Article

Clock and wavefront model for control of the number of repeated structures during animal morphogenesis

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Abstract

Most current models for morphogenesis of repeated patterns, such as vertebrate somites, cannot explain the observed degree of constancy for the number of somites in individuals of a given species. This precision requires a mechanism whereby the lengths of someites (i.e. number of cells per somite) must adjust to the overall size of individual embryos, and one which co-ordinates numbers of somites with position in the whole pattern of body parts. A qualitative model is presented that does admit the observed precision. It is also compatible with experimental observations such as the sequential formation of somites from anterior to posterior in a regular time sequence, the timing of cellular change during development generally, and the increasing evidence for widespread existence of cellular biorhythms. The model involves an interacting “clock” and “wavefront”. The clock is is asmooth cellular oscillator, for which cells throughout the embryo are assumed to be phase-linked. The wavefront is a front of rapid cell change moving slowly down the long axis of the embryo; cells enter a phase of rapid alteration in locomotory and/or adhesive properties at successively later times according to anterior-posterior body position. In the model, the smooth intracellular oscillator itself interacts with the possibility of the rapid primary change or its transmission within cells, thereby gating rhythmically the slow progress of the wavefront. Cells thus enter their rapid change of properties in a succession of separate populations, creating the pattern. It is argued that the elements, a smooth oscillator, a slow wavefront and a rapid cellular change, have biological plausibility. The consequences of combining them were suggested by catastrophe theory. We stress the necessary relation between the present model and the more general concept of positional information (Wolpert, 1969, 1971). Prospective and ongoing experiments stimulated by the model are discussed, and emphasis is placed on how such conceptions of morphogenesis can help reval homology between organisms having developments that are very different to a surface inspection.

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... The predominant view is that segmentation takes place in vertebrates and short-germ insects through a clock and wavefront mechanism (Box 3; Fig 6B, bottom right panel). This model was first proposed by Cooke and Zeeman in 1976 to be the underlying mechanism of vertebrate segmentation [156]. The basis of this model as originally formulated was that a catastrophe leading to abrupt changes in cellular properties takes place in the anterior PSM and underlies somite formation. ...
... The basis of this model as originally formulated was that a catastrophe leading to abrupt changes in cellular properties takes place in the anterior PSM and underlies somite formation. The periodicity of this catastrophe is controlled by an oscillator that interacts with a slowly regressing maturation front, also known as the wavefront [156]. When a specific phase of the oscillator hits the wavefront, the catastrophe is triggered and results in somite individualization. ...
... The clock and wavefront model [156], originally suggested as an underlying mechanism of vertebrate somitogenesis, is, in fact, a periodic version of the wavefront-based speed regulation model (Fig 6B, bottom right). Careful inspection of the axis elongation phases of vertebrate and insect segmentation indicated that segmentation genes in these species are expressed in waves that propagate opposite to the direction of wavefront retraction [4]. ...
Article
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Oscillatory and sequential processes have been implicated in the spatial patterning of many embryonic tissues. For example, molecular clocks delimit segmental boundaries in vertebrates and insects and mediate lateral root formation in plants, whereas sequential gene activities are involved in the specification of regional identities of insect neuroblasts, vertebrate neural tube, vertebrate limb, and insect and vertebrate body axes. These processes take place in various tissues and organisms, and, hence, raise the question of what common themes and strategies they share. In this article, we review 2 processes that rely on the spatial regulation of periodic and sequential gene activities: segmentation and regionalization of the anterior–posterior (AP) axis of animal body plans. We study these processes in species that belong to 2 different phyla: vertebrates and insects. By contrasting 2 different processes (segmentation and regionalization) in species that belong to 2 distantly related phyla (arthropods and vertebrates), we elucidate the deep logic of patterning by oscillatory and sequential gene activities. Furthermore, in some of these organisms (e.g., the fruit fly Drosophila ), a mode of AP patterning has evolved that seems not to overtly rely on oscillations or sequential gene activities, providing an opportunity to study the evolution of pattern formation mechanisms.
... In 1976, Cooke and Zeeman proposed a theoretical model that aimed to explain the formation of periodic structures during vertebrate development. In their Clock and Wavefront model (Cooke and Zeeman, 1976), the authors proposed the existence of two players: a molecular oscillator (clock), responsible for the rhythmic generation of a cell responsive state, and a maturation wavefront, moving slowly in an anterior-to-posterior direction. Exposure of a clock-induced cell population to the wavefront signal would promote a rapid change in cell properties, leading to the formation of a somite. ...
... Together, these two components would translate temporal information into a spatial pattern. According to this model, somite size and number are jointly determined by the period of the clock's oscillations and the speed of the moving wavefront (Cooke and Zeeman, 1976;Oates et al., 2012). However, breakthroughs regarding the identity of the molecules comprising the Clock and the Wavefront were only made 20 years later. ...
... Local inhibition of FGF8 signalling in the anterior PSM resulted in longer somites, suggesting an instructive role for FGF signalling in positioning the somitic boundary (Dubrulle et al., 2001;Sawada et al., 2001). This was consistent with what was previously proposed for the wavefront activity (Cooke and Zeeman, 1976). Further studies elucidated that the chick fgf8 mRNA gradient resulted from the production of stable mRNA transcripts in the tail bud region alone, that degraded over time as the embryo elongated posteriorly, leading to less mRNA levels in the anterior PSM relative to the posterior region (Dubrulle and Pourquié, 2004). ...
Article
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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.
... The rhythmic process of somite formation was proposed to be temporally controlled by repetitive, oscillatory signals even before we had molecular evidence of this kind of regulation [58,59]. In the last decades, experimental evidence has linked the timing of somitogenesis to a system of oscillating genes in the PSM of a wide range of vertebrates, including chick [60], corn snake [46], mouse [61], Xenopus [62], zebrafish [63,64], and medaka [57,65]. ...
... The experiments outlined above can be used not only to formulate a hypothesis for the mechanism of temperature compensation, but also to ask whether predictions from existing models of somite formation are compatible with my results. In addition to the models based on relative-phase encoding described above, the most commonly cited model is known as the "Clock and Wavefront model", first proposed in 1976 [58]. The predictions that can be made from these models, and how we can move forward to test these predictions, will be considered in turn in the sections below. ...
... The regulation of somitogenesis is often described within the framework of the "Clock and Wavefront" model, proposed by Cooke and Zeeman in 1976 [58]. This model suggests that the position of somite boundaries is instructed by two independent factors -the "clock", which encodes temporal information, and the "wavefront", which encodes spatial information. ...
Thesis
Developmental patterning shows remarkable robustness in the face of changing environmental conditions. One particular challenge faced by externally fertilized embryos is how to maintain proper growth and patterning despite temperature variation. In order to address the mechanism behind temperature-invariant patterning, I study somitogenesis in Japanese medaka (Oryzias latipes), which has been shown to tolerate a wide range of temperatures. The periodic formation of somites from the presomitic mesoderm (PSM) in vertebrates is under the control of a molecular “clock”, consisting of oscillatory target genes in the Notch, Wnt and FGF signaling pathways. While it is clear that these periodic signals are involved in regulating the timing of somitogenesis, how oscillations encode information, and how this is coordinated in space is still a matter of ongoing research. To study somitogenesis in medaka, I generated endogenous knock-in reporters to visualize signaling activity in the Notch, Wnt and FGF pathways during somite formation. Importantly, an oscillating Notch signaling reporter, Her7-Venus, allows quantification of segmentation clock oscillations in medaka for the first time. Time-lapse imaging of Her7-Venus oscillations revealed coherent waves that follow a period gradient in the PSM, which is reminiscent of dynamics in higher vertebrates. Imaging of this reporter at different temperatures revealed that segmentation clock oscillations are globally faster at higher temperatures. Importantly, while period changes 2.2 fold, average somite size changes 1.15 fold between 23-35°C. A detailed analysis of the period gradient reveals that oscillations change their period differently in the posterior and anterior PSM, resulting in a constant period gradient amplitude. In addition, the phase gradient amplitude is temperature-invariant. These results provide the first quantitative insight into how underlying signaling dynamics respond to temperature changes and allow robust patterning during somitogenesis. Examining these findings in the context of existing models of somitogenesis could provide insight into how robustness is achieved in this complex system.
... In the 70s, Cooke and Zeeman proposed a theoretical model of periodic tissue segmentation that still prevails in the field (Cooke and Zeeman, 1976). It is based on the existence of two components whose interaction leads to the formation of periodic structures: (1) a genetic oscillation called the clock, i.e., a gene that is expressed periodically by cells, (2) a wavefront of cell maturation. ...
... Subsequent molecular studies revealed the existence of both, oscillatory genes (Palmeirim et al., 1997) and morphogen gradients in the PM (Dubrulle et al., 2001), as postulated by Cooke and Zeeman (1976). Palmeirim et al. (1997) showed that the gene c-hairy oscillates in the PM of the chicken embryo. ...
