Читать книгу Diatom Morphogenesis - Группа авторов - Страница 27

Microorganisms are generally not well studied in terms of quantified symmetry changes over time. Diatoms have distinct amorphous silica frustules that exhibit a variety of geometric shapes and surfaces that lend themselves to analyses of symmetries. Diatoms are pigmented protists that are considered to be a monophyletic phylum. Morphogenesis is a topic of great interest not only to phycologists but also to nanotechnologists [2.42, 2.44, 2.51, 2.85]. In girdle view, diatoms are asymmetrical because of the parent-daughter cell division that occurs within the previously formed cell. In valve view, shape and surface are both open to symmetry considerations.

We have proposed that diatoms possess “uncanny symmetry” [2.134]. By uncanny symmetry is meant that (some) diatoms in valve view (may) exhibit near perfect symmetry. It was shown that by subtracting the rotated image of a given diatom from its original image, an almost completely blacked out image would result, indicating near perfect matching of image pixels, suggesting near perfect symmetry [2.134]. Such results were obtained for Aulacodiscus oregonus and Triceratium formosum var. quinquelobata (Plate 7, Figures 1–4 in [2.134]). “The apparently high degree of perfection of this noncrystalline precipitate deserves quantification, which may prove comparable with the (small) degree of imperfection of crystalline snowflakes [2.83]” [2.134].

Centric diatoms exhibit rotational symmetry in shape and surface, but other symmetries such as dihedral symmetry are present as well. A case in point is Auliscus (Plate 5, Figure 1 in [2.134]). From dihedral symmetry, reflective symmetry of this diatom may be characterized as a 180° rotational symmetry, thereby identifying rotational symmetry as a starting point in the measurement of uncanny symmetry. That multiple symmetries occur simultaneously in centric diatom may be recovered by an uncanny symmetry measurement.

As suggested in [2.134], we propose to quantify centric diatom symmetry generally and uncanny symmetry specifically using concepts from information theory and image processing methods. Because symmetry involves the acquisition of information regarding the “balance” of an organism such as a diatom, information theory is used to develop a measure of centric diatom valve uncanny symmetry.

The incongruity of diatom morphogenesis and uncanny symmetry can be summarized in the question, why should diatoms possess uncanny symmetry? Symmetry is about pattern, and morphogenesis is about process. Why should this specific process produce a near perfect valve pattern and shape in diatoms? We propose to address this question by quantifying uncanny symmetry, quantifying the relation of uncanny symmetry to stability, and analyzing these results to determine the implications that symmetry via stability has on the diatom morphogenetic process.