Stochastic Thermodynamics of Single Enzymes and Molecular Motors

For a single enzyme or molecular motor operating in an aqueous solution of non-equilibrated solute concentrations, a thermodynamic description is developed on the level of an individual trajectory of transitions between states. The concept of internal energy, intrinsic entropy and free energy for states follows from a microscopic description using one assumption on time scale separation. A first-law energy balance then allows the unique identification of the heat dissipated in one transition. Consistency with the second law on the ensemble level enforces both stochastic entropy as third contribution to the entropy change involved in one transition and the local detailed balance condition for the ratio between forward and backward rates for any transition. These results follow without assuming weak coupling between the enzyme and the solutes, ideal solution behavior or mass action law kinetics. The present approach highlights both the crucial role of the intrinsic entropy of each state and the physically questionable role of chemiostats for deriving the first law for molecular motors subject to an external force under realistic conditions.