DeltaC and DeltaD ligands play different roles in the segmentation clock dynamics

The vertebrate segmentation clock drives periodic somite segmentation during embryonic development. Her1 and Her7 clock proteins generate oscillatory expression of their own genes as well as that of deltaC in zebrafish. In turn, DeltaC and DeltaD ligands activate Notch signaling, which then activates transcription of clock genes in neighboring cells. While DeltaC and DeltaD proteins form homo- and heterodimers, only DeltaC-containing oscillatory dimers were expected to be functional. To investigate the contributions of DeltaC and DeltaD proteins on the transcription of her1 and her7 segmentation clock genes, we counted their transcripts by performing single molecule fluorescent in situ hybridization imaging in different genetic backgrounds of zebrafish embryos. Surprisingly, we found that DeltaD homodimers are also functional. We further found that Notch signaling promotes transcription of both deltaC and deltaD genes, thereby creating a previously unnoticed positive feedback loop. Our computational model highlighted the intriguing differential roles of DeltaC and DeltaD dimers on the clock synchronization and transcript numbers, respectively. We anticipate that a mechanistic understanding of the Notch signaling pathway will not only shed light on the mechanism driving robust somite segmentation but also inspire similar quantitative studies in other tissues and organs.

The vertebrate segmentation clock drives segmentation by stabilizing Dusp phosphatases in zebrafish

Pulsatile activity of the extracellular signal-regulated kinase (ERK) controls several cellular, developmental, and regenerative programs. Sequential segmentation of somites along the vertebrate body axis, a key developmental program, is also controlled by ERK activity oscillation. The oscillatory expression of Her/Hes family transcription factors constitutes the segmentation clock, setting the period of segmentation. Although oscillation of ERK activity depends on Her/Hes proteins, the underlying molecular mechanism remained mysterious. Here, we show that Her/Hes proteins physically interact with and stabilize dual-specificity phosphatases (Dusp) of ERK, resulting in oscillations of Dusp4 and Dusp6 proteins. Pharmaceutical and genetic inhibition of Dusp activity disrupt ERK activity oscillation and somite segmentation in zebrafish. Our results demonstrate that post-translational interactions of Her/Hes transcription factors with Dusp phosphatases establish the fundamental vertebrate body plan. We anticipate that future studies will identify currently unnoticed post-translational control of ERK pulses in other systems.

Progress in understanding the vertebrate segmentation clock

The segmentation clock is a molecular oscillator that regulates the periodic formation of somites from the presomitic mesoderm during vertebrate embryogenesis. Synchronous oscillatory expression of a Hairy homologue or Hairy-related basic helix-loop-helix (bHLH) transcriptional repressor in presomitic mesoderm cells regulates periodic expression of downstream factors that control somite segmentation with a periodicity that varies across species. Although many of the key components of the clock have been identified and characterized, less is known about how the clock is synchronized across cells and how species-specific periodicity is achieved. Advances in live imaging, stem cell and organoid technologies, and synthetic approaches have started to uncover the detailed mechanisms underlying these aspects of somitogenesis, providing insight into how morphogenesis is coordinated in space and time during embryonic development.

Cellular and molecular control of vertebrate somitogenesis

Segmentation is a fundamental feature of the vertebrate body plan. This metameric organization is first implemented by somitogenesis in the early embryo, when paired epithelial blocks called somites are rhythmically formed to flank the neural tube. Recent advances in in vitro models have offered new opportunities to elucidate the mechanisms that underlie somitogenesis. Notably, models derived from human pluripotent stem cells introduced an efficient proxy for studying this process during human development. In this Review, we summarize the current understanding of somitogenesis gained from both in vivo studies and in vitro studies. We deconstruct the spatiotemporal dynamics of somitogenesis into four distinct modules: dynamic events in the presomitic mesoderm, segmental determination, somite anteroposterior polarity patterning, and epithelial morphogenesis. We first focus on the segmentation clock, as well as signalling and metabolic gradients along the tissue, before discussing the clock and wavefront and other models that account for segmental determination. We then detail the molecular and cellular mechanisms of anteroposterior polarity patterning and somite epithelialization.

Simplifications and approximations in a single-gene circuit modeling

The absence of detailed knowledge about regulatory interactions makes the use of phenomenological assumptions mandatory in cell biology modeling. Furthermore, the challenges associated with the analysis of these models compel the implementation of mathematical approximations. However, the constraints these methods introduce to biological interpretation are sometimes neglected. Consequently, understanding these restrictions is a very important task for systems biology modeling. In this article, we examine the impact of such simplifications, taking the case of a single-gene autoinhibitory circuit; however, our conclusions are not limited solely to this instance. We demonstrate that models grounded in the same biological assumptions but described at varying levels of detail can lead to different outcomes, that is, different and contradictory phenotypes or behaviors. Indeed, incorporating specific molecular processes like translation and elongation into the model can introduce instabilities and oscillations not seen when these processes are assumed to be instantaneous. Furthermore, incorporating a detailed description of promoter dynamics, usually described by a phenomenological regulatory function, can lead to instability, depending on the cooperative binding mechanism that is acting. Consequently, although the use of a regulating function facilitates model analysis, it may mask relevant aspects of the system's behavior. In particular, we observe that the two cooperative binding mechanisms, both compatible with the same sigmoidal function, can lead to different phenotypes, such as transcriptional oscillations with different oscillation frequencies.

