Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

BNP-Track: a framework for superresolved tracking

Superresolution tools, such as PALM and STORM, provide nanoscale localization accuracy by relying on rare photophysical events, limiting these methods to static samples. By contrast, here, we extend superresolution to dynamics without relying on photodynamics by simultaneously determining emitter numbers and their tracks (localization and linking) with the same localization accuracy per frame as widefield superresolution on immobilized emitters under similar imaging conditions (≈50 nm). We demonstrate our Bayesian nonparametric track (BNP-Track) framework on both in cellulo and synthetic data. BNP-Track develops a joint (posterior) distribution that learns and quantifies uncertainty over emitter numbers and their associated tracks propagated from shot noise, camera artifacts, pixelation, background and out-of-focus motion. In doing so, we integrate spatiotemporal information into our distribution, which is otherwise compromised by modularly determining emitter numbers and localizing and linking emitter positions across frames. For this reason, BNP-Track remains accurate in crowding regimens beyond those accessible to other single-particle tracking tools.

Spectral Phasor Applied to Spectrally-Resolved Single Molecule Localization Microscopy

Spectrally-resolved single-molecule localization microscopy (srSMLM) has emerged as a powerful tool for exploring the spectral properties of single emitters in localization microscopy. By simultaneously capturing the spatial positions and spectroscopic signatures of individual fluorescent molecules, srSMLM opens up the possibility of investigating an additional dimension in super-resolution imaging. However, appropriate and dedicated tools are required to fully capitalize on the spectral dimension. Here, we propose the application of the spectral phasor analysis as an effective method for summarizing and analyzing the spectral information obtained from srSMLM experiments. The spectral phasor condenses the complete spectrum of a single emitter into a two-dimensional space, preserving key spectral characteristics for single-molecule spectral exploration. We demonstrate the effectiveness of spectral phasor in efficiently classifying single Nile Red fluorescence emissions from largely overlapping cyanine fluorescence signals in dual-color PAINT experiments. Additionally, we employed spectral phasor with srSMLM to reveal subtle alterations occurring in the membrane of Gram-positive Enterococcus hirae in response to gramicidin exposure, a membrane-perturbing antibiotic treatment. Spectral phasor provides a robust, model-free analytic tool for the detailed analysis of the spectral component of srSMLM, enhancing the capabilities of multi-color spectrally-resolved single-molecule imaging.

Photophysical image analysis: Unsupervised probabilistic thresholding for images from electron-multiplying charge-coupled devices

We introduce the concept photophysical image analysis (PIA) and an associated pipeline for unsupervised probabilistic image thresholding for images recorded by electron-multiplying charge-coupled device (EMCCD) cameras. We base our approach on a closed-form analytic expression for the characteristic function (Fourier-transform of the probability mass function) for the image counts recorded in an EMCCD camera, which takes into account both stochasticity in the arrival of photons at the imaging camera and subsequent noise induced by the detection system of the camera. The only assumption in our method is that the background photon arrival to the imaging system is described by a stationary Poisson process (we make no assumption about the photon statistics for the signal). We estimate the background photon statistics parameter, λbg, from an image which contains both background and signal pixels by use of a novel truncated fit procedure with an automatically determined image count threshold. Prior to this, the camera noise model parameters are estimated using a calibration step. Utilizing the estimates for the camera parameters and λbg, we then introduce a probabilistic thresholding method, where, for the first time, the fraction of misclassified pixels can be determined a priori for a general image in an unsupervised way. We use synthetic images to validate our a priori estimates and to benchmark against the Otsu method, which is a popular unsupervised non-probabilistic image thresholding method (no a priori estimates for the error rates are provided). For completeness, we lastly present a simple heuristic general-purpose segmentation method based on the thresholding results, which we apply to segmentation of synthetic images and experimental images of fluorescent beads and lung cell nuclei. Our publicly available software opens up for fully automated, unsupervised, probabilistic photophysical image analysis.

Quantitative Super-Resolution Microscopy Reveals the Relationship between CENP-A Stoichiometry and Centromere Physical Size

Centromeric chromatin is thought to play a critical role in ensuring the faithful segregation of chromosomes during mitosis. However, our understanding of this role is presently limited by our poor understanding of the structure and composition of this unique chromatin. The nucleosomal variant, CENP-A, localizes to narrow regions within the centromere, where it plays a major role in centromeric function, effectively serving as a platform on which the kinetochore is assembled. Previous work found that, within a given cell, the number of microtubules within kinetochores is essentially unchanged between CENP-A-localized regions of different physical sizes. However, it is unknown if the amount of CENP-A is also unchanged between these regions of different sizes, which would reflect a strict structural correspondence between these two key characteristics of the centromere/kinetochore assembly. Here, we used super-resolution optical microscopy to image and quantify the amount of CENP-A and DNA within human centromere chromatin. We found that the amount of CENP-A within CENP-A domains of different physical sizes is indeed the same. Further, our measurements suggest that the ratio of CENP-A- to H3-containing nucleosomes within these domains is between 8:1 and 11:1. Thus, our results not only identify an unexpectedly strict relationship between CENP-A and microtubules stoichiometries but also that the CENP-A centromeric domain is almost exclusively composed of CENP-A nucleosomes.

Fluorescence Microscopy: a statistics-optics perspective

Fundamental properties of light unavoidably impose features on images collected using fluorescence microscopes. Modeling these features is ever more important in quantitatively interpreting microscopy images collected at scales on par or smaller than light's wavelength. Here we review the optics responsible for generating fluorescent images, fluorophore properties, microscopy modalities leveraging properties of both light and fluorophores, in addition to the necessarily probabilistic modeling tools imposed by the stochastic nature of light and measurement.

