Coccolith arrangement follows Eulerian mathematics in the coccolithophore Emiliania huxleyi
- 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
- 2017. Coccolith arrangement follows Eulerian mathematics in the coccolithophore Emiliania huxleyi. PeerJ Preprints 5:e3457v1 https://doi.org/10.7287/peerj.preprints.3457v1
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.