Origination and innovation in the vertebrate limb skeleton: an epigenetic perspective

The trabecular architecture of the popliteal sesamoid bone (cyamella) from a New Zealand white rabbit (Oryctolagus cuniculus)

Sesamoid bones are ossified structures that are embedded in tendons near articulation. They consist of an inner trabecular bone architecture surrounded by a thin cortical shell. While the formation of sesamoid bones is probably mainly controlled by genetic factors, the proper development and mineralization of a sesamoid bone depends also on mechanical stimulation. While most sesamoid bones are not loaded directly by other bones during locomotion, they still experience forces directed from the tendon in which they are embedded. In cases when the sesamoid bone is experiencing forces only from a single tendon, such as the cyamella in the rabbit, this may give us a tool to study bone functional adaptation in a relatively simple loading setting. This study investigates the internal trabecular architecture of the popliteal sesamoid bone (cyamellae) in New Zealand white (NZW) rabbits (Oryctolagus cuniculus). Five hind limbs of NZW rabbits were micro-computed tomography scanned and the cortical and trabecular architectures of the cyamellae were evaluated. The results revealed that similar to the patella, the cyamella has a thin cortex and a high trabecular bone volume fraction (BV/TV), which is derived mostly from the high trabecular thickness (Tb.Th). Trabecular BV/TV and Tb.Th were not distributed homogeneously, but they were lower at the periphery and higher closer to the proximal and middle of the cyamella, near the musculotendinous junction. The results also demonstrated that trabeculae tend to align along two recognizable orientations, one with the direction of tensile stresses, in line with the popliteal tendon, and the second bridging the narrow space between the cranial and caudal cortical faces of the bone.

Development and growth of the pelvic fin in the extant coelacanth Latimeria chalumnae

The ontogeny of the paired appendages has been extensively studied in lungfishes and tetrapods, but remains poorly known in coelacanths. Recent work has shed light on the anatomy and development of the pectoral fin in Latimeria chalumnae. Yet, information on the development of the pelvic fin and girdle is still lacking. Here, we described the development of the pelvic fin and girdle in Latimeria chalumnae based on 3D reconstructions generated from conventional and X-ray synchrotron microtomography, as well as MRI acquisitions. As in other jawed vertebrates, the development of the pelvic fin occurs later than that of the pectoral fin in Latimeria. Many elements of the endoskeleton are not yet formed at the earliest stage sampled. The four mesomeres are already formed in the fetus, but only the most proximal radial elements (preaxial radial 0-1) are formed and individualized at this stage. We suggest that all the preaxial radial elements in the pelvic and pectoral fin of Latimeria are formed through the fragmentation of the mesomeres. We document the progressive ossification of the pelvic girdle, and the presence of a trabecular system in the adult. This trabecular system likely reinforces the cartilaginous girdle to resist the muscle forces exerted during locomotion. Finally, the presence of a preaxial element in contact with the pelvic girdle from the earliest stage of development onward questions the mono-basal condition of the pelvic fin in Latimeria. However, the particular shape of the mesomeres may explain the presence of this element in contact with the girdle.

Multiscale modeling of vertebrate limb development

We review the current state of mathematical modeling of cartilage pattern formation in vertebrate limbs. We place emphasis on several reaction-diffusion type models that have been proposed in the last few years. These models are grounded in more detailed knowledge of the relevant regulatory processes than previous ones but generally refer to different molecular aspects of these processes. Considering these models in light of comparative phylogenomics permits framing of hypotheses on the evolutionary order of appearance of the respective mechanisms and their roles in the fin-to-limb transition. This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Mechanistic Models Developmental Biology > Developmental Processes in Health and Disease Analytical and Computational Methods > Analytical Methods.

Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models

The phenomenon of chondrogenic pattern formation in the vertebrate limb is one of the best studied examples of organogenesis. Many different models, mathematical as well as conceptual, have been proposed for it in the last fifty years or so. In this review, we give a brief overview of the fundamental biological background, then describe in detail several models which aim to describe qualitatively and quantitatively the corresponding biological phenomena. We concentrate on several new models that have been proposed in recent years, taking into account recent experimental progress. The major mathematical tools in these approaches are ordinary and partial differential equations. Moreover, we discuss models with non-local flux terms used to account for cell-cell adhesion forces and a structured population model with diffusion. We also include a detailed list of gene products and potential morphogens which have been identified to play a role in the process of limb formation and its growth.

