Extraction of rapid kinetics from smFRET measurements using integrative detectors

Abstract

SUMMARY Hidden Markov models (HMMs) are used to learn single-molecule kinetics across a range of experimental techniques. By their construction, HMMs assume that single-molecule events occur on slower timescales than those of data acquisition. To move beyond that HMM limitation and allow for single-molecule events to occur on any timescale, we must treat single-molecule events in continuous time as they occur in nature. We propose a method to learn kinetic rates from single-molecule Förster resonance energy transfer (smFRET) data collected by integrative detectors, even if those rates exceed data acquisition rates. To achieve that, we exploit our recently proposed “hidden Markov jump process” (HMJP), with which we learn transition kinetics from parallel measurements in donor and acceptor channels. HMJPs generalize the HMM paradigm in two critical ways: (1) they deal with physical smFRET systems as they switch between conformational states in continuous time , and (2) they estimate transition rates between conformational states directly without having recourse to transition probabilities or assuming slow dynamics. Our continuous-time treatment learns the transition kinetics and photon emission rates for dynamic regimes that are inaccessible to HMMs, which treat system kinetics in discrete time. We validate our framework’s robustness on simulated data and demonstrate its performance on experimental data from FRET-labeled Holliday junctions.

Single Photon smFRET. I. Theory and Conceptual Basis

“…When single photon data is available, and to avoid the binning issues inherent to HMM analysis [28, 35, 36]–and leverage, for example, direct noise properties of detectors known for single photon arrivals ( e.g ., IRF), and knowledge of excited photophysical state lifetimes available from pulsed illumination–single photon arrivals can be directly employed in the analysis. This, naturally, comes with added computational cost [33].…”

Single Photon smFRET. III. Application to Pulsed Illumination

“…To help validate BNPs on smFRET single photon data, we start with a simple case of a two state system and select kinetics similar to those of the experimental data sets, cf . the HJ in 10 mm MgCl 2 , which has escape rates, i.e ., the rate of transitions pointing out of system states, at 40 s − 1 [52]. The generated system state trajectory and photon traces over a period of 500 ms from both channels are shown in Fig.…”

“…In this section, we benchmark our method over a wide range of kinetic rates employing experimental data acquired using HJ with different kinetic rates arising from varying the concentration of MgCl 2 in buffer [52, 54]. The HJ kinetic rates have been extensively studied using both fluorescence lifetime correlation spectroscopy (FLCS) [54] and HMM analysis [55] on diffusing HJs assuming a priori a pair of high and low FRET system states.…”

Inferring potential landscapes from noisy trajectories of particles within an optical feedback trap

“…This can be done by either treating the potential as a Markov process where the potential is allowed to vary slightly each frame (Williams and In this work, we assume a Gaussian noise model, but we can, in principle, utilize different noise models by substituting Equation 4 for the desired model. As SKI-GP is general and the measurement noise model can be tuned, moving forward we could apply modified SKIPPER algorithms to map potential landscapes from force spectroscopy (Gupta et al, 2011) or even single molecule fluorescence energy transfer (Kilic et al, 2021;Sgouralis et al, 2018), with applications to inferring protein conformational dynamics or binding kinetics (Schuler and Eaton, 2008;Chung and Eaton, 2018;Sturzenegger et al, 2018;Presse ´et al, 2013Presse ´et al, , 2014. In inferring smooth potentials, we would move beyond the need to require discrete states inherent to traditional analyses paradigms such as hidden Markov models (Rabiner and Juang, 1986;Sgouralis and Presse ´, 2017).…”