INSTABILITIES DURING THE DENDRITIC AND AXONAL DEVELOPMENT OF NEURONALFORM

We present physical mechanisms for both dendritic branching and axonal differentiation during neuronal growth. Neuronal dendritic arbors hav e a growth and form consistent with the concept that shape is controll ed by the local submembrane concentration of the calcium ion. We descr ibe a class of dynamic instabilities for the generation of such dendri tic branching based on diffusion-controlled growth through biologicall y 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 growt h, forming a single, quickly growing axon and inhibiting the growth of the other neurites. The patterns of dendritic and axonal differentiat ion found are compared to the development of real neurons under simila r conditions. (C) 1998 Elsevier Science B.V. All rights reserved.