Computation of exit times for potential landscapes in CRISPR binding

Standard computations of exit times surround numerical routines to determine characteristics of the energy landscape in which CRISPR proteins participate, including stages of the binding process comprised of protein inspection of target sequences for complementarity, in which successful binding occurs through the formation of a stably bound complex. In this work, an IVP associated with a stochastically driven oscillator for the exit time will be presented, from which exit times for varying potential landscapes are obtained. To build upon previous formulations of potential landscape recovery from distributions of exit times in the landscape, we also will discuss novel numerical schemes from which fluctuations to the binding landscape can be realized. The scheme primarily relies on establishing relations between numerical approximations of exit times, in turn enabling us to reconstruct a potential landscape which is valuable for constructing probability measures to quantify likely configurations of different proteins within the Cas family throughout the binding process. Time permitting, comparisons will be established between other statistical mechanics approaches.