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.

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.

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.