How can the temperature dependence of enzyme-catalyzed reaction rates provide evidence for or against the involvement of quantum tunneling?

The temperature dependence of enzyme-catalyzed reaction rates can provide evidence for or against the involvement of quantum tunneling because tunneling is less sensitive to temperature changes compared to classical over-the-barrier reactions. Classically, reaction rates generally increase with temperature following the Arrhenius equation, where the rate constant is proportional to exp(-Ea/RT), with Ea being the activation energy, R the gas constant, and T the temperature. This means a plot of ln(rate) versus 1/T (an Arrhenius plot) should be linear, with the slope related to the activation energy. If quantum tunneling is a significant component of the reaction, the temperature dependence will deviate from this classical behavior. Specifically, if tunneling dominates, the reaction rate becomes less sensitive to temperature. An Arrhenius plot may show a smaller slope (lower apparent activation energy) or even become nearly flat at lower temperatures, indicating that the reaction proceeds via tunneling even when the thermal energy is insufficient to overcome the barrier classically. In some cases, the reaction rate might even show an inverse temperature dependence at very low temperatures, meaning the rate slightly decreases as temperature increases. This can happen because the population of molecules in the optimal tunneling configuration might decrease with increasing temperature due to changes in protein dynamics. Therefore, a significant deviation from Arrhenius behavior, such as a flattened Arrhenius plot or an inverse temperature dependence at low temperatures, provides evidence for the involvement of quantum tunneling in enzyme-catalyzed reactions. Conversely, a linear Arrhenius plot over a wide temperature range suggests that the reaction primarily proceeds via classical over-the-barrier mechanisms, with tunneling playing a minimal role.