Threshold Response to Stochasticity in Morphogenesis

During development of biological organisms, multiple complex structures are formed. In many instances, these structures must exhibit a high degree of order to be functional, although their constituents are intrinsically stochastic. Hence, it has been suggested that biological robustness ultimately relies on clean-up mechanisms. In the context of the Drosophila eye disc, multiple optical units, ommatidia, are positioned in a crystal-like fashion. During the larva-to-pupa-stage of the eye disc development, the centers of the ommatidia are first specified via differentiation of R8 cells by reaction and diffusion of morphogens. Subsequently, the spatial configuration of R8 cells is refined via diffusion of cell proliferation and apoptosis. In this talk, I present our mathematical modeling of these spatio-temporal processes, including measures that quantify order of the resulting patterns in the presence of noise. We observe an interesting universal sigmoidal response to increasing stochasticity: ordered patterns persist up to a threshold noise level in the model parameters. We argue that this sigmoidal dependence is indicative of cryptic variation, whereby underlying differences in gene expression between wild type organisms exist, but do not lead to different phenotypes.