Postdoctoral Seminars

September 11, 2014 10:20 - 11:15AM
Abstract

The intricate machinery of a living cell must function even when subjected to thermal fluctuations. These thermal fluctuations are well described by a stochastic process, called noise, which can take many different forms. While noise can be detrimental, it is also possible that a cell sometimes uses noise to its benefit. One example is using Brownian motion, or diffusion, to transport small molecules throughout the cell. The central motivation of my research is to discover how cells take advantage of noise to do things they could not do otherwise. I will present an overview of my research and discuss in detail the following two projects: (i) active transport in neurons and its role in learning and memory; and (ii) spontaneous neural activity and what it tells us about how small a functional brain can be.

October 02, 2014 10:20 - 11:15AM
Abstract

The functions of living cells are regulated by the complex biochemical network, which consists of stochastic interactions among genes and proteins. However, due to the complexity of biochemical networks and the limit of experimental techniques, identifying entire biochemical interaction network is still far from complete. On the other hand, output of the networks, timecourses of genes and proteins can be easily acquired with advances in technology. I will describe how to use oscillating timecourse data to reveal biochemical network structure by using a fixed-point criteria. Moreover, I will describe how mathematical modeling can be used to understand the dynamics and functions of complex biochemical networks with an example of circadian clock. Finally, in biochemical networks, reactions occur on disparate timescale. This timescale separation has been used to project deterministic models of biochemical networks onto lower-dimensional slow manifolds with quasi-steady state approximation (QSSA). I will discuss whether this reduction technique for deterministic systems can be used for stochastic systems. Specifically, I will show when macroscopic rate functions derived with QSSA (e.g. Hill functions) can be used to derive the propensity functions for microscopic rates in the Gillespie algorithm.

October 23, 2014 10:20 - 11:15AM
Abstract

Nuclei in the Drosophila embryo undergo 8 synchronous division cycles followed by division waves of decreasing speed that travel through the embryo until the 14th cycle. Recent advances in microscopic in vivo imaging allow us to obtain precise timing data for the 10th through 13th divisions, and these division times show remarkable synchronization across local populations. Statistical analysis indicates that these nuclei must be coordinating their cell cycles, and the syncytial nature of the Drosophila embryo suggests a chemical signaling mechanism. Comparison with earlier work further suggests that the communication has a Response / Signaling form with a positive impulse.

In 2007, Calzone et al demonstrated a numerical model of early Drosophila embryogenesis that reproduces many features of the process, but which treats the nuclei as a single mass. By adding a spatial component to the model, we show that cytoplasmic diffusion of Cyclin B and Cdk1 drives local synchrony. Including the breakdown of the nuclear envelope during mitosis reproduces the slowing division waves as well.

October 30, 2014 10:20 - 11:15AM
Abstract

In this two-part talk, I will present a model for the regulation of precipitation of calcium phosphate species in biological tissues. Calcium is an important ion for both structural support and biochemical signaling in vertebrates. As a result, it is necessarily maintained at high concentrations in fluids - at levels whereprecipitation is favored. Yet, such precipitation, when it occurs in an uncontrolled manner, is harmful. Using concepts from classical nucleation theory, I will discuss how biological organisms can regulate this high calcium concentration.

Nucleation and crystallization problems such as this one are often studied through the use of atomic force microscopy (AFM). AFM and related techniques are associated with inverse problems of Brownian motion. In the second part of my talk, I will discuss the inverse problem of potential energy reconstruction for random walkers under non-constant diffusivity. I will present a self-contained, nonparametric, regularized method based on Bayesian inference under which a path integral is used for uncertainty quantification. Under this method, regularization parameters are determined through optimization of an eigenvalue problem for a trace-class operator.

November 13, 2014 10:20 - 11:15AM
Abstract

Mutualism is defined as mutually positive interactions among living agents, whereas symbiosis is defined as persistent physical association among living agents. We define emergent node tree structures: a model of groups in noncooperative game theory, in terms of rank conditions and degeneracies of the payoff tensors. We define a corresponding refined solution concept, hierarchically perfect Nash equilibria, for noncooperative games. We sketch a possible application to plant-pollinator networks. We explain the relationship of cancer to mutualism. We outline the structure of a graphical model for the interaction of the wounded phenotype of cancerous cells and wound healing processes in surrounding tissue. We introduce multi-level selection, for which our work on applying emergent node tree structures is ongoing.

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November 13, 2014 10:20 - 11:15AM
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November 13, 2014 10:20 - 11:15AM
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November 13, 2014 10:20 - 11:15AM
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December 04, 2014 10:20 - 11:15AM
Abstract

The Interleukin-12 (IL-12) cytokine family, which is composed of heterodimeric cytokines, includes IL-12, IL-23, IL-27, and IL-35. IL-12 and IL-23 are mainly pro-inflammatory cytokines with key roles in the development of the TH1 and TH17 subsets of helper T cells, respectively. IL-27 has been regarded as an immunoregulatory cytokine, due to both of pro-inflammatory and anti-inflammatory functions in anti-tumor activity. Notably, recent experiments in transgenic mice indicate that IL-27 significantly enhances the survival of activated tumor antigen specific CD8+ T cells and hence promotes tumor rejection. IL-35, the most recently identified member of IL-12 cytokine family, is a potent inhibitory cytokine. Recent transgenic mouse experiments demonstrate that IL-35 enhances the tumor growth and angiogenesis. I will introduce two mathematical models for IL-27 and IL-35 that we constructed to study the functions of IL-27 and IL-35 in tumor microenvironment. These models qualitatively fit with the experimental results and provide some hypotheses to develop therapeutic protocols in cancer treatment.

December 11, 2014 10:20 - 11:15AM
Abstract

In this talk we present information theoretical approaches to model and analyze data form Next Generation Sequencing Experiments. We focus on the case when the system is Markovian. This assumption makes the analysis of information (entropy, divergence) relatively simple due to the Data Processing Inequality. We present various applications of this approach related to T cell selection as well as gene co-expression analysis. We also discuss the challenges of estimating various divergence measures.

January 15, 2015 10:20 - 11:15AM
Abstract

In our world there are phenomena which appear to be discrete - chairs, sisters, waffles - and phenomena which appear to be continuous - water, air, beer. The continuous phenomena are often easier to analyze than the discrete, and it is therefore slightly unfortunate that many biological objects (including nearly everything in the realm of genetics) happen to be discrete in character.

Fortunately, as 21st-century scientists we have access to data-sets so enormous that, while they may consist of discrete objects, they can justifiably be regarded as continuous. In this talk I'll present a few examples from various realms - phylogenetics, combinatorial genomics, large-scale data-sampling- which illustrate how continuous methods can fruitfully be applied to discrete things.

January 22, 2015 10:20 - 11:15AM
Abstract

Since their discovery in 1944, waves of silence/depolarization in the nervous system have been implicated in many pathologies of the brain ranging from migraines to ischemia. We construct a detailed biophysical model for interacting neurons and astrocytes to explore how specific processes of neurons and astrocytes interact to either generate or prevent such waves. Simulations of the model illustrate how properties of these waves, such as speed and duration, depend on the ATPase pumps' strengths and the NMDA channels maximum conductance. To investigate what processes may help halt the waves, we incorporate the sodium-glutamate cotransporter in the astrocytes. Our results demonstrate that the cotransporter helps prevent the waves for a large range of pump strengths and sodium may play a role in controlling the waves of silence/depolarization.

February 12, 2015 10:20 - 11:15AM
Abstract

Agent-based models (ABMs) have gained popularity in a variety of scientific fields due to their versatility and ease of use. With the ever-increasing use of ABMs for scientific research comes the need for a more rigorous approach to the understanding of their underlying dynamics. In particular, there is a conspicuous lack of rigorous methodology for solving problems using ABMs. In this talk a framework for solving optimization problems using discrete dynamical systems will be presented. A running example will be used to demonstrate the framework and how it is possible to deal with issues such as stochasticity, spatial structure, and varying agent characteristics. The optimization problem in this example has multiple conflicting objectives; a cost-function-free global optimization method will be used to solve the problem. Finally, a three-dimensional ABM of fungal infection in the lung will be presented as an example to which the framework will be applied in the near future, highlighting how in silico models can be used to investigate real-world biological systems.

