Читать книгу Diatom Morphogenesis - Группа авторов - Страница 40

Symmetry in diatoms is a characteristic of morphology that is evident at various scales. Discrete or continuous symmetry [2.167] as well as local or global symmetry are issues of scale. In our study, we used discrete measures at a local scale. Symmetry may be scale dependent over the 3D morphology of the organism. For different structural parts, e.g., honeycomb, repeating hexagonal pores in layers [2.138], of the diatom valve, there may be a hierarchical cumulative symmetry of morphological characters at the nano to micro to macro scale, across the valve face as a result of epigenesis with respect to morphogenesis, differentiation, and growth [2.32]. Hierarchical cumulative symmetry may also change from organelle to the whole diatom cell as a result of cytokinesis and mitosis with respect to morphogenesis. At the 3D surface and boundary shape of the cell, diatoms have structural symmetry changes at each developmental stage as each subsequent whole daughter cell undergoes size diminution, auxosporulation, and production of an initial cell. Our focus on centric diatom vegetative cells and valve formation as well as vegetative and initial cell symmetry was used in assessing symmetry during diatom morphogenesis.

Nano-, micro-, or macro-scale dependent symmetry may be evident as individual or groups of structural features that may not have the same symmetry at the same time (Figure 2.3). Concomitantly, these different kinds of symmetry are measurable implicitly at multiple scales. By isolating sections of the valve face in terms of micro or nanostructure, each kind of symmetry can be measured. Scale dependency occurs if a valve formation sequence is not monotonic or linear. For example, centric diatom symmetry in Cyclotella meneghiniana may be an example of scale dependency (Figure 2.19). In some cases, scale symmetry as scale invariance may be present (Figure 2.3k). Pattern repetition at multiple scales and fractal scaling may be determined by testing for the Hausdorff dimension [2.29].