Dynamics of skeletal pattern formation in developing chick limb

"The Logic of Monsters:" Pere Alberch and the Evolutionary Significance of Experimental Teratology

This paper offers an historical introduction to Pere Alberch's evolutionary thought and his contributions to Evo-Devo, based on his unique approach to experimental teratology. We will take as our point of reference the teratogenic experiments developed by Alberch and Emily A. Gale during the 1980s, aimed at producing monstrous variants of frogs and salamanders. We will analyze his interpretation of the results of these experiments within the framework of the emergence of evolutionary developmental biology (or "Evo-Devo"). The aim is understand how Alberch interpreted teratological anomalies as highly revealing objects of study for understanding the development of organic form, not only in an ontogenetic sense-throughout embryonic development-but also phylogenetically-throughout the evolution of species. Alberch's interpretation of monsters reflects the influence of a long tradition of non-Darwinian evolutionary thought, which began in the nineteenth century and was continued in the twentieth century by people such as Richard Goldschmidt, Conrad H. Waddington, and Stephen Jay Gould. They all proposed various non-gradualist models of evolution, in which embryonic development played a central role. Following this tradition, Alberch argued that, in order to attain a correct understanding of the role of embryological development in evolution, it was necessary to renounce the gradualist paradigm associated with the Darwinian interpretation of evolution, which understood nature as a continuum. According to Alberch, the study of monstrous abnormalities was of great value in understanding how certain epigenetic restrictions in development could give rise to discontinuities and directionality in morphological transformations throughout evolution.

Periodic pattern formation during embryonic development

During embryonic development many organs and structures require the formation of series of repeating elements known as periodic patterns. Ranging from the digits of the limb to the feathers of the avian skin, the correct formation of these embryonic patterns is essential for the future form and function of these tissues. However, the mechanisms that produce these patterns are not fully understood due to the existence of several modes of pattern generation which often differ between organs and species. Here, we review the current state of the field and provide a perspective on future approaches to studying this fundamental process of embryonic development.

Spiking at the edge: Excitability at interfaces in reaction-diffusion systems

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator-prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction-diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media.

Perspectives on Principles of Cellular Behavior from the Biophysics of Protists

Cells are the fundamental unit of biological organization. Although it may be easy to think of them as little more than the simple building blocks of complex organisms such as animals, single cells are capable of behaviors of remarkable apparent sophistication. This is abundantly clear when considering the diversity of form and function among the microbial eukaryotes, the protists. How might we navigate this diversity in the search for general principles of cellular behavior? Here, we review cases in which the intensive study of protists from the perspective of cellular biophysics has driven insight into broad biological questions of morphogenesis, navigation and motility, and decision making. We argue that applying such approaches to questions of evolutionary cell biology presents rich, emerging opportunities. Integrating and expanding biophysical studies across protist diversity, exploiting the unique characteristics of each organism, will enrich our understanding of general underlying principles.

The role of timing in the development and evolution of the limb

The term heterochrony was coined to describe changes in the timing of developmental processes relative to an ancestral state. Limb development is a well-suited system to address the contribution of heterochrony to morphological evolution. We illustrate how timing mechanisms have been used to establish the correct pattern of the limb and provide cases where natural variations in timing have led to changes in limb morphology.

Patterning, From Conifers to Consciousness: Turing's Theory and Order From Fluctuations

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.

Mechanical feedback defines organizing centers to drive digit emergence

During embryonic development, digits gradually emerge in a periodic pattern. Although genetic evidence indicates that digit formation results from a self-organizing process, the underlying mechanisms are still unclear. Here, we find that convergent-extension tissue flows driven by active stresses underlie digit formation. These active stresses simultaneously shape cartilage condensations and lead to the emergence of a compressive stress region that promotes high activin/p-SMAD/SOX9 expression, thereby defining digit-organizing centers via a mechanical feedback. In Wnt5a mutants, such mechanical feedback is disrupted due to the loss of active stresses, organizing centers do not emerge, and digit formation is precluded. Thus, digit emergence does not result solely from molecular interactions, as was previously thought, but requires a mechanical feedback that ensures continuous coupling between phalanx specification and elongation. Our work, which links mechanical and molecular signals, provides a mechanistic context for the emergence of organizing centers that may underlie various developmental processes.