The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro

During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in vitro.

Oscillatory control of embryonic development

Proper embryonic development depends on the timely progression of a genetic program. One of the key mechanisms for achieving precise control of developmental timing is to use gene expression oscillations. In this Review, we examine how gene expression oscillations encode temporal information during vertebrate embryonic development by discussing the gene expression oscillations occurring during somitogenesis, neurogenesis, myogenesis and pancreas development. These oscillations play important but varied physiological functions in different contexts. Oscillations control the period of somite formation during somitogenesis, whereas they regulate the proliferation-to-differentiation switch of stem cells and progenitor cells during neurogenesis, myogenesis and pancreas development. We describe the similarities and differences of the expression pattern in space (i.e. whether oscillations are synchronous or asynchronous across neighboring cells) and in time (i.e. different time scales) of mammalian Hes/zebrafish Her genes and their targets in different tissues. We further summarize experimental evidence for the functional role of their oscillations. Finally, we discuss the outstanding questions for future research.

Species-specific roles of the Notch ligands, receptors, and targets orchestrating the signaling landscape of the segmentation clock

Somitogenesis is a hallmark feature of all vertebrates and some invertebrate species that involves the periodic formation of block-like structures called somites. Somites are transient embryonic segments that eventually establish the entire vertebral column. A highly conserved molecular oscillator called the segmentation clock underlies this periodic event and the pace of this clock regulates the pace of somite formation. Although conserved signaling pathways govern the clock in most vertebrates, the mechanisms underlying the species-specific divergence in various clock characteristics remain elusive. For example, the segmentation clock in classical model species such as zebrafish, chick, and mouse embryos tick with a periodicity of ∼30, ∼90, and ∼120 min respectively. This enables them to form the species-specific number of vertebrae during their overall timespan of somitogenesis. Here, we perform a systematic review of the species-specific features of the segmentation clock with a keen focus on mouse embryos. We perform this review using three different perspectives: Notch-responsive clock genes, ligand-receptor dynamics, and synchronization between neighboring oscillators. We further review reports that use non-classical model organisms and in vitro model systems that complement our current understanding of the segmentation clock. Our review highlights the importance of comparative developmental biology to further our understanding of this essential developmental process.

Spatiotemporal control of pattern formation during somitogenesis

Spatiotemporal patterns widely occur in biological, chemical, and physical systems. Particularly, embryonic development displays a diverse gamut of repetitive patterns established in many tissues and organs. Branching treelike structures in lungs, kidneys, livers, pancreases, and mammary glands as well as digits and bones in appendages, teeth, and palates are just a few examples. A fascinating instance of repetitive patterning is the sequential segmentation of the primary body axis, which is conserved in all vertebrates and many arthropods and annelids. In these species, the body axis elongates at the posterior end of the embryo containing an unsegmented tissue. Meanwhile, segments sequentially bud off from the anterior end of the unsegmented tissue, laying down an exquisite repetitive pattern and creating a segmented body plan. In vertebrates, the paraxial mesoderm is sequentially divided into somites. In this review, we will discuss the most prominent models, the most puzzling experimental data, and outstanding questions in vertebrate somite segmentation.

The Clockwork Embryo: Mechanisms Regulating Developmental Rate

Organismal development requires the reproducible unfolding of an ordered sequence of discrete steps (cell fate determination, migration, tissue folding, etc.) in both time and space. Here, we review the mechanisms that grant temporal specificity to developmental steps, including molecular clocks and timers. Individual timing mechanisms must be coordinated with each other to maintain the overall developmental sequence. However, phenotypic novelties can also arise through the modification of temporal patterns over the course of evolution. Two main types of variation in temporal patterning characterize interspecies differences in developmental time: allochrony, where the overall developmental sequence is either accelerated or slowed down while maintaining the relative duration of individual steps, and heterochrony, where the duration of specific developmental steps is altered relative to the rest. New advances in in vitro modeling of mammalian development using stem cells have recently enabled the revival of mechanistic studies of allochrony and heterochrony. In both cases, differences in the rate of basic cellular functions such as splicing, translation, protein degradation, and metabolism seem to underlie differences in developmental time. In the coming years, these studies should identify the genetic differences that drive divergence in developmental time between species.

