## 2013 Workshop for Young Researchers in Mathematical Biology

### (August 26,2013 - August 29,2013 )

The workshop is intended to broaden the scientific perspective of young researchers (primarily junior faculty, postdocs, and senior graduate students) in mathematical biology and to encourage interactions with other scientists. Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster. We cordially invite young mathematical biologists to participate. For full consideration, please apply by May 1, 2013.

### Accepted Speakers

Fluid Dynamics Division, School of Advanced Sciences, VIT University
Valerie Coffman
Molecular Genetics, The Ohio State University
Eric Eager
Mathematics, University of Wisconsin - La Crosse
Lisa Fauci
Mathematics, Tulane University
Pak-Wing Fok
Mathematical Sciences, University of Delaware
Ashlee Ford Versypt
Chemical Engineering, Massachusetts Institute of Technology
Kresimir Josic
Department of Mathematics, University of Houston
Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University
Michael Kelly
Mathematics, University of Tennessee
Matthew Macauley
Mathematical Sciences, Clemson University
Anuj Mubayi
Mathematics, Northeastern Illinois University
Claudia Neuhauser
Biomedical Informatics and Computational Biology, University of Minnesota Rochester
Angela Peace
Mathematics and Statistical Sciences, Arizona State University
Michael Robert
Mathematics (Biomathematics Graduate Program), North Carolina State University
Sebastian Schreiber
Department of Evolution and Ecology, University of California, Davis
Arthur Sherman
National Institutes of Health
John Tyson
Computational Cell Biology, Virginia Polytechnic Institute and State University
Lani Wu
Green Center for Systems Biology, UT Southwestern Medical Center
Monday, August 26, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:00 AM

Welcome and opening remarks

09:00 AM
10:00 AM
Claudia Neuhauser - A statistical approach for detecting copy number variations for next generation sequencing data

DNA copy number variation (CNV) is a genetic signature for complex diseases such as cancer. High-throughput sequencing technologies combined with efficient mapping algorithms enable fast detection of CNVs. To ascertain statistical significance of candidates, a mathematical model for the distribution of mapped read counts together with a statistical procedure is proposed. The model assumes that reads are mapped to a reference genome. Mapped reads are counted in consecutive windows, and the read counts are assumed to form an m-dependent, strictly stationary stochastic process and are Poisson distributed with a parameter that varies across the genome. This variation is modeled with a gamma distribution. The model is validated using genome data from four genomes that are presumed to lack CNVs. The test is based on extremes of the number of mapped reads in consecutive windows, and thus avoids the problem of multiple hypothesis testing.

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM
Eric Eager - Modeling and Analysis of the Population Dynamics of Fungus-Infected American Chestnut Populations

Density-dependent regulatory factors impact the dynamics of many populations. However, modelers often times only consider one density-dependent factor when constructing nonlinear structured population models, and these factors are often either always increasing or always decreasing with respect to population abundance. In this presentation we will discuss a density-dependent matrix model for populations of the American Chestnut (Castanea dentata), where seedling recruitment is subject to density-dependent feedback from adult conspecifics as well as other potential seedlings. The former exhibits a decreasing relationship while the latter an increasing one. Using methods from systems and control theory we show that, for much of parameter space, there is a unique, globally attracting equilibrium population vector that is independent of initial population vector. We derive a formula for this equilibrium population and show how sensitive each stage of the population is to changes in population data (for example, we show how the equilibrium population changes when the population goes from healthy to diseased). We further show how our results can be extended to integral projection models (IPMs) and numerically explore stochastic versions of this model.

11:00 AM
11:30 AM
Michael Kelly - Optimal fishery harvesting on a nonlinear parabolic PDE in a heterogeneous spatial domain

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is our marine fish population. The overexploitation of fisheries has called for an improved understanding of spatiotemporal dynamics of resource stocks as well as their harvesters. There is pressure to find methods for optimally solving these management problems. One way to protect fish populations from overexploitation is the inclusion of no-take marine reserves, which prohibit the removal of natural resources from an area of the ocean. There has been previous work done on this subject, which sought after yield maximizing strategies without imposing these no-take reserves into the model. All previous work done included Dirichlet boundary conditions, representing a lethal domain boundary. The question of whether the implementation of alternative boundary conditions, deemed more favorable to the fish stock, on a heterogeneous domain could produce an alternative optimal harvesting strategy. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no-take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.

11:30 AM
01:30 PM

Lunch Break

01:30 PM
02:30 PM
Sebastian Schreiber - Population persistence in the face of uncertainty

One of the most fundamental question in population biology is what conditions ensure the long-term persistence of interacting populations?'' Ever since the foundational work of Lotka and Volterra, Nicholson and Bailey, and Kermack and McKendrick, this question has been tackled using deterministic difference and differential equations. However, all population experience demographic and environmental stochasticity. Hence, we must confront the question of what does persistence mean in the face of these uncertainties?'' The goal of this talk is to provide two recent perspectives on this question. The first part of this talk considers demographic stochasticity due to populations consisting of finite number of individuals. Stochastic models, such as finite state Markov chains, accounting for this stochasticity typically predict extinction of all populations in finite time. However, these extinction events may be preceded by long-term transients characterized by the quasi-stationary distributions of the stochastic process. In collaboration with Mathieu Faure, we have shown that these quasi-stationary distributions concentrate on attractors of an appropriate deterministic difference equation. Hence, this work provides a justification for using deterministic models to study long-term persistence. The second part of this talk considers environmental stochasticity where fluctuations in environmental conditions (e.g. temperature, precipitation) cause fluctuations in vital rates of populations. Persistence for stochastic models, such as difference equations with stochastically varying parameters, can be equated a statistical tendency for populations to remain bounded away from extinction. In collaboration with Gregory Roth, we have shown that there is a sufficient condition for stochastic persistence in terms of the population growth rates when rate. This condition naturally extends the permanence condition of Josef Hofbauer for deterministic models. In both parts of the talk, I will illustrate and motivate the theory with empirical results and applications to metapopulations and competing species.

