Mathematical Biology and Physiology Seminar

Fall 2012 Full Schedule

Date: Thursday, August 30th, 2012

Speaker: Tim Reluga

Title: A Crash Course in Immunology for Mathematicians.

Abstract: When modelling biological systems, one of first changes for a mathematician, computer scientist, or modeler of any stripes is coming to terms with the empirical reality of those systems. As an illustrative example, one of the most wonderful and (historically) mysterious aspects of disease is our bodies ability to remember old infections, so we never get sick from diseases like measles more than once. Yet for some diseases, like pertussis, tuberculosis, and HIV, memory seems more complex, and to this day, many research dollars go into understanding exactly how the creation and maintenance of immune memory works. Some good model-based theories may help us make sense of the situation, but to get there, we first have to travel a winding road through genetics, cell biology, physiology, and epidemiology.

Date: Thursday, September 6, 2012

Speaker: Chun Liu, from Math

Title: Energetic Variational Approaches in Studying Ionic Fluids and Ion Channels.

Abstract: The interactions of ions flowing through biological systems has been a central topic in biology for more than 100 years. Flows of ions produce signaling in the nervous system, initiation of contraction in muscle, coordinating the pumping of the heart and regulating the flow of water through kidney and intestine.

Ion concentrations inside cells are controlled by ion channels through the lipid membrane. In this talk, I will propose a continuum model that is derived from the energetic variational approach which include the coupling between the electrostatic forces, the hydrodynamics, diffusion and crowding (due to the finite size effects). The model provides some basic understanding of one of the most important properties of proteins, the ion selectivity.

This is a joint work with Yunkyong Hyon (IMA), Taichia Lin (National Taiwan University) and Robert Eisenberg (Rush Medical School).

Date: Thursday, September 13, 2012

Speaker: David Kennedy, Read Lab

Title: The effects of multi-scale dynamics on the ecology and evolution of an insect virus.

Abstract: A challenge to understanding infectious disease ecology is that processes occurring at multiple scales likely impact the ecological and evolutionary patterns found in nature. Both pathogen growth within hosts and pathogen transmission between hosts are likely important to pathogen dynamics, but studies typically focus on only one of these scales or the other. An integrated approach to disease modeling may thus provide novel insights. The challenge to using an integrated approach is that within-host dynamics are particularly poorly studied, because of difficulties associated with directly tracking pathogen dynamics within hosts. Here we demonstrate a method by which pathogen growth within hosts can be inferred through fitting mechanistic birth-death models to easily collectable dose-response data, alleviating the need to directly track pathogen dynamics over time. We then use this method to test various models of baculovirus growth in gypsy moth (Lymantria dispar) hosts, to identify the biological mechanisms important to pathogen growth in this system. This analysis yields novel insights into the ecology and evolution of the gypsy moth and its baculovirus with implications for strategies to control gypsy moth population outbreaks. Furthermore, this analysis reveals that host differences alone are insufficient to explain the observed variability in host outcomes, and that demographic stochasticity in pathogen growth is likely important in explaining this variability. The importance of demographic stochasticity, in turn, suggests that genetic drift may occur during pathogen growth within hosts. We next combine our birth-death model of baculovirus growth within hosts with a stochastic SEIR disease model that describes transmission dynamics between hosts for this insect baculovirus, and we use this nested model to explore the importance of genetic drift on pathogen diversity within hosts. Using reasonable parameter values, our model predicts that genetic diversity within hosts will be strongly affected by the drift that occurs both during pathogen population bottlenecks at transmission, and during the subsequent population growth of pathogen within hosts. We next compare the levels of pathogen diversity within hosts predicted by the models to Illumina sequence data from 223 field-collected hosts. This analysis shows that genetic drift is indeed important to explaining the observed patterns of pathogen diversity. We take this as evidence that genetic drift occurring within hosts is important to understanding patterns in disease ecology, suggesting that stochasticities that act both within hosts and be- tween hosts need to be accounted for to understand pathogen evolution in general. We then discuss the implications of these findings for evolution of virulence theory and host-pathogen interactions.

Date: Thursday, September 20, 2012

No talk this week.

