Explain the role of kinetic isotope effects (KIEs) in providing experimental evidence for quantum tunneling in enzymatic reactions, including the expected magnitude of the effect.

Kinetic isotope effects (KIEs) are changes in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. This effect is used to investigate reaction mechanisms. In the context of enzyme-catalyzed reactions, KIEs can provide strong evidence for quantum tunneling when a proton or hydrogen atom is transferred. If tunneling is a significant part of the reaction mechanism, replacing hydrogen (H) with deuterium (D), a heavier isotope, will cause a much larger change in the reaction rate than predicted by classical transition state theory. This is because deuterium, being heavier, has a lower probability of tunneling through the reaction's potential energy barrier compared to hydrogen. Classically, the expected KIE from isotopic substitution arises mainly from the change in vibrational frequencies of the bond being broken, typically resulting in a KIE value between 1 and 7. However, if tunneling is dominant, the observed KIE can be significantly larger, sometimes exceeding 10 or even 20. This 'large' KIE is a strong indicator that tunneling is playing a major role in the reaction. Furthermore, the temperature dependence of the KIE can also provide evidence for tunneling. In classical reactions, the KIE usually decreases with increasing temperature. However, for reactions dominated by tunneling, the KIE may be temperature-independent or even increase with temperature. This unusual temperature dependence is because tunneling becomes relatively more important at lower temperatures. Therefore, observing a large KIE, especially one that is temperature-independent or increases with temperature, suggests that quantum tunneling is a significant factor in the enzyme-catalyzed reaction.