02:30 PM
03:00 PM

Break

03:00 PM
03:30 PM
Michael Robert - Optimal control of female-killing strategies to eliminate the dengue vector, Aedes aegypti

Dengue fever is spread primarily by Aedes aegypti mosquitoes. Although traditional control mea- sures have been implemented for many years, dengue remains endemic in many parts of the world. Recently, control strategies involving the release of genetically modi ed mosquitoes have been proposed. Among those for Ae. aegypti that have seen the most progress are Female-Killing (FK) strategies. Cage experiments showed that repeated introductions of individuals from one FK strain of Ae. aegypti led to either reduction or extinction of caged wild-type populations. Any future open releases should be conducted according to plans that consider temporal and nancial constraints. We develop an optimal control model to assess the role that such constraints will play in conducting FK releases. Through numerical simulation, we obtain optimal release strategies for a variety of scenarios and assess the feasibility of integrating FK releases with other forms of vector control.

03:30 PM
04:00 PM
- Adaptive Evolution of Dispersal: A Population Approach
Adaptive Evolution of Dispersal: A Population Approach
04:00 PM
04:10 PM

Break

04:10 PM
05:10 PM

Poster Previews I

05:10 PM
07:00 PM

Poster Session with Reception

07:15 PM

Shuttle pick-up from MBI

Tuesday, August 27, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Arthur Sherman - Bistability of Beta Cell Mass in Diabetes

Insulin is the master hormone that controls fuel usage by body tissues. After a meal, glucose is plentiful and stimulates insulin secretion, which allows muscle and fat to take up glucose. When blood glucose falls, insulin falls as well and tissues revert to using fat as a fuel. Obesity causes insulin resistance, meaning that more insulin is needed to produce a given amount of glucose uptake. If the number of insulin-secreting pancreatic beta cells, or secretion per cell, increases sufficiently, this excess demand for insulin can be met. If expansion of mass is inadequate, type 2 diabetes, a rise in glucose to levels that are harmful to cells, results. Diabetes leads to cardiovascular disease, blindness, kidney failure and premature death. We update the seminal model of Topp et al (J. Theor. Biol. 2001) for the regulation of beta-cell mass by glucose and present a comprehensive picture of how diabetes develops and may either be avoided or reversed. Although many details of the model are in doubt, we show that any successful model results in a bistable bifurcation structure, with normal and elevated glucose levels separated by a threshold. This simple picture unifies and explains a striking diversity of experimental data, including why prevention is much easier than cure and why bariatric surgery is able to reverse longstanding diabetes within a week.

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM
Ashlee Ford Versypt - Mathematical Modeling of Pharmaceuticals: Predictive Design for Better Medicines

Smart designs of drug molecules and pharmaceutical formulations can target treatments to specific tissues, reduce side effects, and improve patient quality of care.Computational models for evaluating pharmaceutical formulations can narrow the range of experiments needed to identify successful designs by predicting performance and thus reducing the development time and driving down costs. Models coupled with sophisticated process control strategies allow for careful monitoring of manufacturing to reduce wasted materials and energy and to adhere to quality standards. I will overview mathematical modeling efforts in several pharmaceutical domains and will highlight work related to predicting drug release from controlled-release formulations that administer medicine over extended periods with a single dosage. I will show how coupled, nonlinear partial differential equations can be used to capture the complex dynamic interactions between simultaneous chemical reactions and mass transfer. I will describe mathematical techniques that can be used to reduce the system size from thousands of equations to just a few while retaining resolution of the biodegradation of the pharmaceutical formulation that strongly influences the drug release dynamics. These techniques can aid in the design of new controlledrelease formulations.

11:00 AM
11:30 AM
Anuj Mubayi - Modeling Swarms and Measuring Information Storage and TransferA Mathematical Model for Optimally Allocating Insecticides for Controlling Visceral Leishmaniasisin Bihar, India

Leishmaniasis is a family of infectious diseases that affect poor and developing countries. The Indian state of Bihar has the highest prevalence and mortality rates of visceral leishmaniasis (VL) in the world. Although insecticide spraying is a primary vector control method in many parts of the world for controlling spread of VL, in Bihar a simple approach is adopted for allocating of insecticides per district. This study proposes a novel optimization model to identify the optimal allocation and choice of insecticides (comparing DDT and Deltamethrin, as an example) across both the human and the cattle populations. The model optimizes the insecticide-induced death rate caused by spraying of human and bovine populations dwellings within the constraint of limited financial resources available. The results suggest that DDT yields more than four times the insect death rate achieved by Deltamethrin until ninety days after spray. The results also verify the present practice of first spraying houses to optimize sandfly mortality ahead of spraying cattle sites.

11:30 AM
01:30 PM

Lunch Break

01:30 PM
02:30 PM
Kresimir Josic - How good are mathematical models of genetic signaling networks

Synthetic biology holds the promise of allowing us to engineer living beings. I will start by reviewing some examples where mathematical models lead to the development of synthetic organisms with particular properties: One such example is a synthetic gene oscillator in Escherichia coli that exhibits robust temperature compensation -- it maintains a constant period over a range of ambient temperatures. A mathematical model predicted and experiments confirmed the particular mechanisms that lead to temperature compensation despite Arrhenius scaling of the biochemical reaction rates.

Such successes are encouraging. But how far can our theoretical models take us? I will argue that our models are still fairly coarse, and do not adequately describe all the important properties of genetic signaling networks. For instance, "transcriptional delay" - the delay between the start of protein production and the time a mature protein finds a downstream target - can have a significant impact on the dynamics of gene circuits. Such delay can inhibit transitions between states of bistable genetic networks, as well as destabilize steady states in other networks. I will show how these effects can be described by reduced, non-Markovian models that are quite different from established models. I will also discuss work with experimental collaborators to characterize the distribution of this delay.

