SummaryDevelopmental signaling is remarkably robust to environmental variation, including temperature. For example, in ectothermic animals such as Drosophila, Notch signaling is maintained within functional limits across a wide temperature range. We combine experimental and computational approaches to show that temperature compensation of Notch signaling is achieved by an unexpected variety of endocytic-dependent routes to Notch activation which, when superimposed on ligand-induced activation, act as a robustness module. Thermal compensation arises through an altered balance of fluxes within competing trafficking routes, coupled with temperature-dependent ubiquitination of Notch. This flexible ensemble of trafficking routes supports Notch signaling at low temperature but can be switched to restrain Notch signaling at high temperature and thus compensates for the inherent temperature sensitivity of ligand-induced activation. The outcome is to extend the physiological range over which normal development can occur. Similar mechanisms may provide thermal robustness for other developmental signals.

In this paper, we illustrate how dynamical systems theory can provide a unifying conceptual framework for evolution of biological regulatory systems. Our argument is that the genotype-phenotype map can be characterized by the phase portrait of the underlying regulatory process. The features of this portrait -such as attractors with associated basins and their bifurcations -define the regulatory and evolutionary potential of a system. We show how the geometric analysis of phase space connects Waddington's epigenetic landscape to recent computational approaches for the study of robustness and evolvability in network evolution. We discuss how the geometry of phase space determines the probability of possible phenotypic transitions. Finally, we demonstrate how the active, self-organizing role of the environment in phenotypic evolution can be understood in terms of dynamical systems concepts. This approach yields mechanistic explanations that go beyond insights based on the simulation of evolving regulatory networks alone. Its predictions can now be tested by studying specific, experimentally tractable regulatory systems using the tools of modern systems biology. A systematic exploration of such systems will enable us to understand better the nature and origin of the phenotypic variability, which provides the substrate for evolution by natural selection.

Spontaneous pattern formation in reaction-diffusion systems on a spatially homogeneous domain has been well studied. However, in embryonic development and elsewhere, pattern formation often takes place on a spatially heterogeneous background. We explore the effects of spatially varying parameters on pattern formation in one and two dimensions using the Gierer-Meinhardt reaction-diffusion model. We investigate the effect of the wavelength of a pre-pattern and demonstrate a novel form of moving pattern. We find that spatially heterogeneous parameters can both increase the range and complexity of possible patterns and enhance the robustness of pattern selection.

To understand how long-range patterning gradients are interpreted at the cellular level, we investigate how a gradient of expression of the Four-jointed kinase specifies planar polarised distributions of the cadherins Fat and Dachsous in the Drosophila wing. We use computational modelling to test different scenarios for how Four-jointed might act and test the model predictions by employing fluorescence recovery after photobleaching as an in vivo assay to measure the influence of Four-jointed on Fat-Dachsous binding. We demonstrate that in vivo, Four-jointed acts both on Fat to promote its binding to Dachsous and on Dachsous to inhibit its binding to Fat, with a bias towards a stronger effect on Fat. Overall, we show that opposing gradients of Fat and Dachsous phosphorylation are sufficient to explain the observed pattern of Fat–Dachsous binding and planar polarisation across the wing, and thus demonstrate the mechanism by which a long-range gradient is interpreted.DOI: http://dx.doi.org/10.7554/eLife.05789.001