The postembryonic transformation of the shell in emydine box turtles

A key trend in the 210-million-year-old history of modern turtles was the evolution of shell kinesis, that is, shell movement during neck and limb retraction. Kinesis is hypothesized to enhance predator defense in small terrestrial and semiaquatic turtles and has evolved multiple times since the early Cretaceous. This complex phenotype is nonfunctional and far from fully differentiated following embryogenesis. Instead, kinesis develops slowly in juveniles, providing a unique opportunity to illustrate the postembryonic origins of an adaptive trait. To this end, we examined ventral shell (plastral) kinesis in emydine box turtles and found that hatchling plastron shape differs from that of akinetic-shelled relatives, particularly where the hinge that enables kinesis differentiates. We also demonstrated shape changes relative to plastron size in juveniles, coinciding with a shift in the carapace-plastron structural connection, rearrangement of ectodermal plates, and bone repatterning. Furthermore, because the shell grows larger relative to the head, complete concealment of the head and extremities is only achieved after relative shell proportions increase. Structural alterations that facilitate the box turtle's transformation are probably prepatterned in embryos but require function-induced changes to differentiate in juveniles. This mode of delayed trait differentiation is essential to phenotypic diversification in turtles and perhaps other tetrapods.

Sesamoids in tetrapods: the origin of new skeletal morphologies

Along with supernumerary bones, sesamoids, defined as any organized intratendinous/intraligamentous structure, including those composed of fibrocartilage, adjacent to an articulation or joint, have been frequently considered as enigmatic structures associated with the joints of the skeletal system of vertebrates. This review allows us to propose a dynamic model to account for part of skeletal phenotypic diversity: during evolution, sesamoids can become displaced, attaching to and detaching from the long bone epiphyses and diaphysis. Epiphyses, apophyses and detached sesamoids are able to transform into each other, contributing to the phenotypic variability of the tetrapod skeleton. This dynamic model is a new paradigm to delineate the contribution of sesamoids to skeletal diversity. Herein, we first present a historical approach to the study of sesamoids, discussing the genetic versus epigenetic theories of their genesis and growth. Second, we construct a dynamic model. Third, we present a summary of literature on sesamoids of the main groups of tetrapods, including veterinary and human clinical contributions, which are the best-studied aspects of sesamoids in recent decades. Finally, we discuss the identity of certain structures that have been labelled as sesamoids despite insufficient formal testing of homology. We also propose a new definition to help the identification of sesamoids in general. This review is particularly timely, given the recent increasing interest and research activity into the developmental biology and mechanics of sesamoids. With this updated and integrative discussion, we hope to pave the way to improve the understanding of sesamoid biology and evolution.

Developmental Bias and Evolution: A Regulatory Network Perspective

Phenotypic variation is generated by the processes of development, with some variants arising more readily than others-a phenomenon known as "developmental bias." Developmental bias and natural selection have often been portrayed as alternative explanations, but this is a false dichotomy: developmental bias can evolve through natural selection, and bias and selection jointly influence phenotypic evolution. Here, we briefly review the evidence for developmental bias and illustrate how it is studied empirically. We describe recent theory on regulatory networks that explains why the influence of genetic and environmental perturbation on phenotypes is typically not uniform, and may even be biased toward adaptive phenotypic variation. We show how bias produced by developmental processes constitutes an evolving property able to impose direction on adaptive evolution and influence patterns of taxonomic and phenotypic diversity. Taking these considerations together, we argue that it is not sufficient to accommodate developmental bias into evolutionary theory merely as a constraint on evolutionary adaptation. The influence of natural selection in shaping developmental bias, and conversely, the influence of developmental bias in shaping subsequent opportunities for adaptation, requires mechanistic models of development to be expanded and incorporated into evolutionary theory. A regulatory network perspective on phenotypic evolution thus helps to integrate the generation of phenotypic variation with natural selection, leaving evolutionary biology better placed to explain how organisms adapt and diversify.

Unmodern Synthesis: Developmental Hierarchies and the Origin of Phenotypes

The question of whether the modern evolutionary synthesis requires an extension has recently become a topic of discussion, and a source of controversy. We suggest that this debate is, for the most part, not about the modern synthesis at all. Rather, it is about the extent to which genetic mechanisms can be regarded as the primary determinants of phenotypic characters. The modern synthesis has been associated with the idea that phenotypes are the result of gene products, while supporters of the extended synthesis have suggested that environmental factors, along with processes such as epigenetic inheritance, and niche construction play an important role in character formation. We argue that the methodology of the modern evolutionary synthesis has been enormously successful, but does not provide an accurate characterization of the origin of phenotypes. For its part, the extended synthesis has yet to be transformed into a testable theory, and accordingly, has yielded few results. We conclude by suggesting that the origin of phenotypes can only be understood by integrating findings from all levels of the organismal hierarchy. In most cases, parts and processes from a single level fail to accurately explain the presence of a given phenotypic trait.