Article
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Somitogenesis refers to the segmentation of the paraxial mesoderm, a tissue located on the back of the embryo, into regularly spaced and sized pieces, i.e., the somites. This periodicity is important to assure, for example, the formation of a functional vertebral column. Prevailing models of somitogenesis are based on the existence of a gene regulatory network capable of generating a striped pattern of gene expression, which is subsequently translated into periodic tissue boundaries. An alternative view is that the pre-pattern that guides somitogenesis is not chemical, but of a mechanical origin. A striped pattern of mechanical strain can be formed in physically connected tissues expanding at different rates, as it occurs in the embryo. Here we argue that both molecular and mechanical cues could drive somite periodicity and suggest how they could be integrated.
... The bulk cells propagate the received information to their neighbors, effectively writing a temporal signal into a spatial pattern. This mechanism is reminiscent of the clock-and-wavefront mechanism in vertebrate somitogenesis, which relies on a temporal oscillation that is converted into a spatial stripe pattern [25][26][27][28] . ...
... A complementary path to achieve programmable pattern formation in cellular systems is to equip biological cells with engineered sensing and response systems 37,38 . Given that our model was not designed to mimic any specific system, it is noteworthy that it led us to a principle of programmable pattern formation, which can be regarded as a generalization of the clock-and-wavefront scheme underlying vertebrate somitogenesis [25][26][27] . The basic principle is the same as that of a tape recorder, where a temporal audio signal is written into a spatial magnetic pattern. ...
Article
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Complex systems, ranging from developing embryos to systems of locally communicating agents, display an apparent capability of “programmable” pattern formation: They reproducibly form target patterns, but those targets can be readily changed. A distinguishing feature of such systems is that their subunits are capable of information processing. Here, we explore schemes for programmable pattern formation within a theoretical framework, in which subunits process local signals to update their discrete state following logical rules. We study systems with different update rules, topologies, and control schemes, assessing their capability of programmable pattern formation and their susceptibility to errors. Only a fraction permits local organizers to dictate any target pattern, by transcribing temporal patterns into spatial patterns, reminiscent of the principle underlying vertebrate somitogenesis. An alternative scheme employing variable rules cannot reach all patterns but is insensitive to the timing of organizer inputs. Our results establish a basis for designing synthetic systems and models of programmable pattern formation closer to real systems.
... Additionally, in the zebrafish, up to two somites are also prepatterned prior to forming the morphological boundary separating the somite blocks from the presomitic mesoderm (Lee et al., 2009, Sawada et al., 2001. The Clock and Wavefront model (Cooke and Zeeman, 1976) has been developed to explain the mechanism which regulates the temporal and spatial formation of somites during axial elongation, Figure 1.6. Through the interaction of her/hes oscillations (Dequéant and Pourquié, 2008) and an anterior to posterior receding threshold of Wnt and FGF signalling , Dubrulle et al., 2001 alongside anteriorly originating Retinoic Acid (Corral et al., 2003), the positioning of the somites at the anterior of the presomitic mesoderm can be achieved; reviewed by Aulehla and Pourquié (2010). ...
... The precise timing of somite formation, regulation of somite size and positioning within the embryo to ensure bilateral symmetry has been a long standing question in developmental biology and one which has received significant amounts of attention, as reviewed in Aulehla and Pourquié (2006) and Holley and Takeda (2002). The clock and wavefront model (Cooke and Zeeman, 1976) was put forward to explain how the positioning, scaling and timing of somite formation is achieved in vertebrate embryos. It is now known that posterior to anterior gradients of Wnt and FGF signalling in zebrafish Pourquié, 2008, Mara andHolley, 2007), and oscillating levels of Wnt and FGF signalling in mice (Dale et al., 2006, Dequéant et al., 2006, which interact with posterior to anterior travelling waves of Notch signalling result in the precise placement of somite boundaries (Aulehla and Pourquié, 2010, Dale and Pourquié, 2000, Gibb et al., 2010. ...
Thesis
As embryos develop, they are required to generate organised patterns of gene expression across developing tissues. Previous hypotheses used to explain how patterns form in developing tissues have relied on the ideas of positional information and gradients of signalling across the developing tissue, which impart spatial coordinates to individual cells. These coordinates then inform the cell of its respective fate, and hence a pattern of gene expression with spatial organisation is generated. This way of thinking about the problem of pattern formation has been highly successful in explaining the patterning of tissues in vertebrate embryos. However, such an approach begins to fail when challenged with tissues where the cells which make it are highly motile. This thesis will examine the extent to which patterning is robust to cell mixing by disrupting early positional information prior to gastrulation, using whole embryonic explants which undergo widespread cell mixing. These explants elongate, form all three germ layers with spatial organisation and anteroposterior patterned neural tissue. This thesis will then examine the robustness of patterning within the presomitic mesoderm, where a posterior to anterior pattern of gene expression is observed despite high levels of cell rearrangement. Within this tissue, the pattern is observed to accurately scale to the shortening anterior to posterior length and is demonstrated to be highly robust to changes in the degree of cell mixing following experimental perturbation, including in vitro culture of individual cells and pharmacological treatment. Together, this thesis will argue that to understand pattern formation in tissues which are also undergoing extensive cell rearrangement, it is important to consider the gene regulatory network dynamics and how these are influenced by signalling. Rather than taking a positional information “bottom up” type view of cell fate decision making, where signalling gradients inform cells of their position and hence their identity, I will argue for a more holistic approach to understanding development. By considering how “top down” regulation of patterning, mediated via the movement of cells and tissues between domains of signalling, it will be demonstrated that pattern formation can be considered an emergent properly of cells, regulated by signalling as well as cell movements.
... Conversely, in haploid embryos generated by treatment with heavy water (D 2 O), which have more but smaller cells than normal embryos, somite size was normal but the cell number per somite was larger (Cooke, 1975). Together with mathematician Christopher Zeeman, a proponent of Thom's 'catastrophe theory' (Thom, 1972), Cooke developed a model to account for the regularity and constancy of segmentation: the 'clock and wavefront' model, to explain how the size of individual somites is determined by the length of tissue available (Cooke and Zeeman, 1976). The model proposes a 'wavefront' (defined as a 'front of rapid cell change') interacting with a 'clock' ('a smooth cellular oscillator') ensuring that a group of cells undergo the change at the same time as they experience the wave and consequently become committed to form a somite (Cooke and Zeeman, 1976). ...
... Together with mathematician Christopher Zeeman, a proponent of Thom's 'catastrophe theory' (Thom, 1972), Cooke developed a model to account for the regularity and constancy of segmentation: the 'clock and wavefront' model, to explain how the size of individual somites is determined by the length of tissue available (Cooke and Zeeman, 1976). The model proposes a 'wavefront' (defined as a 'front of rapid cell change') interacting with a 'clock' ('a smooth cellular oscillator') ensuring that a group of cells undergo the change at the same time as they experience the wave and consequently become committed to form a somite (Cooke and Zeeman, 1976). In the tissue reduction experiments, the front has a shorter distance to travel and therefore a group of cells enters the rapid change sooner, hence fewer cells pinch off to form each somite. ...
Article
Vertebrate segmentation, the process that generates a regular arrangement of somites and thereby establishes the pattern of the adult body and of the musculoskeletal and peripheral nervous systems, was noticed many centuries ago. In the last few decades, there has been renewed interest in the process and especially in the molecular mechanisms that might account for its regularity and other spatial-temporal properties. Several models have been proposed but surprisingly, most of these do not provide clear links between the molecular mechanisms and the cell behaviours that generate the segmental pattern. Here we present a short survey of our current knowledge about the cellular aspects of vertebrate segmentation and the similarities and differences between different vertebrate classes in how they achieve their metameric pattern. Taking these variations into account should help to assess each of the models more appropriately.
... Cooke and Zeeman presented a mathematical model for somitogenesis in 1976, before any of the involved molecular components had been identified (Cooke and Zeeman 1976). It drew on two physical processes, intracellular biochemical oscillations and a traveling morphogenesis-permissive signal sweeping across the length of the embryo. ...
... What determines the sizes, and relative sizes, of the somites? Cooke and Zeeman (1976) proposed "The clock and wavefront model" to answer these questions. ...
Thesis
In vertebrate embryos, a process called somitogenesis lays the foundations of the adult spine. This process involves elongation and segmentation of the paraxial mesoderm to form somites. Although the segmentation aspect of this has been widely studied, the elongation aspect is not well understood. Posterior growth is widely assumed to be the main driver, but there is very little evidence for this – particularly in fast-developing species like zebrafish. In this thesis, I present the first long term, multi-scale, 3D characterisation of the zebrafish paraxial mesoderm, and show that this tissue elongates through some form of convergent extension, not through growth. In fact, the tissue is compressed over time, and so decreases in volume. I suggest that these processes may be functionally linked, and thus propose a novel mechanism of “compression-extension”. Cell tracking, agent-based modelling, and perturbations show that this form of convergent extension does not involve PCP-dependent directional intercalation but, instead, involves convergent flows of cells towards the midline and non-directional intercalation. The cause of compression is not clear, but perturbation experiments suggest that extrinsic forces from the neural tube and TGFβ signalling may be involved. Comparative work in cichlids, chickens, and catsharks suggests that tissue convergence is not unique to zebrafish, and instead is a conserved feature of paraxial mesoderm elongation – even in species that undergo high levels of growth during somitogenesis. This suggests that the relative contributions of growth and tissue convergence to the process of paraxial mesoderm elongation have evolved differently across vertebrate lineages, resulting in a spectrum of elongation strategies.
