Conformations of the Glycine Tripeptide Analog Ac-Gly-Gly-NHMe: A

Article pubs.acs.org/JPCA

Conformations of the Glycine Tripeptide Analog Ac-Gly-Gly-NHMe: A Computational Study Including Aqueous Solvation Effects. Rex E. Atwood and Joseph J. Urban* Chemistry Department, United States Naval Academy, 572 Holloway Road, Annapolis, Maryland 21402, United States ABSTRACT: A computational study of the conformational preferences of the glycine tripeptide analog, Ac-Gly-Gly-NHMe, has been carried out. The molecule is considered in isolation as well as with a continuum model of aqueous solvation. In the absence of solvent, several low-energy conformers are found that exhibit turnlike structures including type I and type II β turns. Upon consideration of aqueous solvation, two conformers, corresponding to the type I and II turn structures are found to be significantly lower in energy than all others. Results from ab initio molecular orbital theory calculations at MP2/aug-cc-pVTZ//MP2/6-311+G(d,p) are compared with those from density functional theory with B3LYP, ωB97X-D, B97-D, and M06-2X as well as several empirical force fields.

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INTRODUCTION There has been a tremendous amount of research effort devoted to the characterization of the conformational properties of small model peptide systems. The motivation for this work is multifaceted, ranging from the desire to establish a body of data that can be used in the benchmarking of new computational methods to developing a greater understanding of protein structure and function by the careful examination of the fundamental interactions present in small model systems. Although a complete review of the work published in this area is beyond the scope of this article, a brief introduction will be endeavored simply to convey the nature of the issues at play in the area. The model systems themselves have often been of the type, X-AA-Y, where AA represents an amino acid residue and X and Y are capping groups such as formyl (X = HC(O)), acetyl (X = CH3C(O)), amino (Y = NH2), or N-methylamino (Y = NHCH3).1−6 These are the so-called dipeptide or diamide analogs and the L-alanine dipeptide analog has received the greatest amount of attention.5,7−11 Tripeptide analogs of the type X-AA(1)-AA(2)-Y, where AA(1) and AA(2) may be identical or different amino acid residues have also been studied, but to a much lesser extent.12−18 Our interest in the study of fluorinated peptide mimics19,20 has brought us to the literature on the conformational preferences of these small model peptides for the purpose of examining the extent to which replacement of peptide bonds with surrogates, such as fluoroalkene moieties, impacts conformational properties. In the course of this work we have discovered an absence of ab initio results derived from correlated wave function theory (WFT) calculations on the conformational preferences of the glycine tripeptide analog, AcGly-Gly-NHMe (Figure 1). We report the results of such a study here of the molecule both in isolation and in aqueous solution and conduct a comparison of the ab initio results with those obtained by more approximate methods such as density functional theory (DFT) and empirical force field methods. Previous research on the Ac-Gly-Gly-NHMe system, and others closely related to it, includes recent density functional This article not subject to U.S. Copyright. Published 2012 by the American Chemical Society

Figure 1. Structure of the glycine tripeptide analog, Ac-Gly-GlyNHMe, with dihedral angles of interest defined.

theory (DFT) calculations with B3LYP/6-31G(d) by Lee, Park, and Lee where conformational energies in the gas phase were considered.12 Gorbunov and Stock have employed gas phase DFT calculations of the glycine tripeptide analog as part of the development of a scheme to model amide I vibrations in peptides, but no conformational energies were reported.13 Guitierrez, Baldoni, and Enriz conducted a DFT study of glycine and alanine tripeptides which was limited to the case where the central bond is in a cis conformation.14 In 1999, Yu, Schafer, and Ramek reported detailed HF/4-21G results on the formyl-(L-Ala)2-NH2 system in the absence of solvent and highlighted the importance of extending model systems beyond the dipeptide to tripeptide level in conformational studies.15 The alanine tripeptide analog system has also been used in the development and evaluation of conformational sampling methods. For example, Rosso, Abrams, and Tuckerman have reported adiabatic free-energy dynamics calculations with the CHARMM22 force field for alanine tripeptide analog in the gas phase and in aqueous solution.16 Jono, Shimizu, and Terada have employed a multicanonical ab initio molecular dynamics approach.17 Received: June 29, 2011 Revised: December 18, 2011 Published: January 3, 2012 1396

dx.doi.org/10.1021/jp206152d | J. Phys. Chem. A 2012, 116, 1396−1408

The Journal of Physical Chemistry A

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gauche − conformers for the 3-fold rotameric ϕ1, ψ1, ϕ2, ψ2 bonds and cis and trans conformers for the amide bonds ω0, ω1, ω2 (Figure 1). This leads to 34 × 23 = 648 conformers, which were then optimized using the MMFF25−29 force field as implemented in Spartan06 and ranked according to their relative energies. Conformers were selected to be optimized with the quantum chemical methods if they were within a ca. 5 kcal/mol threshold above the global minimum or if they exhibited particular traits of interest to this study such as β turn characteristics or cispeptide bonds. The initial quantum mechanical studies employed complete geometry optimizations with the Gaussian0930 suite of programs at B3LYP/6-31+G(d,p),31,32 MP2/ 6-31+G(d,p), and MP2/6-311+G(d,p).33 Stationary points were characterized as minima by frequency calculations at the same level of theory. Single point energies were also obtained at the MP2/6-311+G(d,p) geometries at MP2/aug-cc-pVTZ.34 This level of theory was endorsed by Kaminsky and Jensen as capable of ∼1 kJ/mol accuracy for the calculation of peptide conformational energies.6 The inclusion of the effects of aqueous solvation was accomplished with use of the default IEF-PCM35−38 solvent model as implemented in Gaussian09.30 For simplicity the MP2/aug-cc-pVTZ//MP2/6-311+G(d,p) and MP2/6-311+G(d,p)//MP2/6-311+G(d,p) protocols are at times referred to as MP2-1 and MP2-2, respectively. In conducting these studies, every effort was made to be as exhaustive as possible in terms of the inclusion of input structures that could potentially lead to conformational minima. This was handled through the use of extensive conformational searching to provide initial geometries for optimization with quantum mechanical methods with Gaussian09 as outlined above. But, it was also emphasized in the manner in which the Gaussian09 calculations were approached. For example, if a structure was obtained at B3LYP that was not among the set of those obtained with MP2, it was also explicitly subjected to optimization at the MP2 level. Thus, whenever a method (gas phase, aqueous phase, MMFF, B3LYP, MP2) generated a novel structure, that structure was subjected to optimization with all methods. Any structures reported in the Lee B3LYP study12 that had the potential to be different from those already accounted for were also explicitly considered as input structures. Also, input structures were explicitly generated using literature39 backbone dihedral angle values for prototypical β turn structures to ensure that the lowest-energy versions of those conformations had been identified. In addition, full geometry optimizations and frequency calculations were carried out on selected conformers using three more recently developed density functional methods with the 6-311++G(d,p) basis set: Zhao and Truhlar’s M06-2X,40 and the dispersion-corrected functionals B97-D from Grimme41 and ωB97X-D of Chai and Head-Gordon42 and an expanded set of molecular mechanics force fields beyond the MMFF studies used to generate the initial conformers. The additional force fields included MM2 as implemented in ChemBio3D,43 MM3 and MMX as implemented in PCModel,44 AMBER,45 and UFF46 as implemented in Gaussian09.30 Charges for AMBER were assigned by GaussView in accordance with Cornell et al.45 Charges for UFF were generated by GaussView’s implementation of the Qeq47 approach of Rappe. These force fields were also partnered with continuum solvent models in the following manners. For the PCModel calculations, both available implementations of the GB/SA approach, the analytical Still48 method and Hawkins−Cramer−

In this work, we present a thorough investigation of the conformational preferences of the glycine tripeptide analog, AcGly-Gly-NHMe, as described by high-level ab initio molecular orbital calculations. The results are compared to more computationally efficient methods using popular density functional theory and empirical force field approaches. Of particular interest are the tendencies of this system to engage in intramolecular hydrogen bonding interactions. Such interactions have been characterized in the literature on the basis of the ring size incorporating the hydrogen bond as either C5, C7, or C10. The C10 arrangement is prototypical of β turns. The potential intramolecular hydrogen bonds are shown schematically in Figure 1 in a manner similar to that previously depicted by Chin et al.21

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CONFORMATION NOTATION SCHEME The conformational surface of a dipeptide (capped amino acid) is commonly described by the set of dihedral angles, ϕ and ψ, for the single bonds flanking the α carbon with nine possible conformers resulting from the combination of three rotamers (anti, gauche +, gauche −) at each of those bonds. A variety of notational systems have been used in the literature to describe these peptide backbone conformations.22,23 In this work, we employ the topological scheme of Perczel et al.2 The idealized ϕ, ψ values for each conformer are as depicted in Figure 2.

Figure 2. Schematic showing commonly encountered backbone conformations on a Ramachandran map.

