Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation

Spatial boundaries formed during animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. The accuracy of boundary location is limited by the fluctuations of morphogen concentration that thresholds the expression level of target gene. Producing more morphogen molecules, which gives rise to smaller relative fluctuations, would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-depletion model of morphogen profile formation, the morphogen molecules synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise profile with the minimal cost,λshould be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern theDrosophilaembryo and wing imaginal disk are formed with nearly optimalλ. Our finding underscores the thermodynamic cost as a key physical constraint in the morphogen profile formation inDrosophila development.
Source: eLife - Category: Biomedical Science Tags: Developmental Biology Physics of Living Systems Source Type: research