METHOD FOR ASSESSMENT OF THE CHIRALITY OF PROTEINS AND PHENYLALANINE NANOTUBES AS AN EFFECTIVE TOOL OF NANOBIOENGINEERING
The work is devoted to the consideration of regularities of spatial structure formation in proteins and their application in nanobioengineering. Methods for estimating the chirality of regular and irregular protein structure, as well as helical nanotubes based on phenylalanine are presented. The magnitude and the chirality sign of α-, 310-, and π-helices, β- and α-turns, Ω-loops, and right-handed and left-handed phenylalanine nanotubes have been calculated. The obtained results can be used to control the assembly of natural and artificial proteins.
The regularity of chirality sign reversal in the structural-functional hierarchy of protein structures left (L)-right (D)-left (L)-right (D) has been revealed relatively recently [1, 2]. To confirm this theory, vectorial methods have been developed to determine chirality of regular and irregular protein structures of different hierarchical levels [3-7], which are formed from initially left-handed chains of amino acid residues in the self-organization process.
When a polypeptide chain is stacked into a three-dimensional structure, it forms spirals, superspirals, twists, and loops (Fig.1).
The α-, 310- and π-helices are considered as regular secondary structures, while β- and α-turns, and Ω-loops are considered as irregular ones. While regular structures form the protein framework during folding, irregular structures act as a link between regular secondary structures, constitute 30–50% of the secondary structure of globular proteins and are often present in active centres of protein, contributing to specific interactions between molecules. Development of the author’s method for assessing the sign and magnitude of the different protein structures chirality has improved our knowledge of their structure and, therefore, functions, which can be directly applied in protein design.
The method based on dipole moment vectors enables to calculate chirality of phenylalanine helical nanotubes , which are biomolecular nanostructures that are attractive targets in various fields of biomedicine and biotechnology. Artificial peptides, like natural peptides, are capable of self-assembly depending on a particular function (e.g. cell proliferation axon regeneration, stem cell culture, DNA binding, etc.). Formation of helical structures of diphenylalanine based on phenylalanine amino acid dipeptides (F or Phe) [9–13] present an example of self-assembly of complex biomolecular structures. It was found that the FF dipeptides form exactly spiral nanotubes (PNT) with different chirality [14–16]. At the same time, it turned out that phenylalanine molecules themselves can also form nanofibrils and nanotubes [17, 18]. Diphenylalanine dipeptide and peptide nanotubes (PNT) based on it (FF PNT) are of considerable interest due to their structural and physical properties important in various fields of bioengineering. They are biocompatible and present excellent mechanical and chemical stability and piezoelectric and optical properties. These properties have made them promising candidates for various sensors and devices in nanoindustry. There is also evidence of possible applications of diphenylalanine-based nanotubes in targeted drug delivery [19, 20]. We present here model structures of phenylalanine nanotubes of different chirality  and methods to evaluate their chirality, which could also have promising applications in medicine and nanoindustry.
Protein structures are characterised by a well-defined arrangement of carbon atoms. To assess chirality sign of regular and irregular secondary protein structures, the mutual arrangement of α-carbons – anchor points in spirals, turns and loops (Fig.2) is a sufficient condition [3–5, 7]. This allows to construct consecutive vectors that connect anchor points in protein helices and calculate the magnitude and chirality sign of helical and irregular structures by the mixed vector product method .
Chirality of a superhelix – the structures at the next level of the hierarchy – depend on the direction of twisting of each individual α-helix with respect to the axis of the whole superhelix, that is, the angle between the axis of the superhelix and the axes of the forming spirals. The value of this angle is determined by the scalar product, which is negative for obtuse angles and positive for acute ones. Chirality sign of superhelix is calculated by averaging the cosine value of the corresponding angle for all spirals forming the superhelix (Fig.3) .
As the bioengineering is concerned, based on the above described technique of protein structure chirality estimation [4, 5, 7], a similar method of phenylalanine and diphenylalanine chirality determination was proposed based on distinct spatial sequence in these helices of dipole moment vectors of the individual peptide molecules [6, 7] (Fig.4).
We have analyzed 26,150 chirality structures of α-, 310- and π-helices. All studied α-, 310-helices, according to our method, are overwhelmingly right-handed  which fully agrees with a concept of chiral hierarchy of protein structures [1, 2]. The left-hand α-helices represent 0.06% of the total number of α-helices and the left-hand 310-helices represent 4.6% of the total number of 310-helices. All π-helices (structures from ) are right-handed. Also, 78 α-helices, 850 β-helices and 190 Ω-helices were considered. The results show that for all considered helices and turns the chirality measure depends linearly on the number of atoms in the helix. Given the complex spatial orientation of the loops (Fig.2, c), the value of their chirality, depending on the number of consecutive calculated residues, can change both in sign and quantitatively  (See Table 1).
