  Concentration gradients of signaling molecules are essential for patterning
during development and they have been observed in both unicellular and
multicellular systems. In subcellular systems, clustering of the signaling
molecule has been observed. We develop a theoretical model of cluster- mediated
concentration gradient formation based on the Becker-Doring equations of
aggregation- fragmentation processes. We show that such a mechanism produces
robust concentration gradients on realistic time and spatial scales so long as
the process of clustering does not significantly stabilize the signaling
molecule. Finally, we demonstrate that such a model is applicable to the pom1p
subcellular gradient in fission yeast.
