Perturbation analysis of a multi-morphogen Turing reaction-diffusion stripe patterning system reveals key regulatory interactions.

Periodic patterning is widespread in development and can be modelled by reaction-diffusion (RD) processes. However, minimal two-component RD descriptions are vastly simpler than the multi-molecular events that actually occur and are often hard to relate to real interactions measured experimentally. Addressing these issues, we investigated the periodic striped patterning of the rugae (transverse ridges) in the mammalian oral palate, focusing on multiple previously implicated pathways: FGF, Hh, Wnt and BMP. For each, we experimentally identified spatial patterns of activity and distinct responses of the system to inhibition. Through numerical and analytical approaches, we were able to constrain substantially the number of network structures consistent with the data. Determination of the dynamics of pattern appearance further revealed its initiation by 'activators' FGF and Wnt, and 'inhibitor' Hh, whereas BMP and mesenchyme-specific-FGF signalling were incorporated once stripes were formed. This further limited the number of possible networks. Experimental constraint thus limited the number of possible minimal networks to 154, just 0.004% of the number of possible diffusion-driven instability networks. Together, these studies articulate the principles of multi-morphogen RD patterning and demonstrate the utility of perturbation analysis for constraining RD systems.This article has an associated 'The people behind the papers' interview.

Anteroposterior patterning of the zebrafish ear through Fgf- and Hh-dependent regulation of hmx3a expression.

In the zebrafish, Fgf and Hh signalling assign anterior and posterior identity, respectively, to the poles of the developing ear. Mis-expression of fgf3 or inhibition of Hh signalling results in double-anterior ears, including ectopic expression of hmx3a. To understand how this double-anterior pattern is established, we characterised transcriptional responses in Fgf gain-of-signalling or Hh loss-of-signalling backgrounds. Mis-expression of fgf3 resulted in rapid expansion of anterior otic markers, refining over time to give the duplicated pattern. Response to Hh inhibition was very different: initial anteroposterior asymmetry was retained, with de novo duplicate expression domains appearing later. We show that Hmx3a is required for normal anterior otic patterning, and that otic patterning defects in hmx3a-/- mutants are a close phenocopy to those seen in fgf3-/- mutants. However, neither loss nor gain of hmx3a function was sufficient to generate full ear duplications. Using our data to infer a transcriptional regulatory network required for acquisition of otic anterior identity, we can recapitulate both the wild-type and the double-anterior pattern in a mathematical model.

Cellular interpretation of the long-range gradient of Four-jointed activity in the Drosophila wing.

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.

Compensatory flux changes within an endocytic trafficking network maintain thermal robustness of Notch signaling.

Developmental 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.

Positional signaling and expression of ENHANCER OF TRY AND CPC1 are tuned to increase root hair density in response to phosphate deficiency in Arabidopsis thaliana.

Phosphate (Pi) deficiency induces a multitude of responses aimed at improving the acquisition of Pi, including an increased density of root hairs. To understand the mechanisms involved in Pi deficiency-induced alterations of the root hair phenotype in Arabidopsis (Arabidopsis thaliana), we analyzed the patterning and length of root epidermal cells under control and Pi-deficient conditions in wild-type plants and in four mutants defective in the expression of master regulators of cell fate, CAPRICE (CPC), ENHANCER OF TRY AND CPC 1 (ETC1), WEREWOLF (WER) and SCRAMBLED (SCM). From this analysis we deduced that the longitudinal cell length of root epidermal cells is dependent on the correct perception of a positional signal ('cortical bias') in both control and Pi-deficient plants; mutants defective in the receptor of the signal, SCM, produced short cells characteristic of root hair-forming cells (trichoblasts). Simulating the effect of cortical bias on the time-evolving probability of cell fate supports a scenario in which a compromised positional signal delays the time point at which non-hair cells opt out the default trichoblast pathway, resulting in short, trichoblast-like non-hair cells. Collectively, our data show that Pi-deficient plants increase root hair density by the formation of shorter cells, resulting in a higher frequency of hairs per unit root length, and additional trichoblast cell fate assignment via increased expression of ETC1.

Is a persistent global bias necessary for the establishment of planar cell polarity?

