The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning.

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

Somitic positional information guides self-organized patterning of snake scales.

Two influential concepts in tissue patterning are Wolpert's positional information and Turing's self-organized reaction-diffusion (RD). The latter establishes the patterning of hair and feathers. Here, our morphological, genetic, and functional-by CRISPR-Cas9-mediated gene disruption-characterization of wild-type versus "scaleless" snakes reveals that the near-perfect hexagonal pattern of snake scales is established through interactions between RD in the skin and somitic positional information. First, we show that ventral scale development is guided by hypaxial somites and, second, that ventral scales and epaxial somites guide the sequential RD patterning of the dorsolateral scales. The RD intrinsic length scale evolved to match somite periodicity, ensuring the alignment of ribs and scales, both of which play a critical role in snake locomotion.

Transient agonism of the sonic hedgehog pathway triggers a permanent transition of skin appendage fate in the chicken embryo.

Vertebrate skin appendage early development is mediated by conserved molecular signaling composing a dynamical reaction-diffusion-like system. Variations to such systems contribute to the remarkable diversity of skin appendage forms within and among species. Here, we demonstrate that stage-specific transient agonism of sonic hedgehog (Shh) pathway signaling in chicken triggers a complete and permanent transition from reticulate scales to feathers on the ventral surfaces of the foot and digits. Resulting ectopic feathers are developmentally comparable to feathers adorning the body, with down-type feathers transitioning into regenerative, bilaterally symmetric contour feathers in adult chickens. Crucially, this spectacular transition of skin appendage fate (from nodular reticulate scales to bona fide adult feathers) does not require sustained treatment. Our RNA sequencing analyses confirm that smoothened agonist treatment specifically promotes the expression of key Shh pathway-associated genes. These results indicate that variations in Shh pathway signaling likely contribute to the natural diversity and regionalization of avian integumentary appendages.

Protocol for the rapid intravenous in ovo injection of developing amniote embryos.

We present a technique for precise drug delivery into the vascular system of developing amniote embryos via injection into chorioallantoic veins underlying the eggshell membrane. We describe steps for incubating and candling eggs, removing the shell to expose underlying veins, and precise intravenous injection. In addition to chicken embryos, this protocol is applicable to other amniote species that lay hard-shell eggs, including crocodiles and tortoises. This technique is rapid, is reproducible, is of low cost, and will provide an important resource for developmental biologists. For complete details on the use and execution of this protocol, please refer to Cooper & Milinkovitch.1.

High-resolution confocal and light-sheet imaging of collagen 3D network architecture in very large samples.

Although notoriously difficult, imaging collagen network architecture, a key element affecting tissue mechanical properties, is of paramount importance in developmental and cancer biology. Here, we introduce a simple and robust method of whole-mount collagen staining with the 'Fast Green' dye that provides unmatched visualization of collagen 3D network architecture, via confocal or light-sheet microscopy, compatible with solvent-based tissue clearing and immunostaining.

Modeling convergent scale-by-scale skin color patterning in multiple species of lizards.

Skin color patterning in vertebrates emerges at the macroscale from microscopic cell-cell interactions among chromatophores. Taking advantage of the convergent scale-by-scale skin color patterning dynamics in five divergent species of lizards, we quantify the respective efficiencies of stochastic (Lenz-Ising and cellular automata, sCA) and deterministic reaction-diffusion (RD) models to predict individual patterns and their statistical attributes. First, we show that all models capture the underlying microscopic system well enough to predict, with similar efficiencies, neighborhood statistics of adult patterns. Second, we show that RD robustly generates, in all species, a substantial gain in scale-by-scale predictability of individual adult patterns without the need to parametrize the system down to its many cellular and molecular variables. Third, using 3D numerical simulations and Lyapunov spectrum analyses, we quantitatively demonstrate that, given the non-linearity of the dynamical system, uncertainties in color measurements at the juvenile stage and in skin geometry variation explain most, if not all, of the residual unpredictability of adult individual scale-by-scale patterns. We suggest that the efficiency of RD is due to its intrinsic ability to exploit mesoscopic information such as continuous scale colors and the relations among growth, scales geometries, and the pattern length scale. Our results indicate that convergent evolution of CA patterning dynamics, leading to dissimilar macroscopic patterns in different species, is facilitated by their spontaneous emergence under a large range of RD parameters, as long as a Turing instability occurs in a skin domain with periodic thickness. VIDEO ABSTRACT.

Lizard Skin Patterns and the Ising Model.

