Statistical Kinetics and Nonequilibrium Thermodynamics of Driven Systems: Stochastic Methods and Applications to Single-Molecule Biophysics

Abstract

Advances in condensed-phase spectroscopy have permitted the ability to obtain time traces of biomolecules at the single-molecule level of detail. These real-time trajectories provide details that are typically unavailable in ensemble-averaged experiments, such as the effect of conformational dynamics on enzymatic reactions. From a theoretical perspective, it is therefore valuable to develop kinetic approaches for characterizing measurable quantities in order to connect to such single-molecule experiments. In this thesis, we analyze the statistical kinetics and nonequilibrium thermodynamics of driven biomolecular systems, with a particular emphasis on enzymatic processes. Specifically, we focus on kinetic methodology development; analyzing single-molecule fluctuations for mechanistic insight; examining the modulating influence of conformational interconversion on enzyme catalysis; and characterizing the nonequilibrium thermodynamics of generalized biomolecular machines. For enzymatic turnover reactions, it is found that the turnover rate reduces to the celebrated Michaelis–Menten functional form when conformational detailed balance is satisfied. In the presence of non-vanishing conformational currents, we predict and characterize the rich, cooperative behaviors attainable in conformational nonequilibrium. In addition, enzyme turnover fluctuations are analyzed by studying the Poisson indicator, a normalized measure of stochastic variation. A novel pathway analysis framework is extended to nonrenewal processes (i.e., those with correlated inter-event times) and fully reversible processes, accounting for kinetic network complexities, nontrivial event-averaged initial conditions, and the constraints associated with microscopic reversibility. For a dynamically disordered biomolecular machine involving an observable process coupled to a hidden process, a recently derived time-based fluctuation theorem no longer applies to the observable first-passage time; however, using a stochastic thermodynamics approach to examine fluctuating trajectories, we find that its validity is restored in the absence of hidden flux through the initial state manifold. Thus, the violation of this relation serves as an experimentally verifiable signature of hidden detailed balance breaking. The analysis presented herein provides a novel framework for analyzing a variety of kinetic processes, including enzyme turnover, molecular motor translocation, ion transport, and fluorescence emission.