Title: Diffusion related processes in nanoconfined liquids and in proteins under force
Description: This thesis investigates some diffusion related problems, in acetonitrile confined in silica nanopores, and in modeling single molecule forced rupture experiments of biomacromolecules. Based on a method used to calculate the position-dependent diffusion coefficients in inhomogeneous liquids, we apply absorbing boundary conditions in the analysis of molecular dynamics trajectories of confined acetonitrile. We show that the dynamics of acetonitrile may be described by a two population exchange model that accounts for bulk-like relaxation in the center, frustrated dynamics near the surface of the pore and the self-diffusion. We find that hydrogen-bonding interactions play a large role in engendering this behavior. We compare our method with prior techniques that do not take diffusion into account and discuss their pitfalls. We also calculate the position-dependent diffusion tensors in the center population of acetonitrile. To model single molecule forced rupture experiments under constant velocity conditions, we study the barrier crossing problem of a diffusive particle in a time-dependent potential, We develop an integral equation connecting the first passage time distribution of a Brownian diffusion process in the presence of an absorbing boundary condition and the corresponding Green's function in the absence of the absorbing boundary.

We further investigate the numerical solutions of the integral equation for a diffusion process in a time-dependent potential. Our numerical procedure, based on the exact integral equation, avoids the adiabatic approximation used in the previous analytical theories and is useful for fitting the rupture force distribution data from experiments, especially at larger pulling speeds, large cantilever spring constants, and smaller reaction rates. We also propose a model based on subdiffusion to explain the anomalous rupture force distributions with positive skewness that are observed in some single molecule forced rupture experiments of ligand-receptor complexes.