A Continuous Time Representation of smFRET for the Extraction of Rapid Kinetics

Our goal is to learn kinetic rates from single molecule FRET (smFRET) data even if these exceed the data acquisition rate. To achieve this, we develop a variant of our recently proposed hidden Markov jump process (HMJP) with which we learn transition kinetics from parallel measurements in donor and acceptor channels. Our HMJP generalizes the hidden Markov model (HMM) paradigm in two critical ways: (1) it deals with physical smFRET systems as they switch between conformational states in continuous time; (2) it estimates the transition rates between conformational states directly without having recourse to transition probabilities or assuming slow dynamics (as is necessary of the HMM). Our continuous time treatment learns transition kinetics and photon emission rates for dynamical regimes inaccessible to the HMM which treats system kinetics in discrete time. We validate the robustness of our framework on simulated data and demonstrate its performance on experimental data from FRET labeled Holliday junctions.