Aspects of Stochastic Geometric Mechanics in Molecular Biophysics

Author

David FrostFollow

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://tigerprints.clemson.edu/all_dissertations/3465