Thus, αL = −60°, −60°; βL = +180°, +180°; and so on. The relationship between these and other conformer descriptors that are commonly used in the literature is αLEFT = αD, C7ax = γD, b2 = δL, C5 = βL, α′ = δD, C7eq = γL;, poly proline II = εL, and αRIGHT = αL. This notational scheme is extended to the tripeptide system accordingly. Thus, a conformer with values of −60°, −60°, +180°, +60° for ϕ1, ψ1, ϕ2, ψ2, respectively, is termed αLδL. In classifying the output structures from geometry optimizations a tolerance of ±60° was applied to standard dihedral angle values of +60°, −60°, +180°.

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COMPUTATIONAL METHODS

Conformer identification was accomplished using the default conformer searching routine in the Spartan0624 program which for this system results in consideration of anti, gauche, and 1397



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Table 1. Calculated Relative Energiesa and Dihedral Anglesb for Lowest-Energy Gas Phase Conformers of Ac-Gly-Gly-NHMe Found with MMFFc conformerd

ΔE

ω0

ϕ1

ψ1

ω1

ϕ2

ψ2

ω2

γDαL γLαD γDγL αDαD γLγD γDγD αDγD γDγD γDγD γLεL γDεL γDαD γDδD εLγL γLδL εLγL βLγD γLεD-C2 βLεD βLβL

0.00 0.20 0.45 0.52 0.68 0.90 0.93 1.17 1.24 1.46 1.89 2.20 2.22 2.35 2.44 2.75 2.86 3.21 3.28 3.38

−175.3 176.0 −176.2 166.1 176.3 178.0 165.5 −178.0 178.6 174.1 −174.2 −177.6 −177.7 171.4 178.1 170.8 −179.1 174.1 179.5 179.9

74.7 −75.0 79.5 74.0 −80.8 81.6 74.4 79.6 82.1 −82.9 82.9 79.1 79.2 −89.3 −79.0 −93.3 −179.0 −82.8 178.4 180.0

−107.7 101.3 −83.7 11.0 80.8 −47.1 6.0 −81.6 −47.1 74.4 −74.0 −82.8 −81.7 153.0 80.6 153.9 180.0 74.4 −178.1 −179.7

170.9 −171.1 175.5 −173.0 −172.7 −177.5 −171.6 167.1 −174.6 −163.2 162.6 165.6 169.1 −177.6 −169.4 177.2 179.0 −162.9 −170.4 179.2

−92.4 92.2 −81.2 94.2 77.8 82.4 94.9 80.3 80.4 80.9 −82.8 84.5 165.0 81.4 −163.3 −81.2 83.2 82.8 91.3 178.7

−15.9 6.9 46.5 4.6 −83.4 −45.0 −8.4 −40.8 −78.2 −163.1 168.8 13.6 −17.2 −82.1 25.4 86.0 −48.8 −172.8 −150.1 −178.0

177.5 174.9 170.7 −175.2 172.5 −171.3 178.1 −171.1 172.6 175.8 176.7 −174.3 −173.3 170.8 −177.3 −172.0 −171.6 10.5 175.8 176.2

a

In kcal/mol. bIn degrees. cEmploying the default conformational searching routines and the MMFF force field as implemented in Spartan06. Conformer designation. Cn indicates cis conformation at the indicated ω peptide bond (Figure 1). The N-terminal peptide bond is ω0, the central peptide bond is ω1, and the C-terminus peptide bond is ω2. d

Table 2. Ab Initio-Calculated Relative Energies and Dihedral Anglesa for Gas Phase Conformers of Ac-Gly-Gly-NHMe conformerb

MP2-1 ΔEc

MP2-2 ΔEd

ω0

ϕ1

ψ1

ω1

ϕ2

ψ2

ω2

εDγL γDγL αLγL γLγL γDεL γLγD αDγL γLαL εDγL εLγL-C1 βLγL γDδD-C2 βLβL εDγD-C1 βLγL βLβL-C2 αDβL-C2

0.00 0.74 0.92 0.93 0.97 2.53 2.61 2.64 2.68 2.85 3.29 3.41 3.81 4.41 5.12 5.37 5.95

0.00 0.97 1.40 1.37 0.46 2.83 2.02 2.90 1.95 3.38 3.75 3.08 4.84 4.80 5.60 6.52 6.20

−167.6 −178.6 −169.2 −177.9 −167.0 −174.5 174.5 −178.9 −167.2 164.7 173.2 −167.2 −172.8 −169.6 172.7 172.9 −178.6

56.4 81.8 −70.6 −82.6 78.1 −87.1 65.8 −82.7 54.8 −58.7 −176.9 77.9 170.1 86.6 −176.2 −170.6 63.0

−138.8 −71.4 −21.9 66.0 −79.0 69.3 34.4 72.5 −142.0 151.6 −161.9 −79.4 166.7 −122.0 −160.3 −164.3 29.4

174.8 175.0 175.0 −175.1 157.2 −175.5 −166.6 −168.7 172.6 1.9 −176.1 157.7 −176.8 24.8 −168.8 −173.4 −158.8

−85.3 −79.5 −87.8 −84.5 −56.2 85.1 79.9 −97.8 −80.8 −88.4 −83.5 157.7 174.7 109.9 −93.9 168.3 134.0

3.9 76.2 4.8 69.9 147.4 −1.2 −82.1 −2.5 79.2 14.2 76.4 −65.8 164.4 −115.3 0.1 178.9 −174.9

175.4 −173.0 175.9 −174.6 −174.9 −172.2 166.1 174.1 −165.5 174.1 −172.8 −15.3 164.4 174.4 173.1 14.4 14.0

a In degrees. From MP2/6-311+G(d,p) optimized geometries. bConformer designation. Cn indicates cis conformation at the indicated ω peptide bond (Figure 1). The N-terminal peptide bond is ω0, the central peptide bond is ω1, and the C-terminus peptide bond is ω2. cMP2-1: relative energy calculated at MP2/aug-cc-pVTZ//MP2/6-311+G(d,p). In kcal/mol. dMP2-2: relative energy calculated at MP2/6-311+G(d,p)//MP2/6311+G(d,p). In kcal/mol.

Truhlar49 models, were employed. For the AMBER and UFF force fields implemented within Gaussian09, calculations with the dielectric constant set to 4 and 78.39 were performed.

MP2/6-311+G(d,p), MP2/6-31+G(d,p) and B3LYP/6-31+G(d,p) levels, respectively, in the absence of solvent. In addition, Table 2 includes relative conformational energies obtained from MP2/aug-cc-pVTZ//MP2/6-311+G(d,p) single point energy calculations. In some cases, there were additional conformations obtained but they were not included because of their very high relative energy. Also, only a single representative enantiomer of enantiomeric pairs is included. The MP2-1 column of Table 2 contains the results from the highest level of wave function theory used here, MP2/aug-ccpVTZ//MP2/6-311+G(d,p). The MP2-1 data indicate the

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RESULTS AND DISCUSSION Gas Phase Conformational Energies. Table 1 presents the relative energies of the lowest-energy conformers of AcGlyGly-NHMe found by conformer searching with molecular mechanics (MMFF in Spartan06). Tables 2, 3, and 4 provide the relative conformational energies and key dihedral angles for the structures resulting from geometry optimization at the 1398



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Table 3. MP2/6-31+G(d,p) Relative Energiesa and Dihedral Anglesb for Gas Phase Conformers for Ac-Gly-Gly-NHMe conformerc

ΔE

ω0

ϕ1

ψ1

ω1

ϕ2

ψ2

ω2

εDγL γDγL γLεD γLγL αDγL αDγD εDγL γLγD γLγL γDεL-C2 εLδL-C1 βLγD γDεD-C1 δDεL βLβL εDβL αDβL-C2 αLβL-C2 βLβL-C2 εDβL-C2 δLεD-C2

0.00 0.52 0.66 0.89 1.19 2.19 2.20 2.53 2.63 3.27 3.36 3.58 4.42 4.60 4.81 4.99 6.24 6.40 6.61 6.83 6.86

−168.4 −179.4 167.7 −178.8 172.2 175.5 −167.8 −175.8 −179.1 −168.0 166.0 −173.0 −172.4 175.8 −172.2 −165.4 −177.1 177.7 171.9 −165.1 −175.5

57.1 82.5 −78.7 −82.6 70.6 66.3 55.6 −86.0 −83.1 78.6 −59.6 −178.8 97.4 147.9 173.6 64.2 68.4 −71.8 −171.7 64.4 −147.3

−137.8 −70.5 77.7 66.6 20.2 33.3 −143.7 69.0 70.8 −77.9 151.1 160.8 −109.1 −48.2 165.0 −148.5 23.2 −71.8 −165.6 −150.2 46.6

175.6 176.6 −157.8 −174.3 −174.8 −167.2 173.9 −178.1 −169.5 158.5 2.3 175.3 17.0 152.0 −178.7 175.6 −163.5 166.5 178.7 175.6 −152.2

−86.3 −80.4 57.9 −84.6 90.6 80.5 −81.5 88.8 −103.3 −67.2 −88.4 84.1 111.1 −62.3 −177.7 −179.1 142.3 −153.0 −171.5 −169.4 69.0

6.2 72.2 −149.0 67.3 −7.0 −80.9 77.0 −7.6 −7.6 169.2 15.7 −74.1 −123.2 159.9 163.2 −161.9 −175.3 179.4 −178.2 −176.6 −171.6

176.4 −175.6 176.7 −176.6 −176.4 166.6 −166.6 −173.0 175.3 −14.2 175.0 174.7 177.6 −178.0 177.9 −176.5 12.7 6.7 10.0 8.9 12.7

a Calculated at MP2/6-31+G(d,p)//MP2/6-31+G(d,p). In kcal/mol. bIn degrees. cConformer designation. Cn indicates cis conformation at the indicated ω peptide bond (Figure 1). The N-terminal peptide bond is ω0, the central peptide bond is ω1, and the C-terminus peptide bond is ω2.

