Solvent effects on the φ–ψ potential surfaces of glycine and alanine dipeptides studied by PCM and I-PCM methods

Application of a Distance-Dependent Sigmoidal Dielectric Constant to the REMC/SAAP3D Simulations of Chignolin, Trp-Cage, and the G10q Mutant

The replica-exchange Monte Carlo method based on the single amino acid potential (SAAP) force field, i.e., REMC/SAAP3D, was recently developed by our group for the molecular simulation of short peptides. In this study, the method has been improved by applying a distance-dependent dielectric (DDD) constant and extended to the peptides containing D-amino acid (AA) residues. For chignolin (10 AAs), a sigmoidal DDD model reasonably allocated the native-like β-hairpin structure with all-atom root mean square deviation (RMSD) = 2.0 Å as a global energy minimum. The optimal DDD condition was subsequently applied for Trp-cage (20 AAs) and its G10q mutant. The native-like α-rich folded structures with main-chain RMSD = 3.7 and 3.8 Å were obtained as global energy minima for Trp-cage and G10q, respectively. The results suggested that the REMC/SAAP3D method with the sigmoidal DDD model is useful for structural prediction for the short peptides comprised of up to 20 AAs. In addition, the relative contributions of SAAP to the total energy (%SAAP) were evaluated by energetic component analysis. The ratios of %SAAP were about 40 and 20% for chignolin and Trp-cage (or G10q), respectively. It was proposed that SAAP is more important for the secondary structure formation than for the assembly to a higher-order folded structure, in which the attractive van der Waals interaction may play a more important role.

Conformational Interconversions of Amino Acid Derivatives

Exhaustive conformational interconversions including transition structure analyses of N-acetyl-l-glycine-N-methylamide as well as its alanine, serine, and cysteine analogues have been investigated at the MP2/6-31G** level, yielding a total of 142 transition states. Improved estimates of relative energies were obtained by separately extrapolating the Hartree-Fock and MP2 energies to the basis set limit and adding the difference between CCSD(T) and MP2 results with the cc-pVDZ basis set to the extrapolated MP2 results. The performance of eight empirical force fields (AMBER94, AMBER14SB, MM2, MM3, MMFFs, CHARMM22_CMAP, OPLS_2005, and AMOEBAPRO13) in reproducing ab initio energies of transition states was tested. Our results indicate that commonly used class I force fields employing a fixed partial charge model for the electrostatic interaction provide mean errors in the ∼10 kJ/mol range for energies of conformational transition states for amino acid conformers. Modern reparametrized versions, such as CHARMM22_CMAP, and polarizable force fields, such as AMOEBAPRO13, have slightly lower mean errors, but maximal errors are still in the 35 kJ/mol range. There are differences between the force fields in their ability for reproducing conformational transitions classified according to backbone/side-chain or regions in the Ramachandran angles, but the data set is likely too small to draw any general conclusions. Errors in conformational interconversion barriers by ∼10 kJ/mol suggest that the commonly used force field may bias certain types of transitions by several orders of magnitude in rate and thus lead to incorrect dynamics in simulations. It is therefore suggested that information for conformational transition states should be included in parametrizations of new force fields.

The intrinsic conformational features of amino acids from a protein coil library and their applications in force field development

The local conformational (φ, ψ, χ) preferences of amino acid residues remain an active research area, which are important for the development of protein force fields. In this perspective article, we first summarize spectroscopic studies of alanine-based short peptides in aqueous solution. While most studies indicate a preference for the P(II) conformation in the unfolded state over α and β conformations, significant variations are also observed. A statistical analysis from various coil libraries of high-resolution protein structures is then summarized, which gives a more coherent view of the local conformational features. The φ, ψ, χ distributions of the 20 amino acids have been obtained from a protein coil library, considering both backbone and side-chain conformational preferences. The intrinsic side-chain χ(1) rotamer preference and χ(1)-dependent Ramachandran plot can be generally understood by combining the interaction of the side-chain Cγ/Oγ atom with two neighboring backbone peptide groups. Current all-atom force fields such as AMBER ff99sb-ILDN, ff03 and OPLS-AA/L do not reproduce these distributions well. A method has been developed by combining the φ, ψ plot of alanine with the influence of side-chain χ(1) rotamers to derive the local conformational features of various amino acids. It has been further applied to improve the OPLS-AA force field. The modified force field (OPLS-AA/C) reproduces experimental (3)J coupling constants for various short peptides quite well. It also better reproduces the temperature-dependence of the helix-coil transition for alanine-based peptides. The new force field can fold a series of peptides and proteins with various secondary structures to their experimental structures. MD simulations of several globular proteins using the improved force field give significantly less deviation (RMSD) to experimental structures. The results indicate that the local conformational features from coil libraries are valuable for the development of balanced protein force fields.

