A Bayesian nonparametric approach to super-resolution single-molecule localization

Gabitto, Mariano I.; Marie-Nelly, Hervé; Pakman, Ari; Pataki, Andras; Darzacq, Xavier; Jordan, Michael I.

doi:10.1101/2020.02.15.950873

Cited by 3 publications

(3 citation statements)

References 47 publications

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“…In this case, a collapsed state formulation (one that keeps track of the total population of decreasing numbers of fluorophores) can be used [ 15 , 25 , 26 ]. However, even then, existing methods for enumeration do not sample full Bayesian posteriors and counting would not be possible for cases where the majority of fluorophores are initially inactive such as in the case of photoactivation localization microscopy (PALM) [ 57 , 58 , 59 , 11 ]. Indeed, moving forward, PALM and other superresolution experiments [ 4 , 5 ] could provide exciting in vivo test beds for our method.…”

Section: Discussionmentioning

confidence: 99%

“…Directly enumerating fluorophores and tracking their photophysical dynamics by discriminating between them on the basis of their physical location [ 11 ] is often impossible as typically an entire bright spot lies below the diffraction limit [ 2 , 3 ]. Furthermore, fluorescence ruler methods, which enumerate fluorophores across time by comparing the brightness of a region of interest (ROI) to the brightness of a known calibration standard, are unreliable when the number of fluorophores is large on account of the inherent uncertainty introduced by photon shot noise which increases with growing fluorophore numbers [ 12 , 13 ].…”

Section: Introductionmentioning

confidence: 99%

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Diffraction-limited molecular cluster quantification with Bayesian nonparametrics

2022

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Life’s fundamental processes involve multiple molecules operating in close proximity within cells. To probe the composition and kinetics of molecular clusters confined within small (diffraction-limited) regions, experiments often report on the total fluorescence intensity simultaneously emitted from labeled molecules confined to such regions. Methods exist to enumerate total fluorophore numbers (e.g., step counting by photobleaching). However, methods aimed at step counting by photobleaching cannot treat photophysical dynamics in counting nor learn their associated kinetic rates. Here we propose a method to simultaneously enumerate fluorophores and determine their individual photophysical state trajectories. As the number of active (fluorescent) molecules at any given time is unknown, we rely on Bayesian nonparametrics and use specialized Monte Carlo algorithms to derive our estimates. Our formulation is benchmarked on synthetic and real data sets. While our focus here is on photophysical dynamics (in which labels transition between active and inactive states), such dynamics can also serve as a proxy for other types of dynamics such as assembly and disassembly kinetics of clusters. Similarly, while we focus on the case where all labels are initially fluorescent, other regimes, more appropriate to photoactivated localization microscopy, where fluorophores are instantiated in a non-fluorescent state, fall within the scope of the framework. As such, we provide a complete and versatile framework for the interpretation of complex time traces arising from the simultaneous activity of up to 100 fluorophores.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Diffraction-limited molecular cluster quantification with Bayesian nonparametrics

2022

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“…Furthermore, all prior methods provide a single estimate of molecular count, whereas a probabilis-tic method would provide valuable information for downstream analysis. Bayesian approaches can estimate a likelihood for each possible condition and have previously been used to infer the number of FRET conformational states [30,31], the number of photobleaching steps [19], the assignment of blinking events to specific fluorophores [32,33], and the molecular count from observed intensity [24].…”

Section: Introductionmentioning

confidence: 99%

A Bayesian Solution to Count the Number of Molecules within a Diffraction Limited Spot

Hillsley,

Stein,

Tillberg

et al. 2024

Preprint

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We address the problem of inferring the number of independently blinking fluorescent light emitters, when only their combined intensity contributions can be observed at each timepoint. This problem occurs regularly in light microscopy of objects that are smaller than the diffraction limit, where one wishes to count the number of fluorescently labelled subunits. Our proposed solution directly models the photo-physics of the system, as well as the blinking kinetics of the fluorescent emitters as a fully differentiable hidden Markov model. Given a trace of intensity over time, our model jointly estimates the parameters of the intensity distribution per emitter, their blinking rates, as well as a posterior distribution of the total number of fluorescent emitters. We show that our model is consistently more accurate and increases the range of countable subunits by a factor of two compared to current state-of-the-art methods, which count based on autocorrelation and blinking frequency, Furthermore, we demonstrate that our model can be used to investigate the effect of blinking kinetics on counting ability, and therefore can inform experimental conditions that will maximize counting accuracy.

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Diffraction-Limited Molecular Cluster Quantification with Bayesian Nonparametrics

Sgouralis

Bryan

Pressé

2020

Preprint

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Determining the number of biomolecules within a small, diffraction-limited spot, is key to understanding intermolecular interactions that form the basis of all of information processing relevant to life. To enumerate the number of biomolecules within such a small region of interest (ROI), it is possible to illuminate an ROI containing a collection of fluorescently labeled biomolecules and observe the ROI's brightness over time. As most fluorescent labels (fluorophores) are initially in a fluorescently active state, the brightness diminishes in a step-like pattern as fluorophores photobleach one at a time. Naively, by counting steps, one could determine the number of fluorophores present. However, this analysis is complicated by photon shot noise, camera noise that amplifies intrinsic photon shot noise and fluorophore photophysics (i.e., states with variable emission visited by fluorophores). Current state of the art can typically enumerate as many as 20 fluorophores reliably. Yet in many biophysics problems, fluorophore numbers can vastly exceed 20 within an ROI. For this reason, we develop a method to learn the number of fluorophores alongside other parameters required to achieve high counts simultaneously and self-consistently (e.g., fluorophore photophysical rate parameters and camera parameters). As the number of fluorophores is initially unknown and may be very large, and as not all fluorophores may initially be emitting photons, we cannot rely on a traditional (parametric) Bayesian framework. As such, to achieve our goal of exceeding the state of the art by a factor of about 5, we must abandon the parametric Bayesian paradigm and invoke novel tools within Bayesian nonparametrics never previously used in step counting by photobleaching.

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A Bayesian nonparametric approach to super-resolution single-molecule localization

Cited by 3 publications

References 47 publications

Diffraction-limited molecular cluster quantification with Bayesian nonparametrics

Diffraction-limited molecular cluster quantification with Bayesian nonparametrics

A Bayesian Solution to Count the Number of Molecules within a Diffraction Limited Spot

Diffraction-Limited Molecular Cluster Quantification with Bayesian Nonparametrics

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