Improved mean squared displacement analysis for anomalous single particle trajectories.

Area of Science:

• Physics
• Physical Chemistry
• Biophysics

Background:

• Mean Squared Displacement (MSD) analysis is crucial for diffusion studies in complex media.
• Classical methods struggle with short or ultra-short trajectories due to time-averaging correlations and anomalous diffusion.
• Extracting maximal information from limited trajectory data is essential for accurate diffusion parameter estimation.

Purpose of the Study:

• To develop a robust method for analyzing diffusion processes with limited trajectory data.
• To overcome limitations of classical regression methods in heterogeneous and complex diffusion systems.
• To enable accurate estimation of diffusion parameters from short and ultra-short single-particle trajectories.

Main Methods:

• Application of a generalized least squares framework to time-averaged squared increments.
• Automated analysis requiring no supervision.
• Development of a specialized deconvolution algorithm based on predicted estimation error probability density.

Main Results:

• Substantial reduction in variance and bias for diffusion parameter estimates, particularly for short (≈100 points) and ultra-short (≈10 points) trajectories.
• Fully automated and unsupervised method.
• Prediction of asymptotically Gaussian estimation error probability density for classical and enhanced approaches.
• Successful reconstruction of underlying particle ensemble structure from experimental data.

Conclusions:

• The generalized least squares framework significantly enhances the accuracy of diffusion analysis from limited trajectory data.
• The developed method provides reliable parameter estimation and enables detailed structural insights into particle diffusion.
• This approach offers a powerful tool for studying diffusion in complex systems where data is often scarce.