02:30 PM
03:00 PM

Break

03:00 PM
03:20 PM

Group photo in from of Jennings Hall

03:20 PM
04:45 PM

Panel Discussion

05:00 PM

Shuttle pick-up from MBI

Wednesday, August 28, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Lisa Fauci - Biofluids

The process of fertilization in mammalian reproduction provides a rich example of fluid-structure interactions. Spermatozoa encounter complex, non-Newtonian fluid environments as they make their way through the cilia-lined, contracting conduits of the female reproductive tract. The beat form realized by the flagellum varies tremendously along this journey due to mechanics and biochemical signaling. We will present recent progress on integrative computational models of pumping and swimming in both Newtonian and complex fluids that capture elements of this complex dynamical system.

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM
Pak-Wing Fok - A Mathematical Model of Intimal Thickening: an Application to Atherosclerosis

Atherosclerosis is an inflammatory disease of the artery characterized by an expansion of the intimal region. Intimal thickening is usually attributed to the migration of smooth muscle cells (SMCs) from the surrounding media and proliferation of SMCs already present in the intima. Intimal expansion can give rise to dangerous events such as stenosis (leading to stroke) or plaque rupture (leading to myocardial infarction). We propose and study a mathematical model of intimal thickening, posed as a free boundary problem. Intimal thickening is driven by damage to the endothelium, resulting in the release of cytokines and migration of SMCs. By coupling a boundary value problem for cytokine concentration to an evolution law for the intimal area, we reduce the problem to a single nonlinear differential equation for the luminal radius. We analyze the steady states, perform a bifurcation analysis and compare model solutions to data from rabbits whose iliac arteries are subject to a balloon pullback injury. In order to obtain a favorable fit, we find that migrating SMCs must enter the intima very slowly compared to cells in dermal wounds. This cell behavior is indicative of a weak inflammatory response which is consistent with atherosclerosis being a chronic inflammatory disease.

11:00 AM
11:30 AM
Sree Rama Vara Prasad Bhuvanagiri - Dynamics of additional food provided predator-prey system with mutually interfering predators

Use of additional/alternative food source to predators is one of the widely recognized practices in the eld of biological control. Both theoretical and experimental works point out that quality and quantity of additional food play a vital role in the controllability of the pest. Theoretical studies carried out previously in this direction indicate that incorporating mutual interference between predators can stabilize the system. Experimental evidence also point out that mutual interference between predators can affect the outcome of the biological control programs. In this work, dynamics of additional food provided predator-prey system with mutual interference between predators has been studied. The mutual interference between predators is modeled using Beddington-DeAngelis type functional response. A through system analysis highlights the role of mutual interference on the success of biological control programs when predators are provided with additional food. The model results indicate the possibility of stable coexistence of predators with low prey population levels. This is in contrast to classical predator-prey models where in this stable co-existence at low prey population levels are not possible. This study classifies the characteristics of biological control agents and additional food (of suitable quality and quantity), permitting the eco-managers to enhance the success rate of biological control programs.

11:30 AM
01:30 PM

Lunch Break

01:30 PM
02:30 PM
Lani Wu - Reverse engineering neutrophil polarity network

A central question in biology is how complex, spatial-temporal cellular behaviors arise from biochemical networks. Much work has led to the identification and cataloguing of various network architectures, and the explication of how static network motifs can give rise to dynamic response characteristics, including ultrasensitive, switch-like, and oscillatory behaviors. However, the wiring diagrams of signaling networks are often inferred by combining results from diverse assays. Such diagrams may not represent accurately the operating state of the network in any cell, condition or time point. In this talk, we will discuss recent progress in using perturbation analysis and cellular heterogeneity to constrain network crosstalk from cellular behaviors.

02:30 PM
03:00 PM

Break

03:00 PM
03:30 PM
Matthew Macauley - Asynchronousity in Boolean networks

A Boolean network consists of a finite set of nodes, each taking a Boolean state, and each having an update function depending on a subset of the other states. These functions are assembled to get the dynamical system map which is iterated to generate the dynamics. The common synchronous function update is convenient but often biologically unnatural. In contrast, asynchronousity poses questions about stability and robustness with respect to update order. In this talk, I will introduce toric posets which can be thought of as a cyclic version of ordinary posets and provide a clean combinatorial framework for describing asynchronousity in Boolean networks.

03:30 PM
04:00 PM
Angela Peace - A stoichiometric producer-grazer model incorporating the effects of excess food-nutrient content on consumer dynamics

There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. For example, modeling under this framework allows food quality to affect consumer dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insuffcient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon is known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, and needs to be incorporated into mathematical models. Here we present a Lotka-Volterra type model to investigate the growth response of Daphnia to algae of varying P:C ratios capturing the mechanism of the stoichiometric knife edge.

04:00 PM
04:10 PM

Break

04:10 PM
05:10 PM

Poster Preview II

05:10 PM
07:00 PM

Poster Session II with Reception

07:15 PM

Shuttle pick-up from MBI

Thursday, August 29, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
John Tyson - Mathematical Models of Cell Cycle Progression

Progression through the eukaryotic cell cycle is controlled at a series of checkpoints guarding transitions from one phase of the cycle to the next, e.g., G1-to-S, G2-to-M, metaphase-to-anaphase. These checkpoints ensure that a cell has satisfied certain requirements that are necessary for success of the next phase, e.g., that any DNA damage is repaired before the cell replicates its chromosomes in S phase. These transitions are irreversible: as soon as the conditions of the checkpoint are satisfied, the cell proceeds to the next phase and does not subsequently back up to the immediately preceding phase. The irreversibility of these transitions gives the cell cycle its directionality (G1 â†’ S â†’ G2 â†’ M â†’ G1 ...). The genes and proteins governing these checkpoints have been discovered by molecular geneticists, but the mechanistic basis of irreversibility is still a subject of controversy. Many molecular biologists think that the transitions are irreversible because key proteins are chemically degraded at each transition, but we maintain that irreversibility is a consequence of bistability and hysteresis in the underlying regulatory network. To prove this claim, JJT will describe the mechanism of the G1-S transition in some detail, build and analyze a mathematical model of the mechanism, and compare the implications of the model to experimental facts.

