The chirality quantification is of great importance in structural biology, where the differences in proteins twisting can provide essentially different physiological effects. However, this aspect of the chirality is still poorly studied for helix-like supramolecular structures. In this work, a method for chirality quantification based on the calculation of scalar triple products of dipole moments is suggested. As a model structure, self-assembled nanotubes of diphenylalanine (FF) made of L- and D-enantiomers were considered. The dipole moments of FF molecules were calculated using semi-empirical quantum-chemical method PM3 and the Amber force field method. The obtained results do not depend on the used simulation and calculation method, and show that the D-FF nanotubes are twisted tighter than L-FF. Moreover, the type of chirality of the helix-like nanotube is opposite to that of the initial individual molecule that is in line with the chirality alternation rule general for different levels of hierarchical organization of molecular systems. The proposed method can be applied to study other helix-like supramolecular structures.

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The origin of chiral asymmetry in biology has attracted the attention of the research community throughout the years. In this paper we discuss the role of chirality and chirality sign alternation (L-D-L-D in proteins and D-L-D-L in DNA) in promoting self-organization in biology, starting at the level of single molecules and continuing to the level of supramolecular assemblies. In addition, we also discuss chiral assemblies in solutions of homochiral organic molecules. Sign-alternating chiral hierarchies created by proteins and nucleic acids are suggested to create the structural basis for the existence of selected mechanical degrees of freedom required for conformational dynamics in enzymes and macromolecular machines. Author Contributions: Conceptualization, V.A.T.; investigation, E.V.M.; writing-original draft preparation, V.A.T. and E.V.M. All authors have read and agreed to the published version of the manuscript.

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We review a general regularity concerned with the spontaneous formation of alternating-sign L–D hierarchies of chiral structures that are initially nonequilibrium due to homochirality. Mechanical, hydrodynamic, macromolecular, and liquid-crystal systems, as well as proteins and nucleic acids, are considered. Biomacromolecule chirality is related to the presence of an asymmetric carbon atom and, further, to the formation of helical and superhelical intra- and supramolecular structures. Chirality is a physical vehicle that generates stratification and folding in biological macromolecular systems. The hierarchies of alternating-sign chiral structures underlie the formation of a periodic molecular-biological system of cells.