Force measurement in the presence of Brownian noise: Equilibrium-distribution method versus drift method

Abstract

The study of microsystems and the development of nanotechnologies require alternative techniques to measure piconewton and femtonewton forces at microscopic and nanoscopic scales. Among the challenges is the need to deal with the ineluctable thermal noise, which, in the typical experimental situation of a spatial diffusion gradient, causes a spurious drift. This leads to a correction term when forces are estimated from drift measurements [G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, Phys. Rev. Lett. 104, 170602 (2010)]. Here we provide a systematic study of such an effect by comparing the forces acting on various Brownian particles derived from equilibrium-distribution and drift measurements. We discuss the physical origin of the correction term, its dependence on wall distance and particle radius, and its relation to the convention used to solve the respective stochastic integrals. Such a correction term becomes more significant for smaller particles and is predicted to be on the order of several piconewtons for particles the size of a biomolecule.

Stratonovich-to-Itô transition in noisy systems with multiplicative feedback

“…In our case, Dt should meet the condition Dt ) t; d, which warrants that the data are subsampled with respect to the fast time scales of the process we consider and therefore the estimation of the drift and diffusion of the homogenized low-dimensional model is correct 30 . Furthermore, Dt should also be much smaller than the relaxation time of the system 25 . Both conditions are verified in the experiments presented in this article by subsampling the experimental data at Dt ¼ 10 ms.…”

“…This shift of the equilibrium is a consequence of the non-uniformity of S(y) ( presence of a multiplicative feedback. We remark that S(y) is independent from the interpretation of the underlying SDE 25 . D(y) (symbols in Fig.…”

Hydrodynamics and Brownian motions of a spheroid near a rigid wall

“…43 Indeed, recent experiments showed that neglecting the drift velocity leads to an erroneous qualitative evaluation of the conservative forces acting on Brownian spheres. 44 We would like to point out that the presence of a "drift" velocity does not mean that there is a net particle flux in the velocity direction. The drift velocity is, instead, an effect of the variation of the particle mobility with the configuration of the system, and its adequate evaluation is required to obtain the correct particle equilibrium distribution.…”

Numerical simulation of optically trapped particles

“…How to deal with these cases is explained in Refs. [13,14]. Similar considerations hold also in the case of diffusion gradients induced by, e.g., chemical gradients or temperature gradients [15,16,17].…”