Convex Arrhenius plots and their interpretation

Convex Arrhenius plots and their interpretation

Donald G. Truhlar*,† and
Amnon Kohen†,‡

^*Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455-0431; and ^‡Department of Chemistry, University of Iowa, Iowa City, IA 52242-1294

Edited by Rudolph A. Marcus, California Institute of Technology, Pasadena, CA, and approved November 16, 2000 (received for review September 12, 2000)

Abstract

This paper draws attention to selected experiments on enzyme-catalyzed reactions that show convex Arrhenius plots, which are very rare, and points out that Tolman's interpretation of the activation energy places a fundamental model-independent constraint on any detailed explanation of these reactions. The analysis presented here shows that in such systems, the rate coefficient as a function of energy is not just increasing more slowly than expected, it is actually decreasing. This interpretation of the data provides a constraint on proposed microscopic models, i.e., it requires that any successful model of a reaction with a convex Arrhenius plot should be consistent with the microcanonical rate coefficient being a decreasing function of energy. The implications and limitations of this analysis to interpreting enzyme mechanisms are discussed. This model-independent conclusion has broad applicability to all fields of kinetics, and we also draw attention to an analogy with diffusion in metastable fluids and glasses.

Footnotes

↵ † E-mail: truhlar{at}umn.edu and amnon-kohen{at}uiowa.edu.
This paper was submitted directly (Track II) to the PNAS office.
↵ § Recall that a canonical ensemble is one characterized by a temperature, and a microcanonical ensemble is a slice out of a canonical ensemble such that the slice contains all systems with a given total energy. Note that E _a, E̿, Ē, and dP/dE are all associated with the canonical ensemble and therefore are functions of T, and dP/dE equals the Boltzmann-weighted density of states times a normalization constant (28).
↵ ¶ Microcanonical rate coefficients usually increase with energy in both over-barrier and tunneling regimes except at very low temperature where the reaction occurs entirely by tunneling in the reactant ground state (29, 30).
Abbreviation:

KIE,

Kinetic isotope effect