CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM UNIVERSITY OF COLORADO AT DENVER TITLE: Mathematical and Computational Problems Arising in Models of Biological Molecules and Membranes SPEAKER: Michael Holst, Applied Mathematics, California Institute of Technology DATE: Tuesday, February 20, 1996 PLACE: Math Conference Room - Suite 540 UCD Building, 1250 14th St., Denver TIME: noon - 1 pm ABSTRACT In this talk we will focus on the mathematical formulation and numerical solution of nonlinear electrostatic and elastostatic problems arising in the modeling of biological molecules and membranes. These types of problems have several interesting features impacting both theoretical analysis and numerical algorithms, including discontinuous coefficients, rapid nonlinearities, and complex geometric shapes in three spatial dimensions. Furthermore, numerical solutions to these problems can provide insight into the biological mechanisms which lead to disorders such as Lou Gehrig's disease, multiple sclerosis, and AIDS. A Poisson-Boltzmann equation is first derived from a continuum electrostatic model of a biomolecule in a solvent, which leads to a coupled nonlinear elliptic system when an immersed membrane is modeled with large-deformation elasticity theory. Solvability of the system is considered using standard function-space methods, and inexact-Newton -multilevel methods are developed for the discretized equations. The methods are analyzed using a general operator-theoretic framework, and some numerical results are presented for models of the HIV protease and SOD, an enzyme which has recently been linked to Lou Gehrig's disease. We discuss some preliminary attempts to model myelin breakdown, a process which leads to multiple sclerosis. We briefly outline the implementations in CC++, a minimal superset of C++ developed at Caltech, which provides some convenient tools for parallel computing. This is joint work with several people at the California Institute of Technology, Columbia University, Boston University, and the University of Illinois at Urbana-Champaign.