Symmetry Transformations in Metazoan Evolution and Development

Abstract

In this review, we consider transformations of axial symmetry in metazoan evolution and development, the genetic basis, and phenotypic expressions of different axial body plans. In addition to the main symmetry types in metazoan body plans, such as rotation (radial symmetry), reflection (mirror and glide reflection symmetry), and translation (metamerism), many biological objects show scale (fractal) symmetry as well as some symmetry-type combinations. Some genetic mechanisms of axial pattern establishment, creating a coordinate system of a metazoan body plan, bilaterian segmentation, and left–right symmetry/asymmetry, are analysed. Data on the crucial contribution of coupled functions of the Wnt, BMP, Notch, and Hedgehog signaling pathways (all pathways are designated according to the abbreviated or full names of genes or their protein products; for details, see below) and the axial Hox-code in the formation and maintenance of metazoan body plans are necessary for an understanding of the evolutionary diversification and phenotypic expression of various types of axial symmetry. The lost body plans of some extinct Ediacaran and early Cambrian metazoans are also considered in comparison with axial body plans and posterior growth in living animals.

Aperiodic crystals in biology

“…A suitable example of a geometrical fractal structure, exhibiting a characteristic scaleinvariance symmetry with a scale factor λ = 1 + 2 √ 3/3 is shown in figure 1(A). Various biological structures have been shown to display fractal-like properties, such as an approximate scale invariance over a restricted spatial scale, and a spatial distribution which can be reasonably measured in terms of suitable fractal dimensions [9]. Nevertheless, ideal mathematical fractals are homogeneous structures exhibiting exact scaleinvariance symmetry, whereas in actual biological patterns we observe the emergence of novel structural designs at a given scale which are not present in the scales below and/or above.…”

“…The α-keratin proteins are organized as coiled coils, consisting of two helically wound chains of polypeptides, each one adopting the α-helix conformation structure, causing the duplex chain to twist and exhibit a helical shape about 2 nm in diameter. These dimers then assemble to form the protofilament, and four protofilaments organize into the so-called intermediate filament (figure 3(C)), showing an intermediate size (7)(8)(9)(10) nm in diameter) between microfilaments (7 nm) and microtubules (24 nm) [18]. For β-keratin, the pleated-sheet arrangement (figure 3(D)) consists of laterally packed β-strands which can be parallel or antiparallel (more stable), and the resulting chains are held together by intermolecular hydrogen bonds.…”

“…These dimers then assemble to form the protofilament, and four protofilaments organize into the so-called intermediate filament (Fig. 3C), showing an intermediate size (7)(8)(9)(10) nm in diameter) between microfilaments (7 nm) and microtubules (24 nm) [18]. For β-keratin, the pleated-sheet arrangement (Fig.…”