Scaling of morphogen gradients by an expansion-repression integral feedback control

Despite substantial size variations, proportions of the developing body plan are maintained with a remarkable precision. Little is known about the mechanisms that ensure this adaptation (scaling) of pattern with size. Most models of patterning by morphogen gradients do not support scaling. In contrast, we show that scaling arises naturally in a general feedback topology, in which the range of the morphogen gradient increases with the abundance of some diffusible molecule, whose production, in turn, is repressed by morphogen signaling. We term this mechanism "expansion-repression" and show that it can function within a wide range of biological scenarios. The expansion-repression scaling mechanism is analogous to an integral-feedback controller, a key concept in engineering that is likely to be instrumental also in maintaining biological homeostasis.