From dynamic expression patterns to boundary formation in the presomitic mesoderm

Morphogen-regulated contact-mediated signaling between cells can drive the transitions underlying body segmentation in vertebrates

We propose a unified mechanism that reproduces the sequence of dynamical transitions observed during somitogenesis, the process of body segmentation during embryonic development, that is invariant across all vertebrate species. This is achieved by combining inter-cellular interactions mediated via receptor-ligand coupling with global spatial heterogeneity introduced through a morphogen gradient known to occur along the anteroposterior axis. Our model reproduces synchronized oscillations in the gene expression in cells at the anterior of the presomitic mesoderm as it grows by adding new cells at its posterior, followed by travelling waves and subsequent arrest of activity, with the eventual appearance of somite-like patterns. This framework integrates a boundary-organized pattern formation mechanism, which uses positional information provided by a morphogen gradient, with the coupling-mediated self-organized emergence of collective dynamics, to explain the processes that lead to segmentation.

Time and space in segmentation

Arthropod segmentation and vertebrate somitogenesis are leading fields in the experimental and theoretical interrogation of developmental patterning. However, despite the sophistication of current research, basic conceptual issues remain unresolved. These include: (i) the mechanistic origins of spatial organization within the segment addition zone (SAZ); (ii) the mechanistic origins of segment polarization; (iii) the mechanistic origins of axial variation; and (iv) the evolutionary origins of simultaneous patterning. Here, I explore these problems using coarse-grained models of cross-regulating dynamical processes. In the morphogenetic framework of a row of cells undergoing axial elongation, I simulate interactions between an 'oscillator', a 'switch' and up to three 'timers', successfully reproducing essential patterning behaviours of segmenting systems. By comparing the output of these largely cell-autonomous models to variants that incorporate positional information, I find that scaling relationships, wave patterns and patterning dynamics all depend on whether the SAZ is regulated by temporal or spatial information. I also identify three mechanisms for polarizing oscillator output, all of which functionally implicate the oscillator frequency profile. Finally, I demonstrate significant dynamical and regulatory continuity between sequential and simultaneous modes of segmentation. I discuss these results in the context of the experimental literature.

A mechanical model of early somite segmentation

Somitogenesis is often described using the clock-and-wavefront (CW) model, which does not explain how molecular signaling rearranges the pre-somitic mesoderm (PSM) cells into somites. Our scanning electron microscopy analysis of chicken embryos reveals a caudally-progressing epithelialization front in the dorsal PSM that precedes somite formation. Signs of apical constriction and tissue segmentation appear in this layer 3-4 somite lengths caudal to the last-formed somite. We propose a mechanical instability model in which a steady increase of apical contractility leads to periodic failure of adhesion junctions within the dorsal PSM and positions the future inter-somite boundaries. This model produces spatially periodic segments whose size depends on the speed of the activation front of contraction (F), and the buildup rate of contractility (Λ). The Λ/F ratio determines whether this mechanism produces spatially and temporally regular or irregular segments, and whether segment size increases with the front speed.

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Dorsal pre-somitic mesoderm of chicken embryos epithelializes before somite formation

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Dorsal epithelium shows signs of apical constriction and early segmentation

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A mechanical instability model can reproduce sequential segmentation

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A single ratio describes spatial and temporal patterns of segmentation

A theoretical model of neural maturation in the developing chick spinal cord

Cellular differentiation is a tightly regulated process under the control of intricate signaling and transcription factors interaction network working in coordination. These interactions make the systems dynamic, robust and stable but also difficult to dissect. In the spinal cord, recent work has shown that a network of FGF, WNT and Retinoic Acid (RA) signaling factors regulate neural maturation by directing the activity of a transcription factor network that contains CDX at its core. Here we have used partial and ordinary (Hill) differential equation based models to understand the spatiotemporal dynamics of the FGF/WNT/RA and the CDX/transcription factor networks, alone and in combination. We show that in both networks, the strength of interaction among network partners impacts the dynamics, behavior and output of the system. In the signaling network, interaction strength determine the position and size of discrete regions of cell differentiation and small changes in the strength of the interactions among networking partners can result in a signal overriding, balancing or oscillating with another signal. We also show that the spatiotemporal information generated by the signaling network can be conveyed to the CDX/transcription network to produces a transition zone that separates regions of high cell potency from regions of cell differentiation, in agreement with most in vivo observations. Importantly, one emerging property of the networks is their robustness to extrinsic disturbances, which allows the system to retain or canalize NP cells in developmental trajectories. This analysis provides a model for the interaction conditions underlying spinal cord cell maturation during embryonic axial elongation.

