Features of molecular self-assembled helix peptide nanotubes based on some amino acids molecules and their dipeptides: molecular modelling studies

Features of molecular self-assembled helix peptide nanotubes based on some amino acids molecules and their dipeptides: molecular modelling studies | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Features of molecular self-assembled helix peptide nanotubes based on some amino acids molecules and their dipeptides: molecular modelling studies Vladimir Bystrov This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3952941/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The paper considered the structural and dipole moments features of some amino acids that are important in the formation of the di-peptides and peptide nanotubes on their basis. The influence of the features of their chirality (left L and right D) and the alpha-helix conformations of amino acids also were taken into account. In particular, amino acids with aromatic rings were considered, such as phenylalanine (Phe/F), and branched-chain amino acids (BCAAs) Isoleucine (Ile/I), Leucine (Leu/L), as well as corresponding dipeptides based on them. On their basis, the features and properties of dipeptide structures and peptide nanotubes (PNTs) were investigated using computational molecular modeling and quantum-chemical semi-empirical calculations. Their polar, piezoelectric and photoelectronic properties and features were studied in details. The results of calculations of dipole moments and polarization, as well as piezoelectric coefficients and band gap width, for different types of helical peptide nanotubes are presented. The calculated values of the chirality indices of various nanotubes are given, depending on the chirality of the original dipeptides - the results obtained are consistent with the law of changes in the type of chirality as the hierarchy of molecular structures becomes more complex. Calculations were also carried out on the influence of water molecules in the internal cavity of nanotubes on their physical properties. Comparison of the results of these calculations by various computational chemistry methods with the available experimental data were also be given. аmino acids dipeptides peptide nanotubes molecular modeling quantum semi-empirical methods chirality dipole moments polarization piezoelectricity band gap width Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction One of the important and current topics of modern molecular physics, biophysics and nanobiotechnology is the creation of artificial nanostructures based on the molecules of various amino acids (AA). It is known that AA are capable of the self-assembly into different complex molecular structures. Such self-assembly of molecular structures based on AA is a remarkable phenomenon of living nature, arousing great interest of many researchers involved in the study of the self-organization of molecules, the development of promising new nanotechnologies and nanomaterials [ 1 – 3 ] using the modern methods of molecular modeling, computational and theoretical chemistry in this area [ 4 ]. Complex distributions of electric charges and dipole moments, long-range force fields inherent in AA [ 5 , 6 ], lead them inevitably to the different chemical-physical interactions, self-assembly into various more complex molecular structures, such as dipeptides, polypeptides and proteins, and organize them into hierarchical molecular-crystalline nanostructures, including such as peptide nanotubes (PNTs) [ 6 – 8 ]. Of course, a lot here also depends on the external conditions of the environment (aqueous solutions) in which this or that set of AA molecules is located. But the features of such self-assembled structures and their properties are also influenced by the internal characteristics of the set of the initial molecules, such as, e.g., the chirality of the AA included in them [ 6 , 9 ]. Thus, an important rule for changing the chirality of molecular structures was recently established, according to which the molecular structures of lower and higher hierarchical levels of organization differ in the type of their chirality [ 9 , 10 ] - here there is a change in the sign or type of chirality L ↔ D (change between the left "L " and right "D" chirality types: this terms is from the Latin "laeva" - "L" - left, and "dextra" - "D" - right) [ 8 – 10 ]. This is especially evident in spiral structures. This is especially evident in helix-shaped structures. This striking difference between nanostructures is rooted in rather deep physical reasons for parity violation of the weak interactions, which determine a small but measurable difference in the internal properties of the enantiomers (as was recently established) [ 11 – 17 ]. This symmetry breaking is already evident at the level of the weak nuclear interactions - electrons resulting from a subatomic process known as b-decay are always left-handed. This means that their spin (quantum angular momentum of elementary particles) will always be opposite to the direction of electron motion - these are “left-handed” spin-polarized electrons [ 13 ]. Such polarized electrons are indeed capable of initiating chiral-selective chemical reactions in the gas phase [ 18 , 19 ]. Perhaps this effect is the source of the accumulated fact: the predominant existence in living organisms of “left-handed” amino acids and “right-handed” DNA molecules - this is the so-called homochirality of life [ 8 – 10 ]. Among the possible explanations for the reasons for such homochirality of biomacromolecules, there is the Vester-Ulbricht hypothesis that the homochirality of life is a consequence of precisely the spatial asymmetry of the weak interaction of elementary particles [ 19 ]. Based on this hypothesis, the authors of a recent work [ 20 ] evaluate the possibility generation of homochiral polymers in the environment of molecular clouds of the cosmic nebula. Chiral polymers can be induced in the environment of such a molecular cloud at ultra-low temperatures in deep space, since the polarization and stereoselectivity of chiral biomolecules here is much less than that of homeothermic ones. Also, the pure left-handed polymer chain may be significantly longer in such a low-temperature environment. In this regard, a deeper understanding of the self-organization and physicochemical properties of the molecular helix-shaped nanotubes based on various amino acids and dipeptides is of great importance for the physics of molecules, molecular biology and materials science [ 1 – 10 ]. Currently, a significant amount of experimental data has been accumulated on the structure and properties of nanostructures based on various AA and dipeptides. Among others, the most studied PNTs are those based on phenylalanine AA (Phe or F) and its dipeptide diphenylalanine (FF) [ 21 – 26 ]. These studied FF-PNTs quickly self-organize and are easily grown in an aqueous environment, and various external conditions affect their thickness and length [23, 27, 28]. It has been shown that FF-PNTs have piezoelectric [25, 26, 29, 30], pyroelectric [31], ferroelectric [21,25,29,32] and pronounced photoelectronic properties [32–36], which differ here for dipeptides of different chirality [ 9 , 10 ]. It is also interesting that these properties are also influenced by water molecules trapped in the internal cavity [22, 25, 26, 37–39]. These structures are promising for many applications in nanotechnology, nanoelectronics, pharmacology and biomedicine [ 3 , 7 , 10 ]. Besides FFs with aromatic rings, branched chain dipeptides such as dileucine (Leu-Leu, LL) and diisoleucine (Ile-Ile, II) can also form PNT [ 6 ]. However, most of these nanostructures studied experimentally are so far based on AA and dipeptides of only “left-handed” chirality (L-AA) [40–42]. A useful exception here is a recent study of “right-handed” D-FF PNT [ 23 ]. Crystal structures of such nanostructures (“left-handed”, L, chirality) were obtained by Görbitz, [40, 41] and deposited in the CCDC database [42]. Therefore, computational molecular modeling is now becoming the main tool for studying such PNTs, predicting their structural features and physical properties, taking into account their different types of chirality, for future experimental studies [ 6 , 10 , 21 , 22 , 17 , 24 – 26 ]. In our previous works [ 21 – 26 ], we developed computer models of L-FF and D-FF PNTs, using various computational quantum-chemistry methods, including semi-empirical methods (AM1, PM3 etc.) and methods of density functional theory (DFT), and found good agreement between their calculated properties and known experimental data. For example, computer modeling has shown that nanotubes in the form of a stack of parallel rings [ 10 , 24 – 26 ], a typical scheme for the self-assembly of cyclic peptides [43, 44], are less preferred in the case of the FF-PNT than those formed from helix-shaped coils [10, 23, 24–26, 40, 41]. Thus, a kind of the topological transition [ 10 ] to a more stable organization of these biomacromolecules was demonstrated here. It is also important that the chirality indices of the PNTs, determined using the developed original approach [45] based on the calculation of the dipole moments of the dipeptides forming the helix coils of the helix-shaped nanotube, confirmed the rule for changing the type of chirality [ 9 ]: nanotubes based on the “left” dipeptides L-FF demonstrate “right-handed” D-chirality type, and vice versa, nanotubes based on the right-handed chirality D-FF dipeptides have a left-handed L-chirality type. Thus, based on our previous work, in this article we present the constructed helix-shaped nanotubes based on the LL and II dipeptides of the different chirality (L and D), calculated their chirality indices, dipoles moments, polarizations, piezoelectric and photoelectronic properties. In addition, the influence of water molecules confined inside the nanochannels of these PNTs was investigated. Modeling and all calculations were carried out using quantum chemical semi-empirical methods implemented in the HyperChem package [46]. The initial structure of “left-handed” PNTs is built on the basis of available experimental data using DFT approaches, while artificial “right-handed” PNTs are constructed by analogy, also taking into account the available data on FF PNTs of both types of their chirality. In general, the goal of the work is to analyze a number of such self-organized molecular structures based on AA and their dipeptides with different initial chirality (such as, e.g., L-LL and D-LL, L-II and D-II), calculations of their properties, including predictions of ones for a number of artificially constructed models based on D-AA, using modern computational methods. 2. Main computational details and approaches The main tool for molecular modeling of all studied nanostructures in this work was the HyperChem 8.01 software package [46]. Various computational methods were used, including molecular mechanics methods (MM: MM+, Amber, BIO CHARM from HyperChem package [46]), but mainly quantum mechanical (QM) calculations were used here in the Hartree-Fock (HF) self-consistent field (SCF) approach with various semi-empirical methods (AM1 [47, 48], PM3 [49–51], RM1 [52, 53]) in the restricted Hartree-Fock (RHF) approximation and, in some cases, also in the unlimited Hartree-Fock (UHF) approximation [46]. The use of these methods for molecular modeling makes it possible to obtain the minimum total energy of the molecular system under study on the potential energy surface (PES) of the simulated systems. As a result, all the studied molecular systems achieved an optimal atomic configuration. Optimization of molecular systems and the search for their optimal geometry is carried out in this work using the Polak–Ribeire algorithm (conjugate gradient method), which determines the optimized geometry at the point of their minimum total energy (using PES) [46]. For such optimized structures, dipole moments and electronic energy levels were then calculated. In addition, in this work, the construction of correct models of helix-like molecular structures was carried out in direct correlation with known X-ray diffraction data for structures based on diphenylalanine (FF), both left L-FF [40] and right D -FF [ 23 ] chirality, and for dileucine structures too (LL, but with the chirality known here so far only for the left L-LL [40, 41]). The original structural data for L-LL, D-FF and L-FF were taken from the Cambridge Crystallographic Data Center1 (CCDC) crystallographic database [42]. These data correspond to CCDC No. 16337 for L-FF [40, 42] and CCDC No. 1853771 for D-FF [23, 42]. Based on these data, models of crystallographic cells were constructed and calculated using density functional theory (DFT) methods in the Vienna ab initio Simulation package (VASP) program [54] in our works [ 24 – 26 ] for L-FF and D-FF, as well as for L-LL, which were then transferred to the HyperChem workspace [46] for molecular modeling and all quantum chemical calculations. Currently, we also carry out calculations using DFT methods in Quantum ESPRESSO [55]. Artificial structures based on D-LL, L-II and D-II were built directly in the HyperChem “work-space”. In a some of our work [34], we also used other approaches, including semi-empirical methods PM6, PM7 from the MOPAC package (MOPAC2016) [56], and there we also compared the results of all these different approaches and showed their comparability. In this article, in all current calculations of the polar, piezoelectric, electronic and optical properties of the molecular structures of nanotubes, quantum mechanical semi-empirical methods are used: AM1, PM3, RM1 [47–53] from the HyperChem package [46]). 3. Dipole moments and polarization of a number of different amino acids As mentioned above, all amino acids (AA) have their own electrical properties and dipole moments [57,58], which interact with each other during the self-assembly of amino acids or their dipeptides and polypeptides into more complex molecular structures [ 3 , 6 , 10 ]. These could be, for example, molecular crystal structures. For example, such as molecular crystals in various polymorphic forms based on Glycine AA [6,59,60]. These can also be various molecular tubular helix-like structures, for example, peptide nanotubes (PNTs) based on diphenylalanine (FF) [10, 21–26, 40–42, 61–63] or even the structures of ion channels in biological membranes [64, 65]. Many of them turn out to be relevant and useful in materials science, nanoelectronics and medicine. It has now been established that many of these structures have piezoelectric and ferroelectric properties [21, 29, 63, 66–69] and are considered as an organic ferroelectrics [70]. Currently, they are being intensively studied by various methods, both experimentally and theoretically [63, 71–74]. As it is known, piezoelectricity usually arises as a result of electromechanical coupling in a given material [6,55,63]. The phenomenon is based upon the known general relation between the piezoelectric constant d ik , the electrostriction coefficient Q ik , the permittivity of the material ε, the permittivity of vacuum ε 0 , and the component of polarization P of the whole system [55, 63, 75]. For a simple case, as a first approximation for only one component of the coefficient Q 11 , the piezoelectric constant d 33 , dielectric permittivity ε and spontaneous polarization P , the relationship can be written as [5, 55, 63, 75]: d 33 = 2 Q 11 εε 0 P. (1) On this basis, we can study piezoelectricity and related changes in the dipole moments and polarization of various systems. This coupling is well known in biology – it can be observed in many biological processes: in a voltage-controlled muscle movement, in the nervous system, in ion transport, etc. [63–67, 76]. Such electromechanical coupling between electrical polarization and mechanical response and vice verse can be considered as the heart of the piezoelectric and bioferroelectric phenomena in various molecular and biological systems, including those based on the various AA. First we consider the amino acids (AA) initial properties. In HyperChem tool [46] there is a special database for all main AA and we take it for all our AA modeling and calculations in HyperChem workspace [46] (Fig. 1 a, shown L-chiral and a-helix conformation for AA; Fig. 1 b, e.g., for Glycine). One of the main features is that all AA (as well as their dipeptides) exist in the initial pristine forms (Fig. 1 b, a Glycine), but in the solutions they exist in the zwitterionic form - that is, a water molecule is added here [6,57]. For modeling these forms can be created in HyperChem workspace using an option (Fig. 1 c) and further the zwitterionic structures are used (Fig. 1 d, Glycine as zwitterion). All AA can exist in various conformation (a-helix, b-sheet, etc., Fig. 1 a) and two chirality isomers: L and D [ 6 , 9 , 10 ]. The a-helix (Alpha helix) and left-hand ( l-h ) a-helix (Left-hand alpha) conformations are used further in this our work (Fig. 1 a). The possibility of a piezoelectric effect in various amino acids was indicated earlier by Lemanov [69]. It should be noted that many of the amino acids considered by us have non-centrosymmetrical elements. This suggests a possibility of a piezoelectric effect in them. So, for example, valine, leucine, isoleucine have a symmetry group P2 1 , and alanine and phenylalanine – P2 1 2 1 2 1 , while diphenylalnine (FF) exhibits hexagonal symmetry P6 1 [6, 10, 23, 24, 40,42]. In addition, like crystals based on glycine and FF structures, these all AA have high polarizability, which is manifested when exposed to an electric field. This can be investigated using simulation methods which were widely described in [6, 10, 21–26, 63]. Now we consider, firstly, the computed values of the dipole moment and polarization. We consider not all AA, but several selected AA, which are necessary for our further studies. Using HyperChem tool [46] and the database of amino acids we calculate these values using PM3 RHF method. As a result, we obtained the following data (Table 1 ). Abbreviations of AA types in Table 1 below are: Glycine – is a simplest special case (SC); all the other AA are the AA with Hydrophobic side chain (HSC): Alanine is the simplest of them; Phenylalanine is AA with a benzyl (benzene or aromatic) side chain (BSC); Leucine, Isoleucine and Valine are the branched-chain AA (BCAA). As one can see, upon transition to the Zwitter-Ionic (ZwI) form, the dipole moment D increases significantly, which is not surprising, since in this ZwI form the polar groups NH 3+ and COO − are more pronounced and are located at large distances from each other. The polarization value is calculated using relation [6, 63]: P = 3.33558255*D/V ( C/m 2 - in SI units ), (2) where V is the structure’s volume on the Van der Waals surface. As one can be seen from the results of polarization calculations given in Table 1 , these polarization values turn out to be close in magnitude to many known value for ferroelectrics [58]. Especially, large values of AA will acquire in the zwitterione form (which is not surprising, since there the dipole moment becomes very significant). However, these values are obtained here only for the minimum units - single AA. Further, we will consider and analyse larger AA formations - formation of the dipeptides and their self-assembly into ring and helix-coil structures, molecular AA nano-clusters, and various AA peptide nanotubes. 4. Dipeptides and molecular nanotubes 4.1. Dipeptides and nanotubes based on phenylalanine amino acids 4.1.1. Initial models of diphenylalanine The structure of the initial molecular model of phenylalanine (Phe or F) was taken from a special amino acid database implemented into the HyperChem program [46]. This structure of the molecular model of diphenylalanine (FF) was built in a special “workspace” of the HyperChem program and transferred to the zwitterionic form necessary for further modeling in accordance with experimental data [10, 23, 24, 40–42]. To do this, we first used the Alpha helix (a-helix) conformation of the initial amino acid F and both of its isomers of the different chirality L-F and D-F [46]. On their basis, models of dipeptide—diphenylalanine (FF)—with different chirality: L-FF and D-FF were constructed. For these two models, all necessary parameters were calculated using the quantum semi-empirical PM3 method [46–53] in the restricted (RHF) and unrestricted (UHF) Hartree–Fock approximations [46]. Their geometric optimization was also carried out using the Polak–Ribière conjugate gradient method (from the HyperChem program [46]). During this optimization, the total energy of the system is calculated at each point, depending on the coordinates of all atoms of the system, and the potential energy surface (PES) is determined [46], on which the minimum point of this total energy (or PES) is located, corresponding to the optimal position of all atoms systems. The optimized structures of the L-FF and D-FF models are shown in Fig. 2 a, b. However, the L-FF dipeptide can also be formed on the basis of another conformation of the F molecule - Left-handed ( l-h ) α-helix [ 6 , 10 , 24 ]). In this case, another dipole orientation of the L-FF dipeptide is formed. Its magnitude, direction and components, also calculated using HyperChem, are shown in Fig. 2 c, d and Table 2 . It is this conformation that turns out to be most consistent with experimental X-ray data (see below in sections 4.1.2 ). The main characteristics obtained for these models differ from each other in orientation and values of their total dipole moment (in Debye units), see Table 2 . Note also that structures based on the conformation of the F molecule as a Beta sheet (b-sheet) are also possible here. And some of the first work on modeling FF PNT used beta-sheet-based models of the FF dipeptide [10, 21, 63], as it was believed that this would be consistent with the structures of the amyloids that cause Alzheimer's disease [77]. However, it soon became clear that this FF configuration did not correspond to the obtained X-ray data, which clearly showed the conformation of α-helical structures in these PNT FFs [78], as well as the inclusion of water molecules in the internal cavity. Note that to confirm these results, ab initio and density functional theory (DFT) methods available in the HyperChem package were also used [46]. As follows from the data obtained, given in Table 2 , the parameter values for D-FF are closer in their absolute values to the parameters of L-FF ( l-h ) than to L-FF. Table 2 Calculated data for dipeptides L-FF, L-FF ( l-h ) and D-FF using the PM3 method. Dipeptides consist of 43 atoms and have a volume calculated on their Vander Waals surface. Calculation method Dipeptide chirality Amino acids conform-ation D x , Debye D y , Debye D z , Debye D t , Debye V VDW , Å 3 P , C/m 2 Total energy, a.u. RMS grad PM3 (both RHF & UHF) L-FF α-helix -10.42 -2.53 1.22 10.79 291.720 0.1234 -133.963 < 0.1 L-FF l-h α-helix 11.60 1.09 0.32 11.66 292.075 0.1332 -133.959 ~ 0.08 D-FF α-helix -11.62 1.02 0.35 11.67 291.822 0.1334 -133.959 < 0.1 The influence of the resulting initial structures and properties of these different FF dipeptides on the formation of subsequent more complex structures and FF nanotubes are discussed in the following sections. Let us immediately note that all the considered dipeptides are in their zwitterionic form and contain 43 atoms each, with active groups NH 3+ and COO − , capable of forming hydrogen bonds. Aromatic rings play a neutral but important inertial role, influencing changes in the center of mass of the entire structure. 