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

Abstract

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.

Keywords: SMLM; cluster analysis; localization microscopy; molecular complexes; point clouds; quantification of biological structures; single molecule; super-resolution nanoscopy.

Figure 1

Classification of Super-Resolution Nanoscopy Methods All SMLM methods generate localizations as 2D or 3D point clouds.

Figure 2

Overview of SMLM Quantification Pipeline An overview of the whole framework from imaging to quantification of super-resolution STORM SMLM data: (A) 3D SMLM imaging of the target protein, (B) acquiring the protein localizations and getting a map for the molecular coordinates, and (C) analyzing the super-resolved image to quantify the SMLM clusters. (C) is produced with permission from Nicovich et al.

Figure 3

Illustration of the SMLM Imaging Principle Labeling the yellow circle (i.e., biological structure below the diffraction limit) efficiently with fluorescent dye to be imaged with a fluorescence microscope. The conventional diffraction-limited wide-field microscope produces a blurred image. The SMLM imaging produces a super-resolved image that is constructed from a set of time-separated images, wherein each time frame image a sparse set of excited labeled proteins can be localized using Gaussian PSF to form the final point-cloud super-resolution image for the structure.

Figure 4

The Four-State Photokinetics Model for Photoswitchable Fluorescent Proteins The image used in this illustration is adapted from Frick et al.

Figure 5

Illustration of How the Protein Molecules Cluster Together to Form Complexes Monomers aggregate to form dimers which aggregate to form the small oligomers. Monomers could also cluster directly to form the large mutants and oligomers.

Figure 6

An Example Showing the Behavior of the $H\left(r\right)$ Function for the Different Distributions of Spatial Point Patterns The $H\left(r\right)$ function (D) has positive values for clustered points (A), fluctuates around 0 for uniformly distributed (random) points (B), and has negative values for dispersed points (C). The generated data consist of 50 points for each one of the patterns shown in (A) to (C).

Figure 7

An Example Illustrating the Density-Based DBSCAN Clustering Method Applied to SMLM Data For instance, DBSCAN algorithm is applied when using ε and $MinPts=3$ parameters. Sometimes the subjectivity of selecting the parameters might change the clustering results dramatically. For example, pseudoclusters in SMLM complicate the selection of the algorithm parameters.

Figure 8

Voronoi Tessellation-Based Method Used to Segment the Clustered SMLM Molecular Localizations (A) The input space of molecular localization. It has two clusters and noisy/background localizations. (B) Voronoi tessellation and partitioning the space into polygonal regions (Voronoi cells) in red. The Delaunay triangulation (dual of Voronoi) is shown by gray dashed connections. (C) The Voronoi cells colored with different colors. The white regions are the Voronoi cells with open regions.

Figure 9

Network/Graph-Based Method Used to Model the SMLM Molecular Localizations for Cluster Analysis (A) The input space of molecular localization. It has two clusters and noisy/background localizations. (B) The ε-graph used to construct the network, where every node is connected to all the other nodes within the proximity distance ε. (C) The kNN graph used to construct the network, where every node is connected to only the k closest neighboring nodes. We constructed the 3-NN graph for illustration.

Figure 10

Graph-Based Network Analysis Methods for SMLM Data Proposed by Khater et al. (A) Khater et al.^, proposed the 3D SMLM Network Analysis pipeline to correct for multiple blinking of a single fluorophore, filter out noisy localizations, segment the biological structures into clusters/blobs, and identify the cluster/blob classes. (B) Network community/modularity analysis detecting the modules within caveola and S2 scaffold domains.

Figure 11

SMLM Imaging Techniques and Dimensionality Used in Various Publications (A) The distribution of the publications based on the super-resolution SMLM imaging technique used in the study. (B) The distribution of the publications based on the dimensionality of the super-resolution SMLM cluster analysis method.

Figure 12

Number of Publications per Year (Starting from 2010) Categorized According to Super-Resolution SMLM Cluster Analysis Methods Used in the Study