Topology and dynamics of the zebrafish segmentation clock core circuit

Approximated gene expression trajectories for gene regulatory network inference on cell tracks

The study of pattern formation has benefited from our ability to reverse-engineer gene regulatory network (GRN) structure from spatiotemporal quantitative gene expression data. Traditional approaches have focused on systems where the timescales of pattern formation and morphogenesis can be separated. Unfortunately, this is not the case in most animal patterning systems, where pattern formation and morphogenesis are co-occurring and tightly linked. To elucidate patterning mechanisms in such systems we need to adapt our GRN inference methodologies to include cell movements. In this work, we fill this gap by integrating quantitative data from live and fixed embryos to approximate gene expression trajectories (AGETs) in single cells and use these to reverse-engineer GRNs. This framework generates candidate GRNs that recapitulate pattern at the tissue level, gene expression dynamics at the single cell level, recover known genetic interactions and recapitulate experimental perturbations while incorporating cell movements explicitly for the first time.

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.

Cell coupling compensates for changes in single-cell Her6 dynamics and provides phenotypic robustness

This paper investigates the effect of altering the protein expression dynamics of the bHLH transcription factor Her6 at the single-cell level in the embryonic zebrafish telencephalon. Using a homozygote endogenous Her6:Venus reporter and 4D single-cell tracking, we show that Her6 oscillates in neural telencephalic progenitors and that the fusion of protein destabilisation (PEST) domain alters its expression dynamics, causing most cells to downregulate Her6 prematurely. However, counterintuitively, oscillatory cells increase, with some expressing Her6 at high levels, resulting in increased heterogeneity of Her6 expression in the population. These tissue-level changes appear to be an emergent property of coupling between single-cells, as revealed by experimentally disrupting Notch signalling and by computationally modelling alterations in Her6 protein stability. Despite the profound differences in the single-cell Her6 dynamics, the size of the telencephalon is only transiently altered and differentiation markers do not exhibit significant differences early on; however, a small increase is observed at later developmental stages. Our study suggests that cell coupling provides a compensation strategy, whereby an almost normal phenotype is maintained even though single-cell gene expression dynamics are abnormal, granting phenotypic robustness.

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.

Generation of patterns in the paraxial mesoderm

The Segmentation Clock is a tissue-level patterning system that enables the segmentation of the vertebral column precursors into transient multicellular blocks called somites. This patterning system comprises a set of elements that are essential for correct segmentation. Under the so-called "Clock and Wavefront" model, the system consists of two elements, a genetic oscillator that manifests itself as traveling waves of gene expression, and a regressing wavefront that transforms the temporally periodic signal encoded in the oscillations into a permanent spatially periodic pattern of somite boundaries. Over the last twenty years, every new discovery about the Segmentation Clock has been tightly linked to the nomenclature of the "Clock and Wavefront" model. This constrained allocation of discoveries into these two elements has generated long-standing debates in the field as what defines molecularly the wavefront and how and where the interaction between the two elements establishes the future somite boundaries. In this review, we propose an expansion of the "Clock and Wavefront" model into three elements, "Clock", "Wavefront" and signaling gradients. We first provide a detailed description of the components and regulatory mechanisms of each element, and we then examine how the spatiotemporal integration of the three elements leads to the establishment of the presumptive somite boundaries. To be as exhaustive as possible, we focus on the Segmentation Clock in zebrafish. Furthermore, we show how this three-element expansion of the model provides a better understanding of the somite formation process and we emphasize where our current understanding of this patterning system remains obscure.

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.

The computational capabilities of many-to-many protein interaction networks

Many biological circuits comprise sets of protein variants that interact with one another in a many-to-many, or promiscuous, fashion. These architectures can provide powerful computational capabilities that are especially critical in multicellular organisms. Understanding the principles of biochemical computations in these circuits could allow more precise control of cellular behaviors. However, these systems are inherently difficult to analyze, due to their large number of interacting molecular components, partial redundancies, and cell context dependence. Here, we discuss recent experimental and theoretical advances that are beginning to reveal how promiscuous circuits compute, what roles those computations play in natural biological contexts, and how promiscuous architectures can be applied for the design of synthetic multicellular behaviors.

