Conformational Preferences of Non-Prolyl and Prolyl Residues - The

21338

J. Phys. Chem. B 2006, 110, 21338-21348

Conformational Preferences of Non-Prolyl and Prolyl Residues Young Kee Kang* Department of Chemistry and Basic Science Research Institute, Chungbuk National UniVersity, Cheongju, Chungbuk 361-763, South Korea ReceiVed: July 25, 2006; In Final Form: August 28, 2006

The conformational study on Ac-Ala-NHMe (the alanine dipeptide) and Ac-Pro-NHMe (the proline dipeptide) is carried out using ab initio HF and density functional methods with the self-consistent reaction field method to explore the differences in the backbone conformational preference and the cis-trans isomerization for the non-prolyl and prolyl residues in the gas phase and in the solutions (chloroform and water). For the alanine and proline dipeptides, with the increase of solvent polarity, the populations of the conformation tC with an intramolecular C7 hydrogen bond significantly decrease, and those of the polyproline II-like conformation tF and the R-helical conformation tA increase, which is in good agreement with the results from circular dichroism and NMR experiments. For both the dipeptides, as the solvent polarity increases, the relative free energy of the cis conformer to the trans conformer decreases and the rotational barrier to the cis-trans isomerization increases. It is found that the cis-trans isomerization proceeds in common through only the clockwise rotation with ω′ ≈ +120° about the non-prolyl and prolyl peptide bonds in both the gas phase and the solutions. The pertinent distance d(N‚‚‚H-NNHMe) can successfully describe the increase in the rotational barriers for the non-prolyl and prolyl trans-cis isomerization as the solvent polarity increases and the higher barriers for the non-prolyl residue than for the prolyl residue, as seen in experimental and calculated results. By analysis of the contributions to rotational barriers, the cis-trans isomerization for the non-prolyl and prolyl peptide bonds is proven to be entirely enthalpy driven in the gas phase and in the solutions. The calculated cis populations and rotational barriers to the cis-trans isomerization for both the dipeptides in chloroform and/or water accord with the experimental values.

Introduction In proteins, the peptide bond is known to dominantly prefer the trans conformation. Analyses of X-ray protein structures show that the cis populations are ∼0.04% for the non-prolyl peptide bond and ∼6% for the prolyl peptide bond.1-3 The instability of the cis conformer of the non-prolyl residue is due mainly to the unfavorable interactions between adjacent CHR groups.4 The increase in the cis population for the prolyl peptide bond over that of the non-prolyl peptide bond is ascribed to (1) unfavorable interactions between atoms attached directly to the peptide unit present in both the trans and cis conformations and (2) a favorable electrostatic interaction between Oi and C′i+1 in the trans conformation.4 It has been reported that the cis-trans isomerization of the X-Pro bond is often involved in the rate-determining steps for folding and refolding of various proteins.5-8 The heterogeneity of the unfolded states of proteins is occasionally caused by the prolyl cis-trans isomerization, which leads to the multiple pathways for folding or refolding. Several peptidyl prolyl cistrans isomerases (PPIases) have been identified, which significantly accelerate the isomerization of peptides and denatured proteins.5,6,9 In particular, it has been reported that PPIases are involved in cell signaling and replication and are implicated in several diseases such as cancer, AIDS, and Alzheimer’s disease.8-10 In addition, the prolyl cis-trans isomerization was suggested to be involved in the multiple elastic conformations of cardiac PEVK,11 in the chemo-mechanical coupling within * To whom correspondence should be addressed. Telephone: +82-43261-2285. Fax: +82-43-273-8328. E-mail: [email protected].

actomyosin to propel myosin’s lever-arm swing,12 and in providing the switch to open and close the pore of a neurotransmitter-gated ion channel.13 Several studies on the non-prolyl cis-trans isomerization of mutant proteins, in which prolines are replaced by alanines or other residues, have been carried out to explore the role of the prolyl cis-trans isomerization in the kinetics of folding and refolding and in protein stabilities.14-22 Despite the different kinetics for prolyl and non-prolyl isomerizations, non-prolyl isomerization has been also known to be involved in the slow steps for protein folding and refolding.15,17,18,21-23 Although nonprolyl cis peptide bonds are rare in proteins, they often occur in regions near the active sites of proteins and contribute to regulation of biochemical properties and binding modes.24-30 It was suggested that functional requirements are an important factor in explaining the occurrence of some non-prolyl cis peptide bonds, even though they cannot explain the occurrence of those not directly involved in the function of the protein.2 There are only a limited number of works reported on the kinetics and thermodynamics of the non-prolyl cis-trans isomerization for peptides,31,32 whereas considerable studies have been carried out for secondary amides such as N-methylacetamide and N-methylformamide.8,33-35 In particular, the Hsp70 chaperone DnaK has been identified as the first member of a novel enzyme class of secondary amide peptide bond cis-trans isomerases that selectively accelerate the cis-trans isomerization of non-prolyl peptide bonds.36 N-Acetyl-L-alanine-N′-methylamide (Ac-Ala-NHMe; the alanine dipeptide) has been studied experimentally37-47 and theoretically41,48-65 as a prototype for the non-prolyl backbone

10.1021/jp0647481 CCC: $33.50 © 2006 American Chemical Society Published on Web 09/29/2006

Conformational Preferences of Non-Pro and Pro Residues

Figure 1. Definition of torsion angles and structural parameters for the alanine and proline dipeptides.

of peptides and proteins for last three decades. These studies have been mostly focused on the preferred conformations of the alanine dipeptide with the trans peptide bond and their relative stabilities in the gas phase and in water, and some works53-55,58,64 were concerned about the conformational transitions between local minima. There is only one work reported to date, which studied the cis-trans isomerization of the alanine dipeptide at the low level of theory (HF/3-21G) in the gas phase.60 Considerable experiments38,66-70 and computations71-84 have been carried out on the N-acetyl-L-proline-N′-methylamide (AcPro-NHMe, the proline dipeptide) as a model for the prolyl residue of peptides and proteins. Most of them reported the conformational preference of the backbone and the prolyl cistrans isomerization in the gas phase and in solutions. The prolyl residue has a five-membered ring, which may adopt two distinct down- and up-puckered conformations that are almost equally favorable.71-73,75,82-84 Although the correlations of the cis-trans population and the prolyl puckering were suggested by analyzing X-ray structures of peptides and proteins,3,85,86 it was known that the cis-trans isomerization and the puckering transition is not coupled and that the prolyl ring can flip between the downand up-puckered conformations with either the trans or the cis peptide bond.83,84 Although the previous computational studies have been focused on the conformational preferences of the alanine and proline dipeptides in the gas phase or in water, insufficient information on the differences in non-prolyl and prolyl cistrans isomerizations is available to date. In particular, the conformations of the alanine residue with the cis peptide bond in solutions have not yet been reported. We report here the results on the alanine and proline dipeptides calculated using ab initio HF and density functional methods with the selfconsistent reaction field (SCRF) method to explore the differences in the backbone conformational preference and the cistrans isomerization for the non-prolyl and prolyl residues in the gas phase and in the solutions. Computational Methods Chemical structures and torsional parameters for the alanine and proline dipeptides are defined in Figure 1. All ab initio HF