A design logic for sequential segmentation across organisms

Multitudes of organisms display metameric compartmentalization of their body plan. Segmentation of these compartments happens sequentially in diverse phyla. In several sequentially segmenting species, periodically active molecular clocks and signaling gradients have been found. The clocks are proposed to control the timing of segmentation, while the gradients are proposed to instruct the positions of segment boundaries. However, the identity of the clock and gradient molecules differs across species. Furthermore, sequential segmentation of a basal chordate, Amphioxus, continues at late stages when the small tail bud cell population cannot establish long-range signaling gradients. Thus, it remains to be explained how a conserved morphological trait (i.e., sequential segmentation) is achieved by using different molecules or molecules with different spatial profiles. Here, we first focus on sequential segmentation of somites in vertebrate embryos and then draw parallels with other species. Thereafter, we propose a candidate design principle that has the potential to answer this puzzling question.

Stochastic gene expression and environmental stressors trigger variable somite segmentation phenotypes

Mutations of several genes cause incomplete penetrance and variable expressivity of phenotypes, which are usually attributed to modifier genes or gene-environment interactions. Here, we show stochastic gene expression underlies the variability of somite segmentation defects in embryos mutant for segmentation clock genes her1 or her7. Phenotypic strength is further augmented by low temperature and hypoxia. By performing live imaging of the segmentation clock reporters, we further show that groups of cells with higher oscillation amplitudes successfully form somites while those with lower amplitudes fail to do so. In unfavorable environments, the number of cycles with high amplitude oscillations and the number of successful segmentations proportionally decrease. These results suggest that individual oscillation cycles stochastically fail to pass a threshold amplitude, resulting in segmentation defects in mutants. Our quantitative methodology is adaptable to investigate variable phenotypes of mutant genes in different tissues.

Autoregulation of Transcription and Translation: A Qualitative Analysis

The regulation of both mRNA transcription and translation by down-stream gene products allows for a range of rich dynamical behaviours (e.g. homeostatic, oscillatory, excitability and intermittent solutions). Here, qualitative analysis is applied to an existing model of a gene regulatory network in which a protein dimer inhibits its own transcription and upregulates its own translation rate. It is demonstrated that the model possesses a unique steady state, conditions are derived under which limit cycle solutions arise and estimates are provided for the oscillator period in the limiting case of a relaxation oscillator. The analysis demonstrates that oscillations can arise only if mRNA is more stable than protein and the effect of nonlinear translation inhibition is sufficiently strong. Moreover, it is shown that the oscillation period can vary non-monotonically with transcription rate. Thus the proposed framework can provide an explanation for observed species-specific dependency of segmentation clock period on Notch signalling activity. Finally, this study facilitates the application of the proposed model to more general biological settings where post transcriptional regulation effects are likely important.

Periodic inhibition of Erk activity drives sequential somite segmentation

Sequential segmentation creates modular body plans of diverse metazoan embryos^1-4. Somitogenesis establishes the segmental pattern of the vertebrate body axis. A molecular segmentation clock in the presomitic mesoderm sets the pace of somite formation⁴. However, how cells are primed to form a segment boundary at a specific location remains unclear. Here we developed precise reporters for the clock and double-phosphorylated Erk (ppErk) gradient in zebrafish. We show that the Her1-Her7 oscillator drives segmental commitment by periodically lowering ppErk, therefore projecting its oscillation onto the ppErk gradient. Pulsatile inhibition of the ppErk gradient can fully substitute for the role of the clock, and kinematic clock waves are dispensable for sequential segmentation. The clock functions upstream of ppErk, which in turn enables neighbouring cells to discretely establish somite boundaries in zebrafish⁵. Molecularly divergent clocks and morphogen gradients were identified in sequentially segmenting species^3,4,6-8. Our findings imply that versatile clocks may establish sequential segmentation in diverse species provided that they inhibit gradients.

The vertebrate Embryo Clock: Common players dancing to a different beat

Vertebrate embryo somitogenesis is the earliest morphological manifestation of the characteristic patterned structure of the adult axial skeleton. Pairs of somites flanking the neural tube are formed periodically during early development, and the molecular mechanisms in temporal control of this early patterning event have been thoroughly studied. The discovery of a molecular Embryo Clock (EC) underlying the periodicity of somite formation shed light on the importance of gene expression dynamics for pattern formation. The EC is now known to be present in all vertebrate organisms studied and this mechanism was also described in limb development and stem cell differentiation. An outstanding question, however, remains unanswered: what sets the different EC paces observed in different organisms and tissues? This review aims to summarize the available knowledge regarding the pace of the EC, its regulation and experimental manipulation and to expose new questions that might help shed light on what is still to unveil.

Regulatory mechanisms ensuring coordinated expression of functionally related genes

Coordinated spatiotemporal expression of large sets of genes is required for the development and homeostasis of organisms. To achieve this goal, organisms use myriad strategies where they form operons, utilize bidirectional promoters, cluster genes, share enhancers among genes by DNA looping, and form topologically associated domains and transcriptional condensates. Coexpression achieved by these different strategies is hypothesized to have functional importance in minimizing gene expression variability, establishing dosage balance to ensure stoichiometry of protein complexes, and minimizing accumulation of toxic intermediate metabolites. By combining gene-editing tools with computational modeling, recent studies tested the advantages of adjacent genes located in pairs and clusters. We propose that with the advancement of gene editing, single-cell sequencing, and imaging tools, one could readily test the functional importance of different coexpression strategies in a variety of biological processes.

