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Scaling morphogen gradients during tissue growth by a cell division rule

机译：通过细胞分裂规则缩放组织生长过程中的形态发生子梯度

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Morphogen gradients guide the patterning of tissues and organs during the development of multicellular organisms. In many cases, morphogen signaling is also required for tissue growth. The consequences of this interplay between growth and patterning are not well understood. In the Drosophila wing imaginal disc, the morphogen Dpp guides patterning and is also required for tissue growth. In particular, it was recently reported that cell division in the disc correlates with the temporal increase in Dpp signaling. Here we mathematically model morphogen gradient formation in a growing tissue, accounting also for morphogen advection and dilution. Our analysis defines a new scaling mechanism, which we term the morphogen-dependent division rule (MDDR): when cell division depends on the temporal increase in morphogen signaling, the morphogen gradient scales with the growing tissue size, tissue growth becomes spatially uniform and the tissue naturally attains a finite size. This model is consistent with many properties of the wing disc. However, we find that the MDDR is not consistent with the phenotype of scaling-defective mutants, supporting the view that temporal increase in Dpp signaling is not the driver of cell division during late phases of disc development. More generally, our results show that local coupling of cell division with morphogen signaling can lead to gradient scaling and uniform growth even in the absence of global feedbacks. The MDDR scaling mechanism might be particularly beneficial during rapid proliferation, when global feedbacks are hard to implement.
机译：在多细胞生物体的发育过程中，morphogen梯度指导组织和器官的模式。在许多情况下，组织生长也需要形态发生子信号传导。增长与模式之间相互作用的后果尚不清楚。在果蝇的翼假想盘中，吗啡肽Dpp引导图案形成，并且也是组织生长所必需的。特别地，最近报道了盘中的细胞分裂与Dpp信号转导的时间增加相关。在这里，我们对生长中的组织中的形态发生素梯度形成进行数学建模，同时也考虑了形态发生素平流和稀释。我们的分析定义了一种新的缩放机制，我们将其称为吗啡依赖分裂规则（MDDR）：当细胞分裂取决于吗啡信号转导的时间增加时，吗啡梯度随组织大小的增长而缩放，组织的生长在空间上变得均匀，并且组织自然会达到有限的大小。该模型与机翼盘的许多特性是一致的。但是，我们发现MDDR与缩放缺陷型突变体的表型不一致，从而支持了Dpp信号的瞬时增加不是光盘发育后期细胞分裂的驱动因素的观点。更一般而言，我们的结果表明，即使没有全局反馈，细胞分裂与形态发生子信号的局部偶联也可导致梯度缩放和均匀生长。当全球反馈难以实施时，MDDR缩放机制在快速扩散期间可能特别有益。

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