Statistical learning theory for protein dynamics

This thesis establishes a comprehensive statistical learning framework to extract from single-molecule Forster resonance energy transfer (smFRET) experiments the potential of mean force and diffusion coefficient that characterize the measured protein dynamics. To enable a fundamental understanding of how deterministic mean force and stochastic diffusion combine to affect conformational transitions, we first developed a general trajectory entropy functional for over-damped Langevin dynamics. This functional allows for evaluation of the information content in the dynamic trajectory ensemble. Next, we present a path integral statistical learning approach to infer the hidden trajectory from the data of smFRET measurements of protein dynamics. This methodology also yields a likelihood for the parameters of the equation of motion that can then be optimized to deduce the most probable profiles of mean force and diffusion coefficient for describing the observed dynamical data.

To provide a solid foundation for regularizing the parameters derived from experimental trajectories through statistical learning, the Fisher information metric of Langevin dynamics trajectories is derived via an eigenbasis representation of the time propagator. Using this Fisher information, the maximum entropy distributions for various kinetic constraints can derived for the first time. Finally the knowledge of trajectory entropy and likelihood of smFRET measurements is combined to present a new calculus of representing the Information Thermodynamics in statistical learning. Bayesian analysis using this methodology shows that in the balance between entropy, likelihood, and fluctuations given at the critical point in the phase diagram of information, the ideal force profile and diffusion can be determined from smFRET experiments in a systematic and robust manner.