Complex Non-equilibrium Structural Dynamics in Globular Proteins

Internal structural motions in proteins are essential to their functions. In this present dissertation, we present the results from an extensive set of molecular dynamics simulations of three very different globular proteins and demonstrate that the structural fluctuations observed are highly complex, manifesting in non-ergodic and self-similar subdiffusive dynamics with non-exponential relaxation behavior. The characteristic time of the motion observed at a given timescale is dependent on the length of the observation time, indicating an aging effect. By comparing the simulation results to the existing single-molecule fluorescence spectroscopic data on other globular proteins, we found the characteristic relaxation time for a distance fluctuation within proteins, such as inter-domain motion, increases with the length of the observation time in a simple power-law that appears to be universal and independent of protein species, spanning over enormous 13 decades in time ranging from picoseconds up to hundreds of seconds. We argue that the observed self-similar dynamics arises from the fractal nature of the topology and geometry of the underlying energy landscape. Diffusion of a fictive walker over the complex hierarchical energy landscape leads to structural dynamics that are best described by a noisy, subdiffusive continuous time random walk, consistent with the aging and observed broken ergodicity. In comparison with data from single-molecule experiments in the existing literature, the present results suggest that the structural dynamics of single protein molecules is likely to remain non-ergodic and out of equilibrium on most timescales over which protein functions occur, eventually persists up to typical lifespan of proteins in vivo.