Quantitative approach to the assessment of chirality in hierarchies of protein structures

An approach to the quantitative assessment of the degree of chirality in the hierarchical structures of macromolecular systems is developed. Earlier, the authors revealed a phenomenological regularity: beginning with the level of the "left" asymmetric carbon in the amino acid residues of the primary structure of proteins, the chiral character of the L-D-L-D structural levels alternates: the "right" α-helices of the secondary structure forming a left supercoiling, the quaternary structure of microfilaments – the "right". The proposed approach makes it possible in general to quantify the sign and degree of chirality of the secondary protein structures. A sufficient condition for the method for determining the sign of the chirality of the secondary structure is the choice of the relative arrangement of α-carbons, which allows one or two orders to reduce the amount of information processed compared with the complete description of the system. As a result of the analysis of right and left spiral secondary structures, it is shown that the angle between the direction vector and the sum of vector products reveals the direction of twist of the spiral. Along with the right α-helices and the left polyproline helices, which, forming themselves, form the right super-spirals in the collagen, β-structures were analyzed. Data on the spatial structure are displayed on special "chirality maps", which demonstrate the existence of isolated regions of existence for different types of helicity. The method is implemented as a computer program in Python 3.6 using the SciPy library and can be applied to nucleic acids.