Neuronal dendritic arbors grow in a manner consistent with the concept that cytoskeletal polymerization is catalyzed by the local submembrane concentration of a morphogen believed to be the calcium ion. Linear stability analysis of such diffusion-controlled growth through voltage-gated membranes coupled to active extrusion suggests that dendritic arboring will occur provided the cell is large enough and the membrane is excitable. Numerical simulations confirm this prediction.

• Received 2 December 1993

DOI:https://doi.org/10.1103/PhysRevLett.73.3592