Persistence, period and precision of autonomous cellular oscillators from the zebrafish segmentation clock

Substrate Rigidity Modulates Segmentation Clock Dynamics in Isolated Presomitic Mesoderm Cells

The segmentation clock, a genetic oscillator in the presomitic mesoderm (PSM), is known to be influenced by biochemical signals, yet its potential regulation by mechanical cues remains unclear. The complex PSM microenvironment has made it challenging to isolate the effects of mechanical perturbations on clock behavior. Here we investigated how mechanical stimuli affect clock oscillations by culturing zebrafish PSM cells on PDMS micropost arrays with tunable rigidities (0.6-1200 kPa). We observed an inverse sigmoidal relationship between surface rigidity and both the percentage of oscillating cells and the number of oscillation cycles, with a switching threshold between 3-6 kPa. The periods of oscillating cells showed a consistently broad distribution across rigidity changes. Moreover, these cells exhibited distinct biophysical properties, such as reduced motility, contractility, and sustained circularity. These findings highlight the crucial role of cell-substrate interactions in regulating segmentation clock behavior, providing insights into the mechanobiology of somitogenesis.

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.

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.

Collective intelligence: A unifying concept for integrating biology across scales and substrates

A defining feature of biology is the use of a multiscale architecture, ranging from molecular networks to cells, tissues, organs, whole bodies, and swarms. Crucially however, biology is not only nested structurally, but also functionally: each level is able to solve problems in distinct problem spaces, such as physiological, morphological, and behavioral state space. Percolating adaptive functionality from one level of competent subunits to a higher functional level of organization requires collective dynamics: multiple components must work together to achieve specific outcomes. Here we overview a number of biological examples at different scales which highlight the ability of cellular material to make decisions that implement cooperation toward specific homeodynamic endpoints, and implement collective intelligence by solving problems at the cell, tissue, and whole-organism levels. We explore the hypothesis that collective intelligence is not only the province of groups of animals, and that an important symmetry exists between the behavioral science of swarms and the competencies of cells and other biological systems at different scales. We then briefly outline the implications of this approach, and the possible impact of tools from the field of diverse intelligence for regenerative medicine and synthetic bioengineering.

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.

Intrinsic and extrinsic cues time somite progenitor contribution to the vertebrate primary body axis

During embryonic development, the timing of events at the cellular level must be coordinated across multiple length scales to ensure the formation of a well-proportioned body plan. This is clear during somitogenesis, where progenitors must be allocated to the axis over time whilst maintaining a progenitor population for continued elaboration of the body plan. However, the relative importance of intrinsic and extrinsic signals in timing progenitor addition at the single-cell level is not yet understood. Heterochronic grafts from older to younger embryos have suggested a level of intrinsic timing whereby later staged cells contribute to more posterior portions of the axis. To determine the precise step at which cells are delayed, we performed single-cell transcriptomic analysis on heterochronic grafts of somite progenitors in the chicken embryo. This revealed a previously undescribed cell state within which heterochronic grafted cells are stalled. The delayed exit of older cells from this state correlates with expression of posterior Hox genes. Using grafting and explant culture, we find that both Hox gene expression and the migratory capabilities of progenitor populations are intrinsically regulated at the population level. However, by grafting varied sizes of tissue, we find that small heterochronic grafts disperse more readily and contribute to more anterior portions of the body axis while still maintaining Hox gene expression. This enhanced dispersion is not replicated in explant culture, suggesting that it is a consequence of interaction between host and donor tissue and thus extrinsic to the donor tissue. Therefore, we demonstrate that the timing of cell dispersion and resulting axis contribution is impacted by a combination of both intrinsic and extrinsic cues.

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.

Circadian clock1a coordinates neutrophil recruitment via nfe212a/duox-reactive oxygen species pathway in zebrafish

Neutrophil recruitment to inflammatory sites appears to be an evolutionarily conserved strategy to fight against exogenous insults. However, the rhythmic characteristics and underlying mechanisms of neutrophil migration on a 24-h timescale are largely unknown. Using the advantage of in vivo imaging of zebrafish, this study explored how the circadian gene clock1a dynamically regulates the rhythmic recruitment of neutrophils to inflammatory challenges. We generated a clock1a mutant and found that neutrophil migration is significantly increased in caudal fin injury and lipopolysaccharide (LPS) injection. Transcriptome sequencing, chromatin immunoprecipitation (ChIP), and dual-luciferase reporting experiments suggest that the clock1a gene regulates neutrophil migration by coordinating the rhythmic expression of nfe212a and duox genes to control the reactive oxygen species (ROS) level. This study ultimately provides a visual model to expand the understanding of the rhythmic mechanisms of neutrophil recruitment on a circadian timescale in a diurnal organism from the perspective of ROS.

