MBI Summit on the Rules of Life

Oksana Chkrebtii:
Bayesian Hierarchical Modeling in Systems Biology and Epidemiology 

The Bayesian paradigm is a framework for quantifying evidence by modeling and updating our beliefs about a complex system conditional on observations. Bayesian hierarchical modeling (BHM) can be an efficient way to link multiple mechanistic models with data from different sources and of different types. Through examples from systems biology and epidemiology, I will describe specific challenges in these fields that can be cohesively addressed with the use of BHMs. Specifically, I will discuss data quantity and quality issues, model identifiability, and various challenges with fitting dynamical systems.

Breschine Cummins:
DSGRN: Dynamic Software for Network Discovery
Video

The mathematical field of dynamical systems plays a crucial role in describing the behavior of a cellular or genetic regulatory network over time. Traditional dynamical systems studies concentrate on trajectories and invariant sets as the primary approaches to network analysis. We present a new angle on dynamical systems that instead focuses on a robust, scalable and computable description of dynamics in terms of graphs and partially ordered sets (posets). A poset represents a “dynamic signature” of the network that is constant over a large region of parameter space. The number of such parameter regions is finite, leading to a global description of the dynamics across high dimensional parameter space. Our software tool Dynamic Signatures Generated by Regulatory Networks (DSGRN) ingests a regulatory network and produces the posets representing network dynamics over all of parameter space. The dynamic signatures generated by DSGRN can be used to answer questions about regulatory network performance in the context of network discovery, as well as other goals such as network design in synthetic biology and diagnosis of misbehavior. I will briefly overview the graphical approach of DSGRN and then discuss the role of DSGRN in a pipeline for network discovery using a case study of time series data measured in vitro from the malaria parasite P. falciparum.

Cassandra Extavour:
Cell Competition: How Should it Impact Our Understanding of Evolution?

The process of evolution by natural selection is often thought of as taking place at the level of adult organisms. Competition between organisms for food, mates or habitats, and the benefits and costs of traits relevant to such competition, are examples of phenomena where differential fitness is often considered. We recognize, however, that “differential fitness,” broadly speaking, can be manifest not only at the organismal level, but also at other levels of biological organization, including organ systems, cells, organelles and genes. Here we consider the phenomenon of cell competition, defined as a phenomenon whereby less-fit cells are eliminated from a tissue when faced with more-fit cells. Once considered an unusual or irrelevant process, cell competition has now been documented in a wide variety of cell types and organisms, including prokaryotes and eukaryotes, and in context including embryonic development, post-embryonic homeostasis, and disease. We introduce a number of examples of experimental demonstration of such competition in both somatic and germ line cells. We discuss the possible evolutionary implications of somatic and germ line competition in developing and in fully formed, functioning adult tissues, and propose a number of areas where further experimental and theoretical work will be needed to predict whether and how cell competition impacts the evolutionary process.

Marty Golubitsky:
Mathematical Homeostasis Motivated by Nijhout, Reed, and Best

We say that an input-output map xo(I) has infinitesimal homeostasis at I0 if x′o(I0) = 0. A consequence of infinitesimal homeostasis is that xo(I) is approximately constant on a neighborhood of I0.
An input-output network is a network that has a designated input node , a designated output node o, and a set of regulatory nodes = (i, . . . , n). We assume that the system of network differential equations ˙X = F(X, I) has a stable equilibrium at X0. The implicit function theorem implies that there exists a family of equilibria X(I) = (x(I), x(I), xo(I)), where xo(I) is the network input-output map.
We use the network architecture of input-output networks to classify infinitesimal homeostasis into three types: structural homeostasis, Haldane homeostasis, and appendage homeostasis. The first two types generalize feedforward excitation and substrate inhibition. The third type appears to be a new form of homeostasis.
This research is a joint project with Yangyang Wang, Ian Stewart, Joe Huang, and Fernando Antoneli.

