Mean-squared-displacement statistical test for fractional Brownian motion.

Area of Science:

• Biophysics
• Statistical Mechanics
• Cell Biology

Background:

• Anomalous diffusion is prevalent in crowded biological environments, such as cell cytoplasm.
• Time-averaged mean square displacement (TAMSD) is a key metric for characterizing anomalous diffusion.
• Fractional Brownian motion (FBM) is a common model explaining anomalous diffusion.

Purpose of the Study:

• To develop a rigorous statistical test for validating fractional Brownian motion (FBM) in single-particle tracking data.
• To analyze the distribution of the TAMSD statistic for FBM detection.
• To assess the test's sensitivity and ability to differentiate diffusion models.

Main Methods:

• Analysis of the generalized chi-squared distribution for the TAMSD statistic.
• Monte Carlo simulations to evaluate the power and sensitivity of the proposed statistical test.
• Comparison of the test's performance against FBM and continuous-time random walk (CTRW) models.

Main Results:

• The proposed statistical test, based on TAMSD, is highly sensitive to changes in the Hurst parameter, a key indicator of FBM.
• The test effectively distinguishes between FBM and continuous-time random walk (CTRW) models of subdiffusion.
• The TAMSD statistic follows a generalized chi-squared distribution, providing a theoretical basis for the test.

Conclusions:

• A robust statistical test for identifying FBM in single-particle tracking data has been developed.
• This method offers experimentalists a reliable tool for classifying anomalous diffusion mechanisms in biological systems.
• The test's ability to differentiate between FBM and CTRW enhances the understanding of particle dynamics in complex fluids.