Date: Thursday, September 27, 2012

Speaker: Hong Qian, from the University of Washington Department of Applied Mathematics.

Title: Delbruck-Gillespie Processes: Nonlinear Stochastic Dynamics, Phase Transition, Thermodynamics and Analytical Mechanics

Abstract: Agent-based population dynamics articulates a distribution in the behavior of individuals and considers deterministic behavior at the population level as an emergent phenomenon. Using chemical species inside a small aqueous volume as an example, we introduce Delbruck-Gillespie birth-and-death process for chemical reactions dynamics. Using this formalism, we (1) illustrate the relation between nonlinear saddle-node bifurcation and first-order phase transition; (2) introduce a thermodynamic theory for entropy and entropy production and prove 1st and 2nd Laws of Thermodynamics as theorems; (3) show how an analytical mechanics (i.e., Lagrangian and Hamiltonian systems) arises and the meaning of kinetic energy. We suggest the inter-attractoral stochastic dynamics as a possible mechanism for isogenetic variations in cellular biology.

The related review article is here.

Date: Thursday, October 4, 2012

Speaker: Sheereen Majd, Assistant Professor of Bioengineering, PSU

Title: Nano-Scale Pores for Sensing and Single-Molecule Characterization

Abstract: Biological protein pores and pore-forming peptides can generate a pathway for the flux of ions and other charged and polar species across otherwise impermeable cellular membranes. In nature, these nanopores have diverse and essential functions that range from maintaining cell homeostasis and participating in cell signaling to activating or killing cells. The combination of nano-scale dimensions and inherent sophisticated functionality of these biological pores have them made particularly attractive for the growing field of bionanotechnology where their applications range from single-molecule sensing to drug delivery and targeted killing of malignant cells. Recently, nano-scale pores fabricated in synthetic materials have also emerged as powerful platforms for single-molecule sensing and characterization. In this talk, I present two examples of application of biological and synthetic nanopores for detection and characterization of molecular processes on lipid membranes. In the first example, we applied an ion channel-forming peptide, gramicidin A, for sensing and detection of membrane-associated enzymatic activities and binding interactions. In the second example, we modified a synthetic nanopore by coating its walls with non-fouling lipid bilayers to enable sensing and characterization of single protein molecules as well as molecular processes on lipid bilayers.

Date: Thursday, October 18, 2012

Speaker: Huijing Du from Notre Dame University.

Title: Multiscale modeling of Pseudomonas aeruginosa swarming

Abstract: Many bacteria move in groups, in a mode described as swarming, to colonize surfaces and form biofilms to survive external stresses. One such bacterium is Pseudomonas aeruginosa, which often, but not always, forms branched tendril patterns during swarming; this phenomena occurs only when bacteria produce rhamnolipid, which is regulated by population-dependent signaling called quorum sensing. The experimental results of this work show that P. aeruginosa cells propagate as high density waves that move symmetrically as rings within swarms toward the extending tendrils. Biologically justified cell-based multiscale model simulations suggest a mechanism of wave propagation as well as a branched tendril formation at the edge of the population that depends upon competition between the changing viscosity of the bacterial liquid suspension and the liquid film boundary expansion caused by Marangoni forces. Therefore, P. aeruginosa efficiently colonizes surfaces by controlling the physical forces responsible for expansion of thin liquid film and by propagating toward the tendril tips. The model predictions of wave speed and swarm expansion rate as well as cell alignment in tendrils were confirmed experimentally. The study results suggest that P. aeruginosa responds to environmental cues on a very short timescale by actively exploiting local physical phenomena to develop communities and efficiently colonize new surfaces.

Date: Thursday, October 25, 2012

Speaker: Timothy Jegla, Assistant Professor of Biology, PSU

Title: How does pathological behavior arise in the Kv6.4 knockout mouse?

Abstract: We are characterizing central and peripheral behaviors in a potassium channel knockout mouse (Kv6.4 KO). The mouse has behavioral deficits consistent with disrupted signaling in brain regions in which the Kv6.4 gene is expressed. Kv6.4 is a regulatory subunit that enhances channel activation but paradoxically decreases K+ current size in vitro. It is therefore difficult to predict the neuronal K+ current phenotype of Kv6.4 KO in vivo. We are using a combination of biophysical, behavioral and patch clamp analysis to quantitatively describe the neurophysiological changes that occur following Kv6.4 KO.