4.1.2. Self-assembly formation of 3-dimensional molecular structures based on diphenylalanine Computational molecular modeling of more complex self-organizing nanostructures based on FF dipeptides with different chiralities (LFF and DFF), including tubular structures, was carried out at the first stage of research using HyperChem software [46]. However, in contrast to a number of early works [10, 21 , 6 3], in which models of the structures based on the β-sheet conformations were considered, here we now consider only amino acid conformations in the form of an α-helix (a-helix and left-hand (l-h) a-helix) for the original phenylalanine molecules. For all FF PNTs, we used zwitterionic molecular forms and considered, firstly, ring FF models consisting of 6 FF molecules, and secondly, our previously developed standard two-ring models of tubular PNTs, consisting of 6 FF molecules in each ring. forming a total hexagonal crystallographic structure in accordance with known experimental data [6, 10, 22–26, 40–42]. Such models of nanotubes in the form of a stack of parallel rings [ 10 , 21 ] corresponded to the typical self-assembly scheme of cyclic peptides [43, 44]. After optimization of both molecular models (LFF and DFF) for this case, they have the shape of a single ring containing 258 atoms, and consisting of 6 diphenylalanine molecules (43 atoms for each individual structural segment - the FF molecule), as well as tubular structures in the form of 2 rings (of 516 atoms) built for diphenylalanine L- and D-chirality. For all cases, geometric optimization was carried out using the Polak–Ribière conjugate gradient method. As a result, optimized structures of the PNT LFF and DFF models were obtained, similar to works [10, 21 , 24]. Calculations were carried out using the PM3 [49–51] quantum semi-empirical method using various Hartree–Fock approximations (both RHF and UHF). In some cases, similar semi-empirical methods AM1 [47, 48] and RM1 [52, 53] (included in HyperChem [46]) were used. However, further research and experimental data showed that self-assembled peptide FF nanotubes are not stacks of assembled ring structures, but rather helix-like structures with a helical pitch equal to the double period of the crystal cell of a FF-based molecular crystal, and different for L-FF and D-FF [22, 23, 25, 34, 45]. For analysis, modeling and calculations (optimization of structures, determination of their structural and energy parameters), density functional theory (DFT) approaches were also used here in these above mentioned works. Therefore, further in this work we will mainly consider the helix-shaped structures of nanotubes. Moreover, as is now well known, experimentally synthesized nanotubes (based on various amino acids and dipeptides) can contain water molecules in their internal cavity [25, 26, 78]. However, it is not always possible to experimentally detect a reliably determined number of water molecules using X-ray methods [40, 41]. Therefore, computer modeling methods and DFT calculations are used quite effectively here [ 25 ]. In particular, for FF PNT we managed to do this [44–46] and refine the number of water molecules determined in this way, which is equal to n = 21 [ 25 , 26 ]. However, now we will first of all consider models of anhydrous molecular structures of nanotubes in order to better understand their basic properties. And then we will consider the influence of water molecules on these properties and their features. Using experimental X-ray data [40–42], we will first compare them with our model structures and clarify their features in anhydrous models. Figure 3 shows the conversion of crystallographic data to model FF PNT structures in the HyperChem workspace [46], according to works [25–27, 34]. Table 3 present crystallographic data for P6 1 space group of FF structure and the corresponding parameters of inner cavity inside FF PNT. Table 3 Parameters of the internal hydrophilic cavity of PNT LFF and DFF Parameters L-FF D-FF Original data Opt. (anhydrous) Original data Opt. (anhydrous) a, Å 24.0709 23.8308(284) 23.9468 23.7877(806) b, Å 24.0709 23.8308(284) 23.9468 23.7877(806) c, Å 5.4560 5.4035(861) 5.4411 5.4022(7125) R 0 , Å 12.236 12.091 12.102 12.075 R 1 , Å 15.271(698) 15.042(076) 15.180(569) 15.030(688) R 2 , Å 12.218(349) 12.098(817) 12.135(396) 12.075(906) Etot, eV -1593.31827 -1657.64347 -1608.73564 -1657.60024 Comparing now the experimentally obtained models of a ring of 6 FF dipeptides of left L-FF and right D-FF chirality and selected (“green” colour marked) one symmetrical dipeptides on them ( Fig. 4 a, d), we obtain their configurations, which coincide in the orientation of the NH 3+ and COO − groups with the Left-handed ( l-h ) a-helix conformations for L-FF and a-helix for D-FF (Fig. 2 c, d). We will not dwell here on the ring models of the nanotubes, but will move on mainly to helix-like models, as the most consistent with established experimental data. Let us note here that the FF PNT ring model, consisting form 6 FF dipeptides, shown above in Fig. 3 and Fig. 4 is actually a projection onto the Z-plane of the helix coil of this nanotube. This is clearly visible in Fig. 5 , which represents Z and Y projections of the anhydrous FF PNT helix model, which best matches the experimental X-ray data [40, 42]. 4.2. Dipeptides and nanotubes based on leucine amino acids 4.2.1. Initial models of dileucine Similarly as above for FF consider here the molecular model of the dileucine (LL) dipeptide, based on the leucine (Leu or L) amino acid, using known experimental X-ray data for them [40–42], to construct the corresponding molecular structures of the dipeptide nanotubes based on L-LL. For D-LL PNTs, we have constructed hypothetical structures similarly to how it was done for D-FF [ 23 ]. In this case now we also use the data obtained above, that for left chirality based nanotube L-LL preferred initial L amino acid conformation must be Left-handed (l-h) a-helix. A careful and in-depth analysis of the results of comparison of helical structures for dileucine-based nanotubes, extracted from x-ray data, and constructed from the amino acid database (built into HyperChem), showed that the initial conformations of leucine with chirality L should not only be of the a-helix type, but Left-hand (l-h) a-helix (Fig. 6 , Table 4 ). Just as in FF PNT, only in this case does the required correspondence between the chirality of the helical structure and the directions of the vectors of dipole moments of both individual dipeptides and the total coil of the helix nanotube arise. Table 4 Physical properties for dileucine of various conformation using different semi-empirical methods Calculation method Dipeptide chirality Amino acids conformation D x , Debye D y , Debye D z , Debye D t , Debye Volume, Å 3 Polarization, C/m 2 PM3 RHF L-LL, l-h l-h α-helix 10.399 0.049 -4.262 11.238 243.243 0.1541 D-LL α-helix -10.334 -1.397 -0.110 10.429 244.143 0.1425 AM1 RHF L-LL, l-h l-h α-helix 10.609 0.183 -4.069 11.364 243.243 0.1558 D-LL α-helix -10.765 -1.318 0.0623 10.846 244.143 0.1482 4.2.2. Nanotube formation of the 3-dimensional molecular structures based on dileucine Similarly as for FF consider here the molecular model of the dileucine (LL) helix-like nanotube model, using known experimental X-ray data for them [40–42]. From experimental X-ray crystallographic data for dileucine of left-handed chirality L-LL [40–42], it is possible to identify a clear structure of a helical nanotube. At the same time, 4 dipeptides fit here in one turn, unlike FF PNT (Fig. 7 ). Crystallographic parameters here (for space group P2 1 2 1 2 1 ) a = 5.352 Å, b = 16.76 Å, c = 33.312 Å. Parameter a corresponds to the helix pitch along the axis of the nanotube. Artificial helix-like structures of L-dipeptides were made from the initially constructed ring-stacked models, transformed with a shift of each subsequent dipeptide along the nanotube c axis so that, when going around a helix coil, its step equals to the period of the experimental crystallographic structure along c axis. The helix-like structures based on D-dipeptides were constructed in a similar way, assuming the equivalence of the period along the c axis for L- and D-dipeptides. Figure 7 shows the structure of two-helix coils of L-LL (Figure 7 a, b) and D-LL (Figure 7 c, d) nanotubes each consisting of four LL molecules per coil. The main properties of such LL PNT will be discussed below. 4.3.1. Initial models of diisoleucine Existing experimental data for nanostructures based on the isoleucine (Ile or I) amino acid and diisoleucine (II) dipeptide have several different and rather “entangled” crystallographic structures [41, 42] from which it is not yet possible to identify a clearly defined nanotube structure. Therefore, in this work, we build artificial hypothetical models for the dipeptide based on isoleucine and spiral nanotubes based on diisoleucine, based on analogues with already known structures for FF and LL, and relying on clearly known experimental X-ray data for them. Let us consider in more detail these structures for I and II, also taking into account their different chirality L and D. Figure 8 presents molecular models of II dipeptides built on the basis of I amino acids of different L and D chiralities, also taking into account their conformation: Left-handed a-helix for I amino acids with L chirality and a-helix for I with D chrality. The dipole moment data of the L-II and D-II presented in Table 5 . Table 5 Physical properties for diisoleucine of various conformation using different semi-empirical methods. Calculation method Dipeptide chirality Amino acids conformation D x , Debye D y , Debye D z , Debye D t , Debye Volume, Å 3 Polarization, C/m 2 PM3 RHF L-II, l-h l-h , α-helix 10.477 -0.667 0.193 10.500 244.125 0.1435 D-II α-helix -11.633 0.233 -1.858 11.783 241.918 0.1625 AM1 RHF L-II, l-h l-h , α-helix 13.0570 0.678 -0.415 13.081 244.141 0.1787 D-II α-helix -12.598 -0.064 -0.998 12.598 244.659 0.1718 4.3.2. Nanotube formation of the 3-dimensional molecular structures based on diisoleucine Similarly as for FF and LL consider here the molecular model of the disoileucine (II) helix-like nanotube model, using known experimental X-ray data for them [40–42]. From experimental X-ray crystallographic data for dileucine of the left-handed chirality L-LL [40–42], it is possible to constrcut similar structure of a helical nanotube of the dilisoleucine of the left-handed chirality L-II, and further to make the same artificial modle structure for the D-II. At the same time, 4 dipeptides fit here in one turn as for LL PNT, unlike FF PNT having 6 dipeptide molecules (Fig. 9 ). 4.4. Chirality index calculation of helix-shaped nanotubes To determine the chirality of the helix-shaped structure, we use a method based on the mixed product of dipole moment vectors Di of the successive individual dipeptides that form the helix-like structure of a nanotube. This method was proposed and developed in [45]. In this case, the scalar triple product dipole moments Di of successive individual AA molecules that make up the coils of a helical PNT nanotube is used. The origin of vectors Di is taken relative to the centre of mass of the corresponding molecules. The absolute value of each dipole moment Di is $${D}_{i}=\left|{D}_{i}\right|=\sqrt{{D}_{\text{x,i}}^{2}{\text{+D}}_{\text{y,i}}^{2}{\text{+D}}_{\text{z,i}}^{2}}$$ 3 where D x,i , D y,i , and D z,i are the components of the i -th vector D i in the Cartesian coordinates. According to [45], here the sum of mixed (vector-scalar) products of dipole moments associated with the chirality of the PNT can be written as: $${c}_{\text{total}}={\sum }_{\text{i=}1}^{n-2}\left(\left[{D}_{i}{\text{,D}}_{\text{i}\text{+}1}\right]{\text{,D}}_{\text{i}\text{+}2}\right),$$ 4 It is necessary to note that the summation is taken over i in the range from 1 to n − 2, where n = 4 for one coil of LL PNT and II PNT, while for one coil of FF PNT n = 6 [45]. The c total value can be normalized to the cube of the average total dipole moment of the PNT coil, \({D}_{\text{av}}=\frac{1}{n}{\sum }_{\text{i}\text{=}1}^{n}{D}_{i}\) , to get the universal normalized measure of the chirality index: $${c}_{\text{norm}}=\frac{{c}_{\text{total}}}{{D}_{\text{av}}^{3}}\text{.}$$ 5 The sign of c norm corresponds to the PNT’s chirality type: positive c norm values correspond to the right-handed PNTs - “D”, whereas negative c norm - to the left-handed [45] - “L”. We have developed an algorithm that allows us to calculate each individual selected dipole moment of any dipeptide (LL, FF, II, etc.), leaving it surrounded by all other dipeptide’s molecules of the helix-shaped structure of the peptide nanotube. This makes it possible to obtain a more accurate calculation result, taking into account the interaction of the selected dipeptide with all other dipeptides of the PNT helix-like molecules. To build this algorithm, a special script based on TCL Tool Command Language, a part of Chemist's Developer Kit (CDK) in Hyperchem package [46], was developed. The constructed algorithm makes it possible to select any number n of dipeptides and to carry out calculations not only for one helix coil, but for any number of them, in the case of a more complex structure of the any dipeptide PNT. It is important to correctly specify the sequence of dipeptides when going around the coils of the helix, since in the helix-like structure itself their numbers can be located not one after the other, but differently. This must be checked when performing calculations in each case. This algorithm now we applied for calculation of the chirality index of the various AA and dipeptide’s PNT. Table 6 present the results for calculations of the chirality index (5) for the helix-shaped nanotubes LL PNT, FF PNT and II PNT with the initial dipeptides of the different chirality (L-LL and D-LL; L-FF and D-FF; L-II and D-II), performed using various semi-empirical methods through above mentioned algorithm. The data obtained here are calculated values of the chirality index for the nanotube's model of one coil of the helix and for models of two coils of the helix - based on FF (Fig. 5 ), LL (Fig. 7 ) and II (Fig. 9 ) dipeptides. The directions of the dipole moment vector Di of one of the dipeptides in cases of different chiralities are shown with black arrows (Fig. 9 a, c) using diisoleucine II as an example, and the directions of bypassing the coil of the helix when calculating the chirality value according to formula (5) for both chirality types are shown by the curved blue arrows (Fig. 9 a, c) for II PNT. The vectors of dipeptides and the directions of bypassing of the helical coils for model nanotubes based on LL and FF are oriented similarly (taking into account that FF forms a helix coil of 6 dipeptides, and in the case of LL, the helix coil contains 4 dipeptides). Table 6 Results of calculating the chirality index (3) of dipeptide-based nanotubes AA PNT of different initial chiralities L-AA and D-AA. Models and methds Dipeptides chirality PNT model Calculation method L-AA D-AA 1 coil of LL PNT PM3 RH 1.214 -0.519 AM1 RHF 1.209 -0.485 2 coils LL PNT PM3 RHF 3.968 -1.709 AM1 RHF 3.936 -1.582 1 coil of FF PNT PM3 RHF 1.36 −1.35 AM1 RHF 1.2622 -1.3246 2 coils of FF PNT PM3 RHF 3.1704 -3.5004 AM1 RHF 3.4857 -3.1417 RM1 RHF 3.1441 -3.4889 2coils of II PNT PM3 RHF 3.1888 -1.9349 AM1 RHF 3.1498 -2.0414 Chirality sign of a helix-shaped PNT nanotube Positive «+» Negative « - » PNT helix-shaped nanotube chirality symbol D L It should be noted here that while for the L-FF, D-FF, L-LL PNTs we have a clear basis for its helix-like structure based on experimental data [21–26, 40–42], for the D-LL PNT as well for L-II and D-II we only have an artificial hypothetical structures built on the basis of an analogy of the related structures of both LL PNT and FF PNT. As can be clear seen from Table 6 , the results obtained here show a characteristic change in the sign of the chirality upon transition to a higher level of the molecular hierarchy organization, which is observed in the structures of biomacromolecules [ 9 , 10 ]: the calculated chirality of a helix-shaped nanotube based on dipeptide L-FF, L -LL, L-II has a positive sign – and belong to D-type, and the chirality of the nanotube based on the D-FF, D-LL, D-II dipeptide has a negative sign, corresponding to the L-type chirality. It is striking that this conclusion is independent of the calculation method and is valid for PNT models built on the basis of x-ray data and for artificially created ones. 4.5. Main calculated Physical properties of various AA PNT and discussion The developed AA PNT models were used to calculate the AA PNT’s physical properties, such as dipole moments, polarization ( P ), piezoelectric coefficients ( d 33 ), electronic energy levels ( E HOMO of the highest occupied states of molecular orbitals) and (E LUMO of the lowest unoccupied molecular orbitals), and band gap: Eg = E LUMO − E HOMO . Table 7 presents the results of calculating some physical properties of various PNT models (from 2 turns of a helix) based on different dipeptides, performed using semi-empirical methods AM1, PM1 and PM3: dipole moments, levels of polarization and electron energy, as well as band gap Eg = E_LUMO – E_HOMO. (Here V VDW is the volume of the model PNT structure over the van der Waals surface, calculated by the QSAR program implemented into the HyperChem [46]). Table 7 Calculated physical properties of the studied two-coils PNTs models. Methods and models Calculated physical values PNT model Calculation method D z , Debye D t , Debye V VDW , Å 3 P , C/m 2 E HOMO , eV E LUMO , eV E g , eV L -FF AM1 RHF −140.217 140.757 3365.60 0.1395 −5.9405 −2.4995 3.4410 RM1 RHF −141.075 141.619 3365.60 0.1398 −5.8568 −2.6182 3.2387 D -FF AM1 RHF −140.348 140.384 3346.47 0.1399 −5.9239 −2.3491 3.5748 RM1 RHF −141.118 141.154 3346.47 0.1407 −5.8118 −2.4497 3.3620 L -LL PM3 RHF −78.243 89.739 1854.47 0.1614 −6.0452 −2.8156 3.2296 AM1 RHF −76.4628 87.8063 1854.47 0.1579 −6.0695 −2.5199 3.5496 D -LL PM3 RHF −22.8902 23.2787 1935.33 0.04012 −7.90751 −1.36354 6.6544 AM1 RHF −20.9477 21.3186 1935.33 0.03674 −7.8138 −0.97568 6.8381 L -II AM1 RHF −19.778 20.0483 1930.63 0.03464 −8.0591 −0.8357 7.2234 PM3 RHF −21.412 21.697 1930.63 0.0375 −8.2822 −1.1885 7.0937 D -II AM1 RHF −10.433 11.112 1938.35 0.0192 −8.4417 −0.7794 7.662 PM3 RHF −10.089 10.702 1938.02 0.0185 −8.5859 −1.0844 7.502 The results obtained show that for all calculation methods the values of polarization P and band gap Eg for L-LL, L-FF, and D-FF PNTs based on experimental x-ray data are close to each other (Table 7 ). For all three PNTs, the band gap values are close to the experimental values 3.35–4.13 eV [35] and correspond to the absorption edge in the ultraviolet A region (UV-A, 315–400 nm) [33, 34]. The proposed model structures for D-LL PNT have lower polarization and a wider band gap values. At the same time, it is clear form our studies that with deeper optimization of artificial structures, these values change and approach experimentally observed values. That is, it can be assumed that the tendency to improve the hypothetical structures of D-LL PNT is in the right direction and it can be expected that when experimental samples of nanostructures based on D-LL are obtained, their nanotubes will have characteristics close to those calculated here for L-LL, L-FF and D-FF PNTs. The same could be expected for artificially made nanotubes models on the base of the L-II and D-II dipeptides. Upon obtaining their corresponding experimental implementation, it can be assumed that the magnitude of their polarization will be even greater, and the values of the band gap will be narrower than for the parameters calculated here based on these proposed models. It would be awaited that all these values will be close to the already known experimental values for helix-like nanotubes based on L-FF, D-FF and L-LL dipeptides. For D-LL, D-II, and L-II PNTs, the polarization and band gaps are also close to each other, though they are significantly different from the abovementioned models (Table 3 ). So, their polarizations are 3–4 times lower indicating potentially weaker piezoelectric properties than well-known FF PNTs. However, their band gap values are two times larger than FF PNTs demonstrate, that corresponds to the absorption edge of 180–210 nm belonging to the short-wave UV-C radiation. Such materials are highly demanded for solar-blind ultraviolet photodetectors (SBUV) operating in this spectral range, where the sunlight is completely absorbed by the ozone layer in the atmosphere. SBUV detectors can be used for monitoring ozone holes, fires, high-voltage transmission lines, etc. Currently, such detectors are based mainly on wide-band-gap semiconductors, such as gallium nitride or gallium oxide [79], whereas PNTs can be considered as more sustainable and friendlier alternative. Based on such peptide nanotubes, a prospective heterostructure can be created in combination with polymer ferroelectrics for a photodetector tuned to the different spectral ranges, similar to the recently developed detector based on dichalcogenides of the MoS 2 type driven by ferroelectrics layers [80, 81]. It would be very useful for many related applications. 