A clock and wavefront mechanism for somite formation

Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during embryogenesis and also one of the major unresolved events in developmental biology. In this article, we develop a mathematical formulation of a new version of the Clock and Wavefront model proposed by Pourquié and co-workers (Dubrulle, J., McGrew, M.J., Pourquié, O., 2001. FGF signalling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation. Cell 106, 219-232). Dynamic expression of FGF8 in the presomitic mesoderm constitutes the wavefront of determination which sweeps along the body axis interacting as it moves with the segmentation clock to gate cells into somites. We also show that the model can mimic the anomalies formed when progression of the wavefront is disturbed and make some experimental predictions that can be used to test the hypotheses underlying the model.     

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.     

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?     

The hepatic circadian clock is preserved in a lipid-induced mouse model of non-alcoholic steatohepatitis

Recent studies have correlated metabolic diseases, such as metabolic syndrome and non-alcoholic fatty liver disease, with the circadian clock. However, whether such metabolic changes per se affect the circadian clock remains controversial. To address this, we investigated the daily mRNA expression profiles of clock genes in the liver of a dietary mouse model of non-alcoholic steatohepatitis (NASH) using a custom-made, high-precision DNA chip. C57BL/6J mice fed an atherogenic diet for 5 weeks developed hypercholesterolemia, oxidative stress, and NASH. DNA chip analyses revealed that the atherogenic diet had a great influence on the mRNA expression of a wide range of genes linked to mitochondrial energy production, redox regulation, and carbohydrate and lipid metabolism. However, the rhythmic mRNA expression of the clock genes in the liver remained intact. Most of the circadianly expressed genes also showed 24-h rhythmicity. These findings suggest that the biological clock is protected against such a metabolic derangement as NASH.     

Bifurcations in a mathematical model for circadian oscillations of clock genes

Circadian oscillations with a period of about 24h are observed in nearly all living organisms as conspicuous biological rhythms. In this paper, we investigate various kinds of bifurcation phenomena produced in a circadian oscillator model of Drosophila. In Drosophila, it is known that circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes that code for the two proteins. For studying circadian oscillations of proteins in Drosophila, a mathematical model has been proposed. The model cannot only account for regular circadian oscillations in environmental conditions such as constant darkness, but also give rise to more complex oscillatory phenomena including chaos and birhythmicity. By calculating bifurcations using Kawakami's method, we obtain detailed bifurcation diagrams related to stable and unstable invariant sets, and identify parameter regions in which the model generates complex oscillations as well as regular circadian oscillations. Moreover, we study bifurcations observed in the model incorporating the effect on a light-dark (LD) cycle and show that the waveform of the periodic variation in the light-induced parameter has a marked influence on the global bifurcation structure or the type of dynamic behavior resulting from the forcing term of the circadian oscillator by the LD cycles.     

The Kermack-McKendrick epidemic model revisited

The Kermack-McKendrick epidemic model of 1927 is an age of infection model, that is, a model in which the infectivity of an individual depends on the time since the individual became infective. A special case, which is formulated as a two-dimensional system of ordinary differential ordinary differential equations, has often been called the Kermack-McKendrick model. One of the products of the SARS epidemic of 2002-2003 was a variety of epidemic models including general contact rates, quarantine, and isolation. These models can be viewed as age of infection epidemic models and analyzed using the approach of the full Kermack-McKendrick model. All these models share the basic properties that there is a threshold between disappearance of the disease and an epidemic outbreak, and that an epidemic will die out without infecting the entire population.     

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 circadian clock in the brain: a structural and functional comparison between mammals and insects

The circadian master clocks in the brains of mammals and insects are compared in respect to location, organization and function. They show astonishing similarities. Both clocks are anatomically and functionally connected to the optic system and possess multiple output pathways allowing synchronization with the environmental light-dark cycles as well as the control of diverse endocrine, autonomic and behavioral functions. Both circadian master clocks are composed of multiple neurons, which are organized in populations with different morphology, physiology and neurotransmitter content and appear to subserve different functions. In the hamster and in the cockroach, the master clock consists of a core region that gets input from the eyes, and a shell region from which the majority of output projections originate. Communication between core and shell, between all other populations of clock neurons as well as between the master clocks of both brain hemispheres is a prerequisite of normal rhythmic function. Phenomena like rhythm splitting and internal desynchronization can be observed under constant light conditions and are caused by the uncoupling of the master clocks of both brain hemispheres.     

Stoichiometric interactions between cyanobacterial clock proteins KaiA and KaiC

We determined the stoichiometry of KaiA-KaiC interactions. Using immunoblotting and two-dimensional Native- and SDS-PAGE (2DNS-PAGE) analysis, we demonstrated that the reaction products of KaiA-KaiC interactions in the presence of ATP consisted of only phosphorylated KaiC whereas in the presence of the unhydrolyzable analogue 5'-adenylylimidodiphosphate (AMPPNP) they consisted of KaiA and KaiC. In the presence of ATP, the KE (molar ratio of KaiA dimer to KaiC hexamer giving half saturation in the enhancement of KaiC phosphorylation) was 0.25, and IAsys affinity biosensor analysis demonstrated that 1 molecule of KaiA dimer interacted with 1 molecule of KaiC hexamer. In the presence of AMPPNP, the ratio of KaiA dimer to KaiC hexamer in KaiA-KaiC complexes was determined to be 2 by 2DNS-PAGE, Native-PAGE/Scatchard plot, and IAsys analyses. These results suggest that 2 molecules of KaiA dimer can interact with 1 molecule of KaiC hexamer, and that interactions of at least 1 molecule of KaiA dimer with 1 molecule of KaiC hexamer are enough to enhance the phosphorylation of KaiC by KaiA at an almost saturated level.     

