A Method for Estimating Unknown Parameters from Particle Tracking Experiments

Abstract

Optimal estimation of motion parameters (e.g. diffusion coefficients) from single and multiple particle tracking data has developed substantially over the past several years. The standard approach for estimating these parameters typically involves first localizing the particle(s) within each frame, assembling a time-series of estimated positions, calculating the mean squared displacement (MSD), and finally fitting a known function to the resulting MSD. It has been shown, however, that this approach may lead to erroneous results due the potential subjectivity of the fit [1]. Recently, a powerful method based on the Maximum Likelihood framework was described in [2]. This method, however, cannot estimate parameters other than diffusion coefficients, examples of which include confinement lengths and tether stiffnesses. In addition, the aforementioned method dissociates the localization procedure from the estimation procedure which are inherently coupled processes. In this work, we present a technique which leverages recent work from [3] in which the Expectation Maximization (EM) algorithm is used in conjunction with Sequential Monte Carlo (SMC) methods to simultaneously estimate unknown fixed parameters in addition to time-varying states. Here, we demonstrate the applicability of this technique to the problem of tracking a moving particle undergoing complex modes of motion, including confined diffusion and elastic tethering.[1] M. J. Saxton. “Single-Particle Tracking: The Distribution of Diffusion Coefficients.” Biophysical Journal, vol. 72, no. 4, pp. 1744-1753, 1997.[2] X. Michalet and A. J. Berglund. “Optimal Estimation of Diffusion Coefficients.” Physical Review E, vol. 85, 2012.[3] T. B. Schon, A. Wills, B. Ninness. “System Identification of Nonlinear State-­Space Models.” Automatica, vol. 47, no. 1, pp. 39-49, 2011.