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.

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.

Keeping development on time: Insights into post-transcriptional mechanisms driving oscillatory gene expression during vertebrate segmentation

Biological time keeping, or the duration and tempo at which biological processes occur, is a phenomenon that drives dynamic molecular and morphological changes that manifest throughout many facets of life. In some cases, the molecular mechanisms regulating the timing of biological transitions are driven by genetic oscillations, or periodic increases and decreases in expression of genes described collectively as a "molecular clock." In vertebrate animals, molecular clocks play a crucial role in fundamental patterning and cell differentiation processes throughout development. For example, during early vertebrate embryogenesis, the segmentation clock regulates the patterning of the embryonic mesoderm into segmented blocks of tissue called somites, which later give rise to axial skeletal muscle and vertebrae. Segmentation clock oscillations are characterized by rapid cycles of mRNA and protein expression. For segmentation clock oscillations to persist, the transcript and protein molecules of clock genes must be short-lived. Faithful, rhythmic, genetic oscillations are sustained by precise regulation at many levels, including post-transcriptional regulation, and such mechanisms are essential for proper vertebrate development. This article is categorized under: RNA Export and Localization > RNA Localization RNA Turnover and Surveillance > Regulation of RNA Stability Translation > Regulation.

Deconstructing body axis morphogenesis in zebrafish embryos using robot-assisted tissue micromanipulation

Classic microsurgical techniques, such as those used in the early 1900s by Mangold and Spemann, have been instrumental in advancing our understanding of embryonic development. However, these techniques are highly specialized, leading to issues of inter-operator variability. Here we introduce a user-friendly robotic microsurgery platform that allows precise mechanical manipulation of soft tissues in zebrafish embryos. Using our platform, we reproducibly targeted precise regions of tail explants, and quantified the response in real-time by following notochord and presomitic mesoderm (PSM) morphogenesis and segmentation clock dynamics during vertebrate anteroposterior axis elongation. We find an extension force generated through the posterior notochord that is strong enough to buckle the structure. Our data suggest that this force generates a unidirectional notochord extension towards the tailbud because PSM tissue around the posterior notochord does not let it slide anteriorly. These results complement existing biomechanical models of axis elongation, revealing a critical coupling between the posterior notochord, the tailbud, and the PSM, and show that somite patterning is robust against structural perturbations.

Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock

Living systems exhibit an unmatched complexity, due to countless, entangled interactions across scales. Here, we aim to understand a complex system, that is, segmentation timing in mouse embryos, without a reference to these detailed interactions. To this end, we develop a coarse-grained approach, in which theory guides the experimental identification of the segmentation clock entrainment responses. We demonstrate period- and phase-locking of the segmentation clock across a wide range of entrainment parameters, including higher-order coupling. These quantifications allow to derive the phase response curve (PRC) and Arnold tongues of the segmentation clock, revealing its essential dynamical properties. Our results indicate that the somite segmentation clock has characteristics reminiscent of a highly non-linear oscillator close to an infinite period bifurcation and suggests the presence of long-term feedbacks. Combined, this coarse-grained theoretical-experimental approach reveals how we can derive simple, essential features of a highly complex dynamical system, providing precise experimental control over the pace and rhythm of the somite segmentation clock.

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.

Signaling oscillations in embryonic development

Tight spatiotemporal control of cellular behavior and cell fate decisions is paramount to the formation of multicellular organisms during embryonic development. Intercellular communication via signaling pathways mediates this control. Interestingly, these signaling pathways are not static, but dynamic and change in activity over time. Signaling oscillations as a specific type of dynamics are found in various signaling pathways and model systems. Functions of oscillations include the regulation of periodic events or the transmission of information by encoding signals in the dynamic properties of a signaling pathway. For instance, signaling oscillations in neural or pancreatic progenitor cells modulate their proliferation and differentiation. Oscillations between neighboring cells can also be synchronized, leading to the emergence of waves traveling through the tissue. Such population-wide signaling oscillations regulate for example the consecutive segmentation of vertebrate embryos, a process called somitogenesis. Here, we outline our current understanding of signaling oscillations in embryonic development, how signaling oscillations are generated, how they are studied and how they contribute to the regulation of embryonic development.