4.6. Influence of water molecules Interesting changes in the physical properties of all types of nanotubes considered occur when water molecules are placed in their internal cavity. As mentioned above, in the experimental samples of both FF PNTs of both types of chirality, and in LL PNTs (L-LL chirality), the presence of water molecules is detected. X-ray methods here make it difficult to accurately determine the number of water molecules, and only with the help of computer calculations was it possible to clarify that in the internal cavity of the FF PNT there are 21 water molecules in the PNT model of 2 helix coils (which here corresponds to the period of one cell) [ 25 – 27 ]. Also for L-LL, the presence of 8 water molecules in the internal cavity was established [40–42]. Using these experimental data, molecular models of these PNTs with the presence of water molecules inside them were built (Fig. 10 ). Models with the presence of water molecules were also built for artificial nanotubes D-LL (Fig. 10 e) and similarly, everything was done for L-II and D-II (Table 8 ). Table 8 Properties of AA PNT helix nanotubes under influenced by water molecules Methods and models Basic calculated physical quantities Methods Chirality AA D z , Debye D t , Debye Volume, Å 3 P, C/m 2 E_HOMO, eV E_LUMO, eV Eg, eV Not H2O RM1 RHF L-FF -141.075 141.619 3365.60 0.1398 -5.8568 -2.6182 3.2387 D-FF -141.118 141.154 3346.47 0.1407 -5.8118 -2.4497 3.3620 With H2O RM1 RHF L-FF -155.116 155.878 3972.63 0.1303 -5.7348 -2.8728 2.8620 D-FF -126.781 126.804 3977.08 0.1064 -5.4119 -3.6005 1.8114 Not H2O PM3 RHF L-LL -78.243 89.739 1854.47 0.1614 -6.0452 -2.8156 3.2296 D-LL -22.8902 23.2787 1935.33 0.0401 -7.90751 -1.3635 6.6544 With H2O PM3 RHF L-LL -78.448 91.020 1930.58 0.1573 -5.9298 -2.9753 2.9545 D-LL -23.6836 24.327 2051.15 0.0396 -7.9134 -1.2902 6.6232 Not H2O PM3 RHF L-II −21.412 21.697 1930.63 0.0375 −8.2822 −1.1885 7.094 D-II −10.089 10.702 1938.02 0.0185 −8.5859 −1.0844 7.502 With H2O PM3 RHF L-II -27.757 28.322 2025.96 0.0466 -6.0238 -1.5064 4.517 D-II -12.732 13.213 2033.84 0.0217 -6.4536 -1.1725 5.281 Similarly as for D-LL (on Fig. 10 d) we constructed artificial models for L-II and D-II of the II PNT. Calculations performed by various quantum-chemical semi-empirical methods AM1, PM3, PM1 (from the HiperChem software package) showed the main general picture of changes - when water molecules are introduced into the internal cavity of nanotubes, there is a change in the total dipole moment and polarization of the nanotubes, as well as a change in their electronic levels ( E HOMO and E LUMO ), resulting in a narrowing of the band gap Eg . It should be noted here that mainly after the introduction of water molecules there is an increase in the total dipole moment [ 25 – 27 ]. Although not in all cases (as is the case with D-FF). Apparently, this also depends on the final orientation of all dipoles of the water cluster inside the nanotube plane after optimization of the entire structure as a whole [78]. These questions still require further research [82]. Water structures in such narrow nanocavities represent a special Confined water in nanochannel and form ice-like one-dimensional nanostructures with their own dipole moments, which can have an orientation either coinciding with the general dipole moment of the nanotube or against it. The total dipole moment (and polarization) of the entire structure of a nanotube with water depends on this. Important point here is the change in band gap E g . In all cases, there is a decrease in the gap E g . But this happens differently in different types of nanotubes. Of course, a significant and noticeable jump in E g is visible for both types of FF PNT chirality. In addition to the already mentioned possibilities of using such PNTs as photodetectors, there are other promising developments in the applications of these molecular devices. Noteworthy is the significant jump in E g in our hypothetical model nanotubes based on diisoleucine L-II and D-II. Perhaps this is due to the greater flexibility of the II structure in this case, which responds more actively to the introduction of the water cluster. This may have interesting promising different applications in the practical synthesis of such nanotubes, similar as for FF PNT, for example, in [83]. 4.7. Calculations of piezoelectric coefficients To calculate the piezoelectric coefficients of AA PNT peptide nanotubes based on the considered FF, LL and II dipeptides, this work used the basic electromechanical coupling relationship (1) [6, 58, 63, 75 ]. In this case, molecular models of all the above studied AA PNTs were used, constructed using the amino acid (AA) database of the HyperChem tool [46]. All AA and corresponding dipeptides were taken in the left-handed (l-h) a-helix conformation for L-chiral AA isomers and a-helix for D-chiral AA isomers. In this case, helical AA PNT models (of one and two helix-coils) for the original L-FF, D-FF and L-LL dipeptides were constructed on the basis of experimental x-ray data. For dipeptides D-LL, L-II and D-II and similar helical models artificially created on similar basis, their structural optimization was carried out (by the Polak–Rieber conjugate gradient method [46]) to achieve a more optimal nanostructure of AA PNT. For all these models, all the necessary parameters of these AA PNT structures (dipole moment, volume, polarization, energy levels and band gaps, as well as their chirality indices) were calculated. These data are shown above in Tables 6 , 7 and 8 . Calculations of piezoelectric coefficients d 33 using formula (1) also require determining the magnitude of the electrostriction coefficients Q 11 and changes in the components of the polarization vector P at a certain orientation of the nanotube axes. Here we choose the main axis to be the OZ axis along the AA PNT nanotube axis, along which the main component of polarization P z is mainly located. Next, to carry out all the calculations, we need to apply an electric field E z along this main tubular axis of the AA PNT (using a special option of the electric field E in the HyperChem tool [46]). The basic procedure for these calculations was proposed and described in detail by us in [ 6 ]. Firstly, to carry out calculations of the entire simulated molecular structure of the each AA PNT, located in the applied electric field E z , with fixed initial positions of all atoms (so called “single point” (SP) calculation) - in this case we obtain the initial values of dipole moments D 0 SP (and it’s component D z SP ) and volume V 0 (using QSAR program implemented into HyperChem [46]). Secondly, optimization (or relaxation) of the entire AA PNT structure is carried out in a given electric field E z , and the resulted change ΔD z OPT in the total dipole moment to D OPT with component D z OPT ( ΔD z OPT = D z OPT – D z SP ) is determined, with a corresponding deformation of the volume to the value V OPT ( DV = V OPT -V 0 , and relative change s = (V OPT -V 0 )/V 0 = DV/V 0 ) . As a result, the change in polarization P is determined (according to formula (2)) for it’s component P z : ΔP z OPT = P z OPT – P 0 SP . As a result, we define electrostriction coefficient by relation Q 11 = Q z = s/((ΔP OPT ) 2 , (where s = ΔV/V 0) and the piezoelectric coefficient is finally calculated from the relation d 33 = 2εε 0 Q z ΔP OPT , where e is dielectric permittivity of AA PNT, e 0 -vacuum dielectric constant. All data calculated step by step using this procedure algorithm are presented in Table 9 . We use here the value of dielectric constant ε = 4 - this is a common value for proteins [6, 57, 58, 64, 65]. But in some cases it may not be entirely correct. The dielectric constant of proteins can change, especially if the temperature changes - probably, under different conditions, the dielectric constant can increase greater than e = 10 [64, 65]. We will leave these questions here for other studies. We also note that the data presented here are somewhat different from a number of previous data in the works [6, 10, 21–27, 63]. This is due to some differences in calculation methods and optimization details of models that occur when they are relaxed along possibly different PES optimization trajectories, so that they ultimately arrive at a different PES minimum point. In principle, these details do not change the basic essence of the phenomena occurring. To analyse the data obtained, it is necessary first of all to note that all the studied AA-PNT structures are based on long-range electrostatic interactions (following from dipole-dipole interactions of their molecular components), including van der Waals interactions involving hydrogen bonds inherent in these structures with NH 3 + , CH 3 and COO − sides, especially in their zwitterionic form, including water molecules. Using the HyperChem tool, it is easy to see how the hydrogen bonding process occurs (with direct visualization of all molecular structures on the workspace of the monitor screen) and how it changes during the optimization process. Table 9 Calculated data on piezoelectric coefficients Methods and models Calculated physical values PNT model Calculation method D z SP , Debye D z OPT , Debye ΔD z OPT , Debye ΔP z OPT , C/m 2 (( ΔP z OPT ) 2 , C 2 /m 4 s = (V OPT -V 0 )/V 0 Q z = s/((ΔP z OPT ) 2 , m 4 /C 2 d 33 = 2ee 0 Q z ΔP z OPT , pm/V L-FF AM1 E z = 0.001 -144.54 -141.97 2.563 0.002540 0.0000065 0.0072528 1124.07 200.909 AM1 E z =−0.0005 -138.06 -134.78 3.277 0.003248 0.0000105 0.00723794 686.20 157.859 RM1 E z = -0.001 -136.69 -131.62 5.07 0.005025 0.0000253 0.00467376 185.11 65.886 RM1 E z = 0.001 -145.46 -141.24 4.22 0.004182 0.0000175 0.00468564 267.87 79.358 D-FF AM1 Ez = 0.001 -144.66 -142.58 2.079 0.002072 0.0000043 0.01012114 2357.60 346.010 AM1 Ez= -0.0005 -138.19 -135.24 2.945 0.002936 0.0000086 0.010139 1176.63 244.651 RM1 Ez= -0.0005 -138.93 -133.84 5.084 0.005068 0.0000257 0.00707312 275.45 98.897 RM1, E z =0.001 -145.50 -141.20 4.293 0.00428 0.0000183 0.00709676 387.59 117.477 L-LL PM3 E z = 0.001 -80.25 -77.79 2.464 0.004432 0.0000196 0.016630 846.86 265.788 PM3 E z =−0.001 -76.23 -72.89 3.339 0.006006 0.0000361 0.0165977 460.17 195.759 D-LL PM3 E z =0.001 -24.94 -24.18 0.762 0.001312 0.0000017 0.00072856 422.96 39.320 PM3 E z =−0.001 -20.84 -20.30 0.538 0.000938 0.0000009 0.00062522 711.22 47.234 L-II PM3 E z = 0.001 -23.60 -23.93 0.332 0.000574 0.0000003 0.00077709 2361.98 95.967 PM3 E z =−0.001 -19.23 -19.02 0.202 0.000349 0.0000002 0.00053868 4380.18 108.282 D-II PM3 E z = 0.001 -12.03 -12.60 0.374 0.000644 0.0000004 0.00006192 149.44 6.814 PM3 E z =−0.001 -7.66 -7.52 0.136 0.000234 0.0000005 0.00002580 470.88 7.807 Thus, here we can clearly see exactly how dipole-dipole and van der Waals interactions occur, how hydrogen bonds are formed, changed and influence the entire self-organization of the molecular system. Piezoelectric phenomena in such structures are now the focus of attention of many scientists [29, 30, 59, 60, 66, 67–72, 84–91]. We also note that the values of the electrostriction coefficients, as well as the piezoelectric coefficients, obtained in our calculations are close to the data of many similar molecular and organic structures [68–75]. So, for example, in polyurethane the value is Q = 850 (m 4 /C 2 ) [75]. It is interesting that the values of the piezoelectric coefficients we obtained here for various AA-PNTs in our calculations also correspond to a number of data for some AA-based crystals and hydrogen bonding systems. Thus, in [84], a piezoelectric generator was built based on FF PNT nanotubes. Measurements showed that an estimated piezoelectric constant d 33 = 8.8 pm/V was obtained there. Of course, this does not seem to be a very large value, but here it should be taken into account that these are already measurements at the output of the generator, after passing through the inevitable losses and attenuation that reduce the efficiency of the generator. At the same time, measurements performed in [29] gave values d 33 ~ 60 pm/V for the FF of PNT. Experimental measurements of the longitudinal component d33 with quasi-static forces applied to the (001) plane along the crystallographic axis c of g-glycine single crystals showed values of the coefficient d 33 ~ 9.93 pm/V (compared to the predicted result of calculations using density functional theory (DFT) methods of 10.4 pm/V) [85]. At the same time, for β-glycine, the measured values turn out to be about ~ 178 pm/V, which is close to the DFT calculations predicted there, about 195 pm/V [85]. And this is comparable in value with d 33 = 185 pC/N (pm/V) recently measured in an organic inorganic perovskite crystal [86]. It is an organic-inorganic perovskite ferroelectric material of Me3NCH2ClMnCl3 (TMCM-MnCl3) that shows an excellent piezoelectric response ( d 33 = 185 pC/N) that is close to that of inorganic piezoelectrics of BTO ( d 33 = 190 pC/N) [55]. In the studied systems with hydrogen bonds such as dimer of thiophenol-nitrobenzene (SPH-NBz) and phenol-nitrobenzene (PH-NBz) dimer for the piezoelectric coefficient values of the order of d 33 = 18.89–25.57 pm/V were obtained [87]. A piezoelectric coefficient d 33 ~ 23 pm/V was found for the dimer of aniline-nitrobenzene (aniline:NBz) - this is the calculated value of d 33 obtained at the theoretical level of DFT in calculations with the B3LYP/6-31G* functional [88]. As for other molecular materials, it is interesting to note that Rochelle salt, one of the first discovered piezoelectric materials [89], exhibits strong shear piezoelectricity with a piezoelectric coefficient of the order of d ~ 345 pm/V [90]. Thus, the findings confirm that many more similar H-bonded and AA tubular systems with high piezoresponse can be found due to the ubiquity of hydrogen bonding in chemistry, materials, and biological systems. Recently new dipeptide nanotubes PNT based on the dileucine (LL), diisoleucine (II), combined alanine-isoleucine (Ala-Ile, AI) and diphenylalanine (FF) were also grown and studied using piezo force microscopy (PFM) [72–74, 91]. The local piezoelectric properties of these PNTs were visualized simultaneously using the methods of atomic force microscopy (AFM) in contact mode and piezoresponse force microscopy (PFM) [72–74]. The first experimental local measurements of the piezoelectric response parameters LL, II, AI and FF of PNTs were carried out [91], which showed a linear proportional dependence of their piezoresponse on the magnitude of the applied electrical voltage for all PNTs studied here. This work will continue. 5. Conclusions The new results of modeling and computational studies of the molecular structures of dipeptides and helix-shaped peptide nanotubes based on a number of amino acids, presented in this work, clearly show their wide range of different physical properties, which have numerous promising applications. They have both important polar and piezoelectric properties, as well as useful optical and photoelectronic properties in different energy ranges. This work examines in detail the molecular models of helix tubular nanostructures based on the amino acids phenylalanine and their dipeptide diphenylalanine of both types of chirality (L-FF and D-FF), which have already been experimentally synthesized and whose structure has been well studied using X-rays. Nanostructures based on the amino acid leucine and their dipeptide dileucine are considered similarly, but here only structures based on the left-handed chirality L-LL have been experimentally synthesized and studied by X-ray. For structures of right chirality D-LL, artificial models are constructed here by analogy with already known structures (such as L-FF). Similarly, artificial models were constructed for structures based on isoleucine amino acids and their dipeptide diisoleucine of both types of L-II and D-II chirality. For all nanostructures, extensive calculations of their physical properties: dipole, polar, piezoelectric, optical and photoelectronic — were carried out. Their main wide possibilities for applications as sensors, sensors and other devices based on them are shown. The influence of water molecules in their internal cavity on their basic properties is also considered, which can also be important for various applications. In general, in this work, numerical calculations were carried out on the basis of quantum chemical semi-empirical methods AM1, PM3, RM1 from the HyperChem software package [46]. These methods have already been sufficiently tested and make it possible to carry out calculations and obtain results of all basic physical properties. However, in our other works (cited in this article) we used other approaches, including semi-empirical methods PM6, PM7 from the MOPAC package (MOPAC2016) [34,56,81], as well as density functional theory (DFT) methods with software such as VASP (Vienna Ab initio Simulation Package) [25–27,54], and compared the results of these different approaches. In this work, we summarized and presented the main results obtained using various molecular modeling and computational chemistry methods on calculations of the physical properties of both experimentally studied nanostructures based on amino acids and dipeptides, and for predicted new nanostructures of this type based on dileucine and diisoleucine. For all studied helix-shaped nanostructures, their chirality indices were also calculated (based on the developed approach using vectors of dipole moments of individual dipeptides in a helix coil) [45] and it was shown that the law of changing the type of chirality is valid here when moving to the next hierarchical level of self-organization of molecular structures. Declarations Author Contributions: Conceptualization, investigation, formal analysis, writing—original draft preparation, V.B. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Acknowledgments: The authors are grateful for the opportunity to perform calculations using the computing and information resources of the IMPB RAS. Conflicts of Interest: We declare no potential conflict of interest in this article. References Calvin M (1969) Chemical evolution. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3952941","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":272832926,"identity":"125d505c-db39-4c36-881c-bcf3f992a27d","order_by":0,"name":"Vladimir Bystrov","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAqElEQVRIiWNgGAWjYFACHiCuYGBgYydNyxmgFmaStDC2AWmitRicP3tM8ue8bfJ8zAxsn3mI0nIjL02ad9ttwzZmBubZRGmRnMFjJs247TYjSAszcVr6z5hJ/pxz2554LfwMOWYSvA23E0nQIpGXbM1z7HZyGzNjM+McYrSw8Z89ePNHzW3b+e3NhxneEKMFCFgkIDRjA5EagHH4gWilo2AUjIJRMDIBABgVJ4Kd/1WGAAAAAElFTkSuQmCC","orcid":"","institution":"Institute of Mathematical Problems of Biology, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"Vladimir","middleName":"","lastName":"Bystrov","suffix":""}],"badges":[],"createdAt":"2024-02-13 07:18:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3952941/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3952941/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51154857,"identity":"4f46c503-58fb-40c3-89be-0c39b0a2f25a","added_by":"auto","created_at":"2024-02-15 05:39:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":847343,"visible":true,"origin":"","legend":"\u003cp\u003eAmino acids on the HyperChem workspace [46] (Glycine as example): a) amino acids \u0026nbsp;database in \u0026nbsp;HyperChem (shown with Alpha-helix and L-chirality); b) Glycine in pristine form; c) choose to make of the \u0026nbsp;Zwitterion form in HyperChem menu; d) Glycine in the Zwitterion form (\u003cem\u003e\u003cstrong\u003eDt\u003c/strong\u003e\u003c/em\u003e shows the total dipole moment \u0026nbsp;vector). Atomic colour: Red – Oxygen, Deep Blue – Nitrogen, Cyan – Carbon, Gray – Hydrogen.\u003c/p\u003e","description":"","filename":"Figure1abcd300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/59e085f7271629f0f27cc395.png"},{"id":51154859,"identity":"d0a2651e-27ec-4f98-bdc0-f5c02c1a89e4","added_by":"auto","created_at":"2024-02-15 05:39:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":977252,"visible":true,"origin":"","legend":"\u003cp\u003eMolecular models of diphenylalanine in various isomeric forms: a) L-FF with chirality L \u0026nbsp;(α-helix conformation), b) D-FF with chirality D (α-helix conformation); c) L-FF with chirality L \u0026nbsp;(conformation of Left-handed (\u003cem\u003el-h\u003c/em\u003e) α-helix, d) D-FF with chirality D (conformation of α-helix).\u003c/p\u003e","description":"","filename":"Figure2abcd300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/a0264c25fe7156711a53a8c0.png"},{"id":51155641,"identity":"e0d841b5-ab6b-463e-91c8-91546ecffe27","added_by":"auto","created_at":"2024-02-15 05:47:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1712962,"visible":true,"origin":"","legend":"\u003cp\u003eImages of molecular crystals of diphenylalnine based on Cambridge Crystallographic Data \u0026nbsp;Center (CCDC) data for two different enantiomers of FF: (a) structure of L‑chiral L‑FF with space \u0026nbsp;group P61 and (b) the same central part in the HyperChem workspace; (c) D‑chiral D‑FF structure \u0026nbsp;with space group P65 and (d) the same central part in the HyperChem workspace. Circles in the \u0026nbsp;HyperChem workspace are shown in red, highlighting the structures of nanotube formation from 6 \u0026nbsp;FF molecules in the Z projection. The rest of the designations are the same as in Fig. 1 [25, 27, 34].\u003c/p\u003e","description":"","filename":"Figure3300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/24bca7e587f3b6b8eb908fe5.png"},{"id":51154861,"identity":"d3434cb7-b868-45df-9861-5891f4bef877","added_by":"auto","created_at":"2024-02-15 05:39:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":532827,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of configurations of individual FF dipeptides from models of nanotube rings based on \u0026nbsp;L-FF and D-FF: a) and c) - ring and dipeptide from a model based on L-FF; b) and d) - ring and dipeptide from \u0026nbsp;the model based on D-FF.\u003c/p\u003e","description":"","filename":"Figure4300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/560a3d36272f4b03842157f0.png"},{"id":51154863,"identity":"c8b8bd31-2a80-4d82-ac87-097c7b81a1f8","added_by":"auto","created_at":"2024-02-15 05:39:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1596541,"visible":true,"origin":"","legend":"\u003cp\u003eTwo-helix coils molecular models of FF PNT built in HyperChem using on X-ray data [40]:\u003c/p\u003e\n\u003cp\u003e(a, b) L-FF model and (c, d) D-FF model in (a, c) Z and (b, d) Y planes. Black arrows indicate the direction of \u0026nbsp;the total \u0026nbsp;dipole moment \u003cem\u003e\u003cstrong\u003eDt. \u003c/strong\u003e\u003c/em\u003e(adapted from [45].