The Structure of the Polytope of Hereditary Information

Introduction

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, 1953a, 1953b). 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 proved that sugar molecules and phosphoric acid residues have the highest dimension (Zhizhin, 2016, 2018a, 2018b). The phosphoric acid residue has a dimension of 4, and the sugar molecule has a dimension of 12. In this regard, the geometry of nucleic acids was considered taking into account the highest dimension of the components (Zhizhin, 2018b, 2019a, 2019b, 2020). In addition, for the convenience of images, a simplified three-dimensional model of a sugar molecule was built on the basis of a full twelve-dimensional model of a sugar molecule (Zhizhin, 2019c). This model can be used in further constructions, not forgetting the dimension of its complete model. This model was used to construct images of single nucleic acid helices. When passing to the analysis of nucleic acids consisting of two linked helices, it is necessary to take into account the emerging anti-parallelism of geometric elements in linked spirals (Zhizhin, 2019c). In this article, continuing the research begun in the works (Zhizhin, 2018b, 2019d), it will be shown that sugar molecules located in linked nucleic acid helices form a polytope of dimension 13 of the type of cross-polytope in which there are exactly 12 coordinate planes. In these coordinate planes outlined by rectangles with antiparallel edges, exactly 12 compounds of nitrogen bases currently known can be located (Spirin, 2019). The image of the polytope and its coordinate planes is obtained, its structure is determined. This polytope can be called the polytope of hereditary information, since it transmits hereditary information from one spiral to another using a sequential alternation of nitrogenous bases.

It has been shown that the polytopic of hereditary information is characterized by a powerful stream of incidents between geometric elements of different dimensions (Zhizhin, 2019c), providing an extremely intense exchange of information between the components of nucleic acids. The evidence of the existence of such an exchange of information can be found in the recently discovered inheritance of changes not related to the modification of sequences in DNA, i.e. with methylation - the binding of a methyl group CH₃ to the nitrogenous base of DNA (Mancuso, 2017; Lindquist et al., 2016; Sanbonmatsu et al., 2016).