This paper draws attention to selected experiments on enzymecatalyzed 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.
In recent years, an increasing number of studies have measured the temperature dependence of enzyme reactions for both thermostable and mesostable enzymes (enzymes from organisms that grow optimally at high temperature and at normal body temperature, respectively). The temperature dependence is usually exhibited in an Arrhenius plot, which is the natural logarithm of the rate coefficient vs. reciprocal of the absolute temperature ( Fig. 1). Some of the methodologies for measuring the temperature dependences of reaction rates have been applied to measure the temperature dependences of the kinetic isotope effects (KIEs) of the catalyzed reactions as well, and such experiments provide experimental data very relevant to characterizing the dynamical bottlenecks of the reactions (1-6). A large number of theoretical models have been advanced for the interpretation of this kind of data (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19).Experiments on reactions catalyzed by a variety of thermostable and mesostable dehydrogenase and oxidase enzymes have shown that in some cases the Arrhenius plot for the chemical step is convex (20)(21)(22)(23). In the present paper, we comment on the significance of this observation, and we provide an interpretation of this finding that places it in the broader perspective of nonbiological chemical as well as biochemical kinetics. This paper points out that the convex Arrhenius behavior places a severe constraint on the microcanonical unimolecular rate coefficient for the chemical step. In particular, we can go beyond the obvious interpretation that a convex Arrhenius plot can be interpreted as a lower than expected rate at high temperatures, and we can say, under certain conditions, that the microcanonical unimolecular rate coefficient for the chemical step must actually decrease with increasing energy.In general, it is desirable to separate the interpretation of experimental data into two steps. First, we infer general consequences that rest on solid foundations such as thermody...