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. Mos...

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Bibliographic Details
Published in:PLoS computational biology 2019-07, Vol.15 (7), p.e1007213-e1007213
Main Authors: Rudraraju, Shiva, Moulton, Derek E, Chirat, Régis, Goriely, Alain, Garikipati, Krishna
Format: Article
Language:English
Subjects:
Accretion
Algorithms
Animal Shells - anatomy & histology
Animal Shells - growth & development
Animal Shells - physiology
Animals
Biology
Biology and Life Sciences
Biomechanical Phenomena
Body Patterning - physiology
Calcification
Calcification, Physiologic
Computational Biology
Computer applications
Computer Simulation
Coupling
Deformation
Deposition
Elastic limit
Elasticity
Engineering and Technology
Evolution & development
Exoskeleton
Exoskeletons
Finite Element Analysis
Growth rate
Imaging, Three-Dimensional
Invertebrates
Mantle
Mathematical morphology
Mechanical engineering
Mechanics
Medicine and Health Sciences
Minerals
Models, Biological
Mollusca - anatomy & histology
Mollusca - growth & development
Mollusca - physiology
Mollusks
Morphogenesis
Morphology
Physical Sciences
Shells
Spatio-Temporal Analysis
Studies
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Summary: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.
ISSN:1553-7358
1553-734X
1553-7358
DOI:10.1371/journal.pcbi.1007213