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Abstract
Time series data provided by single-molecule Förster resonance energy transfer (smFRET)
experiments offer the opportunity to infer not only model parameters describing molecular
complexes, e.g., rate constants, but also information about the model itself, e.g.,
the number of conformational states. Resolving whether such states exist or how many
of them exist requires a careful approach to the problem of model selection, here
meaning discrimination among models with differing numbers of states. The most straightforward
approach to model selection generalizes the common idea of maximum likelihood--selecting
the most likely parameter values--to maximum evidence: selecting the most likely model.
In either case, such an inference presents a tremendous computational challenge, which
we here address by exploiting an approximation technique termed variational Bayesian
expectation maximization. We demonstrate how this technique can be applied to temporal
data such as smFRET time series; show superior statistical consistency relative to
the maximum likelihood approach; compare its performance on smFRET data generated
from experiments on the ribosome; and illustrate how model selection in such probabilistic
or generative modeling can facilitate analysis of closely related temporal data currently
prevalent in biophysics. Source code used in this analysis, including a graphical
user interface, is available open source via http://vbFRET.sourceforge.net.