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

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Abstract

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, λ 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 λ. Our finding underscores the thermodynamic cost as a key physical constraint in the morphogen profile formation in Drosophila development.

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All data analyzed in this study are from the figures of previously published works, shown in Figure 2-S1 and Appendix 2 Figure 3. The reference associated with each panel is provided in the respective figure legend.

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Yonghyun Song

Korea Institute for Advanced Study, Seoul, Republic of Korea

Competing interests
The authors declare that no competing interests exist.
Changbong Hyeon

Korea Institute for Advanced Study, Seoul, Republic of Korea

For correspondence
hyeoncb@kias.re.kr

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0002-4844-7237

Funding

Korea Institute for Advanced Study (CG067102)

Yonghyun Song

Korea Institute for Advanced Study (CG035003)

Changbong Hyeon

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

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This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.