Spatial waves and temporal oscillations in vertebrate limb development

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.

A reflux-and-growth mechanism explains oscillatory patterning of lateral root branching sites

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.

A review of regulated self-organizing approaches for tissue regeneration

Tissue and organ regeneration is the dynamic process by which a population of cells rearranges into a specific form with specific functions. Traditional tissue regeneration utilizes tissue grafting, cell implantation, and structured scaffolds to achieve clinical efficacy. However, tissue grafting methods face a shortage of donor tissue, while cell implantation may involve leakage of the implanted cells without a supportive 3D matrix. Cell migration, proliferation, and differentiation in structured scaffolds may disorganize and frustrate the artificially pre-designed structures, and sometimes involve immunogenic reactions. To overcome this limitation, the self-organizing properties and innate regenerative capability of tissue/organism formation in the absence of guidance by structured scaffolds has been investigated. This review emphasizes the growing subfield of the regulated self-organizing approach for neotissue formation and describes advances in the subfield using diverse, cutting-edge, inter-disciplinarity technologies. We cohesively summarize the directed self-organization of cells in the micro-engineered cell-ECM system and 3D/4D cell printing. Mathematical modeling of cellular self-organization is also discussed for providing rational guidance to intractable problems in tissue regeneration. It is envisioned that future self-organization approaches integrating biomathematics, micro-nano engineering, and gene circuits developed from synthetic biology will continue to work in concert with self-organizing morphogenesis to enhance rational control during self-organizing in tissue and organ regeneration.

Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns

The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation. In this paper, we found that the meshwork pattern is formed by four kinds of stalk behaviours: stalk extension, tip bifurcation, side branching and tip fusion. The Turing-type pattern underlying the meshwork pattern is a Turing spot pattern, which indicates that the Turing instability of the spot pattern promotes activator peak formation and then guides the formation of meshwork patterns. Then, we found that the Turing wavelength decreased in turn from tip bifurcation to side branching to tip fusion via statistical evaluation. Through the functional relationship between the Turing wavelength and model parameters ([Formula: see text] and [Formula: see text]), we found that parameters [Formula: see text] and [Formula: see text] had monotonic effects on the Turing wavelength and that parameter [Formula: see text] had nonmonotonic effects. Furthermore, we performed simulations of local meshwork pattern formation under variable model parameter values. The simulation results verified the corresponding relationship between the Turing wavelength and stalk behaviours and the functional relationship between the Turing wavelength and model parameters. The simulation results showed that the Turing wavelength regulated the meshwork pattern and that the small Turing wavelength facilitated dense meshwork pattern formation. Our work provides novel insight into and understanding of the formation of meshwork patterns. We believe that studies associated with network morphogenesis can benefit from our work.

On the evolution and development of morphological complexity: A view from gene regulatory networks

How does morphological complexity evolve? This study suggests that the likelihood of mutations increasing phenotypic complexity becomes smaller when the phenotype itself is complex. In addition, the complexity of the genotype-phenotype map (GPM) also increases with the phenotypic complexity. We show that complex GPMs and the above mutational asymmetry are inevitable consequences of how genes need to be wired in order to build complex and robust phenotypes during development. We randomly wired genes and cell behaviors into networks in EmbryoMaker. EmbryoMaker is a mathematical model of development that can simulate any gene network, all animal cell behaviors (division, adhesion, apoptosis, etc.), cell signaling, cell and tissues biophysics, and the regulation of those behaviors by gene products. Through EmbryoMaker we simulated how each random network regulates development and the resulting morphology (i.e. a specific distribution of cells and gene expression in 3D). This way we obtained a zoo of possible 3D morphologies. Real gene networks are not random, but a random search allows a relatively unbiased exploration of what is needed to develop complex robust morphologies. Compared to the networks leading to simple morphologies, the networks leading to complex morphologies have the following in common: 1) They are rarer; 2) They need to be finely tuned; 3) Mutations in them tend to decrease morphological complexity; 4) They are less robust to noise; and 5) They have more complex GPMs. These results imply that, when complexity evolves, it does so at a progressively decreasing rate over generations. This is because as morphological complexity increases, the likelihood of mutations increasing complexity decreases, morphologies become less robust to noise, and the GPM becomes more complex. We find some properties in common, but also some important differences, with non-developmental GPM models (e.g. RNA, protein and gene networks in single cells).

