Topological data analysis quantifies biological nano-structure from single molecule localization microscopy

Abstract

The study of complex molecular organisation and nanostructure by localization based microscopy is limited by the available analysis tools. We present a segmentation protocol which, through the application of persistence based clustering, is capable of probing densely packed structures which vary in scale. An increase in segmentation performance over state-of-the-art methods is demonstrated. Moreover we employ persistent homology to move beyond clustering, and quantify the topological structure within data. This provides new information about the preserved shapes formed by molecular architecture. Our methods are flexible and we demonstrate this by applying them to receptor clustering in platelets, nuclear pore components and endocytic proteins. Both 2D and 3D implementations are provided within RSMLM, an R package for pointillist based analysis and batch processing of localization microscopy data. Topological data analysis | Persistent Homology | Single Molecule Localization Microscopy| Super-Resolution Microscopy | Clustering Correspondence: j.a.pike@bham.ac.uk or i.b.styles@bham.ac.uk Pike et al. | bioRχiv | November 13, 2018 | 1-15

An Efficient GUI-Based Clustering Software for Simulation and Bayesian Cluster Analysis of Single-Molecule Localization Microscopy Data

“…Since the cluster centers were set to be at least two standard deviations apart from each other, the individual clusters can be correctly identified by eye (Figure 2A) and as well with DBSCAN (Figure 2C) and ToMATo (Figure 2D). In contrast and as shown before (Pike et al, 2020), the approach based on Ripley's K-function (Figure 2B) fails to separate nearby clusters and thus commonly misidentifies cluster number and area (Figures 2E,F). As previously shown, this behavior is due to the incapability of this approach to correctly take into account the local density of the data points (Rubin-Delanchy et al, 2015;Griffié et al, 2017).…”

“…We found that typical runtimes for Ripley's K-based and DBSCAN clustering were 25.78 ± 0.86 and 28.45 ± 0.78 min, respectively (mean ± standard deviation). The ToMATo implementation from the RSMLM package (Pike et al, 2020) had a runtime of 23.87 ± 0.80 min (mean ± standard deviation, Figure 3). By parallelizing the clustering and scoring process to multiple cores, we found the computation time to decrease by 60% for Ripley's K-based, 10.41 ± 0.23 min, and DBSCAN, 11.90 ± 0.27 min (Figure 3).…”

“…Clustering has since developed into an essential readout for membrane protein function in many cellular processes. Over the last years, several cluster algorithms have been adapted specifically for the analysis of single-molecule fluorescence data of membrane proteins (Owen et al, 2010;Annibale et al, 2011a,b;Nicovich et al, 2017;Baumgart et al, 2019;Arnold et al, 2020;Pike et al, 2020). SMLM of membrane proteins and their cluster analysis still requires a high level of experimental and analytical expertise.…”

“…To make cluster analysis more accessible, we here combined a selection of the latest clustering approaches with several useful computational features to speed up and streamline cluster analysis in a single, user-friendly software. Specifically, we implemented Bayesian Cluster Analysis, Ripley's-K-based clustering, DBSCAN (Rubin-Delanchy et al, 2015;Griffié et al, 2016), and ToMATo (Pike et al, 2020) for cluster analysis. We then compared the performance of these approaches on simulated and newly generated experimental data from different cellular systems.…”

A Topological Data Analysis Approach on Predicting Phenotypes from Gene Expression Data

“…In life sciences, topological data analysis (TDA) has previously been applied in medical imaging [13,29], protein characterization [8,17], describing molecular architecture [24,26], and cancer genomics [3,21]. There have been several studies exploring TDA in genomics [7].…”