Marcella Gomez:
In Search of General Design Principles for Collective Behavior
Video

The first wave of systems and synthetic biology has provided general network design principles that lead to robust dynamic behavior seen in nature such as adaptation, oscillations, and bi-stability.  The next frontier in this respect is finding general design principles for collective behavior of systems such as single-strain colonies with cell-to-cell communication or even multi-cellular systems. Mapping single-cell dynamics to collective behavior is not a trivial task. Some of the most well-known work includes theory developed by A. Turing for architectures leading to pattern formation. Here, I discuss a different mechanism, unique from Turing, that leads to similar patterning based on the well-known toggle switch architecture and associated properties.

Jeremy Gunawardena:
Following the Energy: the Hopfield Barrier as an Organising Principle
Video

Hopfield's classic paper on kinetic proofreading conceals an important observation. If a biochemical system implementing a given information processing task is operating at thermodynamic equilibrium, there is an upper limit to how well it can perform that task; the only way to exceed this limit is to maintain the system away from equilibrium by expending energy. We call the limit the Hopfield barrier for the task in question. We will discuss some examples and suggest that identifying Hopfield barriers for the various tasks which biological cells undertake offers a systematic way to rise above molecular complexity and discern the underlying Rules of Life.

Christopher Kuzawa:
The Energetic Constraints of Building a Costly Brain: Implications for the Evolution of Human Childhood and the Developmental Origins of Obesity
Video

Many adults who are overweight were already overweight as children.  What accounts for who gains excess weight early in life and who, as a result, is at increased risk for becoming an overweight or obese adult?  In my talk I will present our recent work that shows that the brain accounts for a lifetime peak of 66% of the body’s resting metabolic expenditure at 4-5 years of age, and that there is a strong inverse relationship between developmental changes in brain energetics and the rate of body weight gain between infancy and puberty. The peak in brain developmental energetics traces to synaptic and other energetically costly processes related to neuronal plasticity and learning, and requires compensatory reductions in other expenditures like body growth.  In the second half of my talk, I will review evidence linking brain energetics with overweight and obesity during childhood, and argue that variation in the timing and intensity of the brain energetics peak could help explain the well-documented finding of an inverse relationship between the BMI and cognitive function.  This framework could also help explain emerging evidence for genetically-mediated trade-offs (pleiotropy) between cognitive development and body fat gain.  In closing, I argue that educational interventions that harness plasticity in these traits, and increase the peak or duration of brain developmental energetics, could lower obesity risk by increasing the brain’s energy needs and the strength of energetic trade-offs with fat deposition.

Bruce Levin:
CRISPR-Cas: Better as a Tool for Molecular Biologists than for Protecting Bacteria from the Ravages of infections with Virulent Viruses