On the Presence of the Patella in Frogs

The patella is one of the most studied sesamoids. Historically, the patella is described as a big sesamoid embedded in the tendon of the quadriceps femoris muscle. This sesamoid is studied from developmental, functional, clinical, and anatomical perspectives. The presence of a patella is reported in squamatans, birds, and mammals. Lissamphibians are identified as the major lineage that fail to develop a patella. However, this sesamoid is reported at least once in anurans, but without detailed anatomical discussions. Through anatomical and histological studies we examined the topography and tissue composition of two structures that we identify as the proximal and distal patellae in several anuran species. We explored the evolution of these sesamoids through ancestral state reconstruction, finding that they are ancestral for amphibians and possibly tetrapods as a whole. The presence of these patellae in anurans would roll back their origin to the last common ancestor of tetrapods. From a functional perspective, the overwhelming evidence of fibrocartilage as a clear response to compression suggests that the fibrocartilaginous patellae could also withstand the mechanical stress generated on the knee undergoing compression during limb extension. Anat Rec, 2017. © 2017 Wiley Periodicals, Inc. Anat Rec, 300:1747-1755, 2017. © 2017 Wiley Periodicals, Inc.

Cognition, Information Fields and Hologenomic Entanglement: Evolution in Light and Shadow

As the prime unification of Darwinism and genetics, the Modern Synthesis continues to epitomize mainstay evolutionary theory. Many decades after its formulation, its anchor assumptions remain fixed: conflict between macro organic organisms and selection at that level represent the near totality of any evolutionary narrative. However, intervening research has revealed a less easily appraised cellular and microbial focus for eukaryotic existence. It is now established that all multicellular eukaryotic organisms are holobionts representing complex collaborations between the co-aligned microbiome of each eukaryote and its innate cells into extensive mixed cellular ecologies. Each of these ecological constituents has demonstrated faculties consistent with basal cognition. Consequently, an alternative hologenomic entanglement model is proposed with cognition at its center and conceptualized as Pervasive Information Fields within a quantum framework. Evolutionary development can then be reconsidered as being continuously based upon communication between self-referential constituencies reiterated at every scope and scale. Immunological reactions support and reinforce self-recognition juxtaposed against external environmental stresses.

Phenotypic Novelty in EvoDevo: The Distinction Between Continuous and Discontinuous Variation and Its Importance in Evolutionary Theory

The introduction of novel phenotypic structures is one of the most significant aspects of organismal evolution. Yet the concept of evolutionary novelty is used with drastically different connotations in various fields of research, and debate exists about whether novelties represent features that are distinct from standard forms of phenotypic variation. This article contrasts four separate uses for novelty in genetics, population genetics, morphology, and behavioral science, before establishing how novelties are used in evolutionary developmental biology (EvoDevo). In particular, it is detailed how an EvoDevo-specific research approach to novelty produces insight distinct from other fields, gives the concept explanatory power with predictive capacities, and brings new consequences to evolutionary theory. This includes the outlining of research strategies that draw attention to productive areas of inquiry, such as threshold dynamics in development. It is argued that an EvoDevo-based approach to novelty is inherently mechanistic, treats the phenotype as an agent with generative potential, and prompts a distinction between continuous and discontinuous variation in evolutionary theory.

Stochastic developmental variation, an epigenetic source of phenotypic diversity with far-reaching biological consequences

This article reviews the production of different phenotypes from the same genotype in the same environment by stochastic cellular events, nonlinear mechanisms during patterning and morphogenesis, and probabilistic self-reinforcing circuitries in the adult life. These aspects of phenotypic variation are summarized under the term 'stochastic developmental variation' (SDV) in the following. In the past, SDV has been viewed primarily as a nuisance, impairing laboratory experiments, pharmaceutical testing, and true-to-type breeding. This article also emphasizes the positive biological effects of SDV and discusses implications for genotype-to-phenotype mapping, biological individuation, ecology, evolution, and applied biology. There is strong evidence from experiments with genetically identical organisms performed in narrowly standardized laboratory set-ups that SDV is a source of phenotypic variation in its own right aside from genetic variation and environmental variation. It is obviously mediated by molecular and higher-order epigenetic mechanisms. Comparison of SDV in animals, plants, fungi, protists, bacteria, archaeans, and viruses suggests that it is a ubiquitous and phylogenetically old phenomenon. In animals, it is usually smallest for morphometric traits and highest for life history traits and behaviour. SDV is thought to contribute to phenotypic diversity in all populations but is particularly relevant for asexually reproducing and genetically impoverished populations, where it generates individuality despite genetic uniformity. In each generation, SDV produces a range of phenotypes around a well-adapted target phenotype, which is interpreted as a bet-hedging strategy to cope with the unpredictability of dynamic environments. At least some manifestations of SDV are heritable, adaptable, selectable, and evolvable, and therefore, SDV may be seen as a hitherto overlooked evolution factor. SDV is also relevant for husbandry, agriculture, and medicine because most pathogens are asexuals that exploit this third source of phenotypic variation to modify infectivity and resistance to antibiotics. Since SDV affects all types of organisms and almost all aspects of life, it urgently requires more intense research and a better integration into biological thinking.

