## 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.

## Laura Miller : How jellyfish can inspire mathematics: A case study of the feeding currents generated by upside-down jellyfish

- Mathematical Biology ( 223 Views )The jellyfish has been the subject of numerous mathematical and physical studies ranging from the discovery of reentry phenomenon in electrophysiology to the development of axisymmetric methods for solving fluid-structure interaction problems. In this presentation, we develop and test mathematical models describing the pulsing dynamics and the resulting fluid flow generated by the upside down jellyfish, Cassiopea. The kinematics of contraction and distributions of pulse frequencies were obtained from videos and used as inputs into numerical simulations. Particle image velocimetry was used to obtain spatially and temporally resolved flow fields experimentally. The immersed boundary method was then used to solve the fluid-structure interaction problem and explore how changes in morphology and pulsing dynamics alter the resulting fluid flow. Unlike pelagic (swimming) jellyfish, there is no evidence of the formation of a train of vortex rings. Instead, significant mixing occurs around and directly above the oral arms and secondary mouths. We found good agreement between the numerical simulations and experiments, suggesting that the presence of porous oral arms induce net horizontal flow towards the bell and mixing.

## Andrew Brouwer : Harnessing environmental surveillance: mathematical modeling in the fight against polio

- Mathematical Biology ( 213 Views )Israel experienced an outbreak of wild poliovirus type 1 (WPV1) in 2013-14, detected through environmental surveillance of the sewage system. No cases of acute flaccid paralysis were reported, and the epidemic subsided after a bivalent oral polio vaccination (bOPV) campaign. As we approach global eradication, polio will increasingly be detected only through environmental surveillance. However, we have lacked the theory to translate environmental surveillance into public health metrics; it is a priori unclear how much environmental surveillance can even say about population-level disease dynamics. We developed a framework to convert quantitative polymerase chain reaction (qPCR) cycle threshold data into scaled WPV1 and OPV1 concentrations for inference within a deterministic, compartmental infectious disease transmission model. We used differential algebra and profile likelihood techniques to perform identifiability analysis, that is, to assess how much information exists in the data for the model, and to quantify inference uncertainty. From the environmental surveillance data, we estimated the epidemic curve and transmission dynamics, determining that the outbreak likely happened much faster than previously thought. Our mathematical modeling approach brings public health relevance to environmental data that, if systematically collected, can guide eradication efforts.

## Stanca Ciupe : Models of antibody responses in HIV

- Mathematical Biology ( 174 Views )One of the first immunologic responses against HIV infection is the presence of neutralizing antibodies that seem able to inactivate several HIV strains. Moreover, in vitro studies have shown the existence of monoclonal antibodies that exhibit broad crossclade neutralizing potential. Yet their number is low and slow to develop in vivo. In this paper, we investigate the potential benefits of inducing poly-specific neutralizing antibodies in vivo throughout immunization. We develop a mathematical model that considers the activation of families of B lymphocytes producing poly-specific and strain-specific antibodies and use it to demonstrate that, even if such families are successful in producing neutralizing antibodies, competition between them may limit the poly-specific response allowing the virus to escape. We modify this model to account for viral evolution under the pressure of antibody responses in natural HIV infection as well as the need to neutralize more than one viral spike. The model can reproduce viral escape under certain conditions of B lymphocyte competition. Using these models we provide explanations for the observed antibody failure in controlling natural infection and predict quantitative measures that need to be satisfied for long-term control of HIV infection.

## Seth Sullivant : Statistically-Consistent k-mer Methods for Phylogenetic Tree Reconstruction

- Mathematical Biology ( 166 Views )Frequencies of k-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between k-mer vectors to approximate a tree metric can be statistically inconsistent. To remedy this, we derive model-based distance corrections for orthologous sequences without gaps, which lead to consistent tree inference. The identifiability of model parameters from k-mer frequencies is also studied. Finally, we report simulations showing the corrected distance out-performs many other k-mer methods, even when sequences are generated with an insertion and deletion process. These results have implications for multiple sequence alignment as well, since k-mer methods are usually the first step in constructing a guide tree for such algorithms. This is joint work with Elizabeth Allman and John Rhodes.

