9126
J. Phys. Chem. B 2008, 112, 9126–9134
Conformational Preferences and Cis-Trans Isomerization of L-Lactic Acid Residue Young Kee Kang* and Byung Jin Byun Department of Chemistry, Chungbuk National UniVersity, Cheongju, Chungbuk 361-763, Republic of Korea ReceiVed: February 10, 2008; ReVised Manuscript ReceiVed: May 30, 2008
The conformational study on N-acetyl-N′-methylamide of L-lactic acid (Ac-Lac-NHMe, the Lac dipeptide) is carried out using ab initio HF and density functional methods with the self-consistent reaction field method to explore its backbone conformational preferences and cis-trans isomerization for the depsipeptide with an ester bond in the gas phase and in solution. In the gas phase and in chloroform, the conformation tB with a trans depsipeptide bond is most preferred for the Lac dipeptide, whose backbone torsion angles are φ ≈ -150° and ψ ≈ -5°, juxtaposed to those of the 310-helical structure. The larger shift in φ is brought to reduce the repulsion between the two carbonyl carbons of the acetyl and NHMe groups. However, the polyproline II-like tF conformation becomes more populated and the relative stability of conformation tB decreases significantly as the solvent polarity increases. This may be ascribed to weakening a C5 hydrogen bond between the depsipeptidyl oxygen and the carboxyl amide hydrogen that plays a role in stabilizing the conformation tB in the gas phase and in chloroform. The cis populations about the depsipeptide bond are nearly negligible in the gas phase and in solution. The rotational barriers to the cis-trans isomerization of the depsipeptide bond for the Lac dipeptide are calculated to be about 11 kcal/mol, which is about half of those for the Ala dipeptide, although they increase somewhat with the increase of solvent polarity. The cis-trans isomerization of the depsipeptide bond proceeds through either clockwise or anticlockwise rotations with torsion angles of about +90° or -90°, respectively, in the gas phase and in solution, whereas it has been known that the isomerization proceeds through only the clockwise rotation for alanyl and prolyl peptide bonds. The pertinent distances between the depsipeptidyl oxygen and the carboxyl amide hydrogen can describe the role of this hydrogen bond in stabilizing the transition state structures in the gas phase and in solution. Introduction Considerable attempts in modifying the backbone of peptides and proteins have been carried out to improve their stability and biological activity.1–4 Peptide and protein that contain an ester linkage instead of an amide linkage are often referred to as depsipeptides.4 Because ester and amide groups are isosteric and have very similar bond lengths and angles,4,5 the amideto-ester mutations have been used in studying the contributions of specific backbone-backbone H-bonds to the formation of β-sheet,6 β-hairpin,7 and β-turns8,9 of peptides and to the folding and stability of proteins.3,4,10–14 The amide-to-ester modification of peptide backbone removes the H-bond donor (N-H) by replacing it with an O and weakens the H-bond acceptor (CdO) of peptides and proteins because the carbonyl of an ester group is a weaker H-bond acceptor than that of an amide group.15 As a result, the amide-to-ester mutations almost always decrease the thermodynamic stability of native proteins and protein-protein complexes.3,4 From single-site mutations on the model alanine oligopeptdes by the L-lactic acid (Lac) residue using the isodesmic reaction approach at the HF/3-21G level of theory, destabilizing effects of the Alato-Lac mutation were calculated to increase in the order type I β-turns tC ≈ tF . tA* ≈ tC* > tF* > cB ) cA . cA* at the HF/6-31+G(d) level and tB > tC . tC* ≈ tA* > tF* ≈ cA ≈ cB . cA* at the B3LYP/6-311++G(d,p) level in the gas phase. The representative conformations tB, tC, and cA with trans and cis depsipeptide bonds, respectively, and the transition states ts1 and ts2 optimized at the B3LYP/6-311++G(d,p) level in the gas phase are shown in Figure 3. The most preferred conformation of the Lac dipeptide is calculated to be tB with the trans depsipeptide bond at both levels in the gas phase. The stability of the conformation tB can be ascribed to the C5 hydrogen bond between the depsipep-
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TABLE 1: Backbone Torsion Angles and Thermodynamic Properties of Local Minima and Transition States for Ac-Lac-NHMe Optimized at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) Levels in the Gas Phasea HF/6-31+G(d) conformerb tB tC tF tC* tA* tF* cA cB cA* ts1 ts2
B3LYP/6-311++G(d,p)
ω′
φ
ψ
ω
∆Eec
∆Hd
∆Ge
ω′
φ
-179.9 -175.3 176.4 171.7 172.7 -174.0 -12.6 -0.1 10.2 82.8 -89.7
-151.0 -91.1 -66.6 78.6 67.6 57.1 -85.1 -139.0 65.0 -160.7 -90.5
-2.3 72.9 141.6 -47.6 30.6 -144.6 -16.1 -5.0 27.7 -9.8 -4.2
179.9 -178.5 -177.3 -176.3 -179.4 177.7 -176.3 -179.5 174.4 -178.6 176.7
0.00 1.05 1.44 4.29 4.46 5.35 7.64 7.76 12.97 11.70 10.37
0.00 1.13 1.44 4.43 4.38 5.37 7.63 7.75 12.99 10.84 9.50
0.00 1.51 1.79 5.08 4.74 6.19 7.98 7.97 13.76 11.55 10.84
-179.9 -174.5
-147.9 -88.3
171.6 172.5 -174.6 -9.4 -0.2 6.6 89.4 -94.8
76.2 67.9 57.0 -90.2 -139.9 65.8 -160.1 -88.1
ω
∆Eec
∆Hd
∆Ge
0.3 78.1
-179.8 -177.1
0.00 0.40
0.00 0.46
0.00 0.87
-53.0 28.6 -140.9 -14.3 -3.1 29.0 -6.1 3.5
-177.2 -178.9 178.3 -176.7 -179.3 175.3 -178.6 176.6
3.43 4.36 5.25 6.53 6.34 11.17 11.84 10.72
3.53 4.29 5.27 6.48 6.29 11.09 10.84 9.75
4.27 4.53 6.33 6.56 6.93 11.78 11.52 11.14
ψ
a Torsion angles are defined in Figure 1; units in degrees. b See the text for definition. For example, the first letter code tB is the backbone conformation B with the trans depsipeptide bond. c Relative electronic energies in kcal/mol. d Relative enthalpy changes in kcal/mol at 25 °C. e Relative Gibbs free energy changes in kcal/mol at 25 °C.