Deep-MSIM: Fast Image Reconstruction with Deep Learning in Multifocal Structured Illumination Microscopy

Fast and precise reconstruction algorithm is desired for for multifocal structured illumination microscopy (MSIM) to obtain the super-resolution image. This work proposes a deep convolutional neural network (CNN) to learn a direct mapping from raw MSIM images to super-resolution image, which takes advantage of the computational advances of deep learning to accelerate the reconstruction. The method is validated on diverse biological structures and in vivo imaging of zebrafish at a depth of 100 µm. The results show that high-quality, super-resolution images can be reconstructed in one-third of the runtime consumed by conventional MSIM method, without compromising spatial resolution. Last but not least, a fourfold reduction in the number of raw images required for reconstruction is achieved by using the same network architecture, yet with different training data.

BNP-Track: A framework for superresolved tracking

Assessing dynamic processes at single molecule scales is key toward capturing life at the level of its molecular actors. Widefield superresolution methods, such as STORM, PALM, and PAINT, provide nanoscale localization accuracy, even when distances between fluorescently labeled single molecules ("emitters") fall below light's diffraction limit. However, as these superresolution methods rely on rare photophysical events to distinguish emitters from both each other and background, they are largely limited to static samples. In contrast, here we leverage spatiotemporal correlations of dynamic widefield imaging data to extend superresolution to simultaneous multiple emitter tracking without relying on photodynamics even as emitter distances from one another fall below the diffraction limit. We simultaneously determine emitter numbers and their tracks (localization and linking) with the same localization accuracy per frame as widefield superresolution does for immobilized emitters under similar imaging conditions (≈50nm). We demonstrate our results for both in cellulo data and, for benchmarking purposes, on synthetic data. To this end, we avoid the existing tracking paradigm relying on completely or partially separating the tasks of emitter number determination, localization of each emitter, and linking emitter positions across frames. Instead, we develop a fully joint posterior distribution over the quantities of interest, including emitter tracks and their total, otherwise unknown, number within the Bayesian nonparametric paradigm. Our posterior quantifies the full uncertainty over emitter numbers and their associated tracks propagated from origins including shot noise and camera artefacts, pixelation, stochastic background, and out-of-focus motion. Finally, it remains accurate in more crowded regimes where alternative tracking tools cannot be applied.

BNP-Track: A framework for multi-particle superresolved tracking

When tracking fluorescently labeled molecules (termed "emitters") under widefield microscopes, point spread function overlap of neighboring molecules is inevitable in both dilute and especially crowded environments. In such cases, superresolution methods leveraging rare photophysical events to distinguish static targets nearby in space introduce temporal delays that compromise tracking. As we have shown in a companion manuscript, for dynamic targets, information on neighboring fluorescent molecules is encoded as spatial intensity correlations across pixels and temporal correlations in intensity patterns across time frames. We then demonstrated how we used all spatiotemporal correlations encoded in the data to achieve superresolved tracking. That is, we showed the results of full posterior inference over both the number of emitters and their associated tracks simultaneously and self-consistently through Bayesian nonparametrics. In this companion manuscript we focus on testing the robustness of our tracking tool, BNP-Track, across sets of parameter regimes and compare BNP-Track to competing tracking methods in the spirit of a prior Nature Methods tracking competition. We explore additional features of BNP-Track including how a stochastic treatment of background yields greater accuracy in emitter number determination and how BNP-Track corrects for point spread function blur (or "aliasing") introduced by intraframe motion in addition to propagating error originating from myriad sources (such as criss-crossing tracks, out-of-focus particles, pixelation, shot and camera artefact, stochastic background) in posterior inference over emitter numbers and their associated tracks. While head-to-head comparison with other tracking methods is not possible (as competitors cannot simultaneously learn molecule numbers and associated tracks), we can give competing methods some advantages in order to perform approximate head-to-head comparison. We show that even under such optimistic scenarios, BNP-Track is capable of tracking multiple diffraction-limited point emitters conventional tracking methods cannot resolve thereby extending the superresolution paradigm to dynamical targets.

Simulation-based inference for non-parametric statistical comparison of biomolecule dynamics

Numerous models have been developed to account for the complex properties of the random walks of biomolecules. However, when analysing experimental data, conditions are rarely met to ensure model identification. The dynamics may simultaneously be influenced by spatial and temporal heterogeneities of the environment, out-of-equilibrium fluxes and conformal changes of the tracked molecules. Recorded trajectories are often too short to reliably discern such multi-scale dynamics, which precludes unambiguous assessment of the type of random walk and its parameters. Furthermore, the motion of biomolecules may not be well described by a single, canonical random walk model. Here, we develop a two-step statistical testing scheme for comparing biomolecule dynamics observed in different experimental conditions without having to identify or make strong prior assumptions about the model generating the recorded random walks. We first train a graph neural network to perform simulation-based inference and thus learn a rich summary statistics vector describing individual trajectories. We then compare trajectories obtained in different biological conditions using a non-parametric maximum mean discrepancy (MMD) statistical test on their so-obtained summary statistics. This procedure allows us to characterise sets of random walks regardless of their generating models, without resorting to model-specific physical quantities or estimators. We first validate the relevance of our approach on numerically simulated trajectories. This demonstrates both the statistical power of the MMD test and the descriptive power of the learnt summary statistics compared to estimates of physical quantities. We then illustrate the ability of our framework to detect changes in α-synuclein dynamics at synapses in cultured cortical neurons, in response to membrane depolarisation, and show that detected differences are largely driven by increased protein mobility in the depolarised state, in agreement with previous findings. The method provides a means of interpreting the differences it detects in terms of single trajectory characteristics. Finally, we emphasise the interest of performing various comparisons to probe the heterogeneity of experimentally acquired datasets at different levels of granularity (e.g., biological replicates, fields of view, and organelles).