Mind the gap: genetic manipulation of basicranial growth within synchondroses modulates calvarial and facial shape in mice through epigenetic interactions

Phenotypic integration patterns in the mammalian skull have long been a focus of intense interest as a result of their suspected influence on the trajectory of hominid evolution. Here we test the hypothesis that perturbation of cartilage growth, which directly affects only the chondrocranium during development, will produce coordinated shape changes in the adult calvarium and face regardless of mechanism. Using two murine models of cartilage undergrowth that target two very different mechanisms, we show that strong reduction in cartilage growth produces a short, wide, and more flexed cranial base. This in turn produces a short, wide face in both models. Cranial base and face are already correlated early in ontogeny, and the relationship between these modules gains structure through postnatal growth and development. These results provide further evidence that there exist physical interactions between developing parts of the phenotype that produce variation at a distance from the actual locus upon which a particular selective pressure is acting. Phenotypic changes observed over the course of evolution may not all require adaptationist explanations; rather, it is likely that a substantial portion of observed phenotypic variation over the history of a clade is not directly adaptive but rather a secondary consequence of some local response to selection.

The developmental origin of zygodactyl feet and its possible loss in the evolution of Passeriformes

The zygodactyl orientation of toes (digits II and III pointing forwards, digits I and IV pointing backwards) evolved independently in different extant bird taxa. To understand the origin of this trait in modern birds, we investigated the development of the zygodactyl foot of the budgerigar (Psittaciformes). We compared its muscular development with that of the anisodactyl quail (Galliformes) and show that while the musculus abductor digiti IV (ABDIV) becomes strongly developed at HH36 in both species, the musculus extensor brevis digiti IV (EBDIV) degenerates and almost disappears only in the budgerigar. The asymmetric action of those muscles early in the development of the budgerigar foot causes retroversion of digit IV (dIV). Paralysed budgerigar embryos do not revert dIV and are anisodactyl. Both molecular phylogenetic analysis and palaeontological information suggest that the ancestor of passerines could have been zygodactyl. We followed the development of the zebra finch (Passeriformes) foot muscles and found that in this species, both the primordia of the ABDIV and of the EBDIV fail to develop. These data suggest that loss of asymmetric forces of muscular activity exerted on dIV, caused by the absence of the ABDIV, could have resulted in secondary anisodactyly in Passeriformes.

Epigenetic resolution of the 'curse of complexity' in adaptive evolution of complex traits

The age of most genes exceeds the longevity of their genomic and physiological associations by many orders of magnitude. Such transient contexts modulate the expression of ancient genes to produce currently appropriate and often highly distinct developmental and functional outcomes. The efficacy of such adaptive modulation is diminished by the high dimensionality of complex organisms and associated vast areas of neutrality in their genotypic and developmental networks (and, thus, weak natural selection). Here I explore whether epigenetic effects facilitate adaptive modulation of complex phenotypes by effectively reducing the dimensionality of their deterministic networks and thus delineating their developmental and evolutionary trajectories even under weak selection. Epigenetic effects that link unconnected or widely dispersed elements of genotype space in ecologically relevant time could account for the rapid appearance of functionally integrated adaptive modifications. On an organismal time scale, conceptually similar processes occur during recurrent epigenetic reprogramming of somatic stem cells to produce, recurrently and reversibly, a bewildering array of differentiated and persistent cell lineages, all sharing identical genomic sequences despite strongly distinct phenotypes. I discuss whether close dependency of onset, scope and duration of epigenetic effects on cellular and genomic context in stem cells could provide insights into contingent modulation of conserved genomic material on a much longer evolutionary time scale. I review potential empirical examples of epigenetic bridges that reduce phenotype dimensionality and accomplish rapid adaptive modulation in the evolution of novelties, expression of behavioural types, and stress-induced ossification schedules.

Systems biology and the integration of mechanistic explanation and mathematical explanation

The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models-which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation (as the analysis of a whole in terms of its structural parts and their qualitative interactions) have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena (rather than the explanation of quantitative details), where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism's ability to respond to perturbations (beyond its actual operation). I offer general conclusions for philosophical accounts of explanation.

