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

The relationship between event-averaged measurements and ensemble averaged measurements can be clarified by averaging along single-molecule trajectori es. As a result, phenomenological chemical kinetics is shown to contain lit tle information about dynamic disorder, and nonequilibrium relaxation exper iments in the bulk state may not be interpreted according to the fluctuatio n -dissipation relation. The desired information about conformational fluct uations can be inferred from the statistics and correlation of half-reactio n events. In particular, the echo time in the two-event probability distrib ution directly measures the conformational relaxation rate, and the amplitu de 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 mod el) confirms the generality of the two-event echo and its quantitative rela tions with conformation dynamics. As a general description of the fluctuati ng rate process, the stochastic rate model and its truncated version provid e the flexibility to incorporate various kinetic schemes and functional for ms and serve as a first-order model for analyzing single-molecule quantitie s.