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Keywords:

  • segmentation clock;
  • oscillation;
  • gene expression dynamics;
  • mathematical modeling;
  • synchronization;
  • Notch pathway;
  • Hes genes;
  • her genes

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

The regular pattern of somite segmentation depends on a clock, the somite segmentation clock, in the form of a gene expression oscillator, operating in the presomitic mesoderm (the PSM) at the tail end of the vertebrate embryo. Genetic screens and other approaches have identified a variety of genes, including components and targets of the Notch signalling pathway, that show transcriptional oscillations in this region and appear to be necessary for correct segmentation. Mathematical modelling shows that the oscillations could plausibly be generated by a simple mechanism of delayed negative feedback, based on autoinhibition of Notch target genes of the Hes/her family by their own protein products. To move beyond plausible models to an experimentally validated theory, however, it is necessary to measure the parameters on which the proposed model is based and to devise ways of probing the dynamics of the system by means of timed disturbances so as to compare with the model's predictions. Some progress is being made in these directions. Developmental Dynamics 236:1410–1415, 2007. © 2007 Wiley-Liss, Inc.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

The regular pattern of somite segmentation, it is generally agreed, depends on a clock—the somite segmentation clock—in the form of a gene expression oscillator, operating in the presomitic mesoderm (the PSM) at the tail end of the vertebrate embryo. Each somite consists of the cells that emerge from the PSM in the course of one oscillator cycle; and when the oscillations of gene expression are disrupted, so is the pattern of somites (Pourquié, 2003). We would like to understand how the clock works, first of all on account of its importance in defining the vertebrate body plan. But there is also a larger reason for focusing on this problem. While developmental biologists have made good progress in explaining how spatial patterns arise, the mechanisms that control the timing of developmental events are largely unexplored. In most cases, we have little more than a vague appreciation that one thing follows another, and that biochemical reactions and cell growth and division take time. The quantitative dynamics of development—the mechanisms and the “laws of motion” that govern the timing of each developmental step—are almost completely unknown. The somite segmentation clock exemplifies in a particularly pure and clear form the general problem of how the tempo of events is controlled. In studying this clock, we may learn how to tackle the dynamics of other developmental processes also, where time is likewise of the essence, even if not marked out in regular repetitive cycles.

THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

The operation of the clock is manifest in the oscillating expression of a number of different genes, and most obviously of genes coding for components of the Notch pathway such as Hes1, Hes7, and Lfng in chick and mouse, and her1, her7, and deltaC in the zebrafish (Pourquié, 2003). Each cell in the PSM periodically makes and degrades the products of these genes, and it does so in synchrony with its neighbours. A basic question, therefore, is whether each cell has its own clock or depends instead on a time signal emitted by some central coordinator. And if each cell does have its own clock, how is synchrony maintained?

An answer to these questions was suggested by study of a set of zebrafish mutants (van Eeden et al., 1996) in which somite segmentation was disrupted by mutations that, as we now know, lie in genes coding for the receptor Notch1a (Holley et al., 2002), for its ligands DeltaD and DeltaC (Holley et al., 2000; Julich et al., 2005), or for the Mind-bomb protein, required to enable the ligands to activate Notch (Jiang et al., 1996; Itoh et al., 2003). In all these mutants, in situ hybridisation revealed that the PSM cells were in a variety of different states, some expressing the oscillator gene deltaC strongly, others expressing it weakly, in a higgledy-piggledy mixture that was precisely what one would expect if each cell was continuing to oscillate, but doing so independently and out of synchrony with its neighbours (Jiang et al., 2000). Moreover, the first few (four to eight) somites in all these mutants showed correct segmentation, correlated with synchronized expression of deltaC in the PSM cells in the period preceding their formation, suggesting that oscillation was triggered synchronously in all the PSM cells at the beginning of somitogenesis and that the mutant cells then took several cycles to drift out of synchrony (Jiang et al., 2000). Given the identity of the mutant genes, this carried two further implications: first, that cell–cell communication via the Notch pathway was required to maintain synchrony between adjacent cells; and, second, that somites (or at least anterior somites) could still form normally in the zebrafish in the absence of Notch signalling so long as neighbouring cells remained synchronized.