... The segmentation clock model of somite development is based on a molecular oscillator that drives the cyclical expression of FGF, Notch, and Wnt genes (Gomez et al., 2008). These findings were interpreted on the basis of the earlier clock-and-wavefront model (Cooke & Zeeman, 1976) and can be used to explain the evolution of serpentiform animals (Gomez et al., 2008;Vonk & Richardson, 2008). ...
Article
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Evolutionary developmental biology (evo-devo) is the study of the evolution of developmental mechanisms. Here, I review some of the theories, models, and laws in evo-devo, past and present. Nineteenth-century evo-devo was dominated by recapitulation theory and archetypes. It also gave us germ layer theory, the vertebral theory of the skull, floral organs as modified leaves, and the “inverted invertebrate” theory, among others. Newer theories and models include the frameshift theory, the genetic toolkit for development, the ABC model of flower development, the developmental hourglass, the zootype, Urbilateria, and the hox code. Some of these new theories show the influence of archetypes and recapitulation. Interestingly, recent studies support the old “primordial leaf,” “inverted invertebrate,” and “segmented head” theories. Furthermore, von Baer's first three laws may now need to be rehabilitated, and the hourglass model modified, in view of what Abzhanov has pointed out about the maternal-zygotic transition. There are many supposed “laws” of evo-devo but I argue that these are merely generalizations about trends in particular lineages. I argue that the “body plan” is an archetype, and is often used in such a way that it lacks any scientific meaning. Looking to the future, one challenge for evo-devo will be to develop new theories and models to accommodate the wealth of new data from high-throughput sequencing, including single-cell sequencing. One step in this direction is the use of sophisticated in silico analyses, as in the “transcriptomic hourglass” models. Research highlights • Laws and other universal concepts, past and present, are reviewed. • I show that many concepts focus on conserved aspects of development. • The puzzle remains as to how embryonic phenotype, natural selection, and developmental mechanisms can be aligned to give an integrated view of evolution and development.
... A key process in early development is the progressive elongation of the embryo along the anterior-posterior axis. In vertebrates, this is coupled with the segmentation of the paraxial mesoderm into somites, that occurs in a clock-like manner from the anterior to the posterior as development continues (Cooke and Zeeman, 1976;Dequéant and Pourquié, 2008;Richardson et al., 1998). To ensure that the appropriate number of somites are generated upon completion of somitogenesis, this process must be balanced with the elongation of the presomitic mesoderm (PSM) (Gomez et al., 2008;Gomez and Pourquié, 2009). ...
Article
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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.
... Interdisciplinary research combining in vivo experiments with mathematical modelling has revealed the molecular mechanism of how Notch signalling synchronizes oscillatory pattern formation [125][126][127]. In Drosophila eye disc development, decreasing the Notch activity showed a striped differentiation pattern [85]. ...
Article
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Notch signalling is a well-conserved signalling pathway that regulates cell fate through cell-cell communication. A typical feature of Notch signalling is ‘lateral inhibition’, whereby two neighbouring cells of equivalent state of differentiation acquire different cell fates. Recently, mathematical and computational approaches have addressed the Notch dynamics in Drosophila neural development. Typical examples of lateral inhibition are observed in the specification of neural stem cells in the embryo and sensory organ precursors in the thorax. In eye disc development, Notch signalling cooperates with other signalling pathways to define the evenly spaced positioning of the photoreceptor cells. The interplay between Notch and epidermal growth factor receptor signalling regulates the timing of neural stem cell differentiation in the optic lobe. In this review, we summarize the theoretical studies that have been conducted to elucidate the Notch dynamics in these systems and discuss the advantages of combining mathematical models with biological experiments.
... This process is conserved among vertebrate species 92 . This rhythmic and sequential pattern is described by the 'clock and wavefront' model 93 , whereby each cell in the presomitic mesoderm contains a genetic oscillator. A differentiation wavefront travelling posteriorly across the tissue arrests the oscillating cells at a given point in the cycle as it passes. ...
Article
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. This Review outlines how approaches from physics can be used to simplify and understand complex patterning events during development. In particular, wavefronts, genetic oscillators and genetic timers are discussed in the context of illustrative developmental processes.
... Cooke and Zeeman presented a mathematical model for somitogenesis in 1976, before any of the involved molecular components had been identified (Cooke and Zeeman 1976). It drew on two physical processes, intracellular biochemical oscillations, and a traveling morphogenesispermissive signal sweeping across the length of the embryo. ...
Preprint
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"Self-organization" has become a watchword in developmental biology, characterizing observations in which embryonic or induced stem cells replicate morphological steps and outcomes seen in intact embryos. While the term was introduced in the 18th century by the philosopher Immanuel Kant to describe the goal-directed properties of living systems, it came into modern use for non-living materials in which complex forms and patterns emerge through dynamical, energy-expending physical processes. What are the relationships among these uses of the term? While multicellular forms arose dozens of times from single-celled organisms, only some of these undergo development, and not all developmental processes are self-organizing. The evolution of the animals (metazoans) from unicellular holozoans was accompanied by the addition of novel gene products which mediated the constitution of the resulting cell clusters as liquid-, liquid crystal-, and solid-like materials with protean morphogenetic propensities. Such materials variously exhibited multilayering, lumen formation and elongation, echoing the self-organizing properties of nonliving matter, "generic" based on such parallels, though with biologically based subunit properties and modes of interaction. These effects provided evolutionary templates for embryonic forms and morphological motifs of diverse metazoan lineages. Embryos and organ primordia of present-day animal species continue to generate forms that resemble the outcomes of these physical effects. Their development, however, employs overdetermined, highly evolved mechanisms that are often disconnected from their originating processes. Using the examples of gastrulation, somitogenesis, and limb skeletal development, this chapter provides instances of, and a conceptual framework for understanding, the relationships between physical and evolved types of developmental self-organization.
... It has been established that segmentation in most arthropods and all vertebrates is driven by a cyclical mechanism where the temporal periodicity of a clock is translated into a repetitive spatial pattern (Cooke and Zeeman, 1976;Palmeirim et al., 1997;Sarrazin et al., 2012). In vertebrates, cell-autonomous oscillatory genes expression is maintained by a posterior Wnt + Fgf signaling gradient. ...
Article
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Wnt signaling pathways are recognized for having major roles in tissue patterning and cell proliferation. In the last years, remarkable progress has been made in elucidating the molecular and cellular mechanisms that underlie sequential segmentation and axial elongation in various arthropods, and the canonical Wnt pathway has emerged as an essential factor in these processes. Here we review, with a comparative perspective, the current evidence concerning the participation of this pathway during posterior growth, its degree of conservation among the different subphyla within Arthropoda and its relationship with the rest of the gene regulatory network involved. Furthermore, we discuss how this signaling pathway could regulate segmentation to establish this repetitive pattern and, at the same time, probably modulate different cellular processes precisely coupled to axial elongation. Based on the information collected, we suggest that this pathway plays an organizing role in the formation of the body segments through the regulation of the dynamic expression of segmentation genes, via controlling the caudal gene, at the posterior region of the embryo/larva, that is necessary for the correct sequential formation of body segments in most arthropods and possibly in their common segmented ancestor. On the other hand, there is insufficient evidence to link this pathway to axial elongation by controlling its main cellular processes, such as convergent extension and cell proliferation. However, conclusions are premature until more studies incorporating diverse arthropods are carried out.
... A key example of ultradian oscillations is the coupling of Wnt and Notch signaling (Sonnen et al., 2018). One of the theoretical frameworks for understanding these protein/gene oscillations in developmental pattern formation has been laid by the clock-and-gradient, or clock-and-wavefront model, originally proposed by Cooke and Zeeman (1976). The dynamic signal encoding based on relative timing of oscillatory protein signals are essential for the development of the embryo. ...
Preprint
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Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems oncology. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored. https://arxiv.org/abs/2201.02055
... The concept of intercalation, for instance, explains how an arbitrary piece of a planarian regenerates the whole worm; the anterior and posterior poles of the stump have non-adjacent "positional values" relative to their neighbors, the continuity of which is then gradually restored leading to the formation of the full original pattern. Most notable mathematical models of patterning are based on either simple diffusion or the more complicated reaction-diffusion mechanisms [19,21,22,24], with some exceptions like the "clock and wavefront model" [31]. A model introduced by Alan Turing, known as "Turing patterns", for instance, is based on a mechanism of "short-range activation and long-range inhibition" driven by inherent dynamical instabilities [32]. ...
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What information-processing strategies and general principles are sufficient to enable self-organized morphogenesis in embryogenesis and regeneration? We designed and analyzed a minimal model of self-scaling axial patterning consisting of a cellular network that develops activity patterns within implicitly set bounds. The properties of the cells are determined by internal ‘genetic’ networks with an architecture shared across all cells. We used machine-learning to identify models that enable this virtual mini-embryo to pattern a typical axial gradient while simultaneously sensing the set boundaries within which to develop it from homogeneous conditions—a setting that captures the essence of early embryogenesis. Interestingly, the model revealed several features (such as planar polarity and regenerative re-scaling capacity) for which it was not directly selected, showing how these common biological design principles can emerge as a consequence of simple patterning modes. A novel “causal network” analysis of the best model furthermore revealed that the originally symmetric model dynamically integrates into intercellular causal networks characterized by broken-symmetry, long-range influence and modularity, offering an interpretable macroscale-circuit-based explanation for phenotypic patterning. This work shows how computation could occur in biological development and how machine learning approaches can generate hypotheses and deepen our understanding of how featureless tissues might develop sophisticated patterns—an essential step towards predictive control of morphogenesis in regenerative medicine or synthetic bioengineering contexts. The tools developed here also have the potential to benefit machine learning via new forms of backpropagation and by leveraging the novel distributed self-representation mechanisms to improve robustness and generalization.