The ocellated lizard (Timon lepidus) exhibits an intricate skin color pattern made of monochromatic black and green skin scales, whose dynamics of color flipping are known to be well modeled by a stochastic cellular automaton. We show that the late-time probability distribution of the pattern corresponds to the canonical probability distribution of the antiferromagnetic Ising model and can be generated by dynamics different from the commonly-used Glauber. We comment on skin scale patterns generated by the Ising model on the triangular lattice in the low-temperature limit.

Elephants evolved strategies reducing the biomechanical complexity of their trunk.

The elephant proboscis (trunk), which functions as a muscular hydrostat with a virtually infinite number of degrees of freedom, is a spectacular organ for delicate to heavy object manipulation as well as social and sensory functions. Using high-resolution motion capture and functional morphology analyses, we show here that elephants evolved strategies that reduce the biomechanical complexity of their trunk. Indeed, our behavioral experiments with objects of various shapes, sizes, and weights indicate that (1) complex behaviors emerge from the combination of a finite set of basic movements; (2) curvature, torsion, and strain provide an appropriate kinematic representation, allowing us to extract motion primitives from the trunk trajectories; (3) transport of objects involves the proximal propagation of an inward curvature front initiated at the tip; (4) the trunk can also form pseudo-joints for point-to-point motion; and (5) the trunk tip velocity obeys a power law with its path curvature, similar to human hand drawing movements. We also reveal with unprecedented precision the functional anatomy of the African and Asian elephant trunks using medical imaging and macro-scale serial sectioning, thus drawing strong connections between motion primitives and muscular synergies. Our study is the first combined quantitative analysis of the mechanical performance, kinematic strategies, and functional morphology of the largest animal muscular hydrostat on Earth. It provides data for developing innovative "soft-robotic" manipulators devoid of articulations, replicating the high compliance, flexibility, and strength of the elephant trunk. VIDEO ABSTRACT.

Reaction-diffusion in a growing 3D domain of skin scales generates a discrete cellular automaton.

We previously showed that the adult ocellated lizard skin colour pattern is effectively generated by a stochastic cellular automaton (CA) of skin scales. We additionally suggested that the canonical continuous 2D reaction-diffusion (RD) process of colour pattern development is transformed into this discrete CA by reduced diffusion coefficients at the borders of scales (justified by the corresponding thinning of the skin). Here, we use RD numerical simulations in 3D on realistic lizard skin geometries and demonstrate that skin thickness variation on its own is sufficient to cause scale-by-scale coloration and CA dynamics during RD patterning. In addition, we show that this phenomenon is robust to RD model variation. Finally, using dimensionality-reduction approaches on large networks of skin scales, we show that animal growth affects the scale-colour flipping dynamics by causing a substantial decrease of the relative length scale of the labyrinthine colour pattern of the lizard skin.

Emergence of self-organizational patterning at the mesoscopic scale.

In this issue of Developmental Cell, Chuyen et al. (2021) suggest that the Scf/Kit pathway controls mutual repulsion of multiciliated cells and their affinity for epidermal cell junctions through soluble and membrane-associated Scf ligands, respectively. Effective self-organizational patterning emerges at the mesoscopic scale as a small set of effective behaviors.

Genome mapping of a LYST mutation in corn snakes indicates that vertebrate chromatophore vesicles are lysosome-related organelles.

Reptiles exhibit a spectacular diversity of skin colors and patterns brought about by the interactions among three chromatophore types: black melanophores with melanin-packed melanosomes, red and yellow xanthophores with pteridine- and/or carotenoid-containing vesicles, and iridophores filled with light-reflecting platelets generating structural colors. Whereas the melanosome, the only color-producing endosome in mammals and birds, has been documented as a lysosome-related organelle, the maturation paths of xanthosomes and iridosomes are unknown. Here, we first use 10x Genomics linked-reads and optical mapping to assemble and annotate a nearly chromosome-quality genome of the corn snake Pantherophis guttatus The assembly is 1.71 Gb long, with an N50 of 16.8 Mb and L50 of 24. Second, we perform mapping-by-sequencing analyses and identify a 3.9-Mb genomic interval where the lavender variant resides. The lavender color morph in corn snakes is characterized by gray, rather than red, blotches on a pink, instead of orange, background. Third, our sequencing analyses reveal a single nucleotide polymorphism introducing a premature stop codon in the lysosomal trafficking regulator gene (LYST) that shortens the corresponding protein by 603 amino acids and removes evolutionary-conserved domains. Fourth, we use light and transmission electron microscopy comparative analyses of wild type versus lavender corn snakes and show that the color-producing endosomes of all chromatophores are substantially affected in the LYST mutant. Our work provides evidence characterizing xanthosomes in xanthophores and iridosomes in iridophores as lysosome-related organelles.

