Predicting embryonic patterning using mutual entropy fitness and in silico evolution

Abstract

SUMMARYDuring vertebrate embryogenesis, the expression of Hox genes that define anterior-posterior identity follows general rules: temporal colinearity and posterior prevalence. A mathematical measure for the quality or fitness of the embryonic pattern produced by a gene regulatory network is derived. Using this measure and in silico evolution we derive gene interaction networks for anterior-posterior (AP) patterning under two developmental paradigms. For patterning during growth (paradigm I), which is appropriate for vertebrates and short germ-band insects, the algorithm creates gene expression patterns reminiscent of Hox gene expression. The networks operate through a timer gene, the level of which measures developmental progression (a candidate is the widely conserved posterior morphogen Caudal). The timer gene provides a simple mechanism to coordinate patterning with growth rate. The timer, when expressed as a static spatial gradient, functions as a classical morphogen (paradigm II), providing a natural way to derive the AP patterning, as seen in long germ-band insects that express their Hox genes simultaneously, from the ancestral short germ-band system. Although the biochemistry of Hox regulation in higher vertebrates is complex, the actual spatiotemporal expression phenotype is not, and simple activation and repression by Hill functions suffices in our model. In silico evolution provides a quantitative demonstration that continuous positive selection can generate complex phenotypes from simple components by incremental evolution, as Darwin proposed.

Evolving phenotypic networks in silico

“…We have used computational evolution for many other problems, including multi stability and oscillators [12], embryonic timing and patterning [19], temperature compensation for circadian clocks [20], Pareto evolution of networks with asymmetric response time [18].…”

Drivers of structural features in gene regulatory networks: From biophysical constraints to biological function

“…6) and mathematical analyses have been used to quantify the consequences of gene duplications on the distribution of degrees of the associated networks [70]. Furthermore, using evolutionary simulations, gene duplication events were shown to be crucial for the evolution of phenotypes consisting of spatial patterning [71].…”

Information as a Manifestation of Development

“…Finally, in a very interesting recent study Francois and Siggia used an information theoretic measure to quantify fitness of computationally simulated developmental gene regulatory networks that were allowed to evolve in silico [49]. Remarkably, this analysis showed that standard (incremental) Darwinian selection for increased fitness can produce gene regulatory networks that developmentally generate axial segmentation, much as occurs in arthropods and vertebrates with Hox genes [30], and involving similar rules and phenomenology [49].…”

“…Remarkably, this analysis showed that standard (incremental) Darwinian selection for increased fitness can produce gene regulatory networks that developmentally generate axial segmentation, much as occurs in arthropods and vertebrates with Hox genes [30], and involving similar rules and phenomenology [49].…”