Table 4. B3LYP/6-31+G(d,p) Relative Energiesa and Dihedral Anglesb for Gas Phase Conformers for Ac-Gly-Gly-NHMe conformerc

ΔE

ω0

ϕ1

ψ1

ω1

ϕ2

ψ2

ω2

γDγL γLγL βLβL εDγL βLγL γLγL αLγL γDεL γLγL γDβL βLβL-C2 βLγL γLγD-C1 εLγL-C1 γDβL-C2 γLεL-C2 γLγD

0.00 0.02 0.54 0.64 1.17 1.32 1.68 1.79 2.02 2.23 2.23 2.61 3.76 3.80 3.87 4.07 4.23

177.0 −176.3 −180.0 −173.8 179.6 −176.6 −169.0 −174.7 −171.9 176.3 179.9 179.6 −176.4 170.7 176.2 −172.9 −170.8

81.9 −81.9 −179.9 62.1 176.3 −82.4 −74.9 80.7 −114.8 109.2 −179.6 175.2 94.9 −67.9 111.9 80.9 −107.8

−66.0 64.9 179.9 −130.0 −176.0 70.3 −10.6 −70.7 13.4 −11.4 179.8 −174.1 −111.3 146.1 −12.6 −70.3 13.9

−177.6 −175.1 −179.9 172.9 −176.6 −171.2 171.2 167.1 −179.8 −178.3 179.9 −171.2 12.1 −0.1 −178.5 164.4 168.3

−80.3 −82.3 179.7 −98.7 −83.6 −112.5 −100.4 −71.9 −82.0 −174.8 179.6 −112.2 117.0 −97.5 −174.9 −84.7 115.6

66.6 62.4 179.5 12.7 70.8 10.2 10.2 150.8 66.9 179.4 −179.2 15.1 −114.7 32.9 −179.7 174.4 −17.1

−170.2 −180.0 179.0 177.3 −177.4 177.1 177.0 −179.6 −177.7 177.7 3.5 175.3 177.7 176.6 4.8 −8.2 −174.4

a

Calculated at B3LYP/6-31+G(d,p)//B3LYP/6-31+G(d,p). In kcal/mol. bIn degrees. cConformer designation. Cn indicates cis conformation at the indicated ω peptide bond (Figure 1). The N-terminal peptide bond is ω0, the central peptide bond is ω1, and the C-terminus peptide bond is ω2.

presence of five minima within 1 kcal/mol of the ground state with the next highest conformer at 2.53 kcal/mol above the ground state. Figure 3 shows these six conformers. It is interesting to note that there is a significant degree of conformational diversity among the group of five low-energy structures. Two of the five structures, those at 0.00 and 0.92 kcal/mol, exhibit β turn characteristics with clear C10-type hydrogen bonding across the turn between the i CO and the i + 3 N−H. The second highest-energy structure, at 0.74 kcal/ mol, exhibits a turn that lacks a specific hydrogen bond and has the peptide bonds occupying positions essentially perpendicular to the mean plane of the turn with the carbonyl dipoles direction alternating around the turn. The two remaining

Figure 3. Lowest-energy conformers in the gas phase for Ac-Gly-GlyNHMe at MP2/aug-cc-pVTZ//MP2/6-311+G(d,p). Calculated relative energies are reported in parentheses, in kcal/mol.

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system under study here, this structure is isoenergetic to the mirror image type II turn (εLγD, not shown). In a computational study of two conformations of Ac-Gly-Gly-NHMe, the extended conformation and a cyclic hydrogen bonded structure corresponding to εDγL, Zhang and Wang18 developed a scheme to decompose this intramolecular interaction into a hydrogen bond stabilizing component (−6.46 to −7.10 kcal/mol) and a steric destabilizing component (+1.67 to +3.39 kcal/mol), relative to the extended conformation. The αLγL structure, 0.92 kcal/mol above the ground state with the MP2-1 protocol, has dihedral angles of −70.6°, −21.9°, −87.8°, +4.8°, which compare well with the classic type I turn values of −60°, −30°, −90°, 0°.52,53 As stated above, both of these structures exhibit intramolecular hydrogen bonding between the i CO and i + 3 N−H, thus effectively creating a cyclic structure incorporating 10 atoms. Rather than cross-turn hydrogen bonding, the γDγL and γLγL structures contain intramolecular hydrogen bonding between the i CO and i + 2 N−H resulting in structures of the C7 type in each adjacent diamide unit (−C(O)−NH−CH2 −C(O)−NH−). This hydrogen bonding pattern produces a seven-membered ring and has been well documented in studies of amino acid dipeptide analogs of the type Ac-X-NHMe.4−6,11,52 The γDεL structure possesses one such intramolecular hydrogen bond. After the set of five low-lying conformations, there is a continuum of structures ranging from 2.61 to 5.95 kcal/mol in energy. All of these conformers are too high in energy to be expected to contribute to the equilibrium conformational distribution at room temperature. However, we have included them in this study as the results in the Table 1 are for the molecule in isolation. These conformers are high in energy from an intrinsic stability standpoint for this model peptide. But, in more complex systems, specific interactions with neighboring groups or the surrounding solvent medium could drastically impact the distribution of conformers actually encountered. For example, Li and Wang54 have recently reported calculated binding energies between pentaglypeptide analog and DNA bases in the range of −10.32 to −13.42 kcal/ mol. Thus, we have taken a liberal approach in terms of inclusion of conformers in this study. Also, inclusion of thermochemical corrections has the result of bringing all conformers closer to each other in energy in terms of ΔG (Table 5). Inspection of the data in Tables 1−5 allows for a comparison among the levels of theory considered here in their description of the gas phase conformational preferences of Ac-Gly-GlyNHMe. For the most part, the results from the MP2-1 protocol (MP2/aug-cc-pVTZ single-point energies at MP2/6-311+G(d,p) geometries) are well approximated by the MP2-2 method (MP2/6-311+G(d,p) optimizations and energies). For example, both levels of theory predict the same structure, εDγL to be the global minimum in terms of ΔE. There is also very good agreement among the six lowest-energy conformers. MP2/6311+G(d,p) optimizations result in five low-energy structures all within 1.40 kcal/mol of the ground state, as compared to a span of 0.97 kcal/mol at MP2-aug-cc-pVTZ//MP2/6-311+G(d,p), with the next highest-energy structure appearing at 2.83 kcal/mol (versus 2.53 kcal/mol at MP2-aug-cc-pVTZ//MP2/ 6-311+G(d,p)). There are some very small discrepancies in the qualitative ordering of conformations. For example, the relative ordering of αLγL, γLγL, and γDεL is different with MP2/6311+G(d,p) than it is at MP2/aug-cc-pVTZ. But, according the higher level of theory, these conformers are essentially

structures, at 0.93 and 0.97 kcal/mol, do exhibit intramolecular hydrogen bonding but do not exhibit β turn characteristics. One might expect, in the absence of an aqueous medium, the conformational landscape of Ac-Gly-Gly-NHMe to be dominated by intramolecular hydrogen bonds. This has been found to be the case in many studies of amino acid analogs such as formyl-Gly-NH2,2 formyl-Ala-NH2,2 Ac-Gly-NHMe,6 and AcAla-NHMe6,50 where C7 conformations, labeled γ here, predominate in the absence of solvent. Though not all of the low-energy structures encountered here for Ac-Gly-Gly-NHMe possess classic hydrogen bonds, turns and folds are clearly intrinsically preferred for this system in the absence of an interacting solvent and ignoring entropic effects. For example, the fully extended βLβL structure is calculated to be 3.81 kcal/ mol above the ground state in terms of ΔE at the highest level of theory employed here. Table 5 shows the thermochemical corrections to the relative energies for the MP2-1 and MP2-2 Table 5. Relative Energies, in kcal/mol, Including Thermochemical Corrections for Selected Ac-Gly-GlyNHMe Conformations in the Gas Phase εDγL