To some arguably, but surely to those who study it or use it as a tool for genome editing and manipulation, CRISPR-Cas has been the single most significant advance in molecular biology and biotechnology this millennium. It is commonly assumed that this “adaptive immune system” evolved and is maintained as a mechanism to protect bacteria against infections with virulent bacteriophage and other deleterious DNAs. In support of this hypothesis (conventional wisdom?) are retrospective DNA sequence data; nestled between the palindromic repeats of the CRISPRCas regions of bacteria and archaea are the 30 or so base pair sequences of DNA, spacers, homologous to the DNA of phage and plasmids. Also consistent with this hypothesis, are the results of in vitro experiments demonstrating that when bacteria with functional CRISPR-Cas systems acquire (or are provided with) spacers, they can prevent the cells from being killed by infections with lytic phage or the establishment of plasmids bearing DNA homologous to those spacers. Included among the observations which are inconsistent with the hypothesis that CRISPR-Cas commonly plays this protective role in natural populations of bacteria and virulent phage are the (i) abundance of species and strains of bacteria that do not have functional CRISPR-Cas systems, (ii) existence of phage with anti-CRISPR systems, (iii) ease with which these systems are lost when not selected for, and (iv) dearth of truly lytic (rather than modified temperate) phage that can provide spacers to bacteria with functional CRISPR-Cas systems. Also inconsistent with this hypothesis are results of (i) a mathematical – computer simulation modeling study of the population and evolutionary dynamics of bacteria with envelope resistance as well a CRISPR-Cas immunity, and (ii) the short term that phage that can provide spacers are maintained in experimental populations of spacer-providing phage and bacteria with functional CRISPR-Cas systems. --- Based on these observations, model-based predictions and experimental results, we postulate that in natural populations of bacteria and phage, the utility of CRISPR-Cas immunity for protection against lytic phage is transient and restricted to relatively avirulent lytic phages. When confronted with these phages, CRISPR-Cas will be selected for and evolve to protect the bacterial population until the phage are eliminated (or are maintained but no longer provide new spacers), at which time because of auto-immunity and/or other costs, this adaptive immune system will be selected against and/or become non-functional or lost. When these now CRISPRCas negative populations of bacteria are again confronted with lytic phage that can provide spacers, by repairing their existing CRISPR-Cas system or acquiring new systems by horizontal transfer, CRISPR-Cas will once again do it’s short-term protection thing. In this interpretation, the spacers with phage-homologous DNA that are considered evidence for CRISPR-Cas serving as an adaptive immune system are more likely to reflect past encounters with phage than this system protecting extant populations of these bacteria from phage infection. In this talk I will suggest, and hopefully stimulate discussion, about how the conditions for the operation of this transient protection hypothesis can be addressed with mathematical and computer simulation models and tested experimentally.

Armin Moczek:
On the Origins of Novelty and Diversity in Development and Evolution: Case Studies on Horned Beetles

The origin of novel traits is among the most intriguing and enduring problems in evolutionary biology. It is intriguing because it lies at the heart of what motivates much of evolutionary biology: to understand the origins of exquisite adaptations and the evolutionary transitions and ecological radiations that they enabled. It is enduring because it embodies a fundamental paradox. On the one hand, Darwin's theory of evolution is based on descent with modification wherein everything new, ultimately, must come from the old. On the other hand, biologists are captivated by complex novel traits precisely because they lack obvious homology to pre­existing traits. How, then, does novelty arise from within the confines of ancestral variation?

Combining approaches from evolutionary developmental genetics, behavioral ecology, and microbiology my research explores the genetic, developmental, and behavioral mechanisms, and the interactions among them, that promote innovation and diversification in the natural world. Most of the work in my research group focuses on the inordinately diverse and bizarre horns of scarab beetles, while side projects have explored the origins of light-­producing organs in fireflies as well as the exuberant helmets of treehoppers. In my talk I will first present recent results on the role of developmental repurposing in the evolution of novel morphological traits and developmental functions. In the second half I will discuss the significance of host microbiome interactions and environment­-engineering in the origins of novelty, when collectives innovate, adapt and problem-­solve in ways single species cannot. Throughout my talk I use our findings to highlight where I believe they expand and revise our current understanding of the genesis of novelty in evolution.

David Murrugarra:
Frequent Regulatory Rules in Molecular Interaction Networks
Video

Understanding the regulatory mechanisms in molecular interaction networks is an important goal in systems biology. This talk will focus on processes at the molecular level that determine the state of an individual cell, involving signaling or cell regulation. The mathematical framework to be used is that of Boolean networks and their multi-state generalization. These models represent the interactions of different molecular species as logical rules that describe how these species combine to regulate others. Regulatory rules that appear in published models tend to have special features such as the property of being nested canalizing, a concept inspired by the concept of canalization in evolutionary biology. This talk will survey a set of results about nested canalizing rules and how these constrain network dynamics. It has been shown that networks comprised of nested canalizing functions have dynamic properties that make them suitable for modeling gene regulatory networks, namely small number of attractors and short limit cycles. In this talk, I will discuss a normal form as polynomial function that applies to any Boolean or multi-state function. This description provides a partition of the inputs of any Boolean function or multi-state function into canalizing and non-canalizing variables and, within the canalizing ones, we can categorize the input variables into layers of canalization. I will also describe the structure of the non-canalizing variables. Applications for how to use this normal form and some other properties of these functions will be given at the end of the talk.

