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MECHANICAL FEEDBACK IN SEASHELL GROWTH AND FORM

Part of: Special subfields of solid mechanics Elastic materials Mathematical biology in general

Published online by Cambridge University Press:  16 April 2018

A. ERLICH ,
R. HOWELL ,
A. GORIELY ,
R. CHIRAT  and
D. E. MOULTON Open the ORCID record for D. E. MOULTON [Opens in a new window]
A. ERLICH
Affiliation:
School of Mathematics, University of Manchester, UK email alexander.erlich@manchester.ac.uk A. Erlich and R. Howell are the co-first authors.
R. HOWELL
Affiliation:
Randall Division of Cell and Molecular Biophysics, King’s College London, UK Francis Crick Institute, London, UK email rowan.howell@gmail.com A. Erlich and R. Howell are the co-first authors.
A. GORIELY
Affiliation:
Mathematical Institute, University of Oxford, Oxford, UK email goriely@maths.ox.ac.uk, moulton@maths.ox.ac.uk
R. CHIRAT
Affiliation:
Université Lyon 1, CNRS UMR 5276 LGL-TPE, France email regis.chirat@univ-lyon1.fr
D. E. MOULTON*
Affiliation:
Mathematical Institute, University of Oxford, Oxford, UK email goriely@maths.ox.ac.uk, moulton@maths.ox.ac.uk
*
✉moulton@maths.ox.ac.uk
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Abstract

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Mollusc seashells grow through the local deposition and calcification of material at the shell opening by a soft and thin organ called the mantle. Through this process, a huge variety of shell structures are formed. Previous models have shown that these structural patterns can largely be understood by examining the mechanical interaction between the deformable mantle and the rigid shell aperture to which it adheres. In this paper we extend this modelling framework in two distinct directions. For one, we incorporate a mechanical feedback in the growth of the mollusc. Second, we develop an initial framework to couple the two primary and orthogonal modes of pattern formation in shells, which are termed antimarginal and commarginal ornamentation. In both cases we examine the change in shell morphology that occurs due to the different mechanical influences and evaluate the hypotheses in light of the fossil record.

Keywords

morphogenesismorphomechanicsmathematical modelmollusc

MSC classification

Primary: 92B05: General biology and biomathematics
Secondary: 74L15: Biomechanical solid mechanics 74B15: Equations linearized about a deformed state (small deformations superposed on large)
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 4 , April 2018 , pp. 581 - 606
Copyright
© 2018 Australian Mathematical Society 

References

Checa, A., “A model for the morphogenesis of ribs in ammonites inferred from associated microsculptures”, Palaeontology 37 (1994) 863–888; http://www.palass.org/publications/palaeontology-journal/archive/37/4/article_pp863-888.Google Scholar
Chirat, R., Moulton, D. E. and Goriely, A., “Mechanical basis of morphogenesis and convergent evolution of spiny seashells”, Proc. Natl Acad. Sci. USA 110 (2013) 6015–6020; http://www.pnas.org/content/110/15/6015.Google Scholar
Dagys, A. S., Bucher, H. and Weitschat, W., “Intraspecific variation of parasibirites kolymensis bychkov (ammonoidea) from the lower triassic (spathian) of arctic asia”, Mitteilungen aus dem Geologisch-Paläontologischen der Institut Universität Hamburg 83 (1999) 163–178.Google Scholar
Erlich, A., “Growth laws in morphoelasticity”, Ph. D. Thesis, University of Oxford, 2017.Google Scholar
Erlich, A., Moulton, D. E., Goriely, A. and Chirat, R., “Morphomechanics and developmental constraints in the evolution of ammonites shell form”, J. Exp. Zool. B 326 (2016) 437–450; doi:10.1002/jez.b.22716.Google Scholar
Howell, P., Kozyreff, G. and Ockendon, J., Applied solid mechanics, 43 (Cambridge University Press, Cambridge, UK, 2009); doi:10.1017/CBO9780511611605.Google Scholar
Hutson, M. S. and Ma, X., “Mechanical aspects of developmental biology: perspectives on growth and form in the (post)-genomic age”, Phys. Biol. 5 (2008) 015001; doi:10.1088/1478-3975/5/1/015001.Google Scholar
Mammoto, T., Mammoto, A. and Ingber, D. E., “Mechanobiology and developmental control”, Ann. Rev. Cell Dev. Biol. 29 (2013) 27–61; doi:10.1146/annurev-cellbio-101512-122340.Google Scholar
Moulton, D. E., Goriely, A. and Chirat, R., “Mechanical growth and morphogenesis of seashells”, J. Theoret. Biol. 311 (2012) 69–79; doi:10.1016/j.jtbi.2012.07.009.Google Scholar
Moulton, D. E., Goriely, A. and Chirat, R., “The morpho-mechanical basis of ammonite form”, J. Theoret. Biol. 364 (2015) 220–230; doi:10.1016/j.jtbi.2014.09.021.CrossRefGoogle ScholarPubMed
Moulton, D. E., Lessinnes, T. and Goriely, A., “Morphoelastic rods. Part 1: a single growing elastic rod”, J. Mech. Phys. Solids 61 (2012) 398–427; doi:10.1016/j.jmps.2012.09.017.Google Scholar
Nelson, C. M., Jean, R. P., Tan, J. L., Liu, W. F., Sniadecki, N. J., Spector, A. A. and Chen, C. S., “Emergent patterns of growth controlled by multicellular form and mechanics”, Proc. Natl Acad. Sci. USA 102 (2005) 11594–11599; doi:10.1073/pnas.0502575102.Google Scholar
O’Keeffe, S. G., Moulton, D. E., Waters, S. L. and Goriely, A., “Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix”, Intl J. Non-Linear Mech. 56 (2013) 94–104; doi:10.1016/j.ijnonlinmec.2013.04.017.Google Scholar
Raup, D. M., “Geometric analysis of shell coiling: coiling in ammonoids”, J. Paleontol. 41 (1967) 43–65; http://www.jstor.org/stable/1301903.Google Scholar
Rodriguez, E. K., Hoger, A. and McCulloch, A. D., “Stress-dependent finite growth in soft elastic tissues”, J. Biomech. 27 (1994) 455–467; doi:10.1016/0021-9290(94)90021-3.Google Scholar
Simkiss, K. and Wilbur, K. M., Biomineralization (Academic Press, New York, 1989); https://www.elsevier.com/books/biomineralization/simkiss/978-0-08-092584-4.Google Scholar