The role of quantum effects in proton transfer reactions in enzymes: quantum tunneling in a noisy environment?

We consider the role of quantum effects in the transfer of hydrogen-like species in enzyme-catalyzed reactions. This review is stimulated by claims that the observed magnitude and temperature dependence of kinetic isotope effects (KIEs) implies that quantum tunneling below the energy barrier associated with the transition state significantly enhances the reaction rate in many enzymes. We review the path integral approach and the Caldeira–Leggett model, which provides a general framework to describe and understand tunneling in a quantum system that interacts with a noisy environment at nonzero temperature. Here the quantum system is the active site of the enzyme, and the environment is the surrounding protein and water. Tunneling well below the barrier only occurs for temperatures less than a temperature T₀, which is determined by the curvature of the potential energy surface near the top of the barrier. We argue that for most enzymes this temperature is less than room temperature. We review typical values for the parameters in the Caldeira–Leggett Hamiltonian, including the frequency-dependent friction and noise due to the environment. For physically reasonable parameters, we show that quantum transition state theory gives a quantitative description of the temperature dependence and magnitude of KIEs for two classes of enzymes that have been claimed to exhibit signatures of quantum tunneling. The only quantum effects are those associated with the transition state, both reflection at the barrier top and tunneling just below the barrier. We establish that the friction and noise due to the environment are weak and only slightly modify the reaction rate. Furthermore, at room temperature and for typical energy barriers environmental fluctuations with frequencies much less than 1000 cm⁻¹ do not have a significant effect on quantum corrections to the reaction rate. This is essentially because the time scales associated with the dynamics of proton transfer are faster than much of the low-frequency noise associated with the protein and solvent.