Exploring Helical Folding in Oligomers of Cyclopentane-Based ϵ-Amino Acids: A Computational Study.

The conformational preferences of oligopeptides of an ϵ-amino acid (2-((1R,3S)-3-(aminomethyl)cyclopentyl)acetic acid, Amc5 a) with a cyclopentane substituent in the Cβ -Cγ -Cδ sequence of the backbone were investigated using DFT methods in chloroform and water. The most preferred conformation of Amc5 a oligomers (dimer to hexamer) was the H16  helical structure both in chloroform and water. Four residues were found to be sufficient to induce a substantial H16 helix population in solution. The Amc5 a hexamer adopted a stable left-handed (M)-2.316 helical conformation with a rise of 4.8 Å per turn. The hexamer of Ampa (an analogue of Amc5 a with replacing cyclopentane by pyrrolidine) adopted the right-handed mixed (P)-2.918/16 helical conformation in chloroform and the (M)-2.416 helical conformation in water. Therefore, hexamers of ϵ-amino acid residues exhibited different preferences of helical structures depending on the substituents in peptide backbone and the solvent polarity as well as the chain length.

Introduction

For two decades, there has been a great advance in the synthesis and structural characterization of various peptide foldamers.[ , , , , , , , , ] Peptide foldamers are oligomers of non‐natural amino acids that adopt well‐defined structural motifs, similar to those of natural peptides and proteins.[ , , , , , , , , ] It has been known that oligomers of β‐, γ‐, or δ‐amino acid residues as well as their hybrids with α‐amino acid residues can adopt various secondary structures as found in structures of peptides and proteins.[ , , , , , , , , ] In particular, peptide foldamers can stabilize various helical structures, of which the type, handedness, and macrodipole direction of helices can be controlled by the substitutions and/or stereochemistry of the residues.[ , , , , , , , , , , , , , , , , , , , ] Helical peptide foldamers have been used to design (a) antimicrobial peptides (AMPs) with cationic groups[ , , , , , ] and (b) catalysts for various organic reactions by incorporating catalytic functional groups.[ , , , , , , ]

It is well known that the polymer nylon 6 of the ϵ‐amino caproic acid (6‐aminohexanoic acid, Ahx; Figure 1a) forms fibrils composed of β‐sheet‐like chain structures.[ , ] A polymer of ϵ‐l‐lysine (2,6‐diaminohexanoic acid; Figure 1b) (ϵ‐PL) was first isolated from culture filtrates of Streptomyces albulus, which is composed of ∼25 lysine residues and exhibits antimicrobial activity against several human microbial pathogens.[ , , ] The spectra of far‐UV circular dichroism measurements for ϵ‐PL in aggregates supported that ϵ‐PL chains in aqueous solution are rich in β‐sheet‐like structure even at room temperature. Oligomers of branched ϵ‐l‐lysines with pendant α‐peptides were suggested as good DNA compaction agents with potential as delivery vectors. However, there has been no report for the synthesis and conformational analysis of peptide foldamers composed of ϵ‐amino acids, probably due to the experimental difficulties in the synthesis and incorporation of chirospecific building blocks. There are only two reports for the conformational preferences of α/ϵ‐hybrid peptides to date. Sharma et al. designed an α/ϵ‐hybrid hexapeptide containing l‐Ala and (S)‐C‐linked carbo‐ϵ‐amino acid [(S)‐ϵ‐Caa(x); Figure 1c] constituents in 1 : 1 alteration and suggested its structure as a novel mixed H14/12 helix by 1H NMR experiments. The synthesis and structural characterization of another α/ϵ‐hybrid tetrapeptide composed of Aib and 3‐(3‐aminophenyl)propanoic acid (Figure 1d) in 1 : 1 alteration were reported by Haldar and his co‐workers. Temperature‐dependent 1H NMR experiments of the α/ϵ‐hybrid tetrapeptide supported the formation of a ribbon‐like structure in CDCl3.

Figure 1

Chemical structures of various ϵ‐amino acid residues reported in the literature: (a) ϵ‐amino caproic acid (6‐aminohexanoic acid, Ahx), (b) ϵ‐l‐lysine (2,6‐diaminohexanoic acid), (c) (S)‐C‐linked carbo‐ϵ‐amino acid [(S)‐ϵ‐Caa(x)], (d) 3‐(3‐aminophenyl)propanoic acid, (e) 2‐(3‐(aminomethyl)cyclopentyl)acetic acid (Amc5a; this work), and (f) 2‐(5‐(aminomethyl)pyrrolidin‐2‐yl)acetic acid (Ampa; this work).

Only limited works studied by quantum‐mechanical methods have focused on the conformational preferences of ϵ‐peptides. Computational studies using density functional theory (DFT) methods have been performed to simulate crystalline structures and infrared/Raman spectra of nylon 6.[ , , ] Hofmann and his co‐workers explored possible helix types with unidirectional H‐bonds in the blocked octapeptide of Ahx residues at HF and B3LPY levels of theory with the 6‐31G(d) basis set.[ , ] The single‐point energies were also calculated using the polarizable continuum model (PCM) at the HF/6‐31G(d) level of theory in water. They obtained 21 helix conformers with H‐bonds only in backward direction and also 21 helix conformers with the H‐bonds in forward direction from the conformational search (see Figure 2 for definition of H‐bonds). The H16 I conformer was most preferred at all levels of theory both in the gas phase and water, which is a forward helix with 16‐membered H‐bonded pseudocycles. The next preferred helices were the conformers H18 I and H9 I, the first with all H‐bonds in backward direction and the second with all H‐bonds in forward direction. The H9 I conformer with a flat periodic turn‐like structure became a comparable stability to the other two helix types in water. ϵ‐Amino acid residue has a unique backbone sequence resembling a dipeptide unit in α/β‐hybrid peptide. The correspondence among some helices of ϵ‐peptide and α/β‐hybrid peptide was suggested as H11 X : H11 I, H11 II : H11/9 I, H9 VI : H9/11 I, H16 IV : H16/18 I, and H18 II : H18/16 I [(helix type in ϵ‐peptide) : (helix type in α/β‐hybrid peptide)].

Figure 2

Feasible H‐bond types in ϵ‐peptides. C denotes the H‐bonded pseudocyle with n atoms: C 9, C 16, and C 23 H‐bonds in forward direction; C 11, C 18, and C 25 H‐bonds in backward direction.

