A biological interpretation of transient anomalous subdiffusion. I. Qualitative model

¹ University of California - Davis

^* To whom correspondence should be addressed. E-mail: mjsaxton{at}ucdavis.edu.

Submitted on July 3, 2006
Revised on August 17, 2006
Accepted on 6 November 2006

	Abstract

Anomalous subdiffusion has been reported for 2D diffusion in the plasma membrane and 3D diffusion in the nucleus and cytoplasm. If a particle diffuses in a suitable infinite hierarchy of binding sites, diffusion is well known to be anomalous at all times. But if the hierarchy is finite, diffusion is anomalous at short times and normal at long times. For a prescribed set of binding sites, Monte Carlo calculations yield the anomalous diffusion exponent and the average time over which diffusion is anomalous. If even a single binding site is present, there is a very short, almost artifactual, period of anomalous subdiffusion, but a hierarchy of binding sites extends the anomalous regime considerably. As is well known, an essential requirement for anomalous subdiffusion due to binding is that the diffusing particle cannot be in thermal equilibrium with the binding sites; an equilibrated particle diffuses normally at all times. Anomalous subdiffusion due to barriers, however, still occurs at thermal equilibrium, and anomalous subdiffusion due to a combination of binding sites and barriers is reduced but not eliminated on equilibration. This physical model is translated directly into a plausible biological model testable by single-particle tracking.

Key Words: Lateral diffusion, anomalous diffusion, membranes, nucleus

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