Calcite-Assisted Localization and Kinetics (CLocK) Microscopy

Localization-based super-resolution imaging techniques have improved the spatial resolution of optical microscopy well below the diffraction limit, yet encoding additional information into super-resolved images, such as anisotropy and orientation, remains a challenge. Here we introduce calcite-assisted localization and kinetics (CLocK) microscopy, a multiparameter super-resolution imaging technique easily integrated into any existing optical microscope setup at low cost and with straightforward analysis. By placing a rotating calcite crystal in the infinity space of an optical microscope, CLocK microscopy provides immediate polarization and orientation information while maintaining the ability to localize an emitter/scatterer with <10 nm resolution. Further, kinetic information an order of magnitude shorter than the integration time of the camera is encoded in the unique point spread function of a CLocK image, allowing for new mechanistic insight into dynamic processes such as single-nanoparticle dissolution and single-molecule surface-enhanced Raman scattering.

Tuning axial and lateral localization precision in 3D super-resolution microscopy with variable astigmatism

Astigmatism imaging is a three-dimensional (3D) single molecule fluorescence microscopy approach that yields super-resolved spatial information on a rapid time scale from a single image. It is ideally suited for resolving structures on a sub-micrometer scale and temporal behavior in the millisecond regime. While traditional astigmatism imaging utilizes a cylindrical lens, adaptive optics enables the astigmatism to be tuned for the experiment. We demonstrate here how the precisions in x, y, and z are inter-linked and vary with the astigmatism, z-position, and photon level. This experimentally driven and verified approach provides a guide for astigmatism selection in biological imaging strategies.

Computational Proposal for Tracking Multiple Molecules in a Multifocus Confocal Setup

Tracking single molecules continues to provide new insights into the fundamental rules governing biological function. Despite continued technical advances in fluorescent and non-fluorescent labeling as well as data analysis, direct observations of trajectories and interactions of multiple molecules in dense environments remain aspirational goals. While confocal methods provide a means to deduce dynamical parameters with high temporal resolution, such as diffusion coefficients, they do so at the expense of spatial resolution. Indeed, on account of a confocal volume's symmetry, typically only distances from the center of the confocal spot can be deduced. Motivated by the need for true three dimensional high speed tracking in densely labeled environments, we propose a computational tool for tracking many fluorescent molecules traversing multiple, closely spaced, confocal measurement volumes providing independent observations. Various realizations of this multiple confocal volumes strategy have previously been used for long term, large area, tracking of one fluorescent molecule in three dimensions. What is more, we achieve tracking by directly using single photon arrival times to inform our likelihood and exploit Hamiltonian Monte Carlo to efficiently sample trajectories from our posterior within a Bayesian nonparametric paradigm. A nonparametric paradigm here is warranted as the number of molecules present are, themselves, a priori unknown. Taken together, we provide a computational framework to infer trajectories of multiple molecules at once, below the diffraction limit (the width of a confocal spot), in three dimensions at sub-millisecond or faster time scales.

Imaging Minimal Bacteria at the Nanoscale: a Reliable and Versatile Process to Perform Single-Molecule Localization Microscopy in Mycoplasmas

Mycoplasmas are the smallest free-living organisms. These bacteria are important models for both fundamental and synthetic biology, owing to their highly reduced genomes. They are also relevant in the medical and veterinary fields, as they are pathogenic to both humans and most livestock species. Mycoplasma cells have minute sizes, often in the 300- to 800-nm range. As these dimensions are close to the diffraction limit of visible light, fluorescence imaging in mycoplasmas is often poorly informative. Recently developed superresolution imaging techniques can break this diffraction limit, improving the imaging resolution by an order of magnitude and offering a new nanoscale vision of the organization of these bacteria. These techniques have, however, not been applied to mycoplasmas before. Here, we describe an efficient and reliable protocol to perform single-molecule localization microscopy (SMLM) imaging in mycoplasmas. We provide a polyvalent transposon-based system to express the photoconvertible fluorescent protein mEos3.2, enabling photo-activated localization microscopy (PALM) in most Mycoplasma species. We also describe the application of direct stochastic optical reconstruction microscopy (dSTORM). We showcase the potential of these techniques by studying the subcellular localization of two proteins of interest. Our work highlights the benefits of state-of-the-art microscopy techniques for mycoplasmology and provides an incentive to further the development of SMLM strategies to study these organisms in the future.

IMPORTANCE Mycoplasmas are important models in biology, as well as highly problematic pathogens in the medical and veterinary fields. The very small sizes of these bacteria, well below a micron, limits the usefulness of traditional fluorescence imaging methods, as their resolution limit is similar to the dimensions of the cells. Here, to bypass this issue, we established a set of state-of-the-art superresolution microscopy techniques in a wide range of Mycoplasma species. We describe two strategies: PALM, based on the expression of a specific photoconvertible fluorescent protein, and dSTORM, based on fluorophore-coupled antibody labeling. With these methods, we successfully performed single-molecule imaging of proteins of interest at the surface of the cells and in the cytoplasm, at lateral resolutions well below 50 nm. Our work paves the way toward a better understanding of mycoplasma biology through imaging of subcellular structures at the nanometer scale.

When Super-Resolution Localization Microscopy Meets Carbon Nanotubes

We recently assisted in a revolution in the realm of fluorescence microscopy triggered by the advent of super-resolution techniques that surpass the classic diffraction limit barrier. By providing optical images with nanometer resolution in the far field, super-resolution microscopy (SRM) is currently accelerating our understanding of the molecular organization of bio-specimens, bridging the gap between cellular observations and molecular structural knowledge, which was previously only accessible using electron microscopy. SRM mainly finds its roots in progress made in the control and manipulation of the optical properties of (single) fluorescent molecules. The flourishing development of novel fluorescent nanostructures has recently opened the possibility of associating super-resolution imaging strategies with nanomaterials’ design and applications. In this review article, we discuss some of the recent developments in the field of super-resolution imaging explicitly based on the use of nanomaterials. As an archetypal class of fluorescent nanomaterial, we mainly focus on single-walled carbon nanotubes (SWCNTs), which are photoluminescent emitters at near-infrared (NIR) wavelengths bearing great interest for biological imaging and for information optical transmission. Whether for fundamental applications in nanomaterial science or in biology, we show how super-resolution techniques can be applied to create nanoscale images “in”, “of” and “with” SWCNTs.