... On top of the movements within the progenitor region of the pre-somitic mesoderm (PSM), patterns of gene expression form, with up to two somites in the zebrafish being prepatterned in the anterior unsegmented presomitic mesoderm prior to forming a true segmented morphological somite [39,40]. The Clock and Wavefront model [41] has been proposed as a mechanism to explain the temporal and spatial formation of somites during axial elongation. Through the interaction of segmentation clock gene oscillations (Her1/Her7 oscillations in zebrafish) [42] and an anterior to posterior receding threshold of Wnt and FGF signalling [43,44] alongside anteriorly originating retinoic acid [45], the positioning of the somites at the anterior of the presomitic mesoderm is achieved; reviewed in [46]. ...
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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.
... A key example of ultradian oscillations is the coupling of Wnt and Notch signaling (95). One of the theoretical frameworks for understanding these protein/gene oscillations in developmental pattern formation has been laid by the clock-and-gradient, or clock-and-wavefront model, originally proposed by Cooke and Zeeman (96). The dynamic signal encoding based on relative timing of oscillatory protein signals are essential for the development of the embryo. ...
Article
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Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.
... Molecular oscillators have also been studied as a fundamental part of morphogenesis. For instance, the clock and wave-front mechanism, in which the state of a local molecular clock is "locked in place" by a traveling wave, provides spatial differentiation [19,20]. Taking inspiration from that mechanism, synthetic oscillators can be applied to the study of morphogenesis [21] and to the creation of novel active materials [22]. ...
Article
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In this article, we study the coupling of a collection of molecular oscillators, called repressilators, interacting indirectly through enzymatic saturation. We extended a measure of autocorrelation to identify the period of the whole system and to detect coupling behaviors. We explored the parameter space of concentrations of molecular species in each oscillator versus enzymatic saturation, and observed regions of uncoupled, partially, or fully coupled systems. In particular, we found a region that provided a sharp transition between no coupling, two coupled oscillators, and full coupling. In practical applications, signals from the environment can directly affect parameters such as local enzymatic saturation, and thus switch the system from a coupled to an uncoupled regime and vice-versa. Our parameter exploration can be used to guide the design of complex molecular systems, such as active materials or molecular robot controllers.
... The rhythm of this segmentation process is species-specific, e.g., every two hours in mice and every 90 min in chicken (47,(51)(52)(53)(54). This evolutionary mechanism is described as the clockwavefront model: a "clock" determines the time of differentiation of the somites and the "wavefront" determines the locations of their segmentation (55). ...
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In humans, the incidence of congenital defects of the intraembryonic celom and its associated structures has increased over recent decades. Surgical treatment of abdominal and diaphragmatic malformations resulting in congenital hernia requires deep knowledge of ventral body closure and the separation of the primary body cavities during embryogenesis. The correct development of both structures requires the coordinated and fine-tuned synergy of different anlagen, including a set of molecules governing those processes. They have mainly been investigated in a range of vertebrate species (e.g., mouse, birds, and fish), but studies of embryogenesis in humans are rather rare because samples are seldom available. Therefore, we have to deal with a large body of conflicting data concerning the formation of the abdominal wall and the etiology of diaphragmatic defects. This review summarizes the current state of knowledge and focuses on the histological and molecular events leading to the establishment of the abdominal and thoracic cavities in several vertebrate species. In chronological order, we start with the onset of gastrulation, continue with the establishment of the three-dimensional body shape, and end with the partition of body cavities. We also discuss well-known human etiologies.
... The philosophical discussion of why models are useful in science is very interesting, but beyond the scope of this piece (a starting point for the interested reader is Roman and Stephan, 2020). For developmental systems, models include the French flag model of morphogenetic patterning and the clock-and-wavefront model of somitogenesis (Cooke and Zeeman, 1976). Another class of models are the material models, which include Watson and Crick's metal model of DNA (Schaffner, 1969). ...
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Recently, developmental systems are investigated with increasing technological power. Still, open questions remain, especially concerning self-organization capacity and its control. Here, we present three areas where synthetic biology tools are used in top-down and bottom-up approaches for studying and constructing developmental systems. First, we discuss how synthetic biology tools can improve stem cell-based organoid models. Second, we discuss recent studies employing user-defined perturbations to study embryonic patterning in model species. Third, we present “toy models” of patterning and morphogenesis using synthetic genetic circuits in non-developmental systems. Finally, we discuss how these tools and approaches can specifically benefit the field of embryo models.
... Even when embryos are experimentally reduced in size prior to somitogenesis, a normal number of somites are produced [Waddington and Deuchar, 1953;Cooke, 1975]. To explain this constancy, Cooke and Zeeman [1976] proposed the "clock-wavefront" model of somitogenesis. Briefly, their model proposed . ...
Article
Why do some species develop rapidly, while others develop slowly? Mammals are highly variable in the pace of growth and development over every stage of ontogeny, and this basic variable – the pace of ontogeny – is strongly associated with a wide range of phenotypes in adults, including allometric patterns of brain and body size as well as the pace of neurodevelopment. This analysis describes variation in the pace of embryonic development in eutherian mammals, drawing on a collected dataset of embryogenesis in fifteen species representing rodents, carnivores, ungulates, and primates. Mammals vary in the pace of every stage of embryogenesis, including stages of early zygote differentiation, blastulation and implantation, gastrulation, neurulation, somitogenesis, and later stages of basic limb, facial, and brain development. This comparative review focuses on the general variation of rapid vs. slow mammalian embryogenesis, with a focus on the pace of somite formation, brain vs. somatic development, and how embryonic pacing predicts later features of ontogeny.
... The periodicity of somitomere formation is produced by the segmentation clock that operates in the presomitic mesoderm, while simultaneously creating the future somatic boundaries, through dynamic signalling effects (Dubrulle et al., 2001). This process is heavily spatiotemporally regulated (Cooke & Zeeman, 1976), and the cells will undergo mesenchymal to epithelial transition (MET) to form somites (Burgess et al., 1996). Mature somites contain two major populations: the sclerotome and dermomyotome. ...
Thesis
The adrenal cortex (AC) is a central steroidogenic organ with key functions in maintaining body homeostasis. Several adrenal diseases (eg Congenital adrenal hyperplasia (CAH)) could in principle be repaired by correcting the mutation (e.g. via recombination) or introduction of a transgene carrying a wildtype form of the mutated gene to permanently restore enzyme activity. However, data from our and other groups demonstrate a rapid turnover of the adrenal cortex. Thus, steroidogenic cells that have been genetically modified are likely to be rapidly replaced by amplifying progenitors that may still carry the mutation. Genetic correction will therefore need to target adrenal stem cell (ASC) populations rather than fully differentiated steroidogenic cells, and in vitro seems to be the better approach. In principle two alternative routes could be envisaged: 1) Generation of induced pluripotent cells (IPSC) from a patient, correction of the mutation using a CRISPR/Cas9 approach and subsequent differentiation towards the adrenal lineage with transplantation in/under the patient's adrenal capsule. 2) Isolation and culture of ASCs, correction in vitro followed by transplantation back into the patient. Aim of this project is to establish a protocol for the in vitro differentiation of mouse ES cells (mESCs) into adrenal progenitor cells and to evaluate their suitability for transplantations under the adrenal capsule. To achieve this goal, I decided to develop a stepwise differentiation procedure that follows as much as possible normal development. The adreno-gonadal primordium (AGP) develops at the interface of the anterior intermediate and lateral plate mesoderm. I developed a robust protocol that allows in vitro differentiation of mESCs via the EpiSC and primitive streak state, into the anterior intermediate and lateral plate mesoderm. Proper differentiation was demonstrated by the expression of cell type specific markers including Brachyury (T) for the primitive streak, Osr1, Gata4 and WT1 for mesodermal lineage, LIM1 and PAX2 for the anterior intermediate, and Foxf1 with Prrx1 for lateral plate mesoderm. The pathways underlying the specification of steroidogenic organs are not yet well established. To obtain further insight into this process, we established a collaboration with Prof. Serge Nef (University of Geneva), whose laboratory has performed single cell RNA-Seq experiments at critical time points of adreno-gonadal differentiation and separation of the adreno-gonadal primordium (AGP) into adrenal primordium (AP) and gonadal primordium (GP). Using information extracted from this cell atlas, and by testing various pathway activators and inhibitors, I was able to further orient differentiation towards the early steroidogenic fate as demonstrated by the upregulation of Nr5a1, a master regulator of steroidogenesis. By testing a range of extracellular matrix proteins, I could show that fibronectin 1 (FN1) enhanced the production of NR5A1 positive cells. Moreover, induction of the PKA pathway using a cAMP derivative (8-Br-cAMP) further increased NR5A1 expression levels in these conditions, both at the RNA and protein level; but still in limiting numbers to claim high efficiency of the protocol. In addition, culturing cells in 3D induced Nr5a1 and other early adrenal progenitor markers over gonadal ones in specific conditions. Further investigation for key aspects of the in vitro differentiation is needed to establish a robust adrenal organoid protocol. Finally, I could partially translate the protocol to hIPSCs, in which the cells were fated correctly for the early steroidogenic progenitor lineage. Taken together these results provide a road map for differentiation of pluripotent stem cells into adrenal progenitors and will form the basis for future work towards transplantation therapies of adrenal diseases.