Randolph Nesse:
Intrinsically Vulnerable Organic Systems
Video

Natural selection shapes living systems to such remarkable efficacy and robustness that disease vulnerability is usually and correctly attributed to the limits of natural selection. Mutation, migration, genetic drift, path dependence and the slow pace of evolution are important explanations for disease vulnerability. Some systems are, however, intrinsically vulnerable to failure for other reasons. The role of tradeoffs is well-recognized, but it may have wider applications than is often appreciated. For instance, antagonistic pleiotropy provides benefits early in life that maximize reproduction at the cost of a shorter life span. Systems that regulate defenses such as immune responses and anxiety are expected to generate false alarms because the costs of not responding are far higher than the costs of a false alarm. Some such systems become more responsive after repeated arousal, making them inherently vulnerable to runaway positive feedback, as may be illustrated by panic disorder and cytokine storm. Traits with cliff-edged fitness functions are especially vulnerable to failure. Strong selection on a trait vulnerable to catastrophic failure, such as racehorse bones, is an example. Even in the absence of strong recent selection, such traits are likely to be vulnerable because natural selection shapes them to a mean value that maximizes multigenerational gene transmission despite the associated increase in the proportion of population with low fitness. Pathogen pressure is likely to also shape fitness functions with steep slopes. Higher telomerase activity and numbers of stem cells provide advantageous tissue repair but increases the risk of cancer. Uric acid concentrations give increasing antioxidant benefits until crystals form and cause gout. The high heritability of many diseases is turning out to arise from the tiny effects of many alleles spread across the entire genome. Some are deleterious mutations subject to mutation selection balance, but some may be maintained because they influence the level of a trait with a cliff-edged fitness function. Disorders that can be considered in this light include epilepsy, atrial fibrillation, migraine headaches, and schizophrenia.

Fred Nijhout:
Causes and Consequences of Robustness and Plasticity in Biological Systems: Two Sides of the Same Coin
Video

Two universal Rules of Life are that all organisms are subject to variable environments, and all are also subject to continuous mutations in genes that are important for normal function and survival. Organisms have evolved a variety of mechanisms that buffer form and function against deleterious environmental and genetic variables. These are collectively called homeostatic and robustness mechanisms, which stabilize the phenotype, so that the same phenotype is produced in spite of genetic and environmental variation. Insofar as natural selection acts only on phenotypes, but heritable change comes from genotypes, it has been thought that robustness mechanisms produce a constraint on evolution by decoupling phenotype form genotype. An apparently contradictory fact is that many organisms have a variable phenotype that depends on environmental conditions. This is called plasticity, and produces different phenotypes from the same genotype. Plasticity, therefore, also seems to uncouple phenotype and genotype. Plasticity, like robustness, can be an adaptation to a variable environment. Using conceptual and mathematical models, I will discuss a diversity of mechanisms that produce robustness and plasticity and show they are closely related. I will also discuss why such mechanisms, rather than constraining evolution, actually enable rapid evolution.

Karl Niklas:
Polarity, Planes of Cell Division, and the Evolution of Multicellularity
Video

Organisms as diverse as bacteria, fungi, plants, and animals manifest a property called “polarity.” The literature shows that polarity emerges as a consequence of different mechanisms in different lineages. However, across all unicellular and multicellular organisms, polarity is evident when cells, organs, or organisms manifest one or more of the following: orientation, axiation, and asymmetry. I will review the relationships among these three features in the context of cell division and the evolution of multicellular polarity primarily in plants (defined here to include the algae). Data from unicellular and unbranched filamentous organisms (e.g., Chlamydomonas and Ulothrix) show that cell orientation and axiation are marked by cytoplasmic asymmetries. Branched filamentous organisms (e.g., Cladophora and moss protonema) require an orthogonal reorientation of axiation, or a localized cell asymmetry (e.g., “tip” growth in pollen tubes and fungal hyphae). The evolution of complex multicellular meristematic polarity required a third reorientation of axiation. These transitions show that polarity and the orientation of the future plane(s) of cell division are dyadic dynamical patterning modules that were critical for multicellular eukaryotic organisms.

