Nanosecond motions in proteins impose bounds on the timescale distributions of local dynamics

We elucidate the physics of the dynamical transition via 10-100ns molecular dynamics simulations at temperatures spanning 160-300K. By tracking the energy fluctuations, we show that the protein dynamical transition is marked by a cross-over from piecewise stationary to stationary processes that underlie the dynamics of protein motions. A two-time-scale function captures the non-exponential character of backbone structural relaxations. One is attributed to the collective segmental motions and the other to local relaxations. The former is well-defined by a single-exponential, nanosecond decay, operative at all temperatures. The latter is described by a set of processes that display a distribution of time-scales. Though their average remains on the picosecond time-scale, the distribution is markedly contracted at the onset of the transition. The collective motions are shown to impose bounds on time-scales spanned by local dynamical processes. The piecewise stationary character below the transition implicates the presence of a collection of sub-states whose interactions are restricted. At these temperatures, a wide distribution of local motion time-scales, extending beyond that of nanoseconds is observed. At physiological temperatures, local motions are confined to time-scales faster than nanoseconds. This relatively narrow window makes possible the appearance of multiple channels for the backbone dynamics to operate.