\u003c/p\u003e","description":"","filename":"Figure5abcd300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/0a1e0e3a22637d00a519186a.png"},{"id":51156780,"identity":"cf1ccd13-a631-4d4c-ad37-67e20ff738c1","added_by":"auto","created_at":"2024-02-15 06:03:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":317638,"visible":true,"origin":"","legend":"\u003cp\u003eModels of dileucine molecules in zwitterionic form.: a) L-LL in Left-hand (\u003cem\u003el-h\u003c/em\u003e) a-helix conformation; b) D-LL in a-helix conformation\u003cstrong\u003e. \u003c/strong\u003eArrows indicate the directions of the total dipole moments \u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"Figure6300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/4e52862ded9d364b7f5adabb.png"},{"id":51155643,"identity":"e118ccc4-9b68-4d46-97c8-5931b05056e1","added_by":"auto","created_at":"2024-02-15 05:47:18","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1389244,"visible":true,"origin":"","legend":"\u003cp\u003eTwo-helix coils molecular models of LL constructed in \u0026nbsp;in HyperChem workspace:\u0026nbsp;(a, b) L-LL model based on experimental data [40-42] and (c, d) artificial helix-like model of D-LL PNT in (a, c) Z and (b, d) Y planes. Black arrows indicate the direction the total dipole moment \u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e.4.2. Dipeptides and nanotubes based on isoleucine amino acids\u003c/p\u003e","description":"","filename":"Figure7LL300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/ae2b0b590d1a981af436b33d.png"},{"id":51154865,"identity":"4fc43d04-d3a1-4c26-bc06-4c8d57c37917","added_by":"auto","created_at":"2024-02-15 05:39:18","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":342348,"visible":true,"origin":"","legend":"\u003cp\u003eModels of diisoleucine molecules in zwitterionic form.: a) L-II in Left-hand (\u003cem\u003el-h\u003c/em\u003e) a-helix conformation; b) D-II in a-helix conformation\u003cstrong\u003e. \u003c/strong\u003eArrows indicate the directions of the total dipole moments \u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"Figure8300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/03a919a9c3321290166f9a1f.png"},{"id":51155645,"identity":"88bd8c4f-f39c-49ae-89d0-e8184edd585b","added_by":"auto","created_at":"2024-02-15 05:47:18","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":1699764,"visible":true,"origin":"","legend":"\u003cp\u003eTwo-helix coils molecular models of II constructed in HyperChem workspace:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e(a, b) L-II model based on experimental data [41, 42] and (c, d) artificial helix-like model of D-II PNT in (a, c)\u0026nbsp;Z and (b, d)\u0026nbsp;Y planes. Black arrows indicate the direction of: (a, c) individual dipeptides’ dipole moment \u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003ei\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e, and (b, d) the total dipole moment \u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e. Curved blue arrows shows the direction of bypassing the helix coils during chirality index calculation.\u003c/p\u003e","description":"","filename":"Figure9300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/a6213776dacf4099491af12f.png"},{"id":51154867,"identity":"e24b7671-ec3d-44a5-9669-dab7567a8d6a","added_by":"auto","created_at":"2024-02-15 05:39:18","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":1214643,"visible":true,"origin":"","legend":"\u003cp\u003eCross-section and images of inner cavity of PNT filled with water molecules: a) and b) left chiral \u0026nbsp;L-FF and right chiral D-FF of the FF PNT; c) and d) left chiral L-LL and right chiral D-FF of the LL PNT (last is artificial hypothetical model).\u003c/p\u003e","description":"","filename":"Figure10300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/db58d938e5db6a9675c3caf8.png"},{"id":51156953,"identity":"2332895e-e119-474d-8705-5a23e4f719a3","added_by":"auto","created_at":"2024-02-15 06:11:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5748461,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/df40f52e-d894-459e-a2af-78db1742ef4d.pdf"},{"id":51156284,"identity":"b503221d-428a-426c-ae0b-a74d7eea467e","added_by":"auto","created_at":"2024-02-15 05:55:18","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":742289,"visible":true,"origin":"","legend":"","description":"","filename":"Table1.docx","url":"https://assets-eu.researchsquare.com/files/rs-3952941/v1/98f289bd4bf5c48c3a33f37b.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Features of molecular self-assembled helix peptide nanotubes based on some amino acids molecules and their dipeptides: molecular modelling studies","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eOne of the important and current topics of modern molecular physics, biophysics and nanobiotechnology is the creation of artificial nanostructures based on the molecules of various amino acids (AA). It is known that AA are capable of the self-assembly into different complex molecular structures. Such self-assembly of molecular structures based on AA is a remarkable phenomenon of living nature, arousing great interest of many researchers involved in the study of the self-organization of molecules, the development of promising new nanotechnologies and nanomaterials [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] using the modern methods of molecular modeling, computational and theoretical chemistry in this area [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Complex distributions of electric charges and dipole moments, long-range force fields inherent in AA [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], lead them inevitably to the different chemical-physical interactions, self-assembly into various more complex molecular structures, such as dipeptides, polypeptides and proteins, and organize them into hierarchical molecular-crystalline nanostructures, including such as peptide nanotubes (PNTs) [\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Of course, a lot here also depends on the external conditions of the environment (aqueous solutions) in which this or that set of AA molecules is located. But the features of such self-assembled structures and their properties are also influenced by the internal characteristics of the set of the initial molecules, such as, e.g., the chirality of the AA included in them [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThus, an important rule for changing the chirality of molecular structures was recently established, according to which the molecular structures of lower and higher hierarchical levels of organization differ in the type of their chirality [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] - here there is a change in the sign or type of chirality L \u0026harr; D (change between the left \"L \" and right \"D\" chirality types: this terms is from the Latin \"laeva\" - \"L\" - left, and \"dextra\" - \"D\" - right) [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. This is especially evident in spiral structures. This is especially evident in helix-shaped structures. This striking difference between nanostructures is rooted in rather deep physical reasons for parity violation of the weak interactions, which determine a small but measurable difference in the internal properties of the enantiomers (as was recently established) [\u003cspan additionalcitationids=\"CR12 CR13 CR14 CR15 CR16\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. This symmetry breaking is already evident at the level of the weak nuclear interactions - electrons resulting from a subatomic process known as b-decay are always left-handed. This means that their spin (quantum angular momentum of elementary particles) will always be opposite to the direction of electron motion - these are \u0026ldquo;left-handed\u0026rdquo; spin-polarized electrons [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Such polarized electrons are indeed capable of initiating chiral-selective chemical reactions in the gas phase [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Perhaps this effect is the source of the accumulated fact: the predominant existence in living organisms of \u0026ldquo;left-handed\u0026rdquo; amino acids and \u0026ldquo;right-handed\u0026rdquo; DNA molecules - this is the so-called homochirality of life [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Among the possible explanations for the reasons for such homochirality of biomacromolecules, there is the Vester-Ulbricht hypothesis that the homochirality of life is a consequence of precisely the spatial asymmetry of the weak interaction of elementary particles [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Based on this hypothesis, the authors of a recent work [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] evaluate the possibility generation of homochiral polymers in the environment of molecular clouds of the cosmic nebula. Chiral polymers can be induced in the environment of such a molecular cloud at ultra-low temperatures in deep space, since the polarization and stereoselectivity of chiral biomolecules here is much less than that of homeothermic ones. Also, the pure left-handed polymer chain may be significantly longer in such a low-temperature environment.\u003c/p\u003e \u003cp\u003eIn this regard, a deeper understanding of the self-organization and physicochemical properties of the molecular helix-shaped nanotubes based on various amino acids and dipeptides is of great importance for the physics of molecules, molecular biology and materials science [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5 CR6 CR7 CR8 CR9\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCurrently, a significant amount of experimental data has been accumulated on the structure and properties of nanostructures based on various AA and dipeptides. Among others, the most studied PNTs are those based on phenylalanine AA (Phe or F) and its dipeptide diphenylalanine (FF) [\u003cspan additionalcitationids=\"CR22 CR23 CR24 CR25\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. These studied FF-PNTs quickly self-organize and are easily grown in an aqueous environment, and various external conditions affect their thickness and length [23, 27, 28].\u003c/p\u003e \u003cp\u003eIt has been shown that FF-PNTs have piezoelectric [25, 26, 29, 30], pyroelectric [31], ferroelectric [21,25,29,32] and pronounced photoelectronic properties [32\u0026ndash;36], which differ here for dipeptides of different chirality [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. It is also interesting that these properties are also influenced by water molecules trapped in the internal cavity [22, 25, 26, 37\u0026ndash;39]. These structures are promising for many applications in nanotechnology, nanoelectronics, pharmacology and biomedicine [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBesides FFs with aromatic rings, branched chain dipeptides such as dileucine (Leu-Leu, LL) and diisoleucine (Ile-Ile, II) can also form PNT [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. However, most of these nanostructures studied experimentally are so far based on AA and dipeptides of only \u0026ldquo;left-handed\u0026rdquo; chirality (L-AA) [40\u0026ndash;42]. A useful exception here is a recent study of \u0026ldquo;right-handed\u0026rdquo; D-FF PNT [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Crystal structures of such nanostructures (\u0026ldquo;left-handed\u0026rdquo;, L, chirality) were obtained by G\u0026ouml;rbitz, [40, 41] and deposited in the CCDC database [42].\u003c/p\u003e \u003cp\u003eTherefore, computational molecular modeling is now becoming the main tool for studying such PNTs, predicting their structural features and physical properties, taking into account their different types of chirality, for future experimental studies [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn our previous works [\u003cspan additionalcitationids=\"CR22 CR23 CR24 CR25\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], we developed computer models of L-FF and D-FF PNTs, using various computational quantum-chemistry methods, including semi-empirical methods (AM1, PM3 etc.) and methods of density functional theory (DFT), and found good agreement between their calculated properties and known experimental data. For example, computer modeling has shown that nanotubes in the form of a stack of parallel rings [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], a typical scheme for the self-assembly of cyclic peptides [43, 44], are less preferred in the case of the FF-PNT than those formed from helix-shaped coils [10, 23, 24\u0026ndash;26, 40, 41]. Thus, a kind of the topological transition [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] to a more stable organization of these biomacromolecules was demonstrated here.\u003c/p\u003e \u003cp\u003eIt is also important that the chirality indices of the PNTs, determined using the developed original approach [45] based on the calculation of the dipole moments of the dipeptides forming the helix coils of the helix-shaped nanotube, confirmed the rule for changing the type of chirality [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]: nanotubes based on the \u0026ldquo;left\u0026rdquo; dipeptides L-FF demonstrate \u0026ldquo;right-handed\u0026rdquo; D-chirality type, and vice versa, nanotubes based on the right-handed chirality D-FF dipeptides have a left-handed L-chirality type.\u003c/p\u003e \u003cp\u003eThus, based on our previous work, in this article we present the constructed helix-shaped nanotubes based on the LL and II dipeptides of the different chirality (L and D), calculated their chirality indices, dipoles moments, polarizations, piezoelectric and photoelectronic properties. In addition, the influence of water molecules confined inside the nanochannels of these PNTs was investigated. Modeling and all calculations were carried out using quantum chemical semi-empirical methods implemented in the HyperChem package [46]. The initial structure of \u0026ldquo;left-handed\u0026rdquo; PNTs is built on the basis of available experimental data using DFT approaches, while artificial \u0026ldquo;right-handed\u0026rdquo; PNTs are constructed by analogy, also taking into account the available data on FF PNTs of both types of their chirality.\u003c/p\u003e \u003cp\u003eIn general, the goal of the work is to analyze a number of such self-organized molecular structures based on AA and their dipeptides with different initial chirality (such as, e.g., L-LL and D-LL, L-II and D-II), calculations of their properties, including predictions of ones for a number of artificially constructed models based on D-AA, using modern computational methods.\u003c/p\u003e"},{"header":"2. Main computational details and approaches","content":"\u003cp\u003eThe main tool for molecular modeling of all studied nanostructures in this work was the HyperChem 8.01 software package [46]. Various computational methods were used, including molecular mechanics methods (MM: MM+, Amber, BIO CHARM from HyperChem package [46]), but mainly quantum mechanical (QM) calculations were used here in the Hartree-Fock (HF) self-consistent field (SCF) approach with various semi-empirical methods (AM1 [47, 48], PM3 [49\u0026ndash;51], RM1 [52, 53]) in the restricted Hartree-Fock (RHF) approximation and, in some cases, also in the unlimited Hartree-Fock (UHF) approximation [46]. The use of these methods for molecular modeling makes it possible to obtain the minimum total energy of the molecular system under study on the potential energy surface (PES) of the simulated systems. As a result, all the studied molecular systems achieved an optimal atomic configuration. Optimization of molecular systems and the search for their optimal geometry is carried out in this work using the Polak\u0026ndash;Ribeire algorithm (conjugate gradient method), which determines the optimized geometry at the point of their minimum total energy (using PES) [46]. For such optimized structures, dipole moments and electronic energy levels were then calculated.\u003c/p\u003e \u003cp\u003eIn addition, in this work, the construction of correct models of helix-like molecular structures was carried out in direct correlation with known X-ray diffraction data for structures based on diphenylalanine (FF), both left L-FF [40] and right D -FF [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] chirality, and for dileucine structures too (LL, but with the chirality known here so far only for the left L-LL [40, 41]). The original structural data for L-LL, D-FF and L-FF were taken from the Cambridge Crystallographic Data Center1 (CCDC) crystallographic database [42]. These data correspond to CCDC No. 16337 for L-FF [40, 42] and CCDC No. 1853771 for D-FF [23, 42]. Based on these data, models of crystallographic cells were constructed and calculated using density functional theory (DFT) methods in the Vienna ab initio Simulation package (VASP) program [54] in our works [\u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] for L-FF and D-FF, as well as for L-LL, which were then transferred to the HyperChem workspace [46] for molecular modeling and all quantum chemical calculations. Currently, we also carry out calculations using DFT methods in Quantum ESPRESSO [55]. Artificial structures based on D-LL, L-II and D-II were built directly in the HyperChem \u0026ldquo;work-space\u0026rdquo;. In a some of our work [34], we also used other approaches, including semi-empirical methods PM6, PM7 from the MOPAC package (MOPAC2016) [56], and there we also compared the results of all these different approaches and showed their comparability.\u003c/p\u003e \u003cp\u003eIn this article, in all current calculations of the polar, piezoelectric, electronic and optical properties of the molecular structures of nanotubes, quantum mechanical semi-empirical methods are used: AM1, PM3, RM1 [47\u0026ndash;53] from the HyperChem package [46]).\u003c/p\u003e"},{"header":"3. Dipole moments and polarization of a number of different amino acids","content":"\u003cp\u003eAs mentioned above, all amino acids (AA) have their own electrical properties and dipole moments [57,58], which interact with each other during the self-assembly of amino acids or their dipeptides and polypeptides into more complex molecular structures [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e]. These could be, for example, molecular crystal structures. For example, such as molecular crystals in various polymorphic forms based on Glycine AA [6,59,60]. These can also be various molecular tubular helix-like structures, for example, peptide nanotubes (PNTs) based on diphenylalanine (FF) [10, 21\u0026ndash;26, 40\u0026ndash;42, 61\u0026ndash;63] or even the structures of ion channels in biological membranes [64, 65]. Many of them turn out to be relevant and useful in materials science, nanoelectronics and medicine. It has now been established that many of these structures have piezoelectric and ferroelectric properties [21, 29, 63, 66\u0026ndash;69] and are considered as an organic ferroelectrics [70]. Currently, they are being intensively studied by various methods, both experimentally and theoretically [63, 71\u0026ndash;74].\u003c/p\u003e\n\u003cp\u003eAs it is known, piezoelectricity usually arises as a result of electromechanical coupling in a given material [6,55,63]. The phenomenon is based upon the known general relation between the piezoelectric constant \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003eik\u003c/em\u003e\u003c/sub\u003e, the electrostriction coefficient \u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003eik\u003c/em\u003e\u003c/sub\u003e, the permittivity of the material \u0026epsilon;, the permittivity of vacuum \u0026epsilon;\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e, and the component of polarization \u003cem\u003eP\u003c/em\u003e of the whole system [55, 63, 75]. For a simple case, as a first approximation for only one component of the coefficient \u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003e11\u003c/em\u003e\u003c/sub\u003e, the piezoelectric constant \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e, dielectric permittivity \u0026epsilon; and spontaneous polarization \u003cem\u003eP\u003c/em\u003e, the relationship can be written as [5, 55, 63, 75]:\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ed\u003c/em\u003e \u003csub\u003e33\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e11\u003c/sub\u003e\u0026epsilon;\u0026epsilon;\u003csub\u003e0\u003c/sub\u003e\u003cem\u003eP.\u003c/em\u003e (1)\u003c/p\u003e\n\u003cp\u003eOn this basis, we can study piezoelectricity and related changes in the dipole moments and polarization of various systems. This coupling is well known in biology \u0026ndash; it can be observed in many biological processes: in a voltage-controlled muscle movement, in the nervous system, in ion transport, etc. [63\u0026ndash;67, 76]. Such electromechanical coupling between electrical polarization and mechanical response and vice verse can be considered as the heart of the piezoelectric and bioferroelectric phenomena in various molecular and biological systems, including those based on the various AA.\u003c/p\u003e\n\u003cp\u003eFirst we consider the amino acids (AA) initial properties. In HyperChem tool [46] there is a special database for all main AA and we take it for all our AA modeling and calculations in HyperChem workspace [46] (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea, shown L-chiral and a-helix conformation for AA; Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb, e.g., for Glycine). One of the main features is that all AA (as well as their dipeptides) exist in the initial pristine forms (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb, a Glycine), but in the solutions they exist in the zwitterionic form - that is, a water molecule is added here [6,57]. For modeling these forms can be created in HyperChem workspace using an option (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec) and further the zwitterionic structures are used (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed, Glycine as zwitterion). All AA can exist in various conformation (a-helix, b-sheet, etc., Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea) and two chirality isomers: L and D [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e]. The a-helix (Alpha helix) and left-hand (\u003cem\u003el-h\u003c/em\u003e) a-helix (Left-hand alpha) conformations are used further in this our work (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea).\u003c/p\u003e\n\u003cp\u003eThe possibility of a piezoelectric effect in various amino acids was indicated earlier by Lemanov [69]. It should be noted that many of the amino acids considered by us have non-centrosymmetrical elements. This suggests a possibility of a piezoelectric effect in them. So, for example, valine, leucine, isoleucine have a symmetry group P2\u003csub\u003e1\u003c/sub\u003e, and alanine and phenylalanine \u0026ndash; P2\u003csub\u003e1\u003c/sub\u003e2\u003csub\u003e1\u003c/sub\u003e2\u003csub\u003e1\u003c/sub\u003e, while diphenylalnine (FF) exhibits hexagonal symmetry P6\u003csub\u003e1\u003c/sub\u003e [6, 10, 23, 24, 40,42]. In addition, like crystals based on glycine and FF structures, these all AA have high polarizability, which is manifested when exposed to an electric field. This can be investigated using simulation methods which were widely described in [6, 10, 21\u0026ndash;26, 63].\u003c/p\u003e\n\u003cp\u003eNow we consider, firstly, the computed values of the dipole moment and polarization. We consider not all AA, but several selected AA, which are necessary for our further studies. Using HyperChem tool [46] and the database of amino acids we calculate these values using PM3 RHF method. As a result, we obtained the following data (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Abbreviations of AA types in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e below are: Glycine \u0026ndash; is a simplest special case (SC); all the other AA are the AA with Hydrophobic side chain (HSC): Alanine is the simplest of them; Phenylalanine is AA with a benzyl (benzene or aromatic) side chain (BSC); Leucine, Isoleucine and Valine are the branched-chain AA (BCAA). As one can see, upon transition to the Zwitter-Ionic (ZwI) form, the dipole moment \u003cem\u003eD\u003c/em\u003e increases significantly, which is not surprising, since in this ZwI form the polar groups NH\u003csup\u003e3+\u003c/sup\u003e and COO\u003csup\u003e\u0026minus;\u003c/sup\u003e are more pronounced and are located at large distances from each other. The polarization value is calculated using relation [6, 63]:\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n\u003cp\u003e\u003cstrong\u003eP\u0026thinsp;=\u0026thinsp;3.33558255*D/V\u003c/strong\u003e (\u003cem\u003eC/m\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e \u003cem\u003e- in SI units\u003c/em\u003e), (2)\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere V is the structure\u0026rsquo;s volume on the Van der Waals surface.