February 26, 2015 10:20 - 11:15AM
Abstract

Mitigating the impacts of global change on ecosystems requires a mechanistic understanding of the processes underlying patterns of biodiversity. My research investigates interactions between plants and their environment and examines the role of these interactions in limiting plant populations and maintaining biodiversity. I will discuss the influence of vertebrates, insects, and pathogens in the sequential stages of early plant recruitment (i.e. from fruit developing in the crown to seedlings on the ground), which are hypothesized to contribute to the coexistence of plant species. With experiments conducted in the tree canopy of a Neotropical forest, I show that variation in plant performance is partly explained by different groups of natural enemies attacking plants and variation in plant functional traits. Using spatially-explicit models, I show that the spatial pattern of seed dispersal, differences in natural enemy life history, and tree abundance influence patterns of plant survivorship. Many of these interactions are disrupted by global change, and I will discuss the consequences of these disruptions for plant communities and ecosystem functions.

March 05, 2015 10:20 - 11:15AM
Abstract

Abstract Not Submitted

March 12, 2015 10:20 - 11:15AM
Abstract

We introduce residence time, a new notion of distance defined on graphs with decay. For example, our primary application is disease spread on community networks with environmental pathogen movement. In this case, decay on a vertex (i.e. in a community) represents pathogen decay in the environment. Unlike standard distance measures between vertices, such as shortest path or commute time, residence time takes decay into account in addition to the network structure. We then define a measure of vertex centrality and develop a community detection algorithm based on residence time. We perform stochastic simulations of disease spread on sample networks which demonstrate how residence time can provide insight into features of the network that are important to disease invasion and control.

March 19, 2015 10:20 - 11:15AM
Abstract

Complex systems is a field of Science that seeks to understand how macroscopic behavior arises from the interaction of a large number of inter-dependent, simpler components. Here, we use Monte-Carlo simulations to understand the emergence of such behavior in two systems. In the first part of the talk, I will describe ongoing work to understand how microtubule (MT) dynamical parameters contribute to the current steady-state (SS) observations of the MT cytoskeleton in the interphase cell cycle stage of the Arabidopsis plant cellular cortex. While severing of MTs is predominantly described as just another source of MTs at SS (along with nucleation), we show that severing may play a far more critical role in the establishment of the SS behavior. In the second part of the talk, I will describe ongoing work aimed at understanding how sensory input modulates aging behavior on a population of flies. It has been shown recently that: 1) exposure to pheromones of the opposite sex increases the mortality rate of Drosophila flies and that 2) removal of exposure reverses the mortality rate of the previous flies to the mortality rate of flies never exposed to pheromones. Our model shows that heterogeneity on the population may play a significant role in enabling the reversible behavior. The two systems described here pose significant challenges in understanding how individual components contribute to experimentally observable population behavior. Our experience suggests that such challenges can only be addressed by close interactions between experimentalists and modelers.

April 02, 2015 10:20 - 11:15AM
Abstract

While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates. In equivalent spiking implementations, firing is assumed to be random such that averaging across populations of neurons recovers the rate-based approach. Recently, however, Deneve and colleagues have suggested that the spiking behavior of neurons may be fundamental to how neuronal networks compute, with precise spike timing determined by each neuron's contribution to producing the desired output. By postulating that each neuron fires in order to reduce the error in the network's output, it was demonstrated that linear computations can be carried out by networks of integrate-and-fire neurons that communicate through instantaneous synapses. This left open, however, the possibility that realistic networks, with conductance-based neurons with subthreshold nonlinearity and the slower timescales of biophysical synapses, may not fit into this framework. Here, we show how the spike-based approach can be extended to biophysically plausible networks. We then show that our network reproduces a number of key features of cortical networks including irregular and Poisson-like spike times and a tight balance between excitation and inhibition. These results significantly increase the biological plausibility of the spike-based approach to network computation.

April 09, 2015 10:20 - 11:15AM
Abstract

A substantial amount of evidence indicates that solid tumors exhibit cellular hierarchy in which only a fraction of thus called cancer stem cells (CSCs) possess the ability to regenerate and differentiate. Remarkably, recent discoveries indicate that, besides these inherent CSCs, previously differentiated cells can also revert to a stem-like state. This process, appropriately referred to as "dedifferentiation," has been shown to escalate when cancer cells are exposed to radiation. This finding clearly has major implications in tumor treatment protocol since radiation prevails as a routine anticancer therapy and tumor regrowth remains a continual concern.

