Tunneling Kinetics and Nonadiabatic Proton-Coupled Electron Transfer in Proteins: The Effect of Electric Fields and Anharmonic Donor–Acceptor Interactions

A proper description of proton donor-acceptor (D-A) distance fluctuations is crucial for understanding tunneling in proton-coupled electron transport (PCET). The typical harmonic approximation for the D-A potential results in a Gaussian probability distribution, which does not appropriately reflect the electronic repulsion forces that increase the energetic cost of sampling shorter D-A distances. Because these shorter distances are the primary channel for thermally activated tunneling, the analysis of tunneling kinetics depends sensitively on the inherently anharmonic nature of the D-A interaction. Thus, we have used quantum chemical calculations to account for the D-A interaction and developed an improved model for the analysis of experimental tunneling kinetics. Strong internal electric fields are also considered and found to contribute significantly to the compressive forces when the D-A distance distribution is positioned below the van der Waals contact distance. This model is applied to recent experiments on the wild type (WT) and a double mutant (DM) of soybean lipoxygenase-1 (SLO). The compressive force necessary to prepare the tunneling-active distribution in WT SLO is found to fall in the ∼ nN range, which greatly exceeds the measured values of molecular motor and protein unfolding forces. This indicates that ∼60-100 MV/cm electric fields, aligned along the D-A bond axis, must be generated by an enzyme conformational interconversion that facilitates the PCET tunneling reaction. Based on the absolute value of the measured tunneling rate, and using previously calculated values of the electronic matrix element, the population of this tunneling-active conformation is found to lie in the range 10 -5 -10 -7 , indicating this is a rare structural fluctuation that falls well below the detection threshold of recent ENDOR experiments. Additional analysis of the DM tunneling kinetics leads to a proposal that a disordered (high entropy) conformation could be tunneling-active due to its broad range of sampled D-A distances.