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

Area of Science:

• Biophysics
• Cell Biology
• Microscopy

Background:

• Single-molecule localization microscopy (SMLM) tracks molecules in biological systems.
• Current methods for calculating diffusion coefficients from SMLM data, like linear fitting of mean-squared displacement curves, are often inaccurate.
• Alternative methods using position increments are better suited for likelihood-based analysis.

Purpose of the Study:

• To develop a more accurate method for extracting diffusion coefficients from single-particle tracking (SPT) data.
• To address challenges in SPT data analysis, including static noise and motion blur.
• To extend diffusion analysis to complex biological systems with multiple molecular subpopulations.

Main Methods:

• Utilizing the principle of maximum likelihood for diffusion coefficient estimation.
• Developing an efficient real-space formulation of the diffusion model.
• Employing the expectation-maximization algorithm to handle mixtures of subpopulations with differing diffusion coefficients.
• Implementing a probabilistic assignment of trajectories to subpopulations.

Main Results:

• The developed method accurately estimates diffusion coefficients even with static noise and motion blur.
• The model successfully identifies and quantifies multiple subpopulations with distinct diffusion behaviors.
• A quality factor is introduced to assess model fit and determine the optimal number of subpopulations.
• Experimental tracking data, previously unexplained by single diffusion coefficients, were analyzed.

Conclusions:

• The new maximum likelihood approach offers a robust and accurate method for analyzing SPT data.
• This method enhances the understanding of molecular dynamics in complex biological environments.
• The open-source implementation facilitates widespread adoption and application in biophysical research.