J. Phys. Chem. B, Vol. 110, No. 42, 2006 21339 and density functional calculations were carried out using the Gaussian 03 package.87 Here, each backbone conformation of the dipeptides is represented by a capital letter depending on its values of φ and ψ for the backbone.71 Conformations C, C*, E, A, A*, F, D, F*, and G are equivalent to the γ-turn (C7eq and C7ax), extended (C5), R-helical (RR and RL), polyproline-like (β or PII), β2, RD, and R′ structures in other works, respectively. Trans and cis conformations for the Ac-X (X ) Ala and Pro) peptide bond are defined by the orientation of the methyl carbon of the acetyl group and the CR of the X residue, which are denoted by “t” and “c”, respectively. Down- and uppuckered conformations of the proline dipeptide are defined as those of which the Cγ atom and the CdO group of the prolyl residue lie on the same and opposite sides, respectively, of the plane defined by the three atoms Cδ, N, and CR (Figure 1), which are represented by “d” and “u”, respectively. Usually, the downand up-puckered conformations have positive and negative values for the endocyclic torsion angle χ1, respectively. The nine local minima identified for Ac-Ala-NHMe with the trans peptide bond72 optimized from the empirical energy optimization using the ECEPP/3 force field73 were used as starting points for the optimization at the HF/6-31+G(d) level of theory. The same backbone conformations with the cis peptide bond were optimized using the ECEPP/3 force field and then minimized again at the HF/6-31+G(d) level. At the HF/6-31+G(d) level, the two conformations optimized adiabatically from the conformation cA with ω′ ) +116 and -65° for the Ac-Ala peptide bond (Figure 1), which were defined as two syn/exo and anti/exo structures, respectively, in ref 74, were used as initial structures to locate the transition states ts1 and ts3, respectively, as done for Ac-Pro-NHMe.82 Local minima and transition states for the alanine and proline82 dipeptides optimized at the HF/6-31+G(d) level were used as initial points for optimizations at the hybrid density functional B3LYP/6-311++G(d,p) level of theory. In a recent work on proline, the B3LYP/6-311++G(d,p) level provided the relative energies very close to those obtained at the extrapolated CBS CCSD(T) level, and the rotational constants are in good agreement with those determined experimentally.88 In addition, the B3LYP/6-311++G(d,p) level was reported to be quite effective in giving satisfactory calculated geometries for a series of organic molecules, compared to the CCSD and MP2 levels with 6-311++G(d,p) and aug-cc-pVDZ basis sets.89 We employed the conductor-like polarizable continuum model (CPCM) SCRF method,90 implemented in the Gaussian 03 package,87 to compute solvation free energies (∆Gsolv) at the HF/6-31+G(d) level with the UAKS cavities, which are the united atom topological model (UATM) radii optimized at the density functional PBE0/6-31G(d) level of theory.91 The solvation free energy is the sum of the electrostatic free energy and the nonelectrostatic energy terms.91 The latter is composed of the cavitation, dispersion, and repulsion energy terms. For CPCM-UAKS calculations, the default average areas of 0.2 Å2 for tesserae were used. The solvents considered here are nonpolar chloroform and polar water, whose dielectric constants are 4.9 and 78.4 at 25 °C, respectively. Recently, the CPCMUAKS calculations for a number of neutral and charged organic molecules at the HF/6-31+G(d)//HF/6-31+G(d) and HF/631+G(d)//B3LYP/6-31+G(d) levels provided hydration free energies in agreement with available experimental data.92 All local minima and transition states for the alanine and proline82 dipeptides optimized at the HF/6-31+G(d) level in the gas phase were used as starting structures for optimizations at the HF/6-31+G(d) level in chloroform and water. The polypro-

21340 J. Phys. Chem. B, Vol. 110, No. 42, 2006

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TABLE 1: Backbone Torsion Angles and Thermodynamic Properties of Local Minima and Transition States for Ac-Ala-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)

B3LYP/6-311++G(d,p)

conformerb

ω′

φ

ψ

ω

∆Eec

∆Hd

∆Ge

ω′

φ

ψ

ω

∆Eec

∆Hd

∆Ge

tC tE tD tC* cA tF* tA* tG cE cA* cG ts1

-178.3 178.9 -168.4 174.8 5.1 -166.8 165.5 168.4 6.1 -12.7 -14.1 121.8

-86.4 -154.8 -102.7 75.9 -88.5 58.1 69.5 -163.5 -148.1 73.5 -159.6 -92.2

79.6 156.5 4.1 -56.5 -14.2 -133.6 26.2 -43.0 141.6 28.4 -42.9 -20.7

-174.5 177.6 174.1 -178.4 -178.9 175.7 -176.7 -172.5 178.0 176.5 -174.4 -174.9

0.00 0.30 2.42 2.87 4.15 4.81 4.98 5.97 6.48 7.78 10.12 18.58

0.00 0.15 2.28 3.01 4.02 4.76 4.81 5.82 6.23 7.70 10.00 17.61

0.40 0.00 1.97 3.68 4.79 5.63 5.60 6.38 6.59 8.79 10.98 19.81

-177.7 177.6 -169.9 175.1 5.8

-83.5 -154.7 -115.3 73.1 -90.9

75.9 159.3 13.7 -56.3 -9.6

-175.4 177.7 174.0 -178.6 -179.0

0.00 1.01 2.60 2.43 4.44

0.00 0.86 2.47 2.53 4.31

0.12 0.00 1.45 2.19 4.03

171.7 3.3 -12.0 -11.3 122.0

-164.5 -148.2 73.1 -161.0 -95.3

-44.8 144.1 27.0 -43.7 -17.7

-174.0 177.6 177.9 -175.6 -175.2

6.45 6.44 7.49 9.90 19.91

6.29 6.15 7.42 9.71 18.74

5.86 4.28 7.52 9.49 19.66

a Torsion angles are defined in Figure 1; units in degrees. b See the text for definition. For example, the first letter code tC is the backbone conformation C with the trans peptide 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.

line-like conformation tF and R-helical conformation tA for the alanine dipeptide are not local minima in the gas phase but could be feasible in the solutions. Thus, they were located by adiabatic optimizations with the (φ, ψ) values fixed at (-75°, 145°) and (-64°, -41°) in the gas phase, which are the average values from X-ray structures of polyproline II93 and R-helices94 in proteins, respectively. Then these two conformations were optimized again in the solutions. The B3LYP/6-311++G(d,p) single-point energies were calculated for all local minima and transition states of the alanine and proline dipeptides located at the HF/6-31+G(d) level in the solutions. Vibrational frequencies were calculated for all stationary points at the HF level in the gas phase and in the solutions and the B3LYP level in the gas phase, which were used to compute enthalpies and Gibbs free energies with the scale factors of 0.8934 and 0.9895 at HF and B3LYP levels, respectively, at 25 °C and 1 atm. A scale factor of 0.89 at the HF/6-31+G(d) level was chosen to reproduce experimental frequencies for the amide I band of N-methylacetamide in Ar and N2 matrixes.34 A scale factor of 0.98 at the B3LYP/6-311++G(d,p) level reproduced well some experimental frequencies of proline in an Ar matrix.95 The zero-point energy correction and the thermal energy corrections were used to calculate the enthalpy (H) and entropy (S) of each conformation.91,96 The analysis uses the standard thermodynamic expressions for an ideal gas in the canonical ensemble. Each transition state was confirmed by checking whether it had one imaginary frequency after frequency calculations at the HF and B3LYP levels. The relative total free energy (∆G) for each conformation in the solutions was computed by taking the sum of the relative conformational free energy (∆Ee), the thermal contributions, and the entropic contribution. The relative conformational free energy (∆Ee) is the sum of the conformational electronic energy (∆Ee,s) and the relative solvation free energy (∆∆Gsolv) in the solutions. The relative total free energies are used here to interpret the conformational preferences in the gas phase and in the solutions. The vicinal coupling constants 3JHNR for Ac-Ala-NHMe were computed by using the Karplus equation: 3JHNR (Hz) ) 6.4 cos2 θ - 1.4 cos θ + 1.9, where θ ) |φ - 60°|.97 The average values of 3JHNR were calculated with the normalized Boltzmann statistical weights derived from the relative Gibbs free energies at 25 °C. Results and Discussion Alanine Dipeptide. The local minima and transition states for the alanine dipeptide optimized at the HF/6-31+G(d) and

