ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
Many-body effects in reaction rates depend on the ratio ε of a rate coefficient to the product of a diffusion coefficient and a radius, and on the reduced volume fraction φ0 of one or more reactants. We present a statistical-mechanical theory of the macroscopic kinetics (deterministic rates) of reactions in solutions, and fluctuations therefrom, for arbitrary ε and φ0, by deriving expressions for effective forward and reverse rate coefficients and their dependence on ε, φ0 to lowest order. We use an enzyme-catalyzed reaction as an example. There are two corrections to rate coefficients (for ε=0, φ0=0) at a given ε, φ0≠0, and both are proportional to φ1/20 (the square root of the total enzyme density in the example). The first is an uncorrelated screening term described by the single enzyme distribution function, which increases the rate; and the second a term described by correlations among enzymes, which decreases the rate. In the limit of very fast reactions the correlation term is negligible, and the screening term reduces to that previously obtained for diffusion controlled reactions. For other cases both terms contribute: for example, in the range φ0∼10−2 to 10−1 and ε∼1–10 the corrections vary from a few percent to 30%, as obtained from numerical solutions of the corrections for the enzyme example. We discuss a quasistationary state of the example and derive a generalization of the Michaelis–Menten equation for all ε, φ0. Fluctuations from the deterministic motion are shown to be small for three-dimensional systems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.456835
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