A CTRW-driven subdiffusive fractional Brownian bridge in the reconstruction of missing experimental data

Area of Science:

• Physics
• Biophysics
• Statistical Mechanics

Background:

• Single-particle tracking (SPT) experiments are crucial for studying molecular dynamics.
• Missing observations in SPT data can introduce significant biases in analysis.
• Subdiffusive motion, common in biological systems, is often characterized by power-law waiting times.

Purpose of the Study:

• To develop a novel stochastic process for reconstructing incomplete subdiffusive trajectories from SPT data.
• To address the challenge of missing data in SPT analysis by providing a robust gap-filling method.
• To ensure that reconstructed trajectories maintain the characteristic statistical properties of subdiffusion.

Main Methods:

• Introduction of the fractional Brownian bridge, an extension of the classical Brownian bridge.
• Incorporation of memory effects using a fractional Fokker-Planck framework.
• Derivation of the process's probability density function and mean-square displacement.
• Development and modification of an efficient simulation algorithm for practical implementation.

Main Results:

• The fractional Brownian bridge accurately reconstructs missing trajectory segments in subdiffusive motion.
• The method preserves the power-law waiting times characteristic of continuous-time random walk (CTRW) dynamics.
• Numerical experiments show reliable gap-filling even with large amounts of missing data.
• A modified algorithm ensures full reconstruction of the probabilistic structure of original trajectories.

Conclusions:

• The fractional Brownian bridge offers a robust framework for gap filling in SPT data analysis.
• This model-conditional imputation scheme is suitable for trajectories governed by CTRW mechanisms.
• The developed method enhances the reliability and accuracy of analyzing incomplete SPT datasets.