High Resolution Fluorescence Lifetime Maps from Minimal Photon Counts

Fluorescence lifetime imaging microscopy (FLIM) may reveal subcellular spatial lifetime maps of key molecular species. Yet, such a quantitative picture of life necessarily demands high photon budgets at every pixel under the current analysis paradigm, thereby increasing acquisition time and photodamage to the sample. Motivated by recent developments in computational statistics, we provide a direct means to update our knowledge of the lifetime maps of species of different lifetimes from direct photon arrivals, while accounting for experimental features such as arbitrary forms of the instrument response function (IRF) and exploiting information from empty laser pulses not resulting in photon detection. Our ability to construct lifetime maps holds for arbitrary lifetimes, from short lifetimes (comparable to the IRF) to lifetimes exceeding interpulse times. As our method is highly data efficient, for the same amount of data normally used to determine lifetimes and photon ratios, working within the Bayesian paradigm, we report direct blind unmixing of lifetimes with subnanosecond resolution and subpixel spatial resolution using standard raster scan FLIM images. We demonstrate our method using a wide range of simulated and experimental data.

A Heuristic Approach to Linking Experimental Descriptors with Product Selectivity in Electrochemical CO2 Reduction

An important challenge in electrochemical CO2 reduction (ECR) is relating experimental conditions to their consequences, particularly in terms of product selectivity. The problem lies in the lack of descriptors which adequately describe the experimental protocols and their associated results. In this study, a machine learning approach is applied to correlate the molar composition of 21 single metals and 23 bimetallic particles, as well as operating parameters, from a large collection of synthetic records compiled from the literature with product selectivity. The decision tree obtained shows the conditions that lead to high desired product selectivity and provides a heuristic insight into its electrochemistry. As such, the data does not provide details. However, machine learning algorithms are capable of identifying hidden patterns in the data, providing a deeper insight into the chemistry involved in product formation in the ECR.

Diffraction-limited molecular cluster quantification with Bayesian nonparametrics

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.

Raw Data to Results: A Hands-On Introduction and Overview of Computational Analysis for Single-Molecule Localization Microscopy

Single-molecule localization microscopy (SMLM) is an advanced microscopy method that uses the blinking of fluorescent molecules to determine the position of these molecules with a resolution below the diffraction limit (∼5-40 nm). While SMLM imaging itself is becoming more popular, the computational analysis surrounding the technique is still a specialized area and often remains a "black box" for experimental researchers. Here, we provide an introduction to the required computational analysis of SMLM imaging, post-processing and typical data analysis. Importantly, user-friendly, ready-to-use and well-documented code in Python and MATLAB with exemplary data is provided as an interactive experience for the reader, as well as a starting point for further analysis. Our code is supplemented by descriptions of the computational problems and their implementation. We discuss the state of the art in computational methods and software suites used in SMLM imaging and data analysis. Finally, we give an outlook into further computational challenges in the field.

A Protocol for Studying Transcription Factor Dynamics Using Fast Single-Particle Tracking and Spot-On Model-Based Analysis

Single-particle tracking (SPT) makes it possible to directly observe single protein diffusion dynamics in living cells over time. Thus, SPT has emerged as a powerful method to quantify the dynamics of nuclear proteins such as transcription factors (TFs). Here, we provide a protocol for conducting and analyzing SPT experiments with a focus on fast tracking ("fastSPT") of TFs in mammalian cells. First, we explore how to engineer and prepare cells for SPT experiments. Next, we examine how to optimize SPT experiments by imaging at low densities to minimize tracking errors and by using stroboscopic excitation to minimize motion-blur. Next, we discuss how to convert raw SPT data into single-particle trajectories. Finally, we illustrate how to analyze these trajectories using the kinetic modeling package Spot-On. We discuss how to use Spot-On to fit histograms of displacements and extract useful information such as the fraction of TFs that are bound and freely diffusing, and their associated diffusion coefficients.

A gain series method for accurate EMCCD calibration

Calibration of the gain and digital conversion factor of an EMCCD is necessary for accurate photon counting. We present a new method to quickly calibrate multiple gain settings of an EMCCD camera. Acquiring gain-series calibration data and analyzing the resulting images with the EMCCD noise model more accurately estimates the gain response of the camera. Furthermore, we develop a method to compare the results from different calibration approaches. Gain-series calibration outperforms all other methods in this self-consistency test.

Fluorescent proteins of the EosFP clade: intriguing marker tools with multiple photoactivation modes for advanced microscopy

Optical fluorescence microscopy has taken center stage in the exploration of biological structure and dynamics, especially on live specimens, and super-resolution imaging methods continue to deliver exciting new insights into the molecular foundations of life. Progress in the field, however, crucially hinges on advances in fluorescent marker technology. Among these, fluorescent proteins (FPs) of the GFP family are advantageous because they are genetically encodable, so that live cells, tissues or organisms can produce these markers all by themselves. A subclass of them, photoactivatable FPs, allow for control of their fluorescence emission by light irradiation, enabling pulse-chase imaging and super-resolution microscopy. In this review, we discuss FP variants of the EosFP clade that have been optimized by amino acid sequence modification to serve as markers for various imaging techniques. In general, two different modes of photoactivation are found, reversible photoswitching between a fluorescent and a nonfluorescent state and irreversible green-to red photoconversion. First, we describe their basic structural and optical properties. We then summarize recent research aimed at elucidating the photochemical processes underlying photoactivation. Finally, we briefly introduce various advanced imaging methods facilitated by specific EosFP variants, and show some exciting sample applications.