... We point instead to a central role played by cell-intrinsic programs of timed transient dynamics and differentiation that are extrinsically modulated during embryonic patterning (39). The long-standing and influential "clock and wavefront" model posited an independent wavefront in the tissue, able to cause a sudden transition where locally coherent oscillations were used to determine which cells would segment together (40). Our work shows that both clock and wavefront activities are autonomous properties of PSM cells. ...
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Sequential segmentation of the body axis is fundamental to vertebrate embryonic patterning. This relies on the segmentation clock, a multi-cellular oscillating genetic-network, which mainifests as tissue-level kinematic waves of gene expression that arrest at the position of each new segment. How this hallmark wave pattern is generated is an open question. We compare cellular-resolution oscillatory patterns in the embryo to those generated cell-autonomously in culture without extrinsic signals. We find striking similarity, albeit with greater variability in the timing of clock arrest in culture. Our simple physical description of a clock controlled by a noisy cell-intrinsic timer captures these dynamics. We propose the segmentation clock integrates an intrinsic, timer-driven oscillatory program, which underlies the waves and arrest, with extrinsic cues regulating the intrinsic timer’s duration and precision. One-sentence Summary Segmentation clock and wavefront activities underlying tissue-level wave patterns are cell-autonomous properties in the PSM.
... Somites are 3D multicellular units, typically with an outer epithelial layer surrounded by a fibronectin-rich extracellular matrix, that form by segmentation of the presomitic mesoderm (PSM) 1,2 . The anteroposterior (AP) length of somites and their left-right symmetry is thought to be determined in the unsegmented PSM by genetic oscillations of a segmentation clock and downstream molecular prepatterns 1,2,[8][9][10][11][12] . Although mechanical processes have also been associated with somite morphogenesis 13-17 , their role in determining AP length and left-right symmetry, if any, is not understood. ...
Article
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The body axis of vertebrate embryos is periodically segmented into bilaterally symmetric pairs of somites1,2. The anteroposterior length of somites, their position and left–right symmetry are thought to be molecularly determined before somite morphogenesis3,4. Here we show that, in zebrafish embryos, initial somite anteroposterior lengths and positions are imprecise and, consequently, many somite pairs form left–right asymmetrically. Notably, these imprecisions are not left unchecked and we find that anteroposterior lengths adjust within an hour after somite formation, thereby increasing morphological symmetry. We find that anteroposterior length adjustments result entirely from changes in somite shape without change in somite volume, with changes in anteroposterior length being compensated by corresponding changes in mediolateral length. The anteroposterior adjustment mechanism is facilitated by somite surface tension, which we show by comparing in vivo experiments and in vitro single-somite explant cultures using a mechanical model. Length adjustment is inhibited by perturbation of molecules involved in surface tension, such as integrin and fibronectin. By contrast, the adjustment mechanism is unaffected by perturbations to the segmentation clock, therefore revealing a distinct process that influences morphological segment lengths. We propose that tissue surface tension provides a general mechanism to adjust shapes and ensure precision and symmetry of tissues in developing embryos.
... On the experimental side, there was increasing interest in the Belousov-Zhabotinsky reaction, renowned for the production of oscillations and moving waves (Field and Burger, 1985;Zhabotinsky, 2007), a phenomenon so striking at the time as to be met frequently by disbelief among chemists when first encountered. This led, on the theoretical side, to an interest in model reaction systems that produced periodic oscillations that could be used to model biological processes, notably circadian rhythms (Winfree, 1980), segmentation (Cooke and Zeeman, 1976;Newman, 1993;Pourquié, 2003), and the mitotic oscillator, where Tyson has continued to make important contributions (e.g., see Tyson and Novák, 2015). ...
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This is a brief account of Turing’s ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of oriented stripes, which proved a disappointment in theoretical terms in the case of Drosophila segmentation, but a boost to theory as applied to skin patterns in fish and model chemical reactions. The concept of “order from fluctuations” is a key component of Turing’s theory, wherein pattern arises by selective amplification of spatial components concealed in the random disorder of molecular and/or cellular processes. For biological examples, a crucial point from an analytical standpoint is knowing the nature of the fluctuations, where the amplifier resides, and the timescale over which selective amplification occurs. The answer clarifies the difference between “inelegant” examples such as Drosophila segmentation, which is perhaps better understood as a programmatic assembly process, and “elegant” ones expressible in equations like Turing’s: that the fluctuations and selection process occur predominantly in evolutionary time for the former, but in real time for the latter, and likewise for error suppression, which for Drosophila is historical, in being lodged firmly in past evolutionary events. The prospects for a further extension of Turing’s ideas to the complexities of brain development and consciousness is discussed, where a case can be made that it could well be in neuroscience that his ideas find their most important application.
Article
We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients— active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.
Article
Research using avian embryos has led to major conceptual advances in developmental biology, virology, immunology, genetics and cell biology. The avian embryo has several significant advantages, including ready availability and ease of accessibility, rapid development with marked similarities to mammals and a high amenability to manipulation. As mechanical forces are increasingly recognised as key drivers of morphogenesis, this powerful model system is shedding new light on the mechanobiology of embryonic development. Here, we highlight progress in understanding how mechanical forces direct key morphogenetic processes in the early avian embryo. Recent advances in quantitative live imaging and modelling are elaborating upon traditional work using physical models and embryo manipulations to reveal cell dynamics and tissue forces in ever greater detail. The recent application of transgenic technologies further increases the strength of the avian model and is providing important insights about previously intractable developmental processes.
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The extracellular signal-regulated kinase (ERK) pathway governs cell proliferation, differentiation and migration, and therefore plays key roles in various developmental and regenerative processes. Recent advances in genetically encoded fluorescent biosensors have unveiled hitherto unrecognized ERK activation dynamics in space and time and their functional importance mainly in cultured cells. However, ERK dynamics during embryonic development have still only been visualized in limited numbers of model organisms, and we are far from a sufficient understanding of the roles played by developmental ERK dynamics. In this Review, we first provide an overview of the biosensors used for visualization of ERK activity in live cells. Second, we highlight the applications of the biosensors to developmental studies of model organisms and discuss the current understanding of how ERK dynamics are encoded and decoded for cell fate decision-making.
Article
Modular, repetitive structures are a key component of complex multicellular body plans across the tree of life. Typically, these structures are prepatterned by temporal oscillations in gene expression or signaling. Although a clock-and-wavefront mechanism was identified and plant leaf phyllotaxis arises from a Turing-type patterning for vertebrate somitogenesis and arthropod segmentation, the mechanism underlying lateral root patterning has remained elusive. To resolve this enigma, we combined computational modeling with in planta experiments. Intriguingly, auxin oscillations automatically emerge in our model from the interplay between a reflux-loop-generated auxin loading zone and stem-cell-driven growth dynamics generating periodic cell-size variations. In contrast to the clock-and-wavefront mechanism and Turing patterning, the uncovered mechanism predicts both frequency and spacing of lateral-root-forming sites to positively correlate with root meristem growth. We validate this prediction experimentally. Combined, our model and experimental results support that a reflux-and-growth patterning mechanism underlies lateral root priming.
Article
The clock and wavefront paradigm is arguably the most widely accepted model for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as segmentation clock, and a differentiation wavefront, which provides the positional information indicating where each pair of somites is formed. Shortly after the clock and wavefront paradigm was introduced, Meinhardt presented a conceptually different mathematical model for morphogenesis in general, and somitogenesis in particular. Recently, Cotterell et al. [A local, self-organizing reaction-diffusion model can explain somite patterning in embryos, Cell Syst. 1, 257-269 (2015)] rediscovered an equivalent model by systematically enumerating and studying small networks performing segmentation. Cotterell et al. called it a progressive oscillatory reaction–diffusion (PORD) model. In the Meinhardt–PORD model, somitogenesis is driven by short-range interactions and the posterior movement of the front is a local, emergent phenomenon, which is not controlled by global positional information. With this model, it is possible to explain some experimental observations that are incompatible with the clock and wavefront model. However, the Meinhardt–PORD model has some important disadvantages of its own. Namely, it is quite sensitive to fluctuations and depends on very specific initial conditions (which are not biologically realistic). In this work, we propose an equivalent Meinhardt–PORD model and then amend it to couple it with a wavefront consisting of a receding morphogen gradient. By doing so, we get a hybrid model between the Meinhardt–PORD and the clock-and-wavefront ones, which overcomes most of the deficiencies of the two originating models.
