Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion

Abstract

Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton transfer and proton-coupled electron transfer in chemical and biological processes. C 2015 AIP Publishing LLC. [http://dx

Hydrostatic Pressure Studies Distinguish Global from Local Protein Motions in C−H Activation by Soybean Lipoxygenase‐1

“…We have previously shown that quite small changes in H-donor-acceptor distances can lead to significant rate differences. [6d] Using previously derived expressions [7a] , we attribute the present increases in rate at 1.034 bar to a very small active site compression, of ca. 0.02 Å, that affects the H-transfer slightly less than that for D-transfer.…”

“…[5] Soybean lipoxygenase-1 (SLO-1, Figure 1), a prototype for the study of enzymatic C-H activation via hydrogen-tunneling, is providing a unique window into the subtle influence of protein motions on catalysis. [6,7] In the present study, we focus on understanding the underlying interaction between two distinct classes of catalysis-linked protein motions in H-transfer reactions: local distance sampling that is dependent on substrate labeling with isotopes and global conformational landscapes that are independent of this labeling. [3,5] We systematically explore the combined impact of temperature and pressure on the full set of kinetics parameters for WT SLO-1 and a range of mutants with established kinetic properties at ambient pressure.…”

“…The pressure-temperature variation in the enzymatic kinetics of WT, I553V and L546A may further provide a set of experimental parameters that can be used to incorporate global protein conformational sampling into current mathematical models for non-adiabatic deep tunneling of hydrogen. [7] Finally, we suggest that these studies, which validate the concept of remote tuning of catalytic efficiency, should be considered in future design studies of biocatalysts. [17] …”

A qualitative quantum rate model for hydrogen transfer in soybean lipoxygenase

“…A successful framework employing Fermi's golden rule is presented by Hammes-Schiffer and co-workers [6][7][8][9][10][11][12]22,40,41 . This rate model provides a good fit to the wild-type SLO KIE data 13 as well as predicting the KIE magnitude and temperature dependence of the mutants M1, M2, M3 (and its variants 30 ) and the double mutant 11 .…”

“…An alternative transfer mechanism is also possible: the transferring particle may tunnel 5 through the barrier instead of hopping over it. This has been discussed in a number of enzymatic systems that catalyse hydrogen transfer and have high kinetic isotope effects (KIEs), such as soybean lipoxygenase (SLO) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] .…”