Extraction of rapid kinetics from smFRET measurements using integrative detectors

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.

Spatial and temporal super-resolution for fluorescence microscopy by a recurrent neural network

A novel spatial and temporal super-resolution (SR) framework based on a recurrent neural network (RNN) is demonstrated. In this work, we learn the complex yet useful features from the temporal data by taking advantage of structural characteristics of RNN and a skip connection. The usage of supervision mechanism is not only making full use of the intermediate output of each recurrent layer to recover the final output, but also alleviating vanishing/exploding gradients during the back-propagation. The proposed scheme achieves excellent reconstruction results, improving both the spatial and temporal resolution of fluorescence images including the simulated and real tubulin datasets. Besides, robustness against various critical metrics, such as the full-width at half-maximum (FWHM) and molecular density, can also be incorporated. In the validation, the performance can be increased by more than 20% for intensity profile, and 8% for FWHM, and the running time can be saved at least 40% compared with the classic Deep-STORM method, a high-performance net which is popularly used for comparison.

Probing Biosensing Interfaces With Single Molecule Localization Microscopy (SMLM)

Far field single molecule localization microscopy (SMLM) has been established as a powerful tool to study biological structures with resolution far below the diffraction limit of conventional light microscopy. In recent years, the applications of SMLM have reached beyond traditional cellular imaging. Nanostructured interfaces are enriched with information that determines their function, playing key roles in applications such as chemical catalysis and biological sensing. SMLM enables detailed study of interfaces at an individual molecular level, allowing measurements of reaction kinetics, and detection of rare events not accessible to ensemble measurements. This paper provides an update to the progress made to the use of SMLM in characterizing nanostructured biointerfaces, focusing on practical aspects, recent advances, and emerging opportunities from an analytical chemistry perspective.

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

The hidden Markov model (HMM) is a framework for time series analysis widely applied to single-molecule experiments. Although initially developed for applications outside the natural sciences, the HMM has traditionally been used to interpret signals generated by physical 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, transitions between states are modeled as occurring at the end of each data acquisition period and are described using transition probabilities. Yet, whereas 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, because 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, because 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. We explicitly show in what limit the hidden Markov jump process 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.

A Programmable DNA-Silicification-Based Nanocavity for Single-Molecule Plasmonic Sensing

Plasmonic nanocavities are highly desirable for optical sensing because of their singular ability to confine light into deep subwavelength volumes. Yet, it remains profoundly challenging to fabricate structurally resilient nanocavities with high fidelity, and to obtain direct, noninvasive visualization of the plasmonic hotspots within such constructs. Herein, highly precise and robust nanocavities, entitled DNA-silicified template for Raman optical beacon (DNA-STROBE), are engineered by using silicified DNA scaffolds for spatial organization of discrete plasmonic nanoparticles. In addition to substantially enhancing structural stability and chemical inertness, DNA silicification significantly improves nanogap control, resulting simultaneously in large and controlled local electromagnetic field enhancement. The ultrasmall mode volume of the DNA-STROBE constructs promotes single-molecule occupancy enabling surface-enhanced Raman spectroscopy (SERS) observations of single-molecule activity even at elevated background concentration, significantly relaxing the restrictive pico- to nanomolar molecular concentration condition typically required for such investigations. Additionally, leveraging super-resolution SERS measurements allows noninvasive and diffraction-unlimited spatial profiling of otherwise unresolvable plasmonic hotspots. The highly programmable and reproducible nature of the DNA-STROBE, coupled with its quantitative label-free molecular readouts, provides a versatile platform with applications across the spectrum of nanophotonics and biomedical sciences.

Viewpoint: Single Molecules at 31: What's Next?

Optical studies of single molecules have taught us much over the past three decades, but these individual quantum-mechanical objects continue to have promise as probes of nanoscale structure and dynamics in complex systems.

Tracking and interpreting long-range chromatin interactions with super-resolution live-cell imaging

Mammalian genomes are organized and regulated through long-range chromatin interactions. Structural loops formed by CCCTC-binding factor (CTCF) and cohesin fold the genome into domains, while enhancers interact with promoters across vast genomic distances to regulate gene expression. Although genomics and fixed-cell imaging approaches help illuminate many aspects of chromatin interactions, temporal information is usually lost. Here, we discuss how 3D super-resolution live-cell imaging (SRLCI) can resolve open questions on the dynamic formation and dissolution of chromatin interactions. We discuss SRLCI experimental design, implementation strategies, and data interpretation and highlight associated pitfalls. We conclude that, while technically demanding, SRLCI approaches will likely emerge as a critical tool to dynamically probe 3D genome structure and function and to study enhancer–promoter interactions and chromatin looping.

Direct Photon-by-Photon Analysis of Time-Resolved Pulsed Excitation Data using Bayesian Nonparametrics

Lifetimes of chemical species are typically estimated by either fitting time-correlated single-photon counting (TCSPC) histograms or phasor analysis from time-resolved photon arrivals. While both methods yield lifetimes in a computationally efficient manner, their performance is limited by choices made on the number of distinct chemical species contributing photons. However, the number of species is encoded in the photon arrival times collected for each illuminated spot and need not be set by hand a priori. Here, we propose a direct photon-by-photon analysis of data drawn from pulsed excitation experiments to infer, simultaneously and self-consistently, the number of species and their associated lifetimes from a few thousand photons. We do so by leveraging new mathematical tools within the Bayesian nonparametric. We benchmark our method for both simulated and experimental data for 1-4 species.