B3LYP/6-311++G(d,p) levels of theory in the gas phase are listed in Table 1. At the HF/6-31+G(d) level, the seven local minima tC, tE, tD, tC*, tF*, tA*, and tG with the trans AcAla peptide bond are found, whereas the four local minima cA, cE, cA*, and cG with the cis peptide bond are identified. However, the polyproline II (tF) or I (cF) structures and the R-helical conformation (tA) are not found to be stationary points, although they are included in the starting structures for optimizations. Our HF/6-31+G(d) local minima with the trans peptide bonds are consistent with those identified previously at various levels of theory.41,48-50,53,57,60,64 Ba´gyi et al. reported the six local minima cA*, cA, cE, cG, cF*, and cF for the alanine dipeptide with the cis peptide bond at the HF/3-21G level,60 whereas two of them (cF* and cF) are not identified as stationary structures and three of them (cA*, cA, and cE) are more stabilized by about 2 kcal/mol in the electronic energy at the HF/6-31+G(d) level in this work. The two local minima tF* and tA* at the HF/6-31+G(d) level disappeared at the B3LYP/6-311++G(d,p) level. In particular, we could locate only one transition state ts1 for the trans-to-cis isomerization of the Ac-Ala peptide bond at both the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels, although two syn/exo and anti/ exo structures were employed as initial points for the optimizations of transition states ts1 and ts2, respectively (see ref 74 for the definition of initial transition state structures). The representative conformations tC, tE, and cA and the transition state ts1 optimized at the B3LYP/6-311++G(d,p) level in the gas phase are presented in Figure 2. The lowest-energy conformation tC of the alanine dipeptide at both the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels has a C7 hydrogen bond between CdO of the N-terminal group and N-H of the C-terminal group, which is known to be responsible for stabilizing the lowest-energy conformations for most of the dipeptides, including the proline dipeptide and its derivatives.75-84,95,98-100 This C7 hydrogen bond appears to cause the polyproline II-like conformation tF to be inaccessible, as seen in the potential energy surfaces of the proline dipeptide82 and its 4(R)-substituted dipeptides.100 At the HF/6-31+G(d) level, the conformational stabilities of Ac-Ala-NHMe in the gas phase are calculated to be in the order tC > tE > tD > tC* > tF* > tA* > tG for the conformers with the trans peptide bond and in the order cA > cE > cA* > cG for the conformers with the cis peptide bond by the relative electronic energies (∆Ee). However, the conformational stabilities of the alanine dipeptide are calculated to be in the order tC > tE > tC* > tD > tG for the trans conformers and in the

Conformational Preferences of Non-Pro and Pro Residues

Figure 2. The representative conformations tC, tE, and cA and the transition state ts1 for the alanine dipeptide optimized at the B3LYP/ 6-311++G(d,p) level in the gas phase. Hydrogen bonds are represented by dotted lines.

order cA > cE > cA* > cG for the cis conformers by ∆Ee at the B3LYP/6-311++G(d,p) level. The conformational stabilities by the relative free energies (∆G) are almost in the same orders as by ∆Ee at both levels, except that the conformation tE is more stabilized than the conformation tC by 0.4 kcal/mol in ∆G at the HF/6-31+G(d) level and by 0.1 kcal/mol in ∆G at the B3LYP/6-311++G(d,p) level. This is caused by the increase of the conformational entropy for the conformation tE over that of the conformation tC (Table 1), which may be ascribed to the broader potential surface around the local minima tE than the local minima tC.57,64 On going from the HF/6-31+G(d) level to the B3LYP/6311++G(d,p) level, there are some shifts in the backbone torsion angles φ and ψ for the local minima and transition state ts1. Most of the shifts in φ and ψ are within (5°, but the local minimum tD has somewhat larger shifts in φ by -12.6° and in ψ by +9.6°. The gas-phase electron diffraction measurements indicated that the conformations tC and tE are predominant, but the existence of the R-helical structure tA was not confirmed.39 The microwave experiments supported the conformation tC to be most preferred in the gas phase.43 Our calculated conformational preference of the alanine dipeptide in the gas phase is consistent with these experimental results. Table 2 lists the local minima and transition states for the alanine dipeptide optimized at the CPCM HF/6-31+G(d) level in chloroform and water. The eight local minima, tC, tE, tF, tA, tC*, tF*, tA*, and tG, with the trans peptide bond and the three local minima, cA, cE, and cA*, with the cis peptide bond are identified in chloroform. The two local minima tD and cG in the gas phase disappeared in chloroform. In water, the lowestenergy conformation tC in the gas phase is no longer a local minimum, which could be ascribed to the hydration of the polar CdO and N-H groups and the breaking of their hydrogen bonds. The conformation cG appeared again as a local minimum in water. The representative conformations tE, tF, tA, and cA and the transition state ts1 optimized at the CPCM HF/631+G(d) level in water are presented in Figure 3. The conformational stabilities of Ac-Ala-NHMe in chloroform are calculated to be in the order tE > tC > tF ≈ tA >

J. Phys. Chem. B, Vol. 110, No. 42, 2006 21341 tC* > tA* > tF* > tG for the conformers with the trans peptide bond and in the order cA > cE > cA* for the conformers with the cis- peptide bond by ∆Ee. However, the conformational stabilities in water are calculated to be in the order tF ≈ tA ≈ tE > tA* > tG > tF* > tC* for the trans conformers and in the order cA > cE > cA* > cG for the cis conformers by ∆Ee. The conformational stabilities acquired by ∆G are almost in the same orders as those noted by ∆Ee in chloroform and water, except that the relative stabilities of the conformations tC and tF as well as the conformations tC* and tA* are reversed in chloroform and that the two conformations tF and tE are isoenergetic and most preferred in water. In addition, the most preferred cis conformation in water is cE instead of the conformation cA. On going from the gas phase to chloroform, there are some shifts in the backbone torsion angles φ and ψ within (5° for the local minima and transition state ts1, except for the local minima tF*, tA*, and tG in φ and the local minimum tG in ψ. On going from chloroform to water, there are a little larger shifts in the backbone torsion angles φ and ψ within (6° for the local minima and transition state ts1, and there are large shifts in φ by -33° for the conformation tG and in ψ by -15° for the conformation tF*. Table 3 lists the thermodynamic properties of Ac-Ala-NHMe corrected by the single-point energies at the B3LYP/6-311++G(d,p)//CPCM HF/6-31+G(d) level in the solutions, which are used in the analysis of the conformational preferences and the cis-trans isomerization below. The conformational stabilities by ∆G at this corrected level are almost in the same order as rated by ∆G at the CPCM HF/6-31+G(d) level in chloroform and water, except that the relative stabilities of the conformations tC and tF are reversed in chloroform and the R-helical conformation tA becomes comparable to the polyproline II-like conformation tF in water. In particular, the most preferred cis conformation is cE in both chloroform and water. The vicinal coupling constants 3JHNR for the alanine dipeptide in the gas phase, chloroform, and water are listed in Table 4. The statistically weighted values of coupling constants are calculated to be 7.45 and 7.38 Hz in the gas phase at the HF/ 6-31+G(d) and B3LYP/6-311++G(d,p) levels, respectively. In chloroform and water, the calculated average values are 7.40 and 6.99 Hz, respectively. The corresponding values from the free energies corrected at the B3LYP/6-311++G(d,p)//CPCM HF/6-31+G(d) level are 7.47 and 7.01 Hz, respectively. The calculated average coupling constants in the gas phase are nearly the same as those in chloroform, but they decrease more in water. The calculated average coupling constants in chloroform are in good agreement with experimental values in chloroform38 and carbon tetrachloride.47 However, the calculated average coupling constants in water appear to be a little overestimated, which may be ascribed to the higher stability of the conformation tE because its coupling constant is computed as 7.75 Hz in water. Proline Dipeptide. The local minima and transition states for the proline dipeptide optimized at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels of theory in the gas phase are listed in Table 5. The calculated results at the HF/6-31+G(d) level were taken from ref 82. At the HF/6-31+G(d) level, the three local minima tCd, tCu, and tAu with the trans Ac-Pro peptide bond are found, whereas the four local minima cAd, cAu, cFd, and cFu with the cis peptide bond are identified. The lowest-energy conformations tCd and tCu at both the HF/631+G(d) and B3LYP/6-311++G(d,p) levels have the C7 hydrogen bonds between CdO of the N-terminal group and