Here, we extensively explored the conformational preferences of oligomers of ϵ‐amino acid with a cyclopentane substitution [2‐((1R,3S)‐3‐(aminomethyl)cyclopentyl)acetic acid, Amc5a; Figure 1e] using DFT methods in chloroform and water. The preferred helical structures of the Amc5a hexamer were compared with those of the canonical unsubstituted Ahx hexamer. In addition, the helical preferences were investigated for the hexamer analogue with pyrrolidines instead of cyclopentanes (Figure 1f). Chemical structure and definition of torsion angles for Amc5a oligomers are defined in Figure 3.

Figure 3

Chemical structure and torsion angles for Ac‐(Amc5a) ‐NHMe (n=1, 2, 4, and 6). Amc5a stands for 2‐((1R,3S)‐3‐(aminomethyl)cyclopentyl)acetic acid.

Results and Discussion

Conformational Preferences of Amc5a Oligomers

. For the Amc5a monomer, we located 34 local minima with the relative free energy (ΔG c) <5 kcal mol−1 in chloroform from the conformational search and three helical structures (H9, H11, and H18 I) of the Amc5a hexamer. The corresponding backbone torsion angles, relative thermodynamic properties, and absolute electronic energies are shown in Tables S1–S3 in the Supporting Information, respectively. The backbone torsion angles and relative free energies (ΔG c in chloroform and ΔG w in water) of 18 local minima with ΔG c <3 kcal mol−1 are listed in Table 1. The eight preferred conformers of the Amc5a monomer in chloroform and water are shown in Figure 4.

Table 1

H‐bond types, torsion angles (°), and relative conformational free energies (kcal mol−1) of 18 local minima of the Amc5a monomer calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water.[a]

Conformer	H‐bond[b]	ϕ	θ	ζ	ρ	μ	ψ	ΔG c [c]	ΔG w [c]
m‐01	C 11	104	−65	−89	113	64	−118	0.00	0.64
m‐02		−78	−61	−159	167	−174	−81	0.37	0.00
m‐03	C 9	105	58	−118	90	54	84	0.41	1.22
m‐04		78	179	−166	163	56	85	0.50	0.30
m‐05	E	78	−178	−163	166	−174	−80	0.97	0.73
m‐06		103	65	−139	160	177	121	1.32	0.89
m‐07		79	−174	−133	158	65	−122	1.37	0.90
m‐08	(H16 I)[d]	−82	−64	−163	166	64	−133	1.65	1.28
m‐09		78	−174	−135	159	178	142	1.97	1.66
m‐10		−104	−180	−157	167	178	123	2.03	2.00
m‐11		103	64	−138	160	64	−145	2.19	1.92
m‐12		−80	−59	−143	163	176	140	2.20	1.79
m‐13		109	−62	−88	114	−175	146	2.21	2.73
m‐14	C 11	104	−70	−106	139	−90	74	2.31	2.86
m‐15		−94	58	−168	165	178	144	2.32	2.23
m‐16		101	63	−137	158	54	84	2.51	2.60
m‐17	C 9	−81	−58	−89	118	−54	−99	2.62	3.33
m‐18	C 9	101	61	−120	146	−74	−121	2.86	3.74

[a] Only conformers with ΔG c<3 kcal mol−1 in chloroform. Torsion angles are defined in Figure 3. [b] C 11 and C 9 are H‐bonded structures with 11‐ and 9‐membered pseudocycles for backbone, respectively. The extended structure was designated by “E”. [c] ΔG c and ΔG w are relative free energies in chloroform and water, respectively. [d] H16 I helical structure defined in Ref. [44].

Figure 4

Preferred conformers of the Amc5a monomer in chloroform and water.

In chloroform, the most preferred conformer was m‐01 (populated at 31 %), which was stabilized by the C 11 H‐bond between C=O(Ac) and H−N(NHMe) with the distance 2.01 Å. The next preferred conformers are m‐02, m‐03, m‐04, and m‐05 with ΔG c=0.37, 0.41, 0.50, and 0.97 kcal mol−1, respectively (populated at 17, 16, 13, and 6 %, respectively). In particular, conformer m‐03 had a C 9 H‐bond between N−H(1) and C=O(1) with the distance 2.02 Å, which probably contributed to stabilize it as the conformer with the second lowest energy (ΔE c=0.75 kcal mol−1 in chloroform and ΔE w=0.92 kcal mol−1 in water, Table S2 in the Supporting Information). In water, the most preferred conformer was m‐02 (populated at 31 %) with the absence of H‐bonds and followed by conformer m‐04, m‐01, m‐05, m‐06, and m‐07 with ΔG w=0.30, 0.64, 0.73, 0.89, and 0.90 kcal mol−1, respectively (populated at 19, 11, 9, 7, and 7 %, respectively). Hence, there were 21 and 12 % decreases of the population for H‐bonded conformer m‐01 and m‐03, respectively, when the solvent polarity changes from chloroform to water. Although conformer m‐08 is capable of forming a H16 I helical structures for oligomers of dimer to hexamer (as discussed in Computational Details), its ΔG c and ΔG w values were 1.65 and 1.28 kcal mol−1 in chloroform and water, respectively (populated at 2 and 4 %, respectively), due to the absence of the C 16 H‐bond.

. In the case of the Amc5a dimer, we located 32 local minima with ΔG c <3 kcal mol−1 in chloroform from the conformational search and four helical structures (H16 I, H9, H11, and H18 I) were also included for comparison. The corresponding backbone torsion angles, relative thermodynamic properties, and absolute electronic energies of the Amc5a dimer are shown in Tables S4–S6 in the Supporting Information, respectively. The backbone torsion angles and relative free energies of 15 local minima with ΔG c <1.5 kcal mol−1 are listed in Table 2. The seven preferred conformers of the Amc5a dimer in chloroform and water are shown in Figure 5.