## Nick Moore : How focused flexibility maximizes the thrust production of flapping wings

- Mathematical Biology ( 154 Views )Birds, insects, and fish all exploit the fact that flexible wings or fins generally perform better than their rigid counterparts. Given the task of designing an optimal wing, though, it is not clear how to best distribute the flexibility: Should the wing be uniformly flexible along its length, or could some advantage be gained by making certain sections more rigid than others? I will discuss this question by using a 2D small-amplitude model for the fluid-structure interaction combined with an efficient Chebyshev PDE solver. Numerical optimization shows that concentrating flexibility near the leading edge of the wing maximizes thrust production, an arrangement that resembles the torsional-joint flexibility mechanism found in insect wings. I will discuss the possibility of extending into three dimensions to address the question of optimal wing architecture more generally.

## Tom Kepler : Microevolution in the Immune System: A Computational Systems Approach--second lecture

- Mathematical Biology ( 149 Views )Vaccines protect their recipients by inducing long-term structural changes in populations of immune cells. Part of that restructuring is exactly analogous to Darwinian Selection. New antibody molecules are created by somatic mutation of existing antibody genes. Subsequently, the immune cell populations that possess these mutated receptors overtake the "wild-type" immune cells due to the selective advantage they have acquired. Thus the immune system is vastly better prepared to recognize and eliminate the eliciting pathogen the next time around. New sequencing and biosynthesis technologies, together with mathematical and computational tools, now allow us to investigate this fascinating and important phenomenon more deeply than ever before. I will illustrate this development with examples from the immune response to HIV infection. Second lecture will focus on specifically mathematical questions.

## 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

## Cecilia Clementi : A multiscale approach to characterize macromolecular dynamics and functions

- Mathematical Biology ( 140 Views )A multiscale approach to characterize macromolecular dynamics and functions The understanding of emerging collective behaviors in biomolecular complexes represents a major challenge in modern biophysics. As a first step toward the study of such processes we have applied multi-resolution nonlinear dimensionality reduction and diffusion analysis to obtain reliable low-dimensional representations and models for the dynamics of apparently high-dimensional complex systems such as proteins in a biological environment. The results clearly show that the proposed methods can efficiently find low dimensional representations of a complex process such as protein folding.

## Anita Layton : Myogenic Response to Systolic Pressure in the Afferent Arteriole

- Mathematical Biology ( 133 Views )Elevations in systolic blood pressure are believed to be closely linked to the pathogenesis and progression of renal diseases. It has been hypothesized that the afferent arteriole (AA) protects the glomerulus from the damaging effects of hypertension by sensing increases in systolic blood pressure and responding with a compensatory vasoconstriction. To investigate this hypothesis, we developed a mathematical model of the myogenic response of an AA smooth muscle cell, based on an arteriole model by Gonzalez-Fernandez and Ermentrout (Math Biosci 1994). renal hemodynamic regulation. The model incorporates ionic transport, cell membrane potential, contraction of the AA smooth muscle cell, and the mechanics of a thick-walled cylinder. The model represents a myogenic response based on a pressure-induced shift in the voltage dependence of calcium channel openings: with increasing transmural pressure, model vessel diameter decreases; and with decreasing pressure, vessel diameter increases. Further, the model myogenic mechanism includes a rate-sensitive component that yields constriction and dilation kinetics similar to behaviors observed in vitro. A parameter set is identified based on physical dimensions of an AA in a rat kidney. Model results suggest that the interaction of Ca2+ and K+ fluxes mediated by voltage-gated and voltage-calcium-gated channels, respectively, gives rise to periodicity in the transport of the two ions. This results in a time-periodic cytoplasmic calcium concentration, myosin light chains phosphorylation, and crossbridges formation with the attending muscle stress. Further, the model predicts myogenic responses that agree with experimental observations, most notably those which demonstrate that the renal AA constricts in response to increases in both steady and systolic blood pressures. The myogenic model captures these essential functions of the renal AA, and it may prove useful as a fundamental component in a multi-scale model of the renal microvasculature suitable for investigations of the pathogenesis of hypertensive renal diseases.

