Morphogenesis at criticality

Dmitry Krotov, Julien O. Dubuis, Thomas Gregor, and William Bialek. PNAS 111 (10): 3683–3688 (2014).

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 genes shows that all these signatures are observed, and that the different signatures are related in ways predicted by theory. While there might be other explanations for these individual phenomena, the confluence of evidence suggests that this genetic network is tuned to criticality.

Significance: Biological networks are described by many parameters, and the behavior of a network is qualitatively different (mono- stable, bistable, oscillating, etc.) in different parts of parameter space. Critical points and surfaces are the borders between such qualitatively different regimes, as with phase transitions in equilibrium thermodynamics. We argue that, as expected from the thermodynamic case, genetic regulatory networks should exhibit behaviors near criticality that are independent of most molecular details. Analyzing recent experiments on the gap gene network in the early Drosophila embryo, we find that these signatures of criticality can be seen, quantitatively. This raises the question of why evolution has tuned this network to such a special point in its parameter space.

PDF of final PNAS version.

PDF of an earlier arXiv version ( [q-bio.MN]).

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