Inferring interaction potentials from stochastic particle trajectories

TL;DR

This paper presents a novel method to infer interaction potentials directly from particle trajectory data, applicable to both equilibrium and non-equilibrium systems, without assuming a specific potential form.

Contribution

The authors introduce a trajectory-based inference method that explicitly solves equations of motion to determine interaction potentials, overcoming limitations of existing equilibrium-based techniques.

Findings

Successfully inferred depletion interactions from experimental colloidal data.

Applicable to large particle systems in typical conditions.

Works for systems both in and out of equilibrium.

Abstract

Accurate interaction potentials between microscopic components such as colloidal particles or cells are crucial to understanding a range of processes, including colloidal crystallization, bacterial colony formation, and cancer metastasis. Even in systems where the precise interaction mechanisms are unknown, effective interactions can be measured to inform simulation and design. However, these measurements are difficult and time-intensive, and often require conditions that are drastically different from in situ conditions of the system of interest. Moreover, existing methods of measuring interparticle potentials rely on constraining a small number of particles at equilibrium, placing limits on which interactions can be measured. We introduce a method for inferring interaction potentials directly from trajectory data of interacting particles. We explicitly solve the equations of motion to find a form of the potential that maximizes the probability of observing a known trajectory. Our method is valid for systems both in and out of equilibrium, is well-suited to large numbers of particles interacting in typical system conditions, and does not assume a functional form of the interaction potential. We apply our method to infer the interactions of colloidal spheres from experimental data, successfully extracting the range and strength of a depletion interaction from the motion of the particles.