The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

Abstract

The time dependence of protein structural fluctuations is highly complex, manifesting subdiusive, non-exponential behaviour with eective relaxation times existing over many decades in time, from ps up to 102 s (refs 14). Here, using

molecular dynamics simulations, we show that, on timescales from 1012 to 105 s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance uctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored. Diusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behaviour persists up to timescales approaching the in vivo lifespan of individual protein molecules.