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.

In this paper, we propose and use a new approach for a relatively simple technique for conducting MD simulation (MDS) of various molecular nanostructures, determining the trajectory of the MD run and forming the final structure using external force actions. A molecular dynamics manipulator (MD manipulator) is a controlled MDS type. As an example, the applicability of the developed algorithm for assembling peptide nanotubes (PNT) from linear phenylalanine (F or Phe) chains of different chirality is presented. The most adequate regimes for the formation of nanotubes of right chirality D from the initial L-F and nanotubes of left chirality L of their initial dipeptides D-F modes were determined. We use the method of a mixed (vector–scalar) product of the vectors of the sequence of dipole moments of phenylalanine molecules located along the nanotube helix to calculate the magnitude and sign of chirality of self-assembled helical phenylalanine nanotubes, which shows the validity of the proposed approach. As result, all data obtained correspond to the regularity of the chirality sign change of the molecular structures with a hierarchical complication of their organization.

In this study we consider the features of spatial-structure formation in proteins and their application in bioengineering. Methods for the quantitative assessment of the chirality of regular helical and irregular structures of proteins are presented. The features of self-assembly of phenylalanine (F) into peptide nanotubes (PNT), which form helices of different chirality, are also analyzed. A method is proposed for calculating the magnitude and sign of the chirality of helix-like peptide nanotubes using a sequence of vectors for the dipole moments of individual peptides.

The quantitative evaluation of the chirality of macromolecule structures remains one of the exciting issues in biophysics. In this paper, we propose methods for quantitative analysis of the chirality of protein helical and superhelical structures. The analysis of the chirality sign of the protein helical structures (α-helices and -helices) is based on determining the mixed product of every three consecutive vectors between neighboring reference points—α-carbons atoms. The method for evaluating the chirality sign of coiled-coil structures is based on determining the direction and value of the angle between the coiled-coil axis and the α-helices axes. The chirality sign of the coiled coil is calculated by averaging the value of the cosine of the corresponding angle for all helices forming the superhelix. Chirality maps of helical and superhelical protein structures are presented. Furthermore, we propose an analysis of the distributions of helical and superhelical structures in polypeptide chains of several protein classes. The features common to all studied classes and typical for each protein class are revealed. The data obtained, in all likelihood, can reflect considerations about molecular machines as chiral formations.

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