Coccolith arrangement follows Eulerian mathematics in the coccolithophore Emiliania huxleyi

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1 College of Fisheries, Jimei University, Xiamen, Fujian, China
2 Department of Biological Sciences, University of Southern California, Los Angeles, California, United States
3 State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen, Fujian, China
DOI
10.7287/peerj.preprints.3457v1
Published
Accepted
Subject Areas
Mathematical Biology
Keywords
coccolith, coccosphere, coccolithophore, Emiliania huxleyi, Euler’s polyhedron formula
Copyright
© 2017 Xu et al.
Licence
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
Cite this article
Xu K, Hutchins D, Gao K. 2017. Coccolith arrangement follows Eulerian mathematics in the coccolithophore Emiliania huxleyi. PeerJ Preprints 5:e3457v1

Abstract

Background. The globally abundant coccolithophore, Emiliania huxleyi, plays an important ecological role in oceanic carbon biogeochemistry by forming a cellular covering of plate-like CaCO3 crystals (coccoliths) and fixing CO2. It is unknown how the cells arrange different sizes of coccoliths to maintain full coverage as the cell surface area changes due to growth and cell division.

Methods. We used Euler’s polyhedron formula and simulation software CaGe, validated with the geometries of coccoliths, to analyses the coccolith topology of coccosphere and the arrange mechanism.

Results. The cells arrange each of the coccoliths to interlock with 4–6 others to keep pace with cell growth and cell division.

Conclusions. This study represents an example of how natural selection has arrived at a solution based on Euler’s polyhedral formula in response to the challenge of maintaining a CaCO3 covering on coccolithophore cells as cell size changes.

Author Comment

This is a submission to PeerJ for review.

Supplemental Information

The polygon composition and the isomer number of polyhedral coccosphere

The polygon compositions of polyhedra (6-22 faces) were predicted based on Euler’s formula, and further examined using the software CaGe to obtain isomer numbers. The face numbers are a list of consecutive positive integers. The isomer number of polyhedral coccosphere was calculated using the software CaGe. The numbers in red color indicate where no polyhedron exist with predicted polygon compositions.

DOI: 10.7287/peerj.preprints.3457v1/supp-2