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 expected small temperature variations of underlying activation/Eyring parameters on this modeling. 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 variation of $\Delta H$ and $\Delta S$ will lead to apparent enthalpy-entropy compensation and may scramble enzyme ordering based on $\Delta H$ or $\Delta S$ . For enzymes from cold and warm-adapted species having largely similar active sites, small temperature variations of $\Delta H$ and $\Delta S$ may explain large differences in apparent $\Delta H$ values. Similar considerations apply to interpretation of van 't Hoff plots of equilibrium measurements and related observations of enthalpy-entropy compensation. Complementary methods including simulations and multi-temperature static and time-resolved atomic-resolution structural studies should play a key role in interpreting temperature-dependent kinetic and equilibrium data from enzymatic systems.