In this work we modify a cell lineage model to describe a tumor population and to include cellular dedifferentiation. We construct a coupled ODE system which tracks stem, committed progenitor, and differentiated cells and investigate various internal feedbacks. Using experimental data to set the model parameters, we observe an increased dedifferentiation rate for irradiated cells. Furthermore, our findings suggest that this elevated dedifferentiation rate can profoundly impact the long-term population size and composition.

April 23, 2015 10:20 - 11:15AM
Abstract

In this talk, I will describe a recent mathematical model that predicts the formation of a plaque as a function of the combined levels of (LDL, HDL) in the blood. The cholesterol levels in the blood reveal the risk of plaque growth in the artery. The model is given by a system of partial differential equations within the plaque. I will also briefly talk about some ongoing projects about aneurysm and red blood cell aggregation, which would have some potential blood biomarkers for diagnosis of AAA.

May 07, 2015 10:20 - 11:15AM
Abstract

We live in an environment that is constantly changing. On a large time scale, climate change has a global effect on the dynamics of plant and animal populations. On a smaller scale, there are seasonal changes of local habitats, for example, flooding and drying of wetland habitats. In this talk, I will present a spatial perspective of the effects of environmental changes. What happens when the suitable habitat of a population changes its location, or its size over time? Can the population cope with the changes by dispersing to the “good” locations?

Are there limits of the population’s ability to cope with these spatial changes? I will present a set of mathematical models aiming at answering these questions.

May 14, 2015 10:20 - 11:15AM
Abstract

Animals use a common set of muscles and motor neurons to generate multiple rhythmic behaviors. Are these distinct behaviors generated by an adaptable multifunctional circuitry, by completely distinct networks, or something in between? Identifying the neural architecture responsible for rhythm generation can be challenging in vertebrates with large central nervous systems. However, experimentalists can investigate network interactions by providing the stimuli that evokes the distinct patterns simultaneously and examining the resultant motor pattern.

The turtle spinal cord can generate rhythmic activity corresponding to forward swimming and three types of scratching. We investigate the circuitry responsible for these distinct rhythms by proposing several simplified mathematical architectures that represent a range of neural connectivity schemes, and fit these models using experimental observations. Results from this analysis suggest that the spinal networks underlying swimming and scratching likely share key components.

Visitor Seminars

September 24, 2014 10:20 - 11:15AM
Abstract

Evolutionary games first arose in the work of Maynard Smith and Price in the 70s, who introduced the concept into ecology in order to explain why conflicts over territory between male animals of the same species are usually of the "limited war" type and do not cause serious damage. A second important application, which involves the famous Prisoner's dilemma game, is to understand the persistence of altruistic behavior. There are many other applications, including recent work seeking to understand the competition (and cooperation) of different types of cells in cancer.

Most of the analyses of evolutioanry game dynamics assume a homogeneously mixing population. However twenty years ago, Nowak and May, and Durrett and Levin showed that space could drastically change the outcome of evolutionary games, for instance allowing cooperators to persist in Prisoner's dilemma. There is now an extensive literature on spatial games, but much of it is based on heuristic principles or approximate analyses. In this talk we will explain how recent work of Cox, Durrett, and Perkins for voter model perturbations can be applied to study spatial evolutionary games in which all relative fitness are close to 1, a situation which covers many applications to cancer.

The main result is that the effect of space is equivalent to (i) changing the entries of the game matrix and (ii) replacing the replicator ODE by a related PDE. The first idea is due to Ohtsuki and Nowak (for the pair approximation) while the second is well known in the theory of stochastic spatial processes. A remarkable aspect of our result is that the limiting PDE depends on the kernel which dictates the interaction between players only through the values of two simple probabilities associated with it (an idea initially proposed by Corina Tarnita et al. Due to results of Aronson and Weinberger, and Fife and McLeod, we can analyze any 2x2 game. However, when there are three strategies the limiting object is a system of reaction diffusion equations. Many results can be derived using techniques from my AMS Memoir "Mutual Invadability implies Coexistence" but it is important open problem to understand what happens in the spatial game when the replicator dynamics show bistability.