γDγL

αLγL

γLγL

γDεL

γLγD

MP2/6-311+G(d,p)//MP2/6-311+G(d,p) ΔE 0.00 0.97 1.40 1.37 0.46 2.83 Δ(E+ZPE) 0.00 1.02 1.00 1.30 0.83 2.44 ΔH(298K) 0.00 1.05 1.15 1.42 0.63 2.66 ΔG(298K) 0.00 0.37 0.36 0.58 1.40 1.23 MP2/aug-cc-pVTZ//MP2/6-311+G(d,p) ΔE 0.00 0.74 0.92 0.93 0.97 2.53 Δ(E+ZPE) 0.00 0.79 0.52 0.87 1.34 2.14 ΔH(298K) 0.00 0.82 0.67 0.98 1.14 2.36 ΔG(298K) 0.13 0.26 0.00 0.27 2.04 1.05 ωB97X-D/6-311++G(d,p)//ωB97X-D/6-311++G(d,p) ΔE 0.00 0.34 0.80 0.54 1.16 1.98 Δ(E+ZPE) 0.00 0.57 0.69 0.67 1.33 1.76 ΔH(298K) 0.00 0.54 0.69 0.69 1.24 1.95 ΔG(298K) 0.00 0.08 0.65 0.15 1.54 0.02 B97-D//6-311++G(d,p)//B97-D//6-311++G(d,p) ΔE 0.43 0.00 1.05 0.29 1.45 1.69 Δ(E+ZPE) 0.36 0.00 0.65 0.27 1.41 1.33 ΔH(298K) 0.36 0.00 0.79 0.27 1.40 1.50 ΔG(298K) 1.13 0.76 1.49 0.93 2.37 1.46 M06-2X//6-311++G(d,p)//M06-2X//6-311++G(d,p) ΔE 0.00 0.99 1.01 1.07 0.70 2.77 Δ(E+ZPE) 0.00 1.16 0.84 1.24 1.00 2.51 ΔH(298K) 0.00 1.19 0.89 1.28 0.82 2.73 ΔG(298K) 1.38 1.78 2.01 1.93 2.96 2.47

βLβL 4.84 3.78 4.33 1.40 3.81 2.74 3.30 0.49 2.24 1.57 1.88 0.56 3.77 2.38 3.03 0.00 2.52 1.38 2.00 0.00

wave function theory protocols and the M06-2X, B97-D, and ωB97X-D density functional methods. On the bssis of ΔG at 298 K, once again, a collection of conformers, εDγL, γDγL, αLγL, and γLγL, are highly favored. Also, the βLβL structure becomes much more viable. This is consistent with the observations of Mons et al. in their investigations of an (ala)4 model peptide that conformations locked by intramolecular hydrogen bonds are disfavored by entropy compared to those that are more open-chain and floppy.51 The MP2/6-311+G(d,p)-calculated ϕ1, ψ1, ϕ2, ψ2 dihedral angles (Table 2) for the global minimum εDγL structure are +56.4°, −138.8°, −85.3°, +3.9°, which compare very closely to the typically cited values for a type II′ turn of +60°, −120°, −85.3°, 0°.52,53 As glycine is the amino acid employed in the 1400



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density functional theory methods. The B3LYP/6-31+G(d,p) results obtained here (Table 4) for the Ac-Gly-Gly-NHMe system represent some of the most general characteristics of the conformational profile that results from the highest level of wave function theory employed here, but there are some key differences. For example, B3LYP/6-31+G(d,p) predicts the ground-state conformation in the gas phase to be γDγL. This is a folded conformation with the peptide bonds not oriented in a manner that allows for the C10-type of hydrogen bonding interaction commonly associated with β turn structures. With MP2, with either 6-311+G(d,p) or 6-31+G(d,p), the εDγL structure, a type II β turn with a C10 hydrogen bond, is found as the ground-state conformation. With B3LYP/631+G(d,p), the γLγL structure is found to be essentially degenerate with the ground state with a ΔE of only 0.02 kcal/ mol. The fully extended conformation βLβL is predicted at B3LYP/6-31+G(d,p) to lie only 0.54 kcal/mol above the ground state. This is in sharp contrast to the MP2 results that place this conformer well over 3 kcal/mol above the ground state. The fourth and fifth highest B3LYP conformers are εDγL at 0.64 kcal/mol and βLγL at 1.17 kcal/mol. The next highest conformer comes at 1.32 kcal/mol. Thus, B3LYP/6-31+G(d,p) also predicts five low-energy conformers within a roughly 1 kcal/mol window. But, they are not the same five as the higher levels of theory with the overestimation of the relative stability of βLβL the most notable discrepancy compared to the MP2 data. Also, the B3LYP/6-31+G(d,p) data span a smaller range of relative energies than the MP2 results, which is consistent with previous results we have seen in the conformational energies of fluorinated peptidomimetics.20 Our B3LYP/631+G(d,p) results agree very closely with the B3LYP/631G(d) results reported by Lee et al.12 for this system, indicating that the expansion of the basis set to include diffuse functions and polarization functions on hydrogen does not result in significantly better agreement with MP2 methods. However, two notable differences between the B3LYP/631+G(d,p) and B3LYP/6-31G(d,p) data are that the latter places βLβL higher in relative energy at 1.68 kcal/mol above the ground state and does locate a β turn similar to εDγL at 1.26 kcal/mol above the ground state. Finally, there are several mismatches in the conformers found between MP2/6-311+G(d,p) and B3LYP/6-31+G(d,p). For example, the αLγD conformer was not found as a minimum on the B3LYP/6-31+G(d,p) potential energy surface but rather resulted in a structure that is not identical to, nor the mirror image of, any of the structures found with MP2/6-311+G(d,p). Also, the B3LYP/6-31+G(d,p) optimizations produced two conformers which both fit the γLγL conformer on the basis of the nomenclature criteria used here at 0.02 and 0.64 kcal/mol. The one at 0.02 kcal/mol corresponds to the conformer found at 0.93 with the MP2-1 protocol. The other is unique to B3LYP/6-31+G(d,p). Although B3LYP has been a very commonly adopted DFT method for the study of organic systems, its performance has come under criticism,55 and much attention has been directed to development of density functionals that provide improved performance overall for organic molecules, especially with respect to dispersive interactions. In Table 5, a comparison is made between the results obtained with the MP2-1 and MP-2 wave function theory protocols and with three newer DFT methods: ωB97X-D, B97-D, and M06-2X. A modest basis set, 6-311+G(d,p) has been employed because we are specifically interested in evaluating the performance of methods that offer a

degenerate as they are within 0.05 kcal/mol of each other. The MP2/6-311+G(d,p) energies are in reasonably good agreement with the MP2/aug-cc-pVTZ results for the higher-energy conformers as well with most ΔE values within ∼0.5 kcal/mol of each other. The largest discrepancies are seen in the case of the fully extended conformers, βLβL and its counterpart with a cis C-terminal peptide bond, βLβL-C2 where MP2/6-311+G(d,p) overestimates the relative energy by just over 1 kcal/mol relative to MP2/aug-cc-pVTZ. A similar result is seen in the Zhang and Wang18 study where the βLβL conformer is found to lie 3.52 kcal/mol above a β turn structure at MP2/6-311+ +G(3df,2p) and 5.43 kcal/mol at MP2/6-311++G(d,p). We have also performed geometry optimizations at MP2/631+G(d,p) and B3LYP/6-31+G(d,p) to determine if these more computationally efficient levels of theory produce acceptable results that would be advantageous in the study of larger systems. Table 3 provides the MP2/6-31+G(d,p)// MP2/6-31+G(d,p) results. With this approach, there is very good correspondence among the lowest-energy conformations to the results obtained with the more robust MP2-1 protocol. At MP2/6-31+G(d,p), the εDγL conformer is found to be the global minimum followed by γDγL next highest at 0.52 kcal/mol, which compares well with the MP2-1 results where the same two conformers are the lowest in energy found with a gap between them of 0.74 kcal/mol. Next, there is a cluster of three conformers, αLγL, γLγL, and γDεL, within 1.19 kcal/mol of the ground state all of which are found within 0.97 at the MP2-1 level, although with different ordering. There are more significant deviations at the higher-energy regime between the MP2/6-31+G(d,p) and MP2-1 computational protocols. There are some conformers found at MP2/6-31+G(d,p) that are not seen as local minima on the MP2/6-311+G(d,p) potential energy surface. For example, at 2.20 kcal/mol in the MP2/631+G(d,p) results, a conformer is found that falls within the boundaries of εDγL according to the conformer classification scheme (Figure 2) but is fundamentally different from the version of εDγL that is the ground-state conformation. They differ in the ψ2 value, which is 77.0° for the εDγL at 2.20 kcal/ mol as opposed to 6.2° for the global minimum. Likewise, a γLγD conformer is seen at 2.53 kcal/mol with MP2/631+G(d,p), which is not the enantiomer of γDγL at 0.89 kcal/ mol, due to differences in the ψ2 values, and has no counterpart on the MP2/6-311+G(d,p) surface. A similar situation exists in the case of the γLγL conformer at 2.63 kcal/mol on the MP2/631+G(d,p) surface. It is not the same conformation as the γLγL found at 0.89 kcal/mol, as evidenced by the ψ2 dihedral angle −7.6° versus +67.3°, and it is not seen among the conformations found with the MP2/6-311+G(d,p) optimizations. There are additional conformations at the very highenergy regime of 4 to 6 kcal/mol that are found at MP2/631+G(d,p) but do not persist as minima at the MP2/6311+G(d,p) level. Density functional theory (DFT) methods have been applied with much success to a number of important research problems in chemistry such as molecular structure, vibrational analysis, and chemical reaction energetics and offer advantages in computing efficiency.55,56 However, it has also been pointed out that an inadequate description of dispersion may result in lower accuracy for conformational energies, where dispersive interactions may play a significant role, than post-Hartree− Fock wave function theory approaches such as MP2 methods.6,57−59 Also, the continuum of systematic improvement offered by wave function theory is harder to discern in 1401