Macroevolutionary diversity of amniote limb proportions predicted by developmental interactions

Mammals, birds, and reptiles exhibit a remarkable diversity of limb proportions. These evolved differences are thought to reflect selection for biomechanical, postural, and locomotor requirements primarily acting on independent variation in later fetal and postnatal segmental growth. However, earlier conserved developmental events also have the potential to impact the evolvability of limb proportions by limiting or biasing initial variation among segments. Notably, proximo-distal patterning of the amniote limb through activation-inhibition dynamics predicts that initial proportions of segments should exhibit both tradeoffs between stylopod and autopod and a diagnostic reduction in variance of the zeugopod. Here it is demonstrated that this developmental "design rule" predicts patterns of macroevolutionary diversity despite the effects of variation in segmental growth over ontogeny, lineage-specific differences in phylogenetic history, or functional adaptation. These results provide critical comparative evidence of a conserved Turing-like mechanism in proximo-distal limb segmentation, and suggest that development has played a previously unrecognized role in the evolvability of limb proportions in a wide range of amniote taxa.

Algorithmic requirements for swarm intelligence in differently coupled collective systems

Swarm systems are based on intermediate connectivity between individuals and dynamic neighborhoods. In natural swarms self-organizing principles bring their agents to that favorable level of connectivity. They serve as interesting sources of inspiration for control algorithms in swarm robotics on the one hand, and in modular robotics on the other hand. In this paper we demonstrate and compare a set of bio-inspired algorithms that are used to control the collective behavior of swarms and modular systems: BEECLUST, AHHS (hormone controllers), FGRN (fractal genetic regulatory networks), and VE (virtual embryogenesis). We demonstrate how such bio-inspired control paradigms bring their host systems to a level of intermediate connectivity, what delivers sufficient robustness to these systems for collective decentralized control. In parallel, these algorithms allow sufficient volatility of shared information within these systems to help preventing local optima and deadlock situations, this way keeping those systems flexible and adaptive in dynamic non-deterministic environments.

Comparative pelvic development of the axolotl (Ambystoma mexicanum) and the Australian lungfish (Neoceratodus forsteri): conservation and innovation across the fish-tetrapod transition

Background

The fish-tetrapod transition was one of the major events in vertebrate evolution and was enabled by many morphological changes. Although the transformation of paired fish fins into tetrapod limbs has been a major topic of study in recent years, both from paleontological and comparative developmental perspectives, the interest has focused almost exclusively on the distal part of the appendage and in particular the origin of digits. Relatively little attention has been paid to the transformation of the pelvic girdle from a small unipartite structure to a large tripartite weight-bearing structure, allowing tetrapods to rely mostly on their hindlimbs for locomotion. In order to understand how the ischium and the ilium evolved and how the acetabulum was reoriented during this transition, growth series of the Australian lungfish Neoceratodus forsteri and the Mexican axolotl Ambystoma mexicanum were cleared and stained for cartilage and bone and immunostained for skeletal muscles. In order to understand the myological developmental data, hypotheses about the homologies of pelvic muscles in adults of Latimeria, Neoceratodus and Necturus were formulated based on descriptions from the literature of the coelacanth (Latimeria), the Australian Lungfish (Neoceratodus) and a salamander (Necturus).

Results

In the axolotl and the lungfish, the chondrification of the pelvic girdle starts at the acetabula and progresses anteriorly in the lungfish and anteriorly and posteriorly in the salamander. The ilium develops by extending dorsally to meet and connect to the sacral rib in the axolotl. Homologous muscles develop in the same order with the hypaxial musculature developing first, followed by the deep, then the superficial pelvic musculature.

Conclusions

Development of the pelvic endoskeleton and musculature is very similar in Neoceratodus and Ambystoma. If the acetabulum is seen as being a fixed landmark, the evolution of the ischium only required pubic pre-chondrogenic cells to migrate posteriorly. It is hypothesized that the iliac process or ridge present in most tetrapodomorph fish is the precursor to the tetrapod ilium and that its evolution mimicked its development in modern salamanders.

Mathematical modeling of vertebrate limb development

In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.

On the evolution of morphogenetic models: mechano-chemical interactions and an integrated view of cell differentiation, growth, pattern formation and morphogenesis

In the 1950s, embryology was conceptualized as four relatively independent problems: cell differentiation, growth, pattern formation and morphogenesis. The mechanisms underlying the first three traditionally have been viewed as being chemical in nature, whereas those underlying morphogenesis have usually been discussed in terms of mechanics. Often, morphogenesis and its mechanical processes have been regarded as subordinate to chemical ones. However, a growing body of evidence indicates that the biomechanics of cells and tissues affect in striking ways those phenomena often thought of as mainly under the control of cell-cell signalling. This accumulation of data has led to a revival of the mechano-transduction concept in particular, and of complexity in general, causing us now to consider whether we should retain the traditional conceptualization of development. The researchers' semantic preferences for the terms 'patterning', 'pattern formation' or 'morphogenesis' can be used to describe three main 'schools of thought' which emerged in the late 1970s. In the 'molecular school', the term patterning is deeply tied to the positional information concept. In the 'chemical school', the term 'pattern formation' regularly implies reaction-diffusion models. In the 'mechanical school', the term 'morphogenesis' is more frequently used in relation to mechanical instabilities. Major differences among these three schools pertain to the concept of self-organization, and models can be classified as morphostatic or morphodynamic. Various examples illustrate the distorted picture that arises from the distinction among differentiation, growth, pattern formation and morphogenesis, based on the idea that the underlying mechanisms are respectively chemical or mechanical. Emerging quantitative approaches integrate the concepts and methods of complex sciences and emphasize the interplay between hierarchical levels of organization via mechano-chemical interactions. They draw upon recent improvements in mathematical and numerical morphogenetic models and upon considerable progress in collecting new quantitative data. This review highlights a variety of such models, which exhibit important advances, such as hybrid, stochastic and multiscale simulations.

