Cracking the armor

Amniotes exhibit a keratinized epidermis preventing water loss and skin appendages that play major roles in thermoregulation, photoprotection, camouflage, behavioral display, and defense against predators. Whereas mammals and birds evolved hairs and feathers, respectively, reptiles developed various types of scales. Although their developmental processes share some signaling pathways, it is unclear whether mammalian hairs, avian feathers and feet scales, and reptilian scales are homologous or if some of them evolved convergently (1). In birds and mammals, a reaction-diffusion mechanism (RDM) (2) generates a spatial pattern of placodes that develop and differentiate into follicular organs with a dermal papilla and cycling growth of an elongated keratinized epidermal structure (hairs or feathers) (3). However, scales in reptiles do not form true follicles and might not develop from placodes (4). Instead, reptilian scales originate in the embryo from regular dermo-epidermal elevations (1). Whereas the regular spatial organization of scales on the largest portion of the reptilian body is determined by a RDM, additional positional cues are likely involved in the development of the scale plates present on the head of many snakes and lizards. These head scales form a predictable symmetrical pattern (Fig. 1A) and provide mechanical protection.

The face and jaws of crocodilians are covered by polygonal scales (hereafter called “head scales”) that are strictly adjoining and nonoverlapping, but these polygons are irregular and their spatial distribution seems largely random (Fig. 1, B and C). Using high-resolution three-dimensional (3D) geometry and texture reconstructions (5–7), as well as developmental biology techniques, we show that crocodilians’ head scales are not genetically controlled developmental units and that their spatial patterning is generated through physical cracking of a living tissue in a stress field. This phenomenon might not involve any specific genetic instruction besides those associated with cell proliferation and general physical parameters such as skin stiffness and thickness.

By marking and analyzing various features directly on 3D models of multiple Nile crocodile (Crocodylus niloticus) individuals (Fig. 1 and movie S1), we show that spatial distribution of head scales is largely random.

First, reflection of the network of scales’ edges across the sagittal plane indicates high variability between the left and right head pattern (Fig. 1B and fig. S1A). Second, nonrigid alignment (8) of head geometries from different individuals indicates a similarly large variability in scale patterns in terms of polygons’ sizes and localizations (Fig. 1C and fig. S1B).

This combination of order and chaos in the distribution of head scales is reminiscent of the topological assemblage of soap foams (9, 10). Recent studies used the 2D foam model for studying self-organizing principles and stochastic processes shaping epithelial topology during growth and homeostasis (11–13) because the causal cell-surface mechanics is comparable to the physics of foam formation (14). Similarly, the pattern of crocodile head scales could result from energy minimization of contact surfaces among genetically determined elements (scales). However, two other mechanisms could generate random distributions of polygonal elements: (i) a RDM patterning the spatial organization of genetically determined developmental units, as for mammalian hairs or avian feathers, and (ii) cracking of a material layer causing its fracture into adjacent polygonal domains (15).

Although stochastic patterns generated by these processes share some universal mathematical properties (see supplementary materials), foams and crack patterns are generated by very different physical phenomena that may be identified on the basis of other statistical features. First, crocodile head scales do not show a good fit to the area distribution function expected for foams (fig. S3). Second, a fundamental difference between foams and crack patterns is that the latter can exhibit incomplete edges (15), of which many are observed on the head of crocodiles (Fig. 2A).

Another key feature is the angle among edges at nodes. In foams, edges are circular arcs intersecting only three at a time with an angle of 120°, as imposed by the three instantaneous equal length-tension force vectors acting at a node. This rule is observed in all types of foams, including animal epithelia (12, 16), although the distribution of angles can be widened due to local stress generated by cell division and growth. On the other hand, crack patterns can generate various angle distributions. Nonhierarchical cracking arises when fractures propagate simultaneously (Fig. 2B), and junctions tend to form at 120° (17, 18). Furthermore, when a crack front splits, or when multiple cracks are nucleated from a single point, the junctions among edges also tend to be 120°. Conversely, crack patterns can be hierarchical (17, 19); that is, fractures are formed successively, and propagating cracks will tend to join previous cracks at a 90° angle. Indeed, the local stress perpendicular to a crack is relaxed and concentrates at the tip of the crack (explaining its propagation), but the stress component parallel to the crack is not affected. Hence, as cracks propagate perpendicularly to the direction of the maximum stress component, a secondary crack can turn when it approaches an older one and tends to join it at 90°. Similarly, if a crack starts on the side of an older crack, it will initially tend to propagate at a right angle (17). Multiple examples of 90° connections and incomplete edges reorienting their propagation front are visible on the crocodiles face and jaws (Fig. 2C). We also observe “laddering” patterns (17) of paired parallel primary fractures with perpendicular multiple secondary cracks (Fig. 2D) and internal edges connecting perpendicularly to the border of the network (Fig. 2E). The distribution function of edge angles is bimodal in many crocodiles analyzed (fig. S4A), suggesting either that hierarchical and nonhierarchical cracking processes coexist or that head scale networks undergo a “maturation” process (20–22) (see supplementary text).

Dome pressure receptors (DPRs) are pigmented round submillimetric sensory organs (Fig. 2F), distributed on the crocodile face and jaws, that detect surface pressure waves, allowing crocodiles to swiftly orient, even in darkness, toward a prey perturbing the water-air interface (23). The dome shape of DPRs is due to a modified epidermis and the presence of a pocket of various cell types in the outermost portion of the dermis (Fig. 2F). We marked the localization of DPRs on the 3D models of all scanned individuals (orange dots, Fig. 2, G and H). Many of the cracks that have stopped their course did so close to a DPR (Fig. 2G and fig. S4C). Given that the most frequent cause for fracture arrest is when the crack front meets a heterogeneity in the system (15), it is likely that the modified skin thickness and composition at and around DPRs constitute such heterogeneities. In addition, the course of many edges avoids DPRs (Fig. 2H and fig. S4C).

