Spatially Distributed Morphogen Production and Morphogen Gradient Formation - Arthur D. Lander; Qing Nie; Frederic Y. M. Wan (Mathematical Biosciences and Engineering)
Partial differential equations and auxiliaryconditions governing the activities of the morphogen Dpp in Drosophila wingimaginal discs were formulated and analyzed as Systems B, R, and C in[7][9][10]. All had morphogens producedat the border of anterior and posterior chamber of the wing disc idealizedas a point, line, or plane in a one-, two-, or three-dimensional model. Inreality, morphogens are synthesized in a narrow region of finite width(possibly of only a few cells) between the two chambers in which diffusionand reversible binding with degradable receptors may also take place. Thepresent investigation revisits the extracellular System R, now allowing fora finite production region of Dpp between the two chambers. It will beshown that this more refined model of the wing disc, designated as System F,leads to some qualitatively different morphogen gradient features. Onesignificant difference between the two models is that System Fimpose no restriction on the morphogen production rate for the existence ofa unique stable steady state concentration of the Dpp-receptor complexes.Analytical and numerical solutions will be obtained for special cases ofSystem F. Some applications of the results for explaining availableexperimental data (to appear elsewhere) are briefly indicated. It willalso be shown how the effects of the distributed source of System F may beaggregated to give an approximating point source model (designated as theaggregated source model or System A for short) that includes System R as aspecial case. System A will be analyzed in considerable detail in [6], and the limitation of System R as an approximation of System F willalso be delineated there.