The unappreciated generative role of cell movements in pattern formation

The mechanisms underpinning the formation of patterned cellular landscapes has been the subject of extensive study as a fundamental problem of developmental biology. In most cases, attention has been given to situations in which cell movements are negligible, allowing researchers to focus on the cell-extrinsic signalling mechanisms, and intrinsic gene regulatory interactions that lead to pattern emergence at the tissue level. However, in many scenarios during development, cells rapidly change their neighbour relationships in order to drive tissue morphogenesis, while also undergoing patterning. To draw attention to the ubiquity of this problem and propose methodologies that will accommodate morphogenesis into the study of pattern formation, we review the current approaches to studying pattern formation in both static and motile cellular environments. We then consider how the cell movements themselves may contribute to the generation of pattern, rather than hinder it, with both a species specific and evolutionary viewpoint.

Intermittent ERK oscillations downstream of FGF in mouse embryonic stem cells

Signal transduction networks generate characteristic dynamic activities to process extracellular signals and guide cell fate decisions such as to divide or differentiate. The differentiation of pluripotent cells is controlled by FGF/ERK signaling. However, only a few studies have addressed the dynamic activity of the FGF/ERK signaling network in pluripotent cells at high time resolution. Here, we use live cell sensors in wild-type and Fgf4-mutant mouse embryonic stem cells to measure dynamic ERK activity in single cells, for defined ligand concentrations and differentiation states. These sensors reveal pulses of ERK activity. Pulsing patterns are heterogeneous between individual cells. Consecutive pulse sequences occur more frequently than expected from simple stochastic models. Sequences become more prevalent with higher ligand concentration, but are rarer in more differentiated cells. Our results suggest that FGF/ERK signaling operates in the vicinity of a transition point between oscillatory and non-oscillatory dynamics in embryonic stem cells. The resulting heterogeneous dynamic signaling activities add a new dimension to cellular heterogeneity that may be linked to divergent fate decisions in stem cell cultures.

A segmentation clock patterns cellular differentiation in a bacterial biofilm

Contrary to multicellular organisms that display segmentation during development, communities of unicellular organisms are believed to be devoid of such sophisticated patterning. Unexpectedly, we find that the gene expression underlying the nitrogen stress response of a developing Bacillus subtilis biofilm becomes organized into a ring-like pattern. Mathematical modeling and genetic probing of the underlying circuit indicate that this patterning is generated by a clock and wavefront mechanism, similar to that driving vertebrate somitogenesis. We experimentally validated this hypothesis by showing that predicted nutrient conditions can even lead to multiple concentric rings, resembling segments. We additionally confirmed that this patterning mechanism is driven by cell-autonomous oscillations. Importantly, we show that the clock and wavefront process also spatially patterns sporulation within the biofilm. Together, these findings reveal a biofilm segmentation clock that organizes cellular differentiation in space and time, thereby challenging the paradigm that such patterning mechanisms are exclusive to plant and animal development.

Diverse role of decoys on emergence and precision of oscillations in a biomolecular clock

Biomolecular clocks are key drivers of oscillatory dynamics in diverse biological processes including cell-cycle regulation, circadian rhythms, and pattern formation during development. A minimal clock implementation is based on the classical Goodwin oscillator, in which a repressor protein inhibits its own synthesis via time-delayed negative feedback. Clock motifs, however, do not exist in isolation; its components are open to interacting with the complex environment inside cells. For example, there are ubiquitous high-affinity binding sites along the genome, known as decoys, where transcription factors such as repressor proteins can potentially interact. This binding affects the availability of transcription factors and has often been ignored in theoretical studies. How does such genomic decoy binding impact the clock's robustness and precision? To address this question, we systematically analyze deterministic and stochastic models of the Goodwin oscillator in the presence of reversible binding of the repressor to a finite number of decoy sites. Our analysis reveals that the relative stability of decoy-bound repressors compared to the free repressor plays distinct roles on the emergence and precision of oscillations. Interestingly, active degradation of the bound repressor can induce sustained oscillations that are otherwise absent without decoys. In contrast, decoy abundances can kill oscillation dynamics if the bound repressor is protected from degradation. Taking into account low copy-number fluctuations in clock components, we show that the degradation of the bound repressors enhances precision by attenuating noise in both the amplitude and period of oscillations. Overall, these results highlight the versatile role of otherwise hidden decoys in shaping the stochastic dynamics of biological clocks and emphasize the importance of synthetic decoys in designing robust clocks.

