Biologically plausible models of neurite outgrowth.

Mathematical modeling and computer simulation are valuable tools in unravelling the complexities underlying the morphological development of neurons. In this chapter, we consider biologically plausible mathematical models of neurite initiation, elongation, and branching. These models attempt to describe the intraand extracellular environments of a developing neuron and determine the limiting factors in neurite outgrowth. This typically involves modeling the production, degradation, and transport of one or more chemicals in one or two spatial dimensions. For example, the one-dimensional diffusion and active transport of tubulin within a neurite, or the two-dimensional diffusion gradient of a chemoattractant in the external environment surrounding a neuron grown in cell culture. Extension to three dimensions to accurately describe neuronal growth in vivo may be desirable, but is highly computationally intensive and likely analytically intractable. The numerical solution of even oneor two-dimensional models is computationally demanding and requires considerable care in specifying appropriate temporal and spatial discretization. As the neuronal morphology changes over time so must the spatial discretization representing the neuron also change. Numerical techniques that address this issue are described. Neurobiology of neurite outgrowth