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM
Claus Kadelka - The Effect of MicroRNA-Mediated Feedforward Loops on Gene Regulatory Networks

The concept of canalization in gene regulation was developed as a possible solution to the question of why the outcome of embryonal development leads to predictable phenotypes in the face of widely varying environmental conditions. The key step of gene expression is fundamentally a stochastic process, which makes the stability of genetic regulation programs all the more surprising. An entirely novel gene regulatory mechanism, discovered and studied during the last decade, which is believed to play an important role in cancer, is shedding some light on how canalization may in fact take place as part of a cell's gene regulatory program. Short segments of single-stranded RNA, so-called microRNAs, which are embedded in several different types of feedforward loops, help smooth out noise and generate canalizing effects in gene regulation by overriding the effect of certain genes on others.

In a computational study, we used the modeling framework of generalized Boolean networks to explore the role that microRNA-mediated feedforward loops play in stabilizing the global dynamics of various gene regulatory networks. We compared the degree of stochasticity of a basic gene network and an extended network, in which various numbers of microRNAs have been introduced in a biologically inspired way, and were thereby able to exactly quantify the stabilizing effect for any gene regulatory network.

Thus, this research contributed to an answer of the question:to what extent do microRNAs stabilize gene regulatory programs?

11:00 AM
11:30 AM
Valerie Coffman - Mathematical modeling of pronuclear rotation in the nematode C. elegans embryo

In preparation for division, cells must position the nucleus in order to properly segregate chromosomes and other factors. During the first cell cycle of the nematode worm C. elegans, the male and female pronuclei meet at the posterior pole of the embryo, and the entire pronuclear complex migrates to the center of the cell. Simultaneously a 90 degree rotation of the centrosomal axis occurs. Centrosomes serve as microtubule organizing centers for the mitotic spindle during cell division. The microtubule minus-end directed motor protein dynein is essential for correct nuclear positioning and spindle orientation. Due to the symmetric distribution of dynein, at the cortex and in the cytoplasm of the early embryo, it is not clear how the forces required to rotate the pronuclear complex are generated. Previous models have considered length-dependent force on microtubules (MTs) from cytoplasmic dynein, but the cortical dynein has been largely ignored. However, disruption of dynein membrane-localization in HeLa cells and C. elegans affects the spindle position. Although intuitively the elliptical geometry of the embryo should promote orientation of the centrosomal axis along the long axis in the presence of symmetric forces, previous studies indicate geometry alone only orients the spindle after it begins to elongate. Anterior/posterior (A/P) polarity of some dynein regulating factors can explain centration of the pronucleus and centrosomes, but if the net anterior force acts equally on both centrosomes, this polarity will not be sufficient for rotation. My hypothesis is that the pronucleus rotates during translocation due to unequal cortical forces acting on the two centrosomes independent of stochastic microtubule dynamics. The proposed project has three main objectives. The first objective will be to take in vivo measurements of forces on the centrosomes during nuclear centering and rotation using a confocal microscope. The measurements will be taken in embryos dissected out of the adult worm after fertilization and in situ. From these measurements, physical parameters such as torque, angular velocity, acceleration and momentum will be calculated. The second objective will be to use these measurements and calculations to develop mechanical models of the nuclear rotation event. Third, predictions of the model will be tested in vivo using genetic knockdowns and other molecular techniques.

