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.

Fluorescence lifetime: Beating the IRF and interpulse window.

Fluorescence lifetime imaging captures the spatial distribution of chemical species across cellular environments employing pulsed illumination confocal setups. However, quantitative interpretation of lifetime data continues to face critical challenges. For instance, fluorescent species with known in vitro excited-state lifetimes may split into multiple species with unique lifetimes when introduced into complex living environments. What is more, mixtures of species, which may be both endogenous and introduced into the sample, may exhibit 1) very similar lifetimes as well as 2) wide ranges of lifetimes including lifetimes shorter than the instrumental response function or whose duration may be long enough to be comparable to the interpulse window. By contrast, existing methods of analysis are optimized for well-separated and intermediate lifetimes. Here, we broaden the applicability of fluorescence lifetime analysis by simultaneously treating unknown mixtures of arbitrary lifetimes-outside the intermediate, Goldilocks, zone-for data drawn from a single confocal spot leveraging the tools of Bayesian nonparametrics (BNP). We benchmark our algorithm, termed BNP lifetime analysis, using a range of synthetic and experimental data. Moreover, we show that the BNP lifetime analysis method can distinguish and deduce lifetimes using photon counts as small as 500.

Single-photon smFRET: II. Application to continuous illumination.

Here we adapt the Bayesian nonparametrics (BNP) framework presented in the first companion article to analyze kinetics from single-photon, single-molecule Förster resonance energy transfer (smFRET) traces generated under continuous illumination. Using our sampler, BNP-FRET, we learn the escape rates and the number of system states given a photon trace. We benchmark our method by analyzing a range of synthetic and experimental data. Particularly, we apply our method to simultaneously learn the number of system states and the corresponding kinetics for intrinsically disordered proteins using two-color FRET under varying chemical conditions. Moreover, using synthetic data, we show that our method can deduce the number of system states even when kinetics occur at timescales of interphoton intervals.

Single-photon smFRET. I: Theory and conceptual basis.

We present a unified conceptual framework and the associated software package for single-molecule Förster resonance energy transfer (smFRET) analysis from single-photon arrivals leveraging Bayesian nonparametrics, BNP-FRET. This unified framework addresses the following key physical complexities of a single-photon smFRET experiment, including: 1) fluorophore photophysics; 2) continuous time kinetics of the labeled system with large timescale separations between photophysical phenomena such as excited photophysical state lifetimes and events such as transition between system states; 3) unavoidable detector artefacts; 4) background emissions; 5) unknown number of system states; and 6) both continuous and pulsed illumination. These physical features necessarily demand a novel framework that extends beyond existing tools. In particular, the theory naturally brings us to a hidden Markov model with a second-order structure and Bayesian nonparametrics on account of items 1, 2, and 5 on the list. In the second and third companion articles, we discuss the direct effects of these key complexities on the inference of parameters for continuous and pulsed illumination, respectively.

Building Fluorescence Lifetime Maps Photon-by-Photon by Leveraging Spatial Correlations.

Fluorescence lifetime imaging microscopy (FLIM) has become a standard tool in the quantitative characterization of subcellular environments. However, quantitative FLIM analyses face several challenges. First, spatial correlations between pixels are often ignored as signal from individual pixels is analyzed independently thereby limiting spatial resolution. Second, existing methods deduce photon ratios instead of absolute lifetime maps. Next, the number of fluorophore species contributing to the signal is unknown, while excited state lifetimes with <1 ns difference are difficult to discriminate. Finally, existing analyses require high photon budgets and often cannot rigorously propagate experimental uncertainty into values over lifetime maps and number of species involved. To overcome all of these challenges simultaneously and self-consistently at once, we propose the first doubly nonparametric framework. That is, we learn the number of species (using Beta-Bernoulli process priors) and absolute maps of these fluorophore species (using Gaussian process priors) by leveraging information from pulses not leading to observed photon. We benchmark our framework using a broad range of synthetic and experimental data and demonstrate its robustness across a number of scenarios including cases where we recover lifetime differences between species as small as 0.3 ns with merely 1000 photons.

Single-photon smFRET. III. Application to pulsed illumination.

Förster resonance energy transfer (FRET) using pulsed illumination has been pivotal in leveraging lifetime information in FRET analysis. However, there remain major challenges in quantitative single-photon, single-molecule FRET (smFRET) data analysis under pulsed illumination including 1) simultaneously deducing kinetics and number of system states; 2) providing uncertainties over estimates, particularly uncertainty over the number of system states; and 3) taking into account detector noise sources such as cross talk and the instrument response function contributing to uncertainty; in addition to 4) other experimental noise sources such as background. Here, we implement the Bayesian nonparametric framework described in the first companion article that addresses all aforementioned issues in smFRET data analysis specialized for the case of pulsed illumination. Furthermore, we apply our method to both synthetic as well as experimental data acquired using Holliday junctions.

