TITLE:

SUBDIFFUSIVE PROCESSES: TRANSPORT AND REACTIONS

DATE:

Friday, Feb 10th, 2012

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Katja Lindenberg.
University of California in San Diego.

ABSTRACT:

The random motion of entities in crowded or disordered environments may be hindered by
obstacles, traps, and dead ends. As a result, the motion may be subdiffusive.
Reaction kinetics among subdiffusive species are highly “anomalous” in that they are very
different from those described by the familiar laws of mass action involving only global
concentrations c(t) as a function of time. It is in general not even
possible to write equations involving only local concentrations c(x,t) as one
does in reaction-diffusion problems. We discuss these issues in the context of the very
simplest binary reactions such as the evanescence reaction A -> 0, the annihilation reactions
A+A -> A and A+A -> 0, and the trapping reaction A+B -> B.

As an application, we will briefly discuss the problem of morphogen gradient formation.
This problem is important because one view of morphogenesis relies on the formation of
gradients that evolve as a balance between morphogen creation at a source point, subsequent
motion through the embryonic environment, and degradation. The resulting morphogen concentration
at the location of a cell then determines the evolution of that cell. If this description
is valid, then the shape of the morphogen gradient as a function of location is an essential
ingredient of embryonic evolution. The shape of the gradient is sensitively dependent on
the motion and degradation mechanisms. Almost all current models of morphogen gradient formation
assume the motion of the morphogens to be diffusive. We investigate the gradient balance for
morphogens moving subdiffusively as described by a continuous time random walk model and
subject to a variety of degradation mechanisms.

HOST:

Dr. Jose Castillo.

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