October 07, 2014 10:20 - 11:15AM
Abstract

Abstract not submitted.

October 21, 2014 10:20 - 11:15AM
Abstract

Existing mathematical models of tumor development are either discrete (cell-based) models or continuum models. Both have advantages and disadvantages; the former allows for incorporation of significant cell-level information but is computationally expensive when growth and mechanics are incorporated, whereas the latter is easy to formulate and computationally straightforward, but to date it has been difficult to accurately translate cell-level information into the continuum description. In this talk we introduce a hybrid model that retains the advantages of both the discrete and the continuum models. In this model the surface layers of a growing multicellular spheroid are described by a cell-based model, whereas the interior quiescent and necrotic zones (when present) are described by a continuum model, as is the extracellular matrix. We will discuss the theoretical foundation of the model and the computational algorithms developed to analyze it, and present numerical results for growing tumors.

October 28, 2014 10:20 - 11:15AM
Abstract

Microscopic rules for pedestrian traffic in a narrow street are discussed and the corresponding stochastic lattice system modeling the pedestrian bi-directional flow is introduced. Then the mesoscopic and macroscopic PDE models for the pedestrian density are derived. The macroscopic PDE model is a system of conservation laws which can change type depending on the strength of interaction between the pedestrian flows and initial conditions. Behavior of the stochastic and coarse-grained models is compared numerically for several different regimes and initial conditions. Finally, nonlinear diffusive corrections to the PDE model are derived systematically. Numerical simulations show that the diffusive terms can play a crucial role when the conservative coarse-grain PDE model becomes non-hyperbolic.

November 12, 2014 10:20 - 11:15AM
Host: TBD
Abstract

When radiation therapy is applied to a tumor, then inevitably, healthy tissue is exposed too. It is quite common that side effects arise or that organs fail. The normal tissue complication probability (NTCP) is an attempt to quantify the risks of side effects. So far, NTCP models have been based on statistical outcomes. In my talk I will develop a mechanistic model for tissue complication which is based on organ-specific and patient-specific model parameters. We get a surprisingly simple formulation of the NTCP, which only requires a few, obtainable, physiological characteristics.

December 02, 2014 10:20 - 11:15AM
Abstract

Polynomial systems arise in a variety of applications, but there are few effective methods for solving them. Recently, several methods have been developed, providing numerical approximations to the solutions of polynomial systems. In this talk, I will introduce some of the main tools from this relatively new toolbox, collectively called numerical algebraic geometry. I will also briefly describe some ongoing applications of these methods to population genetics, chemical reaction networks, and model selection. This will be a gentle introduction, with virtually no assumptions about your knowledge of algebra, geometry, or polynomials.

January 27, 2015 10:20 - 11:15AM
Abstract

Our work is focused on understanding the effects of the mechanochemical environment on vascular endothelial cell (EC) redox status, mitochondrial function, intracellular signaling and survival mechanisms. Since EC dysfunction is the hallmark of cardiovascular diseases/conditions and most of them are associated with altered hemodynamics, identifying the signaling pathways that regulate the EC dysfunction will provide us with new targets for better prevention and/or treatment of the #1 killer in the developed world.

My group discovered that fluid shear stress modulates the EC mitochondrial function leading to increased mitochondrial reactive oxygen species (mtROS) production. Since reperfusion (RP)-induced EC injury following myocardial infarction (heart attack) occurs due to mtROS, we simulated RP as flow of oxygenated media over ischemic ECs and showed that RP leads to mitochondrial dysfunction and EC apoptosis via excessive mitochondrial fission mediated by nitric oxide and ROS/mtROS.

Our first current project focuses on the cell recycling process, called autophagy (for mitochondria, mitophagy), inside ECs. Simulated ischemia followed by reoxygenation or RP modulates autophagy in cultured ECs, and autophagy progression may, in part, determine EC survival. In order to better understand the interplay between EC mitochondria and Ca2+ homeostasis, our second current project utilizes both experiments and mathematical modeling to investigate the role of mitochondrial function in modulating cytosolic Ca2+ levels in ECs exposed to different fluid flow patterns. Findings from these projects may lead to new therapies for EC protection in coronary arteries following cardiac I/RP and in atheroprone regions of human arteries, and may prevent myocardial I/RP injury and atherogenesis, respectively.