Table 2

H‐bond types, torsion angles (°), and relative conformational free energies (kcal mol−1) of 18 local minima of the Amc5a dimer calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water.[a]

Conformer	H‐bond[b]	ϕ	θ	ζ	ρ	μ	ψ	ΔG c [c]	ΔG w [c]
d‐01	H16 I	−85	−70	−162	142	62	−121	0.00	0.00
		−73	−58	−164	169	63	−148
d‐02	C 16	103	57	−167	165	57	−116	0.03	0.55
		−75	−60	−166	166	67	117
d‐03	C 18	79	−173	−122	150	57	−125	0.03	0.28
		−109	63	−141	162	178	154
d‐04	C 11	104	−68	−88	114	65	−115	0.18	1.02
		−77	−64	−158	171	−63	−104
d‐05	C 18	−111	55	−168	165	64	−149	0.39	0.58
		−96	58	−164	143	174	179
d‐06	H16/18	−95	60	−169	170	−67	88	0.77	2.20
		101	−57	−131	158	59	−142
d‐07	C 18,C 9	135	65	−146	121	−65	−109	0.80	2.41
		−108	76	−148	168	78	−132
d‐08	C 16	92	−58	−164	166	70	−79	1.06	2.17
		−62	−52	−148	165	55	64
d‐09	H16/18	−171	−67	−163	168	65	85	1.09	2.57
		100	−64	−87	108	62	−153
d‐10	C 18	−104	176	−167	164	−70	88	1.12	1.22
		96	63	−172	166	171	103
d‐11	C 18	119	−68	−167	165	57	−126	1.13	1.46
		−78	−59	−166	165	178	−92
d‐12	C 16	73	171	−162	148	−58	107	1.22	2.11
		87	−69	−165	159	64	−109
d‐13	C 16/9	104	60	−129	151	50	−103	1.23	1.79
		−162	60	−148	120	−64	−100
d‐14	H18	−92	53	−170	158	63	−158	1.29	1.36
		−115	65	−137	160	71	−137
d‐15	C 18,C 9	109	−59	−148	164	57	−127	1.40	3.05
		−68	−38	−94	128	−44	123
	H9	−82	−57	−88	118	−54	−102	3.78	5.18
		−83	−56	−89	119	−55	−99
	H18 I	104	−74	−109	141	−61	174	5.53	7.12
		110	−58	−129	109	−67	87
	H11	102	−69	−107	139	−90	63	7.16	8.40
		132	−60	−76	102	−152	119

[a] Only conformers with ΔG c<1.5 kcal mol−1 in chloroform. Torsion angles are defined in Figure 3. [b] C is the H‐bond with n‐membered pseudocycle for backbone. The helical structure with n‐membered pseudocycle H‐bonds was represented by H . H16 I and H18 I helical structures are defined in Ref. [44]. [c] ΔG c and ΔG w are relative free energies in chloroform and water, respectively.

Figure 5

Preferred conformers of the Amc5a dimer in chloroform and water.

In chloroform, the most preferred conformer was the H16 I helical structure d‐01 (populated at 16 %), which was stabilized by a C 16 H‐bond between N−H(1) and C=O(2) with the distance 1.93 Å. The following preferred conformers were d‐02, d‐03, and d‐04, which had comparable values of ΔG c=0.03, 0.03, and 0.18 kcal mol−1, respectively (populated at 15, 15, and 12 %, respectively) to conformer d‐01. These conformers were stabilized by a C 16 H‐bond between N−H(1) and C=O(2) with the distance 1.95 Å, a C 18 H‐bond between C=O(Ac) and H−N(NHMe) with the distance 1.98 Å, and a C 11 H‐bond between C=O(Ac) and H−N(2) with the distance 1.97 Å, respectively. The next followed conformers were d‐05 with a C 18 H‐bond between C=O(Ac) and H−N(NHMe) with the distance 1.94 Å; the mixed H16/18 helical structure d‐06 with a C 16 H‐bond between N−H(1) and C=O(2) with the distance 2.09 Å; and d‐07 with a C 18 H‐bond between C=O(Ac) and H−N(NHMe) with the distance 1.90 Å and a C 9 H‐bond between N−H(1) and C=O(1) with the distance 2.00 Å, whose ΔG c values were 0.39, 0.77, and 0.80 kcal mol−1, respectively (populated at 8, 4, and 4 %, respectively).

In water, the most preferred conformer was the H16 I helical structure d‐01 populated at 31 %, which is 15 % greater than that in chloroform. The following preferred conformers were d‐03, d‐02, and d‐05 with ΔG w=0.28, 0.55, and 0.58 kcal mol−1, respectively (populated at 19, 12, and 12 %, respectively). It should be noted that conformer d‐07 was the lowest energy conformer both in chloroform and water, although its ΔG c and ΔG w values were 0.80 and 2.41 kcal mol−1 in chloroform and water, respectively, due to the decrease of entropic contribution (see Table S5 in the Supporting Information).

The conformational stabilities of helical structures of dimer were calculated to be in the order H16 I (d‐01, 0.00)>H16/18 (d‐06, 0.77)>H16/18 (d‐09, 1.09)>H18 (d‐14, 1.29)>H9 (3.78)>H18 I (5.53)>H11 (7.16) in chloroform and H16 I (d‐01, 0.00)>H18 (d‐14, 1.36)>H16/18 (d‐06, 2.20)>H16/18 (d‐09, 2.57)>H9 (5.18)>H18 I (7.12)>H11 (8.40) in water, where ΔG c and ΔG w values (kcal mol−1) were shown in parentheses.

. For the Amc5a tetramer, we located 32 local minima with ΔG c <13 kcal mol−1 in chloroform from consecutively jointing of dimers and three helical structures (H16 I, H9, and H18 I), and the H11 helical structure was also included for comparison. The corresponding backbone torsion angles, relative thermodynamic properties, and absolute electronic energies of the Amc5a tetramer are shown in Tables S7–S9 in the Supporting Information, respectively. The backbone torsion angles and relative free energies of 14 local minima with ΔG c<10 kcal mol−1 and three H18 I, H9 and H11 helical structures are listed in Table 3. The six representative conformers of the Amc5a tetramer in chloroform and water are shown in Figure 6.

