A mathematical investigation of a Clock and Wavefront model for somitogenesis

Somites are transient blocks of cells that form sequentially along the antero-posterior axis of vertebrate embryos. They give rise to the vertebrae, ribs and other associated features of the trunk. In this work we develop and analyse a mathematical formulation of a version of the Clock and Wavefront model for somite formation, where the clock controls when the boundaries of the somites form and the wavefront determines where they form. Our analysis indicates that this interaction between a segmentation clock and a wavefront can explain the periodic pattern of somites observed in normal embryos. We can also show that a simplification of the model provides a mechanism for predicting the anomalies resulting from perturbation of the wavefront.     

Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways

The formation of somites in the course of vertebrate segmentation is governed by an oscillator known as the segmentation clock, which is characterized by a period ranging from 30 min to a few hours depending on the organism. This oscillator permits the synchronized activation of segmentation genes in successive cohorts of cells in the presomitic mesoderm in response to a periodic signal emitted by the segmentation clock, thereby defining the future segments. Recent microarray experiments [Dequeant, M.L., Glynn, E., Gaudenz, K., Wahl, M., Chen, J., Mushegian, A., Pourquie, O., 2006. A complex oscillating network of signaling genes underlies the mouse segmentation clock. Science 314, 1595-1598] indicate that the Notch, Wnt and Fibroblast Growth Factor (FGF) signaling pathways are involved in the mechanism of the segmentation clock. By means of computational modeling, we investigate the conditions in which sustained oscillations occur in these three signaling pathways. First we show that negative feedback mediated by the Lunatic Fringe protein on intracellular Notch activation can give rise to periodic behavior in the Notch pathway. We then show that negative feedback exerted by Axin2 on the degradation of β-catenin through formation of the Axin2 destruction complex can produce oscillations in the Wnt pathway. Likewise, negative feedback on FGF signaling mediated by the phosphatase product of the gene MKP3/Dusp6 can produce oscillatory gene expression in the FGF pathway. Coupling the Wnt, Notch and FGF oscillators through common intermediates can lead to synchronized oscillations in the three signaling pathways or to complex periodic behavior, depending on the relative periods of oscillations in the three pathways. The phase relationships between cycling genes in the three pathways depend on the nature of the coupling between the pathways and on their relative autonomous periods. The model provides a framework for analyzing the dynamics of the segmentation clock in terms of a network of oscillating modules involving the Wnt, Notch and FGF signaling pathways.     

The clock and wavefront model revisited

The currently accepted interpretation of the clock and wavefront model of somitogenesis is that a posteriorly moving molecular gradient sequentially slows the rate of clock oscillations, resulting in a spatial readout of temporal oscillations. However, while molecular components of the clocks and wavefronts have now been identified in the pre-somitic mesoderm (PSM), there is not yet conclusive evidence demonstrating that the observed molecular wavefronts act to slow clock oscillations. Here we present an alternative formulation of the clock and wavefront model in which oscillator coupling, already known to play a key role in oscillator synchronisation, plays a fundamentally important role in the slowing of oscillations along the anterior-posterior (AP) axis. Our model has three parameters which can be determined, in any given species, by the measurement of three quantities: the clock period in the posterior PSM, somite length and the length of the PSM. A travelling wavefront, which slows oscillations along the AP axis, is an emergent feature of the model. Using the model we predict: (a) the distance between moving stripes of gene expression; (b) the number of moving stripes of gene expression and (c) the oscillator period profile along the AP axis. Predictions regarding the stripe data are verified using existing zebrafish data. We simulate a range of experimental perturbations and demonstrate how the model can be used to unambiguously define a reference frame along the AP axis. Comparing data from zebrafish, chick, mouse and snake, we demonstrate that: (a) variation in patterning profiles is accounted for by a single nondimensional parameter; the ratio of coupling strengths; and (b) the period profile along the AP axis is conserved across species. Thus the model is consistent with the idea that, although the genes involved in pattern propagation in the PSM vary, there is a conserved patterning mechanism across species.     

FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation

Vertebrate segmentation requires a molecular oscillator, the segmentation clock, acting in presomitic mesoderm (PSM) cells to set the pace at which segmental boundaries are laid down. However, the signals that position each boundary remain unclear. Here, we report that FGF8 which is expressed in the posterior PSM, generates a moving wavefront at which level both segment boundary position and axial identity become determined. Furthermore, by manipulating boundary position in the chick embryo, we show that Hox gene expression is maintained in the appropriately numbered somite rather than at an absolute axial position. These results implicate FGF8 in ensuring tight coordination of the segmentation process and spatiotemporal Hox gene activation.     

