Exploring the origin of power law distribution in single-molecule conformation dynamics: Energy landscape perspectives

We explored the origin of power law distribution observed in single-molecule conformational dynamics experiments. By establishing a kinetic master equation approach to study statistically the microscopic state dynamics, we show that the underlying landscape with exponentially distributed density of states leads to power law distribution of kinetics. The exponential density of states emerges when the system becomes glassy and landscape becomes rough with significant trapping. We predicted the power law decay coefficient is monotonically dependent on temperature which can be tested from ongoing experiments. This work bridges statistics from single-molecule kinetic experiments and topography of conformational energy landscape.

The power law distribution of kinetics at long times with exponential density of states: The logarithm of the probability of kinetics of conformation dynamics ln P(0, t) versus time ln t at different temperatures T near or below trapping temperature Tg (in the units of Tg) from exponentially distributed density of states.