Secreted growth factors can act as morphogens that form spatial concentration gradients in developing organs, thereby controlling growth and patterning. For some morphogens, adaptation of the gradients to tissue size allows morphological patterns to remain proportioned as the organs grow. In the zebrafish pectoral fin, we found that BMP signaling forms a two-dimensional gradient. The length of the gradient scales with tissue length and its amplitude increases with fin size according to a power-law. Gradient scaling and amplitude power-laws are signatures of growth control by time derivatives of morphogenetic signaling: cell division correlates with the fold change over time of the cellular signaling levels. We show that Smoc1 regulates BMP gradient scaling and growth in the fin. Smoc1 scales the gradient by means of a feedback loop: Smoc1 is a BMP agonist and BMP signaling represses Smoc1 expression. Our work uncovers a layer of morphogen regulation during vertebrate appendage development.

分泌的生长因子可以充当形态发生子，在发育中的器官中形成空间浓度梯度，从而控制生长和模式。对于某些形态发生因子，梯度对组织大小的适应性使形态模式随着器官的生长而保持成比例。在斑马鱼的胸鳍中，我们发现BMP信号形成二维梯度。梯度的长度与组织长度成比例，并且其幅度根据鳍的大小随幂律而增加。梯度定标和幅度幂律是通过形态发生信号的时间导数进行生长控制的标志：细胞分裂与细胞信号水平随时间的倍数变化相关。我们显示Smoc1调节鳍中BMP梯度缩放和增长。Smoc1通过反馈回路缩放梯度：Smoc1是BMP激动剂，BMP信号传导抑制Smoc1表达。我们的工作揭示了脊椎动物附肢发育过程中的形态发生子调控层。