11:30 AM

Shuttle pick-up from MBI

Name Email Affiliation
Afassinou, Komi komia@aims.ac.za School of Mathematics, Statistic and Computer Science, University of KwaZulu-Natal
Agbanusi, Ikemefuna agbanusi@bu.edu Department of Mathematics, Boston University
Albasini Mourao, Marcio Duarte mdam@med.umich.edu Molecular & Integrative Physiology, University of Michigan
Baird, Austin abaird@live.unc.edu Mathemtics, UNC: Chapel Hill
Battista, Christina cbattis2@ncsu.edu Department of Mathematics, North Carolina State University
Boateng, Michael ajenimbkm@yahoo.com mathematics &statistics, youngstown state university
Buchmann, Amy abuchman@nd.edu Applied and Computational Mathematics and Statistics, University of Notre Dame
Caicedo, Angelica caicedaa@mail.uc.edu Mathematical Sciences, University of Cincinnati
Catan, Funda pmxfc3@nottingham.ac.uk School of Mathematical Sciences, University of Nottingham
Chou, Thomas tomchou@ucla.edu Dept. of Biomathematics/Mathematics, UCLA
Coffman, Valerie coffman.147@osu.edu Molecular Genetics, The Ohio State University
Collins, Obiora obioracollins1@gmail.com School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
deForest, Russ russell.f.deforest@gmail.com Mathematics, Pennsylvania State University
Didier, Gustavo gdidier@tulane.edu Mathematics, Tulane University
Donahue, Matthew mdonahu@gmail.com Mathematics, Florida State University
Dovzhenok, Andrey andrey.dovzhenok@uc.edu Mathematical Sciences, University of Cincinnati
Eager, Eric eeager@uwlax.edu Mathematics, University of Wisconsin - La Crosse
Everett, Rebecca rarodger@asu.edu Applied Mathematics, Arizona State University
Fai, Thomas tfai@cims.nyu.edu Mathematics, Courant Institute, New York University
Fauci, Lisa fauci@tulane.edu Mathematics, Tulane University
Fok, Pak-Wing pakwing@udel.edu Mathematical Sciences, University of Delaware
Ford Versypt, Ashlee ashleefv@mit.edu Chemical Engineering, Massachusetts Institute of Technology
Gens, John jgens@indiana.edu Physics, Indiana University
Gong, Xue xg345709@ohio.edu Mathematics, Ohio University
Gonzalez, Laura rgonz@bu.edu Mathematics Department, Boston University
Greene, James jmgreene@math.umd.edu Mathematics, University of Maryland
Gulbudak, Hayriye hgulbudak@ufl.edu Department of Mathematics, University of Florida
Hamlet, Christina chamlet@tulane.edu Mathematics/Center for Computational Science, Tulane University
Huang, Jianjun jhuang3@tulane.edu Mathematics Department, Tulane University
Jacobsen, Karly karlyj@ufl.edu Mathematics, University of Florida
Joshi, Tanvi pmxtj@nottingham.ac.uk School of Mathematical Sciences, University of Nottingham
Josic, Kresimir josic@math.uh.edu Department of Mathematics, University of Houston
Kelly, Michael mkelly14@utk.edu Mathematics, University of Tennessee
Kheibarshekan, Leila lkheibarshekan@gmail.com pharmacy, Universite de Montreal
Kim, Jae Kyoung jaekkim@umich.edu Mathematics,
Kimba Phongi, Eddy kimbaphongi@ukzn.ac.za School of Mathematics, Computer science and Statistic, University of KwaZulu-Natal
Kirst, Christoph ckirst@nld.ds.mpg.de Biology II, Ludwig Maximilians University
Lanz, Aprillya dr.l.lanz@gmail.com Mathematics, Norfolk State University
Lewis, Owen ollewis@math.ucdavis.edu Applied Mathematics Graduate Group, University of California, Davis
Ma, Yanping yma@lmu.edu Mathematics, Loyola Marymount University
Mabuza, Sibusiso smabuza@math.uh.edu Mathematics, University of Houston
Macauley, Matthew macaule@clemson.edu Mathematical Sciences, Clemson University
Magi, Ross magi@math.utah.edu Mathematics, University of Utah
McGee, Reginald mcgee3@purdue.edu Mathematics, Purdue University
Moses, Gregory gm192206@ohio.edu Mathematics, Ohio University
Mubayi, Anuj a-mubayi@neiu.edu Mathematics, Northeastern Illinois University
Murthy, Abhishek amurthy@cs.sunysb.edu Computer Science, Stony Brook University
Neuhauser, Claudia neuha001@umn.edu Biomedical Informatics and Computational Biology, University of Minnesota Rochester
Niu, Xiting xiting@math.uh.edu Mathematics, University of Houston
Norton, Jacob jfnorton@ncsu.edu Biomathematics Graduate Program, North Carolina State University
Numfor, Eric numfor@math.utk.edu Mathematics, University of Tennessee
Oduro, Bismark bo613809@ohio.edu Mathematics, Ohio University
Peace, Angela angela.peace@asu.edu Mathematics and Statistical Sciences, Arizona State University
Robert, Michael mrobert86@gmail.com Mathematics (Biomathematics Graduate Program), North Carolina State University
Rodriguez Martinez, Maria mr2948@columbia.edu Joint Center for Systems Biology, Columbia University
Schreiber, Sebastian sschreiber@ucdavis.edu Department of Evolution and Ecology, University of California, Davis
Sherman, Arthur asherman@nih.gov National Institutes of Health
Simons, Julie jsimons@tulane.edu Mathematics, Tulane University
Sircar, Sarthok sircar1981@gmail.com Applied Mathematics, University of Colorado
Summer, Ilyssa isummer@asu.edu Applied Mathematics, Arizona State University
Tyson, John tyson@vt.edu Computational Cell Biology, Virginia Polytechnic Institute and State University
Wang, Dongyong dongyonw@uci.edu Mathematics, University of California, Irvine
Watts, Margaret margaret.watts@nih.gov Laboratory of Biological Modeling, National Institutes of Health
Williams, Hannah stxhewi@nottingham.ac.uk Mathematics, University of Nottingham
Wrobel, Jacek jacek.k.wrobel@gmail.com Center for Computational Science and Department of Mathematics, Tulane University
Wu, Lani lani.wu@utsouthwestern.edu Green Center for Systems Biology, UT Southwestern Medical Center
Young, Glenn gsy2@pitt.edu Mathematics, University of Pittsburgh
Youngs, Nora s-nyoungs1@math.unl.edu Mathematics, University of Nebraska
Zhang, Tongli tongli.zhang@bioch.ox.ac.uk Biochemistry, University of Oxford
Zhao, Shihai shhzhao@math.uh.edu Mathematics, University of Houston
Zheng, Likun zhen0107@math.umn.edu Department of Mathematics, University of California, Irvine
Dynamics of additional food provided predator-prey system with mutually interfering predators

Use of additional/alternative food source to predators is one of the widely recognized practices in the eld of biological control. Both theoretical and experimental works point out that quality and quantity of additional food play a vital role in the controllability of the pest. Theoretical studies carried out previously in this direction indicate that incorporating mutual interference between predators can stabilize the system. Experimental evidence also point out that mutual interference between predators can affect the outcome of the biological control programs. In this work, dynamics of additional food provided predator-prey system with mutual interference between predators has been studied. The mutual interference between predators is modeled using Beddington-DeAngelis type functional response. A through system analysis highlights the role of mutual interference on the success of biological control programs when predators are provided with additional food. The model results indicate the possibility of stable coexistence of predators with low prey population levels. This is in contrast to classical predator-prey models where in this stable co-existence at low prey population levels are not possible. This study classifies the characteristics of biological control agents and additional food (of suitable quality and quantity), permitting the eco-managers to enhance the success rate of biological control programs.