Advances in Chromatin and Chromosome Research: Perspectives from Multiple Fields

Nucleosomes package genomic DNA into chromatin. By regulating DNA access for transcription, replication, DNA repair, and epigenetic modification, chromatin forms the nexus of most nuclear processes. In addition, dynamic organization of chromatin underlies both regulation of gene expression and evolution of chromosomes into individualized sister objects, which can segregate cleanly to different daughter cells at anaphase. This collaborative review shines a spotlight on technologies that will be crucial to interrogate key questions in chromatin and chromosome biology including state-of-the-art microscopy techniques, tools to physically manipulate chromatin, single-cell methods to measure chromatin accessibility, computational imaging with neural networks and analytical tools to interpret chromatin structure and dynamics. In addition, this review provides perspectives on how these tools can be applied to specific research fields such as genome stability and developmental biology and to test concepts such as phase separation of chromatin.

Super-resolution microscopy reveals majorly mono- and dimeric presenilin1/γ-secretase at the cell surface

γ-Secretase is a multi-subunit enzyme whose aberrant activity is associated with Alzheimer’s disease and cancer. While its structure is atomically resolved, γ-secretase localization in the membrane in situ relies mostly on biochemical data. Here, we combined fluorescent tagging of γ-secretase subunits with super-resolution microscopy in fibroblasts. Structured illumination microscopy revealed single γ-secretase complexes with a monodisperse distribution and in a 1:1 stoichiometry of PSEN1 and nicastrin subunits. In living cells, sptPALM revealed PSEN1/γ-secretase mainly with directed motility and frequenting ‘hotspots’ or high track-density areas that are sensitive to γ-secretase inhibitors. We visualized γ-secretase association with substrates like amyloid precursor protein and N-cadherin, but not with its sheddases ADAM10 or BACE1 at the cell surface, arguing against pre-formed megadalton complexes. Nonetheless, in living cells PSEN1/γ-secretase transiently visits ADAM10 hotspots. Our results highlight the power of super-resolution microscopy for the study of γ-secretase distribution and dynamics in the membrane.

A Review of Super-Resolution Single-Molecule Localization Microscopy Cluster Analysis and Quantification Methods

Single-molecule localization microscopy (SMLM) is a relatively new imaging modality, winning the 2014 Nobel Prize in Chemistry, and considered as one of the key super-resolution techniques. SMLM resolution goes beyond the diffraction limit of light microscopy and achieves resolution on the order of 10-20 nm. SMLM thus enables imaging single molecules and study of the low-level molecular interactions at the subcellular level. In contrast to standard microscopy imaging that produces 2D pixel or 3D voxel grid data, SMLM generates big data of 2D or 3D point clouds with millions of localizations and associated uncertainties. This unprecedented breakthrough in imaging helps researchers employ SMLM in many fields within biology and medicine, such as studying cancerous cells and cell-mediated immunity and accelerating drug discovery. However, SMLM data quantification and interpretation methods have yet to keep pace with the rapid advancement of SMLM imaging. Researchers have been actively exploring new computational methods for SMLM data analysis to extract biosignatures of various biological structures and functions. In this survey, we describe the state-of-the-art clustering methods adopted to analyze and quantify SMLM data and examine the capabilities and shortcomings of the surveyed methods. We classify the methods according to (1) the biological application (i.e., the imaged molecules/structures), (2) the data acquisition (such as imaging modality, dimension, resolution, and number of localizations), and (3) the analysis details (2D versus 3D, field of view versus region of interest, use of machine-learning and multi-scale analysis, biosignature extraction, etc.). We observe that the majority of methods that are based on second-order statistics are sensitive to noise and imaging artifacts, have not been applied to 3D data, do not leverage machine-learning formulations, and are not scalable for big-data analysis. Finally, we summarize state-of-the-art methodology, discuss some key open challenges, and identify future opportunities for better modeling and design of an integrated computational pipeline to address the key challenges.

Quantitative objective-based ring TIRFM system calibration through back focal plane imaging

Being the established imaging tool for cell membrane-associated studies, total internal reflection fluorescence microscopy (TIRFM) still has some limitations. The most important one is the inhomogeneous evanescent excitation field mainly caused by the large-angle and fixed-azimuth illumination scheme, which can be eliminated by using ring-shaped illumination (ring TIRFM). However, it is challenging in assembling a ring TIRFM system with precise parameter control that works well. Here we emphasize the quantification of the ring TIRFM system and introduce a robust calibration routine to simultaneously rectify the asymmetry of the spinning light beam and determine the crucial experimental parameter, i.e., the incident angle. The calibration routine requires no specific sample preparation and is entirely based on the automatic back focal plane manipulation, avoiding possible errors caused by the sample difference and manual measurement. Its effectiveness is experimentally demonstrated by both the qualitative and quantitative comparisons of the images acquired using different samples, illumination schemes, and calibration approaches. These characteristics should enable our approach to greatly improve the practicability of TIRFM in life sciences.

Image reconstruction with a deep convolutional neural network in high-density super-resolution microscopy

An accurate and fast reconstruction algorithm is crucial for the improvement of temporal resolution in high-density super-resolution microscopy, particularly in view of the challenges associated with live-cell imaging. In this work, we design a deep network based on a convolutional neural network to take advantage of its enhanced ability in high-density molecule localization, and introduce a residual layer into the network to reduce noise. The proposed scheme also incorporates robustness against variations of both the full width at half maximum (FWHM) and the pixel size. We validate our algorithm on both simulated and experimental data by achieving performance improvement in terms of loss value and image quality, and demonstrate live-cell imaging with temporal resolution of 0.5 seconds by recovering mitochondria dynamics.

