Distances between points in a macromolecule or binding-unbinding kinetics of molecular actors are quantified at the single molecule level through a technique called fluorescence resonance energy transfer (FRET). Indeed, FRET's success is best measured by how naturally it has been combined with other spectroscopic and microscopy techniques from force spectroscopy to widefield and confocal methods and beyond. Over the recent decades, FRET has been applied to single molecules (smFRET), and their complex behaviors have raised fundamental questions whose answers remain limited to the timescales that we can access and the states that we can discriminate from current smFRET analyses.
As statistical modeling in the natural sciences matured over the past decades, so did the inverse strategies used to deduce from smFRET conformational trajectories, molecular kinetics, states, continuous potentials extracted from smFRET, and even kinetics exceeding detector exposure times for FRET collected with integrative (widefield) detectors. Yet, experiments have always remained a step ahead of theory in presenting uniquely perplexing inverse modeling challenges. In fact, although smFRET data are often gathered at the (rapid) single photon level, most analyses still rely on binning data and applying variations of the perennial hidden Markov model paradigm to the analysis.
The cover art for the March 8 issue of Biophysical Reports, made by Alexey Chizhik from Jӧrg Enderlein’s lab, captures the spirit of our trilogy revisiting the analysis of single-photon smFRET (Single-photon smFRET. I: Theory and conceptual basis; Single-photon smFRET. II: Application to continuous illumination; Single-photon smFRET. III: Application to pulsed illumination) by illustrating a pair of proteins, enhanced green fluorescent protein and mCherry, commonly used in smFRET from which emerge photons forming the basis of the experimental output. On the donor (green) side, we see pulsed excitation, which occasionally directly excites the acceptor (depicted with a red Gaussian pulse). On the acceptor (red) side emerges the observation’s likelihood, a core ingredient of our Bayesian nonparametric analysis. The backdrop highlights key quantities appearing in the theory.
Our trilogy, complete with analysis suite BNP (Bayesian nonparametrics)-FRET, rigorously reformulates single-photon smFRET analysis from scratch and helps us broaden the questions we may now ask of smFRET. Indeed, we show how to reformulate the analysis of single-photon smFRET in a Bayesian nonparametric framework required to unravel information already known to be encoded on the number of molecular states from the fastest acquirable timescale available: individual photon arrivals. Importantly, we systematically revisit, step by step, how to self-consistently incorporate known experimental artefacts into the analysis to avoid biases critical in achieving high time resolution. Equally important in guiding the development of future experiments, we provide a rigorous means to propagate error from all modeled sources into an uncertainty over numbers of states as well as their associated rate parameters.
—Matthew Safar, Ayush Saurabh, Bidyut Sarkar, Mohamadreza Fazel, Kunihiko Ishii, Tahei Tahara, Ioannis Sgouralis, and Steve Pressé