Mathematical Biology Seminar

Paul Atzberger
Mathematics, Rennsaelaer Polytechnic Institute,
Wednesday Jan 11, 2005
3:05pm in LCB 215
"A Stochastic Immersed Boundary Method Incorporating Thermal Fluctuations : Toward Modeling Cellular Micromechanics"

The mechanics of many cellular systems involve elastic structures which interact with a fluid, for example the outer cell membrane deforms during protrusions generated during motility and cell organelles such as the Golgi Apparatus and Mitochondria involve membranes which deform and bud vesicular and tubular structures during biological processes. Modeling, analyzing, and simulating the mechanics of such systems presents many mathematical challenges. The immersed boundary method is one modeling approach for such systems, and has been applied to many macroscopic biological problems, such as blood flow in the heart and lift generation in insect flight. At the length scales of cells and cell organelles, thermal fluctuations also become significant and must be taken into account. In this talk we discuss an extension of the immersed boundary method framework which incorporates thermal fluctuations through appropriate stochastic forcing terms in the fluid equations. This gives a system of stiff SPDE's for which standard numerical approaches perform poorly. We discuss a novel stochastic numerical method which exploits stochastic calculus to handle stiff features of the equations. We further show how this numerical method can be applied in practice to model the basic microscopic mechanics of polymers, polymer knots, membrane sheets, and vesicles. We also discuss preliminary work on modeling the dynamics of cell organelle structures.