Genetic oscillations. A Doppler effect in embryonic pattern formation

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.

Modular control of vertebrate axis segmentation in time and space

How the timing of development is linked to organismal size is a longstanding question. Although numerous studies have reported a correlation of temporal and spatial traits, the developmental or selective constraints underlying this link remain largely unexplored. We address this question by studying the periodic process of embryonic axis segmentation in-vivo in Oryzias fish. Interspecies comparisons reveal that the timing of segmentation correlates to segment, tissue and organismal size. Segment size in turn scales according to tissue and organism size. To probe for underlying causes, we genetically hybridised two closely related species. Quantitative analysis in ~600 phenotypically diverse F2 embryos reveals a decoupling of timing from size control, while spatial scaling is preserved. Using developmental quantitative trait loci (devQTL) mapping we identify distinct genetic loci linked to either the control of segmentation timing or tissue size. This study demonstrates that a developmental constraint mechanism underlies spatial scaling of axis segmentation, while its spatial and temporal control are dissociable modules.

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.

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.

Single-cell transcriptional dynamics in a living vertebrate

The ability to quantify transcriptional dynamics in individual cells via live imaging has revolutionized our understanding of gene regulation. However, such measurements are lacking in the context of vertebrate embryos. We addressed this deficit by applying MS2-MCP mRNA labeling to the quantification of transcription in zebrafish, a model vertebrate. We developed a platform of transgenic organisms, light sheet fluorescence microscopy, and optimized image analysis that enables visualization and quantification of MS2 reporters. We used these tools to obtain the first single-cell, real-time measurements of transcriptional dynamics of the segmentation clock. Our measurements challenge the traditional view of smooth clock oscillations and instead suggest a model of discrete transcriptional bursts that are organized in space and time. Together, these results highlight how measuring single-cell transcriptional activity can reveal unexpected features of gene regulation and how this data can fuel the dialogue between theory and experiment.

Quantitative Live Imaging of Zebrafish Scale Regeneration: From Adult Fish to Signaling Patterns and Tissue Flows

In regeneration, a damaged body part grows back to its original form. Understanding the mechanisms and physical principles underlying this process has been limited by the difficulties of visualizing cell signals and behaviors in regeneration. Zebrafish scales are emerging as a model system to investigate morphogenesis during vertebrate regeneration using quantitative live imaging. Scales are millimeter-sized dermal bone disks forming a skeletal armor on the body of the fish. The scale bone is deposited by an adjacent monolayer of osteoblasts that, after scale loss, regenerates in about 2 weeks. This intriguing regenerative process is accessible to live confocal microscopy, quantifications, and mathematical modeling. Here, I describe methods to image scale regeneration live, tissue-wide and at sub-cellular resolution. Furthermore, I describe methods to process the resulting images and quantify cell, tissue, and signal dynamics.

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.

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

Closing the loop on morphogenesis: a mathematical model of morphogenesis by closed-loop reaction-diffusion

Morphogenesis, the establishment and repair of emergent complex anatomy by groups of cells, is a fascinating and biomedically-relevant problem. One of its most fascinating aspects is that a developing embryo can reliably recover from disturbances, such as splitting into twins. While this reliability implies some type of goal-seeking error minimization over a morphogenic field, there are many gaps with respect to detailed, constructive models of such a process. A common way to achieve reliability is negative feedback, which requires characterizing the existing body shape to create an error signal-but measuring properties of a shape may not be simple. We show how cells communicating in a wave-like pattern could analyze properties of the current body shape. We then describe a closed-loop negative-feedback system for creating reaction-diffusion (RD) patterns with high reliability. Specifically, we use a wave to count the number of peaks in a RD pattern, letting us use a negative-feedback controller to create a pattern with N repetitions, where N can be altered over a wide range. Furthermore, the individual repetitions of the RD pattern can be easily stretched or shrunk under genetic control to create, e.g., some morphological features larger than others. This work contributes to the exciting effort of understanding design principles of morphological computation, which can be used to understand evolved developmental mechanisms, manipulate them in regenerative-medicine settings, or engineer novel synthetic morphology constructs with desired robust behavior.

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.

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.

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.