SMAUG: Analyzing single-molecule tracks with nonparametric Bayesian statistics

Single-molecule fluorescence microscopy probes nanoscale, subcellular biology in real time. Existing methods for analyzing single-particle tracking data provide dynamical information, but can suffer from supervisory biases and high uncertainties. Here, we develop a method for the case of multiple interconverting species undergoing free diffusion and introduce a new approach to analyzing single-molecule trajectories: the Single-Molecule Analysis by Unsupervised Gibbs sampling (SMAUG) algorithm, which uses nonparametric Bayesian statistics to uncover the whole range of information contained within a single-particle trajectory dataset. Even in complex systems where multiple biological states lead to a number of observed mobility states, SMAUG provides the number of mobility states, the average diffusion coefficient of single molecules in that state, the fraction of single molecules in that state, the localization noise, and the probability of transitioning between two different states. In this paper, we provide the theoretical background for the SMAUG analysis and then we validate the method using realistic simulations of single-particle trajectory datasets as well as experiments on a controlled in vitro system. Finally, we demonstrate SMAUG on real experimental systems in both prokaryotes and eukaryotes to measure the motions of the regulatory protein TcpP in Vibrio cholerae and the dynamics of the B-cell receptor antigen response pathway in lymphocytes. Overall, SMAUG provides a mathematically rigorous approach to measuring the real-time dynamics of molecular interactions in living cells.

Inferring effective forces for Langevin dynamics using Gaussian processes

Effective forces derived from experimental or in silico molecular dynamics time traces are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. This helps motivate why it is important to develop methods to efficiently learn effective forces from time series data. A number of methods already exist to do this when data are plentiful but otherwise fail for sparse datasets or datasets where some regions of phase space are undersampled. In addition, any method developed to learn effective forces from time series data should be minimally a priori committal as to the shape of the effective force profile, exploit every data point without reducing data quality through any form of binning or pre-processing, and provide full credible intervals (error bars) about the prediction for the entirety of the effective force curve. Here, we propose a generalization of the Gaussian process, a key tool in Bayesian nonparametric inference and machine learning, which meets all of the above criteria in learning effective forces for the first time.

Single-Virus Tracking: From Imaging Methodologies to Virological Applications

Uncovering the mechanisms of virus infection and assembly is crucial for preventing the spread of viruses and treating viral disease. The technique of single-virus tracking (SVT), also known as single-virus tracing, allows one to follow individual viruses at different parts of their life cycle and thereby provides dynamic insights into fundamental processes of viruses occurring in live cells. SVT is typically based on fluorescence imaging and reveals insights into previously unreported infection mechanisms. In this review article, we provide the readers a broad overview of the SVT technique. We first summarize recent advances in SVT, from the choice of fluorescent labels and labeling strategies to imaging implementation and analytical methodologies. We then describe representative applications in detail to elucidate how SVT serves as a valuable tool in virological research. Finally, we present our perspectives regarding the future possibilities and challenges of SVT.

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

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.

Linking synthesis and structure descriptors from a large collection of synthetic records of zeolite materials

Correlating synthesis conditions and their consequences is a significant challenge, particularly for materials formed as metastable phases via kinetically controlled pathways, such as zeolites, owing to a lack of descriptors that effectively illustrate the synthesis protocols and their corresponding results. This study analyzes the synthetic records of zeolites compiled from the literature using machine learning techniques to rationalize physicochemical, structural, and heuristic insights to their chemistry. The synthesis descriptors extracted from the machine learning models are used to identify structure descriptors with the appropriate importance. A similarity network of crystal structures based on the structure descriptors shows the formation of communities populated by synthetically similar materials, including those outside the dataset. Crossover experiments based on previously overlooked structural similarities reveal the synthesis similarity of zeolites, confirming the synthesis–structure relationship. This approach is applicable to any system to rationalize empirical knowledge, populate synthesis records, and discover novel materials.

Understanding zeolite synthesis-structure relationships remains challenging owing to the number of variables involved in their preparation. Here the authors analyze zeolite synthetic records from the literature via machine learning and find communities of synthetically related materials with previously overlooked similarities.

Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame-acquisition time. We show that these errors result in systematic and nontrivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors but decreased by static errors. Our formula allows for the development of efficient corrections schemes, and we also present in this work a provisional method for reconstructing true potentials from the measured ones.

Quantitative Kinetic Models from Intravital Microscopy: A Case Study Using Hepatic Transport

The liver performs critical physiological functions, including metabolizing and removing substances, such as toxins and drugs, from the bloodstream. Hepatotoxicity itself is intimately linked to abnormal hepatic transport, and hepatotoxicity remains the primary reason drugs in development fail and approved drugs are withdrawn from the market. For this reason, we propose to analyze, across liver compartments, the transport kinetics of fluorescein-a fluorescent marker used as a proxy for drug molecules-using intravital microscopy data. To resolve the transport kinetics quantitatively from fluorescence data, we account for the effect that different liver compartments (with different chemical properties) have on fluorescein's emission rate. To do so, we develop ordinary differential equation transport models from the data where the kinetics is related to the observable fluorescence levels by "measurement parameters" that vary across different liver compartments. On account of the steep non-linearities in the kinetics and stochasticity inherent to the model, we infer kinetic and measurement parameters by generalizing the method of parameter cascades. For this application, the method of parameter cascades ensures fast and precise parameter estimates from noisy time traces.

An alternative framework for fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS), is a widely used tool routinely exploited for in vivo and in vitro applications. While FCS provides estimates of dynamical quantities, such as diffusion coefficients, it demands high signal to noise ratios and long time traces, typically in the minute range. In principle, the same information can be extracted from microseconds to seconds long time traces; however, an appropriate analysis method is missing. To overcome these limitations, we adapt novel tools inspired by Bayesian non-parametrics, which starts from the direct analysis of the observed photon counts. With this approach, we are able to analyze time traces, which are too short to be analyzed by existing methods, including FCS. Our new analysis extends the capability of single molecule fluorescence confocal microscopy approaches to probe processes several orders of magnitude faster and permits a reduction of photo-toxic effects on living samples induced by long periods of light exposure.

Fluorescence correlation spectroscopy is widely used for in vivo and in vitro applications, yet extracting information from experiments still requires long acquisition times. Here, the authors exploit Bayesian non-parametrics to directly analyze the output of confocal fluorescence experiments thereby probing physical processes on much faster timescales.