Figure 3. Representative conformations tB, tC, and cA, and the transition states ts1 and ts2 for the Lac dipeptide optimized at the B3LYP/6-311++G(d,p) level in the gas phase. Hydrogen bonds are represented by dotted lines.
tidyl O7 and the amide H17 of the carboxyl NHMe group. The distances of this hydrogen bond are calculated to be 2.17 and 2.13 Å at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels, respectively. In particular, the backbone torsion angles φ and ψ of the conformation tB at both levels are similar to the φ of conformation tE and the ψ of conformation tD, respectively, for the Ala dipeptide.38 The second preferred conformation tC with the trans depsipeptide bond has a C7 hydrogen bond between the carbonyl O6 of the acetyl group and the amide H17 of the carboxyl group, which plays a role in determining the lowest energy conformations for Ala and Pro dipeptides.38 The distances of this hydrogen bond for the Lac dipeptide are calculated to be 2.22 and 2.12 Å at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels, respectively, which are similar to the values of 2.26 and 2.10 Å for the conformation tC of the Ala dipeptide at the same levels, respectively.38 For the conformation tC, there are only small shifts in the backbone torsion angles φ and ψ by -7° to
+2° from those of the conformation tC for the Ala dipeptide at the same HF and B3LYP levels, respectively.38 Although the distances of hydrogen bonds for two conformations tB and tC are quite similar, the atomic charges of the carbonyl O6 of the acetyl group and the amide H17 of the carboxyl group for the conformation tC are more negative by -0.05 e and more positive by +0.05 e than those of the depsipeptidyl O7 and the amide H17 of the conformation tB, respectively, at both the HF and B3LYP levels.51 This indicates that the hydrogen bond of the conformation tC appears to be stronger than that of the conformation tB. However, the conformation tC has another factor to destabilize the structure, which is a close contact with a distance of 3.2 Å between the two carbonyl carbons of the acetyl and NHMe groups. This close contact can be seen only for the torsion angle φ in a gauche orientation. The values of torsion angle φ are -151° and -91° for conformations tB and tC, respectively, at the HF/6-31+G(d) level. The corresponding values are -148° and -88° at the B3LYP/6-311++G(d,p) level, respectively. It has been reported that this gauche conformation is less stable by 0.4 kcal/mol in ∆Ee than the trans conformation for ethyl acetate at the B3LYP/ 6-311++G(d,p) level,53 which is equal to our calculated value for the conformation tC relative to the conformation tB at the same level (Table 1). At the HF/6-31+G(d) level, the third preferred conformation is a PPII-like conformation tF, whose ∆Ee and ∆G are 1.44 and 1.79 kcal/mol, respectively, which are comparable to those of the second preferred conformation tC. For the Ala dipeptide, the PPII-like conformation tF exists as a local minimum only in chloroform and water.38 However, this conformation tF is no longer a local minimum at the B3LYP/6-311++G(d,p) level. The differences in ∆G for the most preferred cis conformation cA relative to the trans conformations tB and tC are calculated to be 7.98 and 6.47 kcal/mol at the HF/6-31+G(d) level, respectively, and 6.56 and 5.69 kcal/mol at the B3LYP/6311++G(d,p) level, respectively. However, the differences in ∆G for the most preferred cis conformation cA relative to the trans conformation tC for the Ala dipeptide were calculated to be 4.39 and 3.91 kcal/mol at HF/6-31+G(d) and B3LYP/6311++G(d,p) levels, respectively.38 The less stability by ∼2 kcal/mol of the conformation cA for the Lac dipeptide than that of the Ala dipeptide can be ascribed to the shorter distances by ∼0.16 Å between two methyl hydrogens of acetyl group and the HR of the backbone for the Lac dipeptide at both the levels, although a hydrogen bond between the depsipeptidyl O7 and
9130 J. Phys. Chem. B, Vol. 112, No. 30, 2008
