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Local kinetics and self-similar dynamics of morphogen gradients

APR 20, 2012 | 4:00 PM TO 6:00 PM



The Graduate Center
365 Fifth Avenue


April 20, 2012: 4:00 PM-6:00 PM




ITS Applied Mathematics


Initiative for the Theoretical Sciences (ITS) sponsored Applied Mathematics Seminar

Local kinetics and self-similar dynamics of morphogen gradients

Some aspects of pattern formation in developing embryos can be described by nonlinear reaction-diffusion equations. An important class of these models accounts for diffusion and degradation of a locally produced single chemical species and describe formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues. At long times, solutions of such models approach a steady state in which the concentration decays with distance from the source of production. I will present our recent results that characterize the dynamics of this process. These results provide an explicit connection between the parameters of the problem and the time needed to reach a steady state value at a given position. I will also show that the long time behavior of such models, in certain cases, can be described in terms of very singular self-similar solutions. These solutions are associated with a limit of infinitely large signal production strength.

This is a joint work with: C. Muratov, S. Shvartsman, C. Sample and A.Berezhkovskii.