Vertebrate segmentation: from cyclic gene networks to scoliosis

One of the most striking features of the human vertebral column is its periodic organization along the anterior-posterior axis. This pattern is established when segments of vertebrates, called somites, bud off at a defined pace from the anterior tip of the embryo's presomitic mesoderm (PSM). To trigger this rhythmic production of somites, three major signaling pathways--Notch, Wnt/β-catenin, and fibroblast growth factor (FGF)--integrate into a molecular network that generates a traveling wave of gene expression along the embryonic axis, called the "segmentation clock." Recent systems approaches have begun identifying specific signaling circuits within the network that set the pace of the oscillations, synchronize gene expression cycles in neighboring cells, and contribute to the robustness and bilateral symmetry of somite formation. These findings establish a new model for vertebrate segmentation and provide a conceptual framework to explain human diseases of the spine, such as congenital scoliosis.     

Oscillations of the snail genes in the presomitic mesoderm coordinate segmental patterning and morphogenesis in vertebrate somitogenesis

The segmented body plan of vertebrate embryos arises through segmentation of the paraxial mesoderm to form somites. The tight temporal and spatial control underlying this process of somitogenesis is regulated by the segmentation clock and the FGF signaling wavefront. Here, we report the cyclic mRNA expression of Snail 1 and Snail 2 in the mouse and chick presomitic mesoderm (PSM), respectively. Whereas Snail genes' oscillations are independent of NOTCH signaling, we show that they require WNT and FGF signaling. Overexpressing Snail 2 in the chick embryo prevents cyclic Lfng and Meso 1 expression in the PSM and disrupts somite formation. Moreover, cells mis-expressing Snail 2 fail to express Paraxis, remain mesenchymal, and are thereby inhibited from undergoing the epithelialization event that culminates in the formation of the epithelial somite. Thus, Snail genes define a class of cyclic genes that coordinate segmentation and PSM morphogenesis.     

Evolution of the Role of RA and FGF Signals in the Control of Somitogenesis in Chordates

During vertebrate development, the paraxial mesoderm becomes segmented, forming somites that will give rise to dermis, axial skeleton and skeletal muscles. Although recently challenged, the "clock and wavefront" model for somitogenesis explains how interactions between several cell-cell communication pathways, including the FGF, RA, Wnt and Notch signals, control the formation of these bilateral symmetric blocks. In the cephalochordate amphioxus, which belongs to the chordate phylum together with tunicates and vertebrates, the dorsal paraxial mesendoderm also periodically forms somites, although this process is asymmetric and extends along the whole body. It has been previously shown that the formation of the most anterior somites in amphioxus is dependent upon FGF signalling. However, the signals controlling somitogenesis during posterior elongation in amphioxus are still unknown. Here we show that, contrary to vertebrates, RA and FGF signals act independently during posterior elongation and that they are not mandatory for posterior somites to form. Moreover, we show that RA is not able to buffer the left/right asymmetry machinery that is controlled through the asymmetric expression of Nodal pathway actors. Our results give new insights into the evolution of the somitogenesis process in chordates. They suggest that RA and FGF pathways have acquired specific functions in the control of somitogenesis in vertebrates. We propose that the "clock and wavefront" system was selected specifically in vertebrates in parallel to the development of more complex somite-derived structures but that it was not required for somitogenesis in the ancestor of chordates.     

A proposed mechanism for the interaction of the segmentation clock and the determination front in somitogenesis

Background

Recent discoveries in the field of somitogenesis have confirmed, for the most part, the feasibility of the clock and wavefront model. There are good candidates for both the clock (various genes expressed cyclically in the tail bud of vertebrate embryos have been discovered) and the wavefront (there are at least three different substances, whose expression levels vary along the presomitic mesoderm [PSM], that have important effects on the formation of somites). Nevertheless, the mechanisms through which the wavefront interacts with the clock to arrest the oscillations and induce somite formation have not yet been fully elucidated.

Principal Findings

In this work, we propose a gene regulatory network which is consistent with all known experimental facts in embryonic mice, and whose dynamic behaviour provides a potential explanation for the periodic aggregation of PSM cells into blocks: the first step leading to the formation of somites.

Significance

To our knowledge, this is the first proposed mechanism that fully explains how a block of PSM cells can stop oscillating simultaneously, and how this process is repeated periodically, via the interaction of the segmentation clock and the determination front.     

