A General Bayesian Framework for Learning Molecular Kinetics From Single Photon Arrivals.

We present a new unifying Bayesian framework for analyzing conformational dynamics of molecules from single photon traces generated by multi-color Forster Resonance Energy Transfer (FRET) setups under continuous and pulsed illumination. In this framework, the likelihood function for single photon traces is derived using a second-order hidden Markov model (HMM). This allows us to improve upon the  presently available methods in five ways: 1) fast and slow dynamics can now be learned at the same time, 2) time scales faster than the instrument response function (IRF)  and detector dead times can now be estimated, 3) an unknown number of states can be learned through nonparamteric modeling, 4) likelihood function can be now be coveniently computed for different types experimental setups, and 5) parameters of interest are now reported with uncertainties. We apply this framework to study the dynamics of TRBP-sRNA complex using two- and three-color FRET labels. From the single photon arrivals, we learn the relevant lifetimes/transition rates and the number of conformational states involved. The length of RNA is also varied to investigate the discrete motion of the TRBP protein along the RNA.