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Continuum Diffusion Reaction Rate Calculations of Wild-Type and Mutant Mouse Acetylcholinesterase: Adaptive Finite Element Analysis

Yuhua Song ^*, Yongjie Zhang , Chandrajit L. Bajaj  and Nathan A. Baker ^*

^* Department of Biochemistry and Molecular Biophysics, Center for Computational Biology, Washington University in St. Louis, St. Louis, Missouri; and Institute for Computational Engineering and Sciences, Center for Computational Visualization, and Department of Computer Sciences and Institute for Computational Engineering and Sciences, Center for Computational Visualization, The University of Texas at Austin, Austin, Texas

Correspondence: Address reprint requests to Nathan A. Baker, Dept. of Biochemistry and Molecular Biophysics, Center for Computational Biology, Washington University in St. Louis, 700 S. Euclid Ave., Campus Box 8036, St. Louis, MO 63110. Tel.: 314-362-2040; Fax: 314-362-0234; E-mail: baker{at}biochem.wustl.edu.

As described previously, continuum models, such as the Smoluchowski equation, offer a scalable framework for studying diffusion in biomolecular systems. This work presents new developments in the efficient solution of the continuum diffusion equation. Specifically, we present methods for adaptively refining finite element solutions of the Smoluchowski equation based on a posteriori error estimates. We also describe new, molecular-surface-based models, for diffusional reaction boundary criteria and compare results obtained from these models with the traditional spherical criteria. The new methods are validated by comparison of the calculated reaction rates with experimental values for wild-type and mutant forms of mouse acetylcholinesterase. The results show good agreement with experiment and help to define optimal reactive boundary conditions.

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