Two-event echos in single-molecule kinetics: A signature of conformational fluctuations

The relationship between event-averaged measurements and ensemble averaged measurements can be clarified by averaging along single-molecule trajectories. As a result, phenomenological chemical kinetics is shown to contain little information about dynamic disorder, and nonequilibrium relaxation experiments in the bulk state may not be interpreted according to the fluctuation -dissipation relation. The desired information about conformational fluctuations can be inferred from the statistics and correlation of half-reaction events. In particular, the echo time in the two-event probability distribution directly measures the conformational relaxation rate, and the amplitude of the echo probes the variance of the reaction rate. Detailed analysis of four different models (two-channel kinetic scheme, three-channel kinetic scheme, diffusion-modulated reaction, and the Gaussian stochastic rate model) confirms the generality of the two-event echo and its quantitative relations with conformation dynamics. As a general description of the fluctuating rate process, the stochastic rate model and its truncated version provide the flexibility to incorporate various kinetic schemes and functional forms and serve as a first-order model for analyzing single-molecule quantities.