\u003c/p\u003e\n\u003cp\u003eAs one can be seen from the results of polarization calculations given in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, these polarization values turn out to be close in magnitude to many known value for ferroelectrics [58]. Especially, large values of AA will acquire in the zwitterione form (which is not surprising, since there the dipole moment becomes very significant). However, these values are obtained here only for the minimum units - single AA. Further, we will consider and analyse larger AA formations - formation of the dipeptides and their self-assembly into ring and helix-coil structures, molecular AA nano-clusters, and various AA peptide nanotubes.\u003c/p\u003e"},{"header":"4. Dipeptides and molecular nanotubes","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1. Dipeptides and nanotubes based on phenylalanine amino acids\u003c/h2\u003e\n\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\n\u003ch2\u003e4.1.1. Initial models of diphenylalanine\u003c/h2\u003e\n\u003cp\u003eThe structure of the initial molecular model of phenylalanine (Phe or F) was taken from a special amino acid database implemented into the HyperChem program [46]. This structure of the molecular model of diphenylalanine (FF) was built in a special \u0026ldquo;workspace\u0026rdquo; of the HyperChem program and transferred to the zwitterionic form necessary for further modeling in accordance with experimental data [10, 23, 24, 40\u0026ndash;42]. To do this, we first used the Alpha helix (a-helix) conformation of the initial amino acid F and both of its isomers of the different chirality L-F and D-F [46]. On their basis, models of dipeptide\u0026mdash;diphenylalanine (FF)\u0026mdash;with different chirality: L-FF and D-FF were constructed.\u003c/p\u003e\n\u003cp\u003eFor these two models, all necessary parameters were calculated using the quantum semi-empirical PM3 method [46\u0026ndash;53] in the restricted (RHF) and unrestricted (UHF) Hartree\u0026ndash;Fock approximations [46]. Their geometric optimization was also carried out using the Polak\u0026ndash;Ribi\u0026egrave;re conjugate gradient method (from the HyperChem program [46]). During this optimization, the total energy of the system is calculated at each point, depending on the coordinates of all atoms of the system, and the potential energy surface (PES) is determined [46], on which the minimum point of this total energy (or PES) is located, corresponding to the optimal position of all atoms systems. The optimized structures of the L-FF and D-FF models are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea, b.\u003c/p\u003e\n\u003cp\u003eHowever, the L-FF dipeptide can also be formed on the basis of another conformation of the F molecule - Left-handed (\u003cem\u003el-h\u003c/em\u003e) \u0026alpha;-helix [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e]). In this case, another dipole orientation of the L-FF dipeptide is formed. Its magnitude, direction and components, also calculated using HyperChem, are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec, d and Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. It is this conformation that turns out to be most consistent with experimental X-ray data (see below in sections \u003cspan class=\"InternalRef\"\u003e4.1.2\u003c/span\u003e). The main characteristics obtained for these models differ from each other in orientation and values of their total dipole moment (in Debye units), see Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eNote also that structures based on the conformation of the F molecule as a Beta sheet (b-sheet) are also possible here. And some of the first work on modeling FF PNT used beta-sheet-based models of the FF dipeptide [10, 21, 63], as it was believed that this would be consistent with the structures of the amyloids that cause Alzheimer's disease [77]. However, it soon became clear that this FF configuration did not correspond to the obtained X-ray data, which clearly showed the conformation of \u0026alpha;-helical structures in these PNT FFs [78], as well as the inclusion of water molecules in the internal cavity. Note that to confirm these results, ab initio and density functional theory (DFT) methods available in the HyperChem package were also used [46]. As follows from the data obtained, given in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the parameter values for D-FF are closer in their absolute values to the parameters of L-FF (\u003cem\u003el-h\u003c/em\u003e) than to L-FF.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCalculated data for dipeptides L-FF, L-FF (\u003cem\u003el-h\u003c/em\u003e) and D-FF using the PM3 method. Dipeptides consist of 43 atoms and have a volume calculated on their Vander Waals surface.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eCalculation method\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDipeptide\u003c/p\u003e\n\u003cp\u003echirality\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eAmino acids\u003c/p\u003e\n\u003cp\u003econform-ation\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003eVDW\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003e\u0026Aring;\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eP\u003c/em\u003e,\u003c/p\u003e\n\u003cp\u003eC/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eTotal energy, a.u.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eRMS grad\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(both RHF \u0026amp; UHF)\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-10.42\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-2.53\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10.79\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e291.720\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1234\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-133.963\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.1\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003el-h\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.09\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.32\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.66\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e292.075\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1332\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-133.959\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e~\u0026thinsp;0.08\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-11.62\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.02\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.67\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e291.822\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1334\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-133.959\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.1\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe influence of the resulting initial structures and properties of these different FF dipeptides on the formation of subsequent more complex structures and FF nanotubes are discussed in the following sections. Let us immediately note that all the considered dipeptides are in their zwitterionic form and contain 43 atoms each, with active groups NH\u003csup\u003e3+\u003c/sup\u003e and COO\u003csup\u003e\u0026minus;\u003c/sup\u003e, capable of forming hydrogen bonds. Aromatic rings play a neutral but important inertial role, influencing changes in the center of mass of the entire structure.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n\u003ch2\u003e4.1.2. Self-assembly formation of 3-dimensional molecular structures based on diphenylalanine\u003c/h2\u003e\n\u003cp\u003eComputational molecular modeling of more complex self-organizing nanostructures based on FF dipeptides with different chiralities (LFF and DFF), including tubular structures, was carried out at the first stage of research using HyperChem software [46]. However, in contrast to a number of early works [10, \u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e3], in which models of the structures based on the \u0026beta;-sheet conformations were considered, here we now consider only amino acid conformations in the form of an \u0026alpha;-helix (a-helix and left-hand (l-h) a-helix) for the original phenylalanine molecules.\u003c/p\u003e\n\u003cp\u003eFor all FF PNTs, we used zwitterionic molecular forms and considered, firstly, ring FF models consisting of 6 FF molecules, and secondly, our previously developed standard two-ring models of tubular PNTs, consisting of 6 FF molecules in each ring. forming a total hexagonal crystallographic structure in accordance with known experimental data [6, 10, 22\u0026ndash;26, 40\u0026ndash;42]. Such models of nanotubes in the form of a stack of parallel rings [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e] corresponded to the typical self-assembly scheme of cyclic peptides [43, 44].\u003c/p\u003e\n\u003cp\u003eAfter optimization of both molecular models (LFF and DFF) for this case, they have the shape of a single ring containing 258 atoms, and consisting of 6 diphenylalanine molecules (43 atoms for each individual structural segment - the FF molecule), as well as tubular structures in the form of 2 rings (of 516 atoms) built for diphenylalanine L- and D-chirality. For all cases, geometric optimization was carried out using the Polak\u0026ndash;Ribi\u0026egrave;re conjugate gradient method. As a result, optimized structures of the PNT LFF and DFF models were obtained, similar to works [10, \u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e, 24]. Calculations were carried out using the PM3 [49\u0026ndash;51] quantum semi-empirical method using various Hartree\u0026ndash;Fock approximations (both RHF and UHF). In some cases, similar semi-empirical methods AM1 [47, 48] and RM1 [52, 53] (included in HyperChem [46]) were used.\u003c/p\u003e\n\u003cp\u003eHowever, further research and experimental data showed that self-assembled peptide FF nanotubes are not stacks of assembled ring structures, but rather helix-like structures with a helical pitch equal to the double period of the crystal cell of a FF-based molecular crystal, and different for L-FF and D-FF [22, 23, 25, 34, 45]. For analysis, modeling and calculations (optimization of structures, determination of their structural and energy parameters), density functional theory (DFT) approaches were also used here in these above mentioned works. Therefore, further in this work we will mainly consider the helix-shaped structures of nanotubes.\u003c/p\u003e\n\u003cp\u003eMoreover, as is now well known, experimentally synthesized nanotubes (based on various amino acids and dipeptides) can contain water molecules in their internal cavity [25, 26, 78]. However, it is not always possible to experimentally detect a reliably determined number of water molecules using X-ray methods [40, 41]. Therefore, computer modeling methods and DFT calculations are used quite effectively here [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]. In particular, for FF PNT we managed to do this [44\u0026ndash;46] and refine the number of water molecules determined in this way, which is equal to n\u0026thinsp;=\u0026thinsp;21 [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e]. However, now we will first of all consider models of anhydrous molecular structures of nanotubes in order to better understand their basic properties. And then we will consider the influence of water molecules on these properties and their features. Using experimental X-ray data [40\u0026ndash;42], we will first compare them with our model structures and clarify their features in anhydrous models. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows the conversion of crystallographic data to model FF PNT structures in the HyperChem workspace [46], according to works [25\u0026ndash;27, 34]. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e present crystallographic data for \u003cem\u003eP6\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e space group of FF structure and the corresponding parameters of inner cavity inside FF PNT.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eParameters of the internal hydrophilic cavity of PNT LFF and DFF\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eParameters\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eL-FF\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eD-FF\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eOriginal data\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eOpt. (anhydrous)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eOriginal data\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eOpt. (anhydrous)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ea, \u0026Aring;\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e24.0709\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e23.8308(284)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e23.9468\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e23.7877(806)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eb, \u0026Aring;\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e24.0709\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e23.8308(284)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e23.9468\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e23.7877(806)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ec, \u0026Aring;\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5.4560\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5.4035(861)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5.4411\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5.4022(7125)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eR\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/sub\u003e, \u003cstrong\u003e\u0026Aring;\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.236\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.091\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.102\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.075\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eR\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e, \u003cstrong\u003e\u0026Aring;\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e15.271(698)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e15.042(076)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e15.180(569)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e15.030(688)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eR\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e, \u003cstrong\u003e\u0026Aring;\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.218(349)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.098(817)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.135(396)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.075(906)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eEtot, eV\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-1593.31827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-1657.64347\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-1608.73564\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-1657.60024\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eComparing now the experimentally obtained models of a ring of 6 FF dipeptides of left L-FF and right D-FF chirality and selected (\u0026ldquo;green\u0026rdquo; colour marked) one symmetrical dipeptides on them ( Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea, d), we obtain their configurations, which coincide in the orientation of the NH\u003csup\u003e3+\u003c/sup\u003e and COO\u003csup\u003e\u0026minus;\u003c/sup\u003e groups with the Left-handed (\u003cem\u003el-h\u003c/em\u003e) a-helix conformations for L-FF and a-helix for D-FF (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec, d).\u003c/p\u003e\n\u003cp\u003eWe will not dwell here on the ring models of the nanotubes, but will move on mainly to helix-like models, as the most consistent with established experimental data. Let us note here that the FF PNT ring model, consisting form 6 FF dipeptides, shown above in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e is actually a projection onto the Z-plane of the helix coil of this nanotube. This is clearly visible in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, which represents Z and Y projections of the anhydrous FF PNT helix model, which best matches the experimental X-ray data [40, 42].\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003e4.2. Dipeptides and nanotubes based on leucine amino acids\u003c/h2\u003e\n\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\n\u003ch2\u003e4.2.1. Initial models of dileucine\u003c/h2\u003e\n\u003cp\u003eSimilarly as above for FF consider here the molecular model of the dileucine (LL) dipeptide, based on the leucine (Leu or L) amino acid, using known experimental X-ray data for them [40\u0026ndash;42], to construct the corresponding molecular structures of the dipeptide nanotubes based on L-LL. For D-LL PNTs, we have constructed hypothetical structures similarly to how it was done for D-FF [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. In this case now we also use the data obtained above, that for left chirality based nanotube L-LL preferred initial L amino acid conformation must be Left-handed (l-h) a-helix. A careful and in-depth analysis of the results of comparison of helical structures for dileucine-based nanotubes, extracted from x-ray data, and constructed from the amino acid database (built into HyperChem), showed that the initial conformations of leucine with chirality L should not only be of the a-helix type, but Left-hand (l-h) a-helix (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e). Just as in FF PNT, only in this case does the required correspondence between the chirality of the helical structure and the directions of the vectors of dipole moments of both individual dipeptides and the total coil of the helix nanotube arise.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003ePhysical properties for dileucine of various conformation using different semi-empirical methods\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eCalculation method\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDipeptide\u003c/p\u003e\n\u003cp\u003echirality\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eAmino acids\u003c/p\u003e\n\u003cp\u003econformation\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eVolume,\u003c/p\u003e\n\u003cp\u003e\u0026Aring;\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePolarization,\u003c/p\u003e\n\u003cp\u003eC/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-LL, \u003cem\u003el-h\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003el-h\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10.399\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.049\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-4.262\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.238\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e243.243\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1541\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-10.334\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-1.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.110\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10.429\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e244.143\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1425\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-LL, \u003cem\u003el-h\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003el-h\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10.609\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.183\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-4.069\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.364\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e243.243\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1558\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-10.765\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-1.318\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0623\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10.846\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e244.143\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1482\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n\u003ch2\u003e4.2.2. Nanotube formation of the 3-dimensional molecular structures based on dileucine\u003c/h2\u003e\n\u003cp\u003eSimilarly as for FF consider here the molecular model of the dileucine (LL) helix-like nanotube model, using known experimental X-ray data for them [40\u0026ndash;42]. From experimental X-ray crystallographic data for dileucine of left-handed chirality L-LL [40\u0026ndash;42], it is possible to identify a clear structure of a helical nanotube. At the same time, 4 dipeptides fit here in one turn, unlike FF PNT (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eCrystallographic parameters here (for space group P2\u003csub\u003e1\u003c/sub\u003e2\u003csub\u003e1\u003c/sub\u003e2\u003csub\u003e1\u003c/sub\u003e) \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.352 \u0026Aring;, \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;16.76 \u0026Aring;, \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;33.312 \u0026Aring;. Parameter \u003cem\u003ea\u003c/em\u003e corresponds to the helix pitch along the axis of the nanotube. Artificial helix-like structures of L-dipeptides were made from the initially constructed ring-stacked models, transformed with a shift of each subsequent dipeptide along the nanotube \u003cem\u003ec\u003c/em\u003e axis so that, when going around a helix coil, its step equals to the period of the experimental crystallographic structure along \u003cem\u003ec\u003c/em\u003e axis. The helix-like structures based on D-dipeptides were constructed in a similar way, assuming the equivalence of the period along the \u003cem\u003ec\u003c/em\u003e axis for L- and D-dipeptides.\u003c/p\u003e\n\u003cp\u003eFigure 7 shows the structure of two-helix coils of L-LL (Figure 7 a, b) and D-LL (Figure 7 c, d) nanotubes each consisting of four LL molecules per coil. The main properties of such LL PNT will be discussed below.