Ripply suppresses Tbx6 to induce dynamic-to-static conversion in somite segmentation

The metameric pattern of somites is created based on oscillatory expression of clock genes in presomitic mesoderm. However, the mechanism for converting the dynamic oscillation to a static pattern of somites is still unclear. Here, we provide evidence that Ripply/Tbx6 machinery is a key regulator of this conversion. Ripply1/Ripply2-mediated removal of Tbx6 protein defines somite boundary and also leads to cessation of clock gene expression in zebrafish embryos. On the other hand, activation of ripply1/ripply2 mRNA and protein expression is periodically regulated by clock oscillation in conjunction with an Erk signaling gradient. Whereas Ripply protein decreases rapidly in embryos, Ripply-triggered Tbx6 suppression persists long enough to complete somite boundary formation. Mathematical modeling shows that a molecular network based on results of this study can reproduce dynamic-to-static conversion in somitogenesis. Furthermore, simulations with this model suggest that sustained suppression of Tbx6 caused by Ripply is crucial in this conversion.

Orchestration of tissue shape changes and gene expression patterns in development

In development, tissue shape changes and gene expression patterns give rise to morphogenesis. Understanding tissue shape changes requires the analysis of mechanical properties of the tissue such as tissue rigidity, cell influx from neighboring tissues, cell shape changes and cell proliferation. Local and global gene expression patterns can be influenced by neighbor exchange and tissue shape changes. Here we review recent studies on the mechanisms for tissue elongation and its influences on dynamic gene expression patterns by focusing on vertebrate somitogenesis. We first introduce mechanical and biochemical properties of the segmenting tissue that drive tissue elongation. Then, we discuss patterning in the presence of cell mixing, scaling of signaling gradients, and dynamic phase waves of rhythmic gene expression under tissue shape changes. We also highlight the importance of theoretical approaches to address the relation between tissue shape changes and patterning.

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.

Fgf8 dynamics and critical slowing down may account for the temperature independence of somitogenesis

Somitogenesis, the segmentation of the antero-posterior axis in vertebrates, is thought to result from the interactions between a genetic oscillator and a posterior-moving determination wavefront. The segment (somite) size is set by the product of the oscillator period and the velocity of the determination wavefront. Surprisingly, while the segmentation period can vary by a factor three between 20 °C and 32 °C, the somite size is constant. How this temperature independence is achieved is a mystery that we address in this study. Using RT-qPCR we show that the endogenous fgf8 mRNA concentration decreases during somitogenesis and correlates with the exponent of the shrinking pre-somitic mesoderm (PSM) size. As the temperature decreases, the dynamics of fgf8 and many other gene transcripts, as well as the segmentation frequency and the PSM shortening and tail growth rates slows down as T-T_c (with T_c = 14.4 °C). This behavior characteristic of a system near a critical point may account for the temperature independence of somitogenesis in zebrafish.

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.

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.

Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock

The clock and wavefront paradigm is arguably the most widely accepted model for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as segmentation clock, and a differentiation wavefront, which provides the positional information indicating where each pair of somites is formed. Shortly after the clock and wavefront paradigm was introduced, Meinhardt presented a conceptually different mathematical model for morphogenesis in general, and somitogenesis in particular. Recently, Cotterell et al. [A local, self-organizing reaction-diffusion model can explain somite patterning in embryos, Cell Syst. 1, 257-269 (2015)] rediscovered an equivalent model by systematically enumerating and studying small networks performing segmentation. Cotterell et al. called it a progressive oscillatory reaction-diffusion (PORD) model. In the Meinhardt-PORD model, somitogenesis is driven by short-range interactions and the posterior movement of the front is a local, emergent phenomenon, which is not controlled by global positional information. With this model, it is possible to explain some experimental observations that are incompatible with the clock and wavefront model. However, the Meinhardt-PORD model has some important disadvantages of its own. Namely, it is quite sensitive to fluctuations and depends on very specific initial conditions (which are not biologically realistic). In this work, we propose an equivalent Meinhardt-PORD model and then amend it to couple it with a wavefront consisting of a receding morphogen gradient. By doing so, we get a hybrid model between the Meinhardt-PORD and the clock-and-wavefront ones, which overcomes most of the deficiencies of the two originating models.

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.

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.

Arthropod segmentation

There is now compelling evidence that many arthropods pattern their segments using a clock-and-wavefront mechanism, analogous to that operating during vertebrate somitogenesis. In this Review, we discuss how the arthropod segmentation clock generates a repeating sequence of pair-rule gene expression, and how this is converted into a segment-polarity pattern by ‘timing factor’ wavefronts associated with axial extension. We argue that the gene regulatory network that patterns segments may be relatively conserved, although the timing of segmentation varies widely, and double-segment periodicity appears to have evolved at least twice. Finally, we describe how the repeated evolution of a simultaneous (Drosophila-like) mode of segmentation within holometabolan insects can be explained by heterochronic shifts in timing factor expression plus extensive pre-patterning of the pair-rule genes.