Mathematical modeling of pronuclear rotation in the nematode C. elegans embryo

In preparation for division, cells must position the nucleus in order to properly segregate chromosomes and other factors. During the first cell cycle of the nematode worm C. elegans, the male and female pronuclei meet at the posterior pole of the embryo, and the entire pronuclear complex migrates to the center of the cell. Simultaneously a 90 degree rotation of the centrosomal axis occurs. Centrosomes serve as microtubule organizing centers for the mitotic spindle during cell division. The microtubule minus-end directed motor protein dynein is essential for correct nuclear positioning and spindle orientation. Due to the symmetric distribution of dynein, at the cortex and in the cytoplasm of the early embryo, it is not clear how the forces required to rotate the pronuclear complex are generated. Previous models have considered length-dependent force on microtubules (MTs) from cytoplasmic dynein, but the cortical dynein has been largely ignored. However, disruption of dynein membrane-localization in HeLa cells and C. elegans affects the spindle position. Although intuitively the elliptical geometry of the embryo should promote orientation of the centrosomal axis along the long axis in the presence of symmetric forces, previous studies indicate geometry alone only orients the spindle after it begins to elongate. Anterior/posterior (A/P) polarity of some dynein regulating factors can explain centration of the pronucleus and centrosomes, but if the net anterior force acts equally on both centrosomes, this polarity will not be sufficient for rotation. My hypothesis is that the pronucleus rotates during translocation due to unequal cortical forces acting on the two centrosomes independent of stochastic microtubule dynamics. The proposed project has three main objectives. The first objective will be to take in vivo measurements of forces on the centrosomes during nuclear centering and rotation using a confocal microscope. The measurements will be taken in embryos dissected out of the adult worm after fertilization and in situ. From these measurements, physical parameters such as torque, angular velocity, acceleration and momentum will be calculated. The second objective will be to use these measurements and calculations to develop mechanical models of the nuclear rotation event. Third, predictions of the model will be tested in vivo using genetic knockdowns and other molecular techniques.

Modeling and Analysis of the Population Dynamics of Fungus-Infected American Chestnut Populations

Density-dependent regulatory factors impact the dynamics of many populations. However, modelers often times only consider one density-dependent factor when constructing nonlinear structured population models, and these factors are often either always increasing or always decreasing with respect to population abundance. In this presentation we will discuss a density-dependent matrix model for populations of the American Chestnut (Castanea dentata), where seedling recruitment is subject to density-dependent feedback from adult conspecifics as well as other potential seedlings. The former exhibits a decreasing relationship while the latter an increasing one. Using methods from systems and control theory we show that, for much of parameter space, there is a unique, globally attracting equilibrium population vector that is independent of initial population vector. We derive a formula for this equilibrium population and show how sensitive each stage of the population is to changes in population data (for example, we show how the equilibrium population changes when the population goes from healthy to diseased). We further show how our results can be extended to integral projection models (IPMs) and numerically explore stochastic versions of this model.

Biofluids

The process of fertilization in mammalian reproduction provides a rich example of fluid-structure interactions. Spermatozoa encounter complex, non-Newtonian fluid environments as they make their way through the cilia-lined, contracting conduits of the female reproductive tract. The beat form realized by the flagellum varies tremendously along this journey due to mechanics and biochemical signaling. We will present recent progress on integrative computational models of pumping and swimming in both Newtonian and complex fluids that capture elements of this complex dynamical system.

A Mathematical Model of Intimal Thickening: an Application to Atherosclerosis

Atherosclerosis is an inflammatory disease of the artery characterized by an expansion of the intimal region. Intimal thickening is usually attributed to the migration of smooth muscle cells (SMCs) from the surrounding media and proliferation of SMCs already present in the intima. Intimal expansion can give rise to dangerous events such as stenosis (leading to stroke) or plaque rupture (leading to myocardial infarction). We propose and study a mathematical model of intimal thickening, posed as a free boundary problem. Intimal thickening is driven by damage to the endothelium, resulting in the release of cytokines and migration of SMCs. By coupling a boundary value problem for cytokine concentration to an evolution law for the intimal area, we reduce the problem to a single nonlinear differential equation for the luminal radius. We analyze the steady states, perform a bifurcation analysis and compare model solutions to data from rabbits whose iliac arteries are subject to a balloon pullback injury. In order to obtain a favorable fit, we find that migrating SMCs must enter the intima very slowly compared to cells in dermal wounds. This cell behavior is indicative of a weak inflammatory response which is consistent with atherosclerosis being a chronic inflammatory disease.

Mathematical Modeling of Pharmaceuticals: Predictive Design for Better Medicines

Smart designs of drug molecules and pharmaceutical formulations can target treatments to specific tissues, reduce side effects, and improve patient quality of care.Computational models for evaluating pharmaceutical formulations can narrow the range of experiments needed to identify successful designs by predicting performance and thus reducing the development time and driving down costs. Models coupled with sophisticated process control strategies allow for careful monitoring of manufacturing to reduce wasted materials and energy and to adhere to quality standards. I will overview mathematical modeling efforts in several pharmaceutical domains and will highlight work related to predicting drug release from controlled-release formulations that administer medicine over extended periods with a single dosage. I will show how coupled, nonlinear partial differential equations can be used to capture the complex dynamic interactions between simultaneous chemical reactions and mass transfer. I will describe mathematical techniques that can be used to reduce the system size from thousands of equations to just a few while retaining resolution of the biodegradation of the pharmaceutical formulation that strongly influences the drug release dynamics. These techniques can aid in the design of new controlledrelease formulations.

How good are mathematical models of genetic signaling networks

Synthetic biology holds the promise of allowing us to engineer living beings. I will start by reviewing some examples where mathematical models lead to the development of synthetic organisms with particular properties: One such example is a synthetic gene oscillator in Escherichia coli that exhibits robust temperature compensation -- it maintains a constant period over a range of ambient temperatures. A mathematical model predicted and experiments confirmed the particular mechanisms that lead to temperature compensation despite Arrhenius scaling of the biochemical reaction rates.

