Conformational Preferences of Proline Oligopeptides - The Journal of

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J. Phys. Chem. B 2006, 110, 17645-17655

17645

Conformational Preferences of Proline Oligopeptides Young Kee Kang,*,† Jong Suk Jhon,† and Hae Sook Park‡ Department of Chemistry and Basic Science Research Institute, Chungbuk National UniVersity, Cheongju, Chungbuk 361-763, South Korea, and Department of Radiotechnology, Cheju-halla College, Cheju 690-708, South Korea ReceiVed: May 16, 2006; In Final Form: July 10, 2006

A conformational study on the terminally blocked proline oligopeptides, Ac-(Pro)n-NMe2 (n ) 2-5), is carried out using the ab initio Hartree-Fock level of theory with the self-consistent reaction field method in the gas phase and in solutions (chloroform, 1-propanol, and water) to explore the preference and transition between polyproline II (PPII) and polyproline I (PPI) conformations depending on the chain length, the puckering, and the solvent. The mean differences in the free energy per proline of the up-puckered conformations relative to the down-puckered conformations for both diproline and triproline increases for the PPII-like conformations and decreases for the PPI-like conformations as the solvent polarity increases. These calculated results indicate that the PPII-like structures have preferentially all-down puckerings in solutions, whereas the PPI-like structures have partially mixed puckerings. The free energy difference per proline residue between the PPII- and PPI-like structures decreases as the proline chain becomes longer in the gas phase but increases as the proline chain becomes longer in solutions and the solvent polarity increases. In particular, our calculated results indicate that each of the proline oligopeptides can exist as an ensemble of conformations with the trans and cis peptide bonds in solutions, although the PPII-like structure with all-trans peptide bonds is dominantly preferred, which is reasonably consistent with the previously observed results. In diproline Ac-(Pro)2-NMe2, the rotational barrier to the cis-to-trans isomerization for the first prolyl peptide bond increases as the solvent polarity increases, whereas the rotational barrier for the second prolyl peptide bond does not show the monotonic increase as the solvent polarity increases. When the rotational barriers for these two prolyl peptide bonds were compared, it could be deduced that the conformational transition from PPI with the cis peptide bond to PPII with the trans peptide bond is initiated at the C-terminus and proceeds to the N-terminus in water. This is consistent with the results from NMR experiments on polyproline in D2O but opposite to the results from enzymatic hydrolysis kinetics experiments on polyproline.

Introduction Proline (Pro) is unique because the side chain is bonded to the amide nitrogen and the N-CR rotation is restrained at about -60°. The prolyl five-membered ring may adopt two distinct puckered conformations,1 both frequently encountered in X-ray structures of peptides2-4 and proteins.5-7 Down- and uppuckered conformations are defined as those in which the Cγ atom and the CdO group of the Pro residue lie on the same and opposite sides, respectively, of the plane defined by the three atoms Cδ, N, and CR (Figure 1). The Pro residue has a relatively high intrinsic probability (5.2%) of having a cis peptide bond preceding proline as compared with other amino acids (0.03%) from an analysis of a nonredundant set of 571 X-ray protein structures.8 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.9-12 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. In addition, the prolyl cis-trans isomerization was suggested to be involved in the multiple * Author to whom correspondence should be addressed. Phone: +8243-261-2285. Fax: +82-43-273-8328. E-mail: [email protected]. † Chungbuk National University. ‡ Cheju-halla College.

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

elastic conformations of cardiac PEVK,13 in the chemomechanical coupling within actomyosin to propel myosin’s lever-arm swing,14 and in providing the switch to open and close the pore of a neurotransmitter-gated ion channel.15 Poly-L-proline can form two regular conformations known as poly(Pro) II (PPII) and poly(Pro) I (PPI) in the solid state and in solution. Although both conformations have similar values of the backbone torsion angles φ and ψ, i.e., (φ, ψ) ) (-76°, 145°) and (-83°, 158°) for PPII and PPI conformations, respectively, PPII is a left-handed helix with all trans peptide bonds having 3.00 residues per turn and a unit height of 3.12 Å, whereas PPI is a right-handed helix with all cis peptide bonds having 3.33 residues per turn and a unit height of 1.90 Å.16 The PPII conformation predominates in water, organic acids, and benzyl alcohol, while the PPI conformation is stable in