Regulation of Notch output dynamics via specific E(spl)-HLH factors during bristle patterning in Drosophila

The stereotyped arrangement of sensory bristles on the adult fly thorax arises from a self-organized process, in which inhibitory Notch signaling both delimits proneural stripes and singles out sensory organ precursor cells (SOPs). A dynamic balance between proneural factors and Enhancer of split-HLH (E(spl)-HLH) Notch targets underlies patterning, but how this is regulated is unclear. Here, were identify two classes of E(spl)-HLH factors, whose expression both precedes and delimits proneural activity, and is dependent on proneural activity and required for proper SOP spacing within the stripes, respectively. These two classes are partially redundant, since a member of the second class, that is normally cross-repressed by members of the first class, can functionally compensate for their absence. The regulation of specific E(spl)-HLH genes by proneural factors amplifies the response to Notch as SOPs are being selected, contributing to patterning dynamics in the notum, and likely operates in other developmental contexts.

The patterning of sensory bristles on the dorsal thorax of flies is regulated by two transcription factor families but the dynamics of this regulation is unclear. Here, the authors visualize seven E(spl)-HLH proteins, showing their regulated expression promotes mutual inhibition by Notch during notum patterning.

Mechanisms of Notch signaling: a simple logic deployed in time and space

Most cells in our body communicate during development and throughout life via Notch receptors and their ligands. Notch receptors relay information from the cell surface to the genome via a very simple mechanism, yet Notch plays multiple roles in development and disease. Recent studies suggest that this versatility in Notch function may not necessarily arise from complex and context-dependent integration of Notch signaling with other developmental signals, but instead arises, in part, from signaling dynamics. Here, we review recent findings on the core Notch signaling mechanism and discuss how spatial-temporal dynamics contribute to Notch signaling output.

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

Deadenylation by the CCR4-NOT complex contributes to the turnover of hairy-related mRNAs in the zebrafish segmentation clock

In the zebrafish segmentation clock, hairy/enhancer of split-related genes her1, her7, and hes6 encodes components of core oscillators. Since the expression of cyclic genes proceeds rapidly in the presomitic mesoderm (PSM), these hairy-related mRNAs are subject to strict post-transcriptional regulation. In this study, we demonstrate that inhibition of the CCR4-NOT deadenylase complex lengthens poly(A) tails of hairy-related mRNAs and increases the amount of these mRNAs, which is accompanied by defective somite segmentation. In transgenic embryos, we show that EGFP mRNAs with 3'UTRs of hairy-related genes exhibit turnover similar to endogenous mRNAs. Our results suggest that turnover rates of her1, her7, and hes6 mRNAs are differently regulated by the CCR4-NOT deadenylase complex possibly through their 3'UTRs in the zebrafish PSM.

Information flow in the presence of cell mixing and signaling delays during embryonic development

Embryonic morphogenesis is organized by an interplay between intercellular signaling and cell movements. Both intercellular signaling and cell movement involve multiple timescales. A key timescale for signaling is the time delay caused by preparation of signaling molecules and integration of received signals into cells' internal state. Movement of cells relative to their neighbors may introduce exchange of positions between cells during signaling. When cells change their relative positions in a tissue, the impact of signaling delays on intercellular signaling increases because the delayed information that cells receive may significantly differ from the present state of the tissue. The time it takes to perform a neighbor exchange sets a timescale of cell mixing that may be important for the outcome of signaling. Here we review recent theoretical work on the interplay of timescales between cell mixing and signaling delays adopting the zebrafish segmentation clock as a model system. We discuss how this interplay can lead to spatial patterns of gene expression that could disrupt the normal formation of segment boundaries in the embryo. The effect of cell mixing and signaling delays highlights the importance of theoretical and experimental frameworks to understand collective cellular behaviors arising from the interplay of multiple timescales in embryonic developmental processes.

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.

