Mathematical Modeling of Neuronal Polarization During Development

During development of the brain, morphogenesis of neurons is dynamically organized from a simple rounded shape to a highly polarized morphology consisting of soma, one axon, and dendrites, which is a basis for establishing the unidirectional transfer of electric signals between neurons. The mechanism of such polarization is thought to be "local activation-global inhibition"; however, globally diffusing inhibitor molecules have not been identified. In this chapter, we present a theoretical modeling approach of such neuronal development. We first summarize biological research on neuronal polarization and then develop a biophysical model. Through mathematical analysis, principles of local activation global inhibition are illustrated based on active transport, protein degradation, and neurite growth, but not on globally diffusing inhibitor.