High-precision estimation of emitter positions using Bayesian grouping of localizations.

Single-molecule localization microscopy super-resolution methods rely on stochastic blinking/binding events, which often occur multiple times from each emitter over the course of data acquisition. Typically, the blinking/binding events from each emitter are treated as independent events, without an attempt to assign them to a particular emitter. Here, we describe a Bayesian method of inferring the positions of the tagged molecules by exploring the possible grouping and combination of localizations from multiple blinking/binding events. The results are position estimates of the tagged molecules that have improved localization precision and facilitate nanoscale structural insights. The Bayesian framework uses the localization precisions to learn the statistical distribution of the number of blinking/binding events per emitter and infer the number and position of emitters. We demonstrate the method on a range of synthetic data with various emitter densities, DNA origami constructs and biological structures using DNA-PAINT and dSTORM data. We show that under some experimental conditions it is possible to achieve sub-nanometer precision.

Docking of Syk to FcεRI is enhanced by Lyn but limited in duration by SHIP1.

The high-affinity immunoglobulin E (IgE) receptor, FcεRI, is the primary immune receptor found on mast cells and basophils. Signal initiation is classically attributed to phosphorylation of FcεRI ß- and γ-subunits by the Src family kinase (SFK) Lyn, followed by the recruitment and activation of the tyrosine kinase Syk. FcεRI signaling is tuned by the balance between Syk-driven positive signaling and the engagement of inhibitory molecules, including SHIP1. Here, we investigate the mechanistic contributions of Lyn, Syk, and SHIP1 to the formation of the FcεRI signalosome. Using Lyn-deficient RBL-2H3 mast cells, we found that another SFK can weakly monophosphorylate the γ-subunit, yet Syk still binds the incompletely phosphorylated immunoreceptor tyrosine-based activation motifs (ITAMs). Once recruited, Syk further enhances γ-phosphorylation to propagate signaling. In contrast, the loss of SHIP1 recruitment indicates that Lyn is required for phosphorylation of the ß-subunit. We demonstrate two noncanonical Syk binding modes, trans γ-bridging and direct ß-binding, that can support signaling when SHIP1 is absent. Using single particle tracking, we reveal a novel role of SHIP1 in regulating Syk activity, where the presence of SHIP1 in the signaling complex acts to increase the Syk:receptor off-rate. These data suggest that the composition and dynamics of the signalosome modulate immunoreceptor signaling activities.

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.

Robust, fiducial-free drift correction for super-resolution imaging.

We describe a robust, fiducial-free method of drift correction for use in single molecule localization-based super-resolution methods. The method combines periodic 3D registration of the sample using brightfield images with a fast post-processing algorithm that corrects residual registration errors and drift between registration events. The method is robust to low numbers of collected localizations, requires no specialized hardware, and provides stability and drift correction for an indefinite time period.

Comparing lifeact and phalloidin for super-resolution imaging of actin in fixed cells.

Visualizing actin filaments in fixed cells is of great interest for a variety of topics in cell biology such as cell division, cell movement, and cell signaling. We investigated the possibility of replacing phalloidin, the standard reagent for super-resolution imaging of F-actin in fixed cells, with the actin binding peptide 'lifeact'. We compared the labels for use in single molecule based super-resolution microscopy, where AlexaFluor 647 labeled phalloidin was used in a dSTORM modality and Atto 655 labeled lifeact was used in a single molecule imaging, reversible binding modality. We found that imaging with lifeact had a comparable resolution in reconstructed images and provided several advantages over phalloidin including lower costs, the ability to image multiple regions of interest on a coverslip without degradation, simplified sequential super-resolution imaging, and more continuous labeling of thin filaments.

Bayesian Multiple Emitter Fitting using Reversible Jump Markov Chain Monte Carlo.

In single molecule localization-based super-resolution imaging, high labeling density or the desire for greater data collection speed can lead to clusters of overlapping emitter images in the raw super-resolution image data. We describe a Bayesian inference approach to multiple-emitter fitting that uses Reversible Jump Markov Chain Monte Carlo to identify and localize the emitters in dense regions of data. This formalism can take advantage of any prior information, such as emitter intensity and density. The output is both a posterior probability distribution of emitter locations that includes uncertainty in the number of emitters and the background structure, and a set of coordinates and uncertainties from the most probable model.

Template-free 2D particle fusion in localization microscopy.

Methods that fuse multiple localization microscopy images of a single structure can improve signal-to-noise ratio and resolution, but they generally suffer from template bias or sensitivity to registration errors. We present a template-free particle-fusion approach based on an all-to-all registration that provides robustness against individual misregistrations and underlabeling. We achieved 3.3-nm Fourier ring correlation (FRC) image resolution by fusing 383 DNA origami nanostructures with 80% labeling density, and 5.0-nm resolution for structures with 30% labeling density.