Such successes are encouraging. But how far can our theoretical models take us? I will argue that our models are still fairly coarse, and do not adequately describe all the important properties of genetic signaling networks. For instance, "transcriptional delay" - the delay between the start of protein production and the time a mature protein finds a downstream target - can have a significant impact on the dynamics of gene circuits. Such delay can inhibit transitions between states of bistable genetic networks, as well as destabilize steady states in other networks. I will show how these effects can be described by reduced, non-Markovian models that are quite different from established models. I will also discuss work with experimental collaborators to characterize the distribution of this delay.

The Effect of MicroRNA-Mediated Feedforward Loops on Gene Regulatory Networks

The concept of canalization in gene regulation was developed as a possible solution to the question of why the outcome of embryonal development leads to predictable phenotypes in the face of widely varying environmental conditions. The key step of gene expression is fundamentally a stochastic process, which makes the stability of genetic regulation programs all the more surprising. An entirely novel gene regulatory mechanism, discovered and studied during the last decade, which is believed to play an important role in cancer, is shedding some light on how canalization may in fact take place as part of a cell's gene regulatory program. Short segments of single-stranded RNA, so-called microRNAs, which are embedded in several different types of feedforward loops, help smooth out noise and generate canalizing effects in gene regulation by overriding the effect of certain genes on others.

In a computational study, we used the modeling framework of generalized Boolean networks to explore the role that microRNA-mediated feedforward loops play in stabilizing the global dynamics of various gene regulatory networks. We compared the degree of stochasticity of a basic gene network and an extended network, in which various numbers of microRNAs have been introduced in a biologically inspired way, and were thereby able to exactly quantify the stabilizing effect for any gene regulatory network.

Thus, this research contributed to an answer of the question:to what extent do microRNAs stabilize gene regulatory programs?

Optimal fishery harvesting on a nonlinear parabolic PDE in a heterogeneous spatial domain

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is our marine fish population. The overexploitation of fisheries has called for an improved understanding of spatiotemporal dynamics of resource stocks as well as their harvesters. There is pressure to find methods for optimally solving these management problems. One way to protect fish populations from overexploitation is the inclusion of no-take marine reserves, which prohibit the removal of natural resources from an area of the ocean. There has been previous work done on this subject, which sought after yield maximizing strategies without imposing these no-take reserves into the model. All previous work done included Dirichlet boundary conditions, representing a lethal domain boundary. The question of whether the implementation of alternative boundary conditions, deemed more favorable to the fish stock, on a heterogeneous domain could produce an alternative optimal harvesting strategy. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no-take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.

Asynchronousity in Boolean networks

A Boolean network consists of a finite set of nodes, each taking a Boolean state, and each having an update function depending on a subset of the other states. These functions are assembled to get the dynamical system map which is iterated to generate the dynamics. The common synchronous function update is convenient but often biologically unnatural. In contrast, asynchronousity poses questions about stability and robustness with respect to update order. In this talk, I will introduce toric posets which can be thought of as a cyclic version of ordinary posets and provide a clean combinatorial framework for describing asynchronousity in Boolean networks.

Modeling Swarms and Measuring Information Storage and TransferA Mathematical Model for Optimally Allocating Insecticides for Controlling Visceral Leishmaniasisin Bihar, India

Leishmaniasis is a family of infectious diseases that affect poor and developing countries. The Indian state of Bihar has the highest prevalence and mortality rates of visceral leishmaniasis (VL) in the world. Although insecticide spraying is a primary vector control method in many parts of the world for controlling spread of VL, in Bihar a simple approach is adopted for allocating of insecticides per district. This study proposes a novel optimization model to identify the optimal allocation and choice of insecticides (comparing DDT and Deltamethrin, as an example) across both the human and the cattle populations. The model optimizes the insecticide-induced death rate caused by spraying of human and bovine populations dwellings within the constraint of limited financial resources available. The results suggest that DDT yields more than four times the insect death rate achieved by Deltamethrin until ninety days after spray. The results also verify the present practice of first spraying houses to optimize sandfly mortality ahead of spraying cattle sites.

A statistical approach for detecting copy number variations for next generation sequencing data

DNA copy number variation (CNV) is a genetic signature for complex diseases such as cancer. High-throughput sequencing technologies combined with efficient mapping algorithms enable fast detection of CNVs. To ascertain statistical significance of candidates, a mathematical model for the distribution of mapped read counts together with a statistical procedure is proposed. The model assumes that reads are mapped to a reference genome. Mapped reads are counted in consecutive windows, and the read counts are assumed to form an m-dependent, strictly stationary stochastic process and are Poisson distributed with a parameter that varies across the genome. This variation is modeled with a gamma distribution. The model is validated using genome data from four genomes that are presumed to lack CNVs. The test is based on extremes of the number of mapped reads in consecutive windows, and thus avoids the problem of multiple hypothesis testing.

A stoichiometric producer-grazer model incorporating the effects of excess food-nutrient content on consumer dynamics

There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. For example, modeling under this framework allows food quality to affect consumer dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insuffcient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon is known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, and needs to be incorporated into mathematical models. Here we present a Lotka-Volterra type model to investigate the growth response of Daphnia to algae of varying P:C ratios capturing the mechanism of the stoichiometric knife edge.

Optimal control of female-killing strategies to eliminate the dengue vector, Aedes aegypti

Dengue fever is spread primarily by Aedes aegypti mosquitoes. Although traditional control mea- sures have been implemented for many years, dengue remains endemic in many parts of the world. Recently, control strategies involving the release of genetically modi ed mosquitoes have been proposed. Among those for Ae. aegypti that have seen the most progress are Female-Killing (FK) strategies. Cage experiments showed that repeated introductions of individuals from one FK strain of Ae. aegypti led to either reduction or extinction of caged wild-type populations. Any future open releases should be conducted according to plans that consider temporal and nancial constraints. We develop an optimal control model to assess the role that such constraints will play in conducting FK releases. Through numerical simulation, we obtain optimal release strategies for a variety of scenarios and assess the feasibility of integrating FK releases with other forms of vector control.

