StormGraph: A graph-based algorithm for quantitative clustering analysis of diverse single-molecule localization microscopy data

Abstract

1Clustering of proteins is crucial for many cellular processes and can be imaged at nanoscale resolution using 2 single-molecule localization microscopy (SMLM). Existing cluster analysis methods for SMLM data suffer 3 from major limitations, such as unsuitability for heterogeneous datasets, failure to account for uncertainties 4 in localization data, excessive computation time, or inability to analyze three-dimensional data. To address 5 these shortcomings, we developed StormGraph, an algorithm using graph theory and community detection 6 to identify and quantify clusters in heterogeneous 2D and 3D SMLM datasets. StormGraph accounts for 7 localization uncertainties and, by determining thresholds adaptively, it allows many heterogeneous samples 8 to be analyzed using identical parameters. Consequently, StormGraph improves the potential accuracy, 9 objectivity, and throughput of cluster analysis. Furthermore, StormGraph generates a hierarchical clustering, 10 and it quantifies cluster colocalization for two-color SMLM data. We use simulated data to show that 11 StormGraph is superior to existing algorithms. Finally, we demonstrate its application to two-dimensional 12 B-cell antigen receptor clustering and three-dimensional intracellular LAMP-1 clustering. 13 Single-molecule localization microscopy (SMLM) techniques, such as direct stochastic optical reconstruc-15 tion microscopy (dSTORM) (1; 2) and photoactivated localization microscopy (PALM) (3), overcome the 16 diffraction limit of conventional microscopy by acquiring many sequential images, each containing very few 17 fluorescing labels. Individual labels can then be computationally super-resolved and precisely localized to 18 generate a list of localization coordinates, often with estimated positional uncertainties (4; 5; 6). This is 19 possible in both two and three dimensions (7; 8; 9; 10). 20 SMLM is commonly used to investigate nanoscale clustering of cell-membrane and intracellular proteins ), which usually exhibits both cell-to-cell and within-cell heterogene-22 ity. Notwithstanding, clustering is frequently analyzed using spatial summary statistics that fail to capture 23 the heterogeneity of clusters within a sample, such as Ripley's functions (21; 22). Instead, clusters can be 24 individually quantified by using a clustering algorithm to assign localizations to specific clusters. However, 25 using existing clustering algorithms, it is difficult to accurately and objectively analyze multiple heteroge-26 neous samples. Subjective bias can result from algorithm parameter selection, or from selection of a small 27 number of "representative samples" to analyze using slow or cumbersome algorithms. Failure to account for 28 localization uncertainties can also make conclusions unreliable. 29 The most widely used clustering algorithms in SMLM literature, including Density-Based Spatial Cluster-30 ing of Applications with Noise (DBSCAN) (23), identify clusters based on a user-specified minimum number 31 of points within a user-specified radius. However, these ...

Mapping the Nicotinic Acetylcholine Receptor Nanocluster Topography at the Cell Membrane with STED and STORM Nanoscopies

“…We next applied STORMGraph [ 18 ] for the identification and analysis of particle nanoclusters. This analytical approach differentiates these supramolecular aggregates from single nAChR particles at the cell surface.…”

“…Here, we initially analyzed the STORM images using STORMGraph, an approach based on graph theory (see, e.g., PhenoGraph [ 51 ]) and graph merging [ 52 , 53 ] with community detection algorithms [ 54 , 55 ] such as Infomap [ 56 ] or the Louvain method [ 57 ]). STORMGraph determines thresholds adaptively, circumventing user-defined parameters and thus allowing batch analysis over heterogeneous samples using identical settings to avoid bias [ 18 ].…”

“…The STORM single-molecule coordinates were merged using a weighted arithmetic mean with the number of photons of each individual localization as weight [ 13 ]. The STORMGraph [ 18 ] automated quantitative clustering analysis of SMLM images was applied next; initial parameters were configured using the following values: K = 10, minimum cluster size = 15, and α = 0.05, the maximum probability of a completely randomly distributed localization being classified as clustered, with a value of 0.05. The parameter that avoids multiple blinking was disabled.…”

“…The complementary use of two different super-resolution approaches in tandem provides more solid grounds to validate the occurrence of protein molecular aggregates in cell membranes. For the analysis of the state of aggregation of the nAChR we apply STORMGraph, an automated quantitative clustering method developed for SMLM and based on graph theory and community detection [ 18 ]. We also employ a recently introduced analytical tool, ASTRICS, an algorithm and inter-cluster similarity measure based on triangulation of data points and -shapes [ 19 ], and compare the results with those obtained with the original STORMGraph version.…”

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

“…For example, community detection has also been exploited for extracting SMLM clusters. 130 A segmentation protocol based on persistence homology and DBSCAN has been employed to segment and quantify the topological structure within SMLM data. 131 In this persistence homology method, the density modes were constructed from a graph that connects all the localizations within the same search radius.…”