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.

From local resynchronization to global pattern recovery in the zebrafish segmentation clock

Integrity of rhythmic spatial gene expression patterns in the vertebrate segmentation clock requires local synchronization between neighboring cells by Delta-Notch signaling and its inhibition causes defective segment boundaries. Whether deformation of the oscillating tissue complements local synchronization during patterning and segment formation is not understood. We combine theory and experiment to investigate this question in the zebrafish segmentation clock. We remove a Notch inhibitor, allowing resynchronization, and analyze embryonic segment recovery. We observe unexpected intermingling of normal and defective segments, and capture this with a new model combining coupled oscillators and tissue mechanics. Intermingled segments are explained in the theory by advection of persistent phase vortices of oscillators. Experimentally observed changes in recovery patterns are predicted in the theory by temporal changes in tissue length and cell advection pattern. Thus, segmental pattern recovery occurs at two length and time scales: rapid local synchronization between neighboring cells, and the slower transport of the resulting patterns across the tissue through morphogenesis.

Pairing of segmentation clock genes drives robust pattern formation

Gene expression is an inherently stochastic process ^1,2; however, organismal development and homeostasis require that cells spatiotemporally coordinate the expression of large sets of genes. Coexpressed gene pairs in metazoans often reside in the same chromosomal neighborhood, with gene pairs representing 10% - 50% of all genes depending on species ^3–6. As shared upstream regulators can ensure correlated gene expression, the selective advantage of maintaining adjacent gene pairs remains unknown ⁶. Here, using two linked zebrafish segmentation clock genes, her1 and her7, and combining single-cell transcript counting, genetic engineering, real-time imaging and computational modeling, we reveal that gene pairing boosts correlated transcription and provides phenotypic robustness for developmental pattern formation. Our results demonstrate that disrupting gene pairing disrupts oscillations and segmentation, identifying the selective pressure retaining correlated transcription to sustain a robust and rapid developmental clock. We anticipate that these findings will inspire investigating advantages of gene pairing in other systems and engineering precise synthetic clocks in embryos and organoids.

Waiting on the Fringe: cell autonomy and signaling delays in segmentation clocks

The rhythmic and sequential segmentation of the vertebrate body axis into somites during embryogenesis is governed by a multicellular, oscillatory patterning system called the segmentation clock. Despite many overt similarities between vertebrates, differences in genetic and dynamic regulation have been reported, raising intriguing questions about the evolution and conservation of this fundamental patterning process. Recent studies have brought insights into two important and related issues: (1) whether individual cells of segmentation clocks are autonomous oscillators or require cell-cell communication for their rhythm; and (2) the role of delays in the cell-cell communication that synchronizes the population of genetic oscillators. Although molecular details differ between species, conservation may exist at the level of the dynamics, hinting at rules for evolutionary trajectories in the system.

Noise in the Vertebrate Segmentation Clock Is Boosted by Time Delays but Tamed by Notch Signaling

Taming cell-to-cell variability in gene expression is critical for precise pattern formation during embryonic development. To investigate the source and buffering mechanism of expression variability, we studied a biological clock, the vertebrate segmentation clock, controlling the precise spatiotemporal patterning of the vertebral column. By counting single transcripts of segmentation clock genes in zebrafish, we show that clock genes have low RNA amplitudes and expression variability is primarily driven by gene extrinsic sources, which is suppressed by Notch signaling. We further show that expression noise surprisingly increases from the posterior progenitor zone to the anterior segmentation and differentiation zone. Our computational model reproduces the spatial noise profile by incorporating spatially increasing time delays in gene expression. Our results, suggesting that expression variability is controlled by the balance of time delays and cell signaling in a vertebrate tissue, will shed light on the accuracy of natural clocks in multi-cellular systems and inspire engineering of robust synthetic oscillators.

CDK1 and CDK2 regulate NICD1 turnover and the periodicity of the segmentation clock

All vertebrates share a segmented body axis. Segments form from the rostral end of the presomitic mesoderm (PSM) with a periodicity that is regulated by the segmentation clock. The segmentation clock is a molecular oscillator that exhibits dynamic clock gene expression across the PSM with a periodicity that matches somite formation. Notch signalling is crucial to this process. Altering Notch intracellular domain (NICD) stability affects both the clock period and somite size. However, the mechanism by which NICD stability is regulated in this context is unclear. We identified a highly conserved site crucial for NICD recognition by the SCF E3 ligase, which targets NICD for degradation. We demonstrate both CDK1 and CDK2 can phosphorylate NICD in the domain where this crucial residue lies and that NICD levels vary in a cell cycle-dependent manner. Inhibiting CDK1 or CDK2 activity increases NICD levels both in vitro and in vivo, leading to a delay of clock gene oscillations and an increase in somite size.