John Tyson:
Information Processing in Living Organisms: What Does Bifurcation Theory Teach Us?
Video

One of the basic characteristics of living organisms is their ability to process information about their external environment and internal state and to implement adaptive responses to the challenges they face. At the cellular level, these information processing tasks are carried out by complex networks of interacting genes and proteins; quite differently than the information processing done by digital computers or (analog) central nervous systems. Despite the triumphs of molecular biologists over the past 40 years in identifying and characterizing the components of these networks, their information-processing capabilities are still largely mysterious. Is there a basic theory of information-processing by molecular reaction networks that is biochemically realistic, reasonably accurate and comprehensive, and of predictive value? I will make the case that bifurcation theory of dynamical systems provides a framework for thinking about this problem. Briefly put, a one-parameter bifurcation diagram (dynamical variable as a function of control parameter) is the mathematical analog of the physiologist’s “signal-response” curve; and a two-parameter bifurcation diagram (e.g., physiological control parameter versus level of gene expression) can provide insight into the translation from genotype to phenotype. I will illustrate these principles with a number of classic examples from the field of network dynamics and cell physiology, and I will relate this particular problem to broader considerations of the “Rules of Life”.

Lina Aboulmouna:
Application of Cybernetic Control Variables in the Modeling of Lipid Metabolism in Mammalian Systems

Amir Asiaee T:
Explaining Gene Expression Using Twenty-One MicroRNA

MicroRNAs are small non-coding RNAs that regulate gene expression. Many miRNAs have been implicated in the development of cancers. To better understand the relationship between miRNAs and cancer, we used data on 32 cancer types collected from the TCGA. We then used Thresher to cluster the miRNAs. We then fit linear models to predict the expression of individual mRNA genes using the average expression of the miRNA clusters. Using the clusters, we can explain a significant portion of gene expression.

Veronica Ciocanel:
Topological Data Analysis for Biological Ring Channels

Contractile rings are cellular structures made of actin filaments that are important in development, wound healing, and cell division. In the reproductive system of the worm C. elegans, ring channels allow nutrient exchange between developing egg cells and the worm and are regulated by forces exerted by myosin motor proteins. In this poster, I present an agent-based modeling and data analysis framework for understanding the interactions between actin filaments and motor proteins inside cells. This approach provides key insights for the mechanistic differences between two motors that are believed to maintain the rings at a constant diameter. We use tools from topological data analysis to analyze time-series data for ring channel formation and maintenance. Our proposed visualization methods clearly reveal the impact of certain simulation parameters on significant ring formation.

Gheorghe Craciun:
Mathematical Models of Biochemical Systems

Keith Farnsworth:
What is Life?

If we can define life, we can identify the laws which determine its repertoire of behaviours and the constraints that determine its necessary and sufficient conditions. Efforts based on comparative analysis, then on chemistry, have failed to precisely capture it. The Santiago school, defining life as autopoiesis and Shrödinger’s insight that information is central, are brought together here in a more elaborated theory of life as information processing, with the important additions that a) all life includes at least one causal loop with a set-point from which homeostasis emerges and b) it must act as an engine.