Ramachandran Plot for Alanine Dipeptide as Determined from Raman Optical Activity

Accessible values of the φ and ψ torsional angles determining peptide main chain conformation are traditionally displayed in the form of Ramachandran plots. The number of experimental methods making it possible to determine such conformational distribution is limited. In the present study, Raman optical activity (ROA) spectra of Ac-Ala-NHMe were measured and fit by theoretical curves. This revealed the most favored conformers and a large part of the potential energy surface (PES) of this model dipeptide. Such experimental PES compares well to quantum chemical computations, whereas molecular dynamics (MD) modeling reproduces it less faithfully. The surface shape is consistent with the temperature dependence of the spectra, as observed experimentally and predicted by MD. Despite errors associated with spectral modeling and the measurement, the results are likely to facilitate future applications of ROA spectroscopy.

ABEEMσπ FLUCTUATING CHARGE FORCE FIELD APPLIED TO ALANINE DIPEPTIDE AND ALANINE DIPEPTIDE–WATER SYSTEMS

Atom-bond electronegativity equalization method at σπ level fused into molecular mechanics (ABEEMσπ/MM) divides the bond regions into σ and π bond regions on the basis of previous ABEEM/MM. It may suitably reflect intramolecular and intermolecular interaction and polarization. The fitting function k H-bond in the hydrogen bond (HB) interaction region increases the capability of ABEEMσπ/MM to simulate the hydration. Hydration of alanine dipeptide (AD) in aqueous solution is determined by the intramolecular and intermolecular HBs and the competition among the molecular packing effects. The acceptor molecule in HB complex contains at least one pair of lone pair electrons, sometimes contains π bonds, whose orientations directly effect the orientation of HBs. Therefore, ABEEMσπ/MM has obviously predominance to discuss the AD and AD–water systems, which contain many lone pair electrons, π bonds, and abundant HB nets. Properties of six AD conformers, clusters AD +( H2O )1–4 obtained from ABEEMσπ/MM agree well with the results of experiments, ab initio and other force fields. Structural and dynamical properties of the hydration water molecules have just embodied that the ABEEMσπ/MM gives correct hydration description relative to other force fields.

An efficient route towards a new branched tetrahydrofurane δ-sugar amino acid from a pyrolysis product of cellulose

(1R,5S)-1-hydroxy-3,6-dioxa-bicyclo[3.2.1]octan-2-one, is a bicyclic lactone obtained in gram-scale by catalytic pyrolysis of the renewable source cellulose. Now it has been used as a chiral building block in the preparation of the new δ-sugar amino acid, (3R,5S)-5-(aminoethyl)-3-hydroxytetrahydrofurane-3-carboxylic acid, by an efficient synthesis in five steps with a 67% overall yield. The structure of this tetrahydrofurane amino acid, isolated in protonated form, was assigned by extensive mono- and bidimensional (1)H- and (13)C-NMR analysis and mass spectrometry, including measurements by electrospray and matrix-assisted laser desorption ionization techniques, the latter one for high-resolution experiments. This amino acid is an isoster of dipeptide glycine-alanine (H-Gly-Ala-OH), with a potential use in the access of new peptidomimetics with conformationally restricted structures due to the presence of tetrahydrofurane ring. As a preliminary study in order to disclose this effect, density functional theory calculation performed in water using polar continuum model was applied to the new amino acid and H-Gly-Ala-OH dipeptide, so that to evaluate and compare the relative torsional angles for the energy-minimized structures.

