Theory of Electron Transfer and Related Reactions
Abstract
Approved for public release1. Theory of single molecule experiments on free rotation of a biological motor, F1-ATPase Single molecule experiments on biological motors are of two types, one involving free rotation1 and the other using external fields to control the rotation and or stall it2. In the proposed research we focus on several aspects of the free rotation experiments. Questions we will address include why do they obey3 the Michaelis-Menten catalysis equation that was designed for systems having a few reaction steps and rate constants, namely that for the binding of the reactant, here ATP, that for the reverse reaction of ATP release, and thatfor the reaction to form the reaction products, here ADP and inorganic phosphate Pi. The Michaelis-Menten equation contains no angle-dependent rate constants, for example. A successful analysis would permit us to relate the observations in ensemble systems to those in single molecule experiments, as well as to understand the thus far untreated but observed effect of temperature4 on the single molecule free rotation experiments. The entropy of activation of the catalytic step would provide one test of a hypothesis 5 that the catalysis involves a positively charged arginine residue attacking a negatively charged phosphate in the ATP. A cancellation or partial cancellation of the charges of the two reactants (the recombination of two charges) is expected to yield a substantial positive entropy of activation for the reaction step. In relating single molecule studies of free rotation of the motor to the Michaelis-Menten behavior a detailed study of the individual steps is needed. These steps include dwells and jumps between dwells in the rotation. The kinetic behavior during a jump has been treated in the literature, by others10 and by us15 using an overdamped equation. However, the transitions between dwells and jumps require an acceleration, and so require a more general approach that includes it. Itis planned to do soin terms of a torque generated by an entrance or exit of a nucleotide (ATP) into or out of a cleft in the F1-ATPase.2. Theory of electron transfer reactions rates ranging from adiabatic to nonadiabaticIn recent years, there has been extensive interest in studying increasingly faster chemical reactions, including particularly electron transfer reactions. A recent review is given in ref 14. Current studies have been made with increasingly faster techniques so as to now include reactions in the 50 fsec orso time regime. One theoretical equation that is intended to cover this large range of reaction lifetimes, has been given by Heitele et al.6. However, no derivation has been given of this equation and there is reason to believe that it was obtained intuitive as an interpolation between available expressions for the adiabatic and nonadiabatic limits of reaction rate constant. In the present proposal we plan to give a derivation and, in the process, see if the Heitele equation is also a special case of a somewhat more general equation. Application to data on ultrafast electron transfer reactions, including those at semiconductor surfaces, is planned.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 15, 2023
- Source ID
- N000142312401
Entities
People
- Rudolph A. Marcus
Organizations
- California Institute of Technology
- Office of Naval Research
- United States Navy