suggesting that they might drive the respiratory rhythm. In this talk, I will survey some mathematical and computational work that runs counter to this suggestion. The methods involved include slow-fast decomposition and associated bifurcation analysis in single-neuron and few-neuron ODE models as well as a genetic algorithm applied to larger network models. The larger network results may have general implications for networks of nodes with heterogeneous dynamics, coupled in small-world, scale-free, and other architectures

## Stephan Huckemann : Statistics for Non-Euclidean Data

- Mathematical Biology ( 104 Views )This talk provides some fundamentals of statistical techniques for data on non-Euclidean spaces. Such data occur in the analysis of shape of geometrical objects, e.g. in applications studying biological growth. Naturally, shape is modeled on a manifold quotient (e.g. unit size objects) under a Lie group action (e.g. translations and rotations) which can be given a manifold structure, possibly with singularities. We show how this scenario allows for one and two sample tests as well as principal component analysis.

## Eric Lauga : Optimality in cellular hydrodynamics

- Mathematical Biology ( 104 Views )Fluid mechanics plays a crucial role in many cellular processes. One example is the external fluid mechanics of motile cells such as bacteria, spermatozoa, algae, and essentially half of the microorganisms on earth. The most commonly-studied organisms exploit the bending or rotation of a small number of flagella (short whip-like organelles, length scale from a few to tens of microns) to create fluid-based propulsion. Ciliated microorganisms swim by exploiting the coordinated surface beating of many cilia (which are short flagella) distributed along their surface. After a short introduction to the fundamentals of fluid-based locomotion on small scales, we pose separate optimization problems addressing the optimal geometries and locomotion gaits of low-Reynolds-number swimmers. First, we characterize the optimal dynamics of simple flapping swimmers with two degrees of freedom. Second, we derive analytically and computationally the optimal waveform of an elastic flagellum, such as the one employed by eukaryotic cells for propulsion. Third, we investigate the optimal shapes of helical propellers, and use our results to help rationalize the shape selection mechanism in bacterial flagella. Finally, we characterize the optimal locomotion by surface distortions of blunt swimmers, and demonstrate the appearance of waves, reminiscent of the metachronal waves displayed by ciliated organisms.

## Mansoor Haider : Mixture Models for Cartilage Tissue Engineering in Biomaterial Scaffolds Seeded with Chondrocytes

- Mathematical Biology ( 100 Views )Cartilage physiology is regulated by a single population of specialized cells called chondrocytes. The chondroyctes are sparsely distributed within the extracellular matrix (ECM) and maintain a state of homeostasis in healthy tissue. ECM degeneration due to osteoarthritis can lead to compete degradation of cartilage surfaces, necessitating total joint replacement. Chondrocytes can be utilized to regenerate cartilage via tissue engineering approaches in which these cells are seeded in biocompatible and degradable biopolymer or hydrogel scaffolds. In such systems, biosynthetic activity of the cells in response to their non-native environment results in regeneration and accumulation of ECM constituents concurrent with degradation of the surrounding scaffold material. In this talk, mixture models are presented for interactions between biosynthesis of ECM constituents and ECM linking in cell-seeded scaffolds. Both ODE-based (temporal) models for evolution of average apparent densities and PDE-based (spatio-temporal) models will be presented for variables including unlinked ECM, linked ECM and scaffold. Model extensions accounting for cell proliferation will also be discussed. Of particular interest are model predictions for the evolution of solid phase apparent density, which is correlated with the compressive elastic modulus of the tissue construct. These models provide a quantitative framework for assessing and optimizing the design of engineered cell-scaffold systems and guiding strategies for articular cartilage tissue engineering.

## Sorin Mitran : Cytoskeleton multiscale model

- Mathematical Biology ( 99 Views )One of the challenges in biology is relating biochemical reactions that occur at the protein nanoparticle size of 1-100 nm to large scale effects on the cell or tissue scale of 0.01-10 mm. The cytoskeleton is a remarkable example with actin polymerization/depolymerization leading to locomotion, metastasis or apoptosis. This talk presents a recently developed multiscale model that captures large-scale effects produced by changes in biochemical reactions. The model is a computational algorithm that determines effective continuum properties of a homogenized cytoskeleton model by concurrent microscopic simulation. Concepts from information theory and optimal transport are applied to link disparate scales in a computationally efficient manner. One of the interesting aspects of this approach is the combination of standard computational modeling techniques (finite volume, numerical stochastic ODEs) with statistical concepts and learning theory.

## Pierre-Emmanuel Jabin : Selection-Mutation models

- Mathematical Biology ( 98 Views )I present an overview of models of the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Starting from a stochastic birth and death process, several types of deterministic or probabilistic models can be derived. When advantageous mutations are rare and small, a time scale separation takes place in the models leading to the concentration of the population along a few selected traits. Those then evolve according to a PDE of Hamilton-Jacobi type or to the canonical equation of adaptive dynamics.