Single Photon smFRET. I. Theory and Conceptual Basis

Abstract

We present a unified conceptual framework and 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 an smFRET experiment, including: 1) fluorophore photophysics; 2) continuous time dynamics 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, we propose a second order hidden Markov model (HMM) and Bayesian nonparametrics (BNP) on account of items 1, 2 and 5 on the list, respectively. In companion manuscripts II and III, we discuss the direct effects of these key complexities on the inference of parameters for continuous and pulsed illumination, respectively.

Single Photon smFRET. II. Application to Continuous Illumination

“…Moreover, we are provided a route correction matrix (RCM) by the authors of [26, 27] to account for spectral crosstalk, and detection efficiencies of donor and acceptor channels. We defined such an RCM in the first companion paper [21] and specify it here as where channels 1 & 2 are, respectively, designed to receive acceptor and donor photons, and ϕ ij denotes probability of photons intended for channel i to enter channel j . Since all the probabilities ϕ ij appear as ratios in RCM ’, we can normalize it further such that all of the emitted donor photons are detected in one of the two channels.…”

“…In this paper, we implemented the general nonparametric smFRET data analysis frame-work presented in [21] to address the issues associated with smFRET data analysis acquired under continuous illumination. The developed framework is capable of learning posterior distributions over the number of system states as well as the corresponding dynamics ranging from slow to as fast as photon emission rates.…”

“…This matrix governs the evolution of the system-FRET composite via the master equation as described in Sec. 2.2 of the first companion manuscript [21].…”

“…For this reason, we developed a complete Bayesian nonparametric (BNP) framework in the first paper of the current series [21]. This framework incorporates many key complexities of a typical smFRET experimental setup, including background emissions, fluorophore photophysics (blinking, photobleaching, and direct acceptor excitation), instrument response function (IRF), detector dead time, and crosstalk.…”

Single Photon smFRET. III. Application to Pulsed Illumination

“…In this paper, we adapt the general smFRET analysis framework presented in the first companion paper [22] for the case of pulsed illumination to learn full distributions over the system kinetics and photophysical rates, i.e ., donor and acceptor relaxation and FRET rates, while 1) inferring full distributions over the number of system states; and while 2) taking into account experimental factors such as IRF and crosstalk. As our main concern is deducing system state numbers using single photon arrivals while incorporating detector effects, we leverage the formalism of infinite hidden Markov models (iHMM) [23–28] within the Bayesian nonparametric (BNP) paradigm [23, 24, 29–36].…”