Mathematical analysis of competition between sensory ganglion cells for neurotrophic factor in the skin

Abstract

A model is presented of competition between sensory axons for trophic molecules (e.g. a neurotrophin such as NGF), produced in a region of skin small enough to permit their free diffusion throughout it; e.g., a touch dome, or a vibrissal follicle hair sinus. The variables specified are the number of high affinity trophic factor receptors per axon terminal and the concentration of trophic factor in the extracellular space. Previous models of this class predicted the loss of all the axons innervating the region except the one requiring least trophic factor for its maintenance, even with high rates of trophic factor production. In the present model, we have imposed upper limits to axonal growth, thereby introducing new equilibria, and we show by a global analysis using LaSalleÕs theorem, and also by local analysis, that several axons can then coexist if the rate of production of trophic molecules is sufficiently high.

Integrative Utilization of Microenvironments, Biomaterials and Computational Techniques for Advanced Tissue Engineering

“…Developing appropriate tunable biomaterials for a systematic study of neuronal cell growth and differentiation is another important aspect that is considered by many groups [135,[250][251][252], and has resulted in functional materials for improving axonal development [253]. Moreover, computational studies have been employed for predicting the mechanism of neurotrophic factor gradient generation, polarization of growth cone receptors, and cytoskeleton organization [254][255][256][257][258].…”