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Summary: 7326 J. Phys. Chem. 1991, 95, 7326-7330
Competitive Reversible Blnding: A Bimolecular Boundary Condition for the DMusion
Equation
Noam Agmon,*
Department of Physical Chemistry and The Fritz Haber Research Center, The Hebrew University of Jerusalem,
Jerusalem 91904, Israel
Horst Schnorer, and Alexander Blumen
Physical Institute and BIMF, University of Bayreuth, 0-8580Bayreuth, W.Germany
(Received: February 27, 1991)
We simulate one-dimensional competitive reversible binding of many diffusing particles to a single, saturable, static site.
The particles are initially randomly distributed, and either one or none is initially bound to the site. The time dependence
of the binding probability (siteoccupancy)is comparedwith an approximationinvolvingsingleparticlediffusion with a nonlinear,
locally bimolecular, boundary condition representing the mutual site-blocking effect. Our comparison indicates that the
approximation is exact in the limit of low site occupancy (infinite particle dilution) and possibly a strict bound otherwise.
It also indicates that a reciprocity relation derived earlier for the two initial conditionsis exact and that decay to equilibrium
is a power law. This contrasts with an exponentialdecay to equilibriumpredicted from a pseudounimolecularkineticscheme
of conventional chemical kinetics, although the equilibrium value of the binding probability agrees with the conventional
kinetic/thermodynamic prediction.
I. Introduction
The competition of many diffusing particles over a single
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