21342 J. Phys. Chem. B, Vol. 110, No. 42, 2006

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TABLE 2: Backbone Torsion Angles and Thermodynamic Properties of Local Minima and Transition States for Ac-Ala-NHMe Optimized at the CPCM HF/6-31+G(d) Level in Solutionsa chloroform

water

conformerb

ω′

φ

ψ

ω

∆Eec

∆Hd

∆Ge

tC tE tF tA tC* cA tF* tA* tG cE cA* cG ts1

-177.3 -179.8 172.6 -170.3 173.2 3.9 -172.2 169.3 -178.0 4.0 -9.1

-88.0 -152.5 -80.9 -82.8 76.3 -86.7 58.5 65.8 -114.6 -144.8 71.2

77.5 150.9 141.2 -20.6 -53.6 -17.8 -140.1 34.5 -59.3 144.4 28.9

-175.1 176.8 178.4 -179.6 -178.0 -177.7 179.9 179.2 -179.7 176.6 175.3

0.62 0.00 0.88 0.99 2.76 3.51 4.23 3.00 4.93 4.37 6.25

0.74 0.00 0.91 1.01 3.03 3.52 4.21 2.92 4.36 4.32 6.24

1.15 0.00 0.52 1.27 3.82 4.38 4.69 3.61 5.49 4.83 7.37

119.7

-89.2

-25.8

-175.2

19.40

18.57

20.72

a,b,d,e

ω′

φ

ψ

ω

∆Eec

∆Hd

∆Ge

-177.1 178.9 -176.6 173.3 1.5 -175.7 173.7 -178.4 5.7 -4.9 1.1 120.1

-151.5 -76.1 -81.7 77.0 -80.8 61.5 61.7 -147.4 -149.4 68.9 -156.0 -86.3

145.8 146.9 -24.3 -49.8 -22.3 -155.1 40.8 -58.1 146.3 30.1 -56.9 -29.7

176.1 176.2 -177.4 -178.1 -177.2 -173.6 176.2 -179.4 176.5 175.2 -179.0 -175.8

0.20 0.00 0.11 4.84 3.32 3.78 1.84 3.70 3.68 5.55 7.32 20.93

0.32 0.00 0.20 5.25 3.48 3.69 1.64 3.85 3.96 5.33 6.90 20.18

0.00 0.01 0.49 5.90 4.26 3.65 2.38 3.03 3.71 6.45 8.69 22.00

c

See footnotes a, b, d, and e of Table 1. The relative conformational free energy (∆Ee) is the sum of the conformational electronic energy (∆Ee,s) and the relative solvation free energy (∆∆Gsolv) in the solutions; units in kcal/mol.

TABLE 3: Thermodynamic Properties of Ac-Ala-NHMe Computed at the B3LYP/6-311++G(d,p)//CPCM HF/ 6-31+G(d) Level in Solutionsa chloroform

water

conformerb

∆Eec

∆Hd

∆Ge

tC tE tF tA tC* cA tF* tA* tG cE cA* cG ts1

0.05 0.00 1.13 0.88 1.71 3.20 3.87 2.63 4.13 3.48 5.29

0.17 0.00 1.16 0.89 1.97 3.21 3.85 2.55 3.56 3.44 5.27

0.58 0.00 0.77 1.16 2.77 4.08 4.33 3.24 4.69 3.95 6.41

20.28

19.46

21.61

∆Eec

∆Hd

∆Ge

0.40 0.24 0.00 4.23 3.24 3.35 1.50 3.18 2.96 4.73 6.31 22.16

0.42 0.15 0.00 4.54 3.30 3.16 1.21 3.23 3.14 4.42 5.79 21.32

0.00 0.06 0.19 5.09 3.99 3.02 1.85 2.31 2.79 5.43 7.48 23.03

a

Units in kcal/mol. b-e See footnotes b-e of Table 2. c-e 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 3. The representative conformations tE, tF, tA, and cA and the transition state ts1 for the alanine dipeptide optimized at the CPCM HF/6-31+G(d) level in water. Hydrogen bonds are represented by dotted lines.

N-H of the C-terminal group, as found for the alanine dipeptide above. In addition, this C7 hydrogen bond appears to cause the polyproline II-like conformation tF to be inaccessible. At both the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels, the conformational stabilities of Ac-Pro-NHMe in the gas phase are calculated to be in the order tCd > tCu > tAu for the conformers with the trans peptide bond and in the order cAd > cAu > cFd > cFu for the conformers with the cis peptide bond by the relative electronic energies (∆Ee) and the relative free energies (∆G). In particular, we could locate four transition states for the trans-to-cis isomerization of the Ac-Pro peptide bond at both the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels; ts1 and

ts2 are similar to syn/exo structures with down and up puckerings, respectively, whereas ts3 and ts4 resemble anti/exo structures with down and up puckerings, respectively (see ref 74 for the definition of the syn/exo and anti/exo structures). On going from the HF/6-31+G(d) level to the B3LYP/6311++G(d,p) level, there are some shifts in the backbone torsion angles φ and ψ for the local minima and transition states. Their shifts are -4° to +3° and -8° to +6° in φ and ψ, respectively. The shifts in the endocyclic torsion angle χ1 are relatively small and in the range of -1° to +3°. Table 6 lists the local minima and transition states for the proline dipeptide optimized at the CPCM HF/6-31+G(d) level in chloroform and water. All 10 local minima with the transand cis peptide bonds in the gas phase still survive in chloroform. Two additional polyproline II-like conformations tFd and tFu appear in chloroform. In water, the local minimum tCu is no longer a local minimum, as seen in the potential energy surface.82 The representative conformations tFd, tFu, cFd, and cFu and the transition state ts1 optimized at the CPCM HF/631+G(d) level in water are presented in Figure 4. The conformational stabilities of Ac-Pro-NHMe in chloroform are calculated to be almost in the same order as in the gas phase by ∆Ee and ∆G, except that the polyproline II-like conformation tFd with the down puckering becomes the most preferred and

Conformational Preferences of Non-Pro and Pro Residues TABLE 4: Coupling Constants 3JHNr for Ac-Ala-NHMe Calculated at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) Levels in the Gas Phase and in Solutionsa gas phase conformerb tC tE tD tF tA tC* cA tF* tA* tG cE cA* cG ts1 averagec exptl

chloroform

water

HF/ B3LYP/ HF/ HF/ 6-31+G(d) 6-311++G(d,p) 6-31+G(d) 6-31+G(d) 7.51 7.37 9.07 6.47 7.75 6.89 6.74 6.28 8.12 6.59 6.78 8.15 7.45

7.16 7.38 9.65 6.61 8.01 6.15 8.10 6.61 6.60 8.45 7.38

7.69 7.63 6.84 7.08 6.45 7.54 6.90 6.84 9.64 8.44 6.69 7.82 7.40 7.47d 7.5,e 7.51f

7.75 6.23 6.94 6.41 6.83 6.90 6.89 8.19 7.98 6.76 7.22 7.49 6.99 7.01d 6.0,e 6.06f

a Units in hertz. The coupling constant 3J HNR was calculated using the Karplus equation: 3JHNR (Hz) ) 6.4 cos2 θ - 1.4 cos θ + 1.9, where θ ) |φ - 60°|.97 b See footnote b of Tables 1 and 2. c The average values calculated using the normalized Boltzmann statistical weights derived from the relative Gibbs free energies of Tables 1 and 2 at 25 °C. d The free energies corrected by the B3LYP/6-311++G(d,p)// CPCM HF/6-31+G(d) single-point energies in Table 3 were used to calculate the normalized Boltzmann statistical weights at 25 °C. e In chloroform and water, from ref 38. f In CCl4 and water, from ref 47.

