Receptor-mediated BMP degradation has been seen to play an important role in allowing for the formation of relatively stable P Mad patterns. To the extent that receptors act as a "sink" for BMPs, one would predict that the localized over-expression of signaling receptors would cause a net flux of freely diffused BMPs toward the ectopic, i.e., abnormally high concentration, receptor site. One possible consequence would be a depression of BMP signaling in adjacent areas since less BMPs are now available for binding with the same normal concentration of receptors at the adjacent areas. However, recent experiments designed to examine this possible effect were inconclusive. In this paper, we investigate the possibility of depression of Dpp signaling outside the area of elevated tkv in a Drosophila embryo by modeling mathematically the basic biological processes at work in terms of a system of nonlinear reaction diffusion equations with spatially varying (and possibly discontinuous) system properties. The steady state signaling morphogen gradient is investigated by the method of matched asymptotic expansions and by numerical simulations.

中文翻译：

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果蝇胚胎中 Dpp 受体的局部异位表达

受体介导的 BMP 降解已被视为在允许形成相对稳定的 P Mad 模式方面发挥重要作用。就受体作为 BMP 的“汇”的程度而言，人们可以预测信号受体的局部过度表达将导致自由扩散的 BMP 向异位（即异常高浓度）受体位点的净通量。一种可能的后果是相邻区域 BMP 信号的抑制，因为现在可用于与相邻区域相同正常浓度受体结合的 BMP 较少。然而，最近旨在检验这种可能影响的实验尚无定论。在本文中，我们通过根据具有空间变化（并且可能不连续）系统特性的非线性反应扩散方程系统对工作中的基本生物过程进行数学建模，研究了果蝇胚胎中 tkv 升高区域外 Dpp 信号抑制的可能性。通过匹配渐近展开的方法和数值模拟研究稳态信号形态素梯度。