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Generalized crystallography and bound-water modular structures determining morphogenesis and size of biosystems

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Abstract

By now, modern science has studied natural and synthetic crystalline and amorphous materials almost completely. So, in the future, it will be oriented to investigate potential possibilities that can be realized by modeling and subsequent synthesis. The main problem that should be solved by creation of the appropriate method of such modeling is to study the structural mechanisms of self-organization, morphogenesis and functioning of these materials. The question not solved yet is: what is the basis for the crystallography generalization that would retain application of the main method of crystallography, i.e., symmetry? To solve this problem, which includes design of potentially possible structures, a new notion, “module,” was introduced. To provide stability of a solid structure, complete bonding of its atoms is necessary, which is characterized by this notion. Cooperative transformations of some crystal structures to the aperiodic symmetric ones of the same chemical composition are known, which means that a determinate transition to the non-Euclidean structures is possible. Carbon atoms in diamond-like structures and water molecules have tetrahedral symmetry, which is typical to the systems with metric based on golden section. It is natural to assume that the tetrahedral symmetry of water molecules is retained in stable noncrystal structures of bound-water as well. To distinguish, in a heterogeneous biosystem, a homogeneous solid-like system-forming component that determines the biosystem morphology and size, an axiomatic method was applied. It was shown that only bound water can serve as such a system-forming component. To model bound-water structures, the method of modular design was used. The fractal properties of bound-water structures were studied. On this basis, the similarity of forms of biosystems belonging to different hierarchy levels, the properties of protein and biocrystal structures, the water surface-layer structure and its cooperative transformation induced by contact with other phases, the structure of the surfaces of biological tissues, nondissipative propagation of energy in biosystems, and the predetermined character of prebiological evolution and the origin of life were explained.

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Notes

  1. In this paper, the record \(T_{{r_{1} }}^{{C_{2} }} sD_{3}\), \(T_{{r_{1} }} \cap D_{3} = C_{3}\) denotes that the wreath product of the С 3 group, which is a subgroup of Т, with the С 2 group results in the D 3 group (if the corresponding two- and three-fold axes are in a special position r 1 with respect to each other). The commonly accepted notation for such wreath product is C 3  C 2 = D 3, where the symbol denotes the wreath product operation [45]. However, the notation used for wreath products in this paper allows one to more clearly show the hierarchical character of the obtained structures.

  2. In a T-cluster, twisted hexacycles are slightly tightened. As a result, this ratio becomes not 1:τ2, as it should be according to the previous consideration, but 1:τ.

  3. In a rod, the T-clusters are contracted, which results in a decrease of the similarity coefficient from its theoretical value M i j  = (2j(τ + 1) + 1)i. The value of this contraction depends on the interaction potential between the atoms forming a T-cluster. For example, for the potential of tetrahedral C atoms used in HyperChem, M 11  = 6. The expression M ij  = (3jτ + 1)i used for the similarity coefficient is a good approximation, which reflects both contraction of T-clusters and relation to the golden section.

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  1. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninskii prosp. 31, Moscow, Russia, 119071

    N. A. Bulienkov & E. A. Zheligovskaya

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Dedicated to A. L. Mackey.

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Bulienkov, N.A., Zheligovskaya, E.A. Generalized crystallography and bound-water modular structures determining morphogenesis and size of biosystems. Struct Chem 28, 75–103 (2017). https://doi.org/10.1007/s11224-016-0837-3

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