Regulatory Network of the Scoliosis-Associated Genes Establishes Rostrocaudal Patterning of Somites in Zebrafish

Gene regulatory networks govern pattern formation and differentiation during embryonic development. Segmentation of somites, precursors of the vertebral column among other tissues, is jointly controlled by temporal signals from the segmentation clock and spatial signals from morphogen gradients. To explore how these temporal and spatial signals are integrated, we combined time-controlled genetic perturbation experiments with computational modeling to reconstruct the core segmentation network in zebrafish. We found that Mesp family transcription factors link the temporal information of the segmentation clock with the spatial action of the fibroblast growth factor signaling gradient to establish rostrocaudal (head to tail) polarity of segmented somites. We further showed that cells gradually commit to patterning by the action of different genes at different spatiotemporal positions. Our study provides a blueprint of the zebrafish segmentation network, which includes evolutionarily conserved genes that are associated with the birth defect congenital scoliosis in humans.

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A core network establishes rostrocaudal polarity of segmented somites in zebrafish

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mesp genes link the segmentation clock with the FGF signaling gradient

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Gradual patterning is done by the action of different genes at different positions

LlamaTags: A Versatile Tool to Image Transcription Factor Dynamics in Live Embryos

Embryonic cell fates are defined by transcription factors that are rapidly deployed, yet attempts to visualize these factors in vivo often fail because of slow fluorescent protein maturation. Here, we pioneer a protein tag, LlamaTag, which circumvents this maturation limit by binding mature fluorescent proteins, making it possible to visualize transcription factor concentration dynamics in live embryos. Implementing this approach in the fruit fly Drosophila melanogaster, we discovered stochastic bursts in the concentration of transcription factors that are correlated with bursts in transcription. We further used LlamaTags to show that the concentration of protein in a given nucleus heavily depends on transcription of that gene in neighboring nuclei; we speculate that this inter-nuclear signaling is an important mechanism for coordinating gene expression to delineate straight and sharp boundaries of gene expression. Thus, LlamaTags now make it possible to visualize the flow of information along the central dogma in live embryos.

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.

Differential interactions between Notch and ID factors control neurogenesis by modulating Hes factor autoregulation

During embryonic and adult neurogenesis, neural stem cells (NSCs) generate the correct number and types of neurons in a temporospatial fashion. Control of NSC activity and fate is crucial for brain formation and homeostasis. Neurogenesis in the embryonic and adult brain differ considerably, but Notch signaling and inhibitor of DNA-binding (ID) factors are pivotal in both. Notch and ID factors regulate NSC maintenance; however, it has been difficult to evaluate how these pathways potentially interact. Here, we combined mathematical modeling with analysis of single-cell transcriptomic data to elucidate unforeseen interactions between the Notch and ID factor pathways. During brain development, Notch signaling dominates and directly regulates Id4 expression, preventing other ID factors from inducing NSC quiescence. Conversely, during adult neurogenesis, Notch signaling and Id2/3 regulate neurogenesis in a complementary manner and ID factors can induce NSC maintenance and quiescence in the absence of Notch. Our analyses unveil key molecular interactions underlying NSC maintenance and mechanistic differences between embryonic and adult neurogenesis. Similar Notch and ID factor interactions may be crucial in other stem cell systems.

Summary: Computational analysis of transcriptome data from neural stem cells reveals key differences in the synergistic interactions between Notch and inhibitor of DNA-binding factors during embryonic and adult neurogenesis.

Pnrc2 regulates 3'UTR-mediated decay of segmentation clock-associated transcripts during zebrafish segmentation

Vertebrate segmentation is controlled by the segmentation clock, a molecular oscillator that regulates gene expression and cycles rapidly. The expression of many genes oscillates during segmentation, including hairy/Enhancer of split-related (her or Hes) genes, which encode transcriptional repressors that auto-inhibit their own expression, and deltaC (dlc), which encodes a Notch ligand. We previously identified the tortuga (tor) locus in a zebrafish forward genetic screen for genes involved in cyclic transcript regulation and showed that cyclic transcripts accumulate post-splicing in tor mutants. Here we show that cyclic mRNA accumulation in tor mutants is due to loss of pnrc2, which encodes a proline-rich nuclear receptor co-activator implicated in mRNA decay. Using an inducible in vivo reporter system to analyze transcript stability, we find that the her1 3'UTR confers Pnrc2-dependent instability to a heterologous transcript. her1 mRNA decay is Dicer-independent and likely employs a Pnrc2-Upf1-containing mRNA decay complex. Surprisingly, despite accumulation of cyclic transcripts in pnrc2-deficient embryos, we find that cyclic protein is expressed normally. Overall, we show that Pnrc2 promotes 3'UTR-mediated decay of developmentally-regulated segmentation clock transcripts and we uncover an additional post-transcriptional regulatory layer that ensures oscillatory protein expression in the absence of cyclic mRNA decay.

