This talk will describe some of our combined experimental and computational methods for determining the specificity of DNA-binding proteins and for discovering regulatory sites in genomic DNA sequences. It will cover aspects of the algorithms we have developed and the types of experiments we employ to test the predictions and refine the models. Examples from bacteria, yeast and worms will be described.
Bacterial Biofilms are the most ubiquitous form of life on the planet: more than 90% of bacteria live in aggregations called biofilms. Biofilms are primary cause for deaths of people with Cycstic Fibrosis, cause Legionairre's disease, are a major source of nosocomial infections, damage ships, and clog fluid based industrial and food processing machinery causing billions of dollars of damage annually. Biofilms are also used to improve performance of fertilizers, to manufacture many household products, and to clean industrial runoff. Biofilms exhibit complex behavior such as varying surface morphology, cell-to-cell communication, and symbiotic relationships. Consequently, it is important for many reasons to understand the formation, growth, and characteristics of bacterial biofilms so that they can be inhibited where they are undesirable and controlled where they are used to our advantage. In this talk I will discuss our work on modeling and simulation of bacterial biofilms. In particular, I will discuss two biofilm systems: Pseudomonas aeruginosa biofilms which are the most common cause of death for people with CF, and autotroph/heterotroph systems that are used for nitrate and ammonia removal from waste water in activated sludge reactors.
Orexin-producing neurons are clearly essential for the regulation of wakefulness and sleep as loss of these cells produces narcolepsy. However, little is understood about how these neurons dynamically interact with other wake- and sleep-regulatory nuclei to control behavioral states. Using survival analysis of wake bouts in wild type and orexin knockout mice, we characterized the fragmentation of wakefulness observed in orexin knockout mice and identified a surprisingly delayed onset (> 1 min) of functional orexin effects. We incorporated these findings into a mathematical model of the mouse sleep/wake network, and the resulting simulated behavior accurately reflects the fragmented sleep/wake behavior of narcolepsy. Analysis of the model geometry provides insight into the mechanism associated with behavioral state instability in the simulated data and leads to several predictions.
The fungus Magnaporthe grisea, commonly referred to as the rice blast fungus, is responsible for destroying from 10% to 30% of the world's rice crop each year. The fungus attaches to the rice leaf and forms a dome-shaped structure, the appressorium, in which enormous pressures are generated that are used to blast a penetration peg through the rice cell walls and infect the plant. We develop models for both the appressorial development and the penetration peg using exact, nonlinear, elasticity theory for shells and membranes. The model for appressorial design explains the shape of the appressorium, and its ability to maintain that shape under enormous increases in turgor pressure that can occur during the penetration phase. The model for the penetration peg provides the means of studying the effects of external surface stresses and the normal motion of material points on the cell surface.
In mammals, the respiratory rhythm is maintained under a wide range of conditions, depending on age, metabolic demand, and environmental factors. This rhythm is driven by a pacemaker system in the brainstem. Hence, a central question is, how does this pacemaker system generate such robust, adaptable rhythms? One component of the respiratory pacemaker system is the pre-Botzinger complex (pBC), a collection of neurons that can exhibit bursts of activity under appropriate conditions and that are coupled with synaptic excitation. I will discuss the mathematical analysis of the mechanisms by which synaptic coupling and heterogeneity can promote rhythmic activity in a model pBC network. This analysis incorporates fast-slow decomposition, bifurcation analysis, reduction of differential equations to maps, and a bit of graph theory.
The biotechnological advances in the last decade have enabled the possibility of a reverse problem formulation for the modeling of systems structure and dynamics of genetic and metabolic networks. Some major challenges for the development of these reverse engineering methods are related to the construction of efficient algorithms to build robust models with respect to data noise and feasible ways to combine gene expression data with a priori knowledge to produce functional predictions of such networks.
In this talk, we will introduce an evolutionary computation based reverse engineering algorithm for constructing the underlying network structure and dynamics from gene expression data and combine it, when available, with a priori knowledge; in our proposed method, gene expression data include wildtype time courses as well as knockout perturbations. Our framework is that of polynomial dynamical systems (PDS) enabling the use of computational algebra tools to efficiently describe structural characteristics of the desired models. Experiments on artificial genetic networks such as the segment polarity gene network in D. Melanogaster, show the performance of the proposed algorithm in constructing a robust (with respect to data noise) mathematical model.
The adaptive immune system has the convenient feature of being able to remember and defend the body against previously encountered pathogens, rendering long-term immunity to an individual who survives an initial acute infection. T-cell populations accomplish this task through their expansion and differentiation into subtypes of cells with effector (useful for eliminating pathogen) and memory (surviving) capabilities. Simple mathematical models using systems of ordinary differential equations can capture the dynamics of typical immune responses, and these models are useful for predicting proliferation and death rates of various subcategories of T cells. We discuss some findings based on parameter fitting in these basic models which assume a variety of differentiation pathways. We also present and discuss a T-cell population model that assumes that differentiation to memory cells is a continuous process dependent on the strength and duration of antigen exposure. This new model consists of a coupled pair of partial differential equations and results in a translating solution of the heat equation. Interestingly, this same mathematical model has been used to describe and analyze transport along nerve axons.
The reverse engineering of biological network is a major focus of research in the post-omics era. Gene networks are conceptual representations of interactions between genes and may provide important information about the regulatory aspects of the biological system under study. Applications in biomedical engineering include the design of specific drug targets that could maximize the effect of its action across the network. A multitude of methods are available to infer gene networks from data, some of which have specific data requirements in order to satisfy their theoretical framework. I propose to present a new method to reverse engineer gene networks from time series data based on the estimation of gene interactions by least squares fitting. By iteratively selecting genes to be perturbed (i.e., to be knocked out), constraints can be imposed in the network, thereby helping in the inference process.
In current studies on cell movement in tissues, Friedl et al. have observed single metastatic cancer cells as they move through collagen network tissue. They show a characteristic form of movement, called "mesenchymal motion". Based on their observations, I will derive mathematical models for mesenchymal motion. On a mesoscopic level, I will formulate transport equations. To obtain macroscopic models in the form of advection-diffusion equations, I will use hyperboplic and parabolic scaling techniques. Numerical simulations of these models show interesting pattern formation in form of networks. I will discuss specific applications and present new results on steady states.