Molecular Counting with Localization Microscopy: A Bayesian Estimate Based on Fluorophore Statistics

Single-molecule counting applied to the study of GPCR oligomerization

Single-molecule counting techniques enable a precise determination of the intracellular abundance and stoichiometry of proteins and macromolecular complexes. These details are often challenging to quantitatively assess yet are essential for our understanding of cellular function. Consider G-protein-coupled receptors-an expansive class of transmembrane signaling proteins that participate in many vital physiological functions making them a popular target for drug development. While early evidence for the role of oligomerization in receptor signaling came from ensemble biochemical and biophysical assays, innovations in single-molecule measurements are now driving a paradigm shift in our understanding of its relevance. Here, we review recent developments in single-molecule counting with a focus on photobleaching step counting and the emerging technique of quantitative single-molecule localization microscopy-with a particular emphasis on the potential for these techniques to advance our understanding of the role of oligomerization in G-protein-coupled receptor signaling.

Calibration-free counting of low molecular copy numbers in single DNA-PAINT localization clusters

Single-molecule localization microscopy (SMLM) has revolutionized light microscopy by enabling optical resolution down to a few nanometer. Yet, localization precision commonly does not suffice to visually resolve single subunits in molecular assemblies or multimeric complexes. Because each targeted molecule contributes localizations during image acquisition, molecular counting approaches to reveal the target copy numbers within localization clusters have been persistently proposed since the early days of SMLM, most of which rely on preliminary knowledge of the dye photophysics or on a calibration to a reference. Previously, we developed localization-based fluorescence correlation spectroscopy (lbFCS) as an absolute ensemble counting approach for the SMLM-variant DNA-PAINT (points accumulation for imaging in nanoscale topography), for the first time, to our knowledge, circumventing the necessity for reference calibrations. Here, we present an extended concept termed lbFCS+, which allows absolute counting of copy numbers for individual localization clusters in a single DNA-PAINT image. In lbFCS+, absolute counting of fluorescent loci contained in individual nanoscopic volumes is achieved via precise measurement of the local hybridization rates of the fluorescently labeled oligonucleotides ("imagers") employed in DNA-PAINT imaging. In proof-of-principle experiments on DNA origami nanostructures, we demonstrate the ability of lbFCS+ to truthfully determine molecular copy numbers and imager association and dissociation rates in well-separated localization clusters containing up to 10 docking strands. For N ≤ 4 target molecules, lbFCS+ is even able to resolve integers, providing the potential to study the composition of up to tetrameric molecular complexes. Furthermore, we show that lbFCS+ allows resolving heterogeneous binding dynamics, enabling the distinction of stochastically generated and a priori indistinguishable DNA assemblies. Beyond advancing quantitative DNA-PAINT imaging, we believe that lbFCS+ could find promising applications ranging from biosensing to DNA computing.

An expectation-maximization approach to quantifying protein stoichiometry with single-molecule imaging

Motivation

Single-molecule localization microscopy (SMLM) is a super-resolution technique capable of rendering nanometer scale images of cellular structures. Recently, much effort has gone into developing algorithms for extracting quantitative features from SMLM datasets, such as the abundance and stoichiometry of macromolecular complexes. These algorithms often require knowledge of the complicated photophysical properties of photoswitchable fluorophores.

Results

Here, we develop a calibration-free approach to quantitative SMLM built upon the observation that most photoswitchable fluorophores emit a geometrically distributed number of blinks before photobleaching. From a statistical model of a mixture of monomers, dimers and trimers, the method employs an adapted expectation-maximization algorithm to learn the protomer fractions while simultaneously determining the single-fluorophore blinking distribution. To illustrate the utility of our approach, we benchmark it on both simulated datasets and experimental datasets assembled from SMLM images of fluorescently labeled DNA nanostructures.

Availability and implementation

An implementation of our algorithm written in Python is available at: https://www.utm.utoronto.ca/milsteinlab/resources/Software/MMCode/.