Establishing the pattern of the vertebrate limb

The vertebrate limb continues to serve as an influential model of growth, morphogenesis and pattern formation. With this Review, we aim to give an up-to-date picture of how a population of undifferentiated cells develops into the complex pattern of the limb. Focussing largely on mouse and chick studies, we concentrate on the positioning of the limbs, the formation of the limb bud, the establishment of the principal limb axes, the specification of pattern, the integration of pattern formation with growth and the determination of digit number. We also discuss the important, but little understood, topic of how gene expression is interpreted into morphology.

Designer Hydrogel with Intelligently Switchable Stem-Cell Contact for Incubating Cartilaginous Microtissues

Stem-cell-derived organoid can resemble in vivo tissue counterpart and mimic at least one function of tissue or organ, possessing great potential for biomedical application. The present study develops a hydrogel with cell-responsive switch to guide spontaneous and sequential proliferation and aggregation of adipose-derived stem cells (ASCs) without inputting artificial stimulus for in vitro constructing cartilaginous microtissues with enhanced retention of cell-matrix and cell-cell interactions. Polylactic acid (PLA) rods are surface-aminolyzed by cystamine, followed by being involved in the amidation of poly(( l-glutamic acid) and adipic acid dihydrazide (ADH) to form a hydrogel. Along with tubular pore formation in hydrogel after dissolution of PLA rods, aminolyzed PLA molecules with disulfide bonds on rod surfaces are covalently transferred to the tubular pore surfaces of poly(l-glutamic acid)/ADH hydrogel. Because PLA attaches cells, while poly(l-glutamic acid)/ADH hydrogel repels cells, ASCs are found to adhere and proliferate on the tubular pore surfaces of hydrogel first and then cleave disulfide bonds by secreting molecules containing thiol, thus inducing desorption of PLA molecules and leading to their spontaneous detachment and aggregation. Associated with chondrogenic induction by TGF-β1 and IGF-1 in vitro for 28 days, the hydrogel as an all-in-one incubator produces well-engineered columnar cartilage microtissues from ASCs, with the glycosaminoglycans (GAGs) and collagen type II (COL II) deposition achieving 64 and 69% of those in chondrocytes pellet, respectively. The cartilage microtissues further matured in vivo for 8 weeks to exhibit extremely similar histological features and biomechanical performance to native hyaline cartilage. The GAGs and COL II content, as well as compressive modulus of the matured tissue show no significant difference with native cartilage. The designer hydrogel may hold a promise for long-term culture of other types of stem cells and organoids.

Size-Regulated Symmetry Breaking in Reaction-Diffusion Models of Developmental Transitions

The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organisation. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given that such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction-diffusion-driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analysing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer- or switch-like dynamics. Relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions.

Using optogenetics to tackle systems-level questions of multicellular morphogenesis

Morphogenesis of multicellular systems is governed by precise spatiotemporal regulation of biochemical reactions and mechanical forces which together with environmental conditions determine the development of complex organisms. Current efforts in the field aim at decoding the system-level principles underlying the regulation of developmental processes. Toward this goal, optogenetics, the science of regulation of protein function with light, is emerging as a powerful new tool to quantitatively perturb protein function in vivo with unprecedented precision in space and time. In this review, we provide an overview of how optogenetics is helping to address system-level questions of multicellular morphogenesis and discuss future directions.

A dot-stripe Turing model of joint patterning in the tetrapod limb

Iterative joints are a hallmark of the tetrapod limb, and their positioning is a key step during limb development. Although the molecular regulation of joint formation is well studied, it remains unclear what controls the location, number and orientation (i.e. the pattern) of joints within each digit. Here, we propose the dot-stripe mechanism for joint patterning, comprising two coupled Turing systems inspired by published gene expression patterns. Our model can explain normal joint morphology in wild-type limbs, hyperphalangy in cetacean flippers, mutant phenotypes with misoriented joints and suggests a reinterpretation of the polydactylous Ichthyosaur fins as a polygonal joint lattice. By formulating a generic dot-stripe model, describing joint patterns rather than molecular joint markers, we demonstrate that the insights from the model should apply regardless of the biological specifics of the underlying mechanism, thus providing a unifying framework to interrogate joint patterning in the tetrapod limb.