Signalling dynamics in embryonic development

In multicellular organisms, cellular behaviour is tightly regulated to allow proper embryonic development and maintenance of adult tissue. A critical component in this control is the communication between cells via signalling pathways, as errors in intercellular communication can induce developmental defects or diseases such as cancer. It has become clear over the last years that signalling is not static but varies in activity over time. Feedback mechanisms present in every signalling pathway lead to diverse dynamic phenotypes, such as transient activation, signal ramping or oscillations, occurring in a cell type- and stage-dependent manner. In cells, such dynamics can exert various functions that allow organisms to develop in a robust and reproducible way. Here, we focus on Erk, Wnt and Notch signalling pathways, which are dynamic in several tissue types and organisms, including the periodic segmentation of vertebrate embryos, and are often dysregulated in cancer. We will discuss how biochemical processes influence their dynamics and how these impact on cellular behaviour within multicellular systems.

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.

Auto-Regulation of Transcription and Translation: Oscillations, Excitability and Intermittency

Several members of the Hes/Her family, conserved targets of the Notch signalling pathway, encode transcriptional repressors that dimerise, bind DNA and self-repress. Such autoinhibition of transcription can yield homeostasis and, in the presence of delays that account for processes such as transcription, splicing and transport, oscillations. Whilst previous models of autoinhibition of transcription have tended to treat processes such as translation as being unregulated (and hence linear), here we develop and explore a mathematical model that considers autoinhibition of transcription together with nonlinear regulation of translation. It is demonstrated that such a model can yield, in the absence of delays, nonlinear dynamical behaviours such as excitability, homeostasis, oscillations and intermittency. These results indicate that regulation of translation as well as transcription allows for a much richer range of behaviours than is possible with autoregulation of transcription alone. A number of experiments are suggested that would that allow for the signature of autoregulation of translation as well as transcription to be experimentally detected in a Notch signalling system.

Towards a physical understanding of developmental patterning

The temporal coordination of events at cellular and tissue scales is essential for the proper development of organisms, and involves cell-intrinsic processes that can be coupled by local cellular signalling and instructed by global signalling, thereby creating spatial patterns of cellular states that change over time. The timing and structure of these patterns determine how an organism develops. Traditional developmental genetic methods have revealed the complex molecular circuits regulating these processes but are limited in their ability to predict and understand the emergent spatio-temporal dynamics. Increasingly, approaches from physics are now being used to help capture the dynamics of the system by providing simplified, generic descriptions. Combined with advances in imaging and computational power, such approaches aim to provide insight into timing and patterning in developing systems.

Homology of process: developmental dynamics in comparative biology

Comparative biology builds up systematic knowledge of the diversity of life, across evolutionary lineages and levels of organization, starting with evidence from a sparse sample of model organisms. In developmental biology, a key obstacle to the growth of comparative approaches is that the concept of homology is not very well defined for levels of organization that are intermediate between individual genes and morphological characters. In this paper, we investigate what it means for ontogenetic processes to be homologous, focusing specifically on the examples of insect segmentation and vertebrate somitogenesis. These processes can be homologous without homology of the underlying genes or gene networks, since the latter can diverge over evolutionary time, while the dynamics of the process remain the same. Ontogenetic processes like these therefore constitute a dissociable level and distinctive unit of comparison requiring their own specific criteria of homology. In addition, such processes are typically complex and nonlinear, such that their rigorous description and comparison requires not only observation and experimentation, but also dynamical modelling. We propose six criteria of process homology, combining recognized indicators (sameness of parts, morphological outcome and topological position) with novel ones derived from dynamical systems modelling (sameness of dynamical properties, dynamical complexity and evidence for transitional forms). We show how these criteria apply to animal segmentation and other ontogenetic processes. We conclude by situating our proposed dynamical framework for homology of process in relation to similar research programmes, such as process structuralism and developmental approaches to morphological homology.