Table 3

H‐bond types and relative thermodynamic properties (kcal mol−1) of representative structures of the Amc5a tetramers calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water.[a]

Conformer	H‐bond[b]	Chloroform				Water
		ΔE c [c]	ΔH c [c]	ΔG c [c]	w [d]	ΔE c [c]	ΔH c [c]	ΔG c [c]	w [d]
t‐01	H16 I	0.00	0.00	0.00	100.0	0.00	0.00	0.00	100.0
t‐02	H18	2.56	3.00	5.89	0.0	2.93	3.36	6.25	0.0
t‐03	H18/16	1.64	2.31	6.21	0.0	4.41	5.08	8.98	0.0
t‐04	2C 18	8.66	8.56	7.62	0.0	8.51	8.41	7.46	0.0
t‐05	2C 18	9.85	9.56	7.76	0.0	9.70	9.41	7.61	0.0
t‐06	2C 18	7.58	6.97	7.94	0.0	7.29	6.69	7.65	0.0
t‐07	H16/18	2.91	2.79	8.05	0.0	4.51	4.39	9.65	0.0
t‐08	2C 18	9.73	10.14	8.26	0.0	9.53	9.95	8.06	0.0
t‐09	2C 18,C 30	2.73	2.87	8.64	0.0	3.67	3.81	9.58	0.0
t‐10	2C 18	10.70	10.77	8.74	0.0	10.33	10.40	8.38	0.0
t‐11	2C 18	9.78	9.89	8.80	0.0	9.41	9.52	8.44	0.0
t‐12	2C 16,2C 11	5.26	5.73	9.02	0.0	7.25	7.72	11.00	0.0
t‐13	2C 11,C 30	5.43	6.13	9.58	0.0	6.30	7.00	10.45	0.0
t‐14	2C 16/9	6.06	6.99	9.87	0.0	6.10	7.03	9.91	0.0
t‐17	H18 I	6.39	6.39	10.17	0.0	6.58	6.59	10.36	0.0
t‐24	H9	7.99	9.13	11.00	0.0	9.73	10.88	12.74	0.0
	H11	14.58	16.05	17.76	0.0	16.21	17.69	19.40	0.0

[a] Only conformers with ΔG c<10 kcal mol−1 and three helical structures in chloroform. Torsion angles are shown in Table S7 in the Supporting Information. [b] C is the H‐bond with n‐membered pseudocycle for backbone. The Helical structure with n‐membered pseudocycle H‐bonds was represented by H . H16 I and H18 I helical structures are defined in Ref. [44]. [c] ΔE, ΔH, and ΔG are relative electronic energy, enthalpy, and Gibbs free energy of each conformation at 25 °C and 1 atm calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water, respectively. Each value of ΔE was calculated by the sum of ΔE 0,dTZ (the single‐point energy at the M06‐2X/def2‐TZVP level of theory) and ΔΔG solv (the solvation free energy calculated at the PCM M06‐2X/6‐31+G(d) level of theory). [d] Population of each conformation was calculated by its ΔG at 25 °C.

Figure 6

Preferred conformers of the Amc5a tetramer in chloroform and water: t‐01 (H16 I), t‐02 (H18), t‐03 (H18/16), t‐04 (2 C18), t‐05 (2 C18), and t‐06 (2 C18). H‐bond types in parentheses.

Both in chloroform and water, the H16 I helical structure t‐01 was dominantly populated at 100 %, which was stabilized by three C 16 H‐bonds between N−H(i) and C=O(i+1) (i=1, 2, 3) with the distances 1.93–1.97 Å. The H18 helical structure t‐02 with three C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 2, 3) with the distances 1.94–2.03 Å was the second preferred conformer both in chloroform and water (ΔG c=5.89 kcal mol−1 in chloroform and ΔG w=6.25 kcal mol−1 in water).

In chloroform, the third preferred conformer was the mixed H18/16 helical structure t‐03 (ΔG c=6.21 kcal mol−1) with two C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 3) with the distances 1.90 and 1.91 Å, respectively, and one C 16 H‐bond between N−H(2) and C=O(3) with the distance 2.14 Å. The fourth, fifth, and sixth preferred conformers were t‐04, t‐05, and t‐06 with ΔG c=7.62, 7.76, and 7.94 kcal mol−1, respectively, in common stabilized by two C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 3) with the distances 2.04 and 1.98 Å; 1.91 and 1.91 Å; and 1.88 and 1.86 Å, respectively. However, in water conformers t‐04, t‐05, and t‐06 were the third, fourth, and fifth preferred conformers, respectively, stabilized by two C 18 H‐bonds with ΔG w=7.46, 7.61, and 7.65 kcal mol−1, respectively. In particular, the mixed H18/16 helical structure t‐03 became as the sixth preferred conformer with ΔG w=8.98 kcal mol−1 in water.

The conformational stabilities of helical structures of tetramer were calculated to be in the order H16 I (t‐01)≫H18 (t‐02)>H18/16 (t‐03)>H16/18 (t‐07)>H18 I (t‐17)>H9 (t‐24)≫H11 both in chloroform and water with ΔG c=0.00, 5.89, 6.21, 8.05, 10.17, 11.00, and 17.76 kcal mol−1 in chloroform, respectively; and ΔG w=0.00, 6.25, 8.98, 9.65, 10.36, 12.74, and 19.40 kcal mol−1 in water, respectively.

. In the case of the Amc5a hexamer, we located 14 local minima in chloroform, of which ten local minima were obtained from preferred structures of tetramer and four helical structures were included for comparison. The corresponding backbone torsion angles and absolute electronic energies of the Amc5a hexamer are shown in Tables S10 and S11 in the Supporting Information, respectively. The H‐bond types and relative thermodynamic properties of 14 local minima are listed in Table 4. The backbone torsion angles and helical parameters of seven representative helical structures are listed in Table 5 and their 3D structures are depicted in Figure 7, whose Cartesian coordinates are also listed in the Supporting Information.

Table 4

H‐bond types and relative thermodynamic properties (kcal mol−1) of representative structures of the Amc5a hexamers calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water.[a]

Conformer	H‐bond[b]	Chloroform				Water
		ΔE c [c]	ΔH c [c]	ΔG c [c]	w [d]	ΔE c [c]	ΔH c [c]	ΔG c [c]	w [d]
h‐01	H16 I	0.00	0.00	0.00	99.9	0.00	0.00	0.00	100.0
h‐02	H18/16	1.95	2.57	4.25	0.1	4.89	5.50	7.18	0.0
h‐03	H18	4.62	5.02	6.58	0.0	4.95	5.34	6.91	0.0
h‐04	H16/18	3.94	4.85	8.87	0.0	6.80	7.71	11.73	0.0
h‐05	H16/18	7.03	7.95	10.22	0.0	9.29	10.21	12.48	0.0
h‐06	3C 18	14.46	14.37	10.82	0.0	13.44	13.35	9.80	0.0
h‐07	H18/16	7.43	8.38	12.81	0.0	10.35	11.30	15.73	0.0
h‐08	3C 11/18	14.24	15.83	15.68	0.0	13.97	15.56	15.41	0.0
h‐09	2C 16,2C 11	12.14	12.25	16.04	0.0	13.99	14.10	17.88	0.0
h‐10	3C 16/9	13.49	14.77	16.77	0.0	12.80	14.09	16.09	0.0
h‐11	H18 I	14.79	15.36	16.99	0.0	15.24	15.81	17.44	0.0
h‐12	3C 16	16.78	17.39	18.40	0.0	17.87	18.48	19.49	0.0
h‐13	H9	16.16	18.12	18.78	0.0	17.95	19.92	20.57	0.0
h‐14	H11	26.31	27.89	29.42	0.0	28.03	29.61	31.14	0.0