Imaging the onset of oscillatory signaling dynamics during mouse embryo gastrulation

A fundamental requirement for embryonic development is the coordination of signaling activities in space and time. A notable example in vertebrate embryos is found during somitogenesis, where gene expression oscillations linked to the segmentation clock are synchronized across cells in the presomitic mesoderm (PSM) and result in tissue-level wave patterns. To examine their onset during mouse embryo development, we studied the dynamics of the segmentation clock gene Lfng during gastrulation. To this end, we established an imaging setup using selective plane illumination microscopy (SPIM) that enables culture and simultaneous imaging of up to four embryos (‘SPIM- for-4’). Using SPIM-for-4, combined with genetically encoded signaling reporters, we detected the onset of Lfng oscillations within newly formed mesoderm at presomite stages. Functionally, we found that initial synchrony and the first ∼6-8 oscillation cycles occurred even when Notch signaling was impaired, revealing similarities to previous findings made in zebrafish embryos. Finally, we show that a spatial period gradient is present at the onset of oscillatory activity, providing a potential mechanism accounting for our observation that wave patterns build up gradually over the first oscillation cycles.

Summary: A versatile light-sheet imaging setup enabling simultaneous live imaging of multiple mouse embryos for 48 h, an approach that offers insight into the onset of oscillatory signaling dynamics and the segmentation clock.

Competency in Navigating Arbitrary Spaces as an Invariant for Analyzing Cognition in Diverse Embodiments

One of the most salient features of life is its capacity to handle novelty and namely to thrive and adapt to new circumstances and changes in both the environment and internal components. An understanding of this capacity is central to several fields: the evolution of form and function, the design of effective strategies for biomedicine, and the creation of novel life forms via chimeric and bioengineering technologies. Here, we review instructive examples of living organisms solving diverse problems and propose competent navigation in arbitrary spaces as an invariant for thinking about the scaling of cognition during evolution. We argue that our innate capacity to recognize agency and intelligence in unfamiliar guises lags far behind our ability to detect it in familiar behavioral contexts. The multi-scale competency of life is essential to adaptive function, potentiating evolution and providing strategies for top-down control (not micromanagement) to address complex disease and injury. We propose an observer-focused viewpoint that is agnostic about scale and implementation, illustrating how evolution pivoted similar strategies to explore and exploit metabolic, transcriptional, morphological, and finally 3D motion spaces. By generalizing the concept of behavior, we gain novel perspectives on evolution, strategies for system-level biomedical interventions, and the construction of bioengineered intelligences. This framework is a first step toward relating to intelligence in highly unfamiliar embodiments, which will be essential for progress in artificial intelligence and regenerative medicine and for thriving in a world increasingly populated by synthetic, bio-robotic, and hybrid beings.

Waves in Embryonic Development

Embryonic development hinges on effective coordination of molecular events across space and time. Waves have recently emerged as constituting an ubiquitous mechanism that ensures rapid spreading of regulatory signals across embryos, as well as reliable control of their patterning, namely, for the emergence of body plan structures. In this article, we review a selection of recent quantitative work on signaling waves and present an overview of the theory of waves. Our aim is to provide a succinct yet comprehensive guiding reference for the theoretical frameworks by which signaling waves can arise in embryos. We start, then, from reaction-diffusion systems, both static and time dependent; move to excitable dynamics; and conclude with systems of coupled oscillators. We link these theoretical models to molecular mechanisms recently elucidated for the control of mitotic waves in early embryos, patterning of the vertebrate body axis, micropattern cultures, and bone regeneration. Our goal is to inspire experimental work that will advance theory in development and connect its predictions to quantitative biological observations.

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.

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.

Glycolytic flux-signaling controls mouse embryo mesoderm development

How cellular metabolic state impacts cellular programs is a fundamental, unresolved question. Here, we investigated how glycolytic flux impacts embryonic development, using presomitic mesoderm (PSM) patterning as the experimental model. First, we identified fructose 1,6-bisphosphate (FBP) as an in vivo sentinel metabolite that mirrors glycolytic flux within PSM cells of post-implantation mouse embryos. We found that medium-supplementation with FBP, but not with other glycolytic metabolites, such as fructose 6-phosphate and 3-phosphoglycerate, impaired mesoderm segmentation. To genetically manipulate glycolytic flux and FBP levels, we generated a mouse model enabling the conditional overexpression of dominant active, cytoplasmic PFKFB3 (cytoPFKFB3). Overexpression of cytoPFKFB3 indeed led to increased glycolytic flux/FBP levels and caused an impairment of mesoderm segmentation, paralleled by the downregulation of Wnt-signaling, reminiscent of the effects seen upon FBP-supplementation. To probe for mechanisms underlying glycolytic flux-signaling, we performed subcellular proteome analysis and revealed that cytoPFKFB3 overexpression altered subcellular localization of certain proteins, including glycolytic enzymes, in PSM cells. Specifically, we revealed that FBP supplementation caused depletion of Pfkl and Aldoa from the nuclear-soluble fraction. Combined, we propose that FBP functions as a flux-signaling metabolite connecting glycolysis and PSM patterning, potentially through modulating subcellular protein localization.

