Hierarchically-coupled hidden Markov models for learning kinetic rates from single-molecule data

We address the problem of analyzing sets of noisy time-varying signals that all report on the same process but confound straight-forward analyses due to complex inter-signal heterogeneities and measurement artifacts. In particular we consider single-molecule ex-periments which indirectly measure the dis-tinct steps in a biomolecular process via observations of noisy time-dependent sig-nals such as a fluorescence intensity or bead position. Straightforward hidden Markov model (HMM) analyses attempt to character-ize such processes in terms of a set of confor-mational states, the transitions that can oc-cur between these states, and the associated rates at which those transitions occur; but require ad-hoc post-processing steps to com-bine multiple signals. Here we develop a hi-erarchically coupled HMM that allows exper-imentalists to deal with inter-signal variabil-ity in a principled and automatic way. Our approach is a generalized expectation max-imization hyperparameter point estimation procedure with variational Bayes at the level of individual time series that learns an sin-gle interpretable representation of the overall data generating process. 1