The kinetics in mathematical models on segmentation clock genes in zebrafish

Somitogenesis is the process for the development of somites in vertebrate embryos. This process is timely regulated by synchronous oscillatory expression of the segmentation clock genes. Mathematical models expressed by delay equations or ODEs have been proposed to depict the kinetics of these genes in interacting cells. Through mathematical analysis, we investigate the parameter regimes for synchronous oscillations and oscillation-arrested in an ODE model and a model with transcriptional and translational delays, both with Michaelis-Menten type degradations. Comparisons between these regimes for the two models are made. The delay model has larger capacity to accommodate synchronous oscillations. Based on the analysis and numerical computations extended from the analysis, we explore how the periods and amplitudes of the oscillations vary with the degradation rates, synthesis rates, and coupling strength. For typical parameter values, the period and amplitude increase as some synthesis rate or the coupling strength increases in the ODE model. Such variational properties of oscillations depend also on the magnitudes of time delays in delay model. We also illustrate the difference between the dynamics in systems modeled with linear degradation and the ones in systems with Michaelis-Menten type reactions for the degradation. The chief concerns are the connections between the dynamics in these models and the mechanism for the segmentation clocks, and the pertinence of mathematical modeling on somitogenesis in zebrafish.

Synchronized oscillations of dimers in biphasic charged fd-virus suspensions

Micron-sized colloidal spheres that are dispersed in an isotropic-nematic biphasic host suspension of charged rods (fd-virus particles) are shown to spontaneously form dimers, which exhibit a synchronized oscillatory motion. Dimer formation is not observed in the monophase of isotropic and nematic suspensions. The synchronized oscillations of dimers are connected to the inhomogeneous state of the host suspension of charged rods (fd viruses) where nematic domains are in coexistence with isotropic regions. The synchronization of oscillations occurs in bulk states, in the absence of an external field. With a low field strength of an applied electric field, the synchronization is rather reduced, but it recovers again when the field is turned off. In this Rapid Communication, we report this observation as an example of the strange attractor, occurring in the mixture of PS (polystyrene) dimers in an isotropic-nematic coexistence biphasic fd-virus network. Furthermore, we highlight that the synchronization of PS-dimer oscillations is the result of a global bifurcation diagram, driven by a delicate balance between the short-attractive "twisted" interaction of PS dimers and long-ranged electrostatic repulsive interactions of charged fd rods. The interest is then in the local enhancement of "twist-nematic" elasticity in reorientation of the dimer oscillations. An analysis of image-time correlations is provided with the data movies and Fourier transforms of averaged orientations for the synchronized oscillations of dimers in the biphasic I-N coexistence concentration of charged fd-virus suspensions.

Limits of computational biology

Are we close to a complete inventory of living processes so that we might expect in the near future to reproduce every essential aspect necessary for life? Or are there mechanisms and processes in cells and organisms that are presently inaccessible to us? Here I argue that a close examination of a particularly well-understood system— that of Escherichia coli chemotaxis— shows we are still a long way from a complete description. There is a level of molecular uncertainty, particularly that responsible for fine-tuning and adaptation to myriad external conditions, which we presently cannot resolve or reproduce on a computer. Moreover, the same uncertainty exists for any process in any organism and is especially pronounced and important in higher animals such as humans. Embryonic development, tissue homeostasis, immune recognition, memory formation, and survival in the real world, all depend on vast numbers of subtle variations in cell chemistry most of which are presently unknown or only poorly characterized. Overcoming these limitations will require us to not only accumulate large quantities of highly detailed data but also develop new computational methods able to recapitulate the massively parallel processing of living cells.

Signaling Delays Preclude Defects in Lateral Inhibition Patterning

Lateral inhibition represents a well-studied example of biology's ability to self-organize multicellular spatial patterns with single-cell precision. Despite established biochemical mechanisms for lateral inhibition (e.g., Delta-Notch), it remains unclear how cell-cell signaling delays inherent to these mechanisms affect patterning outcomes. We investigate a compact model of lateral inhibition highlighting these delays and find, remarkably, that long delays can ensure defect-free patterning. This effect is underscored by an interplay with synchronous oscillations, cis interactions, and signaling strength. Our results suggest that signaling delays, though previously posited as a source of developmental defects, may in fact be a general regulatory knob for tuning developmental robustness.

Genetic oscillators in development

In development, morphogenetic processes are strictly coordinated in time. Cells in a developing tissue would need mechanisms for time-keeping. One such time-keeping mechanism is to use oscillations of gene expression. Oscillatory gene expression can be generated by transcriptional/translational feedback loops, usually referred to as a genetic oscillator. In this review article, we discuss genetic oscillators in the presence of developmental processes such as cell division, cell movement and cell differentiation. We first introduce the gene regulatory network for generating a rhythm of gene expression. We then discuss how developmental processes influence genetic oscillators. Examples include vertebrate somitogenesis and neural progenitor cell differentiation, as well as the circadian clock for comparison. To understand the behaviors of genetic oscillators in development, it is necessary to consider both gene expression dynamics and cellular behaviors simultaneously. Theoretical modeling combined with live imaging at single-cell resolution will be a powerful tool to analyze genetic oscillators in development.