The hierarchical island model revisited

Formulae were derived for the genetic differentiation between populations within a metapopulation (F_SM), and between metapopulations (F_MT) as functions of migration and mutation rates, size and number of populations and metapopulations. We show that F_MT = 1/(1 + 4N_em), where N_e is the effective size of a metapopulation, and where the migration rate between metapopulations is m. The formulae for F_MT and F_SM were more general than previously proposed since we have relaxed some previously made hypotheses and we included the effect of the mutation rate. Using our formula, some unexpected result of estimation of gene flow, previously obtained, can be explained readily.     

Posterior skeletal development and the segmentation clock period are sensitive to Lfng dosage during somitogenesis

The segmental structure of the axial skeleton is formed during somitogenesis. During this process, paired somites bud from the presomitic mesoderm (PSM), in a process regulated by a genetic clock called the segmentation clock. The Notch pathway and the Notch modulator Lunatic fringe (Lfng) play multiple roles during segmentation. Lfng oscillates in the posterior PSM as part of the segmentation clock, but is stably expressed in the anterior PSM during presomite patterning. We previously found that mice lacking overt oscillatory Lfng expression in the posterior PSM (Lfng^?FCE) exhibit abnormal anterior development but relatively normal posterior development. This suggests distinct requirements for segmentation clock activity during the formation of the anterior skeleton (primary body formation), compared to the posterior skeleton and tail (secondary body formation). To build on these findings, we created an allelic series that progressively lowers Lfng levels in the PSM. Interestingly, we find that further reduction of Lfng expression levels in the PSM does not increase disruption of anterior development. However tail development is increasingly compromised as Lfng levels are reduced, suggesting that primary body formation is more sensitive to Lfng dosage than is secondary body formation. Further, we find that while low levels of oscillatory Lfng in the posterior PSM are sufficient to support relatively normal posterior development, the period of the segmentation clock is increased when the amplitude of Lfng oscillations is low. These data support the hypothesis that there are differential requirements for oscillatory Lfng during primary and secondary body formation and that posterior development is less sensitive to overall Lfng levels. Further, they suggest that modulation of the Notch signaling by Lfng affects the clock period during development.     

Search for informative polymorphisms in candidate genes: clock genes and circadian behaviour in blue tits

The identification of functional polymorphisms in genes that underlie behavioural trait variation is a challenging but intriguing task in evolutionary biology. Given the wealth of genomic data and the increasing number of genotype–phenotype association studies in model organisms, one can ask whether and how this information can be used for non-model organisms. Here we describe two strategies to search for likely functional polymorphisms in candidate genes in a bird species that has been intensively studied by behavioural and population ecologists, the blue tit Cyanistes caeruleus. In the first approach we searched for repeating elements in coding regions of the genome using information about repeats in Gallus gallus genes. The rationale is that tandem-repeat elements have a high potential to be polymorphic and functional. The second strategy aimed to replicate reported genotype–phenotype association studies by extrapolating results from model organisms to our study species. Both strategies showed high success rates with respect to finding homologous gene regions and potentially informative genetic variants in the genes AANAT, ADCYAP1, CKIε, CLOCK, CREB1, NPAS2 and PERIOD2. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

大鼠松果体Clock基因和芳烷脘N-乙酰基转移酶基因的昼夜节律性表达及光照影响

探讨12h光照、12h黑暗交替(12h-light：12h-dark cycle,LD)及持续黑暗(constant darkness,DD)光制下松果体Clock基因和芳烷脘N-乙酰基转移酶基因(arylalkylamine N-acetyltransferase gene,NAT)是否存在昼夜节律性表达及其光反应变化。Sprague-Dawley大鼠在LD和DD光制下分别被饲养4周(n=36)和8周(n=36)后,在一昼夜内每隔4h采集一组松果体组织(n=6),提取总RNA,用竞争性定量RT-PCR测定不同昼夜时点样品中Clock及NAT基因的mRNA相对表达量,通过余弦法和ClockLab软件获取节律参数,并经振幅检验是否存在昼夜节律。结果如下：(1)在DD或LD光制下,松果体Clock和NAT基因mRNA的表达均呈现夜高昼低的节律性振荡(P＜0．05)。(2)与DD光制下比较,LD光制下松果体Clock和NAT基因的表达振幅及峰值相的mRNA水平均降低(P＜0．05)。(3)在DD或LD光制下,Clock和NAT基因之间显示相似的节律性表达(P＞0．05)。结果表明,Clock和NAT基因在松果体中存在同步的内源性昼夜节律表达,光照作用可使其表达下调。