Segmentation of the zebrafish axial skeleton relies on notochord sheath cells and not on the segmentation clock

Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns the paraxial mesoderm and the sclerotome. While the segmentation clock clearly operates in teleosts, the role of the sclerotome in establishing the axial skeleton is unclear. We severely disrupt zebrafish paraxial segmentation, yet observe a largely normal segmentation process of the chordacentra. We demonstrate that axial entpd5+ notochord sheath cells are responsible for chordacentrum mineralization, and serve as a marker for axial segmentation. While autonomous within the notochord sheath, entpd5 expression and centrum formation show some plasticity and can respond to myotome pattern. These observations reveal for the first time the dynamics of notochord segmentation in a teleost, and are consistent with an autonomous patterning mechanism that is influenced, but not determined by adjacent paraxial mesoderm. This behavior is not consistent with a clock-type mechanism in the notochord.

Chemical event chain model of coupled genetic oscillators

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

A damped oscillator imposes temporal order on posterior gap gene expression in Drosophila

Insects determine their body segments in two different ways. Short-germband insects, such as the flour beetle Tribolium castaneum, use a molecular clock to establish segments sequentially. In contrast, long-germband insects, such as the vinegar fly Drosophila melanogaster, determine all segments simultaneously through a hierarchical cascade of gene regulation. Gap genes constitute the first layer of the Drosophila segmentation gene hierarchy, downstream of maternal gradients such as that of Caudal (Cad). We use data-driven mathematical modelling and phase space analysis to show that shifting gap domains in the posterior half of the Drosophila embryo are an emergent property of a robust damped oscillator mechanism, suggesting that the regulatory dynamics underlying long- and short-germband segmentation are much more similar than previously thought. In Tribolium, Cad has been proposed to modulate the frequency of the segmentation oscillator. Surprisingly, our simulations and experiments show that the shift rate of posterior gap domains is independent of maternal Cad levels in Drosophila. Our results suggest a novel evolutionary scenario for the short- to long-germband transition and help explain why this transition occurred convergently multiple times during the radiation of the holometabolan insects.

Different insect species exhibit one of two distinct modes of determining their body segments (known as segmentation) during development: they either use a molecular oscillator to position segments sequentially, or they generate segments simultaneously through a hierarchical gene-regulatory cascade. The sequential mode is ancestral, while the simultaneous mode has been derived from it independently several times during evolution. In this paper, we present evidence suggesting that simultaneous segmentation also involves an oscillator in the posterior end of the embryo of the vinegar fly, Drosophila melanogaster. This surprising result indicates that both modes of segment determination are much more similar than previously thought. Such similarity provides an important step towards our understanding of the frequent evolutionary transitions observed between sequential and simultaneous segmentation.

Multidimensional quantitative analysis of mRNA expression within intact vertebrate embryos

For decades, in situ hybridization methods have been essential tools for studies of vertebrate development and disease, as they enable qualitative analyses of mRNA expression in an anatomical context. Quantitative mRNA analyses typically sacrifice the anatomy, relying on embryo microdissection, dissociation, cell sorting and/or homogenization. Here, we eliminate the trade-off between quantitation and anatomical context, using quantitative in situ hybridization chain reaction (qHCR) to perform accurate and precise relative quantitation of mRNA expression with subcellular resolution within whole-mount vertebrate embryos. Gene expression can be queried in two directions: read-out from anatomical space to expression space reveals co-expression relationships in selected regions of the specimen; conversely, read-in from multidimensional expression space to anatomical space reveals those anatomical locations in which selected gene co-expression relationships occur. As we demonstrate by examining gene circuits underlying somitogenesis, quantitative read-out and read-in analyses provide the strengths of flow cytometry expression analyses, but by preserving subcellular anatomical context, they enable bi-directional queries that open a new era for in situ hybridization.

Small molecule screen in embryonic zebrafish using modular variations to target segmentation

Small molecule in vivo phenotypic screening is used to identify drugs or biological activities by directly assessing effects in intact organisms. However, current screening designs may not exploit the full potential of chemical libraries due to false negatives. Here, we demonstrate a modular small molecule screen in embryonic zebrafish that varies concentration, genotype and timing to target segmentation disorders, birth defects that affect the spinal column. By testing each small molecule in multiple interrelated ways, this screen recovers compounds that a standard screening design would have missed, increasing the hit frequency from the chemical library three-fold. We identify molecular pathways and segmentation phenotypes, which we share in an open-access annotated database. These hits provide insight into human vertebral segmentation disorders and myopathies. This modular screening strategy is applicable to other developmental questions and disease models, highlighting the power of relatively small chemical libraries to accelerate gene discovery and disease study.