Stochastic Regulation of her1/7 Gene Expression Is the Source of Noise in the Zebrafish Somite Clock Counteracted by Notch Signalling

The somite segmentation clock is a robust oscillator used to generate regularly-sized segments during early vertebrate embryogenesis. It has been proposed that the clocks of neighbouring cells are synchronised via inter-cellular Notch signalling, in order to overcome the effects of noisy gene expression. When Notch-dependent communication between cells fails, the clocks of individual cells operate erratically and lose synchrony over a period of about 5 to 8 segmentation clock cycles (2-3 hours in the zebrafish). Here, we quantitatively investigate the effects of stochasticity on cell synchrony, using mathematical modelling, to investigate the likely source of such noise. We find that variations in the transcription, translation and degradation rate of key Notch signalling regulators do not explain the in vivo kinetics of desynchronisation. Rather, the analysis predicts that clock desynchronisation, in the absence of Notch signalling, is due to the stochastic dissociation of Her1/7 repressor proteins from the oscillating her1/7 autorepressed target genes. Using in situ hybridisation to visualise sites of active her1 transcription, we measure an average delay of approximately three minutes between the times of activation of the two her1 alleles in a cell. Our model shows that such a delay is sufficient to explain the in vivo rate of clock desynchronisation in Notch pathway mutant embryos and also that Notch-mediated synchronisation is sufficient to overcome this stochastic variation. This suggests that the stochastic nature of repressor/DNA dissociation is the major source of noise in the segmentation clock.

A balance of positive and negative regulators determines the pace of the segmentation clock

Somitogenesis is regulated by a molecular oscillator that drives dynamic gene expression within the pre-somitic mesoderm. Previous mathematical models of the somitogenesis clock that invoke the mechanism of delayed negative feedback predict that its oscillation period depends on the sum of delays inherent to negative-feedback loops and inhibitor half-lives. We develop a mathematical model that explores the possibility that positive feedback also plays a role in determining the period of clock oscillations. The model predicts that increasing the half-life of the positive regulator, Notch intracellular domain (NICD), can lead to elevated NICD levels and an increase in the oscillation period. To test this hypothesis, we investigate a phenotype induced by various small molecule inhibitors in which the clock is slowed. We observe elevated levels and a prolonged half-life of NICD. Reducing NICD production rescues these effects. These data provide the first indication that tight control of the turnover of positive as well as negative regulators of the clock determines its periodicity.

DOI:http://dx.doi.org/10.7554/eLife.05842.001

During embryo development, animals with backbones (also called vertebrates) repeatedly lay down pairs of segments along the axis that runs from the head to the tail of the embryo. These segments, known as somites, eventually form part of the skeleton, as well as the associated muscle, cartilage, tendons and some skin. Importantly, the segments in some species take longer to form than those in other species, and they also form in proportion to the overall size of the animal.

A ‘segmentation clock’ regulates the timing of somite formation via cycles in which genes are repeatedly switched on and then off again. Some aspects of this process are well understood. Firstly, many ‘clock genes’ are known to produce proteins that can inhibit their own production. However, this ‘negative feedback’ is typically delayed because it takes time to produce and transport protein within a cell. The inhibitory proteins are also unstable and their breakdown leads to an end of their inhibitiory effect. It is also known that: some proteins send signals to neighbouring cells while others, including one called Notch, receive them; and the received signals activate the expression of clock genes. However, until now, no one had studied how the turnover (that is, the production and breakdown) of the proteins that activate clock gene expression could regulate the pace of the clock.

Wiedermann, Bone et al. used a two-pronged approach to investigate this question. First, they developed a computational model that accounted for both inhibition and activation of clock gene expression. The model predicts that the clock slows down when the levels of a positive regulator called Notch intracellular domain (or NICD for short) are high. This is because the negative regulators would have to overcome the increased positive regulators to switch off the clock genes. A slower segmentation clock would be expected to give rise to fewer, larger somites in a given length of time when compared to a similar clock with a faster pace.

To test these predictions, Wiedermann, Bone et al. next conducted experiments on chicken embryos, which are commonly used in studies of animal development. The experiments agreed with the model predictions. That is, when treated with a variety of drugs that affected NICD turnover and thereby increased the levels of NICD, the clock slowed and these chicken embryos developed fewer, but larger somites. As predicted by the mathematical model, these effects were rescued when Wiedermann, Bone et al. reduced the production of NICD. These findings show that a balance of positive and negative regulators determines the pace of the segmentation clock.

