Robust nonparametric quantification of clustering density of molecules in single-molecule localization microscopy.

Shenghang Jiang,Yong Wang,Jingyi Fei,Sai Divya Challapalli,Seongjin Park

doi:10.1371/journal.pone.0179975

Abstract

We report a robust nonparametric descriptor, J′(r), for quantifying the density of clustering molecules in single-molecule localization microscopy. J′(r), based on nearest neighbor distribution functions, does not require any parameter as an input for analyzing point patterns. We show that J′(r) displays a valley shape in the presence of clusters of molecules, and the characteristics of the valley reliably report the clustering features in the data. Most importantly, the position of the J′(r) valley () depends exclusively on the density of clustering molecules (ρc). Therefore, it is ideal for direct estimation of the clustering density of molecules in single-molecule localization microscopy. As an example, this descriptor was applied to estimate the clustering density of ptsG mRNA in E. coli bacteria.

Highlights

Single-molecule localization microscopy (SMLM) has been utilized broadly in imaging biological molecules—proteins, DNA, and RNA—in various biological systems [1,2,3,4,5]
When quantifying the spatial organization of biological molecules in SMLM data, of particular interest in certain situations is the clustering or aggregation of molecules [37,38,39,40], which is featured by an enhancement in the local density of molecules
The enhancement in the molecular density is accompanied by the decrease of intermolecular distances, which could be described by functions based on nearest neighbor distances, such as pair-wise correlation function [16], nearest neighbor function G(r), and spherical contact distribution function F(r) [34]

Summary

Introduction

Single-molecule localization microscopy (SMLM) has been utilized broadly in imaging biological molecules—proteins, DNA, and RNA—in various biological systems [1,2,3,4,5]. Many algorithms have been adopted, utilized, or developed, in the field of SMLM for analyzing localization data of molecules and quantifying inter-molecular organizations [13, 14, 16,17,18,19,20,21,22,23]. These methods provide means to identify statistically the forming of clustering molecules from random populations, to examine complex patterns of molecular organization, to segment molecules into clusters, and to quantify clustering features.

Methods

Results

Conclusion