The zebrafish presomitic mesoderm elongates through compaction-extension

In vertebrate embryos the presomitic mesoderm becomes progressively segmented into somites at the anterior end while extending along the anterior-posterior axis. A commonly adopted model to explain how this tissue elongates is that of posterior growth, driven in part by the addition of new cells from uncommitted progenitor populations in the tailbud. However, in zebrafish, much of somitogenesis is associated with an absence of overall volume increase, and posterior progenitors do not contribute new cells until the final stages of somitogenesis. Here, we perform a comprehensive 3D morphometric analysis of the paraxial mesoderm and reveal that extension is linked to a volumetric decrease and an increase in cell density. We also find that individual cells decrease in volume over successive somite stages. Live cell tracking confirms that much of this tissue deformation occurs within the presomitic mesoderm progenitor zone and is associated with non-directional rearrangement. Taken together, we propose a compaction-extension mechanism of tissue elongation that highlights the need to better understand the role tissue intrinsic and extrinsic forces in regulating morphogenesis.

The zebrafish presomitic mesoderm elongates through compaction-extension

In vertebrate embryos the presomitic mesoderm becomes progressively segmented into somites at the anterior end while extending along the anterior-posterior axis. A commonly adopted model to explain how this tissue elongates is that of posterior growth, driven in part by the addition of new cells from uncommitted progenitor populations in the tailbud. However, in zebrafish, much of somitogenesis is associated with an absence of overall volume increase, and posterior progenitors do not contribute new cells until the final stages of somitogenesis. Here, we perform a comprehensive 3D morphometric analysis of the paraxial mesoderm and reveal that extension is linked to a volumetric decrease and an increase in cell density. We also find that individual cells decrease in volume over successive somite stages. Live cell tracking confirms that much of this tissue deformation occurs within the presomitic mesoderm progenitor zone and is associated with non-directional rearrangement. Taken together, we propose a compaction-extension mechanism of tissue elongation that highlights the need to better understand the role tissue intrinsic and extrinsic forces in regulating morphogenesis.

Positional information encoded in the dynamic differences between neighboring oscillators during vertebrate segmentation

A central problem in developmental biology is to understand how cells interpret their positional information to give rise to spatial patterns, such as the process of periodic segmentation of the vertebrate embryo into somites. For decades, somite formation has been interpreted according to the clock-and-wavefront model. In this conceptual framework, molecular oscillators set the frequency of somite formation while the positional information is encoded in signaling gradients. Recent experiments using ex vivo explants have challenged this interpretation, suggesting that positional information is encoded in the properties of the oscillators, independent of long-range modulations such as signaling gradients. Here, we propose that positional information is encoded in the difference in the levels of neighboring oscillators. The differences gradually increase because both the amplitude and the period of the oscillators increase with time. When this difference exceeds a certain threshold, the segmentation program starts. Using this framework, we quantitatively fit experimental data from in vivo and ex vivo mouse segmentation, and propose mechanisms of somite scaling. Our results suggest a novel mechanism of spatial pattern formation based on the local interactions between dynamic molecular oscillators.

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.

Time and space in segmentation

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

A tale of two rhythms: Locked clocks and chaos in biology

The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.

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.

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.

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.

Gene expression oscillations in C. elegans underlie a new developmental clock

During C. elegans larval development, thousands of genes, accounting for >20% of the transcriptome, exhibit oscillatory expression with large amplitudes. The time of peaking varies for different genes, but expression generally peaks once per larval stage, with both the oscillation period and larval stage duration varying in concert with temperature. This and other evidence support the existence of a gene expression oscillator that functions as a developmental clock. In this article, we review what is known about the biology, architecture and possible mechanisms of this clock. We compare it to other oscillators, and highlight tools and approaches suited to its study. Finally, we point out implications of these wide-spread and dynamic changes of gene expression on any type of gene expression profiling experiment in C. elegans larvae and how such experiments need to be controlled.