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TABLE 2: Backbone Torsion Angles and Thermodynamic Properties of Local Minima and Transition States for Ac-Lac-NHMe Optimized at the CPCM HF/6-31+G(d) Level in Solutiona chloroform conformerb tB tA tF tC tE tA* tF* tC* cB cA cE cA* ts1 ts2
water
ω′
φ
ψ
ω
∆Eec
∆Hd
∆Ge
ω′
φ
ψ
ω
∆Eec
∆Hd
∆Ge
179.9 -175.7 178.3 -175.9 -180.0 174.4 -176.5 170.8 3.4 -3.6 5.1 1.3 86.3 -87.4
-150.5 -83.6 -68.6 -92.2 -152.0 64.9 59.8 79.8 -141.5 -86.7 -147.8 68.1 -154.0 -96.6
-5.5 -23.1 151.3 79.7 119.5 35.6 -152.2 -49.2 -5.7 -19.2 119.0 29.3 -6.0 -8.8
-179.9 -177.1 178.2 -177.3 179.1 176.7 -177.5 -177.2 -179.5 -176.3 179.0 174.4 -179.2 179.2
0.00 0.73 0.74 2.24 2.55 3.71 4.64 5.37 6.73 7.00 11.17 11.58 11.29 10.96
0.00 0.71 0.67 2.30 2.53 3.63 4.60 5.51 6.71 6.99 11.10 11.55 10.40 10.07
0.00 0.78 0.86 2.40 2.12 4.07 5.06 5.98 7.05 7.45 11.01 12.30 11.33 11.22
-179.4 -173.8 -179.1
-149.2 -78.1 -69.8
-7.3 -28.6 151.7
-179.6 -176.9 176.1
0.78 0.78 0.00
0.95 0.89 0.00
0.77 0.99 0.00
178.9 174.9 -177.9
-154.1 62.0 61.9
136.4 40.6 -159.0
176.1 176.8 -174.2
1.59 3.50 4.50
1.66 3.49 4.58
1.24 3.84 4.61
1.0 0.6 2.5 -0.9 91.6 -85.2
-141.9 -86.5 -147.2 68.5 -148.8 -106.1
-2.5 -19.0 142.1 29.3 -3.2 -11.4
179.8 -177.0 175.8 175.5 -179.6 -178.7
6.20 6.36 7.61 10.70 11.29 11.39
6.41 6.51 7.73 10.72 10.52 10.67
6.54 6.90 7.65 11.32 11.50 11.78
a Torsion angles are defined in Figure 1; units in degrees. b See the text for definition. For example, the first letter code tB is the backbone conformation B with the trans depsipeptide bond. c The relative conformational free energy (∆Ee) is the sum of the conformational electronic energy (∆Ee,s) and the relative solvation free energy (∆∆Gsolv) in solution; units in kcal/mol. d Relative enthalpy changes in kcal/mol at 25 °C. e Relative Gibbs free energy changes in kcal/mol at 25 °C.
the amide H17 exists in the conformation cA for the Lac dipeptide, whose distances are 2.26 and 2.21 Å at the HF and B3LYP levels, respectively. The next preferred cis conformation is cB, whose ∆G are 7.97 and 6.93 kcal/mol at the HF and B3LYP levels, respectively, comparable to those of the conformation cA, although the distances of a hydrogen bond between the depsipeptidyl O7 and the amide H17 for the conformation cB are a little shorter by ∼0.1 Å than those for the conformation cA at both the levels. Preferred Conformations in Solution. Table 2 lists the backbone torsion angles and thermodynamic properties of local minima and transition states for the Lac dipeptide optimized at the CPCM HF/6-31+G(d) level in chloroform and water. Most of the local minima in the gas phase are also retained as local minima in chloroform and water. However, new local minima tA, tE, and cE are located in chloroform and two conformations tC and tC* are no longer local minima in water. On going from the gas phase to chloroform, there are some shifts in the backbone torsion angles φ and ψ for the local minima and transition state. Their shifts are (6° in φ and (9° in ψ. On going from chloroform to water, the shifts are calculated to be (5° in φ and (6° in ψ. However, there are somewhat large shifts in ψ by +17° and +23° for conformations tE and cE, respectively. In particular, most of the values of ∆Ee and ∆G for local minima decrease as the solvent polarity increases. However, there are increases in ∆Ee and ∆G for local minima tC and tC* on going from the gas phase to chloroform and for local minima tB and tA on going from chloroform to water. The conformational stabilities of the Lac dipeptide are calculated by ∆G to be in the orders tB > tA ≈ tF > tE ≈ tC . tA* > tF* > tC* > cB > cA . cE > cA* in chloroform and tF > tB ≈ tA > tE . tA* > tF* . cB > cA > cE . cA* in water. This indicates that the R-helical conformation tA and the PPII-like conformation tF become more preferred in chloroform and water, although the conformation tB is still feasible in both the solution. The most preferred conformation of the Lac dipeptide is calculated to be tB in chloroform, as found in the gas phase, but tF in water. The distances of the C5 hydrogen bond between the depsipeptidyl O7 and the amide H17 of the carboxyl group for the conformation tB are calculated to be 2.18 and 2.23 Å in chloroform and water, respectively, which are a little longer