Segmentation clock dynamics is strongly synchronized in the forming somite

During vertebrate somitogenesis an inherent segmentation clock coordinates the spatiotemporal signaling to generate segmented structures that pattern the body axis. Using our experimental and quantitative approach, we study the cell movements and the genetic oscillations of her1 expression level at single-cell resolution simultaneously and scale up to the entire pre-somitic mesoderm (PSM) tissue. From the experimentally determined phases of PSM cellular oscillators, we deduced an in vivo frequency profile gradient along the anterior-posterior PSM axis and inferred precise mathematical relations between spatial cell-level period and tissue-level somitogenesis period. We also confirmed a gradient in the relative velocities of cellular oscillators along the axis. The phase order parameter within an ensemble of oscillators revealed the degree of synchronization in the tailbud and the posterior PSM being only partial, whereas synchronization can be almost complete in the presumptive somite region but with temporal oscillations. Collectively, the degree of synchronization itself, possibly regulated by cell movement and the synchronized temporal phase of the transiently expressed clock protein Her1, can be an additional control mechanism for making precise somite boundaries.

Travelling waves in somitogenesis: Collective cellular properties emerge from time-delayed juxtacrine oscillation coupling

The sculpturing of the vertebrate body plan into segments begins with the sequential formation of somites in the presomitic mesoderm (PSM). The rhythmicity of this process is controlled by travelling waves of gene expression. These kinetic waves emerge from coupled cellular oscillators and sweep across the PSM. In zebrafish, the oscillations are driven by autorepression of her genes and are synchronized via Notch signalling. Mathematical modelling has played an important role in explaining how collective properties emerge from the molecular interactions. Increasingly more quantitative experimental data permits the validation of those mathematical models, yet leads to increasingly more complex model formulations that hamper an intuitive understanding of the underlying mechanisms. Here, we review previous efforts, and design a mechanistic model of the her1 oscillator, which represents the experimentally viable her7;hes6 double mutant. This genetically simplified system is ideally suited to conceptually recapitulate oscillatory entrainment and travelling wave formation, and to highlight open questions. It shows that three key parameters, the autorepression delay, the juxtacrine coupling delay, and the coupling strength, are sufficient to understand the emergence of the collective period, the collective amplitude, and the synchronization of neighbouring Her1 oscillators. Moreover, two spatiotemporal time delay gradients, in the autorepression and in the juxtacrine signalling, are required to explain the collective oscillatory dynamics and synchrony of PSM cells. The highlighted developmental principles likely apply more generally to other developmental processes, including neurogenesis and angiogenesis.

A framework for quantification and physical modeling of cell mixing applied to oscillator synchronization in vertebrate somitogenesis

In development and disease, cells move as they exchange signals. One example is found in vertebrate development, during which the timing of segment formation is set by a 'segmentation clock', in which oscillating gene expression is synchronized across a population of cells by Delta-Notch signaling. Delta-Notch signaling requires local cell-cell contact, but in the zebrafish embryonic tailbud, oscillating cells move rapidly, exchanging neighbors. Previous theoretical studies proposed that this relative movement or cell mixing might alter signaling and thereby enhance synchronization. However, it remains unclear whether the mixing timescale in the tissue is in the right range for this effect, because a framework to reliably measure the mixing timescale and compare it with signaling timescale is lacking. Here, we develop such a framework using a quantitative description of cell mixing without the need for an external reference frame and constructing a physical model of cell movement based on the data. Numerical simulations show that mixing with experimentally observed statistics enhances synchronization of coupled phase oscillators, suggesting that mixing in the tailbud is fast enough to affect the coherence of rhythmic gene expression. Our approach will find general application in analyzing the relative movements of communicating cells during development and disease.

Modeling coexistence of oscillation and Delta/Notch-mediated lateral inhibition in pancreas development and neurogenesis

During pancreas development, Neurog3 positive endocrine progenitors are specified by Delta/Notch (D/N) mediated lateral inhibition in the growing ducts. During neurogenesis, genes that determine the transition from the proneural state to neuronal or glial lineages are oscillating before their expression is sustained. Although the basic gene regulatory network is very similar, cycling gene expression in pancreatic development was not investigated yet, and previous simulations of lateral inhibition in pancreas development excluded by design the possibility of oscillations. To explore this possibility, we developed a dynamic model of a growing duct that results in an oscillatory phase before the determination of endocrine progenitors by lateral inhibition. The basic network (D/N + Hes1 + Neurog3) shows scattered, stable Neurog3 expression after displaying transient expression. Furthermore, we included the Hes1 negative feedback as previously discussed in neurogenesis and show the consequences for Neurog3 expression in pancreatic duct development. Interestingly, a weakened HES1 action on the Hes1 promoter allows the coexistence of stable patterning and oscillations. In conclusion, cycling gene expression and lateral inhibition are not mutually exclusive. In this way, we argue for a unified mode of D/N mediated lateral inhibition in neurogenic and pancreatic progenitor specification.

