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Date of Award

Spring 2024

Document Type

Masters Thesis

Department or Program Affiliation


Degree Name

Master of Science (MS)



First Advisor

McCarty, Jay

Second Advisor

Spiegel, P. Clint

Third Advisor

Kowalczyk, Tim


Molecular Dynamics (MD) simulations use Newtonian mechanics applied at finite time steps to numerically propagate the time-trajectory of a dynamical system. However, many biochemical processes such as catalysis, ion channel gating, substrate binding, and protein folding evolve over time scales which are orders of magnitudes greater than those afforded by MD and the computational power available today. The development of methods that reduce the computational cost of sampling such rare events help to provide a dynamic insight into these processes. This thesis explores the application of a recently developed enhanced sampling method, Variationally Enhanced Sampling (VES), for calculating kinetic rate constants within hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) simulations. In VES, the free energy landscape is modeled with a basis set that is constructed to allow us to obtain kinetic rates using Kramers time-dependent rate theory. First passage times from biased MD simulation are obtained directly from a fit of the biased empirical cumulative distribution function. We demonstrate this approach on two paradigmatic cases: an SN2 reaction and the conformational change of an alanine dipeptide in vacuum. We find that unbiased rate constants can be determined through biased experiments at a 106 fold acceleration with little to no a priori knowledge of the system utilizing the Kramers’ RAte for Variationally Enhanced Sampling (KRAVES) method with a deep-learned Collective Variable (CV). This approach is then utilized in two systems with an enzyme-substrate complex, Diels-Alderase and Chorismate mutase, to explore enzymatic activity. Finally, we explore molecular docking simulations of small drugs and peptide ligands to prepare enzyme-substrate systems for our method.




Variationally Enhanced Sampling, Molecular Dynamics Simulations, Biochemistry, Kramers' Theory, Time-Dependent Rate Theory, First Passage Times, Kinetic Analysis, Reaction Rate Theory, Statistical Mechanics, Stochastic Processes, Markov Processes, Chemical Kinetics, Biochemical Kinetics, Simulation Methods, Mathematical Models, Nonequilibrium Statistical Mechanics


Western Washington University

OCLC Number


Subject – LCSH

Chemical kinetics; Molecular dynamics; Biochemistry; Molecular theory; Statistical mechanics; Stochastic processes; Markov processes; Nonequilibrium statistical mechanics




masters theses




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