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TITLE Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation
KIAS AUTHORS Hyeon, Changbong,Song, Yonghyun
JOURNAL ELIFE, 2021
ARCHIVE not preprint. SCI
ABSTRACT Spatial boundaries formed during animal development originate from the prepatterning 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 lambda. Our theory suggests that in order to attain a precise profile with the minimal cost, lambda should be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern the Drosophila embryo and wing imaginal disk are formed with nearly optimal lambda. Our finding underscores the cost-effectiveness of precise morphogen profile formation in Drosophila development.
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