Planar cell polarity (PCP)--the coordinated polarisation of a whole field of cells within the plane of a tissue-relies on the interaction of three modules: a global module that couples individual cellular polarity to the tissue axis, a local module that aligns the axis of polarisation of neighbouring cells, and a readout module that directs the correct outgrowth of PCP-regulated structures such as hairs and bristles. While much is known about the molecular components that are required for PCP, the functional details of--and interactions between--the modules remain unclear. In this work, we perform a mathematical and computational analysis of two previously proposed computational models of the local module (Amonlirdviman et al., Science, 307, 2005; Le Garrec et al., Dev. Dyn., 235, 2006). Both models can reproduce wild-type and mutant phenotypes of PCP observed in the Drosophila wing under the assumption that a tissue-wide polarity cue from the global module persists throughout the development of PCP. We demonstrate that both models can also generate tissue-level PCP when provided with only a transient initial polarity cue. However, in these models such transient cues are not sufficient to ensure robustness of the resulting cellular polarisation.

Epidermal patterning in Arabidopsis: models make a difference.

The leaf and root epidermis in Arabidopsis provide ideal systems in which to explore the mechanisms that underlie the patterned assignment of cell fates during development. Extensive experimental studies have uncovered a complex interlocked feedback network that operates within the epidermis to coordinate the choice between hair and nonhair fates. A number of recent studies using mathematical models have begun to study this network, highlighting new mechanisms that have subsequently been confirmed in model-directed experiments. These studies illustrate the potential of integrated modeling and experimentation to shed new light on developmental processes. Moreover, these models enable systems-level comparative analyses that may help understand the origin and role of properties, such as robustness and redundancy in developmental systems and, concomitantly, the evolution of development itself.

Robustness of positional specification by the Hedgehog morphogen gradient.

Spatial gradients of Hedgehog signalling play a central role in many patterning events during animal development, regulating cell fate determination and tissue growth in a variety of tissues and developmental stages. Experimental evidence suggests that many of the proteins responsible for regulating Hedgehog signalling and transport are themselves targets of Hedgehog signalling, leading to multiple levels of feedback within the system. We use mathematical modelling to analyse how these overlapping feedbacks combine to regulate patterning and potentially enhance robustness in the Drosophila wing imaginal disc. Our results predict that the regulation of Hedgehog transport and stability by glypicans, as well as multiple overlapping feedbacks in the Hedgehog response network, can combine to enhance the robustness of positional specification against variability in Hedgehog levels. We also discuss potential trade-offs between robustness and additional features of the Hedgehog gradient, such as signalling range and size regulation.

Oscillatory Notch-pathway activity in a delay model of neuronal differentiation.

Lateral inhibition resulting from a double-negative feedback loop underlies the assignment of different fates to cells in many developmental processes. Previous studies have shown that the presence of time delays in models of lateral inhibition can result in significant oscillatory transients before patterned steady states are reached. We study the impact of local feedback loops in a model of lateral inhibition based on the Notch signaling pathway, elucidating the roles of intracellular and intercellular delays in controlling the overall system behavior. The model exhibits both in-phase and out-of-phase oscillatory modes and oscillation death. Interactions between oscillatory modes can generate complex behaviors such as intermittent oscillations. Our results provide a framework for exploring the recent observation of transient Notch-pathway oscillations during fate assignment in vertebrate neurogenesis.

Oscillatory expression of Hes family transcription factors: insights from mathematical modelling.

Oscillatory expression of the Hes family of transcription factors plays a central role in the segmentation of the vertebrate body during embryonic development. Analogous oscillations in cultured cells suggest that Hes oscillations may be important in other developmental processes, and provide an excellent opportunity to explore the origin of these oscillations in a relatively simple setting. Mathematical and computational modelling have been used in combination with quantitative mRNA and protein expression data to analyse the origin and properties of Hes oscillations, and have highlighted the important roles played by time delays in negative feedback circuits. In this chapter, we review recent theoretical and experimental results, and discuss how analysis of existing models suggests potential avenues for further study of delayed feedback oscillators.

A mutual support mechanism through intercellular movement of CAPRICE and GLABRA3 can pattern the Arabidopsis root epidermis.

The patterning of the Arabidopsis root epidermis depends on a genetic regulatory network that operates both within and between cells. Genetic studies have identified a number of key components of this network, but a clear picture of the functional logic of the network is lacking. Here, we integrate existing genetic and biochemical data in a mathematical model that allows us to explore both the sufficiency of known network interactions and the extent to which additional assumptions about the model can account for wild-type and mutant data. Our model shows that an existing hypothesis concerning the autoregulation of WEREWOLF does not account fully for the expression patterns of components of the network. We confirm the lack of WEREWOLF autoregulation experimentally in transgenic plants. Rather, our modelling suggests that patterning depends on the movement of the CAPRICE and GLABRA3 transcriptional regulators between epidermal cells. Our combined modelling and experimental studies show that WEREWOLF autoregulation does not contribute to the initial patterning of epidermal cell fates in the Arabidopsis seedling root. In contrast to a patterning mechanism relying on local activation, we propose a mechanism based on lateral inhibition with feedback. The active intercellular movements of proteins that are central to our model underlie a mechanism for pattern formation in planar groups of cells that is centred on the mutual support of two cell fates rather than on local activation and lateral inhibition.