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.

Tissue tectonics and the multi-scale regulation of developmental timing

Development encompasses processes that occur at multiple length scales, including gene-regulatory interactions, cell movements and reorganization, cell signalling and growth. It is essential that the timing of events in all of these different processes is coordinated to generate well-patterned tissues and organs. However, how the timing of intrinsic cell state changes is coordinated with events occurring at the multi-tissue and whole-organism level is unknown. Here, we argue that an important mechanism that accounts for the integration of timing across levels of organization is provided by tissue tectonics, i.e. how morphogenetic events driving tissue shape changes result in the relative displacement of signalling and responding tissues and coordinate developmental timing across scales. In doing so, tissue tectonics provides a mechanism by which the cell specification events intrinsic to cells can be modulated by the temporal exposure to extracellular signals. This exposure is in turn regulated by higher-order properties of the embryo, such as their physical properties, rates of growth and the combination of dynamic cell behaviours, impacting tissue morphogenesis. Tissue tectonics creates a downward flow of information from higher to lower levels of biological organization, providing an instance of downward causation in development.

A dynamic, spatially periodic, micro-pattern of HES5 underlies neurogenesis in the mouse spinal cord

Ultradian oscillations of HES Transcription Factors (TFs) at the single-cell level enable cell state transitions. However, the tissue-level organisation of HES5 dynamics in neurogenesis is unknown. Here, we analyse the expression of HES5 ex vivo in the developing mouse ventral spinal cord and identify microclusters of 4-6 cells with positively correlated HES5 level and ultradian dynamics. These microclusters are spatially periodic along the dorsoventral axis and temporally dynamic, alternating between high and low expression with a supra-ultradian persistence time. We show that Notch signalling is required for temporal dynamics but not the spatial periodicity of HES5. Few Neurogenin 2 cells are observed per cluster, irrespective of high or low state, suggesting that the microcluster organisation of HES5 enables the stable selection of differentiating cells. Computational modelling predicts that different cell coupling strengths underlie the HES5 spatial patterns and rate of differentiation, which is consistent with comparison between the motoneuron and interneuron progenitor domains. Our work shows a previously unrecognised spatiotemporal organisation of neurogenesis, emergent at the tissue level from the synthesis of single-cell dynamics.

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.

Light Control of Gene Expression Dynamics

The progress in live-cell imaging technologies has revealed diverse dynamic patterns of transcriptional activity in various contexts. The discovery raised a next question of whether the gene expression patterns play causative roles in triggering specific biological events or not. Here, we introduce optogenetic methods that realize optical control of gene expression dynamics in mammalian cells and would be utilized for answering the question, by referring the past, the present, and the future.

Imaging and manipulating the segmentation clock

During embryogenesis, the processes that control how cells differentiate and interact to form particular tissues and organs with precise timing and shape are of fundamental importance. One prominent example of such processes is vertebrate somitogenesis, which is governed by a molecular oscillator called the segmentation clock. The segmentation clock system is initiated in the presomitic mesoderm in which a set of genes and signaling pathways exhibit coordinated spatiotemporal dynamics to establish regularly spaced boundaries along the body axis; these boundaries provide a blueprint for the development of segment-like structures such as spines and skeletal muscles. The highly complex and dynamic nature of this in vivo event and the design principles and their regulation in both normal and abnormal embryogenesis are not fully understood. Recently, live-imaging has been used to quantitatively analyze the dynamics of selected components of the circuit, particularly in combination with well-designed experiments to perturb the system. Here, we review recent progress from studies using live imaging and manipulation, including attempts to recapitulate the segmentation clock in vitro. In combination with mathematical modeling, these techniques have become essential for disclosing novel aspects of the clock.

