title: Mathematical modeling of neuronal polarization during development.
abstract: 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.
authors.affiliation: Imaging Platform for Spatio-Temporal Information, Graduate School of Medicine, Kyoto University, Kyoto, Kyoto, Japan.
authors.forename: Honda
authors.initials: H
authors.lastname: Naoki
authors.affiliation: Graduate School of Informatics, Kyoto University, Uji, Kyoto, Japan.
authors.forename: Shin
authors.initials: S
authors.lastname: Ishii
mesh_terms: D000818:Animals; D055592:Biophysical Phenomena; D016764:Cell Polarity; D048788:Growth and Development; D006801:Humans; D008959:Models, Neurological; D009474:Neurons / Q000166:cytology*
keywords: Active transport; Biophysical model; Computer simulation; Local activation–global inhibition; Mathematical model; Morphogenesis; Symmetry breaking