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Table 6. Molecular Mechanics Relative Energies, ΔE, in kcal/mol, for Selected Ac-Gly-Gly-NHMe Conformations in the Gas Phase force fielda

εDγLb

γDγL

αLγL

γLγL

γDεL

γLγD

βLβL

MM2 MM3 MMX AMBER UFF

2.25 0.45 γDαL 0.07 γDγL 1.58 γDδL 12.28 γDγL

0.29 0.00 0.07 0.00 0.83

0.00 γLγL 0.91 γLαL 1.52 3.04 γLδL 6.20

0.00 0.04 0.00 0.27 0.00

4.81 0.00 γDγL 0.02 γDγL 0.02 γDγL 10.50 γDγL

0.54 0.00 γDγL 0.07 0.01 4.54

8.57 4.78 1.45 1.35 11.78

a

MM2 as implemented in ChemBio3D Ultra 12.0, MM3 and MMX as implemented in PCModel 9.3, and AMBER and UFF as implemented in Gaussian09. See text for additional details. bThe top row provides the conformer designator for the input geometry. In cases where optimization with a given force field led to a different conformer, the output conformer designator is provided to the right of the ΔE value in the row for that force field.

the location of structures as minima than others. This is important if the force fields are to be used simply for the generation of conformers, with accurate energetics coming ultimately from quantum mechanical studies. For example, MM2 significantly overestimates the relative energy of εDγL, but at least captures it as a minimum. For all of the other force fields in Table 6, this structure moves to a different conformer upon optimization. With MM3, as implemented in PCModel, only three of the seven conformers persist as minima upon geometry optimization. Thus, it appears that, at least on the basis of the data available in this study, conformer screening with MMFF is more inclusive and less apt to result in the early elimination of viable conformers than the force fields shown in Table 6. A similar conclusion was reached by Friesner and coworkers in an early study of MMFF in comparison to a wide range of force fields in reproducing a set of 10 conformers of the alanine tetrapeptide analog.60 It should be pointed out that some of the force fields included here, such as AMBER and MMFF, were intended in their original development to be used primarily for solution phase simulations rather than for the study of molecules in isolation. However, their incorporation into commercial molecular modeling software packages, in some cases where a solvent model is not available or is not the default, results in force field energy minimizations in the absence of solvent having become a common practice of many users. Our intention here is not necessarily to endorse that practice, but to evaluate the utility of these readily available force fields simply for conformer generation for subsequent study with ab initio and/or DFT methods. A similar approach has been used by Mons and co-workers.61 Users desiring to obtain the most accurate conformational energies possible from the force fields alone should follow the guidance in the literature from the original developers of the force fields. Aqueous phase results are discussed below. Conformations with Cis Peptide Bonds. Though the preference for the trans conformation of peptide bonds in proteins is clearly established,39 there is also interest in the study of cis peptide bonds in proteins and also small peptides and peptidomimetics.14,62 In our original molecular mechanicsbased conformational searching, the peptide bonds were not restricted to a trans conformation. Thus, many high-energy structures containing cis peptide bonds were found (not shown in Table 1) and some were carried forward into the ab initio and DFT studies. Among the higher-energy sets of conformers, several structures with cis peptide bonds were found as indicated throughout Tables 1−4. Gutierrez, Baldoni, and Enriz recently reported DFT calculations on the conformers of the Ac-Gly-Gly-NHMe system (and its Ala analogs) limited to the

significant computational efficiency over the MP2-1, MP2-1 protocols or more advanced correlated wave function theory approaches. In terms, of ΔE, there is rather close correspondence for all three DFT methods with the MP2/ aug-cc-pVTZ//MP2/6-311+G(d,p) results. Both ωB97X-D and M06-2X predict εDγL to be the lowest in energy among this series of conformers, whereas B97-D predicts γDγL. Across this sampling of conformations, the mean unsigned differences in ΔE, relative to MP2/aug-cc-pVTZ//MP2/6-311+G(d,p), are 0.46, 0.41, and 0.33 kcal/mol for ωB97X-D, B97-D, and M06-2X, respectively. With the MMFF force field as incorporated into Spartan06 with the default conformer searching and energy minimization routines, the global minimum was found to be a γDαL structure. Visual inspection reveals that this conformer is similar to the εDγL conformer found as the global minimum at MP2/aug-ccpVTZ//MP2//6-311+G(d,p) with ϕ1,ψ1,ϕ2,ψ2 dihedral angles of +74.7°, −107.7°, −92.4°, −15.9° compared to +56.4°, −138.8°, −85.3°, +3.9° at MP2. There are instances with the default Spartan06/MMFF protocol where two conformers that are nearly identical to each other (or nearly enantiomers) were found with backbone dihedral angles that differ by only a few degrees and relative energies within tenths of a kcal/mol. For example, the γLαD conformer at ΔE = 0.20 kcal/mol is very nearly the enantiomer of the γDαL conformer at ΔE = 0.00 kcal/mol. The same is true of the γDαL conformer at ΔE = 0.45 kcal/mol and the γLγD conformer at ΔE = 0.68 kcal/mol. The MMFF αDαD conformer at ΔE = 0.52 kcal/mol is nearly the mirror image of the MP2/aug-cc-pVTZ//MP2//6-311+G(d,p) αLγL conformer. There is a similar correspondence between the MMFF γLγL conformers at ΔE = 0.90 and 1.17 kcal/mol and the MP2/aug/-VTZ//MP2//6-311+G(d,p) γDγD conformer at ΔE = 0.93 kcal/mol. Thus, in terms of low-energy structures, the Spartan06/MMFF conformational profile is a reasonable representation of the MP2/aug-cc-pVTZ//MP2//6-311+G(d,p) conformational profile. In fact, it corresponds more closely to the MP2/aug-cc-pVTZ//MP2//6-311+G(d,p) results than B3LYP/6-31+G(d,p) does and is a useful tool for rapid screening of a large number of conformers. The conformations shown in Table 5 were also subjected to optimization with a variety of other molecular mechanics force fields. In many cases, the result of these optimizations was a conformer other than the starting one, which is indicated in the table adjacent to each ΔE value. For example, optimization of the α Lγ L conformer with MM2 (as implemented in ChemBio3D) led to a γLγL structure. Although there is not a strong consensus agreement with the data in Table 5 among the force field methods presented in Table 6 in terms of relative energies, some of these force fields more faithfully reproduce 1402



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Table 7. Ab Initio-Calculated Relative Energies and Dihedral Anglesa for Aqueous Phase Conformers for Ac-Gly-Gly-NHMe conformerb

MP2-1 ΔEc

MP2-2 ΔEd

ω0

ϕ1

ψ1

ω1

ϕ2

ψ2

ω2

αDαD εDαL γLαL αLαD αLγL γLγL γDγL αDβL γDεL εLγL-C1 εDγL αDεL αLεL βLαL εLγL βLγD εDβL βLεD αLβL−C2 βLβL αDβL-C2 δDεD-C1 γDεL-C2 αLεD-C2 βLβL-C2 εDβL-C2

0.00 0.88 3.48 3.62 3.88 3.94 3.95 4.33 4.36 4.56 4.59 4.63 4.73 5.00 5.12 5.53 5.71 5.78 5.85 5.85 5.89 6.56 6.63 6.93 6.94 7.14

0.00 0.65 3.04 2.98 3.08 3.64 3.51 4.16 3.46 4.81 3.72 3.71 3.84 4.84 4.41 5.41 5.11 5.32 6.12 6.14 5.84 6.18 5.81 6.05 8.10 6.83

172.8 −177.4 −175.3 −174.2 −175.1 −174.9 175.9 176.8 179.5 173.7 −172.7 175.1 −175.3 174.5 172.6 −175.4 171.4 175.1 −177.1 −174.4 176.9 170.5 −177.5 −175.2 180.0 −171.5

65.9 57.7 −83.8 −73.5 −69.8 −83.6 83.8 71.7 82.1 −58.1 59.4 77.9 −82.3 −176.6 −62.2 −179.4 61.2 −176.5 −71.8 177.4 71.8 128.5 80.6 −80.0 −179.9 61.2

