Coccolith arrangement follows Eulerianmathematics in the coccolithophore Emiliania huxleyi
- Published
- Accepted
- Subject Areas
- Mathematical Biology
- Keywords
- coccosphere, coccolithophore, Emiliania huxleyi, Euler’s polyhedron formula, coccolith topology
- Copyright
- © 2018 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
- 2018. Coccolith arrangement follows Eulerianmathematics in the coccolithophore Emiliania huxleyi. PeerJ Preprints 6:e3457v2 https://doi.org/10.7287/peerj.preprints.3457v2
Abstract
Background. The globally abundant coccolithophore, Emiliania huxleyi, plays an importantecological role in oceanic carbon biogeochemistry by forming a cellularcovering of plate-like CaCO 3 crystals (coccoliths) and fixing CO 2 .It is unknown how the cells arrange different-size of coccoliths to maintainfull coverage, as the cell surface area of the cell changes during daily cycle.
Methods. We used Euler’s polyhedron formula and CaGe simulationsoftware, validated with the geometries of coccoliths, to analze and simulatethe coccolith topology of the coccosphere and to explore the arrangementmechanisms.
Results. There were only small variations in the geometries ofcoccoliths, even when the cells were cultured under variable light conditions.Because of geometric limits, small coccoliths tended to interlock with fewerand larger coccoliths, and vice versa. Consequently, to sustain a full coverageon the surface of cell, each coccolith was arranged to interlock with four tosix others, which in turn led to each coccosphere contains at least 6coccoliths.
Conclusions. The number of coccoliths per coccosphere must keep pacewith changes on the cell surface area as a result of photosynthesis,respiration and cell division. This study is an example of natural selectionfollowing Euler’s polyhedral formula, in response to the challenge ofmaintaining a CaCO 3 covering on coccolithophore cells as cell sizechanges.
Author Comment
The manuscript was restructured, and more simulation results (see Figs. 4-5)
were added to more clearly explain our points. The following text simply explains our points: As the basic component of the coccosphere, coccoliths
are produced with specific geometry. Thus, we propose that the formation of coccospheres
must follow basic mathematical principles or constraints. We first analyzed the geometry of coccoliths and simulated interlocking
coccoliths on a 2D plane. We found that, because of geometric limits, small
coccoliths tended to interlock with fewer and larger coccoliths, and vice versa.
Thus, each coccolith interlocks with four to six coccoliths. Second, we used Euler’s
formula and the software CaGe to analyze the coccolith topology on the
coccosphere. The simulation results on the 2D plane and 3D polyhedrals matched
very well. Therefore, the coccosphere contains at least six coccoliths to
sustain full coverage. In summary, this study validated the geometries of the coccolith
and demonstrated that the noted coccolith arrangement pattern is the only mathematical
solution to form coccospheres. We also discussed the geometric limit on the
effective coverage area of coccolith, and how coccolith number per coccosphere adjusted
to changing cell surface area during photosynthesis, respiration, and cell
division. Finally, we applied our methods to analyze the coccolith topology of
a specific coccolithophore, Braarudosphaera.
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.