# Learning Rates and States from Biophysical Time Series: A Bayesian Approach to Model Selection and Single-Molecule FRET Data

## TL;DR

This paper introduces a Bayesian variational approach for analyzing single-molecule FRET time series to infer molecular states and rate constants, improving model selection accuracy over traditional methods.

## Contribution

It presents a novel variational Bayes method for model selection in biophysical time series, enabling more reliable inference of molecular states and dynamics.

## Key findings

- Demonstrates superior statistical consistency over maximum likelihood methods
- Shows applicability to complex biophysical time series data
- Provides open-source software for broader use

## Abstract

Time series data provided by single-molecule Forster resonance energy transfer (sm-FRET) 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 or how many of such states exist requires a careful approach to the problem of model selection, here meaning discriminating 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 inference presents a tremendous computational challenge, which we here address by exploiting an approximation technique termed variational Bayes. 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; 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