25.2 −135.3 64.9 −23.9 −27.5 60.7 −64.2 23.4 −73.2 147.0 −146.3 15.7 −18.6 −163.4 −153.5 161.9 −150.3 −166.2 −23.3 163.4 23.2 −66.1 −76.2 −11.8 180.0 −149.8

−177.3 178.0 −173.1 174.9 178.9 −174.3 −179.4 −173.6 169.1 5.5 −176.4 172.7 178.1 −170.7 −178.4 171.3 178.3 −167.9 173.9 −179.7 −174.4 11.6 166.2 −169.9 −180.0 179.7

79.0 −77.2 −78.9 82.6 −82.0 −85.3 −82.9 153.5 −62.3 −91.3 −82.8 −63.7 −64.7 −79.1 −84.0 85.8 −177.9 61.1 −163.9 −178.1 160.4 86.0 −70.7 71.9 179.9 −174.0

3.5 −2.8 −17.6 13.9 69.2 63.1 64.3 −169.8 151.7 16.2 67.5 151.5 149.0 −18.3 60.5 −62.5 −161.3 −155.1 −178.1 162.7 −178.2 −164.3 173.7 −172.7 180.0 −176.1

179.4 177.8 −180.0 179.1 173.0 −177.5 −176.8 −176.6 177.9 174.7 −173.9 178.0 178.4 179.8 −179.5 178.6 −174.2 −177.3 8.2 174.4 9.8 −173.6 −9.2 8.8 −0.1 8.4

a In degrees. From MP2/6-311+G(d,p) optimized geometries. bConformer designation. Cn indicates cis conformation at the indicated ω peptide bond (Figure 1). The N-terminal peptide bond is ω0, the central peptide bond is ω1, and the C-terminus peptide bond is ω2. cMP2-1: relative energy calculated at MP2/aug-cc-pVTZ//MP2/6-311+G(d,p). In kcal/mol. dMP2-2: relative energy calculated at MP2/6-311+G(d,p)//MP2/6311+G(d,p). In kcal/mol.

specific case where the central peptide bond is cis.14 The lowest-energy structure that they found is an εLγL conformer, which is also the lowest-energy conformer among the MP2-1 results in Table 2 with the central peptide bond in a cis conformation. Gas Phase Structures. There is good agreement between the MP2/6-311+G(d,p) and MP2/6-31+G(d,p) structures for the lowest-energy gas phase minima. For example, the ϕ1, ψ1, ϕ2, ψ2 values for the εDγL global minimum are +56.4°, −138.8°, −85.2°, +3.9° and +57.1°, −137.8°, −86.3°, +6.2° at the two levels, respectively. Comparable agreement is seen for the other low-energy minima shown in Figure 3 with the exception of the MP2/6-311+G(d,p) αLγD conformation for which a direct counterpart was not found at MP2/6-31+G(d,p). As stated above, there are some key mismatches between the B3LYP and MP2 conformational potential energy surfaces profiled here. But, a structural comparison can be made among some key conformations that are found in both cases. For example, the B3LYP/6-31+G(d,p) ϕ1, ψ1, ϕ2, ψ2 values for the γDγL of +81.9°, −66.0°, −80.3°, +66.6° compare favorably to the MP2/ 6-311+G(d,p) values of +81.8°, −71.4°, −79.5°, +76.2°. Similarly, the low-energy B3LYP/6-31+G(d,p) version of γLγL, at −81.9°, +64.9°, −82.3°, +62.4° are in good agreement with the MP2/6-311+G(d,p) structure at −82.6°, +66.0°, −84.5°, +69.9°. The DFT methods beyond B3LYP investigated here also produce geometries that agree well with the MP2/6311+G(d,p) results. The mean unsigned deviations of the ϕ1, ψ1, ϕ2, ψ2 values of the conformers in Figure 3 are +5.3°, +4.2°, and +3.6°, for ωB97X-D, B97-D, and M06-2X, respectively.

Aqueous Phase Results. Table 7 contains the relative energies of selected conformers of Ac-Gly-Gly-NHMe calculated in the aqueous phase at MP2/aug-cc-pVTZ//MP2/6311+G(d,p), designated as MP2-1, and MP2/6-311+G(d,p)// MP2/6-311+G(d,p), designated as MP2-2. Tables 8 and 9 contain MP2/6-31+G(d,p)//MP2/6-31+G(d,p) and B3LYP/ 6-31+G(d,p)//B3LYP/6-31+G(d,p) results, respectively. Figure 4 shows the six lowest-energy structures obtained from MP2/6-311+G(d,p) geometry optimizations in the aqueous phase. Table 10 shows the results, with thermochemical corrections applied, for the MP2-1 and MP2-2 protocols and the M06-2X, B97-D, and ωB97X-D density functional methods. A slightly different picture emerges in the aqueous phase in terms of the conformational relative energies of Ac-Gly-GlyNHMe, at least as predicted by the continuum solvent model employed here. The lowest-energy conformer in the aqueous phase with both the MP2-1 and MP2-2 protocols is αDαD (Table 7). The same is true with MP2/6-31+G(d,p) (Table 8) and B3LYP/6-31+G(d,p) (Table 9). In the former case, the structure is labeled as αLαL, which is the enantiomer. In the latter case, the structure is αDγD according to the classification scheme but it is essentially the same conformation with ϕ1ψ1, ϕ2ψ2 values of +69.3°, +18.8°, +88.7°, −0.5° versus +65.9°, +25.2°, +79.0°, +3.5° at the highest level of theory (the change in sign in the near-zero value of ψ2 causes the change in classification). It is interesting to note that an αDαD conformer (or its enantiomer αLαL) is not found among the low-energy structures in the gas phase. To test if the presence of the αDαD structure is derived from solvation more than from intrinsic 1403



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Table 8. MP2/6-31+G(d,p) Relative Energiesa and Dihedral Anglesb for Aqueous Phase Conformers for N-Ac-Gly-Gly-NHMe conformerc

ΔE

ω0

ϕ1

ψ1

ω1

ϕ2

ψ2

ω2

αLαL εDαL γDαD αLαD αLγL γDγL γLγL γDεL αDεL εDγL αDβL αDεL αDβL εLγL εLγL-C1 εDβL βLγD βLεD αLβL-C2 γDεL-C2 αLεD-C2 βLβL δDεD-C1 εDβL-C2 βLβL-C2

0.00 0.88 3.13 3.18 3.29 3.56 3.68 3.76 4.05 4.05 4.14 4.31 4.36 4.69 5.06 5.60 5.65 5.84 6.12 6.18 6.44 6.49 6.77 7.41 8.27

−174.9 −177.8 175.8 −175.9 −176.9 177.3 −175.9 179.5 176.6 −173.3 −177.0 178.4 178.3 173.2 174.4 −172.8 −176.6 175.9 −178.6 −180.0 −176.7 −175.4 170.0 −172.8 −175.0

−66.0 58.4 83.7 −77.1 −71.0 83.5 −83.2 82.5 81.3 61.0 −82.4 73.9 73.4 −64.4 −59.0 63.5 −174.5 179.6 −73.5 82.2 −81.6 −176.7 126.9 63.1 −178.5

−24.3 −134.6 −63.5 −18.5 −24.9 −67.1 60.4 −72.1 10.5 −148.3 −16.6 20.0 21.4 154.7 146.9 −151.4 161.3 −166.0 −20.8 −72.3 −9.7 161.3 −64.4 −150.4 159.5

177.2 178.4 173.9 176.1 −179.8 179.2 −173.9 170.2 172.5 −174.7 178.4 −174.6 −174.5 −179.2 4.8 179.2 171.9 −170.3 174.0 169.7 −172.0 178.3 6.6 179.7 173.7

−79.0 −78.7 80.9 84.3 −82.7 −82.6 −85.2 −64.3 −65.1 −83.4 −66.6 153.0 172.2 −83.6 −91.3 178.9 85.4 63.5 −162.2 −72.4 72.9 −173.3 90.8 −172.0 −174.5

−4.7 −0.9 14.4 11.2 65.4 63.6 61.6 153.6 153.5 62.6 150.8 −166.5 165.9 62.1 17.7 −162.4 −62.5 −155.0 −178.7 173.1 −171.1 163.8 −161.1 −176.4 −177.4

179.7 178.3 179.5 179.0 −175.4 −177.2 −172.7 176.7 176.7 −176.8 176.8 −176.7 −174.5 −178.5 175.7 −176.0 178.5 −176.5 4.8 −5.8 5.8 176.0 −174.6 5.5 5.7

a Calculated at MP2/6-31+G(d,p)//MP2/6-31+G(d,p). In kcal/mol. bIn degrees. cConformer designation. Cn indicates cis conformation at the indicated ω peptide bond (Figure 1). The N-terminal peptide bond is ω0, the central peptide bond is ω1, and the C-terminus peptide bond is ω2.