the polyproline II-like conformation tFu with the up puckering is comparable to the conformation tCd. In particular, two polyproline II-like conformations tFd and tFu become isoenergetic and most preferred in water. In addition, two polyproline I-like conformations cFd and cFu become isoenergetic and more stabilized than helical structures cAd and cAu 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 states. Their shifts are (2° and -5° to +1° in φ and ψ, respectively. However, there is a large shift in ψ by -8° for the conformation tAu. The shifts in the endocyclic torsion angle χ1 are relatively small and within (1°. On going from chloroform to water, there are some small shifts in the backbone torsion angle φ and the endocyclic torsion angle χ1 by (3° and (1°, respectively. The shifts in the backbone torsion angle ψ are relatively large by (6° and there is a large shift in ψ by +15° for the conformation tCd. Table 7 lists the thermodynamic properties of Ac-Pro-NHMe corrected by the single-point energies at the B3LYP/6-311++G(d,p)//CPCM HF/6-31+G(d) level in the solutions, which are used in the analysis of the conformational preferences and the cis-trans isomerization below. 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. However, the stability of the conformation tAd becomes comparable to that of the conformation tCu in chloroform. The polyproline I-like structures cFd and cFu become more stabilized in chloroform. In water, the polyproline II-like conformations tFd and tFu as well as the polyproline I-like conformations cFd and cFu become more stabilized, and the up-puckered conformations become more favorable than the down-puckered conformations. The endocyclic torsion angles and puckering amplitudes of the prolyl ring for the local minima and transition states of AcPro-NHMe optimized at the B3LYP/6-311++G(d,p) level in

J. Phys. Chem. B, Vol. 110, No. 42, 2006 21343 the gas phase and at the CPCM HF/6-31+G(d) level in chloroform and water are listed in Tables S1-S3, respectively, of the Supporting Information. In these tables, three kinds of puckering amplitudes, qR of Han and Kang,101 qz by Cremer and Pople,102 and χm of Altona and Sundaralingam,103 are employed to describe the degree of puckering of the prolyl ring. The puckering amplitude qR is the maximum angle between the mean plane and the line joining the center of mass and each atom of the ring. The puckering amplitude qz is the maximum z-displacement perpendicular to the mean plane of the ring. The puckering amplitude χm is the maximum value attainable by endocyclic torsion angles of the ring. Recently, we reported that these three puckering amplitudes showed the same trend of puckering along the prolyl cis-trans isomerization of Ac-ProNHMe although their absolute values are different.83 The correlations of the cis-trans population and prolyl puckering were suggested by analyzing X-ray structures of peptides and proteins.3,85,86 Calculated populations of the prolyl peptide bond depending on puckering for Ac-Pro-NHMe from the relative free energies for local minima optimized at the HF/ 6-31+G(d) and B3LYP/6-311++G(d,p) levels in the gas phase and the solutions are presented in Table 8. In the gas phase, the trans/down conformations are dominantly populated, which is caused by the higher stability of the conformation tCd, as described above. As the solvent polarity increases, the populations of the trans/down conformations decrease, and the populations of the other conformations increase. In particular, the trans/ up conformations become most preferred in water, which can be attributed to the increase in the populations for the polyproline II-like conformation tFu. Although the populations of the cis/ up conformations for the proline dipeptide are overestimated when compared to those estimated from X-ray structures of proteins, the stability in the order trans/up > trans/down > cis/ up > cis/down computed at the B3LYP/6-311++G(d,p)//CPCM HF/6-31+G(d) level in water is reasonably consistent with that from X-ray structures of proteins.85 Populations of Backbone Structures. The populations of the backbone conformations for the alanine and proline dipeptides are listed in Table 9. 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 the solutions. In the gas phase and in the solutions, the alanine dipeptide prefers the extended conformation tE. Although an intramolecular C7 hydrogen bond between two terminal groups plays a role in stabilizing the conformation tC in the gas phase, the increase of the conformational entropy for the conformation tE over that of the conformation tC leads to the increase in stability of the conformation tE, which is due to the broader potential surface around the former than the latter, as described above. With the increase of solvent polarity, for example from the gas phase to chloroform to water, the populations of the conformation tC significantly decrease, and those of the polyproline IIlike conformation tF and the R-helical conformation tA increase. In particular, the population of the conformation tF becomes comparable to that of the conformation tE in water. The calculated populations for the backbone conformation of the alanine dipeptide in chloroform and water are reasonably consistent with CD and NMR experiments38 and vibrational Raman optical activity (ROA) measurements.40 However, the polyproline II-like conformation tF has been suggested as the dominant structure in water from the Raman/vibrational CD/ ROA spectroscopic study,41 the liquid crystal NMR42,44 and

21344 J. Phys. Chem. B, Vol. 110, No. 42, 2006

Kang

TABLE 5: Backbone Torsion Angles, Endocyclic Torsion Angle χ1, and Thermodynamic Properties of Local Minima and Transition States for Ac-Pro-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)b conformerc tCd tCu cAdg cAu tAu cFd cFu ts1 ts2 ts3 ts4

ω′

φ

-172.8 -86.2 74.9 -174.7 -82.6 84.5 9.2 -89.5 -9.1 5.7 -76.6 -21.9 -171.1 -73.6 -17.7 -0.5 -75.3 155.4 -3.6 -59.1 154.1 116.4 -106.2 -9.9 118.0 -103.1 -13.0 -65.1 -95.5 -0.4 -69.8 -84.3 -10.2

B3LYP/6-311++G(d,p)

ω

χ1

∆Eed

∆He

-176.5 -174.4 -179.7 -177.2 175.4 175.6 175.7 -178.5 -176.4 176.8 178.1

31.8 -14.3 31.1 -23.1 -25.8 32.4 -22.3 20.6 -30.2 20.8 -34.7

0.00 1.69 2.37 3.45 3.66 5.19 5.92 17.62 18.19 19.27 19.80

0.00 1.76 2.21 3.24 3.48 4.92 5.64 16.52 17.06 18.11 18.64

ψ

∆Gf

ω′

φ

ψ

ω

χ1

∆Eed

∆He

0.00 -172.6 -83.6 71.2 -177.2 31.3 0.00 0.00 1.73 -173.9 -81.7 78.0 -175.6 -13.3 1.03 1.14 1.81 10.0 -91.7 -5.0 179.3 31.8 3.31 3.17 2.60 8.2 -79.3 -18.9 -177.3 -22.2 4.13 3.98 3.21 -171.1 -77.7 -11.3 175.9 -22.7 4.76 4.60 3.71 0.7 -75.2 148.1 176.0 31.4 6.09 5.20 4.57 0.1 -62.1 146.3 177.4 -22.9 6.40 6.17 16.97 118.1 -109.3 -5.4 -178.9 21.6 19.60 18.35 17.50 119.2 -107.1 -9.6 -177.0 -28.3 20.34 19.09 17.65 -66.5 -97.5 1.4 176.9 20.8 20.80 19.49 18.69 -65.4 -85.2 -9.7 179.1 -35.2 21.50 20.21

∆Gf 0.00 1.21 2.16 3.70 4.01 5.20 5.26 19.15 19.51 19.50 20.64

a Torsion angles are defined in Figure 1; units in degrees. b From ref 82. c See the text for definition. For example, the first letter code tCd is the down-puckered conformation C with the trans prolyl peptide bond. d-f See footnotes c-e of Table 1. g The backbone conformation should be B according to the definition of Zimmerman et al. (ref 71), but it is represented as A in this work because the values of ψ ) -9.1° at the HF/631+G(d) level and ψ ) -5.0° at the B3LYP/6-311++G(d,p) level are just beyond the boundary ψ ) -10° for the backbone conformation A.

