Systems-matching by degeneration. II. Interpretation of the generation and degeneration of retinal ganglion cells in the chicken by a mathematical model.
Quantitative data on generation and degeneration of retinal ganglion cells during development (Rager and Rager, 1978) are interpreted in terms of a mathematical model which consists of a system of differential equations. By these equations we attempt to describe the formation of retinal ganglion cells and their termination domains in the tectum. Since ganglion cells seem not to degenerate before their axons have arrived at their termination site and start branching, from the arrival time on they may become competent either to continue to mature or to die. Therefore, to find the actual number of competent cells the extension of the fiber pathway between the retina and the optic tectum had also to be measured and computed. The differential equations are united by the principle that at any given time cells in excess of the number of termination domains have to die. By this model the mathematical function was determined. Several parameter values of this function were optimized with the Gauss-Newton method by which the curve was fitted to the measured values. The high correlation obtained by this method allows to conclude that, to a first approximation, the model may be satisfactory. The evidence of competition for termination sites and of systems-matching by cell death is discussed.
D000367:Age Factors; D000818:Animals; D001369:Axons / Q000502:physiology; D002452:Cell Count; D002470:Cell Survival; D002642:Chick Embryo; D005724:Ganglia / Q000254:growth & development*; D008433:Mathematics; D008959:Models, Neurological; D009434:Neural Pathways / Q000502:physiology; D012160:Retina / Q000254:growth & development* / Q000294:innervation; D003336:Tectum Mesencephali / Q000502:physiology