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.

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.

Somite boundary determination in normal and clock-less vertebrate embryos

Vertebrate segments called somites are generated by periodic segmentation of the presomitic mesoderm (PSM). In the most accepted theoretical model for somite segmentation, the clock and wavefront (CW) model, a clock that ticks to determine particular timings and a wavefront that moves posteriorly are presented in the PSM, and somite positions are determined when the clock meets the posteriorly moving wavefront somewhere in the PSM. Over the last two decades, it has been revealed that the molecular mechanism of the clock and wavefront in vertebrates is based on clock genes including Hes family transcription factors and Notch effectors that oscillate within the PSM to determine particular timings and fibroblast growth factor (FGF) gradients, acting as the posteriorly moving wavefront to determine the position of somite segmentation. A clock-less condition in the CW model was predicted to form no somites; however, irregularly sized somites were still formed in mice and zebrafish, suggesting that this was one of the limitations of the CW model. Recently, we performed interdisciplinary research of experimental and theoretical biological studies and revealed the mechanisms of somite boundary determination in normal and clock-less conditions by characterization of the FGF/extracellular signal-regulated kinase (ERK) activity dynamics. Since features of the molecular clock have already been described in-depth in several reviews, we summarized recent findings regarding the role of FGF/ERK signaling in somite boundary formation and described our current understanding of how FGF/ERK signaling contributes to somitogenesis in normal and clock-less conditions in this review.

Spatial Fold Change of FGF Signaling Encodes Positional Information for Segmental Determination in Zebrafish

Signal gradients encode instructive information for numerous decision-making processes during embryonic development. A striking example of precise, scalable tissue-level patterning is the segmentation of somites—the precursors of the vertebral column—during which the fibroblast growth factor (FGF), Wnt, and retinoic acid (RA) pathways establish spatial gradients. Despite decades of studies proposing roles for all three pathways, the dynamic feature of these gradients that encodes instructive information determining segment sizes remained elusive. We developed a non-elongating tail explant system, integrated quantitative measurements with computational modeling, and tested alternative models to show that positional information is encoded solely by spatial fold change (SFC) in FGF signal output. Neighboring cells measure SFC to accurately position the determination front and thus determine segment size. The SFC model successfully recapitulates results of spatiotemporal perturbation experiments on both explants and intact embryos, and it shows that Wnt signaling acts permissively upstream of FGF signaling and that RA gradient is dispensable.

Simsek et al. use an elongation-arrested 3D explant system, integrated with quantitative measurements and computational modeling, to show that positional information for segmentation is encoded solely by spatial fold change (SFC) in FGF signal output. Neighboring cells measure SFC to accurately determine somite segment sizes. Wnt signaling acts permissively upstream of FGF signaling.

Shaping the zebrafish myotome by intertissue friction and active stress

How do tissues self-organize to generate the complex organ shapes observed in vertebrates? Organ formation requires the integration of chemical and mechanical information, yet how this is achieved is poorly understood for most organs. Muscle compartments in zebrafish display a V shape, which is believed to be required for efficient swimming. We investigate how this structure emerges during zebrafish development, combining live imaging and quantitative analysis of cellular movements. We use theoretical modeling to understand how cell differentiation and mechanical interactions between tissues guide the emergence of a specific tissue morphology. Our work reveals how spatially modulating the mechanical environment around and within tissues can lead to complex organ shape formation.

Organ formation is an inherently biophysical process, requiring large-scale tissue deformations. Yet, understanding how complex organ shape emerges during development remains a major challenge. During zebrafish embryogenesis, large muscle segments, called myotomes, acquire a characteristic chevron morphology, which is believed to aid swimming. Myotome shape can be altered by perturbing muscle cell differentiation or the interaction between myotomes and surrounding tissues during morphogenesis. To disentangle the mechanisms contributing to shape formation of the myotome, we combine single-cell resolution live imaging with quantitative image analysis and theoretical modeling. We find that, soon after segmentation from the presomitic mesoderm, the future myotome spreads across the underlying tissues. The mechanical coupling between the future myotome and the surrounding tissues appears to spatially vary, effectively resulting in spatially heterogeneous friction. Using a vertex model combined with experimental validation, we show that the interplay of tissue spreading and friction is sufficient to drive the initial phase of chevron shape formation. However, local anisotropic stresses, generated during muscle cell differentiation, are necessary to reach the acute angle of the chevron in wild-type embryos. Finally, tissue plasticity is required for formation and maintenance of the chevron shape, which is mediated by orientated cellular rearrangements. Our work sheds light on how a spatiotemporal sequence of local cellular events can have a nonlocal and irreversible mechanical impact at the tissue scale, leading to robust organ shaping.

