Investigating rare events with nonequilibrium work measurements. I. Nonequilibrium transition path probabilities

We have developed a formalism for investigating transition pathways and transition probabilities for rare events in biomolecular systems. In this paper, we set the theoretical framework for employing nonequilibrium work relations to estimate the relative reaction rates associated with different classes of transition pathways. Particularly, we derive an extension of Crook's transient fluctuation theorem, which relates the relative transition rates of driven systems in the forward and reverse directions, and allows for the calculation of these relative rates using work measurements (e.g., in Steered Molecular Dynamics). The formalism presented here can be combined with Transition Path Theory to relate the equilibrium and driven transition rates. The usefulness of this framework is illustrated by means of a Gaussian model and a driven proline dimer.