MicroRNA-142-3p regulates TGF-β3-mediated region-dependent chondrogenesis by regulating ADAM9

Position-dependent chondrogenesis is regulated by processes that are both common to and differ among all limb types and limb skeletal elements. Despite intrinsic differences between wing and leg bud mesenchyme, the exact regulatory molecules and mechanisms involved in these processes have not been elucidated. Here, we show the limb type-specific role of TGF-β3 during chondrogenic differentiation of chick limb mesenchymal cells. Exposure of wing cells to TGF-β3 stimulated chondrogenic differentiation, whereas in leg bud mesenchymal cells, TGF-β3 induced apoptotic cell death via G2M arrest. Consistent with a limb type-specific effect of TGF-β3 on chondrogenic differentiation, we found different levels of miR-142-3p induction. Inhibition of miR-142-3p via PNA-based antisense oligonucleotides (ASOs) markedly promoted cell migration and precartilage condensation, while exogenous induction of miR-142-3p reduced cell survival and increased cell death. Overexpression of ADAM9 significantly reduced chondrogenic differentiation via downregulation of cell migration and cell survival and upregulation of apoptotic cell death. Limb type-specific expression levels of ADAM9 induced by TGF-β3 were observed. Collectively, this study demonstrates that differential induction of miR-142-3p is involved in the limb type-specific effect of TGF-β3 on wing vs. leg mesenchymal cells through direct modulation of ADAM9 transcription.

Bare bones pattern formation: a core regulatory network in varying geometries reproduces major features of vertebrate limb development and evolution

BACKGROUND

Major unresolved questions regarding vertebrate limb development concern how the numbers of skeletal elements along the proximodistal (P-D) and anteroposterior (A-P) axes are determined and how the shape of a growing limb affects skeletal element formation. There is currently no generally accepted model for these patterning processes, but recent work on cartilage development (chondrogenesis) indicates that precartilage tissue self-organizes into nodular patterns by cell-molecular circuitry with local auto-activating and lateral inhibitory (LALI) properties. This process is played out in the developing limb in the context of a gradient of fibroblast growth factor (FGF) emanating from the apical ectodermal ridge (AER).

RESULTS

We have simulated the behavior of the core chondrogenic mechanism of the developing limb in the presence of an FGF gradient using a novel computational environment that permits simulation of LALI systems in domains of varying shape and size. The model predicts the normal proximodistal pattern of skeletogenesis as well as distal truncations resulting from AER removal. Modifications of the model's parameters corresponding to plausible effects of Hox proteins and formins, and of the reshaping of the model limb, bud yielded simulated phenotypes resembling mutational and experimental variants of the limb. Hypothetical developmental scenarios reproduce skeletal morphologies with features of fossil limbs.

CONCLUSIONS

The limb chondrogenic regulatory system operating in the presence of a gradient has an inherent, robust propensity to form limb-like skeletal structures. The bare bones framework can accommodate ancillary gene regulatory networks controlling limb bud shaping and establishment of Hox expression domains. This mechanism accounts for major features of the normal limb pattern and, under variant geometries and different parameter values, those of experimentally manipulated, genetically aberrant and evolutionary early forms, with no requirement for an independent system of positional information.

Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays

Turing's pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing's model has received limited attention. Here, we novelly focus on the Gierer-Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing's mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99-130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing's model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing's mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing's mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning.

Looking at the origin of phenotypic variation from pattern formation gene networks

This article critically reviews some widespread views about the overall functioning of development. Special attention is devoted to views in developmental genetics about the superstructure of developmental gene networks. According to these views gene networks are hierarchic and multilayered. The highest layers partition the embryo in large coarse areas and control downstream genes that subsequently subdivide the embryo into smaller and smaller areas. These views are criticized on the bases of developmental and evolutionary arguments. First, these views, although detailed at the level of gene identities, do not incorporate morphogenetic mechanisms nor do they try to explain how morphology changes during development. Often, they assume that morphogenetic mechanisms are subordinate to cell signaling events. This is in contradiction to the evidence reviewed herein. Experimental evidence on pattern formation also contradicts the view that developmental gene networks are hierarchically multilayered and that their functioning is decodable from promoter analysis. Simple evolutionary arguments suggest that, indeed, developmental gene networks tend to be non-hierarchic. Re-use leads to extensive modularity in gene networks while developmental drift blurs this modularity. Evolutionary opportunism makes developmental gene networks very dependent on epigenetic factors.