February 24, 2015 10:20 - 11:10AM
Host: TBD
Abstract

Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for nutrients availability which can differ depending on the situation under consideration, in vivo or in vitro.

We formulate Hele-Shaw type free boundary problems for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, coupled to a diffusion equation for a nutrient. The free boundary model is derived from a description at the cell level using the asymptotic of a stiff pressure limit.

Numerical solutions exhibit, as expected from medical observations, a proliferative rim and a necrotic core. Remarkable is the pressure distribution which vanishes at the boundary of the proliferative rim with a vanishing derivative at the transition point to the necrotic core.

March 03, 2015 10:20 - 11:10AM
Abstract

Cell-to-cell communication is fundamental to biological processes which require cells to coordinate their functions. A simple strategy adopted by many biological systems to achieve this communication is through cell signaling, in which extracellular signaling molecules released by one cell are detected by other cells via specific mechanisms. These signal molecules activate intracellular pathways to induce cellular responses such as cell motility or cell morphological changes. Proper communication thus relies on precise control and coordination of all these actions.

The budding yeast Saccharomyces cerevisiae, a unicellular fungi, has been a model system for studying cell-to-cell communication during mating because of its genetic tractability. In this work, we performed for the first time computer simulations of the yeast mating process. Our computational framework encompassed a moving boundary method for modeling cell shape changes, the extracellular diffusion of mating pheromones, a generic reaction-diffusion model of yeast cell polarization, and both external and internal noise. Computer simulations revealed important robustness strategies for mating in the presence of noise. These strategies included the polarized secretion of pheromone, the presence of the lpha-factor protease Bar1, and the regulation of sensing sensitivity; all were consistent with data in the literature. In summary, we constructed a framework for simulating yeast mating and cell-cell interactions more generally, and we used this framework to reproduce yeast mating behaviors qualitatively and to identify strategies for robust mating.

March 10, 2015 10:20 - 11:10AM
Host: TBD
Abstract

The topological pressure of a finite sequence is a weighted measure of complexity, which is adapted from a well known dynamical invariant in the ergodic theory literature. David Koslicki (Oregon State) and I introduced this concept in a recent paper in the Journal of Mathematical Biology, and implemented it to detect regions of high coding sequence density in DNA sequences. In this talk, I will describe the topological pressure (and the motivations behind its definition), and our application to DNA sequences. We hope that the topological pressure will be a useful tool in other settings where the goal is to detect structure in large and noisy data sets, and I will emphasize some aspirations in this direction, rather than our specific application.

March 17, 2015 10:20 - 11:10AM
Host: TBD
Abstract

Conflict is an inherent part of social life. In animal groups, group members may be in conflict with one another over reproductive opportunities, social status, group size, task allocation, and other aspects of group living. Many evolutionary game theoretical models of conflict assume that individual phenotype is fixed, so that individuals cannot adjust their behavior with respect to their current social environment. In this talk, I will describe a game theoretical model of conflict over within-group reproduction, in which individuals may respond plastically to the behavior of social partners. Incorporating plasticity influences conflict within the group if group members have some common interest in group productivity, but may increase or decrease conflict, depending on the social status of responders. I will discuss evidence for a plastic growth response to social conflict in a highly social fish, and describe a model exploring the conditions under which socially plastic growth leads to stable size structures in social groups.

March 31, 2015 10:20 - 11:10AM
Abstract

The existence of Hopf bifurcations in compartmental epidemiological models with various possible compartments is considered. The possible existence of Hopf bifurcations is explored with the aid of a singular perturbation analysis in a small parameter given by the inverse of the lifetime of the individuals in the population. The difference between the characteristic timescale of the disease (days or weeks) and the lifetime of the organisms (years or decades) allows for a simplified analysis that reveals the possible presence of Hopf bifurcations as other system parameters are varied.

