On the origin of the observed distribution of toponymic substance (TOP) in avian retina

The present study takes as its basis the published data on the distribution of the substance TOP in embryonic chick retina; the data consists of TOP concentration values associated with retinal tissue fragments formed by dissecting retina in a number of different ways. These values are compared with corresponding sets of theoretical values obtained by the numerical evaluation of various alternative models. Each model assumes a hemispherical retina carrying a source of morphogen that may be TOP itself or a separate substance that prepatterns TOP distribution. The geometry of the morphogen source varies between models but in each case the morphogen is assumed to move within the retina by a diffusion-like process. The nature of morphogen loss from the retina also varies between models, this being alternatively attributed to a significant molecular half-life, removal at a sink of variable geometry, or removal by encounter with a diffusing antagonist that itself originates from a source of variable geometry. The free parameters of each model are adjusted to give best agreement with the measured concentrations and selection is then made between the models on the basis of their sets of residuals under best match conditions. It emerges that TOP is probably too large and slowly diffusing to be the postulated morphogen, and requires a separate, more mobile morphogen to prepattern its distribution. It is also found that the most probable source geometry for this morphogen is a wide spherical sector and this accords well with the idea of an initial small arc of morphogen-producing cells that grows naturally into a sector shape as the retina itself grows. It is not resolved whether morphogen loss should be attributed to a finite half-life or to removal by an antagonistic substance.