Activation parameters, enthalpy-entropy compensation and the temperature-dependent activity of enzymes

The increase in enzyme-catalyzed reaction rates with temperature is typically modeled using Arrhenius or Eyring relations. Interpretation of extracted parameters is subject to multiple caveats. Here we analyze the impact of temperature variations of underlying activation or Eyring parameters and of temperature-dependent contributions to overall rates from steps other than a rate-limiting chemical step. Linear Arrhenius/Eyring behavior can still be observed when the underlying activation energy $E_a$ or enthalpy $\Delta H^{‡}$ and entropy $\Delta S^{‡}$ vary with temperature. Modest variations-of the order of an H-bond energy over 60°C-lead to large fractional deviations of $E_a$ , $\Delta H^{‡}$ and $\Delta S^{‡}$ values derived from linear fits from their underlying values and to deviations of Arrhenius prefactors $A$ by orders of magnitude. In a family of related enzymes with similar activation free energies $\Delta G^{‡}$ , small differences in temperature-dependent contributions to overall rates will lead to apparent enthalpy-entropy compensation and may scramble enzyme ordering based on $\Delta H^{‡}$ or $\Delta S^{‡}$ . Similar considerations apply to interpretation of van 't Hoff plots of equilibrium measurements and related observations of enthalpy-entropy compensation. For enzymes exhibiting negative curvature and maximum rates well below the unfolding temperature, fits assuming $\Delta H^{‡}\left(T\right)$ and $\Delta S^{‡}\left(T\right)$ are connected by a negative heat capacity $\Delta C_p^{‡}\left(T\right)$ yield physically implausible values, suggesting the importance of other contributions to observed behavior. Complementary methods including pre-steady-state kinetics, kinetic isotope effect and viscosity-dependence measurements, multi-temperature static and time-resolved atomic-resolution structural studies, and simulations should play a key role in quantitatively interpreting temperature-dependent kinetic and equilibrium data from enzymatic systems.