HMM For Diffusive Processes

Hidden Markov Models for Diffusive Processes

The top panel (a) shows a Monte Carlo simulated trajectory of a molecule diffusing through a spherically symmetric Gaussian collection volume. The next panel (b) shows the reciprocal of the inter-photon time. The delay between excitation and emission of the photon is the lifetime and is shown in panel (c). Panels (b) and (c) are used with three dimensional diffusion of the molecule through the focus of the instrument as the hidden Markov model to reconstruct the Brownian motion trajectory in panel (d). The trajectory was reconstructed by using Monte Carlo sampling of the HMM parameters to maximize the likelihood of the data in (b) and (c).