From diffusion in compartmentalized media to non-Gaussian random walks

Area of Science:

• Physics
• Physical Chemistry
• Biophysics

Background:

• Non-Gaussian diffusion is observed in various complex media.
• Diffusion in compartmentalized environments is crucial for biological and soft matter systems.
• Transient confinement is a key feature in phenomena like hop-diffusion on cell membranes.

Purpose of the Study:

• To establish a link between diffusion in compartmentalized environments and non-Gaussian diffusion.
• To explore a microscopic model that explains transient confinement and non-Gaussian diffusion.
• To derive a general class of random walks applicable to heterogeneous media.

Main Methods:

• Development of a microscopic model with randomly placed barriers to simulate compartmentalization.
• Derivation of a general class of random walks with geometry-dictated jump rules.
• Analysis of positional probability density and mean square displacement.

Main Results:

• The model successfully reproduces transient confinement.
• An exponential decay of the positional probability density was observed.
• A significant decrease in the long-time diffusion constant was quantified.

Conclusions:

• The study establishes a link between compartmentalization and non-Gaussian diffusion.
• Exponential decay of positional probability is a general feature of transient regimes in compartmentalized media.
• The findings provide insights into diffusion dynamics in heterogeneous biological and soft media.