Single Photon smFRET. I. Theory and Conceptual Basis

Abstract We present a unified conceptual framework and the associated software package for single molecule Förster Resonance Energy Transfer (smFRET) analysis from single photon arrivals leveraging Bayesian nonparametrics, BNP-FRET. This unified framework addresses the following key physical complexities of a single photon smFRET experiment, including: 1) fluorophore photophysics; 2) continuous time kinetics of the labeled system with large timescale separations between photophysical phenomena such as excited photophysical state lifetimes and events such as transition between system states; 3) unavoidable detector artefacts; 4) background emissions; 5) unknown number of system states; and 6) both continuous and pulsed illumination. These physical features necessarily demand a novel framework that extends beyond existing tools. In particular, the theory naturally brings us to a hidden Markov model (HMM) with a second order structure and Bayesian nonparametrics (BNP) on account of items 1, 2 and 5 on the list. In the second and third companion manuscripts, we discuss the direct effects of these key complexities on the inference of parameters for continuous and pulsed illumination, respectively. Why It Matters smFRET is a widely used technique for studying kinetics of molecular complexes. However, until now, smFRET data analysis methods required specifying a priori the dimensionality of the underlying physical model (the exact number of kinetic parameters). Such approaches are inherently limiting given the typically unknown number of physical configurations a molecular complex may assume. The methods presented here eliminate this requirement and allow estimating the physical model itself along with kinetic parameters, while incorporating all sources of noise in the data.