## Doron Levy : Modeling the role of the immune response in chronic myelogenous leukemia

- Mathematical Biology ( 130 Views )Tyrosine kinase inhibitors (TKIs), such as imatinib (IM), have significantly improved treatment of chronic myelogenous leukemia (CML). However, the majority of patients are not cured for undetermined reasons. It turns out that many patients who otherwise responded well to IM therapy still show variations in their BCR-ABL transcripts. In this talk we will overview mathematical models for leukemia, drug resistance, and stem cells. Our main focus will be on our recent results concerning mathematical models that integrate CML and an autologous immune response.Â This is a joint work with G. Clapp, T. Lepoutre, and F. Nicolini.

## Rafael Meza : Applications of stochastic models of carcinogenesis in cancer prevention

- Mathematical Biology ( 127 Views )Carcinogenesis is the transformation of normal cells into cancer cells. This process has been shown to be of a multistage nature, with stem cells that go through a series of (stochastic) genetic and epigenetic changes that eventually lead to a malignancy. Since the origins of the multistage theory in the 1950s, mathematical modeling has played a prominent role in the investigation of the mechanisms of carcinogenesis. In particular, two stochastic (mechanistic) models, the Armitage-Doll and the two-stage clonal expansion (TSCE) model, have been widely used in the past for cancer risk assessment and for the analysis of cancer population and experimental data. In this talk, I will introduce some of the biological and mathematical concepts behind the theory of multistage carcinogenesis, and discuss in detail the use of these models in cancer epidemiology and cancer prevention and control. Recent applications of multistage and state-transition Markov models to assess the potential impact of lung cancer screening in the US will be reviewed.

## Casey Diekman : Data Assimilation and Dynamical Systems Analysis of Circadian Rhythmicity and Entrainment

- Mathematical Biology ( 126 Views )Circadian rhythms are biological oscillations that align our physiology and behavior with the 24-hour environmental cycles conferred by the Earthâ??s rotation. In this talk, I will discuss two projects that focus on circadian clock cells in the brain and the entrainment of circadian rhythms to the light-dark cycle. Most of what we know about the electrical activity of circadian clock neurons comes from studies of nocturnal (night-active) rodents, hindering the translation of this knowledge to diurnal (day-active) humans. In the first part of the talk, we use data assimilation and patch-clamp recordings from the diurnal rodent Rhabdomys pumilio to build the first mathematical models of the electrophysiology of circadian neurons in a day-active species. We find that the electrical activity of circadian neurons is similar overall between nocturnal and diurnal rodents but that there are some interesting differences in their responses to inhibition. In the second part of the talk, we use tools from dynamical systems theory to study the reentrainment of a model of the human circadian pacemaker following perturbations that simulate jet lag. We show that the reentrainment dynamics are organized by invariant manifolds of fixed points of a 24-hour stroboscopic map and use these manifolds to explain a rapid reentrainment phenomenon that occurs under certain jet lag scenarios.

## Carina Curto : Convex neural codes

- Mathematical Biology ( 125 Views )Cracking the neural code is one of the central challenges of neuroscience. Typically, this has been understood as finding the relationship between single neurons and the stimuli they represent. More generally, neural activity must also reflect relationships between stimuli, such as proximity between locations in an environment. Convex codes, comprised of activity patterns for neurons with classical receptive fields, may be the brain's solution to this problem. These codes have been observed in many areas, including sensory cortices and the hippocampus. What makes a code convex? Using algebra, we can uncover intrinsic signatures of convexity and dimension in neural codes. I will report on some recent results by multiple authors, including participants in my 2014 AMS Math Research Community.

## Ezra Miller : Applying persistent homology to brain artery and vein imaging

- Mathematical Biology ( 125 Views )Persistent homology measures geometric structures using topological invariants. When the structures are magnetic resonance images of branching arteries, for example, persistent homology records the connectedness of an increasing subset of the vessels. Although the theory of persistent homology is relatively well developed, and many aspects of its behavior are understood in synthetic examples, only recently have applications to genuine experimental data begun. This talk explains what we have learned about the geometry of blood vessels in aging human brains, as well as lessons this exploration has taught us about applications of persistent homology in general. These lessons inform further potential applications of persistent homology in statistical problems from biological and medical imaging. The main results are joint with Paul Bendich, Steve Marron, Aaron Pieloch, and Sean Skwerer (Math junior faculty, Stat faculty, Math undergrad, and Operations Research grad student). The talk will be accessible to advanced mathematics and statistics undergraduates, medical and biological researchers, statistics and mathematics faculty, and everybody in between.