Cell cycle regulation of oscillations yields coupling of growth and form in a computational model of the presomitic mesoderm

A striking example of coupling between growth and form occurs during the segmentation of the vertebrate embryo. During segmentation, pairs of segments, one on either side of the anterior-posterior axis, bud off from the presomitic mesoderm (PSM) at regular intervals in time. In the clock and wavefront model, a multicellular oscillator regulates the time at which the next pair of segments form whilst a wavefront regulates their spatial location. In most mathematical models of segmentation, it is assumed that cells in the PSM are oscillators that have a constant natural frequency. Based on recent experimental findings, here we propose a model in which the natural oscillation frequency of each PSM cell is a function of its position in the cell cycle. Given adequate oscillator coupling and that cells in the PSM are randomly distributed in the cell cycle, we find that the emergent oscillator frequency is a weighted average of the constituent oscillator frequencies with the weightings dependent on the fraction of cells in a given cell cycle state. Here, we show that such a model can allow for coupling between pattern formation and growth rate in PSM tissue.

Low-dimensional Dynamics of Two Coupled Biological Oscillators

The circadian clock and the cell cycle are two biological oscillatory processes that coexist within individual cells. These two oscillators were found to interact, which can lead to their synchronization. Here, we develop a method to identify a low-dimensional stochastic model of the coupled system directly from time-lapse imaging in single cells. In particular, we infer the coupling and non-linear dynamics of the two oscillators from thousands of mouse and human single-cell fluorescence microscopy traces. This coupling predicts multiple phase-locked states showing different degrees of robustness against molecular fluctuations inherent to cellular-scale biological oscillators. For the 1:1 state, the predicted phase-shifts upon period perturbations were validated experimentally. Moreover, the phase-locked states are temperature-independent and evolutionarily conserved from mouse to human, hinting at a common underlying dynamical mechanism. Finally, we detect a signature of the coupled dynamics in a physiological context, explaining why tissues with different proliferation states exhibited shifted circadian clock phases.

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.

Constraints on somite formation in developing embryos

Segment formation in vertebrate embryos is a stunning example of biological self-organization. Here, we present an idealized framework, in which we treat the presomitic mesoderm (PSM) as a one-dimensional line of oscillators. We use the framework to derive constraints that connect the size of somites, and the timing of their formation, to the growth of the PSM and the gradient of the somitogenesis clock period across the PSM. Our analysis recapitulates the observations made recently in ex vivo cultures of mouse PSM cells, and makes predictions for how perturbations, such as increased Wnt levels, would alter somite widths. Finally, our analysis makes testable predictions for the shape of the phase profile and somite widths at different stages of PSM growth. In particular, we show that the phase profile is robustly concave when the PSM length is steady and slightly convex in an important special case when it is decreasing exponentially. In both cases, the phase profile scales with the PSM length; in the latter case, it scales dynamically. This has important consequences for the velocity of the waves that traverse the PSM and trigger somite formation, as well as the effect of errors in phase measurement on somite widths.

Temporal development of Drosophila embryos is highly robust across a wide temperature range

Development is a process precisely coordinated in both space and time. Spatial precision has been quantified in a number of developmental systems, and such data have contributed significantly to our understanding of, for example, morphogen gradient interpretation. However, comparatively little quantitative analysis has been performed on timing and temporal coordination during development. Here, we use Drosophila to explore the temporal robustness of embryonic development within physiologically normal temperatures. We find that development is temporally very precise across a wide range of temperatures in the three Drosophila species investigated. However, we find temperature dependence in the timing of developmental events. A simple model incorporating history dependence can explain the developmental temporal trajectories. Interestingly, history dependence is temperature-specific, with either effective negative or positive feedback at different temperatures. We also find that embryos are surprisingly robust to shifting temperatures during embryogenesis. We further identify differences between tropical and temperate species, potentially due to different mechanisms regulating temporal development that depend on the local environment. Our data show that Drosophila embryonic development is temporally robust across a wide range of temperatures. This robustness shows interesting species-specific differences that are suggestive of different sensitivity to temperature fluctuations between Drosophila species.

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.

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.