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During development of biological organisms, multiple complex structures areformed. In many instances, these structures need to exhibit a high degree oforder to be functional, although many of their constituents are intrinsicallystochastic. Hence, it has been suggested that biological robustness ultimatelymust rely on complex gene regulatory networks and clean-up mechanisms. Here weexplore developmental processes that have evolved inherent robustness againststochasticity. In the context of the Drosophila eye disc, multiple opticalunits, ommatidia, develop into crystal-like patterns. During the larva-to-pupastage of metamorphosis, the centers of the ommatidia are specified initiallythrough the diffusion of morphogens, followed by the specification of R8 cells.Establishing the R8 cell is crucial in setting up the geometric, andfunctional, relationships of cells within an ommatidium and among neighboringommatidia. Here we study a mathematical model of these spatio-temporalprocesses in the presence of stochasticity, defining and applying measures thatquantify order within the resulting spatial patterns. We observe a universalsigmoidal response to increasing transcriptional noise. Ordered patternspersist up to a threshold noise level in the model parameters. As the noise isfurther increased past a threshold point of no return, these ordered patternsrapidly become disordered. Such robustness in development allows for theaccumulation of genetic variation without any observable changes in phenotype.We argue that the observed sigmoidal dependence introduces robustness allowingfor sizable amounts of genetic variation and transcriptional noise to betolerated in natural populations without resulting in phenotype variation.

Threshold Response to Stochasticity in Morphogenesis