[a] Torsion angles are shown in Table S10 in the Supporting Information. [b] C is the H‐bond with n‐membered pseudocycle for backbone. The Helical structure with n‐membered pseudocycle H‐bonds was represented by H . H16 I and H18 I helical structures are defined in Ref. [44]. [c] ΔE, ΔH, and ΔG are relative electronic energy, enthalpy, and Gibbs free energy of each conformation at 25 °C and 1 atm calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water, respectively. Each value of ΔE was calculated by the sum of ΔE 0,dTZ (the single‐point energy at the M06‐2X/def2‐TZVP level of theory) and ΔΔG solv (the solvation free energy calculated at the PCM M06‐2X/6‐31+G(d) level of theory). [d] Population of each conformation was calculated by its ΔG at 25 °C.

Table 5

Torsion angles (°) and helical parameters of representative helical structures of the Amc5a hexamer optimized at the M06‐2X/6‐31+G(d) level of theory.[a]

Conformer	H‐bond[b]	ϕ	θ	ζ	ρ	μ	ψ	Helix type[c]	m [d]	p [e]
h‐01	H16 I	−78	−63	−166	166	54	−106	(M)‐2.316	2.3	4.8
		−80	−66	−154	164	58	−126
		−71	−58	−161	168	52	−127
		−74	−54	−167	164	58	−122
		−72	−57	−166	155	60	−111
		−76	−61	−146	162	65	122
h‐02	H18/16	−114	56	−129	155	−61	125	(P)‐3.518/16	3.5	8.9
		158	−62	−136	157	64	−102
		−95	63	−168	168	−52	108
		173	−63	−130	155	65	−110
		−99	64	−159	172	−55	98
		179	−60	−133	158	62	−109
h‐03	H18	−94	48	−162	136	62	−139	(P)‐2.418	2.4	5.6
		−99	48	−174	161	61	−130
		−106	52	−171	159	69	−143
		−101	51	−157	165	71	−151
		−106	56	−132	154	73	−164
		−105	56	−114	135	65	−178
h‐04	H16/18	−156	−70	−166	162	59	85	(M)‐2.216/18	2.2	4.9
		105	−65	−96	121	61	164
		−60	−48	−167	147	53	22
		118	−60	−157	164	48	−132
		−81	−63	−173	161	54	76
		115	−61	−84	102	64	−153
h‐11	H18 I	176	−62	−129	158	−53	108	(M)‐3.818	3.8	8.4
		111	−67	−143	168	−52	114
		123	−65	−157	170	−61	87
		169	−60	−156	138	−55	105
		142	−73	−123	153	−61	171
		105	−72	−102	134	−61	132
h‐13	H9	−80	−57	−88	118	−54	−101	(P)‐2.89	2.8	10.9
		−84	−55	−89	119	−55	−102
		−83	−55	−88	118	−55	−101
		−83	−54	−89	118	−55	−101
		−84	−54	−89	119	−56	−102
		−82	−55	−90	119	−55	−101
h‐14	H11	103	−68	−107	139	−89	63	(P)‐3.111	3.1	11.9
		130	−58	−77	104	−153	119
		102	−69	−107	139	−88	62
		129	−60	−77	105	−149	117
		100	−70	−106	139	−88	62
		131	−60	−77	103	−152	118

[a] Torsion angles are defined in Figure 3. [b] The helical structure with n‐membered pseudocycle H‐bonds was represented by H . H16 I and H18 I helical structures are defined in Ref. [44]. [c] (M) and (P) stand for left‐ and right‐handed helices, respectively. [d] Number of residues per turn. [e] Rise per turn (pitch) (Å).

Figure 7

Preferred helical conformers of the Amc5a hexamer in chloroform and water: h‐01 (H16 I), h‐02 (H18/16), h‐03 (H18), h‐04 (H16/18), h‐11 (H18 I), h‐13 (H9), and h‐14 (H11). H‐bond types in parentheses.

In chloroform, the most preferred conformer h‐01 (populated at ∼100 %) adopted a H16 I helical structure with five C 16 H‐bonds between N−H(i) and C=O(i+1) (i=1, 2, 3, 4, 5) with the distances 1.92–1.97 Å. The second and third preferred conformers were h‐02 and h‐03 with ΔG c=4.25 and 6.58 kcal mol−1, respectively. The former was a mixed H18/16 helical structure with three C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 3, 5) with the distances 1.87–1.91 Å and two C 16 H‐bonds between N−H(i) and C=O(i+1) (i=2, 4) with the distances 2.21 and 2.09 Å. The latter was a H18 helical structure stabilized by five C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 2, 3, 4, 5) with the distances 1.93–2.08 Å. The fourth preferred conformer h‐04 (ΔG c=8.87 kcal mol−1) was a mixed H16/18 helical structure with three C 16 H‐bonds between N−H(i) and C=O(i+1) (i=1, 3, 5) with the distances 1.90–2.02 Å and two C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=2, 4) with the distances 1.98 and 1.94 Å.

In water, the most preferred conformer h‐01 (populated at ∼100 %) adopted a H16 I helical structure as in chloroform. However, the second and third preferred conformers were the H18 helical structure h‐03 and the mixed H18/16 helical structure h‐02 with ΔG w=6.91 and 7.18 kcal mol−1, respectively. In particular, the fourth preferred conformer h‐06 (ΔG w=9.80 kcal mol−1) adopted a folded structure with three C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 3, 5) with the distances 1.86–1.89 Å as similar to the tetramer t‐06, which was the sixth preferred conformer (ΔG c=10.82 kcal mol−1) in chloroform. The fifth preferred conformer was the mixed H16/18 helical structure h‐04 with ΔG w=11.73 kcal mol−1 in water.

Helical structures H18 I (h‐11), H9 (h‐13), and H11 (h‐14) had favorable four C 18 H‐bonds with the distances 1.95–2.03 Å; six C 9 H‐bonds between N−H and C=O of every residue with the distances 1.98–2.03 Å; and six C 11 H‐bonds between C=O(i−1) and H−N(i+1) of every residue i with the distances 1.94–2.02 Å, respectively. However, relative free energies of these three helical structures were greater than 17 kcal mol−1 both in chloroform and water.

