Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments

TL;DR

This paper introduces a maximum likelihood approach for accurately estimating diffusion coefficients from single-particle tracking data, especially in complex scenarios with multiple subpopulations and noise, improving over traditional methods.

Contribution

It extends likelihood-based analysis to mixtures of subpopulations and provides an efficient, open-source implementation for analyzing multiple trajectories in various dimensions.

Findings

Effective estimation of multiple diffusion coefficients in noisy data

Ability to identify subpopulations with different diffusion behaviors

Validated approach on experimental tracking data

Abstract

Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit on mean-square-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between observed positions provide a good estimate for the diffusion coefficient, and their statistics are well-suited for likelihood-based analysis methods. Here, we revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static and dynamic noise using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate with the help of the expectation-maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously.