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Tetrameric Mouse Acetylcholinesterase: Continuum Diffusion Rate Calculations by Solving the Steady-State Smoluchowski Equation Using Finite Element Methods

Deqiang Zhang ^* , Jason Suen , Yongjie Zhang ^¶, Yuhua Song ^**, Zoran Radic , Palmer Taylor , Michael J. Holst , Chandrajit Bajaj ^¶ ||, Nathan A. Baker ^** and J. Andrew McCammon ^*  

^* Howard Hughes Medical Institute, Department of Chemistry and Biochemistry, and Center for Theoretical Biological Physics, Department of Pharmacology, Department of Mathematics, University of California at San Diego, La Jolla, California 92093; ^¶ Institute of Computational Engineering and Sciences, Center for Computational Visualization, ^|| Department of Computer Sciences, University of Texas at Austin, Texas 78712; and ^** Department of Biochemistry and Molecular Biophysics, Center for Computational Biology, Washington University in St. Louis, Missouri 63110

Correspondence: Address reprint requests to Deqiang Zhang, E-mail: dzhang{at}mccammon.ucsd.edu.

The tetramer is the most important form for acetylcholinesterase in physiological conditions, i.e., in the neuromuscular junction and the nervous system. It is important to study the diffusion of acetylcholine to the active sites of the tetrameric enzyme to understand the overall signal transduction process in these cellular components. Crystallographic studies revealed two different forms of tetramers, suggesting a flexible tetramer model for acetylcholinesterase. Using a recently developed finite element solver for the steady-state Smoluchowski equation, we have calculated the reaction rate for three mouse acetylcholinesterase tetramers using these two crystal structures and an intermediate structure as templates. Our results show that the reaction rates differ for different individual active sites in the compact tetramer crystal structure, and the rates are similar for different individual active sites in the other crystal structure and the intermediate structure. In the limit of zero salt, the reaction rates per active site for the tetramers are the same as that for the monomer, whereas at higher ionic strength, the rates per active site for the tetramers are 67%–75% of the rate for the monomer. By analyzing the effect of electrostatic forces on ACh diffusion, we find that electrostatic forces play an even more important role for the tetramers than for the monomer. This study also shows that the finite element solver is well suited for solving the diffusion problem within complicated geometries.

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