In vitro systems: A new window to the segmentation clock

Segmental organization of the vertebrate body plan is established by the segmentation clock, a molecular oscillator that controls the periodicity of somite formation. Given the dynamic nature of the segmentation clock, in vivo studies in vertebrate embryos pose technical challenges. As an alternative, simpler models of the segmentation clock based on primary explants and pluripotent stem cells have recently been developed. These ex vivo and in vitro systems enable more quantitative analysis of oscillatory properties and expand the experimental repertoire applicable to the segmentation clock. Crucially, by eliminating the need for model organisms, in vitro models allow us to study the segmentation clock in new species, including our own. The human oscillator was recently recapitulated using induced pluripotent stem cells, providing a window into human development. Certainly, a combination of in vivo and in vitro work holds the most promising potential to unravel the mechanisms behind vertebrate segmentation.

Design principles of tissue organisation: How single cells coordinate across scales

Cells act as building blocks of multicellular organisms, forming higher-order structures at different biological scales. Niches, tissues and, ultimately, entire organisms consist of single cells that remain in constant communication. Emergence of developmental patterns and tissue architecture thus relies on single cells acting as a collective, coordinating growth, migration, cell fate transitions and cell type sorting. For this, information has to be transmitted forward from cells to tissues and fed back to the individual cell to allow dynamic and robust coordination. Here, we define the design principles of tissue organisation integrating chemical, genetic and mechanical cues. We also review the state-of-the-art technologies used for dissecting collective cellular behaviours at single cell- and tissue-level resolution. We finally outline future challenges that lie in a comprehensive understanding of how single cells coordinate across biological scales to insure robust development, homoeostasis and regeneration of tissues.

Geometric models for robust encoding of dynamical information into embryonic patterns

During development, cells gradually assume specialized fates via changes of transcriptional dynamics, sometimes even within the same developmental stage. For anterior-posterior (AP) patterning in metazoans, it has been suggested that the gradual transition from a dynamic genetic regime to a static one is encoded by different transcriptional modules. In that case, the static regime has an essential role in pattern formation in addition to its maintenance function. In this work, we introduce a geometric approach to study such transition. We exhibit two types of genetic regime transitions arising through local or global bifurcations, respectively. We find that the global bifurcation type is more generic, more robust, and better preserves dynamical information. This could parsimoniously explain common features of metazoan segmentation, such as changes of periods leading to waves of gene expressions, ‘speed/frequency-gradient’ dynamics, and changes of wave patterns. Geometric approaches appear as possible alternatives to gene regulatory networks to understand development.

Developmental function and state transitions of a gene expression oscillator in Caenorhabditis elegans

Gene expression oscillators can structure biological events temporally and spatially. Different biological functions benefit from distinct oscillator properties. Thus, finite developmental processes rely on oscillators that start and stop at specific times, a poorly understood behavior. Here, we have characterized a massive gene expression oscillator comprising > 3,700 genes in Caenorhabditis elegans larvae. We report that oscillations initiate in embryos, arrest transiently after hatching and in response to perturbation, and cease in adults. Experimental observation of the transitions between oscillatory and non-oscillatory states at high temporal resolution reveals an oscillator operating near a Saddle Node on Invariant Cycle (SNIC) bifurcation. These findings constrain the architecture and mathematical models that can represent this oscillator. They also reveal that oscillator arrests occur reproducibly in a specific phase. Since we find oscillations to be coupled to developmental processes, including molting, this characteristic of SNIC bifurcations endows the oscillator with the potential to halt larval development at defined intervals, and thereby execute a developmental checkpoint function.

Dynamic properties of noise and Her6 levels are optimized by miR-9, allowing the decoding of the Her6 oscillator

Noise is prevalent in biology and has been widely quantified using snapshot measurements. This static view obscures our understanding of dynamic noise properties and how these affect gene expression and cell state transitions. Using a CRISPR/Cas9 Zebrafish her6::Venus reporter combined with mathematical and in vivo experimentation, we explore how noise affects the protein dynamics of Her6, a basic helix-loop-helix transcriptional repressor. During neurogenesis, Her6 expression transitions from fluctuating to oscillatory at single-cell level. We identify that absence of miR-9 input generates high-frequency noise in Her6 traces, inhibits the transition to oscillatory protein expression and prevents the downregulation of Her6. Together, these impair the upregulation of downstream targets and cells accumulate in a normally transitory state where progenitor and early differentiation markers are co-expressed. Computational modelling and double smFISH of her6 and the early neurogenesis marker, elavl3, suggest that the change in Her6 dynamics precedes the downregulation in Her6 levels. This sheds light onto the order of events at the moment of cell state transition and how this is influenced by the dynamic properties of noise. Our results suggest that Her/Hes oscillations, facilitated by dynamic noise optimization by miR-9, endow progenitor cells with the ability to make a cell state transition.

