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MECHANICAL FEEDBACK IN SEASHELL GROWTH AND FORM

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

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)

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 4 , April 2018 , pp. 581 - 606
Copyright
© 2018 Australian Mathematical Society 

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