Article
The mesenchymal tissue of the developing vertebrate limb bud is an excitable medium that sustains both spatial and temporal periodic phenomena. The first of these is the outcome of general Turing-type reaction-diffusion dynamics that generate spatial standing waves of cell condensations. These condensations are transformed into the nodules and rods of the cartilaginous, and eventually (in most species) the bony, endoskeleton. In the second, temporal periodicity results from intracellular regulatory dynamics that generate oscillations in the expression of one or more gene whose products modulate the spatial patterning system. Here we review experimental evidence from the chicken embryo, interpreted by a set of mathematical and computational models, that the spatial wave-forming system is based on two glycan-binding proteins, galectin-1A and galectin-8 in interaction with each other and the cells that produce them, and that the temporal oscillation occurs in the expression of the transcriptional coregulator Hes1. The multicellular synchronization of the Hes1 oscillation across the limb bud serves to coordinate the biochemical states of the mesenchymal cells globally, thereby refining and sharpening the spatial pattern. Significantly, the wave-forming reaction-diffusion-based mechanism itself, unlike most Turing-type systems, does not contain an oscillatory core, and may have evolved to this condition as it came to incorporate the cell-matrix adhesion module that enabled its pattern-forming capability.
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Scoliosis is a complex disease with undetermined pathogenesis and has a strong relationship with genetics. Models of scoliosis in animals have been established for better comprehending its pathogenesis and treatment. In this review, we searched all the genetic animal models with body curvature in databases, and reviewed the related genes and scoliosis types. Meanwhile, we also summarized the pathogenesis of scoliosis reported so far. Summarizing the positive phenotypic animal models contributes to a better understanding on the pathogenesis of scoliosis and facilitates the selection of experimental models when a possible pathogenic factor is concerned.
Chapter
Understanding the cellular principles of odontogenesis requires an incremental and up-to-date understanding of the sequential molecular embryological processes leading to a complete normal dental formation. This topic review provides a state-of-the-art explanation of these dental morphogenetic processes and the subsequent crown development in normal deciduous and permanent teeth, based on an upgraded version of the “odontogenic homeobox code”. The description of these processes is shown from the differential epithelium-ectomesenchyme and epithelium-mesenchyme interaction stand-points, necessary to produce cell-cell and extracellular matrix-cell transformations. These cellular processes lead to the sequential stages of classic histological dental formation, which progressively correspond to the development of dental regions, identities, and forms, to obtain complete deciduous and permanent human dentitions.
Chapter
Multicellular morphogenesis is responsible for generating most living forms in the world around us and lays the structural basis for these forms’ biological activity. The recent years have seen significant advancement in understanding the biochemical and biophysical underpinnings of multicellular morphogenesis, particularly in the important cases presented by phyllotaxis and segmentation. The state of knowledge concerning self-organization effects in phyllotaxis and segmentation is reviewed from the standpoint of integration of biochemical and biomechanical processes, as well as translation of temporal self-organization into spatial one. Connection of fundamental biophysics and biomechanics of phyllotaxis to generative models capable of explaining the various plant growth patterns is covered along with spatial interaction of biological clocks during embryo segmentation.
Article
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.
Article
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 (PSM) as it grows by adding new cells at its posterior, followed by traveling 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.
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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.
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In this paper, we consider reaction–diffusion systems, which describe the propagation of waves with chaotic and time periodic fronts. Using this property, we show that there exist reaction–diffusion models with a few of reagents, which, by a variation of initial data, is capable to generate all possible one-dimensional cell patterns. We describe algorithms, which allow to obtain any prescribed target cell patterns by chaotic waves. Our model can be considered as a reaction–diffusion analogue of universal Turing machine. So, we propose a new robust mechanism of positional information transfer, which, in contrast to Wolpert’ gradients, can work at long distances. Universality of our model helps to explain why genes, responsible for morphogenesis, are highly conservative within long evolution periods.
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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. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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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–Tc (with Tc = 14.4 °C). This behavior characteristic of a system near a critical point may account for the temperature independence of somitogenesis in zebrafish. In Zebrafish, the dynamics of fgf8 and other gene transcripts as well as segmentation frequency, shortening of pre-somitic mesoderm and tail growth rate slows down with lower temperature. This may explain the temperature independence of somitogenesis.
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Ever since their first report in 1984, Antennapedia-type homeobox (Hox) genes have been involved in such a series of interesting observations, in particular due to their conserved clustered organization between vertebrates and arthropods, that one may legitimately wonder about the origin of this heuristic value. In this essay, I first consider different examples where Hox gene clusters have been instrumental in providing conceptual advances, taken from various fields of research and mostly involving vertebrate embryos. These examples touch upon our understanding of genomic evolution, the revisiting of 19th century views on the relationships between development and evolution and the building of a new framework to understand long-range and pleiotropic gene regulation during development. I then discuss whether the high value of the Hox gene family, when considered as an epistemic object, is related to its clustered structure (and the absence thereof in some animal species) and, if so, what is it in such particular genetic oddities that made them so generous in providing the scientific community with interesting information.
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Catastrophe theory research has recently witnessed a distinct proliferation. In this article we apply bibliometric network techniques to examine the conceptual/intellectual structure of this domain based on 1498 Scopus documents written by 2745 authors representing 69 nations and spanning almost five decades (1975–2020). The study aims to explore the catastrophe theory research impactful authors, influential journals, collaboration networks and emerging trends. Additionally, keyword co-occurrence techniques are employed to scrutinize major schools of thought. Results show that the most impactful journals publishing catastrophe theory research are Behavioral Science, Physical Review D, Ecological Modeling, Journal of Physical Chemistry A and the Journal of Theoretical Biology. Results also show that the author collaboration network in catastrophe theory research is sparse. Furthermore, results related to collaborative networks among institutions and countries reveal a global “North-South” schism between developed and developing nations. The multiple correspondence analysis (MCA) applied to obtain the catastrophe theory research conceptual map reflects the depth and breadth of the research's foci. Finally, the reference publication year spectroscopy (RPYS) was used to detect the “citation classics” forming the historical roots of catastrophe theory research. Our analysis has far-reaching implications for aspiring researchers interested in catastrophe theory research as we retrospectively trace the evolution in research output over the last five decades, establish linkages between the authors and articles, and reveal trending topics/hotspots within the broad theme of catastrophe theory research.
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Sir Erik Christopher Zeeman, formerly Foundation Professor of Mathematics at the University of Warwick, Principal of Hertford College, Oxford, and Vice-President of the Royal Society, was for over 40 years a leading figure in British mathematical life. A brilliant mathematician, exceptional lecturer, prodigious polymath and deep-thinking leader and administrator, Christopher Zeeman had a remarkable influence on British mathematics. He made major research contributions to topology, dynamical systems, catastrophe and singularity theory, and applications of mathematics in the physical, biological and social sciences. Particularly notable among his many other achievements were his foundation of the Warwick Mathematics Institute and his contributions to the public understanding of science.
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One of the elementary processes in morphogenesis is the formation of a spatial pattern of tissue structures, starting from almost homogeneous tissue. It will be shown that relatively simple molecular mechanisms based on auto- and cross catalysis can account for a primary pattern of morphogens to determine pattern formation of the tissue. The theory is based on short range activation, long range inhibition, and a distinction between activator and inhibitor concentrations on one hand, and the densities of their sources on the other. While source density is expected to change slowly, e.g. as an effect of cell differentiation, the concentration of activators and inhibitors can change rapidly to establish the primary pattern; this results from auto- and cross catalytic effects on the sources, spreading by diffusion or other mechanisms, and degradation.Employing an approximative equation, a criterium is derived for models, which lead to a striking pattern, starting from an even distribution of morphogens, and assuming a shallow source gradient. The polarity of the pattern depends on the direction of the source gradient, but can be rather independent of other features of source distribution. Models are proposed which explain size regulation (constant proportion of the parts of the pattern irrespective of total size). Depending on the choice of constants, aperiodic patterns, implying a one-to-one correlation between morphogen concentration and position in the tissue, or nearly periodic patterns can be obtained. The theory can be applied not only to multicellular tissues, but also to intracellular differentiation, e.g. of polar cells.The theory permits various molecular interpretations. One of the simplest models involves bimolecular activation and monomolecular inhibition. Source gradients may be substituted by, or added to, sink gradients, e.g. of degrading enzymes. Inhibitors can be substituted by substances required for, and depleted by activation.Sources may be either synthesizing systems or particulate structures releasing activators and inhibitors.Calculations by computer are presented to exemplify the main features of the theory proposed. The theory is applied to quantitative data on hydra — a suitable one-dimensional model for pattern formation — and is shown to account for activation and inhibition of secondary head formation.
