(301e) A Statistical Learning Algorithm for Modeling Protein Dynamics and Allosteric Conformational Changes

We aim to model protein dynamics and allosteric conformational change by analyzing the free energy surface and diffusion coefficient profiles along possible reaction coordinates. Such study provides an understanding of the mechanism and pathway for protein conformational change. Single-molecule experiments, for example Förster resonance energy transfer (FRET), offer a promising source of data on protein dynamics that could be used to determine free energy and diffusion coefficient profiles for analysis and comparison with molecular simulation. Ideally, the distance along a reaction coordinate could be observed directly from experiment by tagging the reactive domains of a protein with FRET chromophores and charting photon intensity with time. However, correctly interpreting single-molecule trajectories is a daunting challenge due to the convolution between protein dynamics and the Poisson statistics of photon emission. Based on recent developments in machine learning algorithms, we developed a comprehensive computational methodology to extract free energy and diffusion coefficient profiles from single-molecule experiments. We begin with the Hidden Markov Model framework and generalize the common ?forward-backward? inference algorithm to treat a continuous reaction coordinate using the stochastic calculus of Brownian dynamics. By time evolving the relevant Fokker-Planck & Kolmogorov equations, the smoothed protein trajectory is extracted from the observations of photon data. A time integral of this smoothed trajectory produces an estimate of the equilibrium probability and corresponding free energy. Through the path integral representation for the stochastic process, an expectation-maximization algorithm is derived to properly interpret the results of HMM inference and predict the most likely free energy surface and position dependent diffusion coefficient. Our results show highly resolved, accurate, and self-consistent estimations of free energy and dynamics from simulated experiments. The free energy and diffusion coefficient profiles determined from actual single-molecule FRET experiments of adenylate kinase will be compared with the results of all-atom MD simulations. We will address how this methodology connects reaction path and free energy simulations to observed single molecule experiments and other scenarios in which system dynamics is inferred from indirect measurements.