TABLE 6: Backbone Torsion Angles, Endocyclic Torsion Angle χ1, and Thermodynamic Properties of Local Minima and Transition States for Ac-Pro-NHMe Optimized at the CPCM HF/6-31+G(d) Level in Solutionsa chloroform conformerb tCd tFd tFu tAd tCu cAd cAu tAu cFd cFu ts1 ts2 ts3 ts4 a,b

ω′

φ

ψ

ω

-172.1 -86.7 70.4 -177.5 180.0 -72.0 147.1 179.0 179.3 -61.7 142.1 -179.6 -170.9 -83.8 -13.4 178.5 -174.4 -82.9 83.4 -174.9 9.4 -88.6 -10.7 -178.9 5.0 -74.7 -23.0 -175.7 -172.4 -71.3 -25.6 -179.7 -0.8 -76.1 156.7 176.0 -4.6 -60.3 154.4 175.5 115.6 -104.1 -13.9 -178.2 116.7 -102.9 -15.2 -176.5 -63.5 -97.4 -6.4 178.8 -68.6 -87.8 -11.7 -179.8

See footnotes a and c of Table 5.

c-e

water χ1

∆Eec

∆Hd

∆Ge

ω′

∆Eec

∆Hd

∆Ge

32.1 29.5 -22.7 28.4 -15.0 31.0 -22.9 -26.4 32.1 -22.4 19.2 -29.8 19.2 -33.8

0.00 0.13 0.37 0.63 1.66 1.21 1.91 1.11 1.93 2.22 17.53 18.18 19.07 19.54

0.02 0.00 0.23 0.53 1.75 1.15 1.79 0.99 1.77 2.05 16.49 17.09 18.02 18.48

0.56 0.00 0.42 0.79 2.20 1.56 1.91 1.37 1.57 1.97 17.72 18.26 18.33 19.18

-173.5 -177.5 -179.6 -171.1

-86.7 85.2 -177.5 30.6 -73.5 151.6 176.6 28.8 -62.6 148.8 176.4 -24.3 -80.8 -19.7 -179.8 27.8

3.20 0.06 0.00 0.80

2.90 0.09 0.00 0.96

4.46 0.00 0.01 1.15

9.4 -86.3 -11.3 -179.2 30.9 3.4 -73.7 -22.7 -176.1 -22.0 -173.7 -68.3 -30.3 -177.6 -26.4 1.6 -76.4 158.2 175.9 31.1 -3.1 -61.9 153.6 175.7 -23.6 116.6 -104.3 -16.1 -178.2 19.6 118.5 -107.9 -14.2 -177.1 -26.1 -62.4 -99.4 -11.7 -179.1 20.8 -66.3 -92.1 -15.8 -177.3 -32.6

1.93 2.20 0.92 1.33 1.44 19.74 20.17 21.04 21.25

2.20 2.29 1.02 1.44 1.42 18.94 19.26 20.44 20.60

2.51 2.21 1.29 1.24 1.38 20.09 20.29 20.90 21.22

φ

ψ

ω

χ1

See footnotes c-e of Table 1 and footnote c of Table 2.

solid-state NMR45 experiments, two-dimensional IR measurements,46 and the crystal from the X-ray diffraction experiment.37 In addition, the experimental values of the coupling constants 3J HNR for the alanine dipeptide may indicate the predominant existence of the polyproline II-like conformation tF in water.38,47 The conformational preference for the polyproline II-like structure of the alanine dipeptide in water was interpreted by (1) the favorable direct interactions between the peptide backbone and water molecules41 and (2) the minimization of the steric conflicts of the peptide backbone by water molecules.59,63 In the case of the proline dipeptide, the conformation tC with an intramolecular C7 hydrogen bond is remarkably depopulated, and the polyproline II-like conformation tF becomes more populated as the solvent polarity increases. The populations of conformations are in the order C > F > A in chloroform and F . A . C in water, which is in good agreement with the results from CD and NMR experiments.38 The conformation tFd with the down puckering and the conformation tFu with the up puckering contribute to the overall population of the polyproline II-like structures by 15.2% and 12.2% in chloroform, respectively, while in water by 40.7% and 27.6%, respectively (estimated by the relative free energies in Table 7). This indicates that the up-puckered polyproline II-like conformation tFu is most preferred in water. The X-ray structure of the proline dipeptide in the crystal is R-helical with the values of (φ, ψ) ) (-76.3°, -15.8°),67 which are similar to our calculated values of (-80.8°, -19.7°) for the conformation tAd optimized at the

CPCM HF/6-31+G(d) level in water (Table 6). The R-helical conformation preferred in the crystal was attributed to the favorable intermolecular or intramolecular hydrogen bonds.67 Relative Stability of Cis Conformers. Table 9 lists the relative free energies (∆Gc/t) of the most probable cis conformation to the most probable trans conformation for the alanine and proline dipeptides computed 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 the solutions. The most probable trans and cis conformations for the alanine dipeptide are tC and cA in the gas phase and tE and cE in chloroform and water, respectively. The relative free energy ∆Gc/t decreases as the solvent polarity increases. The computed value of ∆Gc/t in water is 2.79 kcal/mol, which is consistent with the experimental value of 2.5 kcal/mol for N-methylacetamide33 and the observed mean value of 3.3 kcal/mol for the Ala-Phe, Phe-Ala, Tyr-Ala, and Ala-Tyr peptides.31 In particular, the statistically weighted cis populations are calculated to be 0.1, 0.1, and 0.4% in the gas phase, in chloroform, and in water, respectively. The calculated value of 0.4% in water is in good agreement with the experimental value of 1.4% for N-methylacetamide33 and the observed mean value of 0.4% for the Alacontaining peptides.31 For the proline dipeptide, the most probable trans and cis conformations are tCd and cAd in the gas phase, tCd and cFd in chloroform, and tFu and cFu in water, respectively. The relative free energy ∆Gc/t decreases as the solvent polarity increases, as seen for the alanine dipeptide. The calculated value

Conformational Preferences of Non-Pro and Pro Residues

J. Phys. Chem. B, Vol. 110, No. 42, 2006 21345 TABLE 8: Populations of Prolyl Peptide Bond with Puckering for Ac-Pro-NHMe Calculated at the HF/ 6-31+G(d) and B3LYP/6-311++G(d,p) Levels in the Gas Phase and in Solutionsa level

trans/down

HF B3LYP

89.2 86.3

HF B3LYP HF B3LYP

trans/up

cis/down

cis/up

gas phase 5.2 11.2

4.4 2.3

1.2 0.2

66.5 68.9

chloroform 24.7 22.1

5.7 4.9

3.1 4.1

45.8 32.4

water 43.8 44.4

5.5 9.2

4.9 14.1

a The populations (%) were calculated using the Boltzmann statistical weights at 25 °C, depending on the trans/cis prolyl peptide bond and down/up puckerings in Tables 5-7.

Figure 4. The representative conformations tFd, tFu, cFd, and cFu and the transition state ts1 for the proline dipeptide optimized at the CPCM HF/6-31+G(d) level in water. Hydrogen bonds are represented by dotted lines.