Hence, the conformational stabilities of helical structures of hexamer were calculated to be in the order H16 I≫H18/16>H18>H16/18≫H18 I>H9≫H11 in chloroform and H16 I≫H18>H18/16>H16/18≫H18 I>H9≫H11 in water. The helical parameters of seven representative helical structures of the Amc5a hexamer are shown in Table 5. The helical types of H16 I (h‐01), H16/18 (h‐04), and H18 I (h‐11) structures are left‐handed (M)‐2.316 with a rise of 4.8 Å per turn, (M)‐2.216/18 with a rise of 4.9 Å per turn, and (M)‐3.818 with a rise of 8.4 Å per turn, respectively. However, the helical types of H18/16 (h‐02), H18 (h‐03), H9 (h‐13), and H11 (h‐14) structures are right‐handed (P)‐3.518/16 with a rise of 8.9 Å per turn, (P)‐2.418 with a rise of 5.6 Å per turn, (P)‐2.89 with a rise of 10.9 Å per turn, and (P)‐3.111 with a rise of 11.9 Å per turn, respectively.

Helical Preferences of Ahx and Ampa Hexamers

Next, we compared the helical preferences of Ahx and Ampa hexamers to investigate the changes in helical preference of ϵ‐peptides by introducing cyclopentanes and pyrrolidines into the backbone of the sequence. For the unsubstituted Ahx hexamer (see Figure 1a), we optimized nine helical structures (H18 I, H16 I, H18, H16/18, H18/16, H9 I, H11 I, and H11) at the M06‐2X/6‐31+G(d) level of theory, of which four types of H18 I, H16 I, H9 I, and H11 I were considered in Ref. [44]. The backbone torsion angles and absolute electronic energies of the Ahx hexamer are shown in Tables S12 and S13 in the Supporting Information, respectively. The H‐bond types and relative thermodynamic properties of nine helical structures are listed in Table 6. The structures of three most preferred conformers in chloroform and water are depicted in Figure 8, whose Cartesian coordinates are also listed in the Supporting Information.

Table 6

H‐bond types and relative thermodynamic properties (kcal mol−1) of helical structures of the Ahx hexamers calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water.[a]

Conformer	H‐bond[b]	Chloroform				Water
		ΔE c [c]	ΔH c [c]	ΔG c [c]	w [d]	ΔE c [c]	ΔH c [c]	ΔG c [c]	w [d]
Ahx‐1	H18 I	0.00	0.00	0.00	96.5	0.00	0.00	0.00	91.4
Ahx‐2	H16 I	6.10	6.84	2.18	2.4	5.36	6.09	1.43	8.1
Ahx‐3	H18	2.51	2.63	2.70	1.0	2.92	3.04	3.11	0.5
Ahx‐4	H16/18	7.98	8.71	9.58	0.0	10.15	10.87	11.75	0.0
Ahx‐5	H18/16	8.82	10.01	10.27	0.0	11.58	12.77	13.03	0.0
Ahx‐6	H16/18	10.22	11.22	11.78	0.0	12.77	13.77	14.34	0.0
Ahx‐7	H9 I	18.65	20.45	12.09	0.0	20.58	22.39	14.02	0.0
Ahx‐8	H11 I	23.69	25.86	17.60	0.0	25.43	27.59	19.34	0.0
Ahx‐9	H11	25.71	27.56	23.16	0.0	27.99	29.84	25.44	0.0

[a] Torsion angles are shown in Table S13 in the Supporting Information. [b] The helical structure with n‐membered pseudocycle H‐bonds was represented by H . H18 I, H16 I, H9 I, and H11 I helical structures are defined in Ref. [44]. [c] ΔE, ΔH, and ΔG are relative electronic energy, enthalpy, and Gibbs free energy of each conformation at 25 °C and 1 atm calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water, respectively. Each value of ΔE was calculated by the sum of ΔE 0,dTZ (the single‐point energy at the M06‐2X/def2‐TZVP level of theory) and ΔΔG solv (the solvation free energy calculated at the PCM M06‐2X/6‐31+G(d) level of theory). [d] Population of each conformation was calculated by its ΔG at 25 °C.

Figure 8

Preferred helical conformers of the Ahx hexamer in chloroform and water: Ahx‐1 (H18 I), Ahx‐2 (H16 I), and Ahx‐3 (H18). H‐bond types in parentheses.

Both in chloroform and water, the most preferred conformer Ahx‐1 adopted a left‐handed (M)‐2.418 type of the H18 I helical structure with a rise of 4.6 Å per turn (populated at 97 % in chloroform and 91 % in water) stabilized by five C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 2, 3, 4, 5) with the distances 1.88–1.94 Å. The second and third preferred conformers Ahx‐2 and Ahx‐3 were the H16 I and H18 helical structures with ΔG c=2.18 and 2.70 kcal mol−1 in chloroform and ΔG w=1.43 and 3.11 kcal mol−1 in water, respectively. The former Ahx‐2 structure were stabilized by five C 16 H‐bonds between N−H(i) and C=O(i+1) (i=1, 2, 3, 4, 5) with the distances 1.88–1.92 Å, whereas the latter Ahx‐3 was stabilized by five C18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 2, 3, 4, 5) with the distances 1.88–1.94 Å.

The conformational stabilities of helical structures of the Ahx hexamer were calculated to be in the order H18 I>H16 I>H18≫H16/18>H18/16>H9 I≫H11 I≫H11 both in chloroform and water. However, Schramm and Hofmann estimated the helical propensity of the Ahx hexamer in the order H16 I (0.0)>H18 I (1.0)≫H9 I (5.6)≫H11 I (44.8) at the PCM HF/6‐31G(d) level of theory in water, where relative energies (kcal mol−1) are shown in parentheses and also confirmed the H16 I helical structures as the lowest‐energy conformer at HF/6‐31G(d) and B3LYP/6‐31G(d) levels of theory in the gas phase.

In addition, we designed an analogue Ampa (Figure 1f) hexamer from the Amc5a hexamer by incorporating pyrrolidines instead of cyclopentanes into the backbone of the sequence. The eight helical structures of the Ampa hexamer were optimized at the M06‐2X/6‐31+G(d) level of theory. The backbone torsion angles and absolute electronic energies of the Ampa hexamer are shown in Tables S14 and S15 in the Supporting Information, respectively. The H‐bond types and relative thermodynamic properties of nine helical structures are listed in Table 7. The structures of three most preferred conformers in chloroform and water are depicted in Figure 9, whose Cartesian coordinates are listed in the Supporting Information.