than those in the gas phase. In chloroform, the second preferred conformation is tA and followed by the conformation tF, whose ∆G are 0.78 and 0.86 kcal/mol, respectively, relative to the conformation tB. However, the conformation tF becomes most preferred in water and followed by the conformations tB and tA, whose ∆G are 0.77 and 0.99 kcal/mol, respectively. In particular, the conformation tA has a hydrogen bond between the depsipeptidyl O7 and the amide H17 of the carboxyl group, as seen for the conformation tB, whose distances are computed to be 2.34 and 2.41 Å in chloroform and water, respectively. In chloroform and water, the most preferred cis conformation is cB and followed by the conformation cA, whose ∆G are 7.05 and 7.45 kcal/mol in chloroform, respectively, and 6.54 and 6.90 kcal/mol in water, respectively. Although there are decreases in ∆G for these cis conformations with the increase of solvent polarity, their ∆G values are still higher by ∼2.5 kcal/mol than those of the Ala dipeptide in chloroform and water.38 In addition, the conformations cB and cA have the hydrogen bonds between the depsipeptidyl O7 and the amide H17 of the carboxyl group. Their distances are computed to be 2.18 and 2.30 Å in chloroform, respectively, and 2.20 and 2.33 Å in water, respectively, which are a little longer than those in the gas phase. The thermodynamic properties of the Lac dipeptide corrected by the single-point energies at the B3LYP/6-311++G(d,p)// CPCM HF/6-31+G(d) level in chloroform and water are listed in Table 3, which are used in the analysis of the conformational populations and the cis-trans isomerization below. The representative conformations tF, tB, and cE with trans and cis depsipeptide bonds, respectively, and the transition states ts1 and ts2 obtained at the B3LYP/6-311++G(d,p)//CPCM HF/631+G(d) level in water are shown in Figure 4. It should be noted that most of the values of ∆G decrease more at this corrected level than those at the CPCM HF/6-31+G(d) level in solution, except for some conformations such as tA and tF in chloroform and tA in water. The conformational stabilities by ∆G at this corrected level are similar to the orders by ∆G at the CPCM HF/6-31+G(d) level in chloroform and water, as described above, except that the conformation tE becomes more stable than the conformation tA and comparable to the conformation tB and that the conformation cE becomes more preferred than the conformation cB in water.
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TABLE 3: Thermodynamic Properties of Ac-Lac-NHMe Computed at the B3LYP/6-311++G(d,p)//CPCM HF/ 6-31+G(d) Level in Solutiona chloroform b
water
conformer
∆Ee
c,f
∆Hd,f
∆Ge,f
tB tA tF tC tE tA* tF* tC* cB cA cE cA* ts1 ts2
0.00 0.95 1.17 1.62 2.12 3.59 4.38 4.61 5.29 5.83 8.62 9.71 11.36 11.25
0.00 0.94 1.10 1.67 2.10 3.50 4.34 4.74 5.27 5.82 8.55 9.68 10.48 10.36
0.00 1.01 1.29 1.78 1.70 3.95 4.80 5.21 5.60 6.28 8.46 10.43 11.40 11.51
c,f
∆Hd,f
∆Ge,f
0.60 0.81 0.00
0.77 0.92 0.00
0.59 1.02 0.00
0.97 3.03 3.90
1.04 3.02 3.97
0.62 3.37 4.01
4.55 4.92 4.63 8.49 11.24 11.37
4.76 5.07 4.75 8.52 10.46 10.65
4.89 5.46 4.66 9.11 11.45 11.75
∆Ee
a Units in kcal/mol. b See the text for definition. For example, the first letter code tB is the backbone conformation B with the trans depsipeptide bond. c The relative conformational free energy (∆Ee) is the sum of the conformational electronic energy (∆Ee,s) and the relative solvation free energy (∆∆Gsolv) in solution; units in kcal/mol. d Relative enthalpy changes in kcal/mol at 25 °C. e Relative Gibbs free energy changes in kcal/mol at 25 °C. f The B3LYP/6-311++G(d,p) single-point energies were replaced for the conformational HF/6-31+G(d) electronic energies of Table 2. The vibrational and thermal contributions used are those obtained at the CPCM HF/6-31+G(d) level in Table 2.
Figure 4. Representative conformations tF, tB, and cE, and the transition states ts1 and ts2 for the Lac dipeptide obtained at the B3LYP/ 6-311++G(d,p)//CPCM HF/6-31+G(d) level in water. Hydrogen bonds are represented by dotted lines.
