Topological Nature of the Genetic Code

A model for topological coding of proteins is proposed. The model is based on the capacity of hydrogen bonds (property of connectivity) to fix conformations of protein molecules. The protein chain is modeled by an n -arc graph with the following elements: vertices (α -carbon atoms), structural edges (peptide bonds) and connectivity edges (virtual edges connecting non-adjacent atoms). It was shown that 64 conformations of the 4-arc graph can be described in the binary system by matrices of six variables which form a supermatrix containing four blocks. On the basis of correspondences between the pairs of variables in matrices and four letters of the genetic code matrices and supermatrix are converted, respectively, into the triplets and the table of the genetic code. An algorithm admitting computer programming is proposed for coding the n -arc graph and protein chain. Connectivity operators (polar amino acids) are assigned to blocks of triplets coding for cyclic conformations (G, A—in the second position), while anti-connectivity operators (non-polar amino acids) correspond to blocks of triplets coding for open conformations (C, U—in the second position). Amino acids coded by triplets differing by the first base have different structures. The third base for C, U and G, A is degenerated. Properties of the real genetic code are in full agreement with the model. The model provides an insight into the topological nature of the genetic code and can be used for development of algorithms for the prediction of the protein structure.