Table 7

H‐bond types and relative thermodynamic properties (kcal mol−1) of helical structures of the Ampa hexamers calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water.[a]

Conformer	H‐bond[b]	Chloroform				Water
		ΔE c [c]	ΔH c [c]	ΔG c [c]	w [d]	ΔE c [c]	ΔH c [c]	ΔG c [c]	w [d]
Ampa‐1	H18/16	0.00	0.00	0.00	98.1	0.00	0.12	0.23	34.2
Ampa‐2	H16/18	2.78	1.78	2.39	1.7	0.87	0.00	0.71	15.1
Ampa‐3	H16 I	7.53	6.53	3.92	0.1	3.39	2.52	0.00	50.0
Ampa‐4	H9	12.32	12.25	6.23	0.0	10.75	10.80	4.88	0.0
Ampa‐5	H16/18	6.17	6.29	7.06	0.0	5.76	6.01	6.87	0.0
Ampa‐6	H18	8.86	7.63	7.25	0.0	3.85	2.74	2.46	0.8
Ampa‐7	H18 I	9.21	9.54	10.95	0.0	9.38	9.83	11.35	0.0
Ampa‐8	H11	16.34	16.55	11.83	0.0	15.76	16.09	11.47	0.0

[a] Torsion angles are shown in Table S15 in the Supporting Information. [b] The helical structure with n‐membered pseudocycle H‐bonds was represented by H . H16 I and H18 I helical structures are defined in Ref. [44]. [c] ΔE, ΔH, and ΔG are relative electronic energy, enthalpy, and Gibbs free energy of each conformation at 25 °C and 1 atm calculated at the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory in chloroform and water, respectively. Each value of ΔE was calculated by the sum of ΔE 0,dTZ (the single‐point energy at the M06‐2X/def2‐TZVP level of theory) and ΔΔG solv (the solvation free energy calculated at the PCM M06‐2X/6‐31+G(d) level of theory). [d] Population of each conformation was calculated by its ΔG at 25 °C.

Figure 9

Preferred helical conformers of the Ampa hexamer in chloroform and water: Ampa‐1 (H18/16), Ampa‐2 (H16/18), and Ampa‐3 (H16 I). H‐bond types in parentheses.

In chloroform, the most preferred conformer Ampa‐1 adopted a right‐handed (P)‐2.918/16 type of the mixed H18/16 helical structure with a rise of 5.5 Å per turn (populated at 98 %), which was stabilized by three C 18 H‐bonds between C=O(i−1) and H−N(i+2) (i=1, 3, 5) with the distances 1.90–2.04 Å and two C 16 H‐bonds between N−H(i) and C=O(i+1) (i=2, 4) with the distances 1.96 and 1.93 Å. In particular, there were two additional C 14 H‐bonds for conformer Ampa‐1 between C=O(i−1) and H−N(i+2) of pyrrolidine (i=1, 5) with the distances 2.27 and 2.06 Å. The second and third preferred conformers were Ampa‐2 and Ampa‐3, which are the mixed H16/18 helical structure and the H16 I helical structure with ΔG c=2.39 and 3.92 kcal mol−1 in chloroform, respectively. The former Ampa‐2 structure were stabilized by three C 16 H‐bonds between N−H(i) and C=O(i+1) (i=1, 3, 5) with the distances 1.90–2.00 Å and two C18 H‐bonds between C=O(i−1) and H−N(i+2) (i=2, 4) with the distances 2.19 and 1.90 Å. The latter Ampa‐3 structure had five C16 H‐bonds between N−H(i) and C=O(i+1) (i=1, 2, 3, 4, 5) with the distances 1.93–2.08 Å. However, a left‐handed (M)‐2.416 type of the H16 I helical structure (Ampa‐3) with a rise of 4.7 Å per turn was dominantly populated at 50 % in water and coexisted with the mixed H18/16 and H16/18 helical structures (Ampa‐1 and Ampa‐2, respectively) with ΔG w=0.23 and 0.71 kcal mol−1, respectively (populated at 34 and 15 %, respectively).

The conformational stabilities of helical structures of the Ampa hexamer were calculated to be in the order H18/16≫H16/18>H16 I≫H9>H18≫H18 I>H11 in chloroform and H16 I>H18/16>H16/18>H18≫H9≫H18 I ≈ H11 in water (see the values of ΔG c and ΔG w in Table 7). These helical propensities of the Ampa hexamer are quite different from those of Amc5a and Ahx hexamers, as described above. Hence, hexamers of ϵ‐amino acid residues exhibited different preferences of helical structures depending on the substituents in peptide backbone and the solvent polarity as well as the chain length. In particular, the strong preference of the left‐handed H16 I helical structure for the Amc5a hexamer with cyclopentane substituents in chloroform and water and the right‐handed mixed H18/16 and left‐handed H16 I helical structures for the Ampa hexamer with pyrrolidine substituents in chloroform and water, respectively, may suggest us the possibility of their use in designing bioactive helical peptides in nonpolar or polar solvents.

Conclusion

The conformational preferences of oligopeptides of an ϵ‐amino acid (Amc5a) with a cyclopentane substituent in the Cβ−Cγ−Cδ sequence of the peptide backbone were investigated using DFT methods in chloroform and water. The H16 helical structure was the most preferred conformation of the Amc5a oligomers (dimer to hexamer) both in chloroform and water, although the H16 helical structure and folded structures with C H‐bonded pseudocycles coexisted for the Amc5a dimer. Four residues were found to be sufficient to induce a substantial H16 helix population in solution.

The Amc5a hexamer adopted a stable left‐handed (M)‐2.316 helical conformation with a rise of 4.8 Å per turn, whereas the hexamer of the unsubstituted Ahx residue dominantly exhibited a (M)‐2.418 helical conformation. The hexamer of Ampa (an analogue of Amc5a with cyclopentane replaced by pyrrolidine) adopted the right‐handed mixed (P)‐2.918/16 helical conformation in chloroform and the (M)‐2.416 helical conformation in water. The solvation free energy was found to be crucial to stabilize the left‐handed (M)‐2.316 helical conformation for the Amc5a hexamer both in chloroform and water.