Are current semiempirical methods better than force fields? A study from the thermodynamics perspective

The semiempirical Hamiltonians MNDO, AM1, PM3, RM1, PDDG/MNDO, PDDG/PM3, and SCC-DFTB, when used as part of a hybrid QM/MM scheme for the simulation of biological molecules, were compared on their abilities to reproduce experimental ensemble averages at or near room temperatures for the model system alanine dipeptide in water. Free energy surfaces in the (phi, psi) dihedral angle space, (3)J(H(N),H(alpha)) NMR dipolar coupling constants, basin populations, and peptide-water radial distribution functions (RDF) were calculated from replica exchange simulations and compared to both experiment and fully classical force field calculations using the Amber ff99SB force field. In contrast with the computational chemist's intuitive idea that the more expensive a method the better its accuracy, the ff99SB force field results were more accurate than most of the semiempirical methods, with the exception of RM1. None of the methods, however, was able to accurately reproduce the experimental data. Analysis of the results indicate that the specific QM/MM interactions have little influence on the sampling of free energy surfaces, and the differences are well explained simply by the intrinsic properties of the various QM methods.

Influence of ionization on the conformational preferences of peptide models. Ramachandran surfaces of N-formyl-glycine amide and N-formyl-alanine amide radical cations

Ramachandran maps of neutral and ionized HCO-Gly-NH2 and HCO-Ala-NH2 peptide models have been built at the B3LYP/6-31++G(d,p) level of calculation. Direct optimizations using B3LYP and the recently developed MPWB1K functional have also been carried out, as well as single-point calculations at the CCSD(T) level of theory with the 6-311++G(2df,2p) basis set. Results indicate that for both peptide models ionization can cause drastic changes in the shape of the PES in such a way that highly disallowed regions in neutral PES become low-energy regions in the radical cation surface. The structures localized in such regions, epsilonL+* and epsilonD+* are highly stabilized due to the formation of 2-centre-3-electron interactions between the two carbonyl oxygens. Inclusion of solvent effects by the conductor-like polarizable continuum model (CPCM) shows that the solute-solvent interaction energy plays an important role in determining the stability order.

The SAAP force field: development of the single amino acid potentials for 20 proteinogenic amino acids and Monte Carlo molecular simulation for short peptides

Molecular simulation by using force field parameters has been widely applied in the fields of peptide and protein research for various purposes. We recently proposed a new all-atom protein force field, called the SAAP force field, which utilizes single amino acid potentials (SAAPs) as the fundamental elements. In this article, whole sets of the SAAP force field parameters in vacuo, in ether, and in water have been developed by ab initio calculation for all 20 proteinogenic amino acids and applied to Monte Carlo molecular simulation for two short peptides. The side-chain separation approximation method was employed to obtain the SAAP parameters for the amino acids with a long side chain. Monte Carlo simulation for Met-enkephalin (CHO-Tyr-Gly-Gly-Phe-Met-NH2) by using the SAAP force field revealed that the conformation in vacuo is mainly controlled by strong electrostatic interactions between the amino acid residues, while the SAAPs and the interamino acid Lennard-Jones potentials are predominant in water. In ether, the conformation would be determined by the combination of the three components. On the other hand, the SAAP simulation for chignolin (H-Gly-Tyr-Asp-Pro-Glu-Thr-Gly-Thr-Trp-Gly-OH) reasonably reproduced a native-like beta-hairpin structure in water although the C-terminal and side-chain conformations were different from the native ones. It was suggested that the SAAP force field is a useful tool for analyzing conformations of polypeptides in terms of intrinsic conformational propensities of the single amino acid units.

Ramachandran revisited. DFT energy surfaces of diastereomeric trialanine peptides in the gas phase and aqueous solution

We report DFT calculations at the B3LYP/D95(d,p) level on the gas phase, aqueous solvation and solvated energies as functions of the central psi and phi dihedral angles (in steps of 5 degrees each) of acetyl-(L)Ala-(L)Ala-(L)Ala-NH(2) (3AL) and its diastereomer, acetyl-(L)Ala-(D)Ala-(L)Ala-NH(2) (3AD). In addition to structures without internal H-bonds (C(5) interactions are neglected), many (95) structures containing internal H-bonds were completely optimized. The only minima for non-H-bonding structures in the gas phase correspond to extended beta-strands for both diastereomers. Some (but not all) structures with internal H-bonds are more stable than those without them. The energy landscapes for the solvated species show multiple minima for the non-H-bonding species and a single minimum for the H-bonding species (3(10)-helix), suggesting that the equilibrium conformational mixture in water be composed of the extended beta-strand, polyproline II, 3(10)-helix, and alpha-helix-like (with no H-bonds) conformations which are all within about 1 kcal/mol of each other. Most H-bonding structures are destabilized relative to the non-H-bonding structures in aqueous solution, but some with large dipole moments are not. The large dipole moment of the alpha-helix-like conformation leads to its increased stability in water (vs the gas phase). Significant qualitative and quantitative differences are reported for the energy landscapes of the two diastereomers when one is compared with the mirror image of the other landscape (particularly in the beta-turn region), suggesting that the differences in the energies of the unfolded peptides need to be considered when considering the stabilities of folded peptides and proteins with single amino acid mutations.