Limb bud and flank mesoderm have distinct "physical phenotypes" that may contribute to limb budding

Limb bud outgrowth in chicken embryos is initiated during the third day of development by Fibroblast Growth Factor 8 (FGF8) produced by the newly formed apical ectodermal ridge (AER). One of the earliest effects of this induction is a change in the properties of the limb field mesoderm leading to bulging of the limb buds from the body wall. Heintzelman et al. [Heintzelman, K.F., Phillips, H.M., Davis, G.S., 1978. Liquid-tissue behavior and differential cohesiveness during chick limb budding. J. Embryol. Exp. Morphol. 47, 1-15.] suggested that budding of the limbs is caused by a higher liquid-like cohesivity of limb bud tissue compared with flank. We sought additional evidence relevant to this hypothesis by performing direct measurements of the effective surface tension, a measure of relative tissue cohesivity, of 4-day embryonic chicken wing and leg bud mesenchymal tissue, and adjacent flank mesoderm. As predicted, the two types of limb tissues were 1.5- to 2-fold more cohesive than the flank tissue. These differences paralleled cell number and volume density differences: 4-day limb buds had 2- to 2.5-fold as many cells per unit area of tissue as surrounding flank, a difference also seen at 3 days, when limb budding begins. Exposure of flank tissue to exogenous FGF8 for 24 h increased its cell number and raised its cohesivity to limb-like values. Four-day flank tissue exhibited a novel and unique active rebound response to compression, which was suppressed by the drug latrunculin and therefore dependent on an intact actin cytoskeleton. Correspondingly, flank at this stage expressed high levels of alpha-smooth muscle actin (SMA) mRNA and protein and a dense network of microfilaments. Treatment of flank with FGF8 eliminated the rebound response. We term material properties of tissues, such as cohesivity and mechanical excitability, the "physical phenotype", and propose that changes thereof are driving forces of morphogenesis. Our results indicate that two independent aspects of the physical phenotype of flank mesoderm can be converted to a limb-like state in response to treatment with FGF8. The higher tissue cohesivity induced by this effect will cause the incipient limb bud to phase separate from the surrounding flank, while the active mechanical response of the flank could help ensure that the limb bud bulges out from, rather than becoming engulfed by, this less cohesive tissue.

Activator-inhibitor dynamics of vertebrate limb pattern formation

The development of the vertebrate limb depends on an interplay of cellular differentiation, pattern formation, and tissue morphogenesis on multiple spatial and temporal scales. While numerous gene products have been described that participate in, and influence, the generation of the limb skeletal pattern, an understanding of the most salient feature of the developing limb--its quasiperiodic arrangement of bones, requires additional organizational principles. We review several such principles, drawing on concepts of physics and chemical dynamics along with molecular genetics and cell biology. First, a "core mechanism" for precartilage mesenchymal condensation is described, based on positive autoregulation of the morphogen transforming growth factor (TGF)-beta, induction of the extracellular matrix (ECM) protein fibronectin, and focal accumulation of cells via haptotaxis. This core mechanism is shown to be part of a local autoactivation-lateral inhibition (LALI) system that ensures that the condensations will be regularly spaced. Next, a "bare-bones" model for limb development is described in which the LALI-core mechanism is placed in a growing geometric framework with predifferentiated "apical," differentiating "active," and irreversibly differentiated "frozen" zones defined by distance from an apical source of a fibroblast growth factor (FGF)-type morphogen. This model is shown to account for classic features of the developing limb, including the proximodistal (PD) emergence over time of increasing numbers of bones. We review earlier and recent work suggesting that the inhibitory component of the LALI system for condensation may not be a diffusible morphogen, and propose an alternative mechanism for lateral inhibition, based on synchronization of oscillations of a Hes mediator of the Notch signaling pathway. Finally, we discuss how viewing development as an interplay between molecular-genetic and dynamic physical processes can provide new insight into the origin of congenital anomalies.