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.

Oscillatory expression of Hes1 regulates cell proliferation and neuronal differentiation in the embryonic brain

The expression of the transcriptional repressor Hes1 oscillates in many cell types, including neural progenitor cells (NPCs), but the significance of Hes1 oscillations in development is not fully understood. To examine the effect of altered oscillatory dynamics of Hes1, we generated two types of Hes1 knock-in mice, a shortened (type-1) and an elongated (type-2) Hes1 gene, and examined their phenotypes focusing on neural development. Although both mutations affected Hes1 oscillations, the type-1 mutation dampened Hes1 oscillations more severely, resulting in much lower amplitudes. The average levels of Hes1 expression in type-1 mutant NPCs were also lower than in wild-type NPCs but similar to or slightly higher than those in Hes1 heterozygous mutant mice, which exhibit no apparent defects. Whereas type-2 mutant mice were apparently normal, type-1 mutant mice displayed smaller brains than wild-type mice and upregulated proneural gene expression. Furthermore, proliferation of NPCs decreased and cell death increased in type-1 mutant embryos. When Hes3 and Hes5 were additionally deleted, neuronal differentiation was also accelerated, leading to microcephaly. Thus, robust Hes1 oscillations are required for maintenance and proliferation of NPCs and the normal timing of neurogenesis, thereby regulating brain morphogenesis.

Coupling delay controls synchronized oscillation in the segmentation clock

Individual cellular activities fluctuate but are constantly coordinated at the population level via cell-cell coupling. A notable example is the somite segmentation clock, in which the expression of clock genes (such as Hes7) oscillates in synchrony between the cells that comprise the presomitic mesoderm (PSM)^1,2. This synchronization depends on the Notch signalling pathway; inhibiting this pathway desynchronizes oscillations, leading to somite fusion^3-7. However, how Notch signalling regulates the synchronicity of HES7 oscillations is unknown. Here we establish a live-imaging system using a new fluorescent reporter (Achilles), which we fuse with HES7 to monitor synchronous oscillations in HES7 expression in the mouse PSM at a single-cell resolution. Wild-type cells can rapidly correct for phase fluctuations in HES7 oscillations, whereas the absence of the Notch modulator gene lunatic fringe (Lfng) leads to a loss of synchrony between PSM cells. Furthermore, HES7 oscillations are severely dampened in individual cells of Lfng-null PSM. However, when Lfng-null PSM cells were completely dissociated, the amplitude and periodicity of HES7 oscillations were almost normal, which suggests that LFNG is involved mostly in cell-cell coupling. Mixed cultures of control and Lfng-null PSM cells, and an optogenetic Notch signalling reporter assay, revealed that LFNG delays the signal-sending process of intercellular Notch signalling transmission. These results-together with mathematical modelling-raised the possibility that Lfng-null PSM cells shorten the coupling delay, thereby approaching a condition known as the oscillation or amplitude death of coupled oscillators⁸. Indeed, a small compound that lengthens the coupling delay partially rescues the amplitude and synchrony of HES7 oscillations in Lfng-null PSM cells. Our study reveals a delay control mechanism of the oscillatory networks involved in somite segmentation, and indicates that intercellular coupling with the correct delay is essential for synchronized oscillation.

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.

Coordinated circadian timing through the integration of local inputs in Arabidopsis thaliana

Individual plant cells have a genetic circuit, the circadian clock, that times key processes to the day-night cycle. These clocks are aligned to the day-night cycle by multiple environmental signals that vary across the plant. How does the plant integrate clock rhythms, both within and between organs, to ensure coordinated timing? To address this question, we examined the clock at the sub-tissue level across Arabidopsis thaliana seedlings under multiple environmental conditions and genetic backgrounds. Our results show that the clock runs at different speeds (periods) in each organ, which causes the clock to peak at different times across the plant in both constant environmental conditions and light-dark (LD) cycles. Closer examination reveals that spatial waves of clock gene expression propagate both within and between organs. Using a combination of modeling and experiment, we reveal that these spatial waves are the result of the period differences between organs and local coupling, rather than long-distance signaling. With further experiments we show that the endogenous period differences, and thus the spatial waves, can be generated by the organ specificity of inputs into the clock. We demonstrate this by modulating periods using light and metabolic signals, as well as with genetic perturbations. Our results reveal that plant clocks can be set locally by organ-specific inputs but coordinated globally via spatial waves of clock gene expression.