Translucent in air and iridescent in water: structural analysis of a salamander egg sac.

Females of some Asian salamanders of the genus Hynobius deposit in streams their eggs embedded in a translucent envelope called an 'egg sac'. The edges of the envelope exhibit a spectacular blue-to-yellow iridescent glow, which instantaneously disappears when the sac is removed from water. First, our scanning electron microscopy analyses reveal that the inner surface of the 100 µm-thick envelope displays striations (length scale of about 3 µm), which are themselves covered by much smaller (190 ± 30 nm) and quasi-periodic corrugations. The latter could constitute a surface diffraction grating generating iridescence by light interference. Second, our transmission electron microscopy and focused-ion-beam scanning electron microscopy analyses show that the bulk of the egg sac wall is composed of meandering fibres with a quasi-periodic modulation of 190 ± 60 nm along the thickness of the envelope, generating a photonic crystal. Third, Fourier power analyses of 450 electron microscopy images with varying incident angles indicate that changing the surrounding medium from water to air shifts most of the backscattered power spectrum to the ultraviolet range, hence, explaining that the egg sac loses visible iridescence when removed out of the water. Fourth, the results of our photography and optical spectroscopy experiments of submerged and emerged egg sacs rule out the possibility that the iridescence is due to a thin film or a multilayer, whereas the observed non-specular response is compatible with the backscattering expected from surface diffraction gratings and volumetric photonic crystals with spatial 1D modulation. Finally, although we mention several potential biological functions of the egg sac structural colours and iridescence, we emphasise that these optical properties might be the by-products of the envelope material internal structure selected during evolution for its mechanical properties.

Elastic instability during branchial ectoderm development causes folding of the Chlamydosaurus erectile frill.

We study the morphogenesis and evolutionary origin of the spectacular erectile ruff of the frilled dragon (Chlamydosaurus kingii). Our comparative developmental analyses of multiple species suggest that the ancestor of Episquamata reptiles developed a neck fold from the hyoid branchial arch by preventing it to fully fuse with posterior arches. We also show that the Chlamydosaurus embryonic neck fold dramatically enlarges and its anterior surface wrinkles, establishing three convex ridges on each lobe of the frill. We suggest that this robust folding pattern is not due to localised increased growth at the positions of the ridges, but emerges from an elastic instability during homogeneous growth of the frill skin frustrated by its attachment to adjacent tissues. Our physical analog experiments and 3D computational simulations, using realistic embryonic tissue growth, thickness and stiffness values, recapitulate the transition from two to three ridges observed during embryonic development of the dragon's frill.

Phylogenetic mapping of scale nanostructure diversity in snakes.

BACKGROUND: Many species of snakes exhibit epidermal surface nanostructures that form complex motifs conferring self-cleaning properties, and sometimes structural iridescence, to their skin. RESULTS: Using confocal microscopy, we show that these specialised cells can be greatly elongated along their left-right axis and that different types of nanostructures are generated by cell borders and cell surface. To characterise the complexity and diversity of these surface gratings, we analysed scanning electron microscopy images of skin sheds from 353 species spanning 19 of the 26 families of snakes and characterised the observed nanostructures with four characters. The full character matrix, as well as one representative SEM image of each of the corresponding species, is available as a MySQL relational database at https://snake-nanogratings.lanevol.org . We then performed continuous-time Markov phylogenetic mapping on the snake phylogeny, providing an evolutionary dynamical estimate for the different types of nanostructures. These analyses suggest that the presence of cell border digitations is the ancestral state for snake skin nanostructures which was subsequently and independently lost in multiple lineages. Our analyses also indicate that cell shape and cell border shape are co-dependent characters whereas we did not find correlation between a simple life habit classification and any specific nanomorphological character. CONCLUSIONS: These results, compatible with the fact that multiple types of nanostructures can generate hydrophobicity, suggest that the diversity and complexity of snake skin surface nano-morphology are dominated by phylogenetic rather than habitat-specific functional constraints. The present descriptive study opens the perspective of investigating the cellular self-organisational cytoskeletal processes controlling the patterning of different skin surface nanostructures in snakes and lizards.

Feather arrays are patterned by interacting signalling and cell density waves.