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\n\u003ch2\u003e4.3.1. Initial models of diisoleucine\u003c/h2\u003e\n\u003cp\u003eExisting experimental data for nanostructures based on the isoleucine (Ile or I) amino acid and diisoleucine (II) dipeptide have several different and rather \u0026ldquo;entangled\u0026rdquo; crystallographic structures [41, 42] from which it is not yet possible to identify a clearly defined nanotube structure. Therefore, in this work, we build artificial hypothetical models for the dipeptide based on isoleucine and spiral nanotubes based on diisoleucine, based on analogues with already known structures for FF and LL, and relying on clearly known experimental X-ray data for them. Let us consider in more detail these structures for I and II, also taking into account their different chirality L and D. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e presents molecular models of II dipeptides built on the basis of I amino acids of different L and D chiralities, also taking into account their conformation: Left-handed a-helix for I amino acids with L chirality and a-helix for I with D chrality. The dipole moment data of the L-II and D-II presented in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab5\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003ePhysical properties for diisoleucine of various conformation using different semi-empirical methods.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eCalculation method\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDipeptide\u003c/p\u003e\n\u003cp\u003echirality\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eAmino acids\u003c/p\u003e\n\u003cp\u003econformation\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003eDebye\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eVolume,\u003c/p\u003e\n\u003cp\u003e\u0026Aring;\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePolarization,\u003c/p\u003e\n\u003cp\u003eC/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-II, \u003cem\u003el-h\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003el-h\u003c/em\u003e, \u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10.477\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.667\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.193\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10.500\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e244.125\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1435\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-11.633\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.233\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-1.858\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.783\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e241.918\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1625\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-II, \u003cem\u003el-h\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003el-h\u003c/em\u003e, \u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e13.0570\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.678\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.415\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e13.081\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e244.141\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1787\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026alpha;-helix\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-12.598\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.064\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.998\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e12.598\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e244.659\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1718\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\n\u003ch2\u003e4.3.2. Nanotube formation of the 3-dimensional molecular structures based on diisoleucine\u003c/h2\u003e\n\u003cp\u003eSimilarly as for FF and LL consider here the molecular model of the disoileucine (II) helix-like nanotube model, using known experimental X-ray data for them [40\u0026ndash;42]. From experimental X-ray crystallographic data for dileucine of the left-handed chirality L-LL [40\u0026ndash;42], it is possible to constrcut similar structure of a helical nanotube of the dilisoleucine of the left-handed chirality L-II, and further to make the same artificial modle structure for the D-II. At the same time, 4 dipeptides fit here in one turn as for LL PNT, unlike FF PNT having 6 dipeptide molecules (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n\u003ch2\u003e4.4. Chirality index calculation of helix-shaped nanotubes\u003c/h2\u003e\n\u003cp\u003eTo determine the chirality of the helix-shaped structure, we use a method based on the mixed product of dipole moment vectors \u003cstrong\u003eDi\u003c/strong\u003e of the successive individual dipeptides that form the helix-like structure of a nanotube. This method was proposed and developed in [45]. In this case, the scalar triple product dipole moments \u003cstrong\u003eDi\u003c/strong\u003e of successive individual AA molecules that make up the coils of a helical PNT nanotube is used. The origin of vectors \u003cstrong\u003eDi\u003c/strong\u003e is taken relative to the centre of mass of the corresponding molecules. The absolute value of each dipole moment \u003cstrong\u003eDi\u003c/strong\u003e is\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$${D}_{i}=\\left|{D}_{i}\\right|=\\sqrt{{D}_{\\text{x,i}}^{2}{\\text{+D}}_{\\text{y,i}}^{2}{\\text{+D}}_{\\text{z,i}}^{2}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ex,i\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ey,i\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez,i\u003c/em\u003e\u003c/sub\u003e are the components of the \u003cem\u003ei\u003c/em\u003e-th vector \u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ei\u003c/strong\u003e\u003c/sub\u003e in the Cartesian coordinates.\u003c/p\u003e\n\u003cp\u003eAccording to [45], here the sum of mixed (vector-scalar) products of dipole moments associated with the chirality of the PNT can be written as:\u003c/p\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$${c}_{\\text{total}}={\\sum }_{\\text{i=}1}^{n-2}\\left(\\left[{D}_{i}{\\text{,D}}_{\\text{i}\\text{+}1}\\right]{\\text{,D}}_{\\text{i}\\text{+}2}\\right),$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIt is necessary to note that the summation is taken over \u003cem\u003ei\u003c/em\u003e in the range from 1 to \u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026minus;\u0026thinsp;2, where \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4 for one coil of LL PNT and II PNT, while for one coil of FF PNT \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6 [45]. The \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003etotal\u003c/em\u003e\u003c/sub\u003e value can be normalized to the cube of the average total dipole moment of the PNT coil, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({D}_{\\text{av}}=\\frac{1}{n}{\\sum }_{\\text{i}\\text{=}1}^{n}{D}_{i}\\)\u003c/span\u003e\u003c/span\u003e, to get the universal normalized measure of the chirality index:\u003c/p\u003e\n\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ3\" class=\"mathdisplay\"\u003e$${c}_{\\text{norm}}=\\frac{{c}_{\\text{total}}}{{D}_{\\text{av}}^{3}}\\text{.}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe sign of \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003enorm\u003c/em\u003e\u003c/sub\u003e corresponds to the PNT\u0026rsquo;s chirality type: positive \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003enorm\u003c/em\u003e\u003c/sub\u003e values correspond to the right-handed PNTs - \u0026ldquo;D\u0026rdquo;, whereas negative \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003enorm\u003c/em\u003e\u003c/sub\u003e - to the left-handed [45] - \u0026ldquo;L\u0026rdquo;.\u003c/p\u003e\n\u003cp\u003eWe have developed an algorithm that allows us to calculate each individual selected dipole moment of any dipeptide (LL, FF, II, etc.), leaving it surrounded by all other dipeptide\u0026rsquo;s molecules of the helix-shaped structure of the peptide nanotube. This makes it possible to obtain a more accurate calculation result, taking into account the interaction of the selected dipeptide with all other dipeptides of the PNT helix-like molecules.\u003c/p\u003e\n\u003cp\u003eTo build this algorithm, a special script based on TCL Tool Command Language, a part of Chemist's Developer Kit (CDK) in Hyperchem package [46], was developed. The constructed algorithm makes it possible to select any number n of dipeptides and to carry out calculations not only for one helix coil, but for any number of them, in the case of a more complex structure of the any dipeptide PNT. It is important to correctly specify the sequence of dipeptides when going around the coils of the helix, since in the helix-like structure itself their numbers can be located not one after the other, but differently. This must be checked when performing calculations in each case.\u003c/p\u003e\n\u003cp\u003eThis algorithm now we applied for calculation of the chirality index of the various AA and dipeptide\u0026rsquo;s PNT.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e present the results for calculations of the chirality index (5) for the helix-shaped nanotubes LL PNT, FF PNT and II PNT with the initial dipeptides of the different chirality (L-LL and D-LL; L-FF and D-FF; L-II and D-II), performed using various semi-empirical methods through above mentioned algorithm.\u003c/p\u003e\n\u003cp\u003eThe data obtained here are calculated values of the chirality index for the nanotube's model of one coil of the helix and for models of two coils of the helix - based on FF (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e), LL (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e) and II (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e) dipeptides.\u003c/p\u003e\n\u003cp\u003eThe directions of the dipole moment vector Di of one of the dipeptides in cases of different chiralities are shown with black arrows (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003ea, c) using diisoleucine II as an example, and the directions of bypassing the coil of the helix when calculating the chirality value according to formula (5) for both chirality types are shown by the curved blue arrows (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003ea, c) for II PNT.\u003c/p\u003e\n\u003cp\u003eThe vectors of dipeptides and the directions of bypassing of the helical coils for model nanotubes based on LL and FF are oriented similarly (taking into account that FF forms a helix coil of 6 dipeptides, and in the case of LL, the helix coil contains 4 dipeptides).\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab6\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eResults of calculating the chirality index (3) of dipeptide-based nanotubes AA PNT of different initial chiralities L-AA and D-AA.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eModels and methds\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eDipeptides chirality\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePNT model\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCalculation method\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-AA\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-AA\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e1 coil of LL PNT\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RH\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.214\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.519\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.209\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.485\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e2 coils LL PNT\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.968\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.709\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.936\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.582\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e1 coil of FF PNT\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.36\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;1.35\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.2622\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.3246\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e2 coils of FF PNT\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.1704\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-3.5004\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.4857\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-3.1417\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.1441\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-3.4889\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e2coils of II PNT\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.1888\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.9349\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.1498\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2.0414\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eChirality sign of a helix-shaped PNT nanotube\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePositive \u0026laquo;+\u0026raquo;\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNegative \u0026laquo; - \u0026raquo;\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003ePNT helix-shaped nanotube chirality symbol\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eIt should be noted here that while for the L-FF, D-FF, L-LL PNTs we have a clear basis for its helix-like structure based on experimental data [21\u0026ndash;26, 40\u0026ndash;42], for the D-LL PNT as well for L-II and D-II we only have an artificial hypothetical structures built on the basis of an analogy of the related structures of both LL PNT and FF PNT.\u003c/p\u003e\n\u003cp\u003eAs can be clear seen from Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, the results obtained here show a characteristic change in the sign of the chirality upon transition to a higher level of the molecular hierarchy organization, which is observed in the structures of biomacromolecules [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e]: the calculated chirality of a helix-shaped nanotube based on dipeptide L-FF, L -LL, L-II has a positive sign \u0026ndash; and belong to D-type, and the chirality of the nanotube based on the D-FF, D-LL, D-II dipeptide has a negative sign, corresponding to the L-type chirality.\u003c/p\u003e\n\u003cp\u003eIt is striking that this conclusion is independent of the calculation method and is valid for PNT models built on the basis of x-ray data and for artificially created ones.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003e4.5. Main calculated Physical properties of various AA PNT and discussion\u003c/h2\u003e\n\u003cp\u003eThe developed AA PNT models were used to calculate the AA PNT\u0026rsquo;s physical properties, such as dipole moments, polarization (\u003cem\u003eP\u003c/em\u003e), piezoelectric coefficients (\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e), electronic energy levels (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eHOMO\u003c/em\u003e\u003c/sub\u003e of the highest occupied states of molecular orbitals) and (E\u003csub\u003eLUMO\u003c/sub\u003e of the lowest unoccupied molecular orbitals), and band gap: \u003cem\u003eEg\u0026thinsp;=\u0026thinsp;E\u003c/em\u003e\u003csub\u003e\u003cem\u003eLUMO\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026minus; E\u003c/em\u003e\u003csub\u003e\u003cem\u003eHOMO\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e presents the results of calculating some physical properties of various PNT models (from 2 turns of a helix) based on different dipeptides, performed using semi-empirical methods AM1, PM1 and PM3: dipole moments, levels of polarization and electron energy, as well as band gap Eg\u0026thinsp;=\u0026thinsp;E_LUMO \u0026ndash; E_HOMO. (Here \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003eVDW\u003c/em\u003e\u003c/sub\u003e is the volume of the model PNT structure over the van der Waals surface, calculated by the QSAR program implemented into the HyperChem [46]).\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab7\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCalculated physical properties of the studied two-coils PNTs models.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eMethods and models\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"7\" align=\"left\"\u003e\n\u003cp\u003eCalculated physical values\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePNT model\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCalculation\u003c/p\u003e\n\u003cp\u003emethod\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ez\u003c/strong\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDebye\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDebye\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eV\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eVDW\u003c/strong\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026Aring;\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eP\u003c/strong\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eC/m\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eE\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eHOMO\u003c/strong\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eeV\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eE\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eLUMO\u003c/strong\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eeV\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eE\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eg\u003c/strong\u003e\u003c/sub\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eeV\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"SmallCaps\"\u003eL\u003c/span\u003e-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;140.217\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e140.757\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3365.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1395\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;5.9405\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;2.4995\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.4410\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;141.075\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e141.619\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3365.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1398\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;5.8568\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;2.6182\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.2387\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"SmallCaps\"\u003eD\u003c/span\u003e-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;140.348\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e140.384\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3346.47\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1399\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;5.9239\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;2.3491\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.5748\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;141.118\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e141.154\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3346.47\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1407\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;5.8118\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;2.4497\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.3620\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"SmallCaps\"\u003eL\u003c/span\u003e-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;78.243\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e89.739\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1854.47\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1614\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;6.0452\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;2.8156\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.2296\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;76.4628\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e87.8063\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1854.47\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1579\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;6.0695\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;2.5199\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.5496\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"SmallCaps\"\u003eD\u003c/span\u003e-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;22.8902\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e23.2787\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1935.33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.04012\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;7.90751\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;1.36354\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.6544\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;20.9477\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.3186\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1935.33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.03674\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;7.8138\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;0.97568\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.8381\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"SmallCaps\"\u003eL\u003c/span\u003e-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;19.778\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e20.0483\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1930.63\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.03464\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;8.0591\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;0.8357\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.2234\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;21.412\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.697\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1930.63\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0375\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;8.2822\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;1.1885\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.0937\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"SmallCaps\"\u003eD\u003c/span\u003e-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;10.433\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e11.112\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1938.35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0192\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;8.4417\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;0.7794\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.662\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;10.089\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10.702\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1938.02\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0185\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;8.5859\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;1.0844\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.502\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe results obtained show that for all calculation methods the values of polarization P and band gap Eg for L-LL, L-FF, and D-FF PNTs based on experimental x-ray data are close to each other (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e). For all three PNTs, the band gap values are close to the experimental values 3.35\u0026ndash;4.13 eV [35] and correspond to the absorption edge in the ultraviolet A region (UV-A, 315\u0026ndash;400 nm) [33, 34].