Motion Blur Filtering: A Statistical Approach for Extracting Confinement Forces and Diffusivity from a Single Blurred Trajectory

TL;DR

This paper introduces a maximum likelihood estimation method to accurately extract confinement forces and diffusivity from single particle trajectories affected by motion blur, noise, and temporal correlations, improving analysis reliability.

Contribution

A novel MLE technique that decouples noise sources and accounts for temporal correlations, enabling more reliable parameter extraction from blurred and noisy trajectories.

Findings

Estimator is consistent across various exposure times and diffusion coefficients.

Algorithm reliably extracts motion parameters from confined and non-stationary dynamics.

Software implementation facilitates comparison of trajectories from different imaging modalities.

Abstract

Single Particle Tracking (SPT) can aid in understanding complex spatio-temporal processes. However, quantifying diffusivity and forces from individual live cell trajectories is complicated by inter- & intra-trajectory kinetic heterogeneity, thermal fluctuations, and statistical temporal dependence inherent to the underlying molecule's time correlated confined dynamics experienced in the cell. Experimental artifacts such as localization uncertainty and motion blur also obscure the data. We introduce a new maximum likelihood estimation (MLE) technique that decouples the above noise sources and systematically treats temporal correlation via a likelihood function (permitting more reliable extraction of effective forces from position vs. time data). Our estimator is demonstrated to be consistent over a wide range of exposure times, diffusion coefficients, and confinement "radii". The algorithm and corresponding software can reliably extract motion parameters independent of exposure time in trajectories exhibiting confined and/or non-stationary dynamics and will aid in directly comparing trajectories obtained from different imaging modalities.