Chemical and mechanical efficiencies of molecular motors and implications for motormechanisms

Abstract

Molecular motors operate in an environment dominated by viscous friction and thermalfluctuations. The chemical reaction in a motor may produce an active force at the reactionsite to directly move the motor forward. Alternatively a molecular motor may generate aunidirectional motion by rectifying thermal fluctuations using free energy barriersestablished in the chemical reaction. The reaction cycle has many occupancy states, eachhaving a different effect on the motor motion. The average effect of the chemical reactionon the motor motion can be characterized by the motor potential profile. The biggestadvantage of studying the motor potential profile is that it can be reconstructed fromthe time series of motor positions measured in single-molecule experiments. Inthis paper, we use the motor potential profile to express the Stokes efficiency asthe product of the chemical efficiency and the mechanical efficiency. We showthat both the chemical and mechanical efficiencies are bounded by 100% and,thus, are properly defined efficiencies. We discuss implications of high efficienciesfor motor mechanisms: a mechanical efficiency close to 100% implies that themotor potential profile is close to a constant slope; a chemical efficiency closeto 100% implies that (i) the chemical transitions are not slower than the mechanicalmotion and (ii) the equilibrium constant of each chemical transition is close to one.