Of mice and plants: Comparative developmental systems biology

Multicellular animals and plants represent independent evolutionary experiments with complex multicellular bodyplans. Differences in their life history, a mobile versus sessile lifestyle, and predominant embryonic versus postembryonic development, have led to the evolution of highly different body plans. However, also many intriguing parallels exist. Extension of the vertebrate body axis and its segmentation into somites bears striking resemblance to plant root growth and the concomittant prepatterning of lateral root competent sites. Likewise, plant shoot phyllotaxis displays similarities with vertebrate limb and digit patterning. Additionally, both plants and animals use complex signalling systems combining systemic and local signals to fine tune and coordinate organ growth across their body. Identification of these striking examples of convergent evolution provides support for the existence of general design principles: the idea that for particular patterning demands, evolution is likely to arrive at highly similar developmental patterning mechanisms. Furthermore, focussing on these parallels may aid in identifying core mechanistic principles, often obscured by the highly complex nature of multiscale patterning processes.

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.

Self-Organization in Pattern Formation

Self-organization is pervasive in development, from symmetry breaking in the early embryo to tissue patterning and morphogenesis. For a few model systems, the underlying molecular and cellular processes are now sufficiently characterized that mathematical models can be confronted with experiments, to explore the dynamics of pattern formation. Here, we review selected systems, ranging from cyanobacteria to mammals, where different forms of cell-cell communication, acting alone or together with positional cues, drive the patterning of cell fates, highlighting the insights that even very simple models can provide as well as the challenges on the path to a predictive understanding of development.

The benefits differential equations bring to limb development

Systems biology is a large field, offering a number of advantages to a variety of biological disciplines. In limb development, differential-equation based models can provide insightful hypotheses about the gene/protein interactions and tissue differentiation events that form the core of limb development research. Differential equations are like any other communicative tool, with misuse and limitations that can come along with their advantages. Every theory should be critically analyzed to best ascertain whether they reflect the reality in biology as well they claim. Differential equation-based models have consistent features which researchers have drawn upon to aid in more realistic descriptions and hypotheses. Nine features are described that highlight these trade-offs. The advantages range from more detailed descriptions of gene interactions and their consequence and the capacity to model robustness to the incorporation of tissue size and shape. The drawbacks come with the added complication that additional genes and signaling pathways that require additional terms within the mathematical model. They also come in the translation between the mathematical terms of the model, values and matrices, to the real world of genes, proteins, and tissues that constitute limb development. A critical analysis is necessary to ensure that these models effectively expand the understanding of the origins of a diversity of limb anatomy, from evolution to teratology. This article is categorized under: Vertebrate Organogenesis > Musculoskeletal and Vascular Gene Expression and Transcriptional Hierarchies > Regulatory Mechanisms Establishment of Spatial and Temporal Patterns > Repeating Patterns and Lateral Inhibition.

An autoregulatory cell cycle timer integrates growth and specification in chick wing digit development

A fundamental question is how proliferation and growth are timed during embryogenesis. Although it has been suggested that the cell cycle could be a timer, the underlying mechanisms remain elusive. Here we describe a cell cycle timer that operates in Sonic hedgehog (Shh)-expressing polarising region cells of the chick wing bud. Our data are consistent with Shh signalling stimulating polarising region cell proliferation via Cyclin D2, and then inhibiting proliferation via a Bmp2-p27^kip1 pathway. When Shh signalling is blocked, polarising region cells over-proliferate and form an additional digit, which can be prevented by applying Bmp2 or by inhibiting D cyclin activity. In addition, Bmp2 also restores posterior digit identity in the absence of Shh signalling, thus indicating that it specifies antero-posterior (thumb to little finger) positional values. Our results reveal how an autoregulatory cell cycle timer integrates growth and specification and are widely applicable to many tissues.

