High-performance reconstruction of microscopic force fields from Brownian trajectories

Laura Pérez García,Alejandro V Arzola,Giovanni Volpe,Giorgio Volpe,Jaime Donlucas Pérez

doi:10.1038/s41467-018-07437-x

Laura Pérez García, Alejandro V Arzola + Show 3 more

Open Access

https://doi.org/10.1038/s41467-018-07437-x

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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 analysis (FORMA) to retrieve the force field acting on a Brownian particle from the analysis of its displacements. FORMA estimates accurately 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 demonstrate FORMA performance using optical tweezers, showing how, outperforming other available techniques, it can identify and characterise stable and unstable equilibrium points in generic force fields. Thanks to its high performance, FORMA can accelerate the development of microscopic and nanoscopic force transducers for physics, biology and engineering.

Highlights

The accurate measurement of microscopic force fields is crucial in many branches of science and technology, from biophotonics and mechanobiology to microscopy and optomechanics
We have introduced force reconstruction via maximum-likelihood-estimator analysis (FORMA): a new, powerful algorithm to measure microscopic force fields using the Brownian motion of a microscopic particle based on a linear MLE
We first introduced the 1D version of FORMA; we quantitatively compared it to other standard methods, showing that it needs less samples, it has smaller relative errors, it is more accurate, and it is orders-of-magnitude faster

Summary

Introduction

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. We introduce a powerful algorithm for microscopic force reconstruction via maximum-likelihood-estimator analysis (FORMA) to retrieve the force field acting on a Brownian particle from the analysis of its displacements. Often particles are held by optical, acoustic, or magnetic tweezers in a harmonic trapping potential with stiffness k so that a homogeneous force acting on the particle results in a displacement Δx from the equilibrium position and can be measured as kΔx To perform such measurement, it is necessary to determine the value of k, which is often done by measuring the Brownian fluctuations of the particle around its stable equilibrium position. As it does not need to use the trajectory of a particle held in a potential, it can identify and characterise both stable and unstable equilibrium points in extended force fields, and it is compatible with a broader range of possible scenarios where a freely diffusing particle is used as a tracer, e.g., in microscopy and rheology

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