The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways

In the last few years, the efforts to elucidate the mechanisms underlying the segmentation clock in various vertebrate species have multiplied. Early evidence suggested that oscillations are caused by one of the genes under the Notch signalling pathway (like those of the her or Hes families). Recently, Aulehla et al. [Wnt3a plays a major role in the segmentation clock controlling somitogenesis. Dev. Cell 4, 395-406] discovered that Axin2 (a gene under the Wnt3a signalling pathway) also oscillates in the presomitic mesoderm (PSM) of mice embryos and proposed some mechanisms through which the Notch and Wnt3a pathways may interact. They further suggested that a decreasing concentration of Wnt3a along the PSM may be the gradient the segmentation clock interacts with to form somites. These results were reviewed by Rida et al. [A notch feeling of somite segmentation and beyond. Dev. Biol. 265, 2-22], who introduced a complex clockwork comprising genes Hes1, Lfng (under the Notch pathway), and Axin2, as well as their multiple interactions. In the present work we develop a mathematical model based on the Rida et al. review and use it to tackle some of the questions raided by the Aulehla et al. paper: can the Axin2 feedback loop constitute a clock? Could a decreasing Wnt3a signaling constitute the wavefront, where phase is recorded and the spatial pattern laid down? What is the master oscillator?     

Heterochrony in somitogenesis rate in a model marsupial,Monodelphis domestica

Marsupial newborns are highly altricial and also show a wide array of shifts in the rate or timing of developmental events so that certain neonatal structures are quite mature. One particularly notable feature is the steep gradient in development along the anterior–posterior axis such that anterior structures are generally well developed relative to posterior ones. Here, we study somitogenesis in the marsupial, Monodelphis domestica, and document two heterochronies that may be important in generating the unusual body plan of the newborn marsupial. First, we demonstrate a 4‐fold change in somitogenesis rate along the anterior–posterior axis, which appears to be due to somitogenesis slowing posteriorly. Second, we show that somitogenesis, particularly in the cervical region, initiates earlier in Monodelphis relative to other developmental events in the embryo. The early initiation of somitogenesis may contribute to the early development of the cervical region and forelimbs. Other elements of somitogenesis appear to be conserved. When compared to mouse, we see similar expression of genes involved in the clock and wavefront, and genes of the Wnt, Notch, and fibroblast growth factor (FGF) pathways also cycle in Monodelphis. Further, we could not discern differences in somite maturation rate along the anterior–posterior axis in Monodelphis, and thus rate of maturation of the somites does not appear to contribute to the steep anterior–posterior gradient.     

The vertebrate segmentation clock and its role in skeletal birth defects

The segmental structure of the vertebrate body plan is most evident in the axial skeleton. The regulated generation of somites, a process called somitogenesis, underlies the vertebrate body plan and is crucial for proper skeletal development. A genetic clock regulates this process, controlling the timing of somite development. Molecular evidence for the existence of the segmentation clock was first described in the expression of Notch signaling pathway members, several of which are expressed in a cyclic fashion in the presomitic mesoderm (PSM). The Wnt and fibroblast growth factor (FGF) pathways have also recently been linked to the segmentation clock, suggesting that a complex, interconnected network of three signaling pathways regulates the timing of somitogenesis. Mutations in genes that have been linked to the clock frequently cause abnormal segmentation in model organisms. Additionally, at least two human disorders, spondylocostal dysostosis (SCDO) and Alagille syndrome (AGS), are caused by mutations in Notch pathway genes and exhibit vertebral column defects, suggesting that mutations that disrupt segmentation clock function in humans can cause congenital skeletal defects. Thus, it is clear that the correct, cyclic function of the Notch pathway within the vertebrate segmentation clock is essential for proper somitogenesis. In the future, with a large number of additional cyclic genes recently identified, the complex interactions between the various signaling pathways making up the segmentation clock will be elucidated and refined.     

FGF signaling acts upstream of the NOTCH and WNT signaling pathways to control segmentation clock oscillations in mouse somitogenesis

Fibroblast growth factor (FGF) signaling plays a crucial role in vertebrate segmentation. The FGF pathway establishes a posterior-to-anterior signaling gradient in the presomitic mesoderm (PSM), which controls cell maturation and is involved in the positioning of segmental boundaries. In addition, FGF signaling was shown to be rhythmically activated in the PSM in response to the segmentation clock. Here, we show that conditional deletion of the FGF receptor gene Fgfr1 abolishes FGF signaling in the mouse PSM, resulting in an arrest of the dynamic cyclic gene expression and ultimately leading to an arrest of segmentation. Pharmacological treatments disrupting FGF signaling in the PSM result in an immediate arrest of periodic WNT activation, whereas NOTCH-dependent oscillations stop only during the next oscillatory cycle. Together, these experiments provide genetic evidence for the role of FGF signaling in segmentation, and identify a signaling hierarchy controlling clock oscillations downstream of FGF signaling in the mouse.     

Segmental patterning of the vertebrate embryonic axis

The body axis of vertebrates is composed of a serial repetition of similar anatomical modules that are called segments or metameres. This particular mode of organization is especially conspicuous at the level of the periodic arrangement of vertebrae in the spine. The segmental pattern is established during embryogenesis when the somites--the embryonic segments of vertebrates--are rhythmically produced from the paraxial mesoderm. This process involves the segmentation clock, which is a travelling oscillator that interacts with a maturation wave called the wavefront to produce the periodic series of somites. Here, we review our current understanding of the segmentation process in vertebrates.     

