Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation
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.
Data availability
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.
Article and author information
Author details
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.
Copyright
© 2021, Song & Hyeon
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.
Metrics
-
- 1,257
- views
-
- 212
- downloads
-
- 8
- citations
Views, downloads and citations are aggregated across all versions of this paper published by eLife.
Download links
Downloads (link to download the article as PDF)
Open citations (links to open the citations from this article in various online reference manager services)
Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)
Further reading
-
- Developmental Biology
- Genetics and Genomics
The establishment and growth of the arterial endothelium requires the coordinated expression of numerous genes. However, regulation of this process is not yet fully understood. Here, we combined in silico analysis with transgenic mice and zebrafish models to characterize arterial-specific enhancers associated with eight key arterial identity genes (Acvrl1/Alk1, Cxcr4, Cxcl12, Efnb2, Gja4/Cx37, Gja5/Cx40, Nrp1 and Unc5b). Next, to elucidate the regulatory pathways upstream of arterial gene transcription, we investigated the transcription factors binding each arterial enhancer compared to a similar assessment of non-arterial endothelial enhancers. These results found that binding of SOXF and ETS factors was a common occurrence at both arterial and pan-endothelial enhancers, suggesting neither are sufficient to direct arterial specificity. Conversely, FOX motifs independent of ETS motifs were over-represented at arterial enhancers. Further, MEF2 and RBPJ binding was enriched but not ubiquitous at arterial enhancers, potentially linked to specific patterns of behaviour within the arterial endothelium. Lastly, there was no shared or arterial-specific signature for WNT-associated TCF/LEF, TGFβ/BMP-associated SMAD1/5 and SMAD2/3, shear stress-associated KLF4 or venous-enriched NR2F2. This cohort of well characterized and in vivo-verified enhancers can now provide a platform for future studies into the interaction of different transcriptional and signalling pathways with arterial gene expression.
-
- Developmental Biology
- Genetics and Genomics
Paternal obesity has been implicated in adult-onset metabolic disease in offspring. However, the molecular mechanisms driving these paternal effects and the developmental processes involved remain poorly understood. One underexplored possibility is the role of paternally induced effects on placenta development and function. To address this, we investigated paternal high-fat diet-induced obesity in relation to sperm histone H3 lysine 4 tri-methylation signatures, the placenta transcriptome, and cellular composition. C57BL6/J male mice were fed either a control or high-fat diet for 10 weeks beginning at 6 weeks of age. Males were timed-mated with control-fed C57BL6/J females to generate pregnancies, followed by collection of sperm, and placentas at embryonic day (E)14.5. Chromatin immunoprecipitation targeting histone H3 lysine 4 tri-methylation (H3K4me3) followed by sequencing (ChIP-seq) was performed on sperm to define obesity-associated changes in enrichment. Paternal obesity corresponded with altered sperm H3K4me3 at promoters of genes involved in metabolism and development. Notably, altered sperm H3K4me3 was also localized at placental enhancers. Bulk RNA-sequencing on placentas revealed paternal obesity-associated sex-specific changes in expression of genes involved in hypoxic processes such as angiogenesis, nutrient transport, and imprinted genes, with a subset of de-regulated genes showing changes in H3K4me3 in sperm at corresponding promoters. Paternal obesity was also linked to impaired placenta development; specifically, a deconvolution analysis revealed altered trophoblast cell lineage specification. These findings implicate paternal obesity effects on placenta development and function as one potential developmental route to offspring metabolic disease.