TABLE 7: Thermodynamic Properties of Ac-Pro-NHMe Computed at the B3LYP/6-311++G(d,p)//CPCM HF/ 6-31+G(d) Level in Solutionsa chloroform b

conformer

∆Ee

∆Hd

tCd tFd tFu tAd tCu cAd cAu tAu cFd cFu ts1 ts2 ts3 ts4

0.00 1.36 1.31 1.56 1.07 2.09 2.61 2.15 2.56 2.53 19.69 20.49 20.63 21.20

0.00 1.20 1.14 1.44 1.14 2.00 2.46 2.00 2.37 2.34 18.62 19.38 19.56 20.11

c

water ∆Ge 0.00 0.67 0.80 1.16 1.06 1.88 2.04 1.85 1.64 1.72 19.32 20.01 19.33 20.28

∆Hd

∆Ge

2.89 0.30 0.00 0.93

2.59 0.33 0.00 1.10

4.13 0.23 0.00 1.27

2.06 2.09 1.07 1.02 0.75 21.27 21.79 21.84 22.11

2.33 2.18 1.18 1.13 0.74 20.47 20.88 21.23 21.46

2.63 2.08 1.43 0.91 0.68 21.61 21.89 21.69 22.07

c

∆Ee

a Units in kcal/mol. b-e See footnotes b-e of Table 6. c-e The B3LYP/6-311++G(d,p) single-point energies were replaced for the conformational HF/6-31+G(d) electronic energies of Table 6. The vibrational and thermal contributions used are those obtained at the CPCM HF/6-31+G(d) level in Table 6.

of ∆Gc/t in water is 0.68 kcal/mol, which accords with its experimental value of 0.6 kcal/mol69,70 and the observed values of 0.4 kcal/mol104 and 0.9 kcal/mol105 for Ac-Pro-OMe. The statistically weighted cis populations are estimated as 2.5, 9.0, and 23.3% in the gas phase, in chloroform, and in water, respectively. Our calculated values in chloroform and water are in good agreement with the experimental cis populations of 14%66 and 15 ( 4%68 in chloroform and 24 ( 4%,68 27 ( 3%,69 and 28%70 in water.

Therefore, our calculated results indicate that the relative free energies of cis conformers of the alanine dipeptide are about 2 kcal/mol higher than those of the proline dipeptide in the gas phase and in the solutions. This could explain the reason nonprolyl residues have relatively low populations of cis conformers compared to those of prolyl residues, as found in X-ray structures of proteins.1-3 Cis-Trans Isomerization. In the gas phase, we could locate only one transition state ts1 with the syn/exo structure for the trans-to-cis or cis-to-trans isomerization of the alanine dipeptide at both the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels, whereas four transition states ts1-ts4 with the syn/exo and anti/ exo structures were identified for the proline dipeptide at the same levels, and the transition state ts1 is the most probable one. In chloroform and water, only the ts1 is confirmed as a transition state for both the alanine and proline dipeptides at the CPCM HF/6-31+G(d) level. Although the other three transition states of ts2-ts4 for the proline dipeptide are also located at the CPCM HF/6-31+G(d) level in chloroform and water, their total free energies are higher than that of the transition state, ts1, by the following amounts: (a) in chloroform, 0.53-1.45 kcal/mol at the CPCM HF/6-31+G(d) level and 0.01-0.96 kcal/mol at the B3LYP/6-311++G(d,p)//CPCM HF/ 6-31+G(d) level; (b) in water, 0.19-1.12 kcal/mol at the CPCM HF/6-31+G(d) level and 0.08-0.46 kcal/mol at the B3LYP/6311++G(d,p)//CPCM HF/6-31+G(d) level. This indicates that the cis-trans isomerization proceeds in common through only the clockwise rotation with ω′ ≈ +120° about the non-prolyl and prolyl peptide bonds in the gas phase and in the solutions. In the gas phase, the rotational barriers (∆Gtcq and ∆Gctq) to the trans-to-cis and cis-to-trans isomerizations for the non-prolyl peptide bond of the alanine dipeptide are estimated to be 19.81 and 15.02 kcal/mol at the HF/6-31+G(d) level, respectively, and 19.66 and 15.63 kcal/mol at the B3LYP/6-311++G(d,p) level, respectively (Table 1). At the B3LYP/6-311++G(d,p)// CPCM HF/6-31+G(d) level, these rotational barriers are computed as 21.61 and 17.66 kcal/mol in chloroform, respectively, and 23.03 and 20.24 kcal/mol in water, respectively (Table 3). The rotational barriers ∆Gtcq and ∆Gctq for the prolyl peptide bond of the proline dipeptide in the gas phase are estimated to be 16.97 and 15.16 kcal/mol at the HF/6-31+G(d) level, respectively, and 19.15 and 16.99 kcal/mol at the B3LYP/ 6-311++G(d,p) level, respectively (Table 5). At the B3LYP/ 6-311++G(d,p)//CPCM HF/6-31+G(d) level, these rotational barriers are computed as 19.32 and 17.68 kcal/mol in chloroform, respectively, and 21.61 and 20.93 kcal/mol in water, respectively (Table 7).

21346 J. Phys. Chem. B, Vol. 110, No. 42, 2006

Kang

TABLE 9: Populations of Backbone Conformations, Rotational Barriers, and Relative Free Energies of Cis Conformers for Ac-Ala-NHMe and Ac-Pro-NHMe Calculated at the B3LYP/6-311++G(d,p) Level in the Gas Phase and in Solutions backbone populationsa solvent

C

E

A

F

cise

gas phase chloroform water

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

gas phase chloroform water

97.4 54.9 0.0

2.5 12.2 10.1

0.0 32.9 89.9

2.5 9.0 23.3

rotational barrierb,c exptl cise

relative energyb,d

∆Gtcq

∆Gctq

∆Gc/t

19.66 21.61 23.03 (21.3,f 21.8g)

15.63 17.66 20.24 (18.8,f 18.5,g 17.9h)

4.03 3.95 2.79 (2.5,f 3.3g)

19.15 19.32 21.61 (20.4,k 21.1,m 21.1n)

16.99 17.68 20.93 (19.8,k 20.7,m 20.2n)

2.16 1.64 0.68 (0.6,k,l 0.4,m 0.9n)

Ac-Ala-NHMe 1.4,f 0.4g Ac-Pro-NHMe 14,i 15 ( 4,j 24 ( 4,j 27 ( 3,k 28l

a The populations (%) were computed using the relative Gibbs free energy of each local minimum in Tables 1, 3, 5, and 7. b Units in kcal/mol. Experimental values are listed in parentheses. The lowest Gibbs free energy for each of the trans, cis, and transition state conformations was used for these calculations. Free energies were calculated at 25 °C. c ∆Gtcq and ∆Gctq represent the barriers for the trans-to-cis and cis-to-trans rotations for the Ac-Ala and Ac-Pro peptide bonds. d ∆Gc/t is the relative Gibbs free energy of the cis conformer to the trans conformer. e Cis Ac-Ala or Ac-Pro peptide bonds. f For N-methylacetamide at 333 K. Cis % is estimated using the value 2.5 kcal/mol for ∆Gc/t at 298 K. From ref 33. g Average values for Ala-Phe, Phe-Ala, Tyr-Ala, and Ala-Tyr peptides at 298 K; from ref 31. h Average values for Gly-Gly, Gly-Ala, Ala-Gly, and Ala-Ala peptides at 298 K; from ref 32. i From ref 66. j From ref 68. k From ref 69. l From ref 70. m For Ac-Pro-OMe; from ref 104. n For AcPro-OMe; from ref 105.

