Temperature dependent activation energy for electron transfer between biological molecules

TLDR

This paper examines electron transfer between biological molecules as a nonadiabatic multiphonon nonradiative decay process in a dense medium. The theoretical framework extends quantum mechanical outer‑sphere electron transfer theory by incorporating both low‑frequency medium phonon modes and high‑frequency molecular modes. The authors derive a compact, temperature‑dependent expression for electron‑transfer probability that smoothly transitions from tunneling at low temperatures to an activated rate at high temperatures, diverges from the semiclassical Gaussian approximation at low temperatures, and accurately reproduces De Vault and Chance’s experimental data for cytochrome–chlorophyll transfer in Chromatium. Experimental data from De Vault and Chance (Biophys.

Abstract

This paper considers electron transfer between biological molecules in terms of a nonadiabatic multiphonon nonradiative decay process in a dense medium. This theoretical approach is analogous to an extended quantum mechanical theory of outer sphere electron transfer processes, incorporating the effects of both low-frequency medium phonon modes and the high-frequency molecular modes. An explicit, compact and useful expression for the electron transfer probability is derived, which is valid throughout the entire temperature range, exhibiting a continuous transition from temperature independent tunneling between nuclear potential surfaces at low temperatures to an activated rate expression at high temperatures. This result drastically differs at low temperatures from the common, semiclassical, Gaussian approximation for the transition probability. The experimental data of De Vault and Chance [Biophys. J. 6, 825 (1966)] on the temperature dependence of the rate of electron transfer from cytochrome to the chlorophyll reaction center in the photosynthetic bacterium Chromatium are properly accounted for in terms of the present theory.