Comparison of Structural Parameters. The important structural parameters such as bond lengths and bond angles of local minima and transition states for the Lac dipeptide are compared to those of the Ala dipeptide at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels in the gas phase and at the CPCM HF/6-31+G(d) level in water. The structural parameters for the Ala dipeptide are taken from ref 38. Comparisons are made only for the structural parameters containing nonhydrogens and the amide hydrogen of the feasible conformations for both the Lac and Ala dipeptides. The structural parameters
of local minima and transition states for the Lac dipeptide optimized in the gas phase and in water are listed in Tables S1-S3 of the Supporting Information, in which the differences in bond lengths and bond angles for the Lac dipeptide from those of the Ala dipeptide are shown in parentheses. Most of the bond lengths containing non-hydrogens and the amide hydrogen for the feasible local minima for the Lac dipeptide are almost the same as or shorter by 0.01-0.02 Å than those of the Ala dipeptide at the HF and B3LYP levels in the gas phase and at the CPCM HF level in water. A little larger shortenings by 0.02-0.04 Å are found in the bond lengths r(C5-O7) and r(O7-C8) of the depsipeptidyl group at the HF level in the gas phase and in the bond length r(O7-C8) at the CPCM HF level in water. However, the bond lengths r(C5-O7) and r(O7-C8) for transition states are shorter by 0.04-0.08 Å than the corresponding values of the Ala dipeptide in the gas phase and in water. For the trans local minima of the Lac dipeptide, the bond angles θ(C4-C5-O6) and θ(C4-C5-O7) of the depsipeptidyl group are moved by +4° and -5° from those of the Ala dipeptide, respectively, in both the gas phase and water. The bond angle θ(C5-O7-C8) is narrowed by 3-5° for most of the local minima and transition states in both the gas phase and water. However, most of the other bond angles containing nonhydrogens and the amide hydrogen for the local minima and transition states for the Lac dipeptide are almost the same as or changed within (3° from those of the Ala dipeptide in the gas phase and in water. Comparison with X-Ray Structures. In crystal structures of peptides with one or more Lac residues, the Lac residue is preferred in R- or 310-helical regions and some 310-helical segments in the middle of depsipeptides were formed by the presence of neighboring Lac residues.19–23 In particular, the average torsion angle φ of the Lac residue of 11-mer and 15mer depsipeptides is -82°, which is shifted by -14° from that of non-Lac residues excluding last two residues from the C-terminal end.19–22 From our results calculated here, the conformation tB is found to be most preferred in the gas phase and in chloroform, and feasible even in water, whose the backbone structure is located near by the 310-helical region (Figure 2, parts a, c, and e), although there is a somewhat larger shift in the torsion angle φ, which is brought to reduce the repulsion between the two carbonyl carbons of the acetyl and NHMe groups, as described above. In the crystal structure of t-Boc-Ala-Lac-Obzl, the Lac residue has a PPII-like conformation.24 In this work, we confirmed that the PPII-like conformation tF of the Lac dipeptide is most preferred in water and feasible in chloroform (Tables 2 and 3). These conformational differences may be ascribed to the different lengths and/or end groups of peptides as well as the packing and intermolecular hydrogen bonds in crystal that cannot be considered in the isolated Lac dipeptide. Population of Backbone Conformations. The populations of the backbone conformations for the Lac dipeptide are listed and compared with those of the Ala dipeptide in Table 4. Each population was computed using the normalized Boltzmann weight by the relative free energy at the B3LYP/6-311++G(d,p) level in the gas phase and at the B3LYP/6-311++G(d,p)// CPCM HF/6-31+G(d) level in chloroform and water. In the gas phase, the population of the backbone conformation B for the Lac dipeptide is found to be dominant, which is ascribed to the conformation tB with the trans depsipeptidyl peptide bond and the C5 hydrogen bond between the depsipeptidyl O7 and the amide H17 of the carboxyl group. The population
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TABLE 4: Populations of Backbone Conformations, Rotational Barriers, and Relative Free Energies of Cis Conformers for Ac-Lac-NHMe and Ac-Ala-NHMe Calculated at the B3LYP/6-311++G(d,p) Level in the Gas Phase and in Solution backbone populationsa
rotational barrierb,c
solvent
B
C
E
A
F
cise
gas phase chloroform water
81.3 71.2 19.3
18.6 3.6 0.0
0.0 4.1 18.5
0.0 13.0 9.4
0.0 8.1 52.6
0.00 0.01 0.04
gas phase chloroform water
0.0 0.0 0.0
42.2 20.7 0.0
51.9 55.4 37.1
0.1 7.9 26.8
0.0 15.2 33.5
0.1 0.1 0.4
exptl cise
∆Gtc‡
∆Gct‡
relative energyb,d∆Gc/t
Ac-Lac-NHMe 11.14 11.40 (10.1g) 11.45
4.58 5.80 (5.9g) 6.78
6.56 (8.5 ( 1.0f) 5.60 (4.2g) 4.66
Ac-Ala-NHMeh 0.4i
19.66 21.61 23.03 (21.8i)
15.63 17.66 20.24 (18.5,i 17.9j)
4.03 3.95 2.79 (3.3i)
a
The populations (%) were computed using the relative Gibbs free energy of each local minimum in Tables 1 and 3. b Units in kcal/mol. Experimental values are listed in parentheses. The lowest Gibbs free energy for each of trans, cis, and transition state conformations was used for these calculations. Free energies were calculated at 25 °C. c ∆Gtc‡ and ∆Gct‡ represent the barriers to the trans-to-cis and cis-to-trans rotations for the Ac-Lac depsipeptide bond and Ac-Ala peptide bond. d ∆Gc/t is the relative Gibbs free energy of the cis conformer to the trans conformer. e Cis Ac-Lac depsipeptide bond or Ac-Ala peptide bond. f ∆Hc/t value for methyl acetate from matrix IR experiments; from ref 54. g ∆Htc‡, ∆Hct‡, and ∆Hc/t values for methyl acetate from ultrasonic relaxation measurements in the liquid state; from ref 55. h All calculated results from ref 38. i Average values for Ala-Phe, Phe-Ala, Tyr-Ala, and Ala-Tyr peptides at 298 K, from: Scherer, G.; Kramer, M. L.; Schutkowski, M.; Reimer, U.; Fischer, G. J. Am. Chem. Soc. 1998, 120, 5568. j Average values for Gly-Gly, Gly-Ala, Ala-Gly, and Ala-Ala peptides at 298 K, from: Schiene-Fischer, C.; Fischer, G. J. Am. Chem. Soc. 2001, 123, 6227.
