Reconstructing Langevin Dynamics with HMM

I am currently using HMM to analyze Langevin dynamics on a double-well potential. These HMM use lifetime and the known potential of mean force to reconstruct the photon trajectory for a protein labeled with two chromophores. The goal is to identify limits of barrier heights, friction coefficients, Forster distance, and potential curvature for trajectory reconstruction.

(a) Potential of mean force used to describe the protein dynamics dictated by a FRET fluorophore pair (donor and acceptor) distance attached to a protein. The residence probability distribution function is overlaid.

(b) Simulated photon trajectories recorded by donor (red) and acceptor (blue) channels.

(c-d) Microtime (the time lag between the laser pulse and the arrival of the photon) for each photon recorded in donor channel (c) and acceptor channel (d).

(e) Reconstructed donor-acceptor distance trajectory using hidden Markov model (HMM) with evenly spaced 21 states across the donor-acceptor distance.

(f) “True” donor-acceptor distance trajectory, generated by Langevin dynamics simulation on (a).