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

¹ University of California, San Diego
² The Univ. of Texas at Austin
³ Washington University in St. Louis
⁴ The univeristy of Texas at Austin
⁵ Washington University School of Medicine
⁶ University of California - San Diego

^* To whom correspondence should be addressed. E-mail: dzhang{at}mccammon.ucsd.edu.

Submitted on October 1, 2004
Revised on December 5, 2004
Accepted on 15 December 2004

	Abstract

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 in order 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, while at higher ionic strength, the rates per active site for the tetramers are about 67% to 75% of the rate for the monomer. As a comparison, the reaction rates per active site of a neutral ligand for the tetramers are only 1/4 to 1/3 of the rate for the monomer, indicating a strong rate enhancement by the electrostatic steering forces. This study also shows that the finite element solver is well suited for solving the diffusion problem within complicated geometries.

Key Words: Smoluchowski equation, Tetrameric Mouse Acetylcholinesterase, diffusion, finite element methods, reaction rate, steady state

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