Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms

Gridless sparse spike reconstruction is a rather new research field with significant results for the super-resolution problem, where we want to retrieve fine-scale details from a noisy and filtered acquisition. To tackle this problem, we are interested in optimisation under some prior, typically the sparsity i.e., the source is composed of spikes. Following the seminal work on the generalised LASSO for measures called the Beurling-Lasso (BLASSO), we will give a review on the chief theoretical and numerical breakthrough of the off-the-grid inverse problem, as we illustrate its usefulness to the super-resolution problem in Single Molecule Localisation Microscopy (SMLM) through new reconstruction metrics and tests on synthetic and real SMLM data we performed for this review.

Developing super-resolution fluorescent microscopy for virology research

Taking advantage of the use of photoswitchable probes and high precision localisation of single molecules to surpass the diffraction limit, super-resolution fluorescence microscopy allows observing non-invasive live-cell at sub-diffraction size (<200 nm). Given the advantage of super-resolution fluorescence microscopy, our group has reconstructed the super-resolution fluorescence microscopybased on the single-molecule localisation microscopy technique with a resolution of 20 nm. In this research, the authors present the reconstruction process of the microscopy system and its application in observing hemorrhagic fever Dengue virus. Dengue virus was cultured in baby hamster kidney (BHK-21) cells and was then negative stained for transmission electron microscope (TEM) or immunofluorescent labeled for stochastic optical reconstruction microscopy (STORM). The diameter of the Dengue virus particles is 45-60 nm measured using TEM and is 84±12 nm measured using STORM. After subtraction of the length of the antibody attached to the virus particles, the diameter of Dengue virus particles measured using STORM are close to which measured using TEM. In conclusion, the authors highlight the findings of super-resolution fluorescence microscopy-based Dengue virus studies and their contributions to the understanding of Dengue virus particles. The current advances in super-resolution microscopy may open new avenues for future virology teaching and research.

A single molecule localization microscopy method for tissues reveals nonrandom nuclear pore distribution in Drosophila

Single Molecule Localisation Microscopy (SMLM) can provide nanoscale resolution in thin samples but has rarely been applied to tissues, because of high background from out of focus emitters and optical aberrations. Here we describe a line scanning microscope that provides optical sectioning for SMLM in tissues. Imaging endogenously-tagged nucleoporins and F-actin on this system using DNA- and peptide-PAINT routinely gives 30 nm resolution or better at depths greater than 20 µm. This revealed that the nuclear pores are nonrandomly distributed in most Drosophila tissues, in contrast to cultured cells. Lamin Dm0 shows a complementary localisation to the nuclear pores, suggesting that it corrals the pores. Furthermore, ectopic expression of the tissue-specific Lamin C distributes the nuclear pores more randomly, whereas lamin C mutants enhance nuclear pore clustering, particularly in muscle nuclei. Since nucleoporins interact with specific chromatin domains, nuclear pore clustering could regulate local chromatin organisation and contribute to the disease phenotypes caused by human Lamin A/C laminopathies.

K-Neighbourhood Analysis: A Method for Understanding SMLM Images as Compositions of Local Neighbourhoods

Single molecule localisation microscopy (SMLM) is a powerful tool that has revealed the spatial arrangement of cell surface signalling proteins, producing data of enormous complexity. The complexity is partly driven by the convolution of technical and biological signal components, and partly by the challenge of pooling information across many distinct cells. To address these two particular challenges, we have devised a novel algorithm called K-neighbourhood analysis (KNA), which emphasises the fact that each image can also be viewed as a composition of local neighbourhoods. KNA is based on a novel transformation, spatial neighbourhood principal component analysis (SNPCA), which is defined by the PCA of the normalised K-nearest neighbour vectors of a spatially random point pattern. Here, we use KNA to define a novel visualisation of individual images, to compare within and between groups of images and to investigate the preferential patterns of phosphorylation. This methodology is also highly flexible and can be used to augment existing clustering methods by providing clustering diagnostics as well as revealing substructure within microclusters. In summary, we have presented a highly flexible analysis tool that presents new conceptual possibilities in the analysis of SMLM images.

