Anomalous Diffusion

Typically, in a diffusion process, the mean squared displacement of a particle is a linear function of time. Anomalous diffusion is used to describe a diffusion process with a non-linear dependence on time.

Diffusion is often described by a power law, msd(t) ~ 6Dt^α, where D is the diffusion coefficient and t is the elapsed time. In a typical diffusion process, α = 1. If α > 1, the phenomenon is called superdiffusion. Superdiffusion can be the result of active cellular transport processes. If α < 1, the particle undergoes subdiffusion. Subdiffusion has been proposed as a measure of macromolecular crowding in the cytoplasm.

References

• Avi Caspi, Rony Granek, and Michael Elbaum. "Diffusion and directed motion in cellular transport." Physical Review E 66, 011916 (2002)
• Matthias Weiss, Markus Elsner, Fredrik Kartberg, and Tommy Nilsson. "Anomalous Subdiffusion Is a Measure for Cytoplasmic Crowding in Living Cells." Biophysical Journal 87 : 3518-3524 (2004)