\u003c/p\u003e\n\u003cp\u003eThe proposed model structures for D-LL PNT have lower polarization and a wider band gap values. At the same time, it is clear form our studies that with deeper optimization of artificial structures, these values change and approach experimentally observed values. That is, it can be assumed that the tendency to improve the hypothetical structures of D-LL PNT is in the right direction and it can be expected that when experimental samples of nanostructures based on D-LL are obtained, their nanotubes will have characteristics close to those calculated here for L-LL, L-FF and D-FF PNTs. The same could be expected for artificially made nanotubes models on the base of the L-II and D-II dipeptides. Upon obtaining their corresponding experimental implementation, it can be assumed that the magnitude of their polarization will be even greater, and the values of the band gap will be narrower than for the parameters calculated here based on these proposed models. It would be awaited that all these values will be close to the already known experimental values for helix-like nanotubes based on L-FF, D-FF and L-LL dipeptides.\u003c/p\u003e\n\u003cp\u003eFor D-LL, D-II, and L-II PNTs, the polarization and band gaps are also close to each other, though they are significantly different from the abovementioned models (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). So, their polarizations are 3\u0026ndash;4 times lower indicating potentially weaker piezoelectric properties than well-known FF PNTs. However, their band gap values are two times larger than FF PNTs demonstrate, that corresponds to the absorption edge of 180\u0026ndash;210 nm belonging to the short-wave UV-C radiation. Such materials are highly demanded for solar-blind ultraviolet photodetectors (SBUV) operating in this spectral range, where the sunlight is completely absorbed by the ozone layer in the atmosphere. SBUV detectors can be used for monitoring ozone holes, fires, high-voltage transmission lines, etc. Currently, such detectors are based mainly on wide-band-gap semiconductors, such as gallium nitride or gallium oxide [79], whereas PNTs can be considered as more sustainable and friendlier alternative. Based on such peptide nanotubes, a prospective heterostructure can be created in combination with polymer ferroelectrics for a photodetector tuned to the different spectral ranges, similar to the recently developed detector based on dichalcogenides of the MoS\u003csub\u003e2\u003c/sub\u003e type driven by ferroelectrics layers [80, 81]. It would be very useful for many related applications.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n\u003ch2\u003e4.6. Influence of water molecules\u003c/h2\u003e\n\u003cp\u003eInteresting changes in the physical properties of all types of nanotubes considered occur when water molecules are placed in their internal cavity. As mentioned above, in the experimental samples of both FF PNTs of both types of chirality, and in LL PNTs (L-LL chirality), the presence of water molecules is detected. X-ray methods here make it difficult to accurately determine the number of water molecules, and only with the help of computer calculations was it possible to clarify that in the internal cavity of the FF PNT there are 21 water molecules in the PNT model of 2 helix coils (which here corresponds to the period of one cell) [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e]. Also for L-LL, the presence of 8 water molecules in the internal cavity was established [40\u0026ndash;42]. Using these experimental data, molecular models of these PNTs with the presence of water molecules inside them were built (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e). Models with the presence of water molecules were also built for artificial nanotubes D-LL (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003ee) and similarly, everything was done for L-II and D-II (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab8\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eProperties of AA PNT helix nanotubes under influenced by water molecules\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eMethods and models\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"7\" align=\"left\"\u003e\n\u003cp\u003eBasic calculated physical quantities\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMethods\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eChirality\u003c/p\u003e\n\u003cp\u003eAA\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ez\u003c/strong\u003e\u003c/sub\u003e, \u003cstrong\u003eDebye\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eD\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/sub\u003e, \u003cstrong\u003eDebye\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eVolume,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026Aring;\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eP,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eC/m\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eE_HOMO, eV\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eE_LUMO, eV\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eEg,\u003c/p\u003e\n\u003cp\u003eeV\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eNot\u003c/p\u003e\n\u003cp\u003eH2O\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eRM1 RHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-141.075\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e141.619\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3365.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1398\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-5.8568\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2.6182\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.2387\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-141.118\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e141.154\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3346.47\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1407\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-5.8118\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2.4497\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.3620\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eWith\u003c/p\u003e\n\u003cp\u003eH2O\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eRM1\u003c/p\u003e\n\u003cp\u003eRHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-155.116\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e155.878\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3972.63\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1303\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-5.7348\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2.8728\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.8620\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-126.781\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e126.804\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3977.08\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1064\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-5.4119\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-3.6005\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.8114\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eNot\u003c/p\u003e\n\u003cp\u003eH2O\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eRHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-78.243\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e89.739\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1854.47\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1614\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-6.0452\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2.8156\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.2296\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-22.8902\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e23.2787\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1935.33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0401\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-7.90751\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.3635\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.6544\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eWith\u003c/p\u003e\n\u003cp\u003eH2O\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eRHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-78.448\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e91.020\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1930.58\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1573\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-5.9298\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2.9753\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.9545\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-23.6836\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e24.327\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2051.15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0396\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-7.9134\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.2902\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.6232\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eNot\u003c/p\u003e\n\u003cp\u003eH2O\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eRHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;21.412\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.697\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1930.63\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0375\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;8.2822\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;1.1885\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.094\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;10.089\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10.702\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1938.02\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0185\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;8.5859\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026minus;1.0844\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.502\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eWith\u003c/p\u003e\n\u003cp\u003eH2O\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eRHF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-27.757\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e28.322\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2025.96\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0466\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-6.0238\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.5064\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4.517\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eD-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-12.732\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e13.213\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2033.84\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0217\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-6.4536\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.1725\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5.281\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eSimilarly as for D-LL (on Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003ed) we constructed artificial models for L-II and D-II of the II PNT. Calculations performed by various quantum-chemical semi-empirical methods AM1, PM3, PM1 (from the HiperChem software package) showed the main general picture of changes - when water molecules are introduced into the internal cavity of nanotubes, there is a change in the total dipole moment and polarization of the nanotubes, as well as a change in their electronic levels (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eHOMO\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eLUMO\u003c/em\u003e\u003c/sub\u003e), resulting in a narrowing of the band gap \u003cem\u003eEg\u003c/em\u003e.\u003c/p\u003e\n\u003cp\u003eIt should be noted here that mainly after the introduction of water molecules there is an increase in the total dipole moment [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e]. Although not in all cases (as is the case with D-FF). Apparently, this also depends on the final orientation of all dipoles of the water cluster inside the nanotube plane after optimization of the entire structure as a whole [78]. These questions still require further research [82]. Water structures in such narrow nanocavities represent a special Confined water in nanochannel and form ice-like one-dimensional nanostructures with their own dipole moments, which can have an orientation either coinciding with the general dipole moment of the nanotube or against it. The total dipole moment (and polarization) of the entire structure of a nanotube with water depends on this. Important point here is the change in band gap \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e. In all cases, there is a decrease in the gap \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e. But this happens differently in different types of nanotubes. Of course, a significant and noticeable jump in \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e is visible for both types of FF PNT chirality. In addition to the already mentioned possibilities of using such PNTs as photodetectors, there are other promising developments in the applications of these molecular devices.\u003c/p\u003e\n\u003cp\u003eNoteworthy is the significant jump in \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e in our hypothetical model nanotubes based on diisoleucine L-II and D-II. Perhaps this is due to the greater flexibility of the II structure in this case, which responds more actively to the introduction of the water cluster. This may have interesting promising different applications in the practical synthesis of such nanotubes, similar as for FF PNT, for example, in [83].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n\u003ch2\u003e4.7. Calculations of piezoelectric coefficients\u003c/h2\u003e\n\u003cp\u003eTo calculate the piezoelectric coefficients of AA PNT peptide nanotubes based on the considered FF, LL and II dipeptides, this work used the basic electromechanical coupling relationship (1) [6, 58, 63, 75 ]. In this case, molecular models of all the above studied AA PNTs were used, constructed using the amino acid (AA) database of the HyperChem tool [46]. All AA and corresponding dipeptides were taken in the left-handed (l-h) a-helix conformation for L-chiral AA isomers and a-helix for D-chiral AA isomers. In this case, helical AA PNT models (of one and two helix-coils) for the original L-FF, D-FF and L-LL dipeptides were constructed on the basis of experimental x-ray data. For dipeptides D-LL, L-II and D-II and similar helical models artificially created on similar basis, their structural optimization was carried out (by the Polak\u0026ndash;Rieber conjugate gradient method [46]) to achieve a more optimal nanostructure of AA PNT. For all these models, all the necessary parameters of these AA PNT structures (dipole moment, volume, polarization, energy levels and band gaps, as well as their chirality indices) were calculated. These data are shown above in Tables\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e. Calculations of piezoelectric coefficients d\u003csub\u003e33\u003c/sub\u003e using formula (1) also require determining the magnitude of the electrostriction coefficients Q\u003csub\u003e11\u003c/sub\u003e and changes in the components of the polarization vector P at a certain orientation of the nanotube axes. Here we choose the main axis to be the OZ axis along the AA PNT nanotube axis, along which the main component of polarization P\u003csub\u003ez\u003c/sub\u003e is mainly located. Next, to carry out all the calculations, we need to apply an electric field E\u003csub\u003ez\u003c/sub\u003e along this main tubular axis of the AA PNT (using a special option of the electric field E in the HyperChem tool [46]). The basic procedure for these calculations was proposed and described in detail by us in [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eFirstly, to carry out calculations of the entire simulated molecular structure of the each AA PNT, located in the applied electric field \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e, with fixed initial positions of all atoms (so called \u0026ldquo;single point\u0026rdquo; (SP) calculation) - in this case we obtain the initial values of dipole moments \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eSP\u003c/em\u003e\u003c/sup\u003e (and it\u0026rsquo;s component \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eSP\u003c/em\u003e\u003c/sup\u003e \u003cem\u003e)\u003c/em\u003e and volume \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e (using QSAR program implemented into HyperChem [46]).\u003c/p\u003e\n\u003cp\u003eSecondly, optimization (or relaxation) of the entire AA PNT structure is carried out in a given electric field \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e, and the resulted change \u003cem\u003e\u0026Delta;D\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e in the total dipole moment to \u003cem\u003eD\u003c/em\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e with component \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e (\u003cem\u003e\u0026Delta;D\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e = \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e \u003cem\u003e\u0026ndash; D\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eSP\u003c/em\u003e\u003c/sup\u003e ) is determined, with a corresponding deformation of the volume to the value V\u003csup\u003eOPT\u003c/sup\u003e (\u003cem\u003eDV\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eV\u003c/em\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e-V\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e, and relative change \u003cem\u003es = (V\u003c/em\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e-V\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)/V\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eDV/V\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e)\u003c/em\u003e. As a result, the change in polarization \u003cem\u003eP\u003c/em\u003e is determined (according to formula (2)) for it\u0026rsquo;s component \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e: \u003cem\u003e\u0026Delta;P\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e = \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e \u003cem\u003e\u0026ndash; P\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eSP\u003c/em\u003e\u003c/sup\u003e. As a result, we define electrostriction coefficient by relation \u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003e11\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e= s/((\u0026Delta;P\u003c/em\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e, (where s\u0026thinsp;\u003cem\u003e=\u0026thinsp;\u0026Delta;V/V\u003c/em\u003e\u003csub\u003e\u003cem\u003e0)\u003c/em\u003e\u003c/sub\u003e and the piezoelectric coefficient is finally calculated from the relation \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e=\u0026thinsp;2\u0026epsilon;\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u0026Delta;P\u003c/em\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e, where e is dielectric permittivity of AA PNT, e\u003csub\u003e0\u003c/sub\u003e -vacuum dielectric constant.\u003c/p\u003e\n\u003cp\u003eAll data calculated step by step using this procedure algorithm are presented in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e. We use here the value of dielectric constant \u0026epsilon; = 4 - this is a common value for proteins [6, 57, 58, 64, 65]. But in some cases it may not be entirely correct. The dielectric constant of proteins can change, especially if the temperature changes - probably, under different conditions, the dielectric constant can increase greater than e\u0026thinsp;=\u0026thinsp;10 [64, 65]. We will leave these questions here for other studies. We also note that the data presented here are somewhat different from a number of previous data in the works [6, 10, 21\u0026ndash;27, 63]. This is due to some differences in calculation methods and optimization details of models that occur when they are relaxed along possibly different PES optimization trajectories, so that they ultimately arrive at a different PES minimum point. In principle, these details do not change the basic essence of the phenomena occurring.\u003c/p\u003e\n\u003cp\u003eTo analyse the data obtained, it is necessary first of all to note that all the studied AA-PNT structures are based on long-range electrostatic interactions (following from dipole-dipole interactions of their molecular components), including van der Waals interactions involving hydrogen bonds inherent in these structures with NH\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e, CH\u003csub\u003e3\u003c/sub\u003e and COO\u003csup\u003e\u0026minus;\u003c/sup\u003e sides, especially in their zwitterionic form, including water molecules. Using the HyperChem tool, it is easy to see how the hydrogen bonding process occurs (with direct visualization of all molecular structures on the workspace of the monitor screen) and how it changes during the optimization process.