Toward a study of gene regulatory constraints to morphological evolution of the Drosophila ocellar region

Control of size, fate and time by the Hh morphogen in the eyes of flies

Molecules of the hedgehog (hh) family are involved in the specification and patterning of eyes in vertebrates and invertebrates. These organs, though, are of very different sizes, raising the question of how Hh molecules operate at such different scales. In this paper we discuss the strategies used by Hh to control the development of the two eye types in Drosophila: the large compound eye and the small ocellus. We first describe the distinct ways in which these two eyes develop and the evidence for the key role played by Hh in both; then we consider the potential for variation in the range of action of a "typical" morphogen and measure this range ("characteristic length") for Hh in different organs, including the compound eye and the ocellus. Finally, we describe how different feedback mechanisms are used to extend the Hh range of action to pattern the large and even the small eye. In the ocellus, the basic Hh signaling pathway adds to its dynamics the attenuation of its receptor as cell differentiate. This sole regulatory change can result in the decoding of the Hh gradient by receiving cells as a wave of constant speed. Therefore, in the fly ocellus, the Hh morphogen adds to its spatial patterning role a novel one: patterning along a time axis.

Dynamic Hh signalling can generate temporal information during tissue patterning

The differentiation of tissues and organs requires that cells exchange information in space and time. Spatial information is often conveyed by morphogens: molecules that disperse across receiving cells to generate signalling gradients. Cells translate such concentration gradients into space-dependent patterns of gene expression and cellular behaviour. But could morphogen gradients also convey developmental time? Here, by investigating the developmental role of Hh on a component of the Drosophila visual system, the ocellar retina, we have discovered that ocellar cells use the non-linear gradient of Hh as a temporal cue, collectively performing the biological equivalent of a mathematical logarithmic transformation. In this way, a morphogen diffusing from a non-moving source is decoded as a wave of differentiating photoreceptors that travels at constant speed throughout the retinal epithelium.

Analysis of the transcriptional logic governing differential spatial expression in Hh target genes

This work provides theoretical tools to analyse the transcriptional effects of certain biochemical mechanisms (i.e. affinity and cooperativity) that have been proposed in previous literature to explain the proper spatial expression of Hedgehog target genes involved in Drosophila development. Specifically we have focused on the expression of decapentaplegic, wingless, stripe and patched. The transcription of these genes is believed to be controlled by enhancer modules able to interpret opposing gradients of the activator and repressor forms of the transcription factor Cubitus interruptus (Ci). This study is based on a thermodynamic approach, which provides expression rates for these genes. These expression rates are controlled by transcription factors which are competing and cooperating for common binding sites. We have made mathematical representations of the different expression rates which depend on multiple factors and variables. The expressions obtained with the model have been refined to produce simpler equivalent formulae which allow for their mathematical analysis. Thanks to this, we can evaluate the correlation between the different interactions involved in transcription and the biological features observed at tissular level. These mathematical models can be applied to other morphogenes to help understand the complex transcriptional logic of opposing activator and repressor gradients.

A Method to Categorize 2-Dimensional Patterns Using Statistics of Spatial Organization

We developed a measurement framework of spatial organization to categorize 2-dimensional patterns from 2 multiscalar biological architectures. We propose that underlying shapes of biological entities can be approached using the statistical concept of degrees of freedom, defining it through expansion of area variability in a pattern. To help scope this suggestion, we developed a mathematical argument recognizing the deep foundations of area variability in a polygonal pattern (spatial heterogeneity). This measure uses a parameter called eutacticity. Our measuring platform of spatial heterogeneity can assign particular ranges of distribution of spatial areas for 2 biological architectures: ecological patterns of Namibia fairy circles and epithelial sheets. The spatial organizations of our 2 analyzed biological architectures are demarcated by being in a particular position among spatial order and disorder. We suggest that this theoretical platform can give us some insights about the nature of shapes in biological systems to understand organizational constraints.