Learning Kinetic Models from Single-Molecule FRET Data using Bayesian Inference

Abstract

Single-molecule FRET studies have enabled real-time observation of conformational transitions in individual molecules, allowing targeted investigations into the mechanistic function of molecular machines such as the ribosome. Like in many single-molecule platforms, a fundamental problem with sm-FRET studies is that our noisy fluorescence signal does not unambiguously determine the underlying conformational state. Moreover, a single experiment often yields hundreds of time series, which report on the same underlying process, but exhibit significant variations in photophysical properties and kinetic rates.This combination of lots of data and lots of stochasticity means that interpretation of sm-FRET experiments often requires use of statistical inference techniques. Hidden Markov Models are a widely used tool for parameter estimation in time series data, and have been successfully applied to sm-FRET experiments by several groups. A fundamental limitation of existing approaches is that inference is only performed on one time series at a time, yielding a large number of parameter estimates of variable quality which must now be related to each other using ad-hoc experiment specific post-processing steps.Here, we propose a technique known in the statistical community as Empirical Bayes estimation, to perform combined analysis on the entire collection of trajectories in an experiment. This allows straightforward and statistically principled learning of a consensus kinetic model from an ensemble of time series. Moreover, the method allows significantly better estimates of the kinetic rates associated with conformational transitions. Finally we demonstrate how inference results on models with varying kinetic structures can be compared to directly test detailed mechanistic hypotheses in a statistically principled, adaptable manner.