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In 1952 Turing published a paper which showed how under restricted conditions a class of chemical reactions could give biological patterns in diffusion-coupled cells. Although this theory has been much discussed, little has been learnt about the range and type of pattern it can generate. In order to do this and to see how stable the patterns are, we have examined the system in detail and written a computer program to simulate Turing's kinetics for two morphogens over various assemblies of cells. We find that on one-dimensional lines of cells, patterns can indeed be produced and that the chemical wavelengths follow all of Turing's predictions. The results show that stable repeating peaks of chemical concentration of periodicity 2–20 cells can be obtained in embryos in periods of time of less than an hour. We do find however that these patterns are not reliable: small variations in initial conditions give small but significant changes in the number and positions of observed peaks. Similar results are observed in two-dimensional assemblies of cells. On rectangles, random blotches are observed whose position cannot be reliably predicted. On cylinders whose circumference is less than the chemical wavelength, annular stripes are produced. For larger cylinders, blotches that lie very approximately on helices are generated; again sharp prediction of the detailed pattern is impossible.The significance of these results for the developing embryo is discussed. We conclude that Turing kinetics, at least in the simple cases that we have studied, are too unreliable to serve as the generating mechanism for features such as digits which are characterized by a consistent number of units. The theory is however more than adequate by these criteria to specify less well-defined developing patterns such as those of hair follicles or leaf organization. It is emphasized however that the Turing theory is quite unable to generate regulative systems, only mosaicpatterns can be produced.
Article
The two major aspects of embryonic development are the appearance of differentiated tissues and of organized structures. Most recent investigations have been directed mainly towards the first of these two categories, and have attempted to elucidate the changes in the character of the living substance in terms such as the reactions between organizers and competent tissues, determination by means of gradients or ‘organ-forming substances’, the influence of genetic factors, and the like. Very much less effort has been devoted to the study of the changes of form undergone by the developing tissues. These geometrical changes must, of course, be brought about by the operation of physical forces, and embryonic development offers a whole range of biophysical problems about which our ignorance remains profound. This paper reports a study directed towards this general class of biophysical problem. In most embryonic changes of structure both the initial form and the later ones are geometrically complex and difficult to describe in reasonably precise terms.
Article
It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
Chapter
This chapter discusses that within the conceptual framework of positional information, a new and a simple way of looking at pattern formation may be obtained. In pressing the possibility of universality, the chapter deliberately takes an extreme stand, but at least it serves to counterbalance the special-substance inductive view of pattern formation. Also, in order to show its possible relevance to pattern formation and even cell movement, procrustean view of the data is taken. One of the virtues of the positional information mechanism of pattern formation is that, with the same system for positional information one can generate an enormous number of different patterns, by changing the cell's rules for interpretation. Since interpretation will be gene determined, there is little difficulty in seeing how this can be achieved. In fact, the concept of positional information makes excellent use of a central feature of development, that all the cells carry the same genetic information.
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The basic embryological phenomena do recur at insect metamorphosis. This chapter describes how work with insects has produced some central information. Developing cells are usually polarized in relation to the main axes of symmetry of the organism. During epigenesis, to the continued accompaniment of growth, the possible destinies of individual clones of cells become progressively defined. Once the developmental identity of a cell is established, it is said to be determined and the process which orders requisite determinations in space is called pattern formation. Often the mechanisms of pattern formation are plastic so that they adapt to interference or loss of parts so as to reconstruct the whole pattern from the available material. This process is termed regulation. After a cell reaches its final determined status, it constructs specialized organelles and synthesizes specific biochemical products it differentiates. Although these five features of developing systems—namely, polarity, determination, pattern formation, regulation, and differentiation are each components of one process, they can, to a certain extent, be treated independently. In this chapter they are discussed in relation to development of postembryonic insects.
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In chick blastoderms at primitive streak stage, lengths of the primitive streak were cut out and replaced with their antero-posterior orientation reversed. In some experiments the region immediately in front of the primitive streak (presumptive prechordal head) was also included in the excisedpiece. Control operations involving excision and replacement without reversal were also performed. The embryos were subsequently grown in vitro by Waddington's technique. After reversal of a variety of different parts of the streak at various developmental stages, many cases of regulative development were obtained. In these, the original orientation of the blastoderm was maintained, and while there were abnormalities of various kinds in the embryos, they were no different from the abnormalities found in the controls. Very occasionally the regulated axis was partially doubled after a reversal, though not after a control operation. A few specimens which had undergone reversal of long pieces of the primitive streak and had completely healed showed a failure of regulation in that there was some tendency for the reversed-piece to develop according to its own orientation. But at best this reversed differentiation was very distorted and incomplete. Evidently the orientation of the primitive streak does not at any stage control the orientation of the embryo; and the primitive streak, when it is fully developed and contains most of the presumptive axial material, is highly labile in its powers of differentiation. In spite of its well-known 'organizer' activity, the primitive streak is subject to control by the surrounding blastoderm.
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Eggs of the blowfly Protophormia spec. were separated into anterior and posterior fragments of different sizes. The separations were made between oviposition and the blastoderm stage. The partial larvae produced by the fragments were scored for the cuticular pattern they had formed. The cuticle of the 1st instar larva carries 11 denticle belts, which correspond to the anterior borders of the thoracic and abdominal body segments. Egg fragments of the sizes studied did not produce the complete cuticular pattern. If denticle belts were present on the partial larvae formed in egg fragments these always included the corresponding terminal pattern element. After fragmentation during early development, all the eggs failed to form some pattern elements. The extent and position in the pattern of this gap depend on the level and stage of fragmentation. With increasing egg age (developmental stage) at fragmentation, the gap in the cuticular pattern becomes progressively smaller. Eggs fragmented during or after the formation of the blastodermal cell walls usually form all pattern elements. The progressive reduction of the gap in the cuticular pattern is due to formation of bigger sets of pattern elements in both partner fragments i.e., on average an anterior or posterior fragment of given size will produce more pattern elements if separated from the rest of the egg at a later stage than if separated early. To produce a given set of pattern elements a fragment needs to be bigger on the average when separated early than when separated later. This applies to both anterior and posterior fragments of the fragmentation levels studied. From these results, the egg of Protophormia cannot be considered a mosaic of determinants for the different pattern elements at oviposition. Once the egg has become subdivided into blastoderm cells, it reacts as a developmental mosaic with respect to the pattern studied.
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Deuterium oxide lengthens the period of the endogenous tidal activity rhythm of the sand-beach isopod, Excirolana chiltoni. Heavy water has also been shown to retard the circadian rhythm of deer mice, when added to the animals' drinking water. The average dosage dependence of the effect can be estimated with high precision for both isopod and mouse, and the two values are indistinguishable. A similar slowing of circadian rhythms, due to D2O, has also been reported for an alga, a higher plant, two species of birds and three other rodents. Although data permitting reliable estimates of dosage dependence have not been published for these latter cases, the effect is apparently also of about the same magnitude. This evidence suggests fundamental similarities in the rhythmic mechanisms. Heavy water also produces a reversible slowing of several biological rhythms with periods in the millisecond range: the electric-organ discharge of a gymnotid fish (Stenarchus albifrons); the respiratory cycle of goldfish, as well as of an amphipod (Paraphoxus) and an isopod (Excirolana); and the cardiac cycle of a clam (Donax) and a crab (Emerita). Since these high-frequency rhythms originate in pacemakers dependent on diffusion processes, the experimental results suggest the possibility that long-period biological clocks are also based on diffusion-dependent pacemakers.
Article
THE number of meristic parts in fishes (vertebrae, fin rays, scales, etc.) is often susceptible to modification by temperature or other environmental factors to which the developing embryo is exposed. This has been demonstrated experimentally on at least a dozen fish species1,2. In reptiles, one experiment3 showed that the number of scales on a snake could be raised by higher incubation temperature. Serially repeated parts are less variable in amphibians than in fishes, but among the urodeles the number of vertebrae (or of somites) is known to vary intraspecifically among wild populations, and is sometimes used taxonomically. A hereditary basis to the number of trunk segments in Plethodon cinereus has been demonstrated by rearing young from different populations under constant conditions4. This communication describes the converse experiment, in which urodele eggs from one locality were reared at various temperatures, to determine whether different environments could produce different meristic counts in young having similar genetic background.
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The mechanisms which could underlie circadian rhythms fall naturally into groups with qualitatively different responses to disruption. Experiments designed to distinguish between these mechanisms seem to exclude all of them. It may be that multicellular organisms keep time, not by one `clock' but by averaging many independent circadian oscillators.
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During Xenopus embryogenesis and early growth, somite number stays close to a species-typical value for each morphological stage. This remains true even after operations on blastulae which lead to the development of abnormally small but otherwise complete early embryos, involving reduction in number of cells assigned to each somite. Evidence presented suggests that a body-position gradient may be involved, but in rather different ways at different stages, in controlling total somite number.
Article
The development of the vertebrate limb involves the production of a specific external form arising from cell division and other growth processes at the cellular level, and the origin within it of specific patterns of tissues arising by cellular differentiation, of which the pattern of cartilages which pre-figure the limb skeleton is the most striking.In this paper we propose a model for the differentiation (or the preceding determination) process that, using only localized cell to cell interactions, can approximate the cartilage pattern in any limb shape. The model requires cells to modify their metabolism irreversibly at critical threshold levels of a diffusible morphogen which may be made or destroyed by these cells. Restrictions inherent in the successful development of a total limb pattern using this system lead to the prediction that the process is confined to a distal band which has no significant interaction with more proximal regions but within this band the characteristic features of the anterior-posterior axis of the limb develop without additional interactions. Cartilage elements are initiated as single “cells” and expand centrifugally to their final size; these elements developing sequentially along the anterior-posterior axis, showing a distinct polarity of size. The model also predicts that equivalent cartilage elements in all vertebrate limbs will be roughly the same relative size at determination, the extensive range of adult structures arising by differential growth and fusion, possibly controlled by global aspects of the model.It must be emphasized that this model only satisfactorily simulates the anterior-posterior patterning of cartilage elements, the disto-proximal pattern being externally imposed.The final cartilage pattern is shown to be a function of (1) the developing shape of the limb, (2) the position of an initiator region that starts the patterning process and (3) the rate of production of the diffusible morphogen. Using parameters selected with as much realism as possible the model gives a good approximation to the pattern of c cartilages found in the normal chick limb; modifying the shape of the limb to that of the talpid3 mutant produces the characteristics features of the cartilage pattern found in that mutant and modifying the rate of morphogen production simulates patterns resembling those found in some ancestral vertebrate fossil forms.
