replication of five-fold symmetry within a Triceratium valve face; 5) loop networks are seen in the pores on the valve surface of the Trigonium and Triceratium valves depicted.
Figure 2.1 A drawing composed by JLP that is reminiscent of one of Mezzanotte’s scenes [2.15]. Although the scene is the whole perceived object, individual objects diatom (fish, jelly fish, boat, oars, waves, and shore) and their attributes such as shape, transparency, location, size, and texture and perspective of the scene may be viewed as perception violations.
Figure 2.2 Shape perception of Arachnoidiscus ehrenbergii from image ProvBay5_12lx450. (a-c) Shape deformation via an increasing number of points defining valve features. (d-f) Shape decomposition via an increasing number of contours defining valve features.
Symmetry has implications for evolutionary processes in animals and plants [2.54]. Symmetry may be adaptive so that active organisms or those in rapidly flowing water [2.45] will have reflective symmetry while sedentary organisms in low flow shear regimes will have rotational or dihedral symmetry. Organisms with large surface to volume ratios or repetitive parts tend to have translational symmetry (Figure 2.4). Organisms that exhibit energy efficiency have scale symmetry [2.158]. In general, symmetry is a dynamical property of organisms.
Figure 2.3 Diatom valve face symmetries. (a) Arachnoidiscus ehrenbergii-rotational; (b) Biddulphia sp.-reflective; (c) Coscinodiscus sp. microstructure-translational; (d) Asterolampra marylandica-dihedral; (e) Coscinodiscus sp. microstructure-glide; (f) Trigonium americanum-helical/spiral central area; (g) abnormal Cyclotella meneghiniana-multiple helices/spirals central area; (h) Coscinodiscus sp.-helical/spiral; (i) Actinoptychus splendens-knot (interlooping valve structure); (j) Arachnoidiscus ornatus-knot (interlocking rings under valve ribs); (k) Triceratium pentacrinus fo. quadrata-scale; (l) initial valve of Biddulphia sp. 3D valve surface-conformal symmetry or Mobius transformation; (m) Trigonium dubium-loop network; (n) Triceratium bicorne-loop network. (All SEMs by Mary Ann Tiffany). See “Recognition and symmetry” section in the text.
Figure 2.4 Double translational symmetry at two scales exhibited in a Paralia sulcata chain colony of repetitive cells. Light micrograph by Mary Ann Tiffany.
2.1.2 Symmetry and Growth
Morphogenesis has been characterized as a system of detached movement of ensembles of cells in animals in contrast to lack of detached movement via ensembles of cells in plants. That is, locomotion is one way to associate a specific kind of symmetry to motile organisms in contrast to sessile organisms which may exhibit another kind of symmetry [2.59]. Modes of growth contribute to the recognition of specific types of symmetry. Branching growth exhibits continuous symmetry decrease and increase in size during growth [2.47]. Stepwise growth and size reduction are modes of discrete growth where size increases or decreases over time. Growth changes are concomitant with symmetry changes as potential indicators of stress associated with development, morphogenesis, cytogenesis, epigenesis [2.154], and embryogenesis [2.43, 2.149], depending on evolutionary or ecological conditions. Levels of environmental or teratological stress are said to influence fitness and adaptability of an organism, although this connection has not been quantitatively or definitively formalized [2.53, 2.54, 2.35, 2.68].
Developmental instability has been associated with fluctuating asymmetry which is generally considered as small random deviations from perfect reflective (bilateral) symmetry [2.7, 2.53, 2.60, 2.87, 2.94, 2.128, 2.152]. Instability is presumed to be associated with either side of an organism and developmental processes, and genetics or environmental conditions may influence the size of the fluctuations in asymmetry [2.53]. No explicit or quantitative relation has been given connecting fluctuating asymmetry with instability as a measure of stress. Assessment using fluctuating asymmetry characterizations have been made on a population (species) level and has not been carried out with individuals or at interspecific or higher taxonomic levels [2.53, 2.54].
2.1.3 Diatom Pattern Formation, Growth, and Symmetry
Diatoms are unicellular microalgae that are known for their exquisitely ornamented hydrated silica frustule (cell wall) with geometric intricacies. At a molecular level, ornamentation on the valve surface emanates from silicic acid precipitation [2.47] and interaction with proteins in the silica deposition vesicle (SDV) and silica deposition through the SDV membrane (known as the silicalemma) [2.50, 2.142]. Valve surface patterning occurs as a diversity of geometric structures [2.98]: the multitude of species-specific forms with various symmetries. Anatomically, a diatom frustule is composed of two close-fitting thecae (valves) subtended by cingulae (girdle bands) [2.119, 2.150, 2.151]. During reproduction, the cell undergoes expansion as two daughter cells are created, with each daughter half-cell acquiring each half of the mother cell and one half (valve) of the frustule [2.119]. Each new valve is constructed within an SDV within each daughter cell. Because one valve fits inside the other (like petri dishes) and each daughter cell builds its new valve within the perimeter of the valve it inherited, one daughter cell is usually smaller in size than the mother cell (but cf. [2.117]), and the size diminution process continues until a developmental limit is reached according to the MacDonald-Pfitzer rule [2.90, 2.111, 2.112], which may correlate with a minimal organelle content [2.97]. At this point, size is restored via sexual reproduction and auxosporulation and from this, an initial cell is produced which in turn produces the vegetative cell [2.119].
Diatom symmetry formation is closely tied to pattern formation. Models of pattern formation have been developed that consider diffusion limited precipitation in non-equilibrium conditions where silica diffuses within the thin SDV depositing silica initially on the midring in centric diatoms or the midrib in pennate diatoms [2.47, 2.109]. This process has been observed to take about 10 minutes and is followed by thickening of the valve surface, which occupies an additional 6 hours [2.47]. Alternatively, pattern formation has been modeled as phase separation of two hypothesized liquids [2.82, 2.138] so that the repetitive honeycomb and pore patterns formed in some diatoms occur because of the pH regime and molecular reaction during silica deposition [2.76]. The third phase, the actual solid precipitated silica, is not included in this model [2.82]. In an alternate computer simulation, albeit confined to pore occlusions, a single fluid is involved (cf. concentrating “mother liquor” [2.47]), with solid silica particles free to “redissolve” after precipitation [2.161, 2.162]. This is similar to a simulation of diatom costae that permitted surface diffusion of silica particles along the precipitate surface, after they adhered to it, to approximate sintering [2.47]. The balance between precipitation and sintering has been simulated, using the language of “diffusion limited” versus “reaction limited” [2.25]. The main difference is whether silica particles continued to move in the medium [2.25] or along the surface of the precipitate [2.47]. Pore occlusion simulations [2.25] parallel simulation of precipitation with a centric diatom’s midring [2.47]. Spine formation has been modelled as “a combination of membrane and cyto-skeletal activities creating a mold for silica deposition” [2.11], where the silica presumably sinters. A model has been proposed that regards the SDV, in conjunction