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab9\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCalculated data on piezoelectric coefficients\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eMethods and models\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"8\" align=\"left\"\u003e\n\u003cp\u003eCalculated physical values\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePNT model\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCalculation\u003c/p\u003e\n\u003cp\u003emethod\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eSP\u003c/em\u003e\u003c/sup\u003e, Debye\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e, Debye\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003e\u0026Delta;D\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e, Debye\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003e\u0026Delta;P\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e, C/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e((\u003cem\u003e\u0026Delta;P\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e)\u003csup\u003e2\u003c/sup\u003e, C\u003csup\u003e2\u003c/sup\u003e/m\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003es =\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(V\u003c/em\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e-V\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)/V\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e= s/((\u0026Delta;P\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e,\u003c/p\u003e\n\u003cp\u003em\u003csup\u003e4\u003c/sup\u003e/C\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e=\u0026thinsp;2ee\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u0026Delta;P\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eOPT\u003c/em\u003e\u003c/sup\u003e,\u003c/p\u003e\n\u003cp\u003epm/V\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"4\" align=\"left\"\u003e\n\u003cp\u003eL-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e = 0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-144.54\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-141.97\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.563\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.002540\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000065\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0072528\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1124.07\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e200.909\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e =\u0026minus;0.0005\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-138.06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-134.78\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.277\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.003248\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000105\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00723794\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e686.20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e157.859\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRM1\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e= -0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-136.69\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-131.62\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5.07\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.005025\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000253\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00467376\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e185.11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e65.886\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRM1\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e= 0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-145.46\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-141.24\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4.22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.004182\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000175\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00468564\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e267.87\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e79.358\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"4\" align=\"left\"\u003e\n\u003cp\u003eD-FF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1\u003c/p\u003e\n\u003cp\u003eEz\u0026thinsp;=\u0026thinsp;0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-144.66\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-142.58\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.079\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.002072\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000043\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.01012114\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2357.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e346.010\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAM1\u003c/p\u003e\n\u003cp\u003eEz= -0.0005\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-138.19\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-135.24\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.945\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.002936\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000086\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.010139\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1176.63\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e244.651\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRM1\u003c/p\u003e\n\u003cp\u003eEz= -0.0005\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-138.93\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-133.84\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5.084\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.005068\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000257\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00707312\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e275.45\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e98.897\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRM1,\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e=0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-145.50\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-141.20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4.293\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00428\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000183\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00709676\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e387.59\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e117.477\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eL-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e= 0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-80.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-77.79\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.464\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.004432\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000196\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.016630\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e846.86\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e265.788\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e=\u0026minus;0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-76.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-72.89\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.339\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006006\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000361\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0165977\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e460.17\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e195.759\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eD-LL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e =0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-24.94\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-24.18\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.762\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.001312\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000017\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00072856\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e422.96\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e39.320\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e =\u0026minus;0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-20.84\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-20.30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.538\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000938\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000009\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00062522\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e711.22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e47.234\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eL-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e = 0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-23.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-23.93\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.332\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000574\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000003\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00077709\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2361.98\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e95.967\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e =\u0026minus;0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-19.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-19.02\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.202\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000349\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000002\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00053868\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4380.18\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e108.282\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eD-II\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e = 0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-12.03\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-12.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.374\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000644\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000004\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00006192\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e149.44\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.814\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePM3\u003c/p\u003e\n\u003cp\u003eE\u003csub\u003ez\u003c/sub\u003e =\u0026minus;0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-7.66\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-7.52\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.136\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000234\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000005\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00002580\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e470.88\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.807\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThus, here we can clearly see exactly how dipole-dipole and van der Waals interactions occur, how hydrogen bonds are formed, changed and influence the entire self-organization of the molecular system. Piezoelectric phenomena in such structures are now the focus of attention of many scientists [29, 30, 59, 60, 66, 67\u0026ndash;72, 84\u0026ndash;91].\u003c/p\u003e\n\u003cp\u003eWe also note that the values of the electrostriction coefficients, as well as the piezoelectric coefficients, obtained in our calculations are close to the data of many similar molecular and organic structures [68\u0026ndash;75]. So, for example, in polyurethane the value is Q\u0026thinsp;=\u0026thinsp;850 (m\u003csup\u003e4\u003c/sup\u003e/C\u003csup\u003e2\u003c/sup\u003e) [75].\u003c/p\u003e\n\u003cp\u003eIt is interesting that the values of the piezoelectric coefficients we obtained here for various AA-PNTs in our calculations also correspond to a number of data for some AA-based crystals and hydrogen bonding systems. Thus, in [84], a piezoelectric generator was built based on FF PNT nanotubes. Measurements showed that an estimated piezoelectric constant \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8.8 pm/V was obtained there. Of course, this does not seem to be a very large value, but here it should be taken into account that these are already measurements at the output of the generator, after passing through the inevitable losses and attenuation that reduce the efficiency of the generator. At the same time, measurements performed in [29] gave values \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e~\u003c/em\u003e\u0026thinsp;60 pm/V for the FF of PNT.\u003c/p\u003e\n\u003cp\u003eExperimental measurements of the longitudinal component d33 with quasi-static\u0026nbsp;forces applied to the (001) plane along the crystallographic axis c of g-glycine single crystals showed values of the coefficient \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;9.93 pm/V (compared to the predicted result of calculations using density functional theory (DFT) methods of 10.4 pm/V) [85]. At the same time, for \u0026beta;-glycine, the measured values turn out to be about\u0026thinsp;~\u0026thinsp;178 pm/V, which is close to the DFT calculations predicted there, about 195 pm/V [85].\u003c/p\u003e\n\u003cp\u003eAnd this is comparable in value with \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;185 pC/N (pm/V) recently measured in an organic inorganic perovskite crystal [86]. It is an organic-inorganic perovskite ferroelectric material of Me3NCH2ClMnCl3 (TMCM-MnCl3) that shows an excellent piezoelectric response (\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;185 pC/N) that is close to that of inorganic piezoelectrics of BTO (\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;190 pC/N) [55]. In the studied systems with hydrogen bonds such as dimer of thiophenol-nitrobenzene (SPH-NBz) and phenol-nitrobenzene (PH-NBz) dimer for the piezoelectric coefficient values of the order of \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;18.89\u0026ndash;25.57 pm/V were obtained [87]. A piezoelectric coefficient \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;23 pm/V was found for the dimer of aniline-nitrobenzene (aniline:NBz) - this is the calculated value of \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e obtained at the theoretical level of DFT in calculations with the B3LYP/6-31G* functional [88].\u003c/p\u003e\n\u003cp\u003eAs for other molecular materials, it is interesting to note that Rochelle salt, one of the first discovered piezoelectric materials [89], exhibits strong shear piezoelectricity with a piezoelectric coefficient of the order of \u003cem\u003ed\u003c/em\u003e\u0026thinsp;~\u0026thinsp;345 pm/V [90].\u003c/p\u003e\n\u003cp\u003eThus, the findings confirm that many more similar H-bonded and AA tubular systems with high piezoresponse can be found due to the ubiquity of hydrogen bonding in chemistry, materials, and biological systems.\u003c/p\u003e\n\u003cp\u003eRecently new dipeptide nanotubes PNT based on the dileucine (LL), diisoleucine (II), combined alanine-isoleucine (Ala-Ile, AI) and diphenylalanine (FF) were also grown and studied using piezo force microscopy (PFM) [72\u0026ndash;74, 91]. The local piezoelectric properties of these PNTs were visualized simultaneously using the methods of atomic force microscopy (AFM) in contact mode and piezoresponse force microscopy (PFM) [72\u0026ndash;74]. The first experimental local measurements of the piezoelectric response parameters LL, II, AI and FF of PNTs were carried out [91], which showed a linear proportional dependence of their piezoresponse on the magnitude of the applied electrical voltage for all PNTs studied here. This work will continue.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThe new results of modeling and computational studies of the molecular structures of dipeptides and helix-shaped peptide nanotubes based on a number of amino acids, presented in this work, clearly show their wide range of different physical properties, which have numerous promising applications. They have both important polar and piezoelectric properties, as well as useful optical and photoelectronic properties in different energy ranges. This work examines in detail the molecular models of helix tubular nanostructures based on the amino acids phenylalanine and their dipeptide diphenylalanine of both types of chirality (L-FF and D-FF), which have already been experimentally synthesized and whose structure has been well studied using X-rays. Nanostructures based on the amino acid leucine and their dipeptide dileucine are considered similarly, but here only structures based on the left-handed chirality L-LL have been experimentally synthesized and studied by X-ray. For structures of right chirality D-LL, artificial models are constructed here by analogy with already known structures (such as L-FF). Similarly, artificial models were constructed for structures based on isoleucine amino acids and their dipeptide diisoleucine of both types of L-II and D-II chirality. For all nanostructures, extensive calculations of their physical properties: dipole, polar, piezoelectric, optical and photoelectronic \u0026mdash; were carried out. Their main wide possibilities for applications as sensors, sensors and other devices based on them are shown. The influence of water molecules in their internal cavity on their basic properties is also considered, which can also be important for various applications.\u003c/p\u003e \u003cp\u003eIn general, in this work, numerical calculations were carried out on the basis of quantum chemical semi-empirical methods AM1, PM3, RM1 from the HyperChem software package [46]. These methods have already been sufficiently tested and make it possible to carry out calculations and obtain results of all basic physical properties. However, in our other works (cited in this article) we used other approaches, including semi-empirical methods PM6, PM7 from the MOPAC package (MOPAC2016) [34,56,81], as well as density functional theory (DFT) methods with software such as VASP (Vienna Ab initio Simulation Package) [25\u0026ndash;27,54], and compared the results of these different approaches. In this work, we summarized and presented the main results obtained using various molecular modeling and computational chemistry methods on calculations of the physical properties of both experimentally studied nanostructures based on amino acids and dipeptides, and for predicted new nanostructures of this type based on dileucine and diisoleucine.\u003c/p\u003e \u003cp\u003eFor all studied helix-shaped nanostructures, their chirality indices were also calculated (based on the developed approach using vectors of dipole moments of individual dipeptides in a helix coil) [45] and it was shown that the law of changing the type of chirality is valid here when moving to the next hierarchical level of self-organization of molecular structures.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions:\u003c/strong\u003e Conceptualization, investigation, formal analysis, writing\u0026mdash;original draft preparation, V.B.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e This research received no external funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInstitutional Review Board Statement:\u0026nbsp;\u003c/strong\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInformed Consent Statement:\u0026nbsp;\u003c/strong\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments:\u003c/strong\u003e The authors are grateful for the opportunity to perform calculations using the computing and information resources of the IMPB RAS.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest:\u003c/strong\u003e We declare no potential conflict of interest in this article.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eCalvin M (1969) Chemical evolution. 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Chemistry Select 1:4326-4331. 10.1002/slct.201601043.\u003c/li\u003e\n \u003cli\u003eWerling KA, Griffin M, Hutchison GR, Lambrecht DS (2014) Piezoelectric hydrogen bonding: computational screening for a design rationale. J Phys Chem A118:7404-7410. doi: 10.1021/jp412740j.\u003c/li\u003e\n \u003cli\u003eValasek J (1921) Piezo-electric and allied phenomena in Rochelle salt. Phys Rev 17:475481. DOI: https://doi.org/10.1103/PhysRev.17.475.\u003c/li\u003e\n \u003cli\u003eMason WP (1964) Physical Acoustics: Principles and Methods. Academic Press, New York\u003c/li\u003e\n \u003cli\u003eBystrov VS, Bdikin IK, Singh B,(2019) Piezoelectric and ferroelectric properties of various amino acids and dipeptides strucures: molecular modeling and experiments. In: Bdikin I, Singh B, Simoes R (eds). UA Editora, Universidade de Aveiro, Aveiro. P 44.. ISBN 978-972-789-544-1\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table","content":"\u003cp\u003eTable 1 is available in the Supplementary Files section.\u003c/p\u003e "}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"аmino acids, dipeptides, peptide nanotubes, molecular modeling, quantum semi-empirical methods, chirality, dipole moments, polarization, piezoelectricity, band gap width","lastPublishedDoi":"10.21203/rs.3.rs-3952941/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3952941/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe paper considered the structural and dipole moments features of some amino acids that are important in the formation of the di-peptides and peptide nanotubes on their basis. The influence of the features of their chirality (left L and right D) and the alpha-helix conformations of amino acids also were taken into account. In particular, amino acids with aromatic rings were considered, such as phenylalanine (Phe/F), and branched-chain amino acids (BCAAs) Isoleucine (Ile/I), Leucine (Leu/L), as well as corresponding dipeptides based on them. On their basis, the features and properties of dipeptide structures and peptide nanotubes (PNTs) were investigated using computational molecular modeling and quantum-chemical semi-empirical calculations. Their polar, piezoelectric and photoelectronic properties and features were studied in details. The results of calculations of dipole moments and polarization, as well as piezoelectric coefficients and band gap width, for different types of helical peptide nanotubes are presented. The calculated values of the chirality indices of various nanotubes are given, depending on the chirality of the original dipeptides - the results obtained are consistent with the law of changes in the type of chirality as the hierarchy of molecular structures becomes more complex. Calculations were also carried out on the influence of water molecules in the internal cavity of nanotubes on their physical properties. Comparison of the results of these calculations by various computational chemistry methods with the available experimental data were also be given.\u003c/p\u003e","manuscriptTitle":"Features of molecular self-assembled helix peptide nanotubes based on some amino acids molecules and their dipeptides: molecular modelling studies","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-15 05:39:13","doi":"10.21203/rs.3.rs-3952941/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"75aa19ab-b2cf-4ec8-be54-8a1676371bea","owner":[],"postedDate":"February 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-02-15T05:39:13+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-15 05:39:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3952941","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3952941","identity":"rs-3952941","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}