of the second preferred backbone conformation C is computed to be 18.6%. As the solvent polarity increases, i.e., from the gas phase to chloroform to water, the population of the backbone conformation B decreases and there are increases in the populations of the R-helical conformation A in chloroform and of the extended conformation E and the PP-like conformation F in water. In water, the backbone conformation F is most populated and the populations of the conformations B and E become almost identical. The cis populations about the depsipeptide bond are nearly negligible in the gas phase and in solution, although they increase a little with the increase of solvent polarity. These calculated results indicate that the Lac residue has somewhat different backbone populations from those for the Ala residue in the gas phase and in solution. Cis-Trans Isomerization. Table 4 lists the relative free energies of cis conformers and rotational barriers to cis-trans isomerization of the Ac-Lac and Ac-Ala bonds at the B3LYP/ 6-311++G(d,p) level in the gas phase and at the B3LYP/6311++G(d,p)//CPCM HF/6-31+G(d) level in solution. The most preferred trans and cis conformations for the Lac dipeptide are calculated to be tB and cA in the gas phase, respectively, tB and cB in chloroform, respectively, and tF and cE in water, respectively, as described above. The relative free energies of cis conformers and rotational barriers for methyl acetate at the same levels in the gas phase and in solution are listed in Table S4 of the Supporting Information. In the gas phase, the values of relative enthalpy (∆Hc/t) and relative free energy (∆Gc/t) of the cis conformer to the trans conformer for the Lac dipeptide are computed to be 6.48 and 6.56 kcal/mol, respectively (Tables 1 and 4), whereas the corresponding values for methyl acetate are calculated to be 8.19 and 7.03 kcal/mol, respectively. The computed value of ∆Hc/t for methyl acetate computed is in good agreement with the estimated value of 8.5 ( 1.0 kcal/mol from matrix IR experiments.54 In chloroform, the values of ∆Hc/t and ∆Gc/t for the Lac dipeptide are computed to be 5.27 and 5.60 kcal/mol, respectively (Tables 3 and 4), whereas the corresponding values for methyl acetate are calculated to be 5.57 and 4.44 kcal/mol, respectively, of which the former is comparable to the observed value of 4.2 kcal/mol from ultrasonic relaxation measurements in the liquid state.55 In water, the computed values of ∆Hc/t and
∆Gc/t for the Lac dipeptide are 4.75 and 4.66 kcal/mol, respectively (Tables 3 and 4), whereas the corresponding values for methyl acetate are 3.67 and 2.65 kcal/mol, respectively. Although the free energy differences between cis and trans conformations for both the Lac dipeptide and methyl acetate decrease with the increase of solvent polarity, as found for the Ala dipeptide, the degree of diminution is smaller for the Lac dipeptide than methyl acetate. In the gas phase and in solution, two transition states ts1 and ts2 are located for the cis-trans isomerization of the Ac-Lac depsipeptide bond with ω′ ≈ (90°, whereas only the transition state ts1 with ω′ ≈ +120° exists for the Ala dipeptide.38 In the gas phase, the rotational barriers (∆Gtc‡ and ∆Gct‡) to the transto-cis and cis-to-trans isomerizations for the depsipeptidyl peptide bond are estimated to be 11.14 and 4.58 kcal/mol for the anticlockwise rotation, respectively, and 11.52 and 4.96 kcal/ mol for the clockwise rotation, respectively (Tables 1 and 4). However, the rotational barriers ∆Gtc‡ and ∆Gct‡ for methyl acetate are computed to be 12.41 and 5.38 kcal/mol for both the rotations, respectively. In chloroform, the values of ∆Gtc‡ and ∆Gct‡ are calculated to be 11.40 and 5.80 kcal/mol for the clockwise rotation, respectively, and 11.51 and 5.91 kcal/mol for the anticlockwise rotation, respectively (Tables 3 and 4). The rotational barriers ∆Gtc‡ and ∆Gct‡ for methyl acetate are computed to be 11.25 and 6.81 kcal/mol for both the rotations in chloroform, respectively. In water, the rotational barriers ∆Gtc‡ and ∆Gct‡ for the Lac dipeptide are computed to be 11.45 and 6.79 kcal/mol for the clockwise rotation, respectively, and 11.75 and 7.09 kcal/mol for the anticlockwise rotation, respectively (Tables 3 and 4). The corresponding values for methyl acetate are calculated to be 10.62 and 7.96 kcal/mol for both the rotations, respectively. Thus, the rotational barriers ∆Gtc‡ and ∆Gct‡ for the Lac dipeptide are 1/2 and 1/3, respectively, as high as those for the Ala dipeptide in the gas phase and in solution.38 The rotational barrier ∆Gtc‡ of the Lac dipeptide is lower by ∼1 kcal/mol in the gas phase and higher by ∼0.2 and ∼1 kcal/mol in chloroform and water, respectively, compared to those of methyl acetate. However, all rotational barriers ∆Gct‡ of the Lac dipeptide are lower by 0.4-1.2 kcal/mol than those of methyl acetate in the gas phase and in solution. The value of ∆Htc‡ for the Lac dipeptide is computed to be 10.5 and 10.4 kcal/mol for