Table 9. B3LYP/6-31+G(d,p) Relative Energiesa and Dihedral Anglesb for Aqueous Phase Conformers for N-Ac-Gly-GlyNHMe conformerc

ΔE

ω0

ϕ1

ψ1

ω1

ϕ2

ψ2

ω2

αDγD εDγL αLγD γDβL γLαL βLβL βDαL γLγL γLγL γDεL εDβL γDγL αLεL βLγD βLεD γDεL εDγL γDβL-C2 εLγL βLβL-C2 εDβL-C2 γLεD-C2 εLγL-C1 γDεL-C2 γDγD-C1

0.00 0.72 1.05 1.11 1.22 1.25 1.38 1.71 1.95 1.98 2.10 2.12 2.18 2.25 2.28 2.45 2.68 2.78 2.89 2.92 3.78 4.02 4.38 4.54 6.08

172.0 178.8 −173.7 174.6 −175.0 180.0 179.9 −173.6 −174.3 173.8 −177.5 174.5 −174.0 −179.5 179.6 175.4 −177.9 174.7 177.3 180.0 −177.5 −174.1 178.3 175.4 179.1

69.3 60.6 −94.4 100.2 −82.7 180.0 178.6 −103.8 −81.9 99.7 78.5 82.2 −101.3 −178.8 179.8 82.5 77.9 98.6 −85.5 −179.9 77.7 −97.5 −64.8 83.0 97.4

18.8 −131.2 −5.9 −1.3 65.5 −179.9 −176.4 3.3 58.0 −2.0 −160.4 −62.4 −1.3 176.2 −178.1 −63.0 −159.2 −0.7 176.4 180.0 −159.9 0.5 143.7 −64.8 −111.3

−174.6 175.9 174.4 179.9 −173.2 −180.0 −173.0 −175.3 −175.1 177.8 −176.1 −176.1 177.8 174.0 −176.8 178.1 −170.9 −179.9 −176.1 −180.0 −176.4 −177.3 2.8 176.8 8.4

88.7 −89.5 102.0 −179.8 −99.1 −180.0 −100.7 −82.4 −83.1 −78.9 178.7 −82.0 −83.7 84.0 78.2 −73.8 −83.8 179.9 −83.0 179.9 178.3 93.1 −97.1 −85.5 117.6

−0.5 7.1 −2.1 −179.7 −0.8 180.0 −0.1 59.6 59.2 159.9 −179.2 61.4 164.9 −59.3 −159.8 154.2 58.6 −180.0 60.6 −180.0 −179.8 179.5 27.6 177.9 −101.0

−179.7 178.6 −179.5 179.9 −179.9 180.0 179.8 −180.0 −180.0 176.1 −179.7 −179.5 176.6 −179.8 −176.3 176.1 179.8 0.2 −179.7 −0.1 1.3 0.4 177.0 −0.6 177.1

a

Calculated at B3LYP/6-31+G(d,p)//B3LYP/6-31+G(d,p). In kcal/mol. bIn degrees. cConformer designation. Cn indicates cis conformation at the indicated ω peptide bond (Figure 1). The N-terminal peptide bond is ω0, the central peptide bond is ω1, and the C-terminus peptide bond is ω2.

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these low-energy conformers have β turn characteristics, as can be seen by the dihedral angles summarized in Tables 7−9. The MP2/6-311+G(d,p) global minimum αDαD structure has ϕ1, ψ1, ϕ2, ψ2 values of +65.9°, +25.2°, +79.0°, +3.5° making it a type I′ β turn. The εDαL conformer has values for these dihedral angles of +57.7°, −135.3°, −77.2°, −2.8° which corresponds to a type II′ β turn. In terms of ΔE, for the set of conformers presented in Table 10, there is good agreement between the MP2-1 and MP2-2 WFT protocols and the ωB97X-D, B97-D, and M06-2X DFT methods. All of these methods place αDαD lowest in energy. The εDγL conformers from ωB97X-D, B97-D, and M06-2X optimizations are nearly identical to the εDαL conformer found in the MP2/6-311+G(d,p) optimizations. The difference in conformer designator results because the ψ2 values are very near zero but of different sign. Thus, there is a pair of conformers, αDαD and either εDγL or εDαL, that are consistently found to be much lower in ΔE than all others. After the application of thermochemical corrections, this pair is still very low in terms of ΔG, but the αLαD conformer becomes the most favorable by a very slight margin with wB97X-D and B97-D. Table 11 shows the results of optimizations of selected conformers with several additional molecular mechanics force fields with solvent represented via a continuum model approach. As with the results shown in Table 6 for the gas phase, the intention here is to assess the potential for these force field methods to be used in screening conformers for subsequent study with quantum mechanical methods. Several of the force field protocols used result in a significant fraction of the tested conformers moving to other points on the

Figure 4. Lowest-energy conformers in the aqueous phase for Ac-GlyGly-NHMe at MP2/aug-cc-pVTZ//MP2/6-311+G(d,p). Relative energies are reported in kcal/mol.

stability, the αDαD minimum obtained from the aqueous phase optimization was reoptimized without the solvent model, in which case it moved to the αLγL structure; thus, it remains a type I β turn. In fact, accounting for mirror reflection, the dihedral angles of these two conformations deviate from each other on average by only 6.4° indicating the close similarity between them, despite the different classification in the Perczel nomenclature scheme used here.2 The εDαL conformer is the next highest in energy at 0.88, 0.65, 0.88, and 0.72 kcal/mol at MP2-1, MP2-2, MP2/6-31+G(d,p), and B3LYP/6-31+G(d,p), respectively. At the highest levels of theory employed here, these two conformers are significantly lower in energy than all others. This remains true in terms of ΔG values after thermochemical corrections are made (Table 10). Both of

Table 10. Relative Energies, in kcal/mol, Including Thermochemical Corrections for Selected Ac-Gly-Gly-NHMe Conformations in the Aqueous Phase αDαD

εDαLa

ΔE Δ(E+ZPE) ΔH(298K) ΔG(298K)

0.00 0.00 0.00 0.00

0.67 0.67 0.73 0.54


0.00 0.00 0.00 0.00

0.88 0.90 0.96 0.77


0.00 0.00 0.00 0.08


0.00 0.00 0.00 0.24


0.00 0.00 0.00 0.00

εDγLa

γLαL

αLαD

MP2/6-311+G(d,p)//MP2/6-311+G(d,p) 3.04 2.98 2.86 2.54 3.05 2.84 1.72 1.07 MP2/aug-cc-pVTZ//MP2/6-311+G(d,p) 3.48 3.62 3.30 3.19 3.50 3.49 2.17 1.72 ωB97X-D/6-311++G(d,p)//ωB97X-D/6-311++G(d,p) 1.00 2.88 2.70 0.98 2.65 2.10 1.04 2.88 2.50 0.83 1.52 0.00 B97-D//6-311++G(d,p)//B97-D//6-311++G(d,p) 1.08 2.20 2.29 1.16 2.15 1.83 1.19 2.27 2.17 1.24 1.48 0.00 M06-2X//6-311++G(d,p)//M06-2X//6-311++G(d,p) 0.72 3.49 3.26 0.65 3.20 2.85 0.70 3.46 2.55 0.64 1.74 1.30

αLγL

γLγL

βLβL

3.08 3.06 3.15 2.38

3.64 3.72 3.79 2.83

6.14 5.15 5.73 3.03

3.88 3.86 3.96 3.19

3.94 4.02 4.10 3.13

5.85 4.86 5.44 2.74

3.22 3.04 3.24 1.96

3.62 3.56 3.69 2.69

4.26 3.15 3.74 1.00

2.51 2.42 2.57 1.62

2.65 2.68 2.73 2.12

4.69 3.56 4.19 0.96

3.68 3.49 3.67 2.35

4.13 4.08 4.22 2.79

4.54 3.44 4.05 1.20

The εDαL and εDγL conformers are nearly identical. They have ψ2 values very near zero in value, but of opposite sign, resulting in a conformer designator of αL for one and γL for the other.

a

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Table 11. Molecular Mechanics Relative Energies, in kcal/mol, for Selected Ac-Gly-Gly-NHMe Conformations in the Aqueous Phase force fielda

αDαDb

εDγL

γLαL

αLαD

αLγL

γLγL

βLβL

MMFF-S MMFF-HCT MM3-S MM3-HCT MMX-S MMX-HCT AMBER4 AMBER80 UFF4 UFF80

0.00 0.00 0.86 γDαD 0.86 0.0.0 0.00 4.69 αDγD 1.58 γDδL 2.67 αDγD 9.67

1.14 0.00 αDαD 0.28 γDαL 0.30 1.96 εDαL 2.00 1.71 γDβL 0.00 4.37 γDγL 1.39 εDβL

0.22 αLγL 0.27 αLγL 0.10 γLγL 0.08 γLγL 1.89 εLαL 1.94 0.00 βLβL 3.04 γLδL 0.00 γLγL 0.00 βLβL

0.20 0.55 0.00 γLγL 0.00 0.61 0.73 0.00 βLβL 0.27 0.68 γLγD 0.00 βLβL

0.22 0.27 0.10 γLγL 0.08 γLγL 1.65 αLεL 1.66 0.00 βLβL 0.02 γDγL 0.00 γLγL 0.00 βLβL

0.00 αDαD 0.00 αDαD 0.10 0.08 3.89 3.91 0.00 βLβL 0.01 0.00 0.00 βLβL

3.23 3.53 5.23 5.20 3.90 4.03 0.00 1.35 4.96 βLβL 0.00

a MMFF, MM3, and MMX as implemented in PCModel 9.3 with the analytical Still (S) or the Hawkins−Cramer−Truhlar (HCT) solvation models. AMBER and UFF as implemented in Gaussian09 with a dielectric constant of 4 or ~80 (78.39). See text for additional details. bThe top row provides the conformer designator for the input geometry. In cases where optimization with a given force field led to a different conformer, the output conformer designator is provided to the right of the ΔE value in the row for that force field.

