Date of Award
12-2023
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Peter Kiessler
Committee Member
Keisha Cook
Committee Member
Hugo Sanabria
Committee Member
Brian Fralix
Committee Member
Martin Schmoll
Abstract
In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based on first physics principles and proper dye linker chemistry to match accessible volumes predicted by molecular dynamics simulations. By simulating the dyes' stochastic translational and rotational dynamics, we show that the observed dynamic shift can largely be attributed to the mutual orientational dynamics of the electric dipole moments associated with the dyes and not their accessible volumes.
Furthermore, using nonlinear semi-group convergence methods based on viscosity solutions to associated Hamilton-Jacobi equations developed by Feng and Kurtz and methods of verifying the comparison principle for viscosity solutions introduced by Versendaal et al., we prove a large deviations principle for dynamical systems on Riemannian manifolds perturbed by vanishing Markov noise. Further, using the correspondence between the aforementioned nonlinear semigroup and stochastic control theory, we find explicit representations of the rate function in several cases via a Legendre - Fenchel transform of a corresponding Hamiltonian functional. This provides a generalization of classical Friedlin-Wentzell theory to the case of degenerate general Markov perturbations on complete Riemannian manifolds.
Recommended Citation
Frost, David, "Aspects of Stochastic Geometric Mechanics in Molecular Biophysics" (2023). All Dissertations. 3465.
https://open.clemson.edu/all_dissertations/3465
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