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.