Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000Cd., México, Mexico.
Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, UK.
Nat Commun. 2018 Dec 4;9(1):5166. doi: 10.1038/s41467-018-07437-x.
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.
微观力场的精确测量在生物光子学、机械生物学、显微镜学和光机械等众多科学和技术领域至关重要。这些力通常通过分析它们对布朗粒子运动的影响来探测。在这里，我们通过最大似然估计分析（FORMA）引入了一种强大的微观力重建算法，从布朗粒子的位移分析中恢复作用在其上的力场。FORMA 能够准确估计力场的保守和非保守分量，与已有技术相比具有重要优势，它是无参数的，所需数据量少十倍，执行速度快几个数量级。我们使用光镊演示了 FORMA 的性能，展示了它如何在识别和表征通用力场中的稳定和不稳定平衡点方面优于其他可用技术。由于其高性能，FORMA 可以加速用于物理、生物和工程的微观和纳观力传感器的发展。