Sequential pattern formation governed by signaling gradients

Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the interplay of cell oscillations with tissue elongation and shortening and with signaling gradients, is still missing. Here we show that a set of coupled genetic oscillators in an elongating tissue that is regulated by diffusing and advected signaling molecules can account for segmentation as a self-organized patterning process. This system can form a finite number of segments and the dynamics of segmentation and the total number of segments formed depend strongly on kinetic parameters describing tissue elongation and signaling molecules. The model accounts for existing experimental perturbations to signaling gradients, and makes testable predictions about novel perturbations. The variety of different patterns formed in our model can account for the variability of segmentation between different animal species.

A Local, Self-Organizing Reaction-Diffusion Model Can Explain Somite Patterning in Embryos

During somitogenesis in embryos, a posteriorly moving differentiation front arrests the oscillations of "segmentation clock" genes, leaving behind a frozen, periodic pattern of expression stripes. Both mathematical theories and experimental observations have invoked a "clock and wavefront" model to explain this phenomenon, in which long-range molecular gradients control the movement of the front and therefore the placement of the stripes in the embryo. Here, we develop a fundamentally different model-a progressive oscillatory reaction-diffusion (PORD) system driven by short-range interactions. In this model, posterior movement of the front is a local, emergent phenomenon that, in contrast to the clock and wavefront model, is not controlled by global positional information. The PORD model explains important features of somitogenesis, such as size regulation, that previous reaction-diffusion models could not explain. Moreover, the PORD and clock and wavefront models make different predictions about the results of FGF-inhibition and tissue-cutting experiments, and we demonstrate that the results of these experiments favor the PORD model.

Time-Delayed Models of Gene Regulatory Networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.

Modelling coupled oscillations in the Notch, Wnt, and FGF signaling pathways during somitogenesis: a comprehensive mathematical model

Somite formation in the early stage of vertebrate embryonic development is controlled by a complicated gene network named segmentation clock, which is defined by the periodic expression of genes related to the Notch, Wnt, and the fibroblast growth factor (FGF) pathways. Although in recent years some findings about crosstalk among the Notch, Wnt, and FGF pathways in somitogenesis have been reported, the investigation of their crosstalk mechanisms from a systematic point of view is still lacking. In this study, a more comprehensive mathematical model was proposed to simulate the dynamics of the Notch, Wnt, and FGF pathways in the segmentation clock. Simulations and bifurcation analyses of this model suggested that the concentration gradients of both Wnt, and FGF signals along the presomitic mesoderm (PSM) are corresponding to the whole process from start to stop of the segmentation clock. A number of highly sensitive parameters to the segmentation clock's oscillatory pattern were identified. By further bifurcation analyses for these sensitive parameters, and several complementary mechanisms in respect of the maintenance of the stable oscillation of the segmentation clock were revealed.

Fast synchronization of ultradian oscillators controlled by delta-notch signaling with cis-inhibition

While it is known that a large fraction of vertebrate genes are under the control of a gene regulatory network (GRN) forming a clock with circadian periodicity, shorter period oscillatory genes like the Hairy-enhancer-of split (Hes) genes are discussed mostly in connection with the embryonic process of somitogenesis. They form the core of the somitogenesis-clock, which orchestrates the periodic separation of somites from the presomitic mesoderm (PSM). The formation of sharp boundaries between the blocks of many cells works only when the oscillators in the cells forming the boundary are synchronized. It has been shown experimentally that Delta-Notch (D/N) signaling is responsible for this synchronization. This process has to happen rather fast as a cell experiences at most five oscillations from its 'birth' to its incorporation into a somite. Computer simulations describing synchronized oscillators with classical modes of D/N-interaction have difficulties to achieve synchronization in an appropriate time. One approach to solving this problem of modeling fast synchronization in the PSM was the consideration of cell movements. Here we show that fast synchronization of Hes-type oscillators can be achieved without cell movements by including D/N cis-inhibition, wherein the mutual interaction of DELTA and NOTCH in the same cell leads to a titration of ligand against receptor so that only one sort of molecule prevails. Consequently, the symmetry between sender and receiver is partially broken and one cell becomes preferentially sender or receiver at a given moment, which leads to faster entrainment of oscillators. Although not yet confirmed by experiment, the proposed mechanism of enhanced synchronization of mesenchymal cells in the PSM would be a new distinct developmental mechanism employing D/N cis-inhibition. Consequently, the way in which Delta-Notch signaling was modeled so far should be carefully reconsidered.

