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Paul Atzberger
Department of Mathematical Sciences

Rensselaer Polytechnic Institute


A Stochastic Immersed Boundary Method Incorporating Thermal Fluctuations: Toward Modeling Membrane Dynamics of the Cell

The dynamics of biomembranes play an important role both mechanically and chemically in many cellular processes from the protrusions generated in cell motility to the functioning of complex organelles such as the golgi apparatus.  To a first approximation a membrane can be regarded as a mutable elastic sheet which interacts with a fluid.  For macroscopic systems the immersed boundary method has been successfully applied in modeling many problems in which elastic structures interact with a fluid.  These include blood flow in the heart, lift generation in insect flight, and wave propogation in the cochlea.  In this talk the framework of the immersed boundary method is extended to model biomembranes.  At the length scale of cells and cell organelles thermal fluctuations become significant and are incorporated in the immersed boundary method through appropriate stochastic forcing terms in the fluid equations. A practical simulation method is presented overcoming stiffness in the governing equations by making use of techniques from stochastic calculus.  The numerical scheme allows for long time steps by under-resolving the fastest degrees of freedom associated with the fluid while accounting for their statistical contributions over the time step.  Simulations of membrane sheets and vesicles are then discussed along with preliminary results for a model of the golgi apparatus.



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