Research article

Kinetics of diffusion-controlled enzymatic reactions with charged substrates

Benzhuo Lu¹* and J Andrew McCammon²

• * Corresponding author: Benzhuo Lu bzlu@lsec.cc.ac.cn

Author Affiliations

¹ State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

² Department of Chemistry and Biochemistry, Center for Theoretical Biological Physics, Department of Pharmacology, Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA, 92093-0365, USA

For all author emails, please log on.

PMC Biophysics 2010, 3:1 doi:10.1186/1757-5036-3-1

Published: 18 January 2010

Abstract

The Debye-Hückel limiting law (DHL) has often been used to estimate rate constants of diffusion-controlled reactions under different ionic strengths. Two main approximations are adopted in DHL: one is that the solution of the linearized Poisson-Boltzmann equation for a spherical cavity is used to estimate the excess electrostatic free energy of a solution; the other is that details of electrostatic interactions of the solutes are neglected. This makes DHL applicable only at low ionic strengths and dilute solutions (very low substrate/solute concentrations). We show in this work that through numerical solution of the Poisson-Nernst-Planck equations, diffusion-reaction processes can be studied at a variety of conditions including realistically concentrated solutions, high ionic strength, and certainly with non-equilibrium charge distributions. Reaction rate coefficients for the acetylcholine-acetylcholinesterase system are predicted to strongly depend on both ionic strength and substrate concentration. In particular, they increase considerably with increase of substrate concentrations at a fixed ionic strength, which is open to experimental testing. This phenomenon is also verified on a simple model, and is expected to be general for electrostatically attracting enzyme-substrate systems.

PACS Codes: 82.45.Tv, 87.15.Vv

MSC Codes: 92C30