Multiple versus single pathways in electron transfer in proteins: Influence of protein dynamics and hydrogen bonds

Abstract

The present work addresses the question of how electron tunneling matrix elements can be quantitatively calculated. In particular, we demonstrate how to go beyond Pathways methods, which have been shown to be qualitatively appropriate to do such calculations. Utilizing a combination of molecular dynamics with semiempirical and ab initio (Hartree–Fock) quantum chemistry calculations, we quantify how the dynamics and quality of the electronic Hamiltonian affect the outcome of the tunneling matrix elements. We show that tunneling is dominated by either one or, at most, a few constructively interfering pathway tubes. Even when equilibrium structures have destructive interference, tunneling is dominated by structures reached by fluctuations, where this interference is destroyed. In this limit, when one or a few constructive pathway tubes dominate, properly selected semiempirical methods are sufficiently powerful to provide quantitative predictions of the tunneling matrix elements. This combined methodology allows us to investigate quite large protein complexes. Calculations involving the electron transfer processes in azurin are used to validate these conclusions.