Analysis of 116 superspirals showed that these structures formed from the right-hand helices are left-hand, and from the left-hand helices – the right-hand , which fully corresponds to the literature data and the chiral hierarchy concept of protein structures [1, 2].
Chirality of the turns in the spirals of right (D-PNT) and left (L-PNT) nanotubes (Fig.5) was calculated from dipole moments of individual phenylalanine (F) molecules (Fig.4c, d) of left (L-F) and right (D-F) chirality  by the semiempirical RM1 quantum chemical method [27, 28]. Nanotube models of right-hand (D-PNT) chirality were obtained from initially left-hand (L-F) phenylalanine monomers and nanotube models of left-hand (L-PNT) chirality were obtained from initially right-hand (D-F) monomers (Table 2), which also fully corresponds to the concept of chirality type change during hierarchical peptide structure complexity [1, 2].
Analysis of the considered helices and turns showed a linear dependence of chirality magnitude on the number of atoms in these structures. The spatial orientation of the loops affects chirality magnitudes of these structures: depending on the number of consecutive residues taken for the calculation, chirality can change up or down. Analysis of coiled coil superhelixes chirality demonstrated that such structures are left-handed in vast majority , and vast majority of the helices studied are right-handed, which is in good agreement with the data known from scientific literature and the chiral hierarchy concept of protein structures [1, 2].
Given the frequency of helices, superhelixes, α- and β-helixes as well as Ω-loops, this study provides a better understanding of structure formation of proteins, both natural and artificial. Correlations between amino acid sequence and structure are currently used in the field of protein design not only for helices but also for more complex structures (e.g. superhelixes). This led to considerable success in the design of de novo super helical structures, which can be a tool for controlling the assembly of both natural proteins and artificial constructs in protein engineering and materials science. The use of superspiral chirality calculation method in computational design will allow of solving some bioengineering problems.
Calculations of dipole moments of individual coils of F PNT nanotubes have shown that, similarly to change of the chirality sign in the transition to a higher level of hierarchical organization – from helical to super helical, nanotubes show a characteristic change of chirality sign – from monomer to helical nanotubes. This makes it possible to define the modes of simulation of self-assembly of both phenylalanine and other, very different amino acid sequences, as the most adequate for the formation of such artificial nanotubes . Since the helical structures chirality of nanotubes determines their biological activity, this aspect must be taken into consideration in the interaction of natural biopolymers with artificially created biochemical structures, which is particularly important in pharmacology.
The results obtained showed that the fundamentally new method for determining chirality of protein structures – regular (helical and superhelical) and irregular (turns and loops) is based on the calculation of mixed vector product of vectors, that connect the anchor points in protein structures, fully confirms the regularity of regular protein structures chirality reversal. Only mutual arrangement of α-carbons is a necessary and sufficient condition of this method. This enables to reduce, by an order of magnitude, the information block to be processed, which is a distinct advantage when processing large data quantity. The method is essential for structural analysis and protein design.
Computer ECPHS and ECSSP software have been developed to evaluate chirality of helical and superhelical structures. PrEPC functionality. The program language is Python 3.7. The graphical interface is implemented with the help of tkinter library. The program allows to load a model from a file, output a list of spiral structures, determine a sign of their chirality and produce a three-dimensional image with the help of matplotlib library. Input data are .pdb or .txt files; average calculation time is up to 50 milliseconds. The Certificates of state registration for the computer: No. 2021613546 dated 10.03.2021; No. 2021665783 dated 1.10.2021.
Based on the method of protein structure chirality determination, a method for calculation of chirality magnitude and sign of phenyl and diphenylalanine via mixed vector product of dipole moments has been developed. The results obtained for L- and D-nanotubes formed from phenylalanine correlate well with the experimental and theoretical data . Therefore, this method of calculating the magnitude and sign of chirality [3–5, 7] for different helical biomacromolecules can be successfully applied in bioengineering to estimate chirality of self-assembled helical nanostructures based on various amino acids as well as peptides and dipeptides.
Artificial proteins allow the principles of protein engineering to be defined and tested by recreating and extending the natural functions of protein structures; for their construction it is essential to determine chirality of both monomers and the more complex structures formed from them. An in-depth understanding of the interrelationships and structures of different types of proteins allows of enhancing the ability to control assembly of both natural proteins and artificial constructions in nanobiotechnology.
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Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.