Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2014 Mar 11;111(10):3683-8.
doi: 10.1073/pnas.1324186111. Epub 2014 Feb 10.

Morphogenesis at criticality

Dmitry Krotov  1 , Julien O Dubuis, Thomas Gregor, William Bialek
Affiliations

Morphogenesis at criticality

Dmitry Krotov et al. Proc Natl Acad Sci U S A. .

Abstract

Spatial patterns in the early fruit fly embryo emerge from a network of interactions among transcription factors, the gap genes, driven by maternal inputs. Such networks can exhibit many qualitatively different behaviors, separated by critical surfaces. At criticality, we should observe strong correlations in the fluctuations of different genes around their mean expression levels, a slowing of the dynamics along some but not all directions in the space of possible expression levels, correlations of expression fluctuations over long distances in the embryo, and departures from a Gaussian distribution of these fluctuations. Analysis of recent experiments on the gap gene network shows that all these signatures are observed, and that the different signatures are related in ways predicted by theory. Although there might be other explanations for these individual phenomena, the confluence of evidence suggests that this genetic network is tuned to criticality.

Keywords: Drosophila embryo; genetic networks.

PubMed Disclaimer

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Normalized gap gene expression levels in the early Drosophila embryo, from ref. . Measurements by simultaneous immunofluorescent staining of all four proteins, along the dorsal edge of the midsagittal plane of the embryo, 38–49 min into nuclear cycle 14; error bars are SDs across [Image: see text] embryos. (Upper Left) Expanded view of the shaded regions, near the crossings between Hb and Kr levels, where just these two genes have significant expression, and similarly for the Kr–Kni, Kni–Gt, and Gt–Hb crossings (Upper) from left to right.
Fig. 2.
Fig. 2.
Fluctuations in gap gene expression levels. (A) Pairwise correlation coefficients between fluctuations in the different gap genes vs. anterior–posterior position, from the same data as in Fig 1 (7). Mean expression levels at top to guide the eye, colors as in Fig 1; error bars are from bootstrap analysis. Correlations which are not significant at [Image: see text] are shown as zero. Major crossing points of the mean expression profiles are labeled A, B, C, and D; other points marked as described in the text. (B) Scatter plot of expression levels for pairs of genes in individual embryos: Kr vs. Hb at point A (gray circles), Kni vs. Kr at point B (blue diamonds), Gt vs. Kni at point C (green squares), and Hb vs. Gt at point D (red triangles). (C) Probability distribution of expression fluctuations. In each of the crossing regions from Fig 1, we form the combinations [Image: see text] (fast modes, cyan) and [Image: see text] (slow modes, magenta), and normalize the fluctuations across embryos to have unit variance at each position. Data from all four regions are pooled to estimate the distributions; error bars are from random divisions of the set of 24 embryos. Gaussian distribution (black) shown for comparison.
Fig. 3.
Fig. 3.
Dynamics at the Hb–Kr crossing point. (A) Normalized expression levels of the individual genes, plotted vs. time during nuclear cycle 14; data from ref. . (B) Linear combinations of expression levels corresponding to the small variance (fast) and large variance (slow) directions in Fig 2B. Curves are best-fit single exponentials for each mode and are also shown projected back into the individual expression levels in A. Eigenvalues, as in Eq. 5, are [Image: see text] and [Image: see text].
Fig. 4.
Fig. 4.
Spatial correlations of the fluctuations in gene expression. (A) Autocorrelations of slow (magenta) and fast (cyan) modes near the Hb–Kr crossing, as defined in Eq. 11. Line shows a fit to the exponential form in Eq. 10 with [Image: see text]. (B) Correlations between the slow mode at the Hb–Kr crossing and slow modes at other crossings, as defined in Eq. 14, indicated by the colors. All correlation functions are evaluated at [Image: see text] with y varying as shown. Middle peak is the same (auto-)correlation function [Image: see text] as in A. Dashed line corresponds to Eq. 10 with [Image: see text].
See this image and copyright information in PMC

References

    1. Hasty J, McMillen D, Isaacs F, Collins JJ. Computational studies of gene regulatory networks: In numero molecular biology. Nat Rev Genet. 2001;2(4):268–279. - PubMed
    1. Gardner TS, Cantor CR, Collins JJ. Construction of a genetic toggle switch in Escherichia coli. Nature. 2000;403(6767):339–342. - PubMed
    1. Nüsslein-Volhard C, Wieschaus EF. Mutations affecting segment number and polarity in Drosophila. Nature. 1980;287(5785):795–801. - PubMed
    1. Lawrence PA. The Making of a Fly: The Genetics of Animal Design. Oxford: Blackwell Scientific; 1992.
    1. Gerhardt J, Kirschner M. Cells, Embryos, and Evolution. Malden, MA: Blackwell Science; 1997.

Publication types

MeSH terms

LinkOut - more resources