Evidence against tetrapod-wide digit identities and for a limited frame shift in bird wings

In crown group tetrapods, individual digits are homologized in relation to a pentadactyl ground plan. However, testing hypotheses of digit homology is challenging because it is unclear whether digits represent distinct and conserved gene regulatory states. Here we show dramatic evolutionary dynamism in the gene expression profiles of digits, challenging the notion that five digits have conserved developmental identities across amniotes. Transcriptomics shows diversity in the patterns of gene expression differentiation of digits, although the anterior-most digit of the pentadactyl limb has a unique, conserved expression profile. Further, we identify a core set of transcription factors that are differentially expressed among the digits of amniote limbs; their spatial expression domains, however, vary between species. In light of these results, we reevaluate the frame shift hypothesis of avian wing evolution and conclude only the identity of the anterior-most digit has shifted position, suggesting a 1,3,4 digit identity in the bird wing.

Self-organization across scales: from molecules to organisms

Creating ordered structures from chaotic environments is at the core of biological processes at the subcellular, cellular and organismic level. In this perspective, we explore the physical as well as biological features of two prominent concepts driving self-organization, namely phase transition and reaction-diffusion, before closing with a discussion on open questions and future challenges associated with studying self-organizing systems.This article is part of the theme issue 'Self-organization in cell biology'.

Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Complexity: the organizing principle at the interface of biological (dis)order

The term complexity means several things to biologists.When qualifying morphological phenotype, on the one hand, it is used to signify the sheer complicatedness of living systems, especially as a result of the multicomponent aspect of biological form. On the other hand, it has been used to represent the intricate nature of the connections between constituents that make up form: a more process-based explanation. In the context of evolutionary arguments, complexity has been defined, in a quantifiable fashion, as the amount of information, an informatic template such as a sequence of nucleotides or amino acids stores about its environment. In this perspective, we begin with a brief review of the history of complexity theory. We then introduce a developmental and an evolutionary understanding of what it means for biological systems to be complex.We propose that the complexity of living systems can be understood through two interdependent structural properties: multiscalarity of interconstituent mechanisms and excitability of the biological materials. The answer to whether a system becomes more or less complex over time depends on the potential for its constituents to interact in novel ways and combinations to give rise to new structures and functions, as well as on the evolution of excitable properties that would facilitate the exploration of interconstituent organization in the context of their microenvironments and macroenvironments.

The vertebrate limb: An evolving complex of self-organizing systems

The paired appendages (fins or limbs) of jawed vertebrates contain an endoskeleton consisting of nodules, bars and, in some groups, plates of cartilage, or bone arising from replacement of cartilaginous templates. The generation of the endoskeletal elements occurs by processes involving production and diffusion of morphogens, with, variously, positive and negative feedback circuits, adhesion, and receptor dynamics with similarities to the mechanism for chemical pattern formation proposed by Alan Turing. This review presents a unified interpretation of the evolution and functioning of these mechanisms. Studies are described indicating that protocondensations, compacted mesenchymal cell aggregates that prefigure the appendicular skeleton, arise through the adhesive activity of galectin-1, a matricellular protein with skeletogenic homologs in all jawed vertebrates. In the cartilaginous and lobe-finned fishes (and to a variable extent in ray-finned fishes) it additionally cooperates with an isoform of galectin-8 to constitute a self-organizing network capable of generating arrays of preskeletal nodules, bars and plates. Further, in the tetrapods, a putative galectin-8 control module was acquired that may have enabled proximodistal increase in the number of protocondensations. In parallel to this, other self-organizing networks emerged that acted, via Bmp, Wnt, Sox9 and Runx2, as well as transforming factor-β and fibronectin, to convert protocondensations into skeletal tissues. The progressive appearance and integration of these skeletogenic networks over evolution occurred in the context of an independently evolved system of Hox protein and Shh gradients that interfaced with them to tune the spatial wavelengths and refine the identities of the resulting arrays of elements.