Circadian genes, xBmal1 and xNocturnin, modulate the timing and differentiation of somites in Xenopus laevis

We have been investigating whether xBmal1 and xNocturnin play a role in somitogenesis, a cyclic developmental process with an ultradian period. Previous work from our lab shows that circadian genes (xPeriod1, xPeriod2, xBmal1, and xNocturnin) are expressed in developing somites. Somites eventually form the vertebrae, muscles of the back, and dermis. In Xenopus, a pair of somites is formed about every 50 minutes from anterior to posterior. We were intrigued by the co-localization of circadian genes in an embryonic tissue known to be regulated by an ultradian clock. Cyclic expression of genes involved in Notch signaling has been implicated in the somite clock. Disruption of Notch signaling in humans has been linked to skeletal defects in the vertebral column. We found that both depletion (morpholino) and overexpression (mRNA) of xBMAL1 protein (bHLH transcription factor) or xNOCTURNIN protein (deadenylase) on one side of the developing embryo led to a significant decrease in somite number with respect to the untreated side (p<0.001). These manipulations also significantly affect expression of a somite clock component (xESR9; p<0.05). We observed opposing effects on somite size. Depletion of xBMAL1 or xNOCTURNIN caused a statistically significant decrease in somite area (quantified using NIH ImageJ; p<0.002), while overexpression of these proteins caused a significant dose dependent increase in somite area (p<0.02; p<0.001, respectively). We speculate that circadian genes may play two separate roles during somitogenesis. Depletion and overexpression of xBMAL1 and NOCTURNIN both decrease somite number and influence expression of a somite clock component, suggesting that these proteins may modulate the timing of the somite clock in the undifferentiated presomitic mesoderm. The dosage dependent effects on somite area suggest that xBMAL1 and xNOCTURNIN may also act during somite differentiation to promote myogenesis.

Rbm24a and Rbm24b are required for normal somitogenesis

We recently demonstrated that the gene encoding the RNA binding motif protein 24 (RBM24) is expressed during mouse cardiogenesis, and determined the developmental requirement for its zebrafish homologs Rbm24a and Rbm24b during cardiac development. We demonstrate here that both Rbm24a and Rbm24b are also required for normal somite and craniofacial development. Diminution of rbm24a or rbm24b gene products by morpholino knockdown resulted in significant disruption of somite formation. Detailed in situ hybridization-based analyses of a spectrum of somitogenesis-associated transcripts revealed reduced expression of the cyclic muscle pattering genes dlc and dld encoding Notch ligands, as well as their respective target genes her7, her1. By contrast expression of the Notch receptors notch1a and notch3 appears unchanged. Some RBM-family members have been implicated in pre-mRNA processing. Analysis of affected Notch-pathway mRNAs in rbm24a and rbm24b morpholino-injected embryos revealed aberrant transcript fragments of dlc and dld, but not her1 or her7, suggesting the reduction in transcription levels of Notch pathway components may result from aberrant processing of its ligands. These data imply a previously unknown requirement for Rbm24a and Rbm24b in somite and craniofacial development. Although we anticipate the influence of disrupting RBM24 homologs likely extends beyond the Notch pathway, our results suggest their perturbation may directly, or indirectly, compromise post-transcriptional processing, exemplified by imprecise processing of dlc and dld.

The precise timeline of transcriptional regulation reveals causation in mouse somitogenesis network

Background

In vertebrate development, the segmental pattern of the body axis is established as somites, masses of mesoderm distributed along the two sides of the neural tube, are formed sequentially in the anterior-posterior axis. This mechanism depends on waves of gene expression associated with the Notch, Fgf and Wnt pathways. The underlying transcriptional regulation has been studied by whole-transcriptome mRNA profiling; however, interpretation of the results is limited by poor resolution, noisy data, small sample size and by the absence of a wall clock to assign exact time for recorded points.

Results

We present a method of Maximum Entropy deconvolution in both space and time and apply it to extract, from microarray timecourse data, the full spatiotemporal expression profiles of genes involved in mouse somitogenesis. For regulated genes, we have reconstructed the temporal profiles and determined the timing of expression peaks along the somite cycle to a single-minute resolution. Our results also indicate the presence of a new class of genes (including Raf1 and Hes7) with two peaks of activity in two distinct phases of the somite cycle. We demonstrate that the timeline of gene expression precisely reflects their functions in the biochemical pathways and the direction of causation in the regulatory networks.

Conclusions

By applying a novel framework for data analysis, we have shown a striking correspondence between gene expression times and their interactions and regulations during somitogenesis. These results prove the key role of finely tuned transcriptional regulation in the process. The presented method can be readily applied to studying somite formation in other datasets and species, and to other spatiotemporal processes.