The overall distribution of DPRs seems rather homogeneous except where the density is increased near the teeth and decreased at the back of the jaws and on the top of the face (fig. S5). Different crocodile individuals differ by as much as 21% and 48% in their total number of DPRs and crack edges, respectively. Remarkably, these two interindividual variations are inversely correlated: Crocodiles with fewer DPRs have more crack edges (fig. S4D). Given that the development of DPRs precedes cracking, this correlation suggests that DPRs constrain cracking, as already implied by Fig. 2, G and H. Despite the fact that the distributions of cracks and DPRs both have a strong stochastic component, the constraining effect of DPRs on cracking is noticeable: The edges tend to travel along the zones of DPRs lowest local density (fig. S4E).

The archetypal cracking process in physics is due to shrinkage [through removal of a diffusing quantity, either heat or a liquid (20)] of a material layer adherent to a nonshrinking substrate (15, 17), such that a stress field builds up and causes fractures when the stress exceeds a threshold characteristic of the material. Crocodiles have a particularly thick and rigid skin due to the presence of a highly collagenous dermis and an epidermis rich in β-keratins (24). The skin covering their head shows a yet thicker (about 2×) and more keratinized epidermis. We suggest that the rapid growth of the crocodile embryonic facial and jaw skeleton (relative to the size of the neurocranium), combined with the development of a very keratinized skin, generates the mechanical stress that causes cracking. Here, it is not the cracking layer that shrinks but the underlying substrate layer that grows. It explains that first-order cracks (fig. S6) tend to traverse the width of the face because the head is growing longitudinally faster than in other directions.

In snakes and lizards, scales are developmental units: Each scale differentiates and grows from a primordium that can be identified by in situ hybridization with probes targeting genes belonging to signaling pathways involved in early skin appendage development (1, 4). The large head scales form a predictable pattern following positional cues, such that the identity of adult snake head scales can be recognized while they develop from primordia in the embryo (Fig. 3A). In crocodiles, all postcranial scales follow that same principle of development (Fig. 3B): Spatial distribution of primordia is established, then each primordium differentiates, first into a symmetrical elevation and second as an oriented asymmetrical scale overlapping with more posterior scales (Fig. 3C).

However, crocodile head scales do not form from scale primordia or further developmental stages. Instead, a pattern of DPRs primordia is generated on the face and jaws: The dome shape of DPRs has already started to form before any scale appears (Fig. 3D). Afterward, grooves progressively appear, propagate, and interconnect (while avoiding DPRs) to form a continuous network across the developing skin (Fig. 4A). The process generates polygonal domains of skin, each containing a random number of DPRs. Therefore, scales on the face and jaws of crocodiles (i) are not serial homologs of scales elsewhere on the body and (ii) are not even genetically controlled developmental units. Instead, they emerge from physical cracking.

During a typical cracking process, fractures are nucleated at the upper surface but quickly spread downward and affect the whole thickness of the material layer (19). The developing skin on the crocodile’s head similarly reacts to the stress field as it develops deep groves that can reach the stiff underlying tissues (Fig. 4B). Our analyses indicate that cell proliferation in the epidermis layer is vastly increased in the deepest region of the skin grooves corresponding to cracks (Fig. 4C), suggesting that a healing process allows the skin layer to maintain its continuous covering. The local biological process (cell proliferation) might be driven by the purely physical parameter (mechanical stress) as follows: In zones of highest stress, local bulging is nucleated. The local stress component perpendicular to the bulge is relaxed and concentrates at its tip, explaining the propagation of both the stress and proliferation maxima (hence, the corresponding propagation of the bulge). In a manner entirely analogous to true physical cracking, the bulge front would propagate perpendicularly to the direction of maximum stress components, explaining the topology of the resulting random polygonal domains of skin. The role of proliferation reinforces the above suggestion that crack patterns in crocodiles might experience maturation (20–22), explaining the observed mixture of hierarchical and nonhierarchical features (see supplementary text and fig. S4A).

We have shown that the irregular polygonal domains of skin on the crocodile face and jaws are produced by cracking, a mechanism that is distinct from those generating scales on the postcranial portion of the crocodile body, as well as on the body and head of all other reptiles. This cracking process is primarily physical. However, it does not mean that genetically controlled parameters are irrelevant. For example, although a crack pattern is visible in all crocodilian species, spatial distribution varies considerably, possibly because of species-specific skull geometry and growth but also skin composition and thickness. Given that these parameters, as well as cell proliferation, are genetically controlled, the variation of head crack patterns among crocodilian species is likely due to an interplay between physically and genetically controlled parameters. Our study suggests that, besides RDM, a larger set of physical self-organizational processes contribute to the production of the enormous diversity of patterns observed in living systems.

Supplementary Materials

www.sciencemag.org/cgi/content/full/science.1226265/DC1

Material and Methods

Supplementary Text

Figs. S1 to S6

Table S1

Movie S1

References (25–33)

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Acknowledgments: This work was supported by the University of Geneva, the Swiss National Science Foundation, and the Schmidheiny Foundation. A. Tzika helped with in situs. H. Li assisted with nonrigid registration. We thank R. Pellet for assistance in mechanics design and A. Roux, M. Gonzalez-Gaitan, B. Chopard, U. Schibler, and anonymous reviewers for useful comments and suggestions.