High-performance reconstruction of microscopic force fields from Brownian trajectories

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.

Enhanced Signal-to-Noise and Fast Calibration of Optical Tweezers Using Single Trapping Events

“…The start of the selected in-fall events are marked with crosses in Figure 5 a. From these events, we are able to construct a position-force curve, where the viscous force has the estimator, , where is the assumed Stokes drag for the particle [ 14 ].…”

“…It uses comparatively larger amount of the information stored in the recorded bead trajectory than the standard calibration approaches. Another alternative method is force reconstruction via maximum likelihood estimation (FORMA) [ 14 ], in which one retrieves the force field acting on a Brownian particle from the analysis of its observed motion within the macroscopic force field. FORMA is an attractive alternative to many of the other techniques, as it only consists of determining the ratio of two sums that arise from analysis of the occupation probability within the trap.…”

“…The probability distribution for the mean regressed linear response problem is given by where we have set the estimator to have the property as . Finding the maximum of the natural logarithm of the resulting likelihood function with respect to ( ) we obtain the key result of FORMA [ 14 ] for 1D: where the difference in position at two sequential time-steps is . We have assumed that is the estimator of velocity (and thus ), but this is not exactly the case.…”

Using the transient trajectories of an optically levitated nanoparticle to characterize a stochastic Duffing oscillator

“…Moreover, the trajectories simulated by the SDE could be in principle used directly to obtain the parameters of the experimental system together with the concept of machine learning 59 . Here the artificial neural network (ANN) would be trained using the simulated trajectories or some features acquired of such trajectories and later the ANN would predict parameters of the experimental system based on the measured data.…”

Optical Tweezers Exploring Neuroscience

“…This usually involves using the thermal motion of the particle to calibrate the optical potential. Methods such as FORMA (García et al, 2018;García, 2019) enable estimation of both the conservative and nonconservative parts of the optical potential. When the scenario can be accurately modeled, it is sometimes possible to fit the available experimental measurements to the model in order to estimate the optical force.…”