Population persistence in the face of uncertainty

One of the most fundamental question in population biology is what conditions ensure the long-term persistence of interacting populations?'' Ever since the foundational work of Lotka and Volterra, Nicholson and Bailey, and Kermack and McKendrick, this question has been tackled using deterministic difference and differential equations. However, all population experience demographic and environmental stochasticity. Hence, we must confront the question of what does persistence mean in the face of these uncertainties?'' The goal of this talk is to provide two recent perspectives on this question. The first part of this talk considers demographic stochasticity due to populations consisting of finite number of individuals. Stochastic models, such as finite state Markov chains, accounting for this stochasticity typically predict extinction of all populations in finite time. However, these extinction events may be preceded by long-term transients characterized by the quasi-stationary distributions of the stochastic process. In collaboration with Mathieu Faure, we have shown that these quasi-stationary distributions concentrate on attractors of an appropriate deterministic difference equation. Hence, this work provides a justification for using deterministic models to study long-term persistence. The second part of this talk considers environmental stochasticity where fluctuations in environmental conditions (e.g. temperature, precipitation) cause fluctuations in vital rates of populations. Persistence for stochastic models, such as difference equations with stochastically varying parameters, can be equated a statistical tendency for populations to remain bounded away from extinction. In collaboration with Gregory Roth, we have shown that there is a sufficient condition for stochastic persistence in terms of the population growth rates when rate. This condition naturally extends the permanence condition of Josef Hofbauer for deterministic models. In both parts of the talk, I will illustrate and motivate the theory with empirical results and applications to metapopulations and competing species.

Bistability of Beta Cell Mass in Diabetes

Insulin is the master hormone that controls fuel usage by body tissues. After a meal, glucose is plentiful and stimulates insulin secretion, which allows muscle and fat to take up glucose. When blood glucose falls, insulin falls as well and tissues revert to using fat as a fuel. Obesity causes insulin resistance, meaning that more insulin is needed to produce a given amount of glucose uptake. If the number of insulin-secreting pancreatic beta cells, or secretion per cell, increases sufficiently, this excess demand for insulin can be met. If expansion of mass is inadequate, type 2 diabetes, a rise in glucose to levels that are harmful to cells, results. Diabetes leads to cardiovascular disease, blindness, kidney failure and premature death. We update the seminal model of Topp et al (J. Theor. Biol. 2001) for the regulation of beta-cell mass by glucose and present a comprehensive picture of how diabetes develops and may either be avoided or reversed. Although many details of the model are in doubt, we show that any successful model results in a bistable bifurcation structure, with normal and elevated glucose levels separated by a threshold. This simple picture unifies and explains a striking diversity of experimental data, including why prevention is much easier than cure and why bariatric surgery is able to reverse longstanding diabetes within a week.

Mathematical Models of Cell Cycle Progression

Progression through the eukaryotic cell cycle is controlled at a series of checkpoints guarding transitions from one phase of the cycle to the next, e.g., G1-to-S, G2-to-M, metaphase-to-anaphase. These checkpoints ensure that a cell has satisfied certain requirements that are necessary for success of the next phase, e.g., that any DNA damage is repaired before the cell replicates its chromosomes in S phase. These transitions are irreversible: as soon as the conditions of the checkpoint are satisfied, the cell proceeds to the next phase and does not subsequently back up to the immediately preceding phase. The irreversibility of these transitions gives the cell cycle its directionality (G1 Ã¢â€ â€™ S Ã¢â€ â€™ G2 Ã¢â€ â€™ M Ã¢â€ â€™ G1 ...). The genes and proteins governing these checkpoints have been discovered by molecular geneticists, but the mechanistic basis of irreversibility is still a subject of controversy. Many molecular biologists think that the transitions are irreversible because key proteins are chemically degraded at each transition, but we maintain that irreversibility is a consequence of bistability and hysteresis in the underlying regulatory network. To prove this claim, JJT will describe the mechanism of the G1-S transition in some detail, build and analyze a mathematical model of the mechanism, and compare the implications of the model to experimental facts.

Reverse engineering neutrophil polarity network

A central question in biology is how complex, spatial-temporal cellular behaviors arise from biochemical networks. Much work has led to the identification and cataloguing of various network architectures, and the explication of how static network motifs can give rise to dynamic response characteristics, including ultrasensitive, switch-like, and oscillatory behaviors. However, the wiring diagrams of signaling networks are often inferred by combining results from diverse assays. Such diagrams may not represent accurately the operating state of the network in any cell, condition or time point. In this talk, we will discuss recent progress in using perturbation analysis and cellular heterogeneity to constrain network crosstalk from cellular behaviors.

Bistability of Beta Cell Mass in Diabetes

Progression through the eukaryotic cell cycle is controlled at a series of checkpoints guarding transitions from one phase of the cycle to the next, e.g., G1-to-S, G2-to-M, metaphase-to-anaphase. These checkpoints ensure that a cell has sati

Biofluids
Lisa Fauci

The process of fertilization in mammalian reproduction provides a rich example of fluid-structure interactions. Spermatozoa encounter complex, non-Newtonian fluid environments as they make their way through the cilia-lined, contracting condu

Synthetic biology holds the promise of allowing us to engineer living beings. I will start by reviewing some examples where mathematical models lead to the development of synthetic organisms with particular properties: One such example is a

Bistability of Beta Cell Mass in Diabetes
Arthur Sherman

Insulin is the master hormone that controls fuel usage by body tissues. After a meal, glucose is plentiful and stimulates insulin secretion, which allows muscle and fat to take up glucose. When blood glucose falls, insulin falls as well and

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