Long-term Visitor Seminars
All seminars will be held in the MBI Lecture Hall - Jennings Hall, Room 355 - unless otherwise noted.Remarkable progress in advanced microscopy has yielded unprecedented access to a path-wise observation of the diffusive behavior of bacteria, viruses, organelles and various invasive particulates in biological fluids. Upon inspection of the data one immediately notes, "That's not Brownian motion!" Perhaps not surprisingly, media such as human mucus are highly heterogeneous and exhibit significant viscoelastic properties. In this talk, I will provide a survey of recent experimental observations along with mathematical models that are currently in use. Wherever possible I will point out open problems in this burgeoning area of research.
Classical mathematical formulation of the dynamics of chemical reaction systems involves setting up and analyzing a system of ODEs, or PDEs if spatial effects are considered. However, a system may be sensitive to the stochasticity inherent in the mechanism of chemical reactions, for example due to having small numbers of molecules, or reaction rates which vary over several orders of magnitude. We consider such a reaction system in a cellular environment, and also impose a 'global' cell division mechanism, which adds noise to the concentrations of chemical species along a given lineage, and find parameter regimes for which this produces a qualitative change in the dynamics. We model these reaction and division processes as Jump Markov Processes, and discuss some toy models in which the stochasticity can allow the system to exhibit behavior that is not possible with a deterministic formulation. One such behavior is bistability, for which we find two processes that have similar macroscopic signatures but whose underlying causes are fundamentally different; one such case leads to the Large-Deviation theory of Freidlin and Wentzell. Such bistability is characteristic of many gene expression systems that effectively incorporate an ON/OFF switch, but the framework is very general and is applicable in other areas, such as population genetics, where bistability may represent alternating dominance of allelic types in a population. This is joint work with Lea Popovic of Concordia University (Montreal).
This talk will attempt to provide a synthesis of the topics discussed at the workshop and to distill some central themes that point to opportunities and challenges in the field.
Complex gene regulatory networks underlie many cellular and developmental processes. While a variety of experimental approaches can be used to discover how genes interact, few biological systems have been systematically evaluated to the extent required for an experimental definition of the underlying network. Therefore, the development of computational methods that can use limited experimental data would provide a useful tool to extract relevant information from existing data, identify unexpected regulatory relationships, and prioritize future experiments.
We have developed a hybrid modeling method that combines two existing methods: a recently development tool from algebraic geometry and a traditional statistical tool. We reverse engineered a mathematical model from time-course gene expression data collected from wildtype C. elegans embryos and compared it to an existing knowledge-driven biological model based on the same data set. We show that the mathematical model predicts more interactions observed in subsequent perturbation experiments than does the knowledge-driven model. It provides new insights into the function of a key transcriptional regulator and identifies distinctive activities of two genes previously thought to be redundant. This work provides a strong example that data-driven mathematical models can complement knowledge-driven models to identify non-intuitive network relationships and to guide future experiments.