DOI:http://dx.doi.org/10.7554/eLife.05842.002

Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves

The vertebrate segmentation clock is a gene expression oscillator controlling rhythmic segmentation of the vertebral column during embryonic development. The period of oscillations becomes longer as cells are displaced along the posterior to anterior axis, which results in traveling waves of clock gene expression sweeping in the unsegmented tissue. Although various hypotheses necessitating the inclusion of additional regulatory genes into the core clock network at different spatial locations have been proposed, the mechanism underlying traveling waves has remained elusive. Here, we combined molecular-level computational modeling and quantitative experimentation to solve this puzzle. Our model predicts the existence of an increasing gradient of gene expression time delays along the posterior to anterior direction to recapitulate spatiotemporal profiles of the traveling segmentation clock waves in different genetic backgrounds in zebrafish. We validated this prediction by measuring an increased time delay of oscillatory Her1 protein production along the unsegmented tissue. Our results refuted the need for spatial expansion of the core feedback loop to explain the occurrence of traveling waves. Spatial regulation of gene expression time delays is a novel way of creating dynamic patterns; this is the first report demonstrating such a control mechanism in any tissue and future investigations will explore the presence of analogous examples in other biological systems.

Nonlinearity arising from noncooperative transcription factor binding enhances negative feedback and promotes genetic oscillations

We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show that this increased nonlinearity is reflected in enhanced oscillations, with larger amplitudes over wider oscillatory ranges. Although the study is motivated by genetic oscillations in the zebrafish segmentation clock, our findings may reveal a general principle for gene regulation.

Pulses of Notch activation synchronise oscillating somite cells and entrain the zebrafish segmentation clock

Formation of somites, the rudiments of vertebrate body segments, is an oscillatory process governed by a gene-expression oscillator, the segmentation clock. This operates in each cell of the presomitic mesoderm (PSM), but the individual cells drift out of synchrony when Delta/Notch signalling fails, causing gross anatomical defects. We and others have suggested that this is because synchrony is maintained by pulses of Notch activation, delivered cyclically by each cell to its neighbours, that serve to adjust or reset the phase of the intracellular oscillator. This, however, has never been proved. Here, we provide direct experimental evidence, using zebrafish containing a heat-shock-driven transgene that lets us deliver artificial pulses of expression of the Notch ligand DeltaC. In DeltaC-defective embryos, in which endogenous Notch signalling fails, the artificial pulses restore synchrony, thereby rescuing somite formation. The spacing of segment boundaries produced by repetitive heat-shocking varies according to the time interval between one heat-shock and the next. The induced synchrony is manifest both morphologically and at the level of the oscillations of her1, a core component of the intracellular oscillator. Thus, entrainment of intracellular clocks by periodic activation of the Notch pathway is indeed the mechanism maintaining cell synchrony during somitogenesis.

Dynamics matter: differences and similarities between alternatively designed mechanisms

Cells selectively respond to external stimuli to maintain cellular homeostasis by making use of different regulatory mechanisms. We studied two classes of signal-dependent regulatory inhibition and activation mechanisms in this study. Inhibition mechanisms assume that inhibition can occur in two different ways: either by increasing the degradation rate or decreasing the production rate. Similarly, it is assumed that signal-triggered activation can occur either through increasing production rate or decreasing degradation rate. We devised mathematical models (deterministic and stochastic) to compare and contrast responses of these activation and inhibition mechanisms to a time dependent discrete signal. Our simulation results show that the signal-dependent increased degradation mechanism is a more effective, noisier and quicker way to inhibit the protein abundance compared to the signal-dependent decreased activation mechanism. On the other hand, the signal-dependent increased production mechanism can produce a much stronger and faster response than the signal-dependent decreased degradation mechanism. However, our simulations predict that both of the activation mechanisms have roughly similar noise structures. Our analysis exemplifies the importance of mathematical modeling in the analysis of biological regulatory networks.

Modeling the zebrafish segmentation clock's gene regulatory network constrained by expression data suggests evolutionary transitions between oscillating and nonoscillating transcription

During segmentation of vertebrate embryos, somites form in accordance with a periodic pattern established by the segmentation clock. In the zebrafish (Danio rerio), the segmentation clock includes six hairy/enhancer of split-related (her/hes) genes, five of which oscillate due to negative autofeedback. The nonoscillating gene hes6 forms the hub of a network of 10 Her/Hes protein dimers, which includes 7 DNA-binding dimers and 4 weak or non-DNA-binding dimers. The balance of dimer species is critical for segmentation clock function, and loss-of-function studies suggest that the her genes have both unique and redundant functions within the clock. However, the precise regulatory interactions underlying the negative feedback loop are unknown. Here, we combine quantitative experimental data, in silico modeling, and a global optimization algorithm to identify a gene regulatory network (GRN) designed to fit measured transcriptional responses to gene knockdown. Surprisingly, we find that hes6, the clock gene that does not oscillate, responds to negative feedback. Consistent with prior in silico analyses, we find that variation in transcription, translation, and degradation rates can mediate the gain and loss of oscillatory behavior for genes regulated by negative feedback. Extending our study, we found that transcription of the nonoscillating Fgf pathway gene sef responds to her/hes perturbation similarly to oscillating her genes. These observations suggest a more extensive underlying regulatory similarity between the zebrafish segmentation clock and the mouse and chick segmentation clocks, which exhibit oscillations of her/hes genes as well as numerous other Notch, Fgf, and Wnt pathway genes.