Chemical and mechanical efficiencies of molecular motors and implications for motor mechanisms

Molecular motors operate in an environment dominated by viscous friction and thermal fluctuations. The chemical reaction in a motor may produce an active force at the reaction site to directly move the motor forward. Alternatively a molecular motor may generate a unidirectional motion by rectifying thermal fluctuations using free energy barriers established in the chemical reaction. The reaction cycle has many occupancy states, each having a different effect on the motor motion. The average effect of the chemical reaction on the motor motion can be characterized by the motor potential profile. The biggest advantage of studying the motor potential profile is that it can be reconstructed from the time series of motor positions measured in single-molecule experiments. In this paper, we use the motor potential profile to express the Stokes efficiency as the product of the chemical efficiency and the mechanical efficiency. We show that both the chemical and mechanical efficiencies are bounded by 100% and, thus, are properly defined efficiencies. We discuss implications of high efficiencies for motor mechanisms: a mechanical efficiency close to 100% implies that the motor potential profile is close to a constant slope; a chemical efficiency close to 100% implies that (i) the chemical transitions are not slower than the mechanical motion and (ii) the equilibrium constant of each chemical transition is close to one.