## Nicolas Buchler : Coupling of redox rhythms to the plant circadian clock and the yeast cell division cycle .

- Mathematical Biology ( 123 Views )Biological oscillators such as the cell cycle, circadian clocks, and metabolic rhythms are ubiquitous across the domains of life. These biochemical oscillators co-exist in the same cells, often sharing and competing for resources. Are there mechanisms and regulatory principles that ensure harmony between these oscillators? Recent studies have shown that in addition to the transcriptional circadian clock, many organisms (including Arabidopsis) have a circadian redox rhythm driven by the organism's metabolic activities. It has been hypothesized that the redox rhythm is linked to the circadian clock, but the mechanism and the biological significance of this link have only begun to be investigated. In the first half of my talk, I will describe our work (in collaboration with the Dong lab at Duke) on the coupling of redox rhythms and the plant circadian clock. In the second half of my talk, I will discuss our work on the coupling of yeast metabolic cycle and the cell division cycle.

## Tom Kepler : Microevolution in the Immune System: A Computational Systems Approach

- Mathematical Biology ( 122 Views )Vaccines protect their recipients by inducing long-term structural changes in populations of immune cells. Part of that restructuring is exactly analogous to Darwinian Selection. New antibody molecules are created by somatic mutation of existing antibody genes. Subsequently, the immune cell populations that possess these mutated receptors overtake the "wild-type" immune cells due Â to the selective advantage they have acquired. Thus the immune system is vastly better prepared to recognize and eliminate the eliciting pathogen the next time around.

New sequencing and biosynthesis technologies, together with mathematical and computational tools, now allow us to investigate this fascinating and important phenomenon more deeply than ever before. I will illustrate this development with examples from the immune response to HIV infection.

## L. Mahadevan : Mechanochemistry and motility: individual and collective behavior

- Mathematical Biology ( 121 Views )I will describe three different types of problems inspired by the dynamics of the cytoskeleton: (i) the structural and kinetic aspects of dynamic instability in macromolecular assemblies, (ii) the collective flagella-like dynamics of ordered assemblies of active particles and cells, and (iii) the onset of oscillations and the persistence of strain in disordered aggregates of motors and filaments. In all cases, I will show how simple aspects of geometry, chemical kinetics and statistical and continuum mechanics allow us to explain biological observations in a minimal setting.

## Joshua Goldwyn : Analysis of stochastic auditory nerve models with applications to cochlear implant psychophysics

- Mathematical Biology ( 120 Views )Cochlear implants are neural prostheses that restore a sense of hearing to individuals with severe to profound deafness. Two fundamental theoretical questions that we face are: How does the auditory nerve respond to electrical stimulation? And how is sound information represented in the spike trains of auditory nerve fibers? We will discuss model-based efforts to investigate these questions. I will focus on the development of reduced models that incorporate essential biological features of this complicated system, and remain useful tools for analyzing neural coding.

Using a point process model of the auditory nerve, I simulate amplitude modulation detection, a common test of temporal resolution. I find that the temporal information in the simulated spike trains does not limit modulation sensitivity in cochlear implant users, and discuss how the point process framework can be extended to include additional biophysical mechanisms. Next, I illustrate how spatial spread of excitation and neural degeneration can lead to of within- and across-patient variability in listening outcomes. This points toward an important goal of computational modeling: to develop patient-specific models that can be used to optimize stimulation strategies for individual cochlear implant users.

## 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.

## John Tyson : Irreversible Transitions, Bistability and Checkpoints in the Eukaryotic Cell Cycle

- Mathematical Biology ( 113 Views )

"Perhaps a proper understanding of the complex

regulatory networks making up cellular systems

like the cell cycle will require a shift from common

sense thinking...to a more abstract world, more

readily analyzable in terms of mathematics."

(Paul Nurse, Cell, 7 January 2000)

The cell cycle is a striking example of the necessity of systems-level

thinking in 21st century molecular cell biology. The resolute reductionism

of the last century, albeit necessary for identifying the molecular

components of cellular control systems and their interactions, has failed

to provide a comprehensive, integrative understanding of the molecular

basis of cell physiology. Putting the pieces back together requires new

ways of thinking about and doing molecular biology--an approach now

known as molecular systems biology. In this lecture I will show how

systems-level thinking reveals deep and unexpected principles of cell

cycle regulation.