Feng Fu:
Social Learning of Prescribing Behavior Can Promote Population Optimum of Antibiotic Use

Punit Gandhi:
Water Transport in Models of Dryland Vegetation Patterns

Reaction-advection-diffusion models that capture the interactions between plants, surface water and soil moisture can qualitatively reproduce community-scale vegetation patterns that are observed in dryland ecosystems. On gently sloped terrain, these patterns often appear as bands of vegetation growth alternating with bare soil. The vegetation bands can be tens of meters thick with spacing on the order of a hundred meters, and form a regular striped pattern that often occupy tens of square kilometers on the landscape. I will focus on aspects of the surface/subsurface water dynamics within these models. Capturing these hydrological processes on appropriate timescales may allow us to better utilize observational data as we work to identify the dominant mechanisms underlying the formation of dryland vegetation patterns and understand how environmental factors influence pattern characteristics.

David Gurarie:
Immune Selection and Evolution of Multi-Strain Malaria Quasi-Species

Gregg Hartvigsen:
Engaging Undergraduates in Modeling Biological Systems

Jinsu Kim:
Stationary Distributions for Stochastically Modeled Reaction Networks : Existence and Estimation

Colin Klaus:
The Ca2+ Dependent Elasticity of Tip Link Cadherins in Hearing: Interfacing MD Measured Forces with Cl assical Mechanics Models

Carlos Mariscal:
There are at Least Three Ways to Universalize Biology and They are Not Equivalent

Pedro Marquez Zacarias:
Symmetry Breaking and the Origins of Primitive Multicellular Morphology

Sarah Marzen:
An Information-Theoretic View of Sensory Processing: The Costs and Benefits of More Information

Hong Qin:
A Probabilistic Gene Network Model for Cellular Aging and its Applications

Why would a genotypically homogeneous population of cells live to different ages? We propose a mathematical model of cellular aging based on gene interaction network.  This model network is made of only non-aging components, and interactions among genes are inherently stochastic. Death of a cell occurs in the model when an essential gene loses all of its interactions. The key characteristic of aging, the exponential increase of mortality rate over time, can arise from this model network with non-aging components. Hence, cellular aging is an emergent property of this model network. The model predicts that the rate of aging, defined by the Gompertz coefficient, is proportional to the number of active interactions per gene and that stochastic heterogeneity is an important factor in shaping the dynamics of the aging process. Hence, the Gompertz parameter is a proxy of network robustness. Preliminary studies on how aging is influenced by power-law configuration, synthetic lethal interaction, and allelic interactions can be modeled. A general framework to study network aging as a quantitative trait has also been found, and the results has implication on missing heritability. Preprint for the basic model is available at http://arxiv.org/abs/1305.5784.

Ivan Ramirez Zuniga:
A Data-driven Mathematical Study of the Role of Energy in Sepsis

When pathogens enter the human body a chain of immune reactions occur to eliminate the invader. However, in some cases the initial response may escalate into an overwhelming systemic inflammation. Such overreaction of the immune system is called sepsis and it can lead to tissue damage, organ failure, and possibly death. Experimental studies have found an association between severe infections and depletion in levels of adenosine triphosphate (ATP), suggesting that tissue energetics is compromised. In this work, we extend a previous model of the acute inflammatory response that includes energy consumption. The extended model is calibrated by fitting animal data from a study done in thirty-three baboons of the species Papio ursinus. Using Bayesian analysis, in particular, a delayed rejection adaptive metropolis (DRAM) algorithm, we quantify uncertainty in identifiable model parameters to investigate differences across survivors and non survivors.

Marissa Renardy:
Evaluating Vaccination Strategies for Tuberculosis in Endemic and Non-Endemic Settings

Omar Saucedo:
Human Movement and Vector-Borne Diseases

Vector-borne diseases affects approximately 1 billion people and accounts for 17% of all infectious diseases. With travel becoming more frequent across the world, it is important to understand how spatial dynamics impact the spread of the disease.  Human movement plays a key part on how a disease can be distributed as it enables a pathogen to invade a new environment, and helps the persistence of a disease in locations that would otherwise be isolated.  In this project, we explore how spatial heterogeneity combines with mobility network structure to influence vector-borne disease dynamics.  In addition, we will derive an approximation for the basic reproduction number for a n-patch ODE system using a Laurent series expansion, and construct sensitivity equations to determine which parameters should be targeted for intervention strategies.