10.1021/jp0629792 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/11/2006

17646 J. Phys. Chem. B, Vol. 110, No. 35, 2006 pyridine and aliphatic alcohols.17,18 In aqueous or acid solutions, PPI converts to PPII in a few hours. The NMR19 and Raman optical activity20 experiments implied that the prolyl ring of PPII has two puckered conformations in water. In the solid state, the prolyl rings of PPII and PPI helices were also confirmed to have two puckerings from 13C NMR measurements.21,22 From the measurement of considerable changes of the specific optical rotation of polyproline in a narrow interval of solvent compositions, it was suggested that the reversible PPII-to-PPI and PPI-to-PPII transitions are cooperative; i.e., the equilibrium and rate constants for the transitions depend on the conformations of neighboring residues.17,18,23 From the NMR experiments on polyproline in D2O, it was suggested that the conversion of PPI into PPII begins at the carboxyl end of the chain and proceeds in a stepwise fashion down the chain.24 However, the enzymatic hydrolysis kinetics experiments on polyproline showed that the PPI-to-PPII transition in water begins at nearly the same rate step by step from the N-terminus rather than the C-terminus.25,26 On the basis of the CR proton resonance from NMR experiments on polyproline in D2O, it was suggested that the polyproline has about 2-3% cis residues in the chain in water.27 In particular, the Fourier transform infrared and electronic/vibrational circular dichroism studies on the transition of PPI to PPII in D2O demonstrated the presence of an intermediate during the transition, which has a distribution of cis and trans linkages in the chain.28 This result contrasts with the cooperative and sequential conformational transition from PPI to PPII in water.24-26 Considerable spectroscopic studies have been carried out on the proline oligopeptides to monitor the transition between PPI and PPII depending on the chain length and the solvent.29-38 When the chain is shorter than a pentapeptide, it was found that these oligopeptides contained nearly random distributions of cis and trans peptide bonds in water. When the chain is equal to or longer than a pentapeptide, the population of PPII in water increases as the chain length becomes longer. Recent circular dichroism experiments on proline oligopetides composed of 13, 6, and 4 proline residues showed that the dominant conformation of the tetraproline is PPII in methanol, 1-propanol, and water and that the propensity to form the PPI conformation increases as the peptide chain becomes longer in alcohols.38 In the solid state, the diproline,39-41 triproline,42 and tetraproline43 oligopeptides preferentially have the down-puckered PPII structures, followed by the up-puckered PPII ones. The conformations of proline oligopeptides have been theoretically studied using empirical force fields as models for polyproline.44-50 These studies have been mostly focused on the preferred conformations of diproline and their relative stabilities in the gas phase. Some works were concerned about the conformational preferences for diproline to tetraproline or pentaproline.44-46 There are only a limited number of works reported to date that studied the conformational preferences of proline oligopeptides depending on the trans/cis peptide bonds and the puckering in the gas phase.44,46,47 Recently, the prolyl cis-trans isomerization of HCO-(Pro)2-NH2 was studied at the HF/6-31+G(d) level in the gas phase, and it was identified that the transition state structure has a torsion angle of ω′ ) 113.8° and an energy of 16.4 kcal/mol for the trans-to-cis isomerization of the peptide bond between the two proline residues.51 The energy difference between PPII- and PPI-like structures of Ac-(Pro)9-NHMe was computed to be 13.8 kcal/ mol at the HF/6-31G level in the gas phase and 3.3 kcal/mol at the B3LYP/6-31G(d) level using the conductor-like screening model (COSMO) in water.52 The puckerings of PPII-like

