Analytical theory of the nonequilibrium spatial distribution of RNA polymerase translocations

A continuum Fokker-Planck model is considered for the RNA polymerase in the elongation phase, where the topology of a single free energy profile as a function of the translocation variable distinguishes the Brownian ratchet and power stroke mechanisms. The model yields a simple analytical stationary solution for arbitrary functional forms of the free energy. With the translocation potential of mean force estimated by the time-series data of the recent high-resolution single-molecule experiment [Abbondanzieri et al., Nature (London) 438, 460 (2005)], predictions of the model for the mechanical properties agree with experiments quantitatively with reasonable values of parameters. The evolution of the spatial distribution of translocation variable away from equilibrium with increasing nucleoside triphosphate concentration shows qualitatively different behavior in the two alternative scenarios, which could serve as an additional measurable signature of the underlying mechanism.