## Scott Schmidler : Stochastic Models of Protein Evolution

- Mathematical Biology ( 109 Views )Stochastic evolutionary models of biological sequences are widely used for phylogenetic inference and ancestral reconstruction. However, at long divergence times sequences enter the "twilight zone" of homology detection and reconstruction becomes very difficult. We describe a stochastic evolutionary model for protein 3D structure using elements of shape theory. This model significantly resolves this uncertainty and stabilizes evolutionary inferences. We also provide theoretical bounds on inferring evolutionary divergence times via connections to the probabilistic "cutoff phenomenon", in which a Markov chain remains far equilibrium for an extended period followed by a rapid transition into equilibrium. We show that this cutoff explains several previously reported problems with common default priors for Bayesian phylogenetic analysis, and suggest a new class of priors to address these problems.

## Paul Magwene : Taking a dip in the gene pool: Insights from pooled population sequencing

- Mathematical Biology ( 109 Views )Advances in high-throughput genomics have facilitated the development of pooled population sequencing techniques which involve the en masse sequencing of tens to hundreds of individual genomes in a single sequencing reaction. Pooled population sequencing methods have numerous applications in quantitative, population and evolutionary genetics. I will discuss some of the statistical and computational challenges associated with the analysis of pooled sequence data in the context of quantitative trait locus (QTL) mapping and detecting selection during experimental evolution.

## Sharon Lubkin : Model perspectives on self-organizing tissues

- Mathematical Biology ( 108 Views )Tissues grow, change shape, and differentiate, function normally or abnormally, get diseased or injured, repair themselves, and sometimes atrophy. This complex suite of behaviors is governed by a complex suite of controls. Nonetheless, we can identify some general principles at work in the dynamics of tissues. Our goal is to understand how a tissueÂ?s mechanics and biology regulate each other. Our models use a biologically-based framework to track the mechanics, biology, and mechanobiology of the component cells, fluids, signaling molecules, and extracellular matrix materials. The presentation will describe our modeling approach, reveal some of the general principles we have identified, and discuss some of the questions our findings have raised about specific morphogenetic systems such as the lung.

## Lydia Bilinsky : A Mathematical Model of Glutamate and Glutamine Metabolism in the Rat: Implications for Glutathione Production

- Mathematical Biology ( 107 Views )Glutathione (GSH), a tripeptide formed from glutamate, cysteine, and

glycine, is arguably the most important antioxidant in the body. NAPQI, a

byproduct of acetaminophen (APAP) metabolism which is toxic to liver

cells, is neutralized by GSH. Although produced in great quantity by the

liver, in cases of APAP overdose demand for GSH can outstrip supply,

causing liver failure. Currently, patients presenting to the ER with APAP

overdose are given an infusion of cysteine since it is believed to be the

rate-limiting amino acid in GSH synthesis, however, there is evidence that

under some circumstances glutamate can become rate-limiting. Complicating

the issue is that in most hepatocytes, glutamate is not absorbable from

blood plasma but is formed from glutamine, which is produced in large

amounts by the skeletal muscle. In order to develop better rescue

protocols for APAP overdose, we have developed a mathematical model of

glutamate and glutamine metabolism in the rat. We have also investigated

how model parameters should change in the case of increased cortisol

production, such as occurs during sepsis, trauma, burns, and other

pathological states; the cortisol-stressed state has been studied in rats

by giving them dexamethasone. We compare model predictions with

experimental data for the normal, healthy rat and dexamethasone-stressed

rat. Biological parameters are taken from the literature wherever possible.

## 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

## Dennis Frank-Ito : The Future of Computational Fluid Dynamics Modeling in Assessing Upper Airway Respiratory Physiology

- Mathematical Biology ( 102 Views )The complexity of the human airway coupled with advances in computational technology have led to the growing interest in the use of computational fluid dynamics (CFD) techniques to simulate airway physiology in order to collect objective data due to inter-individual anatomy and pre- & post-surgical changes. Outcomes from airway surgery are sometimes difficult to predict a priori, and it is not known whether topical medications are reaching target sites within the human air passage. This talk will give an overview of how CFD is used to explore these issues, as well as demonstrate the potential ability of this methodology in pre-surgical planning.