Conformational Preferences of Ac-Lac-NHMe the clockwise and anticlockwise rotations in chloroform, respectively (Table 3), which is consistent with the estimated value of 10.1 kcal/mol for methyl acetate from ultrasonic relaxation measurements in the liquid state.55 As the solvent polarity increases, the rotational barriers ∆Gct‡ for the Lac dipeptide increase, as seen for the Ala dipeptide,38 which can be ascribed to the decrease of the ∆Gc/t. However, the rotational barrier ∆Gtc‡ for the Lac dipeptide increases for the anticlockwise rotation, but is nearly constant for the clockwise rotation with the increase of solvent polarity. In particular, the similar values of the rotational barriers of the Lac dipeptide for both the rotations may indicate that the cis-trans isomerization of the depsipeptide bond can proceed through either clockwise or anticlockwise rotations in the gas phase and in solution, whereas it has been known that the isomerization proceeds through only the clockwise rotation for alanyl and prolyl peptide bonds.38 By analysis of the contributions to rotational barriers, the cis-trans isomerizations for the depsipeptide bond are proven to be entirely enthalpy driven in the gas phase and in solution, to which the electronic energies have contributed considerably, as seen for alanyl and prolyl peptide bonds.38 This is consistent with the experimental results on proline-containing peptides, kinetically determined as a function of temperature.56 The transition states ts1 and ts2 have in common the hydrogen bond between the depsipeptidyl O7 and the amide H17 of the carboxyl group in the gas phase and in solution. In the gas phase, the distances of d(O7 · · · H17-NNHMe) for ts1 and ts2 are computed to be 2.17 and 2.28 Å at the HF/6-31+G(d) level, respectively, and 2.10 and 2.30 Å at the B3LYP/6-311++G(d,p) level, respectively. The corresponding distances are calculated to be 2.17 and 2.24 Å in chloroform, respectively, and 2.20 and 2.26 Å in water, respectively. The distances of ts1 are comparable to those of the conformation tB in the gas phase and in solution. Thus, the pertinent distance d(O7 · · · H17-NNHMe) can describe the role of this hydrogen bond in stabilizing the transition state structures. However, its role in lowering the rotational barrier to trans-to-cis isomerization for the Lac dipeptide can be rationalized only in the gas phase, because the rotational barrier is lower in the gas phase but higher in solution than those of methyl acetate, as described above. From kinetic and spectroscopic studies on model prolyl peptides, it has been suggested that the intramolecular hydrogen bond between the prolyl nitrogen and the following amide N-H group for the transition state is capable of catalyzing the prolyl isomerization by up to 260-fold in organic and organic/aqueous solutions.57 Conclusions In the gas phase and in chloroform, the conformation tB with a trans depsipeptide bond is most preferred for the Lac dipeptide, whose backbone torsion angles are φ ≈ -150° and ψ ≈ -5°, juxtaposed to those of the 310-helical structure. The larger shift in φ is brought to reduce the repulsion between the two carbonyl carbons of the acetyl and NHMe groups. However, the polyproline II-like tF conformation becomes more populated and the relative stability of conformation tB decreases significantly as the solvent polarity increases. This may be ascribed to weakening a C5 hydrogen bond between the depsipeptidyl oxygen and the carboxyl amide hydrogen that plays a role in stabilizing the conformation tB in the gas phase and in chloroform. The cis populations about the depsipeptide bond are nearly negligible in the gas phase and in solution, although they increase a little with the increase of solvent polarity. The