Supplementary information

Supplementary data are available at Bioinformatics Advances online.

Estimating the dynamic range of quantitative single-molecule localization microscopy

In recent years, there have been significant advances in quantifying molecule copy number and protein stoichiometry with single-molecule localization microscopy (SMLM). However, as the density of fluorophores per diffraction-limited spot increases, distinguishing between detection events from different fluorophores becomes progressively more difficult, affecting the accuracy of such measurements. Although essential to the design of quantitative experiments, the dynamic range of SMLM counting techniques has not yet been studied in detail. Here, we provide a working definition of the dynamic range for quantitative SMLM in terms of the relative number of missed localizations or blinks and explore the photophysical and experimental parameters that affect it. We begin with a simple two-state model of blinking fluorophores, then extend the model to incorporate photobleaching and temporal binning by the detection camera. From these models, we first show that our estimates of the dynamic range agree with realistic simulations of the photoswitching. We find that the dynamic range scales inversely with the duty cycle when counting both blinks and localizations. Finally, we validate our theoretical approach on direct stochastic optical reconstruction microscopy (dSTORM) data sets of photoswitching Alexa Fluor 647 dyes. Our results should help guide researchers in designing and implementing SMLM-based molecular counting experiments.

A pairwise distance distribution correction (DDC) algorithm to eliminate blinking-caused artifacts in SMLM

Single-molecule localization microscopy (SMLM) relies on the blinking behavior of a fluorophore, which is the stochastic switching between fluorescent and dark states. Blinking creates multiple localizations belonging to the same fluorophore, confounding quantitative analyses and interpretations. Here we present a method, termed distance distribution correction (DDC), to eliminate blinking-caused repeat localizations without any additional calibrations. The approach relies on obtaining the true pairwise distance distribution of different fluorophores naturally from the imaging sequence by using distances between localizations separated by a time much longer than the average fluorescence survival time. We show that, using the true pairwise distribution, we can define and maximize the likelihood, obtaining a set of localizations void of blinking artifacts. DDC results in drastic improvements in obtaining the closest estimate of the true spatial organization and number of fluorescent emitters in a wide range of applications, enabling accurate reconstruction and quantification of SMLM images.

A pairwise distance distribution correction (DDC) algorithm to eliminate blinking-caused artifacts in SMLM

Single-molecule localization microscopy (SMLM) relies on the blinking behavior of a fluorophore, which is the stochastic switching between fluorescent and dark states. Blinking creates multiple localizations belonging to the same fluorophore, confounding quantitative analyses and interpretations. Here we present a method, termed distance distribution correction (DDC), to eliminate blinking-caused repeat localizations without any additional calibrations. The approach relies on obtaining the true pairwise distance distribution of different fluorophores naturally from the imaging sequence by using distances between localizations separated by a time much longer than the average fluorescence survival time. We show that, using the true pairwise distribution, we can define and maximize the likelihood, obtaining a set of localizations void of blinking artifacts. DDC results in drastic improvements in obtaining the closest estimate of the true spatial organization and number of fluorescent emitters in a wide range of applications, enabling accurate reconstruction and quantification of SMLM images.

Blinking Statistics and Molecular Counting in direct Stochastic Reconstruction Microscopy (dSTORM)

MOTIVATION

Many recent advancements in single molecule localisation microscopy exploit the stochastic photo-switching of fluorophores to reveal complex cellular structures beyond the classical diffraction limit. However, this same stochasticity makes counting the number of molecules to high precision extremely challenging, preventing key insight into the cellular structures and processes under observation.

RESULTS

Modelling the photo-switching behaviour of a fluorophore as an unobserved continuous time Markov process transitioning between a single fluorescent and multiple dark states, and fully mitigating for missed blinks and false positives, we present a method for computing the exact probability distribution for the number of observed localisations from a single photo-switching fluorophore. This is then extended to provide the probability distribution for the number of localisations in a dSTORM experiment involving an arbitrary number of molecules. We demonstrate that when training data is available to estimate photoswitching rates, the unknown number of molecules can be accurately recovered from the posterior mode of the number of molecules given the number of localisations. Finally, we demonstrate the method on experimental data by quantifying the number of adapter protein Linker for Activation of T cells (LAT) on the cell surface of the T cell immunological synapse.

AVAILABILITY

Software available at https://github.com/lp1611/mol_count_dstorm.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The Decade of Super-Resolution Microscopy of the Presynapse

The presynaptic compartment of the chemical synapse is a small, yet extremely complex structure. Considering its size, most methods of optical microscopy are not able to resolve its nanoarchitecture and dynamics. Thus, its ultrastructure could only be studied by electron microscopy. In the last decade, new methods of optical superresolution microscopy have emerged allowing the study of cellular structures and processes at the nanometer scale. While this is a welcome addition to the experimental arsenal, it has necessitated careful analysis and interpretation to ensure the data obtained remains artifact-free. In this article we review the application of nanoscopic techniques to the study of the synapse and the progress made over the last decade with a particular focus on the presynapse. We find to our surprise that progress has been limited, calling for imaging techniques and probes that allow dense labeling, multiplexing, longer imaging times, higher temporal resolution, while at least maintaining the spatial resolution achieved thus far.

Microampere Electric Current Causes Bacterial Membrane Damage and Two-Way Leakage in a Short Period of Time

Physical agents, such as low electric voltage and current, have recently gained attention for antimicrobial treatment due to their bactericidal capability. Although microampere electric current was shown to suppress the growth of bacteria, it remains unclear to what extent the microampere current damaged the bacterial membrane. Here, we investigated the membrane damage and two-way leakage caused by microampere electric current (≤100 μA) with a short exposure time (30 min). Based on MitoTracker staining, propidium iodide staining, filtration assays, and quantitative single-molecule localization microscopy, we observed significant membrane damage, which allowed two-way leakage of ions, small molecules, and proteins. This study paves the way to new development of antimicrobial applications for ultralow electric voltage and current.IMPORTANCE Although electric voltage and current have been studied for a long time in terms of their ability to suppress the growth of bacteria and to kill bacteria, increasing interest has been aroused more recently due to the prevalence of antibiotic resistance of microbes in past decades. Toward understanding the antimicrobial mechanism of low electric voltage and current, previous studies showed that treating bacteria with milliampere electric currents (≥5 mA) for ≥72 h led to significant damage of the bacterial membrane, which likely resulted in leakage of cellular contents and influx of toxic substances through the damaged membrane. However, it remains unclear to what extent membrane damage and two-way (i.e., inward and outward) leakage are caused by lower (i.e., microampere) electric current in a shorter time frame. In this work, we set out to answer this question. We observed that the membrane damage was caused by microampere electric current in half an hour, which allowed two-way leakage of ions, small molecules, and proteins.

Toward Absolute Molecular Numbers in DNA-PAINT

Single-molecule localization microscopy (SMLM) has revolutionized optical microscopy, extending resolution down to the level of individual molecules. However, the actual counting of molecules relies on preliminary knowledge of the blinking behavior of individual targets or on a calibration to a reference. In particular for biological applications, great care has to be taken because a plethora of factors influence the quality and applicability of calibration-dependent approaches to count targets in localization clusters particularly in SMLM data obtained from heterogeneous samples. Here, we present localization-based fluorescence correlation spectroscopy (lbFCS) as the first absolute molecular counting approach for DNA-points accumulation for imaging in nanoscale topography (PAINT) microscopy and, to our knowledge, for SMLM in general. We demonstrate that lbFCS overcomes the limitation of previous DNA-PAINT counting and allows the quantification of target molecules independent of the localization cluster density. In accordance with the promising results of our systematic proof-of-principle study on DNA origami structures as idealized targets, lbFCS could potentially also provide quantitative access to more challenging biological targets featuring heterogeneous cluster sizes in the future.

Single-molecule localization microscopy as nonlinear inverse problem

We present a statistical framework to model the spatial distribution of molecules based on a single-molecule localization microscopy (SMLM) dataset. The latter consists of a collection of spatial coordinates and their associated uncertainties. We describe iterative parameter-estimation algorithms based on this framework, as well as a sampling algorithm to numerically evaluate the complete posterior distribution. We demonstrate that the inverse computation can be viewed as a type of image restoration process similar to the classical image deconvolution methods, except that it is performed on SMLM images. We further discuss an application of our statistical framework in the task of particle fusion using SMLM data. We show that the fusion algorithm based on our model outperforms the current state-of-the-art in terms of both accuracy and computational cost.

Antisense and yet sensitive: Copy number control of rolling circle-replicating plasmids by small RNAs

Bacterial plasmids constitute a wealth of shared DNA amounting to about 20% of the total prokaryotic pangenome. Plasmids replicate autonomously and control their replication by maintaining a fairly constant number of copies within a given host. Plasmids should acquire a good fitness to their hosts so that they do not constitute a genetic load. Here we review some basic concepts in plasmid biology, pertaining to the control of replication and distribution of plasmid copies among daughter cells. A particular class of plasmids is constituted by those that replicate by the rolling circle mode (rolling circle-replicating [RCR]-plasmids). They are small double-stranded DNA molecules, with a rather high number of copies in the original host. RCR-plasmids control their replication by means of a small short-lived antisense RNA, alone or in combination with a plasmid-encoded transcriptional repressor protein. Two plasmid prototypes have been studied in depth, namely the staphylococcal plasmid pT181 and the streptococcal plasmid pMV158, each corresponding to the two types of replication control circuits, respectively. We further discuss possible applications of the plasmid-encoded antisense RNAs and address some future directions that, in our opinion, should be pursued in the study of these small molecules. This article is categorized under: Regulatory RNAs/RNAi/Riboswitches > Regulatory RNAs RNA Structure and Dynamics > Influence of RNA Structure in Biological Systems.

The Effect of Fluorophore Conjugation on Antibody Affinity and the Photophysical Properties of Dyes

Because the degree of labeling (DOL) of cell-bound antibodies, often required in quantitative fluorescence measurements, is largely unknown, we investigated the effect of labeling with two different fluorophores (AlexaFluor546, AlexaFluor647) in a systematic way using antibody stock solutions with different DOLs. Here, we show that the mean DOL of the cell-bound antibody fraction is lower than that of the stock using single molecule fluorescence measurements. The effect is so pronounced that the mean DOL levels off at approximately two fluorophores/IgG for some antibodies. We developed a method for comparing the average DOL of antibody stocks to that of the isolated, cell-bound fraction based on fluorescence anisotropy measurements confirming the aforementioned conclusions. We created a model in which individual antibody species with different DOLs, present in an antibody stock solution, were assumed to have distinct affinities and quantum yields. The model calculations confirmed that a calibration curve constructed from the anisotropy of antibody stocks can be used for determining the DOL of the bound fraction. The fluorescence intensity of the cell-bound antibody fractions and of the antibody stocks exhibited distinctly different dependence on the DOL. The behavior of the two dyes was systematically different in this respect. Fitting of the model to these data revealed that labeling with each dye affects quantum yield and antibody affinity differentially. These measurements also implied that fluorophores in multiply labeled antibodies exhibit self-quenching and lead to decreased antibody affinity, conclusions directly confirmed by steady-state intensity measurements and competitive binding assays. Although the fluorescence lifetime of antibodies labeled with multiple fluorophores decreased, the magnitude of this change was not sufficient to account for self-quenching indicating that both dynamic and static quenching processes occur involving H-aggregate formation. Our results reveal multiple effects of fluorophore conjugation, which must not be overlooked in quantitative cell biological measurements.