Evolution of antero-posterior patterning of the limb: Insights from the chick

The developing limbs of chicken embryos have served as pioneering models for understanding pattern formation for over a century. The ease with which chick wing and leg buds can be experimentally manipulated, while the embryo is still in the egg, has resulted in the discovery of important developmental organisers, and subsequently, the signals that they produce. Sonic hedgehog (Shh) is produced by mesenchyme cells of the polarizing region at the posterior margin of the limb bud and specifies positional values across the antero-posterior axis (the axis running from the thumb to the little finger). Detailed experimental embryology has revealed the fundamental parameters required to specify antero-posterior positional values in response to Shh signaling in chick wing and leg buds. In this review, the evolution of the avian wing and leg will be discussed in the broad context of tetrapod paleontology, and more specifically, ancestral theropod dinosaur paleontology. How the parameters that dictate antero-posterior patterning could have been modulated to produce the avian wing and leg digit patterns will be considered. Finally, broader speculations will be made regarding what the antero-posterior patterning of chick limbs can tell us about the evolution of other digit patterns, including those that were found in the limbs of the earliest tetrapods.

The evolutionary origin of digit patterning

The evolution of tetrapod limbs from paired fins has long been of interest to both evolutionary and developmental biologists. Several recent investigative tracks have converged to restructure hypotheses in this area. First, there is now general agreement that the limb skeleton is patterned by one or more Turing-type reaction–diffusion, or reaction–diffusion–adhesion, mechanism that involves the dynamical breaking of spatial symmetry. Second, experimental studies in finned vertebrates, such as catshark and zebrafish, have disclosed unexpected correspondence between the development of digits and the development of both the endoskeleton and the dermal skeleton of fins. Finally, detailed mathematical models in conjunction with analyses of the evolution of putative Turing system components have permitted formulation of scenarios for the stepwise evolutionary origin of patterning networks in the tetrapod limb. The confluence of experimental and biological physics approaches in conjunction with deepening understanding of the developmental genetics of paired fins and limbs has moved the field closer to understanding the fin-to-limb transition. We indicate challenges posed by still unresolved issues of novelty, homology, and the relation between cell differentiation and pattern formation.

Programmable assembly of pressure sensors using pattern-forming bacteria

Biological systems can generate microstructured materials that combine organic and inorganic components and possess diverse physical and chemical properties. However, these natural processes in materials fabrication are not readily programmable. Here, we use a synthetic-biology approach to mimic such natural processes to assemble patterned materials.. We demonstrate programmable fabrication of three-dimensional (3D) materials by printing engineered self-patterning bacteria on permeable membranes that serve as a structural scaffold. Application of gold nanoparticles to the colonies creates hybrid organic-inorganic dome structures. The dynamics of the dome structures' response to pressure is determined by their geometry (colony size, dome height and pattern), which is easily modified by varying the properties of the membrane (e.g., pore size and hydrophobicity). We generate resettable pressure sensors that process signals in response to varying pressure intensity and duration.

Inhibition of Shh signalling in the chick wing gives insights into digit patterning and evolution

In an influential model of pattern formation, a gradient of Sonic hedgehog (Shh) signalling in the chick wing bud specifies cells with three antero-posterior positional values, which give rise to three morphologically different digits by a self-organizing mechanism with Turing-like properties. However, as four of the five digits of the mouse limb are morphologically similar in terms of phalangeal pattern, it has been suggested that self-organization alone could be sufficient. Here, we show that inhibition of Shh signalling at a specific stage of chick wing development results in a pattern of four digits, three of which can have the same number of phalanges. These patterning changes are dependent on a posterior extension of the apical ectodermal ridge, and this also allows the additional digit to arise from the Shh-producing cells of the polarizing region – an ability lost in ancestral theropod dinosaurs. Our analyses reveal that, if the specification of antero-posterior positional values is curtailed, self-organization can then produce several digits with the same number of phalanges. We present a model that may give important insights into how the number of digits and phalanges has diverged during the evolution of avian and mammalian limbs.

Highlighted Article: In the chick wing, the relative timing of the specification of antero-posterior positional values and self-organising mechanisms determines digit patterning and identity.

