Multi-parameter photon-by-photon hidden Markov modeling

Abstract

Single molecule FRET (smFRET) is a useful tool for studying biomolecular sub-populations and their dynamics. Advanced smFRET-based techniques often track multiple parameters simultaneously, increasing the information content of the measurement. Photon-by-photon hidden Markov modelling (H2MM) is a smFRET analysis tool that quantifies FRET dynamics of single biomolecules, even if they occur in sub-milliseconds. However, sub-populations can be characterized by additional experimentally-derived parameters other than the FRET efficiency. We introduce multiparameter H2MM (mpH2MM) that identifies sub-populations and their transition dynamics based on multiple experimentally-derived parameters, simultaneously. We show the use of this tool in deciphering the number of underlying sub-populations, their mean characteristics and the rate constants of their transitions for a DNA hairpin exhibiting milliseconds FRET dynamics, and for the RNA polymerase promoter open complex exhibiting sub-millisecond FRET dynamics of the transcription bubble. Overall, we show that using mpH2MM facilitates the identification and quantification of biomolecular sub-populations in smFRET measurements that are otherwise difficult to identify. Finally we provide the means to use mpH2MM in analyzing FRET dynamics in advanced multi-color smFRET-based measurements.

Identification and Quantification of Within-Burst Dynamics in Singly-Labeled Single-Molecule Fluorescence Lifetime Experiments

“…MpH 2 MM is an analytical method that extends classical hidden Markov modelling to the domain of single-molecule measurements. It has previously been used to identify within-burst dynamics originating from both conformational and photophysical dynamics in smFRET experiments 19 . As such, it excels at distinguishing between data containing a mixture of states, and data with a single state of more mixed nature.…”

“…We test from one to for divisors in the non-IRF scheme, and 1 to 4 divisors (which have n+1 divisors due to the additional divisor of the IRF) in the IRF scheme. All analyses were performed using the H2MM_C python package 19 . Model optimizations were performed on single-, two- and three-state models.…”

“…Therefore, we aspired to develop a method to quantify within-burst dynamics in single-dye single-molecule fluorescence lifetime-based measurements such as smPIFE. For this, we sought to adapt the multi-parameter photon-by-photon hidden Markov modeling (mpH 2 MM) framework 19 that we recently introduced to function with photon nanotime data. We therefore introduce a simple and widely implementable scheme to transform the exponential distribution of photon nanotimes into set of tractable parameters, amenable for use with mpH 2 MM.…”

Structural and Dynamic Insights Into α-Synuclein Dimer Conformations

“…Nevertheless, it is noteworthy that at the moment we cannot exclude the possibility that each mean nanotime sub-population is the result of time-averaging of transitions faster than typical burst duration timescales, better known as within-burst dynamics . We have recently developed an analysis approach such dynamics in single-molecule FRET experiments 48 , and will soon extend this approach to analyze time-resolved smPIFE within-burst dynamics.…”

Inferring kinetic rate constants from single-molecule FRET trajectories – a blind benchmark of kinetic analysis tools

“…The HMM formalism is based on a discrete memoryless Markov process that infers a set of parameters (probabilities of states, transitions, and observations) to describe the observed sequence of FRET efficiencies. Many extensions of the HMM formalism have been developed [10][11][12][13][14][15] including Bayesian approaches [16][17][18][19] , and very fast kinetics (low energy barrier crossings) can be inferred from singlephoton arrival times 54,20,55 .…”