Hidden markov analysis of short single molecule intensity trajectories.

Photon trajectories from single molecule experiments can report on biomolecule structural changes and motions. Hidden Markov models (HMM) facilitate extraction of the sequence of hidden states from noisy data through construction of probabilistic models. Typically, the true number of states is determined by the Bayesian information criteria (BIC); however, constraints resulting from short data sets and Poisson-distributed photons in radiative processes like fluorescence can limit successful application of goodness-of-fit statistics. For single molecule intensity trajectories, additional information criteria such as peak localization error (LE) and chi-square probabilities can incorporate theoretical constraints on experimental data while modifying normal HMM. Chi-square minimization also serves as a stopping point of the iteration in which the system parameters are trained. Peak LE enables exclusion of overfitted and overlapped states. These constraints and criteria are tested against BIC on simulated single molecule trajectories to best identify the true number of emissive levels in any sequence.