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Published November 17, 2015 | Published
Journal Article Open

Theory for rates, equilibrium constants, and Brønsted slopes in F₁-ATPase single molecule imaging experiments

Abstract

A theoretical model of elastically coupled reactions is proposed for single molecule imaging and rotor manipulation experiments on F₁-ATPase. Stalling experiments are considered in which rates of individual ligand binding, ligand release, and chemical reaction steps have an exponential dependence on rotor angle. These data are treated in terms of the effect of thermodynamic driving forces on reaction rates, and lead to equations relating rate constants and free energies to the stalling angle. These relations, in turn, are modeled using a formalism originally developed to treat electron and other transfer reactions. During stalling the free energy profile of the enzymatic steps is altered by a work term due to elastic structural twisting. Using biochemical and single molecule data, the dependence of the rate constant and equilibrium constant on the stall angle, as well as the Brønsted slope are predicted and compared with experiment. Reasonable agreement is found with stalling experiments for ATP and GTP binding. The model can be applied to other torque-generating steps of reversible ligand binding, such as ADP and Pi release, when sufficient data become available.

Additional Information

© 2015 National Academy of Sciences. Contributed by Rudolph A. Marcus, September 17, 2015 (sent for review August 25, 2015; reviewed by Attila Szabo and Arieh Warshel). Published online before print October 19, 2015. We thank Drs. Long Cai, Attila Szabo, David Thirumulai, and Arieh Warshel for their helpful comments. The authors would like to acknowledge support from the Office of the Naval Research, the Army Research Office, and the James W. Glanville Foundation.

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August 22, 2023
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