A Sequential Monte Carlo Method for Identifying Motion Parameters from Particle Tracking Trajectories

Abstract

Optimal estimation of diffusion coefficients from single- and multiple-particle tracking data has undergone several breakthroughs in the past few years. Prior to these breakthroughs, the most common method for extracting motion parameters from trajectories was by fitting a curve to the mean square displacement [1]; it has been known for quite some time, however, that this a possibly inaccurate and unreliable method due to the presence of noise in the trajectory [2]. As a result, recent efforts by A. J. Berglund and X. Michalet have provided an optimal framework for trajectories corrupted by motion blur and Gaussian white noise [3]. These methods typically require that localization be performed prior to the estimation of motion parameters rather than in conjunction. These two problems, however, are dependent on each other. In this work, we present a Sequential Monte Carlo approach that utilizes the Expectation Maximization algorithm to simultaneously localize particle positions and estimate motion parameters from raw data (e.g. image sequences). The method provides a clear accuracy-vs-complexity trade-off and can be parallelized for greater efficiency. We demonstrate its effectiveness by detailing its use on arbitrary point spread functions, such as the double helix, and motion models, such as those driven by Markov jump processes.[1] M. J. Saxton. “Single-Particle Tracking: Applications to Membrane Dynamics.” Annual Review of Biophysics and Biomolecular Structure, vol. 26, pp. 373-399, 1997.[2] M. J. Saxton. “Single-Particle Tracking: The Distribution of Diffusion Coefficients.” Biophysical Journal, vol. 72, pp. 1744-1753, 1997.[3] X. Michalet and A. J. Berglund. “Optimal Estimation of Diffusion Coefficients.” Physical Review E, vol. 85, 2012.