J. Phys. Chem. B, Vol. 112, No. 30, 2008 9133 rotational barriers to the cis-trans isomerization of the depsipeptide bond for the Lac dipeptide are calculated to be about 11 kcal/mol, which is about half of those for the Ala dipeptide, although they increase somewhat with the increase of solvent polarity. The cis-trans isomerization of the depsipeptide bond proceeds through either clockwise or anticlockwise rotations with torsion angles of about +90° or -90°, respectively, in the gas phase and in solution, whereas it has been known that the isomerization proceeds through only the clockwise rotation for alanyl and prolyl peptide bonds. The pertinent distances between the depsipeptidyl oxygen and the carboxyl amide hydrogen can describe the role of this hydrogen bond in stabilizing the transition state structures in the gas phase and in solution. Supporting Information Available: Tables giving the structural parameters of local minima and transition states for the Lac dipeptide optimized at the HF/6-31+G(d) and B3LYP/ 6-311++G(d,p) levels in the gas phase and at the CPCM HF/ 6-31+G(d) level in water and the thermodynamic properties of methyl acetate at the same levels in the gas phase and in solution. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Gellman, S. H. Acc. Chem. Res. 1998, 31, 173. (2) Patch, J. A.; Barron, A. E. Curr. Opin. Chem. Biol. 2002, 6, 872. (3) Yang, X.; Wang, M.; Fitzgerald, M. C. Bioorg. Chem. 2004, 32, 438. (4) Powers, E. T.; Deechongkit, S.; Kelly, J. W. AdV. Protein Chem. 2006, 72, 39, and references therein. (5) Wiberg, K. B.; Laidig, K. E. J. Am. Chem. Soc. 1987, 109, 5935. (6) Skelton, N. J.; Harding, M. M.; Mortishire-Smith, R. J.; Rahman, S. K.; Williams, D. H.; Rance, M. J.; Ruddock, J. C. J. Am. Chem. Soc. 1991, 113, 7522. (7) Haque, T. S.; Little, J. C.; Gellman, S. H. J. Am. Chem. Soc. 1996, 118, 6975. (8) Gallo, E. A.; Gellman, S. H. J. Am. Chem. Soc. 1993, 115, 9774. (9) Williamson, D. A.; Bowler, B. E. J. Am. Chem. Soc. 1998, 120, 10902. (10) Koh, J. T.; Cornish, V. W.; Schultz, P. G. Biochemistry 1997, 36, 11314. (11) Deechongkit, S.; Dawson, P. E.; Kelly, J. W. J. Am. Chem. Soc. 2004, 126, 16762. (12) Wang, M.; Wales, T. E.; Fitzgerald, M. C. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 2600. (13) Fu, Y.; Gao, J.; Bieschke, J.; Dendle, M. A.; Kelly, J. W. J. Am. Chem. Soc. 2006, 128, 15948. (14) Scheike, J. A.; Baldauf, C.; Spengler, J.; Albericio, F.; Pisabarro, M. T.; Koksch, B. Angew. Chem., Int. Ed. 2007, 46, 7766. (15) Arnett, E. M.; Mitchell, E. J.; Murty, T. S. S. R. J. Am. Chem. Soc. 1974, 96, 3875. (16) Cieplak, A. S.; Su¨rmeli, N. B. J. Org. Chem. 2004, 69, 3250. (17) Jenkins, C. L.; Vasbinder, M. M.; Miller, S. J.; Raines, R. T. Org. Lett. 2005, 7, 2619. (18) Bieschke, J.; Siegel, S. J.; Fu, Y.; Kelly, J. W. Biochemistry 2008, 47, 50. (19) Ohyama, T.; Oku, H.; Hiroki, A.; Maekawa, Y.; Yoshida, M.; Katakai, R. Biopolymers 2000, 54, 375. (20) Ohyama, T.; Oku, H.; Yoshida, M.; Katakai, R. Biopolymers 2001, 58, 636. (21) Aravinda, S.; Shamala, N.; Das, C.; Balaram, P. Biopolymers 2002, 64, 255. (22) Oku, H.; Ohyama, T.; Hiroki, A.; Yamada, K.; Fukuyama, K.; Kawaguchi, H.; Katakai, R. Biopolymers 2004, 75, 242. (23) Oku, H.; Yamada, K.; Katakai, R. Acta Crystallogr., Sect. E 2004, 60, o927. (24) Oku, H.; Suda, T.; Yamada, K.; Katakai, R. Acta Crystallogr., Sect. E 2004, 60, o720. (25) Flory, P. J. Statistical Mechanics of Chain Molecules; Interscience Publishers: New York, 1969; Chapter 7. (26) Ingwall, R. T.; Goodman, M. Macromolecules 1974, 7, 598. (27) Bateman, K. S.; Huang, K.; Anderson, S.; Lu, W.; Qasim, M. A.; Laskowski, M., Jr.; James, M. N. G. J. Mol. Biol. 2001, 305, 839. (28) Valiyaveetil, F. I.; Sekedat, M.; MacKinnon, R.; Muir, T. W. J. Am. Chem. Soc. 2006, 128, 11591.
9134 J. Phys. Chem. B, Vol. 112, No. 30, 2008 (29) Read, R. J.; Fujinaga, M.; Sielecki, A. R.; James, M. N. G. Biochemistry 1983, 22, 4420. (30) Zhou, Y.; Morais-Cabral, J. H.; Kaufman, A.; MacKinnon, R. Nature 2001, 414, 43. (31) Schmidt, R. K.; Fready, J. E. THEOCHEM 2000, 498, 101. (32) Borba, A.; Go´mez-Zavaglia, A.; Lapinski, L.; Fausto, R. Vibr. Spectrosc. 2004, 36, 79. (33) Ottaviani, P.; Velino, B.; Caminati, W. Chem. Phys. Lett. 2006, 428, 236. (34) Pszczoˇłkowski, L.; Białkowska-Jaworska, E.; Kisiel, Z. J. Mol. Spectrosc. 2005, 234, 106. (35) Losada, M.; Tran, H.; Xu, Y. J. Chem. Phys. 2008, 128, 014508. (36) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, reVision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (37) Zimmerman, S. S.; Pottle, M. S.; Ne´methy, G.; Scheraga, H. A. Macromolecules 1977, 10, 1. (38) Kang, Y. K. J. Phys. Chem. B 2006, 110, 21338. (39) Frisch, A.; Dennington, R. D., II; Keith, T. A. GaussView, Version 3.0; Gaussian, Inc.: Pittsburgh, PA, 2003. (40) Fischer, S.; Dunbrack, R. L., Jr.; Karplus, M. J. Am. Chem. Soc. 1994, 116, 11931. (41) Wiberg, K. B. J. Comput. Chem. 2004, 25, 1342.
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