Stochastic mathematical and computational models in microbiology
Wednesday, February 27, 2008 - 11:15am - 12:15pm
I shall discuss three areas of current research involving the use of stochastic methods for the physical modeling for microscopic processes in physiology. First, I exhibit a variation of the immersed boundary method designed, in joint work with Paul Atzberger (UCSB) and Charles Peskin (NYU) for simulating microbiological systems where thermal effects play a significant role, such as molecular motors, DNA and other polymer dynamics, and gel swelling. Statistical mechanical principles indicate that the thermal fluctuations should manifest themselves through a random force density in the fluid component of the immersed boundary equations. Secondly, I briefly review the mathematical procedure, currently being developed with Juan Latorre and Grigorios Pavliotis (Imperial), for coarse-graining stochastic molecular motor models. Finally, I shall discuss recent explorations with Adnan Khan (Lahore) and Shekhar Garde (Rensselaer, Biochemical Engineering) concerning the parameterization of a simple stochastic model for the behavior of water molecules near a solute surface which has the potential for improving substantially upon Brownian dynamics models more conventionally used in engineering applications. We use exactly solvable mathematical models as a testbed for addressing some basic data-driven parameterization issues.