Kang et al. structures of HCO-(Pro)3-NH2 were explored at the B3LYP/ 6-31G(d,p) level using the COSMO in water, and the differences in energies for down- and up-puckered conformations are calculated to be about 0.6 kcal/mol, although the conformation with all-down puckerings is the most preferred.20 In particular, Zhong and Carlson53 studied the conformational preferences of diproline Ac-(Pro)2-OMe and hexaproline Ac-(Pro)6-OMe depending on the puckerings at the HF/6-31G(d) and B3LYP/ 6-31G(d) levels in the gas phase and reported that the all-downpuckered structures are more preferred than other structures with mixed or all-up puckerings for both the PPII- and the PPI-like conformations. It was also known that the PPI-like structure of the hexaproline in solutions becomes more preferred than the PPII-like structure as the solvent polarity increases, where the solvation free energies were calculated using the isodensity surface-polarized continuum model (IPCM)54 at the HF/6-31G(d) level. Despite the several theoretical studies previously reported, the conformational preferences of the proline oligopeptides observed in solution have been not well described yet. We report here the results on the proline oligopeptides calculated using the ab initio HF level of theory with the self-consistent reaction field (SCRF) method in the gas phase and in solutions to explore the preference and transition between PPII and PPI conformations depending on the chain length, the puckering, and the solvent. Computational Methods Chemical structures and torsional parameters for the proline residue are defined in Figure 1. All ab initio HF and density functional calculations were carried out using the Gaussian 9855 and Gaussian 0356 packages. In this work, each backbone conformation is represented by a capital letter depending on its values of φ and ψ for the backbone.57 Conformation F is defined by the backbone torsion angles φ and ψ in the ranges of -110° < φ < -40° and 130° < ψ < 180° or -180° < ψ < -140°. Trans and cis conformations for the Ac-Pro and Pro-Pro peptide bonds are denoted by “t” and “c”, respectively. Downand up-puckered conformations of each proline residue are defined as those in 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 subscripts “d” and “u”, respectively. Usually, the down- and up-puckered conformations have positive and negative values of the endocyclic torsion angle χ1, respectively. Therefore, the conformations tFd and tFu correspond to the PPII structures with the down and up puckerings, respectively, whereas the conformations cFd and cFu correspond to the PPI structures with the down and up puckerings, respectively. The values of the backbone torsion angles ω′, φ, and ψ for the local minima tFd, tFu, cFd, and cFu of Ac-Pro-NMe2 optimized at the HF/6-31+G(d) level58,59 were used as starting points for the empirical energy optimization of the proline oligopetides Ac-(Pro)n-NMe2 (n ) 2-5) using the ECEPP/3 force field.60 These minimized conformations from empirical energy calculations were used as initial structures for the optimization of Ac-(Pro)n-NMe2 (n ) 2-5) at the HF/631+G(d) level. The observed conformational preferences (especially, the cis-trans isomerization) for amides, proline dipeptide, and its derivatives have been reasonably described at the HF/6-31+G(d) level.58,59,61-69 However, the local minima and transition state ts1 of Ac-Pro-NMe2 optimized at the HF/ 6-31+G(d) level were reoptimized at the hybrid density

Conformational Preferences of Pro Peptides functional B3LYP/6-31+G(d) and B3LYP/6-311++G(d,p) levels to determine how the electron correlation affects the conformations and the relative stabilities of the prolyl residue. Because each proline residue can have four feasible conformations depending on the preceding peptide bond and the prolyl puckering, the 16 and 64 local minima optimized using the ECEPP/3 force field were used as starting points for the optimization of Ac-(Pro)2-NMe2 and Ac-(Pro)3-NMe2, respectively, at the HF/6-31+G(d) level. For Ac-(Pro)4-NMe2 and Ac-(Pro)5-NMe2, the 8 and 10 local minima generated from the ECEPP/3 force field depending on the preceding peptide bonds, respectively, were employed as initial structures for the optimization at the HF/6-31+G(d) level, in which all prolyl rings are taken to be down-puckered. This assumption is based on the calculated results for Ac-(Pro)3-NMe2, as described below. The cis-trans isomerization of the diproline Ac-(Pro)2NMe2 is explored as a model for that of the polyproline. The two conformations optimized adiabatically from the conformations cFdtFd and cFdcFd with ωi-1 ) +120.8°, φi ) -73.7°, and φi ) -41.8°, taken from the transition state ts1 (also known as the syn/exo structure in ref 70) of Ac-Pro-NMe2,58 were used as initial structures to locate the transition states ts1 and ts2, respectively. The ts1 is the transition state for the cistrans isomerization of the Ac-Pro peptide bond for the conformations tFdtFd and cFdtFd, whereas the ts2 is that of the Pro-Pro peptide bond for the conformations cFdtFd and cFdcFd. We employed the conductor-like polarizable continuum model (CPCM) SCRF method,71 implemented in the Gaussian 03 package,56 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.72 The solvation free energy is the sum of the electrostatic free energy and the nonelectrostatic energy terms.72 The latter is composed of the cavitation, dispersion, and repulsion energy terms. For CPCM-UAKS calculations, the default mean areas of 0.2 Å2 for tesserae were used. Solvation free energies were calculated for all local minima, and transition states were optimized in the gas phase. The solvents considered here are chloroform, 1-propanol, and water, whose dielectric constants are 4.9, 20.1, and 78.4 at 25 °C, respectively. Recently, the CPCM-UAKS calculations for a number of neutral and charged organic molecules at the HF/6-31+G(d)//HF/6-31+G(d) level provided hydration free energies in agreement with available experimental data.73 In particular, the experimental populations of the backbone and cis conformations for Ac-Pro-NMe258 and AcPro-NHMe66 in chloroform and water were satisfactorily reproduced using the single-point CPCM HF/6-31+G(d) solvation free energies for the conformations optimized at the HF/ 6-31+G(d) level in the gas phase. However, the local minima and transition state ts1 of Ac-Pro-NMe2 optimized at the HF/ 6-31+G(d) level in the gas phase were reoptimized at the CPCM HF/6-31+G(d) level in chloroