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Theory and Simulation of Diffusion-Controlled Michaelis-Menten Kinetics for a Static Enzyme in Solution
 

Summary: Theory and Simulation of Diffusion-Controlled Michaelis-Menten Kinetics for a Static
Enzyme in Solution
Soohyung Park and Noam Agmon*
Institute of Chemistry and the Fritz Haber Research Center, The Hebrew UniVersity, Jerusalem 91904, Israel
ReceiVed: July 27, 2007; In Final Form: NoVember 5, 2007
We develop a uniform theory for the many-particle diffusion-control effects on the Michaelis-Menten scheme
in solution, based on the Gopich-Szabo relaxation-time approximation (Gopich, I. V.; Szabo, A. J. Chem.
Phys. 2002, 117, 507). We extend the many-particle simulation algorithm to the Michaelis-Menten case by
utilizing the Green function previously derived for excited-state reversible geminate recombination with different
lifetimes (Gopich, I. V.; Agmon, N. J. Chem. Phys. 2000, 110, 10433). Running the simulation for representative
parameter sets in the time domain and under steady-state conditions, we find poor agreement with classical
kinetics but excellent agreement with some of the modern theories for bimolecular diffusion-influenced
reactions. Our simulation algorithm can be readily extended to the biologically interesting case of dense
patches of membrane-bound enzymes.
I. Introduction
How important are diffusion effects on chemical reactions
in biological systems? Diffusion is the primary transport
mechanism on the cellular scale, yet diffusion is not usually
depicted as a major factor influencing the kinetics of biochemical
reactions. The example analyzed here is that of enzymatic

  

Source: Agmon, Noam - Institute of Chemistry, Hebrew University of Jerusalem

 

Collections: Chemistry