April 07, 2015 10:20 - 11:10AM
Host: TBD
Abstract

Living systems maintain their normal physiological states by responding to environmental changes and insults and genetic mutations through feedback loops within highly connected networks of genes, proteins, and other bio-molecules. Unfortunately, this complexity makes it difficult to accurately parse ‘driver genes’ that are critical for the establishment and maintenance of these networks from passenger genes that play a less important role and are somewhat redundant. This problem is in part responsible for the surprising lack of efficacy of drugs that target individual genes for complex disease such as cancer. Side-effects from medications are another consequence of the connectivity in underlying networks. If accurate models of gene networks were available, they could be used to compute how effective therapies for diseases can be designed.

In the past most of the attention of on the protein coding genes. In the last decade there is emerging evidence to indicate that the no-coding genome makes substantial contributions to the regulation of protein coding gene networks. A lot is now understood about the smallest non-coding RNAs, microRNAs in relation to their role as post-transcriptional regulators that integrate protein coding gene networks.

In collaborating with physicists and biostatisticians at the Neils Bohr Institute (Mogens Jensen and Lykke Pedersen), University of Houston (Gemunu Gunaratne) and Chad Creighton (Baylor College of Medicine) we have developed methods to reveal the microRNA-regulated transcriptome. Using mmethods that employ a modified independent component analysis (mICA-Pederson) and “solution surfaces” of the gene networks associated with a biological process (Gemunu Gunaratne) and Integrated microRNA-mRNA target pair analysis (Cregihton – SigTerms) we have identified functionally correlated microRNA-mRNA pairs in big datasets. Applying these methods to The Cancer Genome Atlas (TCGA) ovarian cancer dataset we have identified clinically significant tumor suppressor microRNAs and new druggable targets for this the most lethal gynecological malignancy.

April 21, 2015 10:20 - 11:10AM
Abstract

I will present ordinary and delay differential equation models of solid tumor treatment with taxanes (anti-mitotic drugs) and platinum-based compounds. Issues of model identifiability will be discussed, together with several numerical examples. Necessary and sufficient conditions for stability of the cancer free equilibrium are derived, and in the cases where chemotherapy is administered periodically, the existence of periodic solutions is investigated analytically. Finally, an application of the model to ovarian cancer xenograft treatment with carboplatin will be presented.

May 05, 2015 10:20 - 11:10AM
Host: TBD
Abstract

In contrast to random diffusion without orientation, chemotaxis is the biased movement of organisms toward the region that contains higher concentration of beneficial or lower concentration of unfavorable chemicals. The former often refers to the attractive chemotaxis and latter to the repulsive chemotaxis. Chemotaxis has been advocated as a leading mechanism to account for the morphogenesis and self-organization of a variety of biological coherent structures such as aggregates, fruiting bodies, clusters, spirals, spots, rings, labyrinthine patterns and stripes, which have been observed in experiments. In this talk, I will present some recent results regarding the rigorous analysis of a nonlinear PDE model arising from the study of repulsive chemotaxis. In particular, local/global well-posedness, long-time asymptotic behavior and diffusion limits of classical solutions will be discussed. The long-time behavior results show that constant equilibrium states are stable, which indicates that chemo-repulsion problem with logarithmic chemotactic sensitivity exhibits a strong tendency against pattern formation. The diffusion limit results demonstrate that the chemically diffusive model is consistent with the non-diffusive model under certain boundary conditions, which may help reduce the computational cost for numerical simulation of the model.

May 12, 2015 10:20 - 11:10AM
Host: TBD
Abstract

Collagen type 1 is the most abundant extracellular matrix protein in adult tissues. The collagen fiber assembly is a complex multi-step process involving several intermediate stages. My research focus is to understand the collagen fiber structure and regulation at the molecular level and how it affects cell-matrix interactions and mechanical properties of the underlying tissue. In particular we are studying how discoidin domain receptors (DDR1 and DDR2) interact with collagen type 1. DDRs are receptor tyrosine kinases expressed in a variety of mammalian cells. We have elucidated that by binding to collagen DDRs inhibit the fibrillogenesis and native structure of collagen fibers. These are critical findings as the quantity and quality of collagen fibers can be altered in a number of pathologies. Our ongoing work aims to elucidate the functional consequences of an altered collagen fiber ultrastructure. We employ biophysical techniques such as atomic force microscopy (AFM), transmission electron microscopy (TEM) and fluorescence microscopy along with cell and molecular biology approaches towards this goal.