Non-linear Arrhenius plots in temperature-dependent kinetic studies of enzyme reactions: I. Single transition processes

In the present studies, I have attempted to formulate mathematical expressions for the apparent activation energies of two rate parameters, k α and k β , of steady-state enzyme kinetics. In these expressions, perturbation terms, φ( H), called shape factors can adequately predict the transition curvatures in Arrhenius plots of the kinetic parameters. Factors that may produce non-linearity in Arrhenius plots and that determine φ( H) functions can be classified into two categories: (i) thermodynamic factors including all of secondary equilibrium reactions that modify the elementary processes of enzyme reactions, and (ii) kinetic factors that are attributed to changes in rate-limiting steps occurring in experimental temperature ranges. The expressions of φ( H) terms can vary with mechanisms of enzyme reactions. In the case of a single-step transition mechanism, φ(H) = ΔH∘ (1 + ϑ) where ϑ = K or K [ A] for unimolecular or bimolecular reactions respectively. Δ H∘ terms are the enthalpy changes in the equilibrium reactions that modify the elementary kinetic processes and determine the sharpness of the curvatures in Arrhenius plots. The φ( H) functions represent the effective fraction of the enthalpy changes that offset the primary activation energies and suggest continuity of the transition curvatures of Arrhenius plots. Non-linearity in Arrhenius plots seen in enzyme reactions can be attributed to the susceptibility of enzyme proteins to temperature as well as complexity of reaction mechanisms of enzyme catalysis, and can be readily explained by various factors we have considered. It is suggested that one ought to be able to analyze properly the temperature-dependent behavior of kinetic parameters in terms of reaction mechanisms before discussing the true meaning of the activation energies of enzyme reactions.