Feathers are arranged in a precise pattern in avian skin. They first arise during development in a row along the dorsal midline, with rows of new feather buds added sequentially in a spreading wave. We show that the patterning of feathers relies on coupled fibroblast growth factor (FGF) and bone morphogenetic protein (BMP) signalling together with mesenchymal cell movement, acting in a coordinated reaction-diffusion-taxis system. This periodic patterning system is partly mechanochemical, with mechanical-chemical integration occurring through a positive feedback loop centred on FGF20, which induces cell aggregation, mechanically compressing the epidermis to rapidly intensify FGF20 expression. The travelling wave of feather formation is imposed by expanding expression of Ectodysplasin A (EDA), which initiates the expression of FGF20. The EDA wave spreads across a mesenchymal cell density gradient, triggering pattern formation by lowering the threshold of mesenchymal cells required to begin to form a feather bud. These waves, and the precise arrangement of feather primordia, are lost in the flightless emu and ostrich, though via different developmental routes. The ostrich retains the tract arrangement characteristic of birds in general but lays down feather primordia without a wave, akin to the process of hair follicle formation in mammalian embryos. The embryonic emu skin lacks sufficient cells to enact feather formation, causing failure of tract formation, and instead the entire skin gains feather primordia through a later process. This work shows that a reaction-diffusion-taxis system, integrated with mechanical processes, generates the feather array. In flighted birds, the key role of the EDA/Ectodysplasin A receptor (EDAR) pathway in vertebrate skin patterning has been recast to activate this process in a quasi-1-dimensional manner, imposing highly ordered pattern formation.

Locally-curved geometry generates bending cracks in the African elephant skin.

An intricate network of crevices adorns the skin surface of the African bush elephant, Loxodonta africana. These micrometre-wide channels enhance the effectiveness of thermal regulation (by water retention) as well as protection against parasites and intense solar radiation (by mud adherence). While the adaptive value of these structures is well established, their morphological characterisation and generative mechanism are unknown. Using microscopy, computed tomography and a custom physics-based lattice model, we show that African elephant skin channels are fractures of the animal brittle and desquamation-deficient skin outermost layer. We suggest that the progressive thickening of the hyperkeratinised stratum corneum causes its fracture due to local bending mechanical stress in the troughs of a lattice of skin millimetric elevations. The African elephant skin channels are therefore generated by thickening of a brittle material on a locally-curved substrate rather than by a canonical tensile cracking process caused by frustrated shrinkage.

A living mesoscopic cellular automaton made of skin scales.

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction-diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction-diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces.

In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace-Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.

Reorganisation of Hoxd regulatory landscapes during the evolution of a snake-like body plan.

Within land vertebrate species, snakes display extreme variations in their body plan, characterized by the absence of limbs and an elongated morphology. Such a particular interpretation of the basic vertebrate body architecture has often been associated with changes in the function or regulation of Hox genes. Here, we use an interspecies comparative approach to investigate different regulatory aspects at the snake HoxD locus. We report that, unlike in other vertebrates, snake mesoderm-specific enhancers are mostly located within the HoxD cluster itself rather than outside. In addition, despite both the absence of limbs and an altered Hoxd gene regulation in external genitalia, the limb-associated bimodal HoxD chromatin structure is maintained at the snake locus. Finally, we show that snake and mouse orthologous enhancer sequences can display distinct expression specificities. These results show that vertebrate morphological evolution likely involved extensive reorganisation at Hox loci, yet within a generally conserved regulatory framework.

The anatomical placode in reptile scale morphogenesis indicates shared ancestry among skin appendages in amniotes.

Most mammals, birds, and reptiles are readily recognized by their hairs, feathers, and scales, respectively. However, the lack of fossil intermediate forms between scales and hairs and substantial differences in their morphogenesis and protein composition have fueled the controversy pertaining to their potential common ancestry for decades. Central to this debate is the apparent lack of an "anatomical placode" (that is, a local epidermal thickening characteristic of feathers' and hairs' early morphogenesis) in reptile scale development. Hence, scenarios have been proposed for the independent development of the anatomical placode in birds and mammals and parallel co-option of similar signaling pathways for their morphogenesis. Using histological and molecular techniques on developmental series of crocodiles and snakes, as well as of unique wild-type and EDA (ectodysplasin A)-deficient scaleless mutant lizards, we show for the first time that reptiles, including crocodiles and squamates, develop all the characteristics of an anatomical placode: columnar cells with reduced proliferation rate, as well as canonical spatial expression of placode and underlying dermal molecular markers. These results reveal a new evolutionary scenario where hairs, feathers, and scales of extant species are homologous structures inherited, with modification, from their shared reptilian ancestor's skin appendages already characterized by an anatomical placode and associated signaling molecules.