Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity.

Area of Science:

• Physics
• Biophysics
• Statistical Mechanics

Background:

• Biological cells exhibit spatially varying diffusivity, impacting tracer particle motion.
• Understanding heterogeneous diffusion is crucial for interpreting single-particle tracking experiments.

Purpose of the Study:

• To analyze the heterogeneous diffusion process (HDP) in a 2D medium with spatially varying diffusivity.
• To investigate the non-ergodic properties of HDP for accurate physical interpretation.
• To provide a framework for rationalizing tracer particle diffusion in biological cells.

Main Methods:

• Simulations of the 2D stochastic Langevin equation.
• Analysis of mean squared displacement (MSD), time-averaged MSD, and probability density functions.
• Examination of first passage time dynamics and non-ergodic properties.

Main Results:

• MSDs along radial and azimuthal directions show anomalous and Brownian scaling, respectively.
• Time-averaged MSD remains linear with lag time, indicating weak ergodicity breaking.
• The study provides insights into the physical interpretation of diffusion in heterogeneous environments.

Conclusions:

• The findings enable rationalization of diffusive motion for larger tracer particles (e.g., viruses, beads) in cells.
• This research clarifies the complex diffusion dynamics within heterogeneous cellular environments.
• Understanding HDP is key for advancing biophysical models of intracellular transport.