Stability analysis in spatial modeling of cell signaling

Advances in high-resolution microscopy and other techniques have emphasized the spatio-temporal nature of information transfer through signal transduction pathways. The compartmentalization of signaling molecules and the existence of microdomains are now widely acknowledged as key features in biochemical signaling. To complement experimental observations of spatio-temporal dynamics, mathematical modeling has emerged as a powerful tool. Using modeling, one can not only recapitulate experimentally observed dynamics of signaling molecules, but also gain an understanding of the underlying mechanisms in order to generate experimentally testable predictions. Reaction-diffusion systems are commonly used to this end; however, the analysis of coupled nonlinear systems of partial differential equations, generated by considering large reaction networks is often challenging. Here, we aim to provide an introductory tutorial for the application of reaction-diffusion models to the spatio-temporal dynamics of signaling pathways. In particular, we outline the steps for stability analysis of such models, with a focus on biochemical signal transduction. WIREs Syst Biol Med 2018, 10:e1395. doi: 10.1002/wsbm.1395 This article is categorized under: Biological Mechanisms > Cell Signaling Analytical and Computational Methods > Dynamical Methods Models of Systems Properties and Processes > Mechanistic Models.

EVOLUTION AND MORPHOGENETIC RULES: THE SHAPE OF THE VERTEBRATE LIMB IN ONTOGENY AND PHYLOGENY

The notion of a "developmental constraint" has become a catchphrase for a collection of poorly defined notions about how ontogeny affects phylogeny. In this paper, we shall attempt to define this idea more precisely by examining the vertebrate limb from three viewpoints. First, theoretical models of morphogenesis suggest several generalizations about how limb geometry is laid down during development. Comparative studies and experimental manipulations of developing limbs independently confirm these generalizations, which amount to a set of "construction rules" for determining how the major features of limb architecture are established in ontogeny. Armed with these rules, we can inquire how limb morphology can be varied during evolution and suggest a more precise operational definition of "developmental constraints" on morphological evolution.

On the Formation of Digits and Joints during Limb Development

Critical steps in forming the vertebrate limb include the positioning of digits and the positioning of joints within each digit. Recent studies have proposed that the iterative series of digits is established by a Turing-like mechanism generating stripes of chondrogenic domains. However, re-examination of available data suggest that digits are actually patterned as evenly spaced spots, not stripes, which then elongate into rod-shaped digit rays by incorporating new cells at their tips. Moreover, extension of the digit rays and the patterning of the joints occur simultaneously at the distal tip, implying that an integrated model is required to fully understand these processes.

The origins, scaling and loss of tetrapod digits

Many of the great morphologists of the nineteenth century marvelled at similarities between the limbs of diverse species, and Charles Darwin noted these homologies as significant supporting evidence for descent with modification from a common ancestor. Sir Richard Owen also took great care to highlight each of the elements of the forelimb and hindlimb in a multitude of species with focused attention on the homology between the hoof of the horse and the middle digit of man. The ensuing decades brought about a convergence of palaeontology, experimental embryology and molecular biology to lend further support to the homologies of tetrapod limbs and their developmental origins. However, for all that we now understand about the conserved mechanisms of limb development and the development of gross morphological disturbances, little of what is presented in the experimental or medical literature reflects the remarkable diversity resulting from the 450 million year experiment of natural selection. An understanding of conserved and divergent limb morphologies in this new age of genomics and genome engineering promises to reveal more of the developmental potential residing in all limbs and to unravel the mechanisms of evolutionary variation in limb size and shape. In this review, we present the current state of our rapidly advancing understanding of the evolutionary origin of hands and feet and highlight what is known about the mechanisms that shape diverse limbs.This article is part of the themed issue 'Evo-devo in the genomics era, and the origins of morphological diversity'.

'Biogeneric' developmental processes: drivers of major transitions in animal evolution

