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Finite Element Analysis of the Time-Dependent Smoluchowski Equation for Acetylcholinesterase Reaction Rate Calculations

Yuhui Cheng ^* , Jason K. Suen , Deqiang Zhang , Stephen D. Bond , Yongjie Zhang ^¶, Yuhua Song ^||, Nathan A. Baker ^||, Chandrajit L. Bajaj ^¶ **, Michael J. Holst  and J. Andrew McCammon ^*  

^* Howard Hughes Medical Institute, Department of Chemistry and Biochemistry, and Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California; Accelrys, San Diego, California; Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, Illinois; ^¶ Institute of Computational Engineering and Sciences, Center for Computational Visualization, University of Texas at Austin, Texas; ^|| Department of Biochemistry and Molecular Biophysics, Center for Computational Biology, Washington University in St. Louis, Missouri; ^** Department of Computer Sciences, University of Texas at Austin, Texas; and Department of Mathematics, Department of Pharmacology, University of California at San Diego, La Jolla, California

Correspondence: Address reprint requests to Y. Cheng, Tel.: 858-822-2771; E-mail: ycheng{at}mccammon.ucsd.edu.

This article describes the numerical solution of the time-dependent Smoluchowski equation to study diffusion in biomolecular systems. Specifically, finite element methods have been developed to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to the mouse acetylcholinesterase (mAChE) monomer and several tetramers. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different time steps. Calculated rates show very good agreement with experimental and theoretical steady-state studies. Furthermore, these finite element methods require significantly fewer computational resources than existing particle-based Brownian dynamics methods and are robust for complicated geometries. The key finding of biological importance is that the rate accelerations of the monomeric and tetrameric mAChE that result from electrostatic steering are preserved under the non-steady-state conditions that are expected to occur in physiological circumstances.

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