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TopIntroduction
In 1953, James Watson and Francis Crick based on the analysis of diffractograms proposed a three - dimensional model of a DNA molecule consisting of two chains twisted into a spiral (Watson, & Crick, 1953 a, b). At the same time, sugar molecules and phosphoric acid residues included in the DNA molecule were also considered three - dimensional. However, it was not indicated which three - dimensional figures correspond to sugar molecules and phosphoric acid residues. According to this model, flat nitrogenous bases, being in different chains, using two complementary hydrogen bonds connected two spirals into a single whole. But how exactly the flat nitrogenous bases are located in space remained unknown. And this is despite the fact that it is these relations that determine the most important issue of the transmission of hereditary information. Recently it was found (Zhizhin, 2019 a, b) that in the vicinity of each pair of nitrogenous bases connecting nucleic acids, a polytope of dimension 13 forms. This dimension is a consequence of the combination of two sugar molecules, each of which has a dimension of 12 (Zhizhin, 2016; 2018 a, b; 2019 c, d, e) (Figure 1).
Figure 1. A polytope of a sugar molecule (B – ribose) of dimension 12
Since the number of atoms and functional groups on Figure 1 is 13, the closest convex closed figure that can be obtained from Figure 1 is a simplex of dimension 12. The dimension of the simplex is n - 1, where n is the number of vertices (Zhizhin, 2019 c). Moreover, each vertex is connected to all other vertices by edges, i.e. 12 edges emanate from each vertex. A spatial image of the B - ribose molecule is given in the article (Zhizhin, 2016). If, as a simplification, we leave, in addition to the edges corresponding to chemical bonds, only the edges of the external contour in the projection of the spatial figure onto the plane, we get an image of the B - ribose molecule, as shown in Figure 1.
Moreover, these two molecules are in different nucleic acids and, as a result, have the antiparallel direction of the edges corresponding to them polytopes. By calculating the shape of the sugar molecule, taking into account the angles between the valence bonds, it was shown that in a simplified form a polytope of dimension 12 corresponding to a sugar molecule can be depicted in three - dimensional space, as it is shown in Figure 2.
Figure 2. A simplified three - dimensional image of a sugar (B – ribose) molecule
Two such polytopes in antiparallel position form a cross - polytope of dimension 13. This polytope was called the polytope of hereditary information (Zhizhin, 2019 a, b).
Methods
In this paper investigated geometry of polytope of hereditary information to aim definition the possibilities of arranging pairs of bound nitrogen bases in the space of a polytope of dimension 13. For this, the previously simplified and complete images of the polytopic of hereditary information in projection onto a two - dimensional plane are used.
Results
It was found that each of the four planar possible canonical coupled pairs of nitrogenous bases can be located on the five coordinate planes of the polytope of hereditary information from a total of 12 of its coordinate planes. Thus, the total number of location options for the coupled planar canonical pairs of nitrogenous bases is 20, i.e. as much as there are various types of amino acids that make up proteins.