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The Uncanny Symmetry of Some Diatoms and Not of Others: A Multi-Scale Morphological Characteristic and a Puzzle for Morphogenesis*

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Janice L. Pappas1+, Mary Ann Tiffany2 and Richard Gordon3,4

1Department of Mathematics, Michigan Math and Science Scholars, University of Michigan, Ann Arbor, MI, United States

2Dept. of Biology, San Diego State University, San Diego, CA, United States

3Gulf Specimen Marine Laboratory & Aquarium, Panacea, FL, United States

4C.S. Mott Center for Human Growth & Development, Department of Obstetrics & Gynecology, Wayne State University, Detroit, MI, United States

Abstract

Organism symmetry via body plan is the balanced arrangement of structural features (internally or externally) that is definable in terms of dimension (2D or 3D) and geometry (contours, surfaces, boundaries). Symmetry is evident at the endpoint of morphogenesis and at each scale, from genes to cells to organism to population or higher taxonomic level. Symmetry may change from juvenile to adult stages as well as between sexual and asexual reproduction. The arrangement of morphological features reiterates symmetry antecedents so that at any given time, degrees of symmetry may be directed, random or chaotic outcomes signifying degrees of instability throughout morphogenesis.

With their geometric surface ornamentation, diatoms exhibit a high degree of rotational and/or reflective symmetry depending on the ontogenetic path, either commencing with an annulus or a sternum for centrics and pennates, respectively. Sometimes this symmetry is remarkable, whence we call it “uncanny symmetry”. Using centric diatom examples, surface features are used in uncanny rotational symmetry assessment via digital image processing techniques and include analysis of vegetative valve formation stage, initial valves, and abnormally developed cells. Quantitatively, entropy as digital image information content is related to symmetry states and is used to determine random and chaotic instability in morphogenesis.

Keywords: Rotational symmetry, reflective symmetry, centric diatoms, diatom morphogenesis, fluctuating asymmetry, uncanny symmetry, entropy, developmental instability

Diatom Morphogenesis

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