Using three examples drawn from animal systems, I advance the hypothesis that major transitions in multicellular evolution often involved the constitution of new cell-based materials with unprecedented morphogenetic capabilities. I term the materials and formative processes that arise when highly evolved cells are incorporated into mesoscale matter 'biogeneric', to reflect their commonality with, and distinctiveness from, the organizational properties of non-living materials. The first transition arose by the innovation of classical cell-adhesive cadherins with transmembrane linkage to the cytoskeleton and the appearance of the morphogen Wnt, transforming some ancestral unicellular holozoans into 'liquid tissues', and thereby originating the metazoans. The second transition involved the new capabilities, within a basal metazoan population, of producing a mechanically stable basal lamina, and of planar cell polarization. This gave rise to the eumetazoans, initially diploblastic (two-layered) forms, and then with the addition of extracellular matrices promoting epithelial-mesenchymal transformation, three-layered triploblasts. The last example is the fin-to-limb transition. Here, the components of a molecular network that promoted the development of species-idiosyncratic endoskeletal elements in gnathostome ancestors are proposed to have evolved to a dynamical regime in which they constituted a Turing-type reaction-diffusion system capable of organizing the stereotypical arrays of elements of lobe-finned fish and tetrapods. The contrasting implications of the biogeneric materials-based and neo-Darwinian perspectives for understanding major evolutionary transitions are discussed.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

The fin-to-limb transition as the re-organization of a Turing pattern

A Turing mechanism implemented by BMP, SOX9 and WNT has been proposed to control mouse digit patterning. However, its generality and contribution to the morphological diversity of fins and limbs has not been explored. Here we provide evidence that the skeletal patterning of the catshark Scyliorhinus canicula pectoral fin is likely driven by a deeply conserved Bmp–Sox9–Wnt Turing network. In catshark fins, the distal nodular elements arise from a periodic spot pattern of Sox9 expression, in contrast to the stripe pattern in mouse digit patterning. However, our computer model shows that the Bmp–Sox9–Wnt network with altered spatial modulation can explain the Sox9 expression in catshark fins. Finally, experimental perturbation of Bmp or Wnt signalling in catshark embryos produces skeletal alterations which match in silico predictions. Together, our results suggest that the broad morphological diversity of the distal fin and limb elements arose from the spatial re-organization of a deeply conserved Turing mechanism.

Mouse digit patterning is controlled by a Turing network of Bmp, Sox9, and Wnt. Here, Onimaru et al. show that fin patterning in the catshark, Scyliorhinus canicula, is controlled by the same network with a different spatial organization; thus, the Turing network is deeply conserved in limb development.

Where to Go: Breaking the Symmetry in Cell Motility

Cell migration in the “correct” direction is pivotal for many biological processes. Although most work is devoted to its molecular mechanisms, the cell’s preference for one direction over others, thus overcoming intrinsic random motility, epitomizes a profound principle that underlies all complex systems: the choice of one axis, in structure or motion, from a uniform or symmetric set of options. Explaining directional motility by an external chemo-attractant gradient does not solve but only shifts the problem of causation: whence the gradient? A new study in PLOS Biology shows cell migration in a self-generated gradient, offering an opportunity to take a broader look at the old dualism of extrinsic instruction versus intrinsic symmetry-breaking in cell biology.

Directional cell motility is enabled by chemoattractant gradient and symmetry-breaking. This Primer argues that the recent observation of cells generating a gradient in a uniformly distributed nutrient reveals the multilayered nature of symmetry-breaking in cell locomotion.

Positional information and reaction-diffusion: two big ideas in developmental biology combine

One of the most fundamental questions in biology is that of biological pattern: how do the structures and shapes of organisms arise? Undoubtedly, the two most influential ideas in this area are those of Alan Turing's 'reaction-diffusion' and Lewis Wolpert's 'positional information'. Much has been written about these two concepts but some confusion still remains, in particular about the relationship between them. Here, we address this relationship and propose a scheme of three distinct ways in which these two ideas work together to shape biological form.

Orientation of Turing-like Patterns by Morphogen Gradients and Tissue Anisotropies

Patterning of periodic stripes during development requires mechanisms to control both stripe spacing and orientation. A number of models can explain how stripe spacing is controlled, including molecular mechanisms, such as Turing's reaction-diffusion model, as well as cell-based and mechanical mechanisms. However, how stripe orientation is controlled in each of these cases is poorly understood. Here, we model stripe orientation using a simple, yet generic model of periodic patterning, with the aim of finding qualitative features of stripe orientation that are mechanism-independent. Our model predicts three qualitatively distinct classes of orientation mechanism: gradients in production rates, gradients in model parameters, and anisotropies (e.g. in diffusion or growth). We provide evidence that the results from our minimal model may also apply to more specific and complex models, revealing features of stripe orientation that may be common to a variety of biological systems.