A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth

Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates' exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify to form a new incremental layer of the exoskeleton. Most of the existing literature on the morphology of mollusks is descriptive. The mathematical understanding of the underlying coupling between pre-existing shell morphology, de novo surface deposition and morpho-elastic volume growth is at a nascent stage, primarily limited to reduced geometric representations. Here, we propose a general, three-dimensional computational framework coupling pre-existing morphology, incremental surface growth by accretion, and morpho-elastic volume growth. We exercise this framework by applying it to explain the stepwise morphogenesis of seashells during growth: new material surfaces are laid down by accretive growth on the mantle whose form is determined by its morpho-elastic growth. Calcification of the newest surfaces extends the shell as well as creates a new scaffold that constrains the next growth step. We study the effects of surface and volumetric growth rates, and of previously deposited shell geometries on the resulting modes of mantle deformation, and therefore of the developing shell's morphology. Connections are made to a range of complex shells ornamentations.Comment: Main article is 20 pages long with 15 figures. Supplementary material is 4 pages long with 6 figures and 6 attached movies. To be published in PLOS Computational Biolog

Shell microstructure and morphogenesis of the ornamentation in Cymatoceras Hyatt, 1883, Cretaceous Nautilida. Systematic implications

International audienceThe transverse ridges or so-called ‘ribs' of Cretaceous Cymatoceras correspond to the juxtaposition of thick, projected and imbricated radial tile-shaped lamellae of outer prismatic layer. Each of these lamellae formed in a cycle including an outward extension and secreting phase of the mantle edge, followed by his temporary withdrawal behind the periphery of the lamella. The sculpture of the underlying nacreous layer reflects only the underlying morphology of the juxtaposed adapical parts of the imbricated lamellae of outer prismatic layer. On internal moulds, the subdued symmetric undulations, which reflect the internal surface of the nacreous layer, can easily be mistaken for imprints of comarginal ribs (this last term is restricted here to undulations of the outer shell without structural discontinuities other than growth lines). Distinction of this kind of ornamentation challenges the monophyly of the family Cymatoceratidae, classically interpreted to include all ‘ribbed' post-Triassic Nautilida, the so-called ‘ribbing pattern' encompassing lamellae, fasciculate growth lines and divaricate ornamentation. Whether or not radial tile-shaped lamellae of outer prismatic layers a synapomorphy of an emended ‘cymatoceratid' clade cannot be solved until its history can be traced through a well-corroborated phylogeny, allowing in turn the evaluation of the hypothesized heterochronic (paedomorphic) shifting of the embryonic growth pattern trough postembryonic development

Snail shell coiling (re-)evolution and the evo-devo revolution

International audienceDuring the last two decades evolutionary developmental biology has become a major research programme whose findings put into question some concepts lying at the core of the _Synthetic Theory_. However, some authors are waiting for a _revolution_ in biology, one in which the existing genetic determinism will give way to a new conceptual understanding of the complexity of living organisms. This _revolution_ should necessarily pass through the elaboration of an appropriate theoretical framework integrating the non-linear dynamics of development as its fundamental basis. This objective implies a drastic shift in the way causality is generally understood as well as a purge of numerous convenient but misleading metaphors such as genetic or developmental programmes. Although most authors do not take these metaphors too literally, some persist in employing such _instructionist_ notions in a more literal perspective, and, in doing so, deny some concepts at the core of evolutionary developmental biology. We critically review two recent studies suggesting that shell coiling has re-evolved in a family of limpets (Calyptraeidae, Gastropoda). We stress that this putative re-evolution of snail shell coiling results only from an arbitrary scoring procedure leading us to consider shell coiling as a binary discrete character. We show that the way in which these authors connect this case study to evolutionary theories stems from the unwarranted premise of a linear mapping of genes onto phenotypes where particulate inheritance of morphological characters seems implicitly assumed. We illustrate how the persisting unclear role of genes in morphogenesis allows the maintenance of the adaptationist programme

The physical basis of mollusk shell chiral coiling

International audienceA theoretical model suggests that a mechanically induced twist of the soft body underlies the formation of helicospiral shells in snails and ammonites and also accounts for the startling and unique meandering shells observed in certain species. This theory addresses fundamental developmental issues of chirality and symmetry breaking: in the case of ammonites, how a bilaterally symmetric body can sometimes secrete a nonsymmetric shell; for gastropods, how an intrinsic twist possibly due to the asymmetric development of musculature can provide a mechanical motor for generating a chiral shell. Our model highlights the importance of physical forces in biological development and sheds light on shell coiling in snails, which have been used for a century as model organisms in genetic research

Mechanics unlocks the morphogenetic puzzle of interlocking bivalved shells

International audienceA striking feature in bivalved seashells is that the 2 valves fit together perfectly when closed. This trait has evolved in 2 phyla from a common shell-less ancestor and has been described for hundreds of years. While its functional advantage is clear, there is no understanding of how this feature is generated. A mathematical model of the shell growth process explains how geometry and mechanics conspire to generate an interlocking pattern. This model provides a physical explanation for a prominent example of convergent evolution. By showing how variations in the mechanism create a wide variety of morphological trends the model provides insight into how biophysical processes, probably modulated by genetic factors, are manifest across scales to produce a predictable pattern

Developmental integration related to buoyancy control in nautiloids: Evidence from unusual septal approximation and ontogenetic allometries in Jurassic species.

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Aturia from the Miocene Paratethys : An exceptional window on nautilid habitat and lifestyle

International audienceMany examples of drifted Aturia shells in shallow littoral deposits have been reported worldwide, suggesting that the paleobiogeographic distribution of this Cenozoic nautilid could be a mere post-mortem artifact. An exceptional Lower Miocene deposit from the Central Paratethys yields abundant (about 500 specimens) and very well-preserved newly hatched as well as adult shells, associated with upper and lower jaws, representing the first unequivocal case of autochthonous Aturia and one of the most exceptional nautilid deposits reported so far. Oxygen isotope ratios show that Aturia lived like Nautilus, being nektobenthic at all stages of its development. But unlike Nautilus, both newly hatched and adult Aturia lived at the same water depth and temperature (about 240-330 m and 13-17.6 degrees C) in which the eggs were laid. The dysoxic paleoenvironmental setting in which Aturia occurs in abundance may be interpreted in light of both the capacity of Nautilus to exploit/tolerate oxygen-depleted waters, and the molecular phylogenetic tree of cephalopods, suggesting plesiomorphic physiological traits associated with hypoxia tolerance. Since the last common ancestor of Aturia and Nautilus may be traced back at least into the Jurassic, this sheds new light onto the relative scarcity of Mesozoic and Cenozoic nautilids in well-oxygenated, epicontinental shelf deposits. (C) 2011 Elsevier B.V. All rights reserve