The calculated results 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 the solutions are summarized in Table 9. The rotational barriers ∆Gtcq and ∆Gctq for both the non-prolyl and prolyl peptide bonds increase as the solvent polarity increases. In particular, the barrier ∆Gtcq for the non-prolyl peptide bond is higher by 0.51, 2.29, and 1.42 kcal/mol than the prolyl peptide bond in the gas phase, chloroform, and water, respectively, whereas the barrier ∆Gctq for the former becomes lower by 1.36, 0.02, and 0.69 kcal/mol than the latter in the gas phase, chloroform, and water, respectively. The lower barriers ∆Gctq for the alanine dipeptide are ascribed to the relative free energies of their cis conformers that are higher than those of the proline dipeptide, as described in the previous section. In a recent work on the alanine dipeptide, Ba´gyi et al. reported four transition states at ω′ ≈ (110° with the relative electronic energies of 19.75-25.16 kcal/mol at the HF/3-21G level in the gas phase and estimated the activation energies for the vertical transition from the trans conformation (tC or tC*) to the similar cis conformation using the isodesmic reactions.60 Their rotational electronic energies are larger than our values of 18.58 and 19.91 kcal/mol calculated at the HF/6-31+G(d) and B3LYP/6311++G(d,p) levels, respectively (Table 1). In addition, their backbone structures of the transitions states are different from that of our transition state ts1. The calculated barriers ∆Gtcq and ∆Gctq for the alanine dipeptide in water are reasonably consistent with the experimental values of N-methylacetamide33 and the observed mean values of the Ala-Phe, Phe-Ala, Tyr-Ala, and Ala-Tyr peptides.31 In particular, the good agreement of our calculated values of ∆Gtcq and ∆Gctq for the proline dipeptide with the experimental results for Ac-Pro-NHMe69 and Ac-Pro-OMe104,105 may support the validity of the methods employed in this work. By analyis of the contributions to rotational barriers, cis-trans isomerizations for non-prolyl and prolyl peptide bonds are proven to be entirely enthalpy driven in the gas phase and the solutions, to which the electronic energies have contributed considerably. This is consistent with the experimental results on prolinecontaining peptides, kinetically determined as a function of temperature.106 From the comparison of molecular geometries for the transition state ts1 optimized at the B3LYP/6-311++G(d,p)

level in the gas phase and the B3LYP/6-311++G(d,p)//CPCM HF/6-31+G(d) level in the solutions for the alanine and proline dipeptides, it is found that the bond length r(C′-N) of the AcAla peptide bond is longer by about 0.007 Å than that of the Ac-Pro peptide bond. In a recent work, we estimated the degree of nonplanarity (i.e., the pyramidal sp3 character) of the imide nitrogen by the quantity δ defined as S - 360°, where S is the sum of three bond angles (i.e., C′-N-Cγ, C′-N-CR, and CγN-CR for the prolyl ring) around the nitrogen.100 As the quantity δ becomes more negative, the degree of nonplanarity of the nitrogen increases more. The calculated values of the quantity δ are -33° and -26° for the alanine and proline residues in the gas phase, respectively, which are similar to the experimental values of -37° and -27° for ammonia and trimethylamine, respectively.107 The corresponding computed values are -30° and -23° in chloroform and water, respectively. Thus, the solvation appears to drive the nonplanarity of the nitrogen to decrease by about 3°. From the kinetic and spectroscopic studies on proline-containing peptide with and without the C-terminal N-H group, it was suggested that the intramolecular hydrogen bond between the prolyl nitrogen and the following amide N-H group could stabilize the transition state and accelerate the prolyl cis-trans isomerization.108 The calculated distances d(N‚‚‚HNNHMe) between the nitrogen and the following hydrogen of the NHMe group for the transition state ts1 in the gas phase, chloroform, and water are 2.21, 2.33, and 2.39 Å for the alanine dipeptide, respectively, and 2.17, 2.28, and 2.32 Å for the proline dipeptide, respectively. For both the dipeptides, the distance d(N‚‚‚H-NNHMe) becomes longer as the solvent polarity increases. The distance d(N‚‚‚H-NNHMe) for the alanine dipeptide is somewhat longer than that for the proline dipeptide in the gas phase and the solutions. From these analyses of three kinds of geometrical parameters, the pertinent distance d(N‚‚‚HNNHMe) can successfully describe the increase in the rotational barriers for the non-prolyl and prolyl trans-cis isomerization as the solvent polarity increases and can describe barriers for the non-prolyl residue that are higher than that for the prolyl residue, as seen in experimental and calculated results. Conclusions For the alanine and proline dipeptides as the models for the non-prolyl and prolyl residues, the populations of the conforma-

Conformational Preferences of Non-Pro and Pro Residues tion tC with an intramolecular C7 hydrogen bond significantly decrease, and those of the polyproline II-like conformation tF and the R-helical conformation tA increase with the increase of solvent polarity, which is in good agreement with the results from CD and NMR experiments. The calculated average vicinal coupling constants 3JHNR for the alanine dipeptide in chloroform and water are reasonably consistent with the experimental values, although the calculated value in water appears to be a little overestimated due to the preferred stability of the conformation tE in water. In the case of the proline dipeptide, the trans/up conformations become most preferred in water, which is ascribed to the increase in the populations for the polyproline II-like conformation tFu. The stability in the order trans/up > trans/down > cis/up > cis/down computed in water is reasonably consistent with that from X-ray structures of proteins. For both the alanine and proline dipeptides, the relative free energy of the cis conformer to the trans conformer decreases and the rotational barrier to the cis-trans isomerization increases as the solvent polarity increases. It is found that the cis-trans isomerization proceeds in common through only the clockwise rotation with ω′ ≈ +120° about the non-prolyl and prolyl peptide bonds in the gas phase and the solutions. The pertinent distance d(N‚‚‚H-NNHMe) can successfully describe the increase in the rotational barriers for the non-prolyl and prolyl transcis isomerization as the solvent polarity increases and the higher barriers for the non-prolyl residue than those for the prolyl residue, as seen in experimental and calculated results. By analysis of the contributions to rotational barriers, the cis-trans isomerization for the non-prolyl and prolyl peptide bonds is proven to be entirely enthalpy driven in the gas phase and in the solutions, to which the electronic energies have considerably contributed. The calculated cis populations and rotational barriers to the cis-trans isomerization for both the dipeptides in chloroform and/or water accord with the experimental values. Supporting Information Available: Backbone torsion angles, endocyclic torsion angles, and puckering amplitudes of Ac-Pro-NHMe optimized at the B3LYP/6-311++G(d,p) level of theory in the gas phase and at the B3LYP/6-311++G(d,p)// CPCM HF/6-31+G(d) level of theory in chloroform and water. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Stewart, D. E.; Sarkar, A.; Wampler, J. E. J. Mol. Biol. 1990, 214, 253. (2) Jabs, A.; Weiss, M. S.; Hilgenfeld, R. J. Mol. Biol. 1999, 286, 291. (3) Pal, D.; Chakrabarti, P. J. Mol. Biol. 1999, 294, 271. (4) Zimmerman, S. S.; Scheraga, H. A. Macromolecules 1976, 9, 408. (5) Schmid, F. X.; Mayr, L. M.; Mu¨cke, M.; Scho¨nbrunner, E. R. AdV. Protein Chem. 1993, 44, 25. (6) Balbach, J.; Schmid, F. X. In Mechanisms of Protein Folding, 2nd ed.; Pain, R. H., Ed.; Oxford University Press: New York, 2000; Chapter 8. (7) Wedemeyer, W. J.; Welker, E.; Scheraga, H. A. Biochemistry 2002, 41, 14637. (8) Dugave, C.; Demange, L. Chem. ReV. 2003, 103, 2475. (9) Fischer, G. Angew. Chem., Int. Ed. Engl. 1994, 33, 1415. (10) Lu, K. P.; Liou, Y.-C.; Zhou, X. Z. Trends Cell Biol. 2002, 12, 164. (11) Li, H.; Oberhauser, A. F.; Redick, S. D.; Carrion-Vazquez, M.; Erickson, H. P.; Fernandez, J. M. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 10682. (12) Tchaicheeyan, O. FASEB J. 2004, 18, 783. (13) Lummis, S. C. R.; Beene, D. L.; Lee, L. W.; Lester, H. A.; Broadhurst, R. W.; Dougherty, D. A. Nature 2005, 438, 248. (14) Schultz, D. A.; Schmid, F. X.; Baldwin, R. L. Protein Sci. 1992, 1, 917.

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