Conformational Preferences of N-Acetyl-l-leucine-N‘-methylamide. Gas-Phase and Solution Calculations on the Model Dipeptide

A DFT study of N-acetyl-l-leucine-N'-methylamide conformers in the gas phase and in solution was carried out. The theoretical computational analysis revealed 43 different conformations at the B3LYP/6-31G(d) level of theory in the gas phase. In addition, the effects of three solvents (water, acetonitrile, and chloroform) were included in the calculations using the isodensity polarizable continuum model (IPCM) and the Poisson-Boltzmann self-consistent reaction field (PB-SCRF) method. The stability order of the different conformers in solution has been analyzed. The theoretical results were compared with some experimental data (X-ray, IR, and NMR).

Implementation of the SCC-DFTB method for hybrid QM/MM simulations within the amber molecular dynamics package

Self-consistent charge density functional tight-binding (SCC-DFTB) is a semiempirical method based on density functional theory and has in many cases been shown to provide relative energies and geometries comparable in accuracy to full DFT or ab initio MP2 calculations using large basis sets. This article shows an implementation of the SCC-DFTB method as part of the new QM/MM support in the AMBER 9 molecular dynamics program suite. Details of the implementation and examples of applications are shown.

Accurate ab Initio Study on the Hydrogen-Bond Pairs in Protein Secondary Structures

Ab initio calculations up to the MP2/aug-cc-pVQZ//MP2/6-311+G** level have been carried out to characterize the four patterns of hydrogen-bond (H-bond) pairs in protein secondary structures. The unblocked and methyl-blocked glycine dipeptide dimers were arranged to model the H-bond pairs in α-helix (αHH) and antiparallel (Aββ-C5 and Aββ-C7) and parallel β-sheet (Pββ) secondary structures. The study uncovers that, in addition to the primary CO⋯NH H-bonds and the crossing secondary interactions, the CH⋯OC H-bonds and the tertiary effect (as we call it) also contribute substantially. The tertiary effect is due to the interpolarization between the donor and acceptor of a H-bond. This effect, which enhances the dipole-dipole interactions between two nearby H-bonds, stabilizes the β-sheet-like but destabilizes the helix-like H-bond pairs. The MP2 binding energies of the complexes were further refined by extrapolating to the complete basis set limit (CBS) according to Truhlar and co-workers and by a three-basis-set-based method. The best extrapolated CBS(aD-aT-aQ) binding energies of the unblocked dimers are -13.1 (αHH), -11.3 (Aββ-C5), -19.2 (Aββ-C7), and -14.8 kcal/mol (Pββ). For the methyl-blocked counterparts, the best extrapolated CBS(D-T-Q) binding energies are -14.8, -13.4, -20.8, and -16.7 kcal/mol, respectively. The interactions in the parallel β conformations are very close to the averages of the C5 and C7 antiparallel β conformations, and both are stronger than the helical dimers. Because the additive force fields are unable to account for the tertiary effect owing to the lack of polarization, all examined additive force fields significantly overestimate the interaction energies of the helix conformations relative to the β-sheet conformations. Notably, the agreement between molecular mechanical and quantum mechanical binding energies is improved after turning on the polarization. The study provides reference ab initio structures and binding energies for characterizing the backbone H-bonds of the protein secondary structures, which can be used for the parametrization of empirical molecular mechanics force fields.