Active receptor tyrosine kinases, but not Brachyury, are sufficient to trigger chordoma in zebrafish

The aberrant activation of developmental processes triggers diverse cancer types. Chordoma is a rare, aggressive tumor arising from transformed notochord remnants. Several potentially oncogenic factors have been found to be deregulated in chordoma, yet causation remains uncertain. In particular, sustained expression of TBXT – encoding the notochord regulator protein brachyury – is hypothesized as a key driver of chordoma, yet experimental evidence is absent. Here, we employ a zebrafish chordoma model to identify the notochord-transforming potential of implicated genes in vivo. We find that Brachyury, including a form with augmented transcriptional activity, is insufficient to initiate notochord hyperplasia. In contrast, the chordoma-implicated receptor tyrosine kinases (RTKs) EGFR and Kdr/VEGFR2 are sufficient to transform notochord cells. Aberrant activation of RTK/Ras signaling attenuates processes required for notochord differentiation, including the unfolded protein response and endoplasmic reticulum stress pathways. Our results provide the first in vivo evidence against a tumor-initiating potential of Brachyury in the notochord, and imply activated RTK signaling as a possible initiating event in chordoma. Furthermore, our work points at modulating endoplasmic reticulum and protein stress pathways as possible therapeutic avenues against chordoma.

Summary: An injection-based chordoma model in zebrafish shows that the hypothesized chordoma oncogene brachyury is insufficient, whereas EGFR and VEGFR2 are sufficient, to trigger notochord hyperplasia in our model.

Communication codes in developmental signaling pathways

A handful of core intercellular signaling pathways play pivotal roles in a broad variety of developmental processes. It has remained puzzling how so few pathways can provide the precision and specificity of cell-cell communication required for multicellular development. Solving this requires us to quantitatively understand how developmentally relevant signaling information is actively sensed, transformed and spatially distributed by signaling pathways. Recently, single cell analysis and cell-based reconstitution, among other approaches, have begun to reveal the 'communication codes' through which information is represented in the identities, concentrations, combinations and dynamics of extracellular ligands. They have also revealed how signaling pathways decipher these features and control the spatial distribution of signaling in multicellular contexts. Here, we review recent work reporting the discovery and analysis of communication codes and discuss their implications for diverse developmental processes.

Synchronization dynamics of mobile oscillators in the presence of coupling delays

Individual biological oscillators can synchronize to generate a collective rhythm. During vertebrate development, mobile cells exchange signals to synchronize a rhythmic pattern generator that makes the embryonic segments. Previous theoretical works have shown that cell mobility can enhance synchronization of coupled oscillators when signal exchange is instantaneous. However, in vertebrate segmentation, the exchange of signals is thought to comprise delays from signal sending and processing, which could alter the effect of mobility on synchronization. Here, we study synchronization dynamics of mobile phase oscillators in the presence of coupling delays. We find that mobility can speed up synchronization when coupling delays are present. We derive an analytical expression for the characteristic time of synchronization dynamics, which is in very good agreement with numerical simulations. This analytical expression suggests a subdivision of the mobility range into different dynamical regimes and reveals that, with delayed coupling, synchronization is enhanced at a lower mobility rate than with instantaneous coupling. We argue that these results may be relevant to the synchronization of mobile oscillators in vertebrate segmentation.

Continuous dynamic adjustment of the plant circadian oscillator

The clockwork of plant circadian oscillators has been resolved through investigations in Arabidopsis thaliana. The circadian oscillator is an important regulator of much of plant physiology, though many of the mechanisms are unclear. New findings demonstrate that the oscillator adjusts phase and period in response to abiotic and biotic signals, providing insight in to how the plant circadian oscillator integrates with the biology of the cell and entrains to light, dark and temperature cycles. We propose that the plant circadian oscillator is dynamically plastic, in constant adjustment, rather than being an isolated clock impervious to cellular events.