Abstract
The essay is dedicated to the relation of symmetry and asymmetry-chirality in Nature. The Introduction defines symmetry and its impact on basic definitions in science and human activities. The following section Chirality of molecules reveals breifly development of notion of chirality and its significance in living organisms and science. Homochirality is a characteristic hallmark of life and its significance is presented in the section Homochirality of Life. Proteins, important constituents of living cells performing versatile functions are chiral macromolecules composed of L-amino acids. In particular, the protein assemblies are of a great importance in functions of a cell. Therefore, they have attracted researches to examine them from different points of view. Among proteins of known three-dimensional structures about 50–80% of them exist as homomeric protein complexes. Protein monomers lack any intrinsic, underlying symmetry, i.e. enantiomorphic protein molecules involve left-handed amino acids but their asymmetry does not appear to extend to the level of quaternary structures (homomeric complexes) as observed by Chothia in 1991. In the section Homomeric assemblies we performed our analysis of very special cases of homomers revealing non-crystallographic symmetry in crystals. Homochiral proteins can crystallize only in enantiomorphic space groups. Among 230 existing space groups 65 are enantiomorphic containing limited symmetry elements that are rotation and screw-rotation axes. Any axis of rotation symmetry of a crystal lattice must be two-fold, three-fold, four-fold, or six-fold. Five-fold, seven-fold, and higher-fold rotation symmetry axes are incompatible with the symmetry under spatial displacement of the three-dimensional crystal lattice.
Highlights
The essay is dedicated to the relation of symmetry and asymmetry-chirality in Nature
Five-fold, seven-fold, and higher-fold rotation symmetry axes are incompatible with the symmetry under spatial displacement of the three-dimensional crystal lattice
The operation that is not compatible with the periodicity of a crystal pattern, the term non-crystallographic symmetry (NCS), commonly used in biological crystallography is not welcomed in fundamental crystallography.) In the case of space group symmetry the periodicity of the unit cell greatly reduces the possible rotational symmetry to 2, 3, 4 and 6-fold symmetry axis, whereas in the local symmetry these rotations are, in principle, allowed to be of any order
Summary
Symmetry is one of the most powerful concepts in science and can be used to describe animate and inanimate objects of nature and man-made ‘products’. The symmetry breaking leads to new orders and structures, and transitions from unstable to balanced states involving processes of self-assembling governed by the laws of nonlinear dynamics. Symmetry and chirality have been recognized in Nature since the prehistoric times (Figure 5). The symmetry of an object is defined in terms of transformations that bring the object into its initial form; it means that the object is unchanged or invariant upon transformation Such transformations can be operated by rotation, inversion, and reflection (mirror plane) (Figure 6). Proteins that are chiral molecules, representing asymmetry, can be assembled into homomeric, symmetric structures. The term chirality (in Greek means hand; Figures 13 a) and b) has been saved from the past to the present days It originates from Lord Kelvin in 1884 [23]. Kenji Mori for his seminal contributions to the importance of chirality of pheromones in signalling processes
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