Sub-diffraction error mapping for localisation microscopy images

Assessing the quality of localisation microscopy images is highly challenging due to the difficulty in reliably detecting errors in experimental data. The most common failure modes are the biases and errors produced by the localisation algorithm when there is emitter overlap. Also known as the high density or crowded field condition, significant emitter overlap is normally unavoidable in live cell imaging. Here we use Haar wavelet kernel analysis (HAWK), a localisation microscopy data analysis method which is known to produce results without bias, to generate a reference image. This enables mapping and quantification of reconstruction bias and artefacts common in all but low emitter density data. By avoiding comparisons involving intensity information, we can map structural artefacts in a way that is not adversely influenced by nonlinearity in the localisation algorithm. The HAWK Method for the Assessment of Nanoscopy (HAWKMAN) is a general approach which allows for the reliability of localisation information to be assessed.

A framework for evaluating the performance of SMLM cluster analysis algorithms

Single molecule localisation microscopy (SMLM) generates data in the form of Cartesian coordinates of localised fluorophores. Cluster analysis is an attractive route for extracting biologically meaningful information from such data and has been widely applied. Despite the range of developed cluster analysis algorithms, there exists no consensus framework for the evaluation of their performance. Here, we use a systematic approach based on two metrics, the Adjusted Rand Index (ARI) and Intersection over Union (IoU), to score the success of clustering algorithms in diverse simulated clustering scenarios mimicking experimental data. We demonstrate the framework using three analysis algorithms: DBSCAN, ToMATo and KDE, show how to deduce optimal analysis parameters and how they are affected by fluorophore multiple blinking. We propose that these standard conditions and metrics become the basis for future analysis algorithm development and evaluation.

Single-molecule localisation microscopy: accounting for chance co-localisation between foci in bacterial cells

Using single-molecule fluorescence microscopes, individual biomolecules can be observed within live bacterial cells. Using differently coloured probes, physical associations between two different molecular species can be assessed through co-localisation measurements. However, bacterial cells are finite and small (~ 1 μm) relative to the resolution limit of optical microscopes (~ 0.25 μm). Furthermore, the images produced by optical microscopes are typically two-dimensional projections of three-dimensional objects. These limitations mean that a certain proportion of object pairs (molecules) will inevitably be assigned as being co-localised, even when they are distant at molecular distance scales (nm). What is this proportion? Here, we attack this problem, theoretically and computationally, by creating a model of the co-localisation expected purely due to chance. We thus consider a bacterial cell wherein objects are distributed at random and evaluate the co-localisation in a fashion that emulates an experimental analysis. We consider simplified geometries where we can most transparently investigate the effect of a finite size of the cell and the effect of probing a three-dimensional cell in only two dimensions. Coupling theory to simulations, we also study the co-localisation expected due to chance using parameters relevant to bacterial cells. Overall, we show that the co-localisation expected purely due to chance can be quite substantial and describe the parameters that it depends upon.

Blinking fluorescent probes for tubulin nanoscopy in living and fixed cells

Here we report a small molecule probe for single molecule localisation microscopy (SMLM) of tubulin in living and fixed cells. We explored a series of constructs composed of taxanes and spontaneously blinking far-red dye hydroxymethyl silicon-rhodamine (HMSiR). We found that the linker length profoundly affects the probe permeability and off-targeting. The best performing probe, HMSiR-tubulin, is composed of cabazitaxel and 6'-regioisomer of HMSiR bridged by a C6 linker. Microtubule diameters of <50 nm can be routinely measured in SMLM experiments on living and fixed cells. HMSiR-tubulin also performs well in 3D stimulated emission depletion (STED) microscopy, allowing a complementary use of both nanoscopy methods for investigating microtubule functions in living cells.