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

Abstract

Single molecule Förster resonance energy transfer (smFRET) experiments are a powerful way to probe switching kinetics between the conformational states of a molecule where a portion of the molecule is attached to a donor fluorophore and another to an acceptor fluorophore. In order to learn the kinetic rates of a molecule from smFRET data, hidden Markov models (HMMs) are often used. HMMs treat time traces in discrete time even though molecule kinetics evolve continuously in time. In addition, HMMs inherently assume that the probed kinetic rates are slower than the data acquisition rate. Therefore, if the smFRET data acquisition rate is not sufficiently high, then HMMs become inappropriate for extracting the molecule's switching kinetics. Here, we would like to learn kinetic rates from smFRET data even if switching kinetics are faster than the data acquisition rate. To achieve our goal of inferring the kinetic rates, we use a variant of a hidden Markov jump process (HMJP), for the analysis of parallel measurements from donor and acceptor channels. Our HMJP approach generalizes HMM in two critical ways: (1) it models the molecule as switching between different conformational states in continuous time and (2) it allows us to learn the kinetic rates without approximating them as discrete transition probabilities nor assuming that the rates are slower than the data acquisition rate. In our HMJP setup, we infer switching kinetics and photon emission rates that go beyond the dynamics regimes that HMMs can deal with. The robustness of our method is validated on simulated data and we demonstrated its performance on experimental data from FRET labeled Holliday junctions.