Learning the nonlinear interactions from particle trajectories

TL;DR

This paper introduces a new statistical method to infer nonlinear membrane protein interactions from particle trajectory data, demonstrating improved robustness over traditional mean square displacement analysis.

Contribution

The authors develop a novel cumulant-based analysis technique to learn nonlinear potentials from particle displacement data, validated through simulations and analytical predictions.

Findings

Effective identification of nonlinear potentials from trajectory data

Robust analysis at lower temporal resolutions

Validation through numerical simulations and analytical models

Abstract

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a novel statistical analysis technique for learning the characteristics of the nonlinear potential from the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of kurtosis of the displacement distribution of the particle traveling on a membrane in a cage-type potential. Results of numerical simulations are supported by analytical predictions. We show that the approach allows robust identification of the potential for the much lower temporal resolution compare with the mean square displacement analysis.