Lander A D, Nie Q, Wan F Y M, Zhang Y-T
Department of Developmental and Cell Biology, University of California, Irvine, Irvine, CA 92697-3875.
Stud Appl Math. 2009 Aug 1;123(2):175-214. doi: 10.1111/j.1467-9590.2009.00450.x.
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.
受体介导的骨形态发生蛋白（BMP）降解在形成相对稳定的磷酸化母亲抗五同源物（P Mad）模式中发挥着重要作用。就受体作为BMP的“汇”而言，可以预测信号受体的局部过表达会导致自由扩散的BMP向异位（即异常高浓度）受体位点的净通量。一个可能的结果是相邻区域的BMP信号传导受到抑制，因为现在较少的BMP可用于与相邻区域相同正常浓度的受体结合。然而，最近旨在研究这种可能影响的实验尚无定论。在本文中，我们通过用具有空间变化（可能不连续）系统特性的非线性反应扩散方程组对基本生物学过程进行数学建模，研究果蝇胚胎中tkv升高区域外Dpp信号传导受抑制的可能性。通过匹配渐近展开法和数值模拟研究稳态信号形态发生素梯度。