Putative binding sites for mir-125 family miRNAs in the mouse Lfng 3'UTR affect transcript expression in the segmentation clock, but mir-125a-5p is dispensable for normal somitogenesis

BACKGROUND

In vertebrate embryos, a "segmentation clock" times somitogenesis. Clock-linked genes, including Lunatic fringe (Lfng), exhibit cyclic expression in the presomitic mesoderm (PSM), with a period matching the rate of somite formation. The clock period varies widely across species, but the mechanisms that underlie this variability are not clear. The half-lives of clock components are proposed to influence the rate of clock oscillations, and are tightly regulated in the PSM. Interactions between Lfng and mir-125a-5p in the embryonic chicken PSM promote Lfng transcript instability, but the conservation of this mechanism in other vertebrates has not been tested. Here, we examine whether this interaction affects clock activity in a mammalian species.

RESULTS

Mutation of mir-125 binding sites in the Lfng 3'UTR leads to persistent, nonoscillatory reporter transcript expression in the caudal-most mouse PSM, although dynamic transcript expression recovers in the central PSM. Despite this, expression of endogenous mir-125a-5p is dispensable for mouse somitogenesis.

CONCLUSIONS

These results suggest that mir-125a sites in the Lfng 3' untranslated region influence transcript turnover in both mouse and chicken embryos, and support the existence of position-dependent regulatory mechanisms in the PSM. They further suggest the existence of compensatory mechanisms that can rescue the loss of mir-125a-5p in mice. Developmental Dynamics 246:740-748, 2017. © 2017 Wiley Periodicals, Inc.

Dynamic patterning by the Drosophila pair-rule network reconciles long-germ and short-germ segmentation

Drosophila segmentation is a well-established paradigm for developmental pattern formation. However, the later stages of segment patterning, regulated by the "pair-rule" genes, are still not well understood at the system level. Building on established genetic interactions, I construct a logical model of the Drosophila pair-rule system that takes into account the demonstrated stage-specific architecture of the pair-rule gene network. Simulation of this model can accurately recapitulate the observed spatiotemporal expression of the pair-rule genes, but only when the system is provided with dynamic "gap" inputs. This result suggests that dynamic shifts of pair-rule stripes are essential for segment patterning in the trunk and provides a functional role for observed posterior-to-anterior gap domain shifts that occur during cellularisation. The model also suggests revised patterning mechanisms for the parasegment boundaries and explains the aetiology of the even-skipped null mutant phenotype. Strikingly, a slightly modified version of the model is able to pattern segments in either simultaneous or sequential modes, depending only on initial conditions. This suggests that fundamentally similar mechanisms may underlie segmentation in short-germ and long-germ arthropods.

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.

Determining the impact of cell mixing on signaling during development

Cell movement and intercellular signaling occur simultaneously to organize morphogenesis during embryonic development. Cell movement can cause relative positional changes between neighboring cells. When intercellular signals are local such cell mixing may affect signaling, changing the flow of information in developing tissues. Little is known about the effect of cell mixing on intercellular signaling in collective cellular behaviors and methods to quantify its impact are lacking. Here we discuss how to determine the impact of cell mixing on cell signaling drawing an example from vertebrate embryogenesis: the segmentation clock, a collective rhythm of interacting genetic oscillators. We argue that comparing cell mixing and signaling timescales is key to determining the influence of mixing. A signaling timescale can be estimated by combining theoretical models with cell signaling perturbation experiments. A mixing timescale can be obtained by analysis of cell trajectories from live imaging. After comparing cell movement analyses in different experimental settings, we highlight challenges in quantifying cell mixing from embryonic timelapse experiments, especially a reference frame problem due to embryonic motions and shape changes. We propose statistical observables characterizing cell mixing that do not depend on the choice of reference frames. Finally, we consider situations in which both cell mixing and signaling involve multiple timescales, precluding a direct comparison between single characteristic timescales. In such situations, physical models based on observables of cell mixing and signaling can simulate the flow of information in tissues and reveal the impact of observed cell mixing on signaling.

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.

Elements of biological oscillations in time and space

Oscillations in time and space are ubiquitous in nature and play critical roles in dynamic cellular processes. Although the molecular mechanisms underlying the generation of the dynamics are diverse, several distinct regulatory elements have been recognized as being critical in producing and modulating oscillatory dynamics. These include negative and positive feedback, time delay, nonlinearity in regulation, and random fluctuations ('noise'). Here we discuss the specific roles of these five elements in promoting or attenuating oscillatory dynamics, by drawing on insights from quantitative analyses of natural or synthetic biological networks.