Multiscale models for vertebrate limb development

Dynamical systems in which geometrically extended model cells produce and interact with diffusible (morphogen) and nondiffusible (extracellular matrix) chemical fields have proved very useful as models for developmental processes. The embryonic vertebrate limb is an apt system for such mathematical and computational modeling since it has been the subject of hundreds of experimental studies, and its normal and variant morphologies and spatiotemporal organization of expressed genes are well known. Because of its stereotypical proximodistally generated increase in the number of parallel skeletal elements, the limb lends itself to being modeled by Turing-type systems which are capable of producing periodic, or quasiperiodic, arrangements of spot- and stripe-like elements. This chapter describes several such models, including, (i) a system of partial differential equations in which changing cell density enters into the dynamics explicitly, (ii) a model for morphogen dynamics alone, derived from the latter system in the "morphostatic limit" where cell movement relaxes on a much slower time-scale than cell differentiation, (iii) a discrete stochastic model for the simplified pattern formation that occurs when limb cells are placed in planar culture, and (iv) several hybrid models in which continuum morphogen systems interact with cells represented as energy-minimizing mesoscopic entities. Progress in devising computational methods for handling 3D, multiscale, multimodel simulations of organogenesis is discussed, as well as for simulating reaction-diffusion dynamics in domains of irregular shape.

Postnatal bone elongation of the manus versus pes: analysis of the chondrocytic differentiation cascade in Mus musculus and Eptesicus fuscus

Bones elongate postnatally by endochondral ossification as cells of the cartilaginous growth plate undergo a differentiation cascade of proliferation, cellular hypertrophy and matrix synthesis. Interspecific comparisons of homologous bones elongating at different rates has been a useful approach for studying the dynamics of this process. The purpose of this study was to measure quantitative stereological parameters of growth plates of the third digit of the manus and pes of the laboratory mouse, and make comparisons to chondrocytic performance parameters in the homologous bones of the big brown bat, Eptesicus fuscus, where extremely rapid postnatal elongation of bones of the manus is associated with skeletal modifications for powered flight. Measurements were made across all zones of forelimb and hindlimb autopod growth plates by dividing each growth plate into strata of equal height (from thirteen 200-mum-high strata in the metacarpus to five 40-mum-high strata in phalangeal bones of the pes). Results indicate that all chondrocytic performance parameters known to quantitatively contribute to the elongation potential of a growth plate change together. A significant finding was that in growth plates of the chiropteran manus, final hypertrophic cell size and shape were achieved early in the zone of hypertrophy, indicating that interstitial expansion of the growth plate resulting from the incremental chondrocytic height increase in the direction of elongation was completed soon after the transition from the cessation of proliferation to the initiation of hypertrophy. This is unlike what has been reported in most mammalian growth plates previously analyzed, but is the situation in the proximal tibial growth plate of rapidly growing frogs and precocial birds. This suggests that a similar adaptation for stabilization of a rapidly elongating bone has evolved independently in three widely separated groups that have in common rapid growth in limbs to be used for early active, powered locomotion.

Patterns of mesenchymal condensation in a multiscale, discrete stochastic model

Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced “islands” of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of “cell condensations,” in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction–diffusion process and cell-matrix adhesion (haptotaxis) as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales), and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development.

The development of an organism from embryo to adult includes processes of pattern formation that involve the interactions over space and time of independent cells to form multicellular structures. Computational models permit exploration of possible alternative mechanisms that reproduce biological patterns and thereby provide hypotheses for empirical testing. In this article, we describe a biologically motivated discrete stochastic model that shows that the patterns of spots and stripes of tightly packed cells observed in cultures derived from the embryonic vertebrate limb can occur by a mechanism that uses only cell–cell signaling via diffusible molecules (morphogens) and cell substratum adhesion (haptotaxis). Moreover, similar-looking patterns can arise both from stable stationary dynamics and unstable transient dynamics of the same underlying core molecular–genetic mechanism. Simulations also show that spot and stripe patterns (which also correspond to the nodules and bars of the developing limb skeleton in vivo) are close in parameter space and can be generated in multiple ways with single-parameter variations. An important implication is that some developmental processes do not require a strict progression from one stable dynamic regime to another, but can occur by a succession of transient dynamic regimes tuned (e.g., by natural selection) to achieve a particular morphological outcome.

On the origins of morphological disparity and its diverse developmental bases

It has been repeatedly claimed that morphological novelties are an unresolved problem in evolutionary theory. Several definitions of novelty exist but most emphasize that novelties imply qualitative changes on the phenotype and not the quantitative gradual changes favored in the neo-Darwinian approach to evolutionary theory. This article discusses how the concept of novelty is used to describe aspects of morphological evolution that are not satisfactorily explained under the modern synthesis. In this article, it is suggested that there is a repertoire of morphological changes rather than two discrete qualitatively different types of morphological change. How these different types of morphological changes can be understood from the diversity of developmental mechanisms existing in animal development is explored. Specifically, it is proposed that animal morphology and its variation can be understood from the spatial patterns produced by a set of basic developmental mechanisms and their combination. Some specific examples of these kinds of morphologic changes are explained.