High-Performance Reconstruction of Microscopic Force Fields from Brownian Trajectories

TL;DR

The paper introduces FORMA, a fast, parameter-free algorithm for accurately reconstructing microscopic force fields from Brownian motion data, significantly improving speed and data efficiency over existing methods.

Contribution

FORMA is a novel maximum-likelihood-based algorithm that accurately estimates both conservative and non-conservative force components from Brownian trajectories with minimal data and computational resources.

Findings

FORMA outperforms existing techniques in accuracy and speed.

It can identify stable and unstable equilibrium points in complex force fields.

Requires ten times less data than traditional methods.

Abstract

The accurate measurement of microscopic force fields is crucial in many branches of science and technology, from biophotonics and mechanobiology to microscopy and optomechanics. These forces are often probed by analysing their influence on the motion of Brownian particles. Here, we introduce a powerful algorithm for microscopic Force Reconstruction via Maximum-likelihood-estimator (MLE) Analysis (FORMA) to retrieve the force field acting on a Brownian particle from the analysis of its displacements. FORMA yields accurate simultaneous estimations of both the conservative and non-conservative components of the force field with important advantages over established techniques, being parameter-free, requiring ten-fold less data and executing orders-of-magnitude faster. We first demonstrate FORMA performance using optical tweezers. We then show how, outperforming any other available technique, FORMA can identify and characterise stable and unstable equilibrium points in generic extended force fields. Thanks to its high performance, this new algorithm can accelerate the development of microscopic and nanoscopic force transducers capable of operating with high reliability, speed, accuracy and precision for applications in physics, biology and engineering.