Subsequent experiments by several groups have directly examined the ability of PSM cells to oscillate autonomously. Thus, in the chick, Hes1 genes (c-hairy1 and c-hairy2) continue to show regular oscillation in small fragments of PSM tissue, but less regular behaviour in isolated cells (Maroto et al., 2005). Similarly in the mouse, Hes1 expression oscillates (as shown by a luciferase reporter) even in isolated PSM cells, but less regularly than in the intact tissue (Masamizu et al., 2006). Individual cells, it seems, do indeed contain their own oscillators; but these are erratic, and require cell–cell communication to keep them all going regularly and at the same rate. Further support for this view has come from experiments in the zebrafish, in which cells were grafted between wild-type embryos and embryos injected with morpholinos to knock down components of the Notch pathway and the results were analysed with the help of some mathematical modelling. The conclusion was that Notch signalling coordinates the oscillations of adjacent cells, which, in the absence of such communication, oscillate somewhat irregularly (Horikawa et al., 2006).

The somite segmentation clock, as observed at the tissue level, is therefore a collective phenomenon, reflecting the operation of the many little clocks in the individual cells, all entrained to the same rhythm by Notch-mediated cell–cell communication. A gene-expression clock in a single isolated cell is inevitably imprecise, if only because of the stochastic nature of biochemical reactions (Lewis, 2003); but by coupling many such clocks in parallel, a high precision can be attained.

As we discuss below, it is possible that the somite segmentation clock is made of many little clocks in another sense also: it is conceivable that the individual cell may contain several parallel systems of molecules that are capable of generating oscillations and have evolved to oscillate with a similar period. These could be held in synchrony by some coupling between them, combining to create a sophisticated timepiece with all the required properties of temperature dependence, buffering against changes of environmental chemistry, responsiveness to levels of Fgf8, and so on. The way the system adjusts to changes in temperature is particularly impressive. The rate of growth in the PSM, and presumably the kinetics of Fgf8 signalling, vary steeply with temperature, but the period of the clock changes in a precisely coordinated way, so that, regardless of the temperature, somites of the same standard size are produced.

GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

From the foregoing, it seems reasonable to break down the problem of the clock into two parts: How are oscillations generated in the individual cells, and how are the oscillations in neighbouring cells coupled?

To answer such questions at a molecular level, one has to begin by identifying the components of the underlying control system. We have already mentioned several of them. Even before the discovery of the clock, mutagenesis studies revealed a critical role in somite segmentation for the Notch pathway. Knockout mutations of Notch1 and Delta1 in the mouse caused disruption of somite segmentation (Conlon et al., 1995; Hrabe de Angelis et al., 1997), while a large-scale mutagenesis screen in the zebrafish (van Eeden et al., 1996) identified a rather small set of genes that had similar effects; and most of these subsequently turned out also to code for components of the Notch signalling pathway. But while these findings suggested that the Notch pathway was somehow central to the mechanism of segmentation, they gave no hint of how this might be so. Moreover, since the zebrafish screens fell short of saturation, and in any case were liable to disregard mutations causing drastic disruption of the body plan before the onset of somite formation, it remained possible that other important players had been missed.

The discovery that Hes1 (c-hairy-1) shows oscillating expression in the PSM, matching the rhythm of somitogenesis, transformed the situation (Palmeirim et al., 1997). Hes genes are primary targets of regulation by Notch, mediate most of the effects of Notch signalling, and can regulate the expression of Notch ligands. Their oscillating expression not only revealed the existence of the somite segmentation clock, but also hinted at a way in which the two parts of the clock problem might be reduced to molecular terms. An intracellular oscillator based on the dynamics of Hes gene expression would be susceptible to regulation by Notch signalling, and would be capable of regulating expression of Notch ligands so as to influence Hes gene expression in neighbouring cells; oscillations in neighbouring cells would thus be coupled.

The discovery that Hes1 expression oscillates in chick and mouse (Jouve et al., 2000) was soon followed by the finding that certain other Hes family genes—her1 and her7 in the zebrafish (Holley et al., 2000; Sawada et al., 2000; Henry et al., 2002; Oates and Ho, 2002; Gajewski et al., 2003), Hes7 in the mouse (Bessho et al., 2001, 2003)—not only oscillated in the PSM, but were required to oscillate to give rise to regular somite segmentation. These clearly were essential elements of the clock—either components of the basic pacemaker (like the pendulum of a pendulum clock) or components needed, like the hands of a clock, for readout of the clock state (Giudicelli and Lewis, 2004).

SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

Other studies, in a variety of vertebrates, implicated other Notch pathway genes, such as Lfng (Forsberg et al., 1998; McGrew et al., 1998; Dale et al., 2003), in the somite clock mechanism, adding to the evidence that the Notch pathway had a central role. But the picture began to seem less simple when it was found that, in the mouse at least, cells in the PSM also showed oscillating expression of the Wnt pathway components Axin2, Nkd1, and Dact1 (Aulehla et al., 2003; Ishikawa et al., 2004; Suriben et al., 2006).

If components of the Notch and Wnt pathway oscillate in the PSM, are there still other classes of molecules that also do so? Recent work in the Pourquié lab has tackled this question directly and found that the answer is yes, through a micro-array screen for genes whose expression level oscillates in the PSM with a periodicity matching that of the segmentation clock (Dequéant et al., 2006). Meanwhile, a separate study has demonstrated that Snail genes (Snail1 in the mouse, Snail2 in the chick, coding for transcription factors not generally thought to lie in the Notch pathway) also show oscillating expression in the PSM (Dale et al., 2006). Moreover, we cannot exclude the possibility that, underlying the observed transcriptional oscillations, there is some other type of oscillator, based for example on cycles of protein phosphorylation and dephosphorylation, as has been beautifully demonstrated for the circadian clock of the cyanobacterium Synechococcus (Kageyama et al., 2006).

In this situation, how can we work out which genes are essential components of the ultimate pacemaker of the segmentation clock?

GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

In principle, we can narrow the field of candidates through a simple genetic test: if component X still oscillates when component Y is missing, but the reverse is not true, then Y cannot be an essential component of the master oscillator, but X might be. In reality, such tests are difficult to interpret because of problems of genetic redundancy, and they are dubious at a more profound level, because the concept of a master oscillator may be misconceived. Instead of a single master oscillator, there may be several weakly-coupled oscillation mechanisms that normally operate in parallel but can also function in isolation. In the mouse, the Axin2 oscillations were reported to persist, with coordination between cells, even when the Notch pathway was blocked (Aulehla et al., 2003; Hirata et al., 2004), and the same was found for the Snail oscillations, which did, however, depend on the Wnt oscillator (Dale et al., 2006). These findings suggested that the master oscillator in the mouse and chick was after all not based on Notch signalling, but merely required the Notch pathway for proper readout so as to define the pattern of somite boundaries. An alternative interpretation would be that in the mouse and chick, a Notch-related oscillator and a Wnt-related oscillator are present in parallel, with a loose coupling between them to maintain coordination under normal circumstances.

In the zebrafish, in any case, the situation is different. No evidence of oscillation in homologs of Axin2 or Snail has so far been reported, and Notch pathway components remain strong candidates to be the key elements of a master oscillator.

Identifying the molecules that form the clock is, however, only a first step. To understand the mechanism, we need to know how each of the relevant components interacts with the others, as linked elements of a control system. And even that is not enough. We need to explain how these interactions between the components cause the control system to behave in the way we observe.

HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

Hes genes (in mouse and chick) and their counterparts the her genes (in fish) code for inhibitory transcription factors. Negative feedback is the general mechanism underlying oscillations in biological systems. An obvious suggestion, therefore, is that the intracellular oscillations of the segmentation clock might arise simply as a consequence of a direct autoinhibitory feedback loop, in which the protein products of Hes or her genes would act back as negative regulators of their own transcription. Bessho et al. supported this idea with experiments in the mouse showing that Hes7 protein binds to the Hes7 promoter region and does indeed inhibit Hes7 transcription (Bessho et al., 2003). Morpholino knock-down experiments in the zebrafish to test whether the products of her1 and her7 inhibited their own expression led to results that were not so clear. Different laboratories drew different conclusions (Henry et al., 2002; Holley et al., 2002; Oates and Ho, 2002; Gajewski et al., 2003), but autoinhibition remained a possibility for these genes too. Other negative feedback loops, involving Lfng or Axin2, were also suggested as a possible basis for the oscillations (Aulehla et al., 2003; Dale et al., 2003), but autoinhibition of Hes7 (in the mouse) or her1/7 (in the fish) was the simplest proposal.

Whichever of these hypotheses one might espouse, two questions have to be answered. Is the hypothesized mechanism capable in principle of giving rise to the observed oscillations? If so, is that hypothetical mechanism the actual mechanism at work in the embryo?

EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

Traditionally, developmental biologists have been content to summarise their mechanistic findings and speculations in the form of little diagrams, in which the molecules of interest are linked by arrows that show which components regulate which other components, and in each case whether the effect is positive or negative. For simple linear pathways without feedback, this can indeed be a useful kind of description; but even in those cases, such cartoons convey no information about the dynamics of the system. For control mechanisms with feedback, which is to say for almost all biological control systems, and certainly for all those that generate oscillations, simple circuit diagrams by themselves do not explain the behaviour. One cannot look at such a diagram and predict, by unaided intuition and without quantitative information, what the system will do. Newton did not explain the orbits of the planets simply by saying that the Sun exerts an attraction, or even by saying that the attraction obeys an inverse square law: he had to show that these postulates lead to the elliptical orbits observed. To understand the mechanism of the segmentation clock, or of any other control system with feedback, we have to do some mathematical analysis, or at least some computer modelling. Given a hypothesis as to the mechanism, we need to examine it mathematically to discover whether it could in principle work.

MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

The idea that Hes or her genes might generate intracellular oscillations through direct autoinhibition, and that the link between these genes and Notch signalling might serve to synchronize adjacent cells, has been formulated in a simple mathematical model based on the case of the zebrafish, with her1 and her7 jointly playing the pacemaker role, and the Notch ligand DeltaC expressed in an oscillatory fashion under their control (Lewis, 2003).

Translating this qualitative idea into a quantitative mathematical model led to some conclusions that might not have been obvious. It showed that a simple her1/7 autoinhibition circuit could indeed give rise to oscillations, but only if it incorporated transcriptional and/or translational delays, that is, delays in the relationship between the amount of Her1/7 protein and the rate of production of mature her1/7 mRNA molecules, or between the amount of her1/7 mRNA molecules and the rate at which molecules of Her1/7 appear in the cell nucleus. Quantitative estimates from other systems suggested that the most important of these delays would be the transcriptional delay, the delay from the moment when a molecule of inhibitory protein dissociates from its DNA binding site in the her1/7 promoter region, permitting transcription to begin, to the moment when the mature mRNA molecule emerges into the cytoplasm to direct protein synthesis. The modelling showed that for sustained oscillation, the sum of the transcriptional and translational delays must be long compared with the lifetimes of the oscillating molecules. The oscillations that then occur are predicted to have a period that is roughly twice the sum of the total feedback circuit delay. Notch signalling can indeed synchronise the oscillations of individual cells according to this model, but only if the delays in Notch-mediated communication between the neighbouring cells lie within the right range. Judging from crude estimates based on information from other biological systems, it seemed plausible that all these quantitative requirements might be met, and plausible, too, that the result could be oscillations with the observed 30-min period of the zebrafish somite segmentation clock.

Playing with the model led to some other insights. It showed that even a quite severe general inhibition of the rate of protein synthesis might be expected to leave the mRNA oscillations practically unaffected (Lewis, 2003), explaining observations of Palmeirim et al. (1997). Likewise, thanks to negative feedback, even a quite severe morpholino knockdown of her1 or her7 translation would not necessarily be expected to have much impact on the oscillatory transcription of these genes (explaining some of the puzzling findings from such experiments in the zebrafish: Henry et al., 2002; Holley et al., 2002; Oates and Ho, 2002; Gajewski et al., 2003). Applied to the mouse, the model showed too that a modest increase in Hes7 protein lifetime would be expected to lead to damping and rapid failure of the clock oscillations, just as observed (Hirata et al., 2004).

ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

The mathematical model survives the most basic test. It shows that the ideas that it embodies could in principle give rise to the observed behaviour, including some experimental phenomena that might seem at first sight contradictory. Quantitatively and qualitatively, the model appears plausible.

But a plausible hypothesis is not the same thing as a true theory. To decide whether the model represents the actual mechanism at work in the embryo, we need to measure the parameters that the modelling identifies as crucial, and to carry out experiments that will test the predictions quantitatively and so discover whether the postulates of the model are right or wrong.