Table 12. Selected Calculated Geometrical Parameters in β Turn Conformationsa of Ac-Gly-Gly-NHMe H---Ob level of theory MP2/6-311+G(d,p) MP2/6-31+G(d,p) B3LYP/6-31+G(d,p) ωB97X-D/6-311++G(d,p) B97-D/6-311++G(d,p) M06-2X/6-311++G(d,p)

gas aq gas aq gas aq gas aq gas aq gas aq

N---Oc

CH3---CH3d

type I

type II

type I

type II

type I

type II

2.085 2.012 2.086 2.017 2.197 2.122 2.101 2.021 2.197 2.074 2.072 2.004

2.025 1.991 2.029 1.996 2.103 2.073 2.024 1.991 2.095 2.057 2.018 1.989

3.045 3.000 3.046 3.004 3.163 3.114 3.057 3.007 3.143 3.058 3.034 2.994

3.001 2.958 3.006 2.965 3.091 3.048 3.001 2.956 3.068 3.024 2.994 2.951

5.555 5.544 5.498 5.541 5.668 5.621 5.486 5.501 5.605 5.531 5.567 5.599

5.349 5.321 5.359 5.339 5.601 5.618 5.381 5.369 5.403 5.409 5.421 5.389

Gas phase conformations (Figure 3) are type I = αLγL, type II = εDγL. Aqueous phase conformations (Figure 4) are type I = αDαD, type II = εDαL for MP2, B3LYP and εDγL for ωB97X-D, B97-D, and M06-2X. bThe cross-turn oxygen−hydrogen distance, in ångstroms, between the iCO and the i + 3 H−N. cThe cross-turn oxygen−nitrogen distance, in ångstroms, between the iCO and the i + 3 H−N. dThe carbon−carbon distance, in ångstroms, between the two methyl groups in Figure 1. a

I′ backbone conformations produce structures that are true enantiomers, as is the case with the type II and type II′ structures. We are not aware of experimental results on the gas phase conformations of Ac-Gly-Gly-NHMe. However, β turn structures, in addition to γ turns (C7), have been observed experimentally21 in the gas phase for the Ac-Phe-Gly-NH2 and Ac-Gly-Phe-NH2 systems in IR and UV spectra obtained by laser desorption coupled to supersonic expansion. In these studies, the β turns, though secondary to γ turns, were found to be intrinsically stable enough to exist in the gas phase. However, interactions involving the aromatic ring of the phenylalaine side chain were also found to play a role determining the conformational equilibria in those systems. Also, it is generally believed that incorporation of glycine along the fold is conducive to β turn formation; thus, it is not surprising that β turn (C10) structures are found here among the lowest energy Ac-Gly-Gly-NHMe conformers in the gas phase. Among the aqueous phase structures in Figure 4, αDαD is a type I′ turn and εDαL is a type II′ turn. Table 12 shows the key distance relationships associated with the cross-turn interaction between the carbonyl of the i residue and the N−H of the i + 3 residue and Figure 5 compares the aqueous phase type I′ and

conformational energy surface upon optimization raising the possibility that conformers would be missed in a screening process. For example, use of UFF and AMBER, with solvent modeled simply by use of a dielectric constant greater than unity, shows a strong tendency to produce extended structures even from optimization of folded input structures. AMBER (with ε = 4) results in highly extended structures (βLβL or γDβL) in six of the seven instances tested. Thus, much of the conformational potential surface complexity is lost and screening with this approach would miss many viable conformers. The more sophisticated continuum models that were tested, the analytical Still and Hawkins−Cramer−Truhlar (HCT) methods as implemented in PCModel, performed better, especially with the MMFF or MMX force fields. In fact, the MMX force field, coupled with the HCT aqueous solvent model, captured all seven structures as minima. β Turns. With three linked peptide bonds, Ac-Gly-GlyNHMe is a model system of fundamental importance because it represents the simplest fragment capable of exhibiting a β turn. On the basis of the ϕ1, ψ1, ϕ2, ψ2 dihedral angles, the global minimum εDγL structure in Figure 3 would be classified as a type II′ turn and the αLγL structure a type I turn.39,53 Because Ac-Gly-Gly-NHMe is achiral, the mirror-image type I and type 1406



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(d,p)//MP2/6-311+G(d,p) and MP2/6-31+G(d,p)//MP2/631+G(d,p), agree reasonably well with those from MP2/aug-ccpVTZ//MP2/6-311+G(d,p). There is also quite reasonable agreement between the most compute-intesive WFT theory approach taken here and results obtained with the far less computationally demanding ωB97X-D, B97-D, and M06-2X density functionals with the 6-311++G(d,p) basis set. The B3LYP/6-31+G(d,p) results show some key differences as compared to those obtained at higher levels of theory. The MMFF force field appears to be a useful tool for the generation of a large inclusive set of conformers for subsequent study with ab initio and density functional theory calculations.

type II′ MP2/6-311+G(d,p) structures. In the gas phase, the type II turn is found to be tighter as evidenced by closer H---O,

Figure 5. Aqueous phase MP2/6-311+G(d,p)-calculated type I′ (αDαD) (left) and type II′ (εDαL) (right) turn structures. The dotted line indicates a hydrogen bonding interaction between the i CO and the i + 3 H−N group.

■

N---O, and CH3---CH3 contacts, and this trend is preserved across all methods considered. At MP2/6-311+G(d,p), for example, the H---O distance across the type I turn is 2.085 Å but only 2.025 Å across the type II turn. Similar trends are seen for the N---O and CH3---CH3 distances at all levels of theory. In both cases, the CH3---CH3 distances, 5.555 Ǻ for type I and 5.349 Å for type II, are in good agreement with the oft-quoted value of approximately 5 Å for a β turn.39 On average, the MP2/6-311+G(d,p) results are better represented by the other methods than by B3LYP/6-31+G(d,p). For the interatomic distances summarized in Table 12, the average deviation from the MP2/6-311+G(d,p) results is 0.010, 0.036, 0.064, and 0.018 Å with MP2/6/-31+G(d,p), ωB97X-D, B97-D, and M062X, respectively. But it is 0.125 Å with B3LYP. Also, the inclusion of aqueous solvation via a continuum solvation model does not introduce significant structural changes for either of the β turns. Table 13 provides a summary of the occurrence of β turns among the set of conformers identified as a function of level of theory. In all cases, type II turns are found to be more

Corresponding Author

*E-mail: [email protected].

level of theory

type I

type II

type I

type II

1.40 1.19 1.68 0.80 1.05 1.01

0.00 0.00 0.64 0.00 0.43 0.00

0.00 0.00 0.00 0.00 0.00 0.00

0.64 0.88 0.72 1.00 1.08 0.72

ACKNOWLEDGMENTS

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REFERENCES

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aqueous phase

MP2/6-311+G(d,p) MP2/6-31+G(d,p) B3LYP/6-31+G(d,p) ωB97X-D/6-311++G(d,p) B97-D/6-311++G(d,p) M06-2X/6-311++G(d,p)

■

Financial support for this work was provided from the Defense Threat Reduction Agency (DTRA) and the Naval Academy Research Office through the Office of Naval Research (ONR). A grant of computing time was also received from the DoD High Performance Computing Modernization Program. This support is gratefully acknowledged.

Table 13. Relative Energies, in kcal/mol, of the LowestEnergy Type I and Type II β Turns gas phase

AUTHOR INFORMATION

stable in the gas phase than type I, and that trend is reversed when aqueous solvation is included.

■

CONCLUSIONS A thorough investigation of the conformational preferences of the model tripeptide analog Ac-Gly-Gly-NHMe has been carried out. At MP2/aug-cc-pVTZ//MP2/6-311+G(d,p) five low-energy conformations are found in the gas phase. Two of these conformers exhibit characteristic type I and II β turn structures. One exhibits two adjacent γ turns (C7-type). In addition, a conformation that resembles a β turn but lacks an intramolecular C10 hydrogen bond is also found to be low in energy. Upon consideration of aqueous solvation via a continuum solvent model, two conformers, the type I and II turns, are found to be significantly lower in energy than alternative conformers. The results from the moderate wave function theory approaches considered here, MP2/6-311+G1407



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Conformations of the Glycine Tripeptide Analog Ac-Gly-Gly-NHMe: A

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