Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images.

Ye Lin,Sean B Andersson,Antonio Agudo

doi:10.1371/journal.pone.0243115

Abstract

Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the location of the emitter inside each frame of a sequence of camera images is estimated using, for example, Gaussian fitting (GF), and these locations are linked to provide an estimate of the trajectory. Trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood Estimation (MLE) techniques to determine motion parameters such as diffusion coefficients. However, the problems of localization and parameter estimation are clearly coupled. Motivated by this, we have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM). Using diffusion in two-dimensions as a prototypical example, we conduct quantitative investigations on localization and parameter estimation performance across a wide range of signal to background ratios and diffusion coefficients and compare our methods to the standard techniques based on GF-MSD/MLE. To demonstrate the flexibility of the EM based framework, we do comparisons using two different camera models, an ideal camera with Poisson distributed shot noise but no readout noise, and a camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) camera. Our results indicate our EM based methods outperform the standard techniques, especially at low signal levels. While U-EM and SMC-EM have similar accuracy, U-EM is significantly more computationally efficient, though the use of the Unscented Kalman Filter limits U-EM to lower diffusion rates.

Highlights

Single particle tracking (SPT) is an important class of techniques for studying the motion of single biological macromolecules
We have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM)
Localization refinement is often done using Gaussian Fitting (GF) [12, 13] while model parameters are extracted from the trajectories using the Mean Square Displacement (MSD) [14, 15] or Maximum Likelihood Estimation (MLE) [16, 17]

Summary

Introduction

Single particle tracking (SPT) is an important class of techniques for studying the motion of single biological macromolecules. Compared to the SMC-EM approach, U-EM significantly decreases the computational load, allowing the method to be applied to larger data sets and to more complicated models This reduction in complexity comes, at the cost of generality in the EM framework for joint localization and parameter estimation in single particle tracking from segmented images posterior distribution describing the position in the particle at each time point since the UKF-URTSS approximates this distribution as a Gaussian while the SMC-EM can represent essentially arbitrary distributions [22]. This comparison is done across a wide range of SBRs and across a wide range of diffusion coefficients, validating the performance of our methods and guiding users in algorithm selection based on their particular experimental conditions

Methods

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Findings

Discussion and conclusion