Delta-Notch signalling in segmentation

Modular body organization is found widely across multicellular organisms, and some of them form repetitive modular structures via the process of segmentation. It's vastly interesting to understand how these regularly repeated structures are robustly generated from the underlying noise in biomolecular interactions. Recent studies from arthropods reveal similarities in segmentation mechanisms with vertebrates, and raise the possibility that the three phylogenetic clades, annelids, arthropods and chordates, might share homology in this process from a bilaterian ancestor. Here, we discuss vertebrate segmentation with particular emphasis on the role of the Notch intercellular signalling pathway. We introduce vertebrate segmentation and Notch signalling, pointing out historical milestones, then describe existing models for the Notch pathway in the synchronization of noisy neighbouring oscillators, and a new role in the modulation of gene expression wave patterns. We ask what functions Notch signalling may have in arthropod segmentation and explore the relationship between Notch-mediated lateral inhibition and synchronization. Finally, we propose open questions and technical challenges to guide future investigations into Notch signalling in segmentation.

Multiple binding sites for transcriptional repressors can produce regular bursting and enhance noise suppression

Cells may control fluctuations in protein levels by means of negative autoregulation, where transcription factors bind DNA sites to repress their own production. Theoretical studies have assumed a single binding site for the repressor, while in most species it is found that multiple binding sites are arranged in clusters. We study a stochastic description of negative autoregulation with multiple binding sites for the repressor. We find that increasing the number of binding sites induces regular bursting of gene products. By tuning the threshold for repression, we show that multiple binding sites can also suppress fluctuations. Our results highlight possible roles for the presence of multiple binding sites of negative autoregulators.

Muscular dystrophy modeling in zebrafish

Skeletal muscle performs an essential function in human physiology with defects in genes encoding a variety of cellular components resulting in various types of inherited muscle disorders. Muscular dystrophies (MDs) are a severe and heterogeneous type of human muscle disease, manifested by progressive muscle wasting and degeneration. The disease pathogenesis and therapeutic options for MDs have been investigated for decades using rodent models, and considerable knowledge has been accumulated on the cause and pathogenetic mechanisms of this group of human disorders. However, due to some differences between disease severity and progression, what is learned in mammalian models does not always transfer to humans, prompting the desire for additional and alternative models. More recently, zebrafish have emerged as a novel and robust animal model for the study of human muscle disease. Zebrafish MD models possess a number of distinct advantages for modeling human muscle disorders, including the availability and ease of generating mutations in homologous disease-causing genes, the ability to image living muscle tissue in an intact animal, and the suitability of zebrafish larvae for large-scale chemical screens. In this chapter, we review the current understanding of molecular and cellular mechanisms involved in MDs, the process of myogenesis in zebrafish, and the structural and functional characteristics of zebrafish larval muscles. We further discuss the insights gained from the key zebrafish MD models that have been so far generated, and we summarize the attempts that have been made to screen for small molecules inhibitors of the dystrophic phenotypes using these models. Overall, these studies demonstrate that zebrafish is a useful in vivo system for modeling aspects of human skeletal muscle disorders. Studies using these models have contributed both to the understanding of the pathogenesis of muscle wasting disorders and demonstrated their utility as highly relevant models to implement therapeutic screening regimens.

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.

Quadruple zebrafish mutant reveals different roles of Mesp genes in somite segmentation between mouse and zebrafish

The segmental pattern of somites is generated by sequential conversion of the temporal periodicity provided by the molecular clock. Whereas the basic structure of this clock is conserved among different species, diversity also exists, especially in terms of the molecular network. The temporal periodicity is subsequently converted into the spatial pattern of somites, and Mesp2 plays crucial roles in this conversion in the mouse. However, it remains unclear whether Mesp genes play similar roles in other vertebrates. In this study, we generated zebrafish mutants lacking all four zebrafish Mesp genes by using TALEN-mediated genome editing. Contrary to the situation in the mouse Mesp2 mutant, in the zebrafish Mesp quadruple mutant embryos the positions of somite boundaries were clearly determined and morphological boundaries were formed, although their formation was not completely normal. However, each somite was caudalized in a similar manner to the mouse Mesp2 mutant, and the superficial horizontal myoseptum and lateral line primordia were not properly formed in the quadruple mutants. These results clarify the conserved and species-specific roles of Mesp in the link between the molecular clock and somite morphogenesis.

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.