Diffusion-regulated control of cellular dendritic morphogenesis.

Highly branched dendritic shapes are distinguishing characteristics of neurons and certain other cell types, but the physical mechanisms responsible for their formation are not well understood. Here, we model the growth of cells under the control of diffusible growth-regulating factors (morphogens such as calcium ion) whose local internal concentration results from influx and active extrusion across the cell membrane. Nonlinearities in voltage-dependent ionic permeabilities enhance unstable growth, so that branching dendritic outgrowths results from self-sustaining internal morphogen gradients. Simulations display complex patterns of branching growth, influenced by membrane conductance, galvanotropism and chemotropism. This self-organizing pattern formation is in agreement with the development of real neurons under corresponding conditions.