Article
Bistable control circuits like those in bacteriophage lambda may function in Drosophila development.
Article
The structure of any differentiated tissue results from a well-defined sequence of events in which the spatial and temporal organization of the developing tissue mass are intimately related. It is as though every cell has access to, and can read, a clock and a map (Wolpert's positional information). A model developed in the present paper is one in which the map arises from wave-like propagation of activity from localized clocks or pacemakers. Individual cells are supposed temporally organized in the sense that biochemical events essential for the control of development recur periodically. This temporal organization of an individual cell is converted by functional coupling between cells into a spatial ordering of the temporal organization. More explicitly a periodic event is postulated which propagates outward from a pacemaker region, synchronizing the tissue and providing a time base for development. Intercellular signalling, entrainment of all cells in the tissue by the fastest cells in the pacemaker region, and a refractory period to guarantee unidirectional propagation are the essential features of the propagation; they permit the derivation of a wave equation and a set of boundary conditions. An underlying gradient of frequency of the event establishes the position of the pacemaker region and the sense of propagation. A second event which propagates more slowly than the first provides positional information in the form of a one-dimensional sequence of surfaces of constant phase difference between the two events. A third event is used to regulate the pattern of phase difference and thus establish size-independent structures. The longest trajectory orthogonal to the surfaces of constant phase difference beginning at the pacemaker region and terminating at the regulating region defines a developmental axis of definite polarity. The model is readily extended to more than one axis, i.e. multi-dimensional positional information. It has a high informational capacity and is readily applied to the discussion of particular developmental phenomena. To illustrate its utility, we discuss development and regeneration in Hydra, positional in the early amphibian embryo, and the retinal-neural tectal projection of the amphibian visual system. Specific experiments to test for the existence of the postulated periodic events and their consequences are suggested. Some preliminary experimental results on Hydra tending to confirm the model are reported. Possible detailed realizations of the model in terms of, biochemical control circuits within the cell, are conjectured and discussed to show that the formal features of the model can be realized by well-recognized biochemical processes.
Article
The problem of pattern is considered in terms of how genetic information can be translated in a reliable manner to give specific and different spatial patterns of cellular differentiation. Pattern formation thus differs from molecular differentiation which is mainly concerned with the control of synthesis of specific macromolecules within cells rather than the spatial arrangement of the cells. It is suggested that there may be a universal mechanism whereby the translation of genetic information into spatial patterns of differentiation is achieved. The basis of this is a mechanism whereby the cells in a developing system may have their position specified with respect to one or more points in the system. This specification of position is positional information. Cells which have their positional information specified with respect to the same set of points constitute a field. Positional information largely determines with respect to the cells' genome and developmental history the nature of its molecular differentiation. The specification of positional information in general precedes and is independent of molecular differentiation. The concept of positional information implies a co-ordinate system and polarity is defined as the direction in which positional information is specified or measured. Rules for the specification of positional information and polarity are discussed. Pattern regulation, which is the ability of the system to form the pattern even when parts are removed, or added, and to show size invariance as in the French Flag problem, is largely dependent on the ability of the cells to change their positional information and interpret this change. These concepts are applied in some detail to early sea urchin development, hydroid regeneration, pattern formation in the insect epidermis, and the development of the chick limb. It is concluded that these concepts provide a unifying framework within which a wide variety of patterns formed from fields may be discussed, and give new meaning to classical concepts such as induction, dominance and field. The concepts direct attention towards finding mechanisms whereby position and polarity are specified, and the nature of reference points and boundaries. More specifically, it is suggested that the mechanism is required to specify the position of about 50 cells in a line, relatively reliably, in about 10 hours. The size of embryonic fields is, surprisingly, usually less than 50 cells in any direction.
Article
D(2)O is the only "chemical" agent that consistently affects the frequency of circadian oscillations: its effect is now known to be so widespread and predictable that its action merits closer study as a potential clue to the currently obscure concrete nature of circadian oscillators. The great diversity of D(2)O effects on biological systems in general is briefly reviewed and the need for rejectable hypotheses concerning the action of D(2)O on circadian clocks is stressed because current speculation on its action yields "predictions" expected from almost any hypothesis. We consider the hypothesis that it "diminishes the apparent temperature" of the cell and proceed to test this by examining the effect of D(2)O on temperature-dependent and temperature-compensated aspects of the circadian system in Drosophila. We find these components respond as differentially to D(2)O as they do to temperature; we conclude, however, with a warning that this result may be equivocal if, as we now suspect, the frequency of circadian oscillations is generally homeostatically conserved-not only in the face of temperature change, but change in any variable to which it is sensitive. More crucial tests of the temperature-equivalence hypothesis for D(2)O action are defined.
Article
Pattern formation by the cells of a growing organism depends on coordination of changes in space and time. Evidence is presented here for the control of morphogenesis by positional information specified by an autonomous timing mechanism that operates in a ``progress zone'' at the tip of the limb bud.
Article
The engrailed (en) mutation leads to the transformation of the posterior structures of the dorsal mesothoracic disc into those characteristic of the anterior region of the same disc. Similar posterior-anterior duplications have been detected in dorsal as well as ventral structures of all the thoracic segments. -Genetic combinations of en with other pattern mutants have shown their synergistic effect on the posterior wing pattern.-A clonal analysis of the en wing disc shows that en affects its development in a characteristic way. The genetic change, by induced mitotic recombination, of en(+) into en cells is followed by the corresponding transformation, except when it takes place some cell divisions prior to differentiation.-The en posterior wing disc cells show positive affinities with normal anterior wing disc cells in aggregates.-The mode of action of the en(+) locus controlling wing disc development is discussed.
Article
The biological clock may be a feedback system involving ions and ion-transport channels.
Article
Proto-organisms probably were randomly aggregated nets of chemical reactions. The hypothesis that contemporary organisms are also randomly constructed molecular automata is examined by modeling the gene as a binary (on-off) device and studying the behavior of large, randomly constructed nets of these binary “genes”. The results suggest that, if each “gene” is directly affected by two or three other “genes”, then such random nets: behave with great order and stability; undergo behavior cycles whose length predicts cell replication time as a function of the number of genes per cell; possess different modes of behavior whose number per net predicts roughly the number of cell types in an organism as a function of its number of genes; and under the stimulus of noise are capable of differentiating directly from any mode of behavior to at most a few other modes of behavior. Cellular differentation is modeled as a Markov chain among the modes of behavior of a genetic net. The possibility of a general theory of metabolic behavior is suggested.
  • L Wolpmzt
WOLPmZT, L. (1969). d. theor. Biol. 25, 1.
CIBA Symposium no. 29. CellPatterning Amsterdam
WOLP~RT, L. (1975). CIBA Symposium no. 29. CellPatterning Amsterdam: Elsevier. ZmnV~AN, E. C. (1974). Am. Math. Soc. 7, in press.
  • H Stumpr
  • D Summerbell
  • J H Lewis
  • L Wolpert
  • R Thom
STUMPr, H. (1968). J. exp. BioL 49, 49. SUMMERBELL, D. LEWIS, J. H. & WOLPERT, L. (1973). Nature, Land. 244, 492. THOM, R. (1973). Am. Math. Soc. 5.
  • S A Kaurrman
KAUrrMAN, S. A. (1969). J'. theor. BioL 22, 437. KAU~N, S. A. (1973). Science N. t". 181, 310.
  • E M Dl 'ucrar
  • A M C Burgess
DL'UCRAR, E. M. & BURGESS, A. M. C. (1967). J. EmbryoL exp. Morph. 17, 349. ENmGHT, J. T. (1971). Z. vergl. PhysioL 72, 1.
  • C H Schmidt
WADDXNOTON, C. H. & SCHMIDT, G. A. (1933). Wilhelm Roux Arch. Entw Mech. Org. 128, 521.
In Current Topics in Development
  • L Wolrert
WOLrERT, L. (1971). In Current Topics in Development. pp. 183. N.Y. and London: Academic Press.
  • E C Zmzman
ZmZMAN, E. C. (1975). Ann. Rev. Biophys. Bioeng. 4, 210.
  • C H Deuchar
WADDINGTON, C. H. & DEUCHAR, E. M. (1953). J. Embryol exp. Morph. 1, 349.
CIBA Symposium no. 29. Cell Patterning
  • R Maynard
  • J Smith
MARK, R. (1975). CIBA Symposium no. 29. Cell Patterning. Amsterdam: Elsevier. MAYNARD SMITH, J. (1960). Proc. Roy. Soc. 152, 397.
  • Child
  • Stumpf