Quantifying Protein Copy Number in Super Resolution Using an Imaging-Invariant Calibration

The use of super-resolution microscopy in recent years has revealed that proteins often form small assemblies inside cells and are organized in nanoclusters. However, determining the copy number of proteins within these nanoclusters constitutes a major challenge because of unknown labeling stoichiometries and complex fluorophore photophysics. We previously developed a DNA-origami-based calibration approach to extract protein copy number from super-resolution images. However, the applicability of this approach is limited by the fact that the calibration is dependent on the specific labeling and imaging conditions used in each experiment. Hence, the calibration must be repeated for each experimental condition, which is a formidable task. Here, using cells stably expressing dynein intermediate chain fused to green fluorescent protein (HeLa IC74 cells) as a reference sample, we demonstrate that the DNA-origami-based calibration data we previously generated can be extended to super-resolution images taken under different experimental conditions, enabling the quantification of any green-fluorescent-protein-fused protein of interest. To do so, we first quantified the copy number of dynein motors within nanoclusters in the cytosol and along the microtubules. Interestingly, this quantification showed that dynein motors form assemblies consisting of more than one motor, especially along microtubules. This quantification enabled us to use the HeLa IC74 cells as a reference sample to calibrate and quantify protein copy number independently of labeling and imaging conditions, dramatically improving the versatility and applicability of our approach.

Resolving Cytosolic Diffusive States in Bacteria by Single-Molecule Tracking

The trajectory of a single protein in the cytosol of a living cell contains information about its molecular interactions in its native environment. However, it has remained challenging to accurately resolve and characterize the diffusive states that can manifest in the cytosol using analytical approaches based on simplifying assumptions. Here, we show that multiple intracellular diffusive states can be successfully resolved if sufficient single-molecule trajectory information is available to generate well-sampled distributions of experimental measurements and if experimental biases are taken into account during data analysis. To address the inherent experimental biases in camera-based and MINFLUX-based single-molecule tracking, we use an empirical data analysis framework based on Monte Carlo simulations of confined Brownian motion. This framework is general and adaptable to arbitrary cell geometries and data acquisition parameters employed in two-dimensional or three-dimensional single-molecule tracking. We show that, in addition to determining the diffusion coefficients and populations of prevalent diffusive states, the timescales of diffusive state switching can be determined by stepwise increasing the time window of averaging over subsequent single-molecule displacements. Time-averaged diffusion analysis of single-molecule tracking data may thus provide quantitative insights into binding and unbinding reactions among rapidly diffusing molecules that are integral for cellular functions.

A method for single molecule tracking using a conventional single-focus confocal setup

One way to achieve spatial resolution using fluorescence imaging-and track single molecules-is to use wide-field illumination and collect measurements over multiple sensors (camera pixels). Here we propose another way that uses confocal measurements and a single sensor. Traditionally, confocal microscopy has been used to achieve high temporal resolution at the expense of spatial resolution. This is because it utilizes very few, and commonly just one, sensors to collect data. Yet confocal data encode spatial information. Here we show that non-uniformities in the shape of the confocal excitation volume can be exploited to achieve spatial resolution. To achieve this, we formulate a specialized hidden Markov model and adapt a forward filtering-backward sampling Markov chain Monte Carlo scheme to efficiently handle molecular motion within a symmetric confocal volume characteristically used in fluorescence correlation spectroscopy. Our method can be used for single confocal volume applications or incorporated into larger computational schemes for specialized, multi-confocal volume, optical setups.

SMALL-LABS: Measuring Single-Molecule Intensity and Position in Obscuring Backgrounds

Single-molecule and super-resolution imaging relies on successful, sensitive, and accurate detection of the emission from fluorescent molecules. Yet, despite the widespread adoption of super-resolution microscopies, single-molecule data processing algorithms can fail to provide accurate measurements of the brightness and position of molecules in the presence of backgrounds that fluctuate significantly over time and space. Thus, samples or experiments that include obscuring backgrounds can severely, or even completely, hinder this process. To date, no general data analysis approach to this problem has been introduced that is capable of removing obscuring backgrounds for a wide variety of experimental modalities. To address this need, we present the Single-Molecule Accurate LocaLization by LocAl Background Subtraction (SMALL-LABS) algorithm, which can be incorporated into existing single-molecule and super-resolution analysis packages to accurately locate and measure the intensity of single molecules, regardless of the shape or brightness of the background. Accurate background subtraction is enabled by separating the foreground from the background based on differences in the temporal variations of the foreground and the background (i.e., fluorophore blinking, bleaching, or moving). We detail the function of SMALL-LABS here, and we validate the SMALL-LABS algorithm on simulated data as well as real data from single-molecule imaging in living cells.

A Bayesian Nonparametric Approach to Single Molecule Förster Resonance Energy Transfer

We develop a Bayesian nonparametric framework to analyze single molecule FRET (smFRET) data. This framework, a variation on infinite hidden Markov models, goes beyond traditional hidden Markov analysis, which already treats photon shot noise, in three critical ways: (1) it learns the number of molecular states present in a smFRET time trace (a hallmark of nonparametric approaches), (2) it accounts, simultaneously and self-consistently, for photophysical features of donor and acceptor fluorophores (blinking kinetics, spectral cross-talk, detector quantum efficiency), and (3) it treats background photons. Point 2 is essential in reducing the tendency of nonparametric approaches to overinterpret noisy single molecule time traces and so to estimate states and transition kinetics robust to photophysical artifacts. As a result, with the proposed framework, we obtain accurate estimates of single molecule properties even when the supplied traces are excessively noisy, subject to photoartifacts, and of short duration. We validate our method using synthetic data sets and demonstrate its applicability to real data sets from single molecule experiments on Holliday junctions labeled with conventional fluorescent dyes.