Importance of the Single Amino Acid Potential in Water for Secondary and Tertiary Structures of Proteins

The structure of a protein molecule is considered to be primarily determined by the inter-amino-acid nonbonded interactions, such as hydrogen bonds. However, the conformational space of the polypeptide chain should be simultaneously restricted by the intrinsic conformational preferences of the individual amino acids. We present here precise single amino acid potential (SAAP) surfaces for glycine (For-Gly-NH(2)) and alanine (For-Ala-NH(2)) in water (epsilon = 78.39) and ether (epsilon = 4.335), which were calculated at the HF/6-31+G(d,p) level applying the self-consistent isodensity polarizable continuum model (SCIPCM) reaction field with geometry optimization in the corresponding solvents. The obtained Ramachandran potential surfaces in water showed distinct potential wells in the alpha- and beta-regions. The profiles were in almost perfect agreement with the Ramachandran plots of glycine and alanine residues in folded proteins, suggesting the Boltzmann distributions on the SAAP surfaces. Molecular simulations of polyalanines (For-Ala(n)-NH(2); n = 3-5) by using the SAAP force field equipped with the SCIPCM potentials revealed that the polyalanines readily form 3(10)-helical structures in water but not in vacuo. In ether (hydrophobic environments), the helical structures were relatively stable, but the most stable structure was assigned to a different one. These results indicated that the intrinsic conformational preferences of the individual amino acids (i.e., the SAAPs) in water are of significant importance not only for describing conformations of a polypeptide chain in the random coil state but also for understanding the folding to the secondary and tertiary structures.

Solvation effects on alanine dipeptide: A MP2/cc-pVTZ//MP2/6-31G** study of (Phi, Psi) energy maps and conformers in the gas phase, ether, and water

The effects of solvation on the conformations and energies of alanine dipeptide (AD) have been studied by ab initio calculations up to MP2/cc-pVTZ//MP2/6-31G**, utilizing the polarizable continuum model (PCM) to mimic solvation effects. The energy surfaces in the gas phase, ether, and water bear similar topological features carved by the steric hindrance, but the details differ significantly due to the solvent effects. The gas-phase energy map is qualitatively consistent with the Ramachandran plot showing seven energy minima. With respect to the gas-phase map, the significant changes of the aqueous map include (1) the expanded low-energy regions, (2) the emergence of an energy barrier between C5-beta and alpha(R)-beta(2) regions, (3) a clearly pronounced alpha(R) minimum, a new beta-conformer, and the disappearance of the gas-phase global minimum, and (4) the shift of the dominant region in LEII from the gas-phase C7(ax) region to the alpha(L) region. These changes bring the map in water to be much closer to the Ramachandran plot than the gas-phase map. The solvent effects on the geometries include the elongation of the exposed N-H and C=O bonds, the shortening of the buried HN--CO peptide bonds, and the enhanced planarity of the peptide bonds. The energy surface in ether has features similar to those both in the gas phase and in water. The free energy order computed in the gas phase and in ether is in good agreement with experimental studies that concluded that C5 and C7(eq) are the dominant species in both the gas phase and nonpolar solvents. The free energy order in water is consistent with the experimental observation that the dominant C7(eq) in the nonpolar solvent was largely replaced by P(II)-like (i.e., beta) and alpha(R) in the strong polar solvents. Based on calculations on AD + 4H(2)O and other AD-water clusters, we suggest that explicit water-AD interactions may distort C5 and beta (or alpha(R) and beta) to an intermediate conformation. Our analysis also shows that the PCM calculations at the MP2/cc-pVTZ//MP2/6-31G** level give good descriptions to the bulk solvent polarization effect. The results presented in this article should be of sufficient quality to characterize the peptide bonds in the gas phase and solvents. The energy surfaces may serve as the basis for developing of strategies enabling the inclusion of solvent polarization in the force field.

Solvation model induced structural changes in peptides. A quantum chemical study on Ramachandran surfaces and conformers of alanine diamide using the polarizable continuum model

Potential energy surfaces of the model peptide HCO-L-Ala-NH2 were calculated using polarizable continuum model (PCM) for the description of aqueous solution at RHF/3-21G, RHF/6-31+G(d), and B3LYP/6-31+G(d) levels of theory. Energy minima were optimized at all three levels as well as at B3LYP/PCM/6-311++G(d,p) level of theory. Results were correlated to experimental data of protein structures retrieved from PDB SELECT. It is concluded that alanine residues of proteins are modeled better by PCM results than by gas-phase calculations on the alanine diamide model (frequently called alanine dipeptide model). The currently available version of the PCM model implemented in Gaussian 03 provides a reasonable alternative to anticipate solvation effects without the computational costs of introducing explicit solvent molecules into the model system. Frequencies calculated at RHF/PCM/6-31+G(d) and B3LYP/PCM/6-31+G(d) levels of theory show high correlation; thus, RHF results have their own merit.

