Hierarchical Structure of Protein Sequence

Most non-communicable diseases are associated with dysfunction of proteins or protein complexes. The relationship between sequence and structure has been analyzed for a long time, and the analysis of the sequences organization in domains and motifs remains an actual research area. Here, we propose a mathematical method for revealing the hierarchical organization of protein sequences. The method is based on the pentapeptide as a unit of protein sequences. Employing the frequency of occurrence of pentapeptides in sequences of natural proteins and a special mathematical approach, this method revealed a hierarchical structure in the protein sequence. The method was applied to 24,647 non-homologous protein sequences with sizes ranging from 50 to 400 residues from the NRDB90 database. Statistical analysis of the branching points of the graphs revealed 11 characteristic values of y (the width of the inscribed function), showing the relationship of these multiple fragments of the sequences. Several examples illustrate how fragments of the protein spatial structure correspond to the elements of the hierarchical structure of the protein sequence. This methodology provides a promising basis for a mathematically-based classification of the elements of the spatial organization of proteins. Elements of the hierarchical structure of different levels of the hierarchy can be used to solve biotechnological and medical problems.