Promoting modes and demoting modes in enzyme-catalyzed proton transfer reactions: A study of models and realistic systems

A number of proton transfer reactions have been studied to reveal the identity of modes that influence the rate constant, especially in the context of enzyme catalysis. Results with analytic model potentials confirmed the general notion that the effect of a given mode on the proton transfer rate depends on the symmetry of its coupling with the proton transfer coordinate. Symmetrically coupled modes have promoting effects at both high and. low temperatures, although the origin of promotion is largely classical at room temperature and the increase of tunneling is important only at low temperature. Antisymmetric modes have "demoting effects" mainly because the antisymmetric coupling gives rise to asymmetry in the effective potential along the proton transfer coordinate and therefore restricts tunneling to occur effectively only when the mode is vibrationally excited. Thus, vibrational excitation of both types of modes can be important for the proton transfer rate. Calculations on TIM with a QM/MM potential clearly demonstrated that the proton transfer is strongly coupled to a large number of vibrations (including both symmetric and antisymmetric modes), which in general are localized to atoms in the active site. One of the modes is the donor-acceptor stretch, which modulates the effective barrier for the proton transfer and also the effect of tunneling. There are also other modes that are symmetrically or antisymmetrically coupled to the proton-transfer coordinate, and they involve nearby residues such as Ala 212 and Ile 170. Their effect is to adjust the enzyme environment by lowering the effective proton-transfer barrier. We propose procedures to identify motions that are important for the proton transfer based on reaction path curvature and coupling coefficients. We also emphasize that the minimum energy path (MEP) involves changes in environmental variables, such as the donor-acceptor stretch, as the primary part in the reactant and product regions and includes significant proton motion only near the barrier. Thus, there is no fundamental conflict between the MEP description of proton transfers at room temperature and Marcus type of models in the adiabatic regime; that is, both include contributions from change in the zero-point energies.