July 30-August 2, 2008
Society for Mathematical Biology Conference

Models of Eukaryotic Chemotaxis: How cells use stochastic Pde's to figure out where to go
Many types of eukaryotic cells are able to detect chemical gradients and move accordingly. Unlike the case for bacteria, these cells are large enough for the gradient detection to rely on differential receptor binding probabilities on the cell membrane. It is not yet understood how this noisy input data is processed by the cell to make the motion decision; thus we cannot a priori predict the detection threshold, the response kinetics and the plasticity to changing stimuli. This talk will focus on some recent nonlinear models of this cellular information processing system and on experiments in progress on the amoeba Dictyostelium discoideum to test some of the resulting expectations.

Engineering an Ecosystem: Taking Cues from Nature's Paradigm to Build Tissue in the Lab and the Body
All life on Earth is water derived, and all living biological materials contain water. Cyclic loading due to weight bearing activities in Earth's gravitational environment as well as natural forces such as wind induce fluid to flow through biological materials, including live wood, tissue, and soil. Flowing fluid is the medium of life for cells inhabiting Earth's ecosystems, including human tissue. A major impasse in understanding fluid flow through biological materials is the difficulty in visualizing complex flow fields that result from physiologic or natural activity. During the past decade, great emphasis has been placed on elucidation of load-induced flow through bone tissue, which serves as a model system for a relatively stiff yet porous two-phase material comprising 25% water. The fluid and solid phases of bone exhibit anisotropy at multiple length and time scales. In this talk I will review recent insights into solid-fluid interactions of bone tissue constituents and their role in maintenance of bone in health and disease. I will then show how we use multiscale computational modeling and novel experimental methods to predict, engineer and manufacture bone tissue in the laboratory and in the human body.

Stochastic modeling of cancer
Even though much progress has been made in main stream experimental cancer research at the molecular level, traditional methodologies alone are insufficient to resolve many important conceptual issues in cancer biology. For example, for the most part, it is still unknown how cancer originates, what drives its progression, and how treatment failure can be prevented. In this talk, I will describe novel mathematical tools which help obtain new insights into these processes. I will also show how the mathematical insights are combined with experimental studies through collaborations with cancer biologists. The main idea is to study cancer as an evolutionary dynamical system on a selection-mutation network. I will discuss the following topics: Stem cells and tissue architecture; Cancer and aging, and Drug resistance in cancer.

Mechanochemistry and motility
I will discuss aspects of biological motility, including the mechanics of actin polymerization engines, the collective dynamics in and of eukaryotic flagella, and the mechanochemistry of biological spring-like assemblies. Time permitting, I will also discuss how a combination of quantitative models, experiments and comparative studies might help us to uncover the design principles that govern these biological systems, which are engineered by evolution but constrained by physics.

Coupled Systems in Neuroscience
Beginner models for specific functions in the neurosystem often have the form of coupled systems with special structure. Examples include quadruped locomotor central pattern generators, the canal-neck projection in the vestibular system, and the auditory receptor cells on the basilar membrane in the cochlea. On the mathematical side Ian Stewart and I have been studying the general question: What does the network architecture of a couple system tell you about bifurcations from a synchronous equilibrium. In this lecture we discuss the special structure of these examples and some of the relevant mathematics.

Dynamics of emerging wildlife diseases
In this talk I will present recent progress in modelling the dynamics of emerging wildlife diseases. I will focus on two examples, one involving interactions between hosts (birds) and disease vectors (mosquitoes) in the outbreak of West Nile virus, and the other involving a "spill over" and "spill back" disease between net pen aquaculture and wild salmon.
The focus of the talk will be quantitative assessment of the disease dynamics using dynamical systems, and the resulting interplay between models and data.

Growth and structural adaptation of blood vessels in normal and tumor tissues
The circulatory system is a dynamic structure. Blood vessels grow or regress during development and in a variety of normal and disease states, over time scales of hours, days and longer. Under normal conditions, these structural changes ensure that all parts of the tissue are supplied with blood, and that the microvascular network structure is well organized and efficient with regard both to the volume of blood needed and the energy required to drive the flow. Theoretical models have been used to investigate how this is achieved through vessel responses to several stimuli, including wall shear stress, tension in vessel walls, metabolic needs, growth factors, and information transfer along vessel walls, and how perturbations of these processes lead to abnormal structural and functional characteristics in tumor tissues.

Discrete TB Transmission Model with Age and Infection Age Structures
Tuberculosis (TB) is a bacterial infection that spreads from one person to another by the airborne route. Initial infection with TB occurs when bacteria within aerosolized droplets are inhaled into the lung. Latently infected individuals become active TB after a variable latency period. Latent periods range from months to decades. Most infected individuals never progress towards the active TB state. It is in general felt that about 5% will develop active TB within 2 years of exposure, and another 5% will develop active TB more than 2 years from the time of exposure. On the other hand, average infectious periods are relatively short. There is strong evidence from statistical data that active TB cases are more among elder individuals. We formulate a discrete TB transmission model with age and infection age structures to incorporate those features of TB transmission. The basic reproductive number is defined and the dynamical behavior of the model is studied. The nationwide sampling survey data of tuberculosis epidemiology in China is used to estimate the parameters and to predict TB infection.