Vicinal disulfide bridge conformers by experimental methods and by ab initio and DFT molecular computations

A systematic comparison is made between experimental and computational data gained on vicinal disulfide bridges in proteins and peptides. Structural and stability data of ab initio and density functional theory (DFT) calculations on the model compound 4,5-ditiaheptano-7-lactam and the model peptide HCO-ox-[Cys-Cys]-NH2 at RHF/3-21G*, B3LYP/6-31+G(d), and B3LYP/6-311++G(d,p) levels of theory are presented. The data on Xxx-Cys-Cys-Yyy type amino acid sequence units retrieved from PDB SELECT, along with data on sequence units that have vicinal disulfide bridge, taken from the Brookhaven Protein Data Bank, are conformationally characterized. Amino acid backbone conformations, cis-trans isomerism of the amide bond between the two cysteine residues, and ring puckering are studied. Ring puckers are characterized by their relation to the conformers of the parent 4,5-ditiaheptano-7-lactam. Computational precision and accuracy are proved by frequency calculation and solvent model optimization on selected conformers. It is found that the ox-[Cys-Cys] unit is able to accept types I, II, VIa, VIb, and VIII beta-turn structures.

The SAAP force field. A simple approach to a new all-atom protein force field by using single amino acid potential (SAAP) functions in various solvents

A simple strategy to compose a new all-atom protein force field (named as the SAAP force field), which utilizes the single amino acid potential (SAAP) functions obtained in various solvents by ab initio molecular orbital calculation applying the isodensity polarizable continuum model (IPCM), is presented. We considered that the total energy function of a protein force field (E(TOTAL)) is divided into three components; a single amino acid potential term (E(SAAP)), an interamino acid nonbonded interaction term (E(INTER)), and a miscellaneous term (E(OTHERS)), which is ignored (or considered to be constant) at the current version of the force field. The E(INTER) term consists of electrostatic interactions (E(ES')) and van der Waals interactions (E(LJ')). Despite simplicity, the SAAP force field implicitly involves the correlation among individual terms of the Lifson's potential function within a single amino acid unit and can treat solvent effects unambiguously by choosing the SAAP function in an appropriate solvent and the dielectric constant (D) of medium. Application of the SAAP force field to the Monte Carlo simulation of For-Ala(2)-NH(2) in vacuo reasonably reproduced the results of the extensive conformational search by ab initio molecular orbital calculation. In addition, the preliminary Monte Carlo simulations for For-Gly(10)-NH(2) and For-Ala(10)-NH(2) showed reversible transitions from the extended to the pseudosecondary structures in water (D = 78.39) as well as in ether (D = 4.335). The result suggested that the new approach is efficient for fast modeling of protein structures in various environments. Decomposition analysis of the total energy function (E(TOTAL)) by using the SAAP force field suggested that conformational propensities of single amino acids (i.e., the E(SAAP) term) may play definitive roles on the topologies of protein secondary structures.

Computational study of conformational preferences of thioamide-containing azaglycine peptides

The effect of thioamide substitution on the conformational stability of an azaglycine-containing peptide, For-AzaGly-NH2 (1), was investigated for the sake of finding possible applications by using ab initio and DFT methods. As model compounds, For-[psiCSNH]-AzaGly-NH2 (2), For-AzaGly-[psiCSNH]-NH2 (3), and For-[psiCSNH]-AzaGly-[psiCSNH]-NH2 (4) were used. Two-dimensional phi-psi potential energy surfaces (PESs) for 2-4 were calculated at the B3LYP/6-31G*//HF/6-31G* level in gas (epsilon = 1.0) and in water (epsilon = 78.4) by applying the isodensity polarizable continuum model (IPCM) method. On the basis of these PESs, the minimum energy conformations for 2-4 were characterized at the B3LYP level with 6-31G*, 6-311G**, and 6-31+G** basis sets. The remarkable structural effect of thioamide substitution for 2-4 is that beta-strand structure is observed as a global or local minimum. The minima of 2-4 are also compared with those for glycine and thioamide-containing glycine peptides. Our theoretical results demonstrate that compounds 2-4 would be used to design controllable secondary structures.