Dissecting the dynamics of the Hes1 genetic oscillator.

Serum stimulation of a number of different mouse cell lines results in sustained oscillations of Hes1, a member of this Hes/Her family of transcription factors. Quantitative time-course expression data obtained in this system provide an excellent opportunity to explore transcriptional oscillations in a relatively simple setting. Simple models of the Hes1 regulatory circuit are capable of generating oscillations that share many features with those observed in mouse fibroblasts, and highlight the central role played by delayed negative feedback. However, taking into account constraints on model parameters imposed by experimental data, these models can only generate oscillations with quite low peak-to-trough expression ratios. To explore the origin of this limitation, we develop a more detailed model of the Hes1 circuit, incorporating nucleo-cytoplasmic transport, Hes1 dimerisation, and differential stability of Hes1 monomers and dimers. We show that differential protein stability can increase the amplitude of Hes1 oscillations, but that the resulting expression profiles do not fully match experimental data. We extend the model by incorporating periodic forcing of the Hes1 circuit by cyclic phosphorylation of the protein Stat3. We show that time delays and differential stability act synergistically in this extended model to generate large amplitude oscillatory solutions that match the experimental data well.

Identifying dynamical modules from genetic regulatory systems: applications to the segment polarity network.

BACKGROUND: It is widely accepted that genetic regulatory systems are 'modular', in that the whole system is made up of smaller 'subsystems' corresponding to specific biological functions. Most attempts to identify modules in genetic regulatory systems have relied on the topology of the underlying network. However, it is the temporal activity (dynamics) of genes and proteins that corresponds to biological functions, and hence it is dynamics that we focus on here for identifying subsystems. RESULTS: Using Boolean network models as an exemplar, we present a new technique to identify subsystems, based on their dynamical properties. The main part of the method depends only on the stable dynamics (attractors) of the system, thus requiring no prior knowledge of the underlying network. However, knowledge of the logical relationships between the network components can be used to describe how each subsystem is regulated. To demonstrate its applicability to genetic regulatory systems, we apply the method to a model of the Drosophila segment polarity network, providing a detailed breakdown of the system. CONCLUSION: We have designed a technique for decomposing any set of discrete-state, discrete-time attractors into subsystems. Having a suitable mathematical model also allows us to describe how each subsystem is regulated and how robust each subsystem is against perturbations. However, since the subsystems are found directly from the attractors, a mathematical model or underlying network topology is not necessarily required to identify them, potentially allowing the method to be applied directly to experimental expression data.

Speed of reaction diffusion in embryogenesis.

Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns formed and the robustness of pattern selection, much less is known about the time scales required for pattern formation. Studies of gradient formation by the diffusion of a single morphogen from a localized source have shown that patterning can occur on realistic time scales over distances of a millimeter or less. Reaction diffusion has the potential to give rise to patterns on a faster time scale, since all points in the domain can act as sources of morphogen. However, the speed at which patterning can occur has hitherto not been explored in depth. In this paper, we investigate this issue in specific reaction diffusion models and address the question of whether patterning via reaction diffusion is fast enough to be applicable to morphogenesis.

Oscillatory expression of Hes1, p53, and NF-kappaB driven by transcriptional time delays.

Feedback inhibition of gene expression is a widespread phenomenon in which the expression of a gene is downregulated by its protein product. Feedback in eukaryotic cells involves time delays resulting from transcription, transcript splicing and processing, and protein synthesis. In principle, such delays can result in oscillatory mRNA and protein expression. However, experimental evidence of such delay-driven oscillations has been lacking. Using mathematical modeling informed by recent data, I show that the observed oscillatory expression and activity of three proteins is most likely to be driven by transcriptional delays. Each protein (Hes1, p53, and NF-kappaB) is a component of a short feedback inhibition loop. The oscillatory period is determined by the delay and the protein and mRNA half-lives, but it is robust to changes in the rates of transcription and protein synthesis. In contrast to nondelayed models, delayed models do not require additional components in the feedback loop. These results provide direct evidence that transcriptional delays can drive oscillatory gene activity and highlight the importance of considering delays when analyzing genetic regulatory networks, particularly in processes such as developmental pattern formation, where short half-lives and feedback inhibition are common.