Anastasios Stefanou:
Reeb Graphs are Fixed Betti Tractable

Inspired by the interval decomposition of persistence modules and the extended Newick format of phylogenetic networks, using category theory, we show that every Reeb graph with n leaves and first Betti number, s, decomposes into a coproduct of at most 2^s trees with (n + s) leaves. Reeb graphs are therefore classified up to isomorphism by their tree decomposition. An implication of this result, is that Reeb graphs are fixed parameter tractable when the parameter is the first Betti number.

Ivan Sudakov:
The Influence of Environmental Forcing and Feedback on Extinction in a Competing Population

The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such models to provide quantitative formalization of changes to Earth’s biosphere. Here, we propose and study a conceptual resource model that describes a simple and easily understandable mechanism for resource competition, generalizes the well-known Huisman and Weissing model (1999), and takes into account species self-regulation, extinctions, and time dependence of resources. We use analytical investigations and numerical simulations to study the dynamics of our model under chaotic and periodic climate variability, and show that the stochastic dynamics of our model exhibit strong dependence on initial parameters. This model is apparently the first of its kind to include a feedback mechanism coupling climate and population dynamics. We also demonstrate that extinctions in our model are inevitable if an ecosystem has the maximal possible biodiversity and uses the maximal amount of resources. Our conceptual modeling provides theoretical support for suggestions that non-linear processes were important during major extinction events in Earth history.

Parul Verma:
Computational Analysis of a 9D Small DRG Neuron Model

Small dorsal root ganglia (DRG) neurons are sensory neurons that can sense pain. Specific alterations due to genetic mutations or external injury can change its dynamics and eventually lead to conditions such as gain or loss of pain sensation, or neuropathic pain. In this work, we attempt to understand the excitability properties of this neuron using dynamical systems theory. We consider a 9-D model consisting of two sodium channels, two potassium channels and one leak channel as the voltage-gated ion channels. Analysis revealed different parameter regimes where the system attains stable steady state, periodic firing, mixed-mode oscillations or bistability. We also demonstrate how  change in specific kinetic parameters (equivalent to mutation in ion channel) alters excitability of this neuron.

Alexandria Volkening:
Modeling Pattern Formation on the Skin of Zebrafish

Wild-type zebrafish (Danio rerio) feature black and yellow stripes across their body and fins, but mutants display a range of altered patterns, including spots and labyrinth curves. All these patterns form due to the interactions of pigment cells, which sort out through movement, birth, competition, and transitions in cellular shape during early development. The diversity of patterns on zebrafish makes it a useful organism for helping elucidate how genes, cell behavior, and visible animal characteristics are related, and this is the motivation for my work. Using an agent-based approach to describe pigment cells, I couple deterministic cell migration by ODEs with stochastic rules for updating population size on growing domains. Our model suggests the unknown cellular signals behind newly observed cell behaviors and makes experimentally-testable predictions about how various Danio fish may be related evolutionarily. 

Yangyang Wang:
Analysis for Neuromechanical Motor Control System with Hard Boundary

Many neuromechanical motor control systems exhibit periodic motions that make and break contact with constraint surfaces, and adjust the shape and timing of the motion in response to external perturbations to enhance robustness for motor control. The existing methods of variational and phase response curve analysis are well established for quantifying changes in timing and shape for smooth systems and have recently been extended to nonsmooth dynamics with transversal crossing boundaries. In this work, we further extend both methods to nonsmooth systems with hard boundaries, for both instantaneous and sustained perturbations. These analyses are applied to a control system of feeding movements in the sea slug Aplysia to uncover the mechanism of the robust sensory feedback control.

Glenn Young:
Probability of Fixation in a Stochastic Model with Competitive Trade-Offs