Date: Thursday, November 1, 2012

No talk this week.

Date: Thursday, November 8, 2012

Speaker: Manfred Denker

Title: Avalanche Process in Neural Dynamics

Abstract: The integrate and fire model for time evolution of potentials in neuronal cells goes back to Lapicque in 1907. In 2002 a discrete model was defined by Eurich, Hermann and Ernst, which is the starting point of the discussion in this talk. I will shortly describe the neurophysiological basis and then present a random dynamical model for its description. In particular, I will concentrate on the avalanche size distribution and the associated power law. This law is conjectured to be of order 3/2 and I will give mathematical rigorous arguments for it, one based on branching processes, another based on Cayley's theorem for the number of trees with a given number of vertices.

Date: Thursday, November 15, 2012

Speaker: Colin Campbell, Postdoc in Biology

Title: A dynamic model of cancerous tumor pathogenesis

Abstract: CD8+ T cells play an important role in determining cancer pathogenesis. In this talk I will discuss a dynamic model of the interactions between CD8+ T cells and cancerous tumors of the brain, pancreas, and bones. The model replicates five categories of response ranging ranging from tumor clearance to unrestrained tumor growth, and several predictions from the model have been experimentally confirmed. Importantly, the model highlights differences in apoptosis rates that contribute to compromised CD8+ T cell responses and tumor progression, knowledge of which is essential for development of cancer immunotherapy. I will focus the talk on the mathematical model, specifically (1) the biological and mathematical motivations for its form and (2) the relationship between the parameter space and resulting dynamic behavior.

Date: Thursday, November 29, 2012

Speaker: Jay Newby, Postdoc at MBI, Columbus, Ohio

Title: Piecewise deterministic and hybrid stochastic modeling of intracellular transport and cell physiology

Abstract: As the title implies, my work focuses on applying stochastic processes to biological problems. All living organisms are made up of cells, and cells - from single-celled bacteria to neurons within the human brain - have a single common feature: they are small. A typical cell is about 10 micrometers in diameter, which is 20 times less than the width of a human hair. Despite its size, a cell must organize and process massive amounts of information stored within in DNA and use this information to perform the many functions necessary to obtain energy, reproduce, and adapt to its environment - all while competing with other species. Indeed, their microscopic size creates an interesting challenge because thermal fluctuations become significant. When thermal fluctuations constantly bombard the delicate cellular machinery, its behavior becomes unpredictable and random. Cells have not simply learned to overcome this difficulty, to function in spite of random fluctuations, they have learned to exploit and use it to their advantage. In my talk, I will discuss a few of these mechanisms and how their use by neurons is important for learning and memory.

Date: Thursday, December 6, 2012

Speaker: Nicole Mideo

Title: Bridging scales in the evolution of infectious disease life histories

Abstract: Although parasite fitness is often equated with between-host transmission, such a simple assumption overlooks the fact that transmission is a consequence of processes acting on at least two different biological scales: within and between hosts. Studying the evolution of disease life histories (e.g., patterns of virulence and transmission over the course of an infection) therefore requires an understanding of the interactions between parasites, host resources, and immunity at the within-host level; of parasite transmission, host demography, and epidemiology at the between-host level; and of the links between levels. Mathematically, there is a straightforward way to nest models of within-host dynamics into between-host models for studying disease life history evolution. However, for many parasites the required mechanistic details of the within-host dynamics are often unknown, so generating evolutionary predictions is not possible. I will present an alternative, function-valued trait' approach that allows for interactions between scales without requiring a mechanistic within-host model. Instead, this approach captures constraints at the within-host level phenomenologically, through estimates of genetic covariance functions. I will demonstrate how this approach works, in principle, by applying it to data from experimental rodent malaria infections, and reveal how patterns of covariance can interact with epidemiological dynamics to affect the evolutionary trajectories of disease life history traits.