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. 2a, 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. 2c, 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
|
Dx,
Debye
|
Dy,
Debye
|
Dz,
Debye
|
Dt,
Debye
|
VVDW,
Å3
|
P,
C/m2
|
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 NH3+ 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, 63], 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 P61 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)
|
R0, Å
|
12.236
|
12.091
|
12.102
|
12.075
|
R1, Å
|
15.271(698)
|
15.042(076)
|
15.180(569)
|
15.030(688)
|
R2, 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. 4a, d), we obtain their configurations, which coincide in the orientation of the NH3+ and COO− groups with the Left-handed (l-h) a-helix conformations for L-FF and a-helix for D-FF (Fig. 2c, 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
|
Dx,
Debye
|
Dy,
Debye
|
Dz,
Debye
|
Dt,
Debye
|
Volume,
Å3
|
Polarization,
C/m2
|
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 P212121) 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
|
Dx,
Debye
|
Dy,
Debye
|
Dz,
Debye
|
Dt,
Debye
|
Volume,
Å3
|
Polarization,
C/m2
|
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 Dx,i, Dy,i, and Dz,i are the components of the i-th vector Di 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 ctotal 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 cnorm corresponds to the PNT’s chirality type: positive cnorm values correspond to the right-handed PNTs - “D”, whereas negative cnorm - 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. 9a, 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. 9a, 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 (d33), electronic energy levels (EHOMO of the highest occupied states of molecular orbitals) and (ELUMO of the lowest unoccupied molecular orbitals), and band gap: Eg = ELUMO − EHOMO.
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 VVDW 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
|
Dz,
Debye
|
Dt,
Debye
|
VVDW,
Å3
|
P,
C/m2
|
EHOMO,
eV
|
ELUMO,
eV
|
Eg,
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 MoS2 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. 10e) 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
|
Dz, Debye
|
Dt, Debye
|
Volume,
Å3
|
P,
C/m2
|
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. 10d) 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 (EHOMO and ELUMO), 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 Eg. In all cases, there is a decrease in the gap Eg. But this happens differently in different types of nanotubes. Of course, a significant and noticeable jump in Eg 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 Eg 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 d33 using formula (1) also require determining the magnitude of the electrostriction coefficients Q11 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 Pz is mainly located. Next, to carry out all the calculations, we need to apply an electric field Ez 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 Ez, with fixed initial positions of all atoms (so called “single point” (SP) calculation) - in this case we obtain the initial values of dipole moments D0SP (and it’s component DzSP ) and volume V0 (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 Ez, and the resulted change ΔDzOPT in the total dipole moment to DOPT with component DzOPT (ΔDzOPT = DzOPT – DzSP ) is determined, with a corresponding deformation of the volume to the value VOPT (DV = VOPT-V0, and relative change s = (VOPT-V0)/V0 = DV/V0 ). As a result, the change in polarization P is determined (according to formula (2)) for it’s component Pz: ΔPzOPT = PzOPT – P0SP. As a result, we define electrostriction coefficient by relation Q11 = Qz = s/((ΔPOPT)2, (where s = ΔV/V0) and the piezoelectric coefficient is finally calculated from the relation d33 = 2εε0QzΔPOPT, where e is dielectric permittivity of AA PNT, e0 -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 NH3+, CH3 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
|
DzSP, Debye
|
DzOPT, Debye
|
ΔDzOPT, Debye
|
ΔPzOPT, C/m2
|
((ΔPzOPT)2, C2/m4
|
s =
(VOPT-V0)/V0
|
Qz = s/((ΔPzOPT)2,
m4/C2
|
d33 = 2ee0QzΔPzOPT,
pm/V
|
L-FF
|
AM1
Ez = 0.001
|
-144.54
|
-141.97
|
2.563
|
0.002540
|
0.0000065
|
0.0072528
|
1124.07
|
200.909
|
AM1
Ez =−0.0005
|
-138.06
|
-134.78
|
3.277
|
0.003248
|
0.0000105
|
0.00723794
|
686.20
|
157.859
|
RM1
Ez= -0.001
|
-136.69
|
-131.62
|
5.07
|
0.005025
|
0.0000253
|
0.00467376
|
185.11
|
65.886
|
RM1
Ez= 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,
Ez=0.001
|
-145.50
|
-141.20
|
4.293
|
0.00428
|
0.0000183
|
0.00709676
|
387.59
|
117.477
|
L-LL
|
PM3
Ez= 0.001
|
-80.25
|
-77.79
|
2.464
|
0.004432
|
0.0000196
|
0.016630
|
846.86
|
265.788
|
PM3
Ez=−0.001
|
-76.23
|
-72.89
|
3.339
|
0.006006
|
0.0000361
|
0.0165977
|
460.17
|
195.759
|
D-LL
|
PM3
Ez =0.001
|
-24.94
|
-24.18
|
0.762
|
0.001312
|
0.0000017
|
0.00072856
|
422.96
|
39.320
|
PM3
Ez =−0.001
|
-20.84
|
-20.30
|
0.538
|
0.000938
|
0.0000009
|
0.00062522
|
711.22
|
47.234
|
L-II
|
PM3
Ez = 0.001
|
-23.60
|
-23.93
|
0.332
|
0.000574
|
0.0000003
|
0.00077709
|
2361.98
|
95.967
|
PM3
Ez =−0.001
|
-19.23
|
-19.02
|
0.202
|
0.000349
|
0.0000002
|
0.00053868
|
4380.18
|
108.282
|
D-II
|
PM3
Ez = 0.001
|
-12.03
|
-12.60
|
0.374
|
0.000644
|
0.0000004
|
0.00006192
|
149.44
|
6.814
|
PM3
Ez =−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 (m4/C2) [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 d33 = 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 d33 ~ 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 d33 ~ 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 d33 = 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 (d33 = 185 pC/N) that is close to that of inorganic piezoelectrics of BTO (d33 = 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 d33 = 18.89–25.57 pm/V were obtained [87]. A piezoelectric coefficient d33 ~ 23 pm/V was found for the dimer of aniline-nitrobenzene (aniline:NBz) - this is the calculated value of d33 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.