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Abstract

Understanding the kinetic behavior of complex systems is crucial for the study of physical, chemical, and biological phenomena. While conventional methods such as molecular dynamics or enhanced sampling have been successful in characterizing the dynamics for a variety of systems, the computational cost to explore the configuration space is prohibitive and becomes infeasible for more complex systems with transition events that happen on longer timescales. Here, I will explore two powerful computational methodologies built upon statistical analysis and statistical mechanical frameworks to efficiently and accurately extract the kinetics, as well as other important observables for thermodynamics or transition pathways. First, I will construct Markov state models to study the binding and unbinding of a protein-protein complex. I will demonstrate the robustness of this methodology under various parameters and simulation conditions, and then I will propose an improved approach using a sensitivity analysis on the observables for the addition of biased simulations. Next, I will present a novel string method algorithm that allows for finding an optimal transition pathway on the free energy surface by taking into account the reactive probability. Drawing upon concepts from transition path sampling, the present framework aims to variationally minimize the steady state flux by way of the committor probability and notably can predict slow kinetic pathways for anisotropic systems, which are ubiquitous in biology and chemistry. Both of these proposed approaches allow the estimation of dynamic observables in a more efficient and more accurate manner.

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