Proton-Coupled Electron Transfer and the “Linear Approximation” for Coupling to the Donor–Acceptor Distance Fluctuations

Abstract

The often-used "linear approximation" for treating the coupling of proton donor-acceptor (D-A) distance fluctuations to proton-coupled electron transfer tunneling reactions is systematically examined. The accuracy of this approximation is found to depend on the potential energy surfaces that are used to describe both the tunneling particle vibrations and the D-A coordinate probability distribution. Harmonic treatment of both the tunneling particle and the D-A coordinates results in a significant breakdown of the linear approximation when the width of the D-A distribution exceeds ∼0.05 Å. When a symmetric back-to-back Morse potential is used to describe the tunneling particle vibrations in the reactant and product states, the D-A distribution width can be expanded up to ∼0.09 Å before the rates calculated using the linear approximation exceed the exact result by an order of magnitude. Incorporation of a more realistic anharmonic D-A potential, based on quantum calculations, includes the important electronic D-A repulsion energy so that the sampling of short D-A distances is reduced. This approach improves the linear approximation as long as the D-A distribution has a width less than ∼0.1 Å. The conditions for the validity of the linear approximation are found to be more fragile when the calculated kinetic isotope effect (KIE) and its temperature dependence are also taken into account.

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

“…As might be expected, this also reduces the calculated tunneling rate and minimizes the need for proton-level adiabatic corrections. , Under some conditions where strong external forces are applied, the inclusion of the anharmonic electronic repulsion can tightly localize the D–A distribution. Such localization helps to improve the linear Taylor’s expansion approximation (“linear approximation”) that is sometimes used to treat the “coupling” of the D–A motion to the tunneling reaction. ,,− …”

The Soybean Lipoxygenase–Substrate Complex: Correlation between the Properties of Tunneling-Ready States and ENDOR-Detected Structures of Ground States

“…This is the origin of the increase in the enthalpic barrier for D relative to H-transfer (i.e., Δ E a ≫ 0). Both linear and quadratic treatments of an anharmonic DAD sampling coordinate, and its exponential coupling to the tunneling rate, have been described previously. − While the quadratic analysis is the more mathematically complete, the series of SLO mutants characterized herein is well fit within the linear region of the function. , …”

“…33,34 In conjunction with averaged X-ray structures for SLO in the absence of a substrate, 22,28,35 ENDOR has the power to quantify distributions of active (conformer a) and inactive (conformer b) ground-state E−S complexes, allowing correlation of these distributions with catalytic function. 31 We recently applied 13 C ENDOR spectroscopy to SLO using a high-spin (S = 5 / 2 ) Mn 2+ spin reporter substituted for the native Fe 2+ cofactor. This approach provides an exceptional spatial "horizon" of ≤6 Å for measuring the through-space Mn− 13 C metal−substrate carbon distances in WT and in a number of SLO variants.…”

“…Catalytically important residues are shown as spheres;yellow spheres represent Leu754. The substrate (green sticks; the reactive carbon, C11, is colored black) was modeled using previous ENDOR geometries of the dominant ground-state conformer 31. The Mn 2+ (OH 2 ) cofactor is shown as purple and red spheres, respectively.…”

“…While the mounting kinetic evidence from studies of the temperature dependence of the kinetic isotope effect, Δ E a , sheds light on the compactness of the TRS, it has remained unclear how the structure of the ground-state enzyme–substrate (E–S) complex is modulated by size reducing mutations and, more importantly, how ground-state perturbations impact and correlate with the transient compaction of the DAD. Herein, we apply the high-resolution capabilities of electron–nuclear double-resonance (ENDOR) spectroscopy to compare the conformational distributions of ground-state E–S complexes for the native (wild-type, WT) SLO to those of a series of six selected site-directed mutations. , In conjunction with averaged X-ray structures for SLO in the absence of a substrate, ,, ENDOR has the power to quantify distributions of active (conformer a ) and inactive (conformer b ) ground-state E–S complexes, allowing correlation of these distributions with catalytic function …”