Instabilities during the dendritic and axonal development of neuronal form

We present physical mechanisms for both dendritic branching and axonal differentiation during neuronal growth. Neuronal dendritic arbors have a growth and form consistent with the concept that shape is controlled by the local submembrane concentration of the calcium ion. We describe a class of dynamic instabilities for the generation of such dendritic branching based on diffusion-controlled growth through biologically active membranes. The interaction of diffusion and active transport of a morphogen whose concentration at the neurite tips influences the growth rate can lead to an instability involving winner-take-all growth, forming a single, quickly growing axon and inhibiting the growth of the other neurites. The patterns of dendritic and axonal differentiation found are compared to the development of real neurons under similar conditions.