An analogy can be drawn with the problem of understanding the mechanism of the nerve action potential. When Hodgkin and Huxley began their work, there were many competing theories, invoking different mechanisms and assigning the key roles to different molecules. Hodgkin and Huxley established the true mechanism by focusing on a certain subset of factors (primarily the concentrations of Na+ and K+ ions, and the membrane potential), which they suspected to be crucial, and making careful quantitative measurements of how each one influenced the others. From these measurements they were able to compute the predicted behaviour of the system as a whole. Precise agreement between the predictions and the observations showed convincingly that their chosen set of factors, interacting according to the dynamical rules that their experiments had defined, were indeed the crucial ingredients of the action potential mechanism, and that their model was a true theory (Hodgkin, 1964).

Making measurements of the dynamics of molecular oscillations in the cells of the PSM is hard, and we can scarcely hope to achieve the accuracy and completeness that was possible for Hodgkin and Huxley in their very different system. But we have to try, if we are to understand truly how the clock works. The model itself highlights the things that we need to check and to measure: the logic of the control circuitry, the lengths of the delays, the molecular lifetimes, the synthesis rate constants, the steepness of the autoinhibition, and a handful of other factors.

ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES

In efforts to analyse the genetic control circuity of the segmentation clock, the traditional approach, used in most studies up to now, has been to use mutants or morphants to knock down or misexpress a gene that is suspected to be important, and examine the consequences for expression of other candidate oscillator genes. In this type of experiment, the genetic perturbation operates from the beginning of development, and it is difficult or impossible to know whether a given observed effect is direct or indirect. The timing of action of one component on another remains unclear. Moreover, the same molecule may have different actions at different steps in the operation of the segmentation machinery, and in this case we see only the composite, cumulative effect. For example, Notch signalling in the mouse is suspected to be important both in the operation of the segmentation clock and in the events in the anterior PSM that convert the clock oscillations into a spatial pattern; we cannot disentangle these actions simply by looking at Notch mutants. Thus, although mutant and morphant studies have helped to identify candidate components of the oscillator and have suggested regulatory relationships between them, they have not allowed firm conclusions about the basic circuitry or dynamics of the clock control mechanism.

To make better progress and to test our hypotheses properly, we need above all two kinds of experimental tools: ways of perturbing individual components at defined times, and ways of following the consequences temporally. Such tools already exist, but they are crude. In the zebrafish, transgenic lines carrying a gene of interest under a heat-shock promoter allow us to switch on expression of that gene at any time we please, more or less abruptly (within about 7 min). Transgenic lines carrying GFP (or similar) reporter constructs let us monitor in the living state the level of expression of a chosen gene, though with a temporal precision that is rather severely limited by the lifetime of the fluorescent reporter protein. As we describe elsewhere (Giudicelli et al., 2007; E.O. and J.L., unpublished data), we have begun to use these tools to analyse and measure the circuitry and dynamics of the zebrafish segmentation clock and to test our simple mathematical model. So far, the model seems to survive the tests. But there is a long way still to go. If we are ever to reach the end of the road and establish the true mechanism of the segmentation clock, we shall need to improve on the tools for temporal analysis that we currently have. Effort devoted to tackling the problem of the somite segmentation clock in this way should help equip us for the larger enterprise of understanding how the tempo of development in general is controlled.

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. THE SEGMENTATION CLOCK IS A COMPOSITE OF MANY LITTLE CLOCKS
  5. GENETIC STUDIES IDENTIFY ESSENTIAL CLOCK COMPONENTS
  6. SYSTEMATIC MICROARRAY SCREENING REVEALS ADDITIONAL GENES THAT OSCILLATE IN THE PSM
  7. GENETIC ANALYSIS CAN NARROW THE FIELD OF CANDIDATE PACEMAKER COMPONENTS
  8. HES/HER AUTOINHIBITION COULD BE THE SOURCE OF OSCILLATIONS
  9. EXPLANATION OF THE CLOCK MECHANISM REQUIRES SOME MATHEMATICS
  10. MATHEMATICAL MODELLING CONFIRMS THAT A SIMPLE HES/HER AUTOINHIBITION OSCILLATOR COULD WORK, BUT ONLY ON CERTAIN CONDITIONS
  11. ANALYSIS OF THE CLOCK MECHANISM REQUIRES A QUANTITATIVE EXPERIMENTAL APPROACH
  12. ANALYSIS OF CLOCK DYNAMICS REQUIRES TEMPORAL INTERVENTIONS AND OBSERVATIONS
  13. Acknowledgements
  14. REFERENCES
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