A Bayesian Nonparametric Approach to Single Molecule Förster Resonance Energy Transfer

Sgouralis, Ioannis; Madaan, Shreya; Djutanta, Franky; Kha, Rachael; Hariadi, Rizal F.; Pressé, Steve

doi:10.1021/acs.jpcb.8b09752

Cited by 44 publications

(93 citation statements)

References 73 publications

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“…Furthermore, armed with a transformative framework, founded upon rigorous statistics, it is now possible to extend the proof-of-principle study to treat effects that lie beyond the current scope of this work. In particular, we can extend our framework to treat multiple color imaging [93], triplet effect, and complex molecule photophysics [94] (such as molecular blinking [46,95] and photobleaching [96,97]), more complex molecule motion models [98,99] other than free diffusion [48], distorted, or abberated PSF models [100], or even incorporate chemical reactions among the molecules [101,102]. As our BNP framework explicitly represents the instantaneous position of each involved molecule throughout the experiment's time course, these are extensions that require modest modifications.…”

Section: Discussionmentioning

confidence: 99%

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Pitching Single-Focus Confocal Data Analysis One Photon at a Time with Bayesian Nonparametrics

et al. 2020

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Fluorescence time traces are used to report on dynamical properties of molecules. The basic unit of information in these traces is the arrival time of individual photons, which carry instantaneous information from the molecule, from which they are emitted, to the detector on timescales as fast as microseconds. Thus, it is theoretically possible to monitor molecular dynamics at such timescales from traces containing only a sufficient number of photon arrivals. In practice, however, traces are stochastic and in order to deduce dynamical information through traditional means-such as fluorescence correlation spectroscopy (FCS) and related techniques-they are collected and temporally autocorrelated over several minutes. So far, it has been impossible to analyze dynamical properties of molecules on timescales approaching data acquisition without collecting long traces under the strong assumption of stationarity of the process under observation or assumptions required for the analytic derivation of a correlation function. To avoid these assumptions, we would otherwise need to estimate the instantaneous number of molecules emitting photons and their positions within the confocal volume. As the number of molecules in a typical experiment is unknown, this problem demands that we abandon the conventional analysis paradigm. Here, we exploit Bayesian nonparametrics that allow us to obtain, in a principled fashion, estimates of the same quantities as FCS but from the direct analysis of traces of photon arrivals that are significantly smaller in size, or total duration, than those required by FCS.

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Section: Discussionmentioning

confidence: 99%

“…arrivals. The underlying theory, Bayesian nonparametrics (BNPs) [40], is a powerful set of tools still under active development and largely unknown to the physical sciences [4,39,[41][42][43][44][45][46][47][48].…”

Section: Fig 2 Estimates Of Diffusion Coefficients From Photon Arrivalmentioning

confidence: 99%

Pitching Single-Focus Confocal Data Analysis One Photon at a Time with Bayesian Nonparametrics

et al. 2020

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“…In addition, armed with a rigorous framework, it is now possible to extend the proof-of-principle framework we put forward to treat different effects that lie beyond the current scope of this work. In particular, we can think of extending our framework to treat multiple colors [22], triplet effects, complex biomolecule photophysics [41] (such as biomolecular blinking [89,104] and photobleaching [56,91]), more complex biomolecule motion models [103] other than free diffusion [50], complex distorted PSF models [29], or even incorporate chemical reactions among the biomolecules [8,100].…”

Section: Discussionmentioning

confidence: 99%

“…While BNPs have had a deep impact on Data Sci-ence since their inception, they are relatively new to Biophysics with a handful of papers [18,47,73] published to date using BNPs in Biophysical applications [50,55,[87][88][89][90]92].…”

Section: Introductionmentioning

confidence: 99%

Pitching single-focus confocal data analysis one photon at a time with Bayesian nonparametrics

Tavakoli

Jazani

Sgouralis

et al. 2019

Preprint

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Fluorescence time traces are used to report on dynamical properties of biomolecules. The basic unit of information drawn from these traces is the individual photon. Single photons carry instantaneous information from the biomolecule, from which they are emitted, to the detector on timescales as fast as microseconds. Thus from confocal microscope it is theoretically possible to monitor biomolecular dynamics at such timescales. In practice, however, signals are stochastic and in order to deduce dynamical information through traditional means-such as fluorescence correlation spectroscopy (FCS) and related techniques-fluorescence signals are collected and temporally auto-correlated over several minutes. So far, it has been impossible to analyze dynamical properties of biomolecules on timescales approaching data acquisition as this demands that we estimate the instantaneous number of biomolecules emitting photons and their positions within the confocal volume. The mathematical structure of this problem demands that we abandon the normal ("parametric") Bayesian paradigm. Here, we exploit novel mathematical tools, namely Bayesian nonparametrics, that allow us to deduce in a principled fashion the same information normally deduced from FCS but from the direct analysis of significantly smaller datasets starting from individual photon arrivals. We discuss the implications of this method in helping dramatically reduce phototoxic damage on the sample and the ability to monitor out-of-equilibrium processes.

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“…The assumption of a known number of states has been lifted thanks to extensions of the HMM (34,(37)(38)(39)(40)(41)(42)(43) afforded by nonparametrics that we discuss elsewhere (33,34,(38)(39)(40)43).…”

Section: Introductionmentioning

confidence: 99%

Generalizing HMMs to Continuous Time for Fast Kinetics: Hidden Markov Jump Processes

Kilic

Sgouralis

Pressé

2020

Preprint

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The hidden Markov model (HMM) is a framework for time series analysis widely applied to single molecule experiments. It has traditionally been used to interpret signals generated by systems, such as single molecules, evolving in a discrete state space observed at discrete time levels dictated by the data acquisition rate. Within the HMM framework, originally developed for applications outside the Natural Sciences, such as speech recognition, transitions between states, such as molecular conformational states, are modeled as occurring at the end of each data acquisition period and are described using transition probabilities. Yet, while measurements are often performed at discrete time levels in the Natural Sciences, physical systems evolve in continuous time according to transition rates. It then follows that the modeling assumptions underlying the HMM are justified if the transition rates of a physical process from state to state are small as compared to the data acquisition rate. In other words, HMMs apply to slow kinetics. The problem is, as the transition rates are unknown in principle, it is unclear, a priori, whether the HMM applies to a particular system. For this reason, we must generalize HMMs for physical systems, such as single molecules, as these switch between discrete states in continuous time. We do so by exploiting recent mathematical tools developed in the context of inferring Markov jump processes and propose the hidden Markov jump process (HMJP). We explicitly show in what limit the HMJP reduces to the HMM. Resolving the discrete time discrepancy of the HMM has clear implications: we no longer need to assume that processes, such as molecular events, must occur on timescales slower than data acquisition and can learn transition rates even if these are on the same timescale or otherwise exceed data acquisition rates.

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A Bayesian Nonparametric Approach to Single Molecule Förster Resonance Energy Transfer

Cited by 44 publications

References 73 publications

Pitching Single-Focus Confocal Data Analysis One Photon at a Time with Bayesian Nonparametrics

Pitching Single-Focus Confocal Data Analysis One Photon at a Time with Bayesian Nonparametrics

Pitching single-focus confocal data analysis one photon at a time with Bayesian nonparametrics

Generalizing HMMs to Continuous Time for Fast Kinetics: Hidden Markov Jump Processes

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