Abstract
While most processes in biology are highly deterministic, stochastic mechanisms are sometimes used to increase cellular diversity. In human and Drosophila eyes, photoreceptors sensitive to different wavelengths of light are distributed in stochastic patterns, and one such patterning system has been analyzed in detail in the Drosophila retina. Interestingly, some species in the dipteran family Dolichopodidae (the “long legged” flies, or “Doli”) instead exhibit highly orderly deterministic eye patterns. In these species, alternating columns of ommatidia (unit eyes) produce corneal lenses of different colors. Occasional perturbations in some individuals disrupt the regular columns in a way that suggests that patterning occurs via a posterior-to-anterior signaling relay during development, and that specification follows a local, cellular-automaton-like rule. We hypothesize that the regulatory mechanisms that pattern the eye are largely conserved among flies and that the difference between unordered Drosophila and ordered dolichopodid eyes can be explained in terms of relative strengths of signaling interactions rather than a rewiring of the regulatory network itself. We present a simple stochastic model that is capable of explaining both the stochastic Drosophila eye and the striped pattern of Dolichopodidae eyes and thereby characterize the least number of underlying developmental rules necessary to produce both stochastic and deterministic patterns. We show that only small changes to model parameters are needed to also reproduce intermediate, semi-random patterns observed in another Doli species, and quantification of ommatidial distributions in these eyes suggests that their patterning follows similar rules.
Highlights
The development of multicellular animals is highly reproducible, with deterministic and orderly processes generating reliable outcomes
Our simulations (Fig 2d) agree qualitatively with the image of a real fly shown in Fig 1d; a detailed experimental study of its geometrical correlations needs to be performed to get more quantitative agreement. This formalism allows us to present a generic phase diagram (Fig 4), in which any given fly eye can be defined; the specific location, along with the theory above, enables us to identify the specific mechanisms associated with the morphogenesis, e.g. whether the fly is derived from a perturbation of the Uniform Fly, the hypothetical fly with completely ordered eye colors, or from Doli, and so on
Statistical physics can be usefully applied to biology when searching for organizational principles [25,26,27]
Summary
The development of multicellular animals is highly reproducible, with deterministic and orderly processes generating reliable outcomes. The generation of the very different patterns observed might be due to changes in the initial expression of Ss. In this paper, we Patterning the insect eye present a simple mathematical model that captures the essence of these ideas, by attributing the diverse patterning in the three fly species (stochastic, ordered and semi-ordered) to a single switching mechanism.
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