Tyrosine kinase-activating growth factors potentiate thrombin- and AIF4- -induced phosphoinositide breakdown in hamster fibroblasts. Evidence for positive cross-talk between the two mitogenic signaling pathways

Basic fibroblast growth factor (FGF) and alpha-thrombin can stimulate DNA synthesis in Chinese hamster fibroblasts (CCL39) by two separate signaling pathways (Chambard, J.C., Paris, S., L'Allemain, G., and Pouysségur, J. (1987) Nature 326, 800-803) but can also act synergistically. We have examined whether this synergism might depend upon changes in inositol lipid metabolism. Indeed, FGF, which has no effect on its own on phosphoinositide hydrolysis, potentiates (by up to 2-fold) thrombin-induced formation of inositol phosphates. This enhancing effect is also observed upon direct activation by AIF4- of the GTP-binding protein coupled to phospholipase C, and is best revealed when phospholipase C is weakly stimulated. With low thrombin concentrations or with AIF4-, the formation of inositol phosphates is immediately increased with a marked reduction of the initial lag, whereas at high thrombin concentrations, the stimulation by FGF becomes pronounced only after desensitization of phospholipase C to thrombin. FGF-induced potentiation is not mimicked by calcium ionophores, but is likewise elicited by epidermal growth factor, platelet-derived growth factor, and to a lesser extent by insulin, other growth factors known to activate receptor tyrosine kinases. We therefore propose that the tyrosine kinase-activating growth factors enhance the coupling between GTP-binding protein and phospholipase C, presumably through the phosphorylation of one of these two proteins. Treatment of cells with pertussis toxin attenuates thrombin-induced phospholipase C activity but does not impede the potentiation by FGF. Comparison of the potentiating effects of FGF on inositol phosphate formation and on DNA synthesis suggests than an increased production of second messengers by the inositol lipid pathway in the first hours of stimulation might be, at least in part, responsible for the synergistic actions of FGF and thrombin on DNA synthesis.     

From head to tail: links between the segmentation clock and antero-posterior patterning of the embryo

Periodic production of somites along the anteroposterior axis of the vertebrate body involves a molecular oscillator, the 'segmentation clock', which can be visualized through the periodic activation of genes linked to the Notch pathway. Recent findings show that oscillations initiate at gastrula stages and point to a role for FGF signaling in positioning the segmental boundaries. This clock also controls aspects of spatio-temporal Hox gene activation thus ensuring a perfect match between segment boundary position and future regional identity of the somites.     

The vertebrate segmentation clock: the tip of the iceberg

The vertebrate segmentation clock was identified 10 years ago as a molecular oscillator associated with the rhythmic production of embryonic somites. Since then, three major signaling pathways--Notch, FGF, and Wnt--have been shown to be activated periodically during segmentation and proposed to constitute the clockwork of the system. However, recent results from zebrafish embryonic studies demonstrate that Notch signaling is involved in the coupling of oscillations among cells rather than in the pacemaker of the oscillator. Furthermore, genetic analyses in mouse indicate that Wnt and FGF play only a permissive role in the control of the oscillations. Therefore, the nature of the segmentation clock pacemaker still remains elusive.     

Analysis of her1 and her7 mutants reveals a spatio temporal separation of the somite clock module

Somitogenesis is controlled by a genetic network consisting of an oscillator (clock) and a gradient (wavefront). The "hairy and Enhancer of Split"- related (her) genes act downstream of the Delta/Notch (D/N) signaling pathway, and are crucial components of the segmentation clock. Due to genome duplication events, the zebrafish genome, possesses two gene copies of the mouse Hes7 homologue: her1 and her7. To better understand the functional consequences of this gene duplication, and to determine possible independent roles for these two genes during segmentation, two zebrafish mutants her1(hu2124) and her7(hu2526) were analyzed. In the course of embryonic development, her1(hu2124) mutants exhibit disruption of the three anterior-most somite borders, whereas her7(hu2526) mutants display somite border defects restricted to somites 8 (+/-3) to 17 (+/-3) along the anterior-posterior axis. Analysis of the molecular defects in her1(hu2124) mutants reveals a her1 auto regulatory feedback loop during early somitogenesis that is crucial for correct patterning and independent of her7 oscillation. This feedback loop appears to be restricted to early segmentation, as cyclic her1 expression is restored in her1(hu2124) embryos at later stages of development. Moreover, only the anterior deltaC expression pattern is disrupted in the presomitic mesoderm of her1(hu2124) mutants, while the posterior expression pattern of deltaC remains unaltered. Together, this data indicates the existence of an independent and genetically separable anterior and posterior deltaC clock modules in the presomitic mesdorm (PSM).