Hence, hexamers of ϵ‐amino acid residues exhibited different preferences of helical structures depending on the substituent in peptide backbone and the solvent polarity as well as the chain length. In particular, the strong propensity to form specific types of helical structures for the Amc5a/Ampa hexamer with cyclopentane/pyrrolidine substituents in solution may suggest the possibility of their use in designing bioactive helical peptides in nonpolar or polar solvents.

Computational Methods

Chemical structure and definition of torsion angles for Amc5a oligomers are defined in Figure 3. GaussView was used for the generation of initial structures and the peptide structure editing. All HF and DFT calculations were carried out using the Gaussian 09 programs. All DFT calculations were performed using the M06‐2X functional method. The M06‐2X is a hybrid‐meta‐GGA functional with an improved medium‐range correlation energy. For all local minima of Amc5a oligomers optimized at the M06‐2X/6‐31+G(d) level of theory, the relative energies (ΔE s) of each local minimum in chloroform and water were calculated as the sum of the relative single‐point energy (ΔE 0,dTZ) at the M06‐2X/def2‐TZVP level of theory and the relative solvation free energies (ΔΔG solv) obtained at the M06‐2X/6‐31+G(d) level of theory using the PCM method. Vibrational frequencies were calculated for all local minima at the M06‐2X/6‐31+G(d) level of theory at 25 °C and 1 atm. The scale factor used is 0.9440 that was chosen to reproduce experimental frequency of 1707 cm−1 for the amide I band of N‐methylacetamide in Ar and N2 matrixes. The zero‐point energy correction and the thermal energy corrections were employed in calculating the Gibbs free energy of each conformation, from which enthalpic and entropic contributions (i. e., ΔΔH and −TΔΔS, respectively) were computed. The relative Gibbs free energy (ΔG s) of each local minimum in solution was calculated by the sum of ΔE s, ΔΔH, and −TΔΔS, from which the populations of all local minima were estimated at 25 °C in solution. Here, the ideal gas, rigid rotor, and harmonic oscillator approximations were used for the translational, rotational, and vibrational contributions to the Gibbs free energy, respectively. Recently, the M06‐2X/def2‐TZVP//M06‐2X/6‐31+G(d) level of theory with the PCM method appeared to be appropriate in predicting the conformational preferences and the cis–trans isomerization of the longer peptides containing Pro or Pro derivatives in chloroform.

First, we performed the conformational search of monomer and dimer of Amc5a residues in order to investigate the feasible initial structures of short Amc5a peptides. The 648 and 949 initial structures were generated for monomer and dimer of Amc5a residues, respectively, by the systematic search of the Discovery Studio package using the CHARMm force field with the maximum systematic conformations=1000 and the energy threshold=20 kcal mol−1. In the conformational search, a systematic variation of each of the torsion angles Φ, θ, μ, and ψ of the backbone (Figure 3) was done using steps of 60°. These initial structures were optimized at the HF/3‐21G(d) level of theory and we obtained 63 and 168 local minima for monomer and dimer of Amc5a residues, respectively, with the relative energy (ΔE 0) <10 kcal mol−1, which were reoptimized at M06‐2X/6‐31G(d) and M06‐2X/6‐31+G(d) levels of theory. Hence, we located 41 monomer and 91 dimer structures with ΔE 0 <10 kcal mol−1 at the M06‐2X/6‐31+G(d) level of theory. For the tetramer, the initial structures were built by consecutively jointing of 62 dimers with ΔE 0 <6 kcal mol−1 at the M06‐2X/6‐31+G(d) level of theory and reoptimized at M06‐2X/6‐31G(d) and M06‐2X/6‐31+G(d) levels of theory. Finally, we obtained 44 local minima of tetramer at the M06‐2X/6‐31+G(d) level of theory. Then, 13 local minima of tetramer with the relative Gibbs free energy (ΔG c) <4 kcal mol−1 in chloroform were used to generate the initial structures of the hexamer and reoptimized at M06‐2X/6‐31G(d) and M06‐2X/6‐31+G(d) levels of theory.

Feasible H‐bond types in Amc5a oligomers are depicted in Figure 2; C denotes the H‐bonded pseudocyle with n atoms (C 9, C 16, and C 23 H‐bonds in forward direction; C 11, C 18, and C 25 H‐bonds in backward direction). In this work, only helical structures with C 9, C 16, C 11, and C 18 H‐bonds were considered for Amc5a oligomers due to the very high relative energies of C 23 and C 25 H‐bonded helical conformations for the Ahx octamer. Torsion angles of helical structures of the Ahx octamer with C 9, C 16, C 11, and C 18 H‐bonds were used to generate initial helical structures for the Amc5a hexamer. We obtained only six helical structures (H9 III, H9 IV, H16 II, H11 VII, H18 I, and H18 IV types) for the Amc5a hexamer, which were optimized at the M06‐2X/6‐31G(d) level of theory. However, three H9 IV, H16 II, and H18 IV helical structures of the Amc5a hexamer exhibited higher conformational energies than H9 III, H16 I, and H18 I helical structures, respectively. Hence, only three helical structures (H9 III, H11 VII, and H18 I types) of the Amc5a hexamer were optimized at the M06‐2X/6‐31+G(d) level of theory. Because the optimized backbone torsion angles of H9 III and H11 VII helical structures of the Amc5a hexamer were somewhat different from those of the Ahx octamer, they were represented as H9 and H11 in this work, respectively. Although the H16 I helical structure of the Ahx octamer was found as the most stable one at all three HF/6‐31G(d), B3LYP/6‐31G(d), and PCM HF/6‐31G(d) levels of theory, its torsion angles were not correctly reported in Ref. [44]. Hence, the initial H16 I helical structure of the Amc5a hexamer was built by using conformer m‐08 of the Amc5a monomer (Table 1) and the structure depicted in Figure 2 of Ref. [44] and optimized at the M06‐2X/6‐31+G(d) level of theory. From H9, H11, H16 I, and H18 I helical structures of the Amc5a hexamer optimized at the M06‐2X/6‐31+G(d) level of theory, the corresponding helical structures of monomer, dimer, and tetramer were generated and optimized at the same level of theory. The helical parameters of hexamers were calculated from a set of six consecutive δ‐carbons (see Figure 3) with the HELFIT program, which uses the total least squares algorithm for helix fitting and requires at least four data points for the analysis. All 3D graphics of optimized structures of oligomers were prepared using PyMOL.

Conflict of interest

The authors declare no conflict of interest.

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

Supporting Information

Click here for additional data file.