A Study of Particle Motion in the Presence of Clusters

TL;DR

This paper develops and compares variational models using Wasserstein and MMD distances to detect particle clustering in single molecule localization microscopy data, aiding understanding of molecular behavior in cells.

Contribution

It introduces novel variational models based on Wasserstein and MMD distances for cluster detection, validated through simulations.

Findings

Models effectively distinguish clustered from non-clustered particles

Wasserstein-based models outperform MMD in detection accuracy

Simulation results demonstrate robustness of proposed methods

Abstract

The motivation for this study came from the task of analysing the kinetic behavior of single molecules in a living cell based on Single Molecule Localization Microscopy. Given measurements of both the motion of clusters and molecules, the main task consists in detecting if a molecule belongs to a cluster. While the exact size of the clusters is usually unknown, upper bounds are available. In this study, we simulate the cluster movement by a Brownian motion and those of the particles by a Gaussian mixture model with two modes depending on the position of the particle within or outside a cluster. We propose various variational models to detect if a particle lies within a cluster based on the Wasserstein and maximum mean discrepancy distances between measures. We compare the performance of the proposed models for simulated data.