Dynamics in Model Genetic Networks: Evolution and the Inverse Problem
Dr. Leon Glass
McGill University, Rosenfeld Chair in Cardiology and Professor of Physiology
December 3, 2010
12:50 - 1:40 pm
Genetic activity is partially regulated by a complicated network of proteins called transcription factors. I will describe a mathematical framework to relate the structure and dynamics of these genetic networks. The networks are represented by differential equations with switchlike nonlinearities. These piecewise linear equations represent a continuous implementation of Kauffman gene switching networks. These model equations display robust dynamics that are largely insensitive to changes in parameters. The framework offers ways to study the evolution of rhythmic patterns in model equations and also in electronic circuits that simulate the differential equations. It is possible to estimate the amount of data that is needed to determine the connection matrix, as well as the interactions between the elements. These results can be applied to partially determine the underlying network of a real electronic circuit (that models the differential equations) and also transcriptional control data in biological systems.
Leon Glass, obtained a Ph.D. in Chemistry in 1968 from the University of Chicago studying theory of atomic motions in simple liquids. He then was a Postdoctoral Fellow in Machine Intelligence and Perception (University of Edinburgh), Theoretical Biology (University of Chicago), and Physics and Astronomy (University of Rochester). He has been at McGill University, Montreal, Quebec, Canada since 1975, where he is now the Isadore Rosenfeld Chair in Cardiology, and Professor in the Department of Physiology. He was a Visiting Professor at the University of California at San Diego (1984-5), and in 1994-5 he was a recipient of a Guggenheim Fellowship to study "Nonlinear Dynamics and Sudden Cardiac Death" at Beth Israel Deaconess Medical Center, Harvard Medical School. In 2001-2, he was a Visiting Professor at the Department of Biomedical Engineering, Boston University. He has carried out studies on various aspects of the application of mathematical and physical methods to biology with special interest in vision, cardiac arrhythmias, genetic networks. He is a Fellow of the Royal Society of Canada, the American Physical Society, and the Society of Industrial and Applied Mathematics. In 2003, he was a recipient of the Jacques-Rousseau Prize for Interdisciplinary Research awarded by the Acfas. He is a former President of the Society for Mathematical Biology and currently sits on the editorial boards of Chaos, the International Journal of Bifurcation and Chaos, and the Springer-Verlag Interdisciplinary Applied Mathematics book series. He has published over 170 articles and reviews. His book From Clocks to Chaos: the Rhythms of Life (Princeton University Press, 1988) with Michael C. Mackey has been translated into Russian, Chinese, and Portuguese. In addition to his scientific interests, he plays the French horn in the I Medici di McGill orchestra, and is an avid hiker in the Adirondacks and other mountains.