A framework for evaluating the performance of SMLM cluster analysis algorithms.

Single-molecule localization microscopy (SMLM) generates data in the form of coordinates of localized fluorophores. Cluster analysis is an attractive route for extracting biologically meaningful information from such data and has been widely applied. Despite a range of cluster analysis algorithms, there exists no consensus framework for the evaluation of their performance. Here, we use a systematic approach based on two metrics to score the success of clustering algorithms in simulated conditions mimicking experimental data. We demonstrate the framework using seven diverse analysis algorithms: DBSCAN, ToMATo, KDE, FOCAL, CAML, ClusterViSu and SR-Tesseler. Given that the best performer depended on the underlying distribution of localizations, we demonstrate an analysis pipeline based on statistical similarity measures that enables the selection of the most appropriate algorithm, and the optimized analysis parameters for real SMLM data. We propose that these standard simulated conditions, metrics and analysis pipeline become the basis for future analysis algorithm development and evaluation.

Blinking statistics and molecular counting in direct stochastic reconstruction microscopy (dSTORM).

MOTIVATION: Many recent advancements in single-molecule localization microscopy exploit the stochastic photoswitching 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 photoswitching 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 localizations from a single photoswitching fluorophore. This is then extended to provide the probability distribution for the number of localizations in a direct stochastic optical reconstruction microscopy experiment involving an arbitrary number of molecules. We demonstrate that when training data are 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 localizations. Finally, we demonstrate the method on experimental data by quantifying the number of adapter protein linker for activation of T cells on the cell surface of the T-cell immunological synapse. AVAILABILITY AND IMPLEMENTATION: Software and data available at https://github.com/lp1611/mol_count_dstorm. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Microscope calibration protocol for single-molecule microscopy.

Single-molecule microscopy allows for the investigation of the dynamics of individual molecules and the visualization of subcellular structures at high spatial resolution. For single-molecule imaging experiments, and particularly those that entail the acquisition of multicolor data, calibration of the microscope and its optical components therefore needs to be carried out at a high level of accuracy. We propose here a method for calibrating a microscope at the nanometer scale, in the sense of determining optical aberrations as revealed by point source localization errors on the order of nanometers. The method is based on the imaging of a standard sample to detect and evaluate the amount of geometric aberration introduced in the optical light path. To provide support for multicolor imaging, it also includes procedures for evaluating the geometric aberration caused by a dichroic filter and the axial chromatic aberration introduced by an objective lens.

Improving axial resolution in Structured Illumination Microscopy using deep learning.

Structured Illumination Microscopy (SIM) is a widespread methodology to image live and fixed biological structures smaller than the diffraction limits of conventional optical microscopy. Using recent advances in image up-scaling through deep learning models, we demonstrate a method to reconstruct 3D SIM image stacks with twice the axial resolution attainable through conventional SIM reconstructions. We further demonstrate our method is robust to noise and evaluate it against two-point cases and axial gratings. Finally, we discuss potential adaptions of the method to further improve resolution. This article is part of the Theo Murphy meeting issue 'Super-resolution structured illumination microscopy (part 1)'.

A novel and robust method for counting components within bio-molecular complexes using fluorescence microscopy and statistical modelling.

Cellular biology occurs through myriad interactions between diverse molecular components, many of which assemble in to specific complexes. Various techniques can provide a qualitative survey of which components are found in a given complex. However, quantitative analysis of the absolute number of molecules within a complex (known as stoichiometry) remains challenging. Here we provide a novel method that combines fluorescence microscopy and statistical modelling to derive accurate molecular counts. We have devised a system in which batches of a given biomolecule are differentially labelled with spectrally distinct fluorescent dyes (label A or B), and mixed such that B-labelled molecules are vastly outnumbered by those with label A. Complexes, containing this component, are then simply scored as either being positive or negative for label B. The frequency of positive complexes is directly related to the stoichiometry of interaction and molecular counts can be inferred by statistical modelling. We demonstrate this method using complexes of Adenovirus particles and monoclonal antibodies, achieving counts that are in excellent agreement with previous estimates. Beyond virology, this approach is readily transferable to other experimental systems and, therefore, provides a powerful tool for quantitative molecular biology.

Testing for complete spatial randomness on three dimensional bounded convex shapes.

There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus relies on Euclidean geometry and is therefore inappropriate for analysis of point patterns observed in non-Euclidean spaces. Recently, there has been extensions to the analysis of point patterns on a sphere, however, many other shapes are left unexplored. This is in part due to the challenge of defining the notion of stationarity for a point process existing on such a space due to the lack of rotational and translational isometries. Here, we construct functional summary statistics for Poisson processes defined on convex shapes in three dimensions. Using the Mapping Theorem, a Poisson process can be transformed from any convex shape to a Poisson process on the unit sphere which has rotational symmetries that allow for functional summary statistics to be constructed. We present the first and second order properties of such summary statistics and demonstrate how they can be used to construct a test statistics to determine whether an observed pattern exhibits complete spatial randomness or spatial preference on the original convex space. We compare this test statistic with one constructed from an analogue L -function for inhomogeneous point processes on the sphere. A study of the Type I and II errors of our test statistics are explored through simulations on ellipsoids of varying dimensions.

Resolution limit of image analysis algorithms.

The resolution of an imaging system is a key property that, despite many advances in optical imaging methods, remains difficult to define and apply. Rayleigh's and Abbe's resolution criteria were developed for observations with the human eye. However, modern imaging data is typically acquired on highly sensitive cameras and often requires complex image processing algorithms to analyze. Currently, no approaches are available for evaluating the resolving capability of such image processing algorithms that are now central to the analysis of imaging data, particularly location-based imaging data. Using methods of spatial statistics, we develop a novel algorithmic resolution limit to evaluate the resolving capabilities of location-based image processing algorithms. We show how insufficient algorithmic resolution can impact the outcome of location-based image analysis and present an approach to account for algorithmic resolution in the analysis of spatial location patterns.

Fusing multimodal microscopy data for improved cell boundary estimation and fluorophore localization of Pseudomonas aeruginosa.

With advances in experimental technologies, the use of biological imaging has grown rapidly and there is need for procedures to combine data arising from different modalities. We propose a procedure to combine yellow fluorescence protein excitation and differential interference contrast microscopy time lapse videos to better estimate the cellular boundary of Pseudomonas aeruginosa (P. aeruginosa) and localization of it's type VI secretion system (T6SS). By approximating the shape by an ellipse, we construct a penalized objective function which accounts for both sources; the minimum of which provides an elliptical approximation to their cellular boundaries. Our approach suggests improved localization of the T6SS on the estimated cell boundary of P. aeruginosa constructed using both sources of data compared to using each in isolation.

3D Bayesian cluster analysis of super-resolution data reveals LAT recruitment to the T cell synapse.

Single-molecule localisation microscopy (SMLM) allows the localisation of fluorophores with a precision of 10-30 nm, revealing the cell's nanoscale architecture at the molecular level. Recently, SMLM has been extended to 3D, providing a unique insight into cellular machinery. Although cluster analysis techniques have been developed for 2D SMLM data sets, few have been applied to 3D. This lack of quantification tools can be explained by the relative novelty of imaging techniques such as interferometric photo-activated localisation microscopy (iPALM). Also, existing methods that could be extended to 3D SMLM are usually subject to user defined analysis parameters, which remains a major drawback. Here, we present a new open source cluster analysis method for 3D SMLM data, free of user definable parameters, relying on a model-based Bayesian approach which takes full account of the individual localisation precisions in all three dimensions. The accuracy and reliability of the method is validated using simulated data sets. This tool is then deployed on novel experimental data as a proof of concept, illustrating the recruitment of LAT to the T-cell immunological synapse in data acquired by iPALM providing ~10 nm isotropic resolution.