Unusual dynamics of hydration water around motor proteins with long-ranged hydrodynamic fluctuations

A fluctuation-driven dynamic model is formulated to study the translational diffusion of water molecules around the surface of motor proteins under the combined influence of the thermal fluctuations and the external active forces. The dynamics of such a system, explored within the tenets of generalized Langevin equation is captured by two different models that characterizes the interplay between the active and thermal fluctuations. The results establish that hydration water dynamics is primarily super-diffusive when the active conformational fluctuations of motor proteins outweigh the random thermal fluctuations in the environment. The conformational fluctuations of protein disrupts the hydrogen bonded network of water and enhances its dynamics in a homogeneous environment. First passage time distribution and the survival probability are evaluated from the effective Fokker–Planck equation for both models under two different boundary conditions. The results depict an asymmetric unimodal distribution of FPTD with curves of varying amplitudes obtained at definite intervals of time for two different models. The FPT distribution of water molecules displays broad peaks with a lower amplitude for the hydration layers of increasing thickness. The survival probability of hydration water molecules exhibits a stretched exponential decay for both models with a faster decay rate for the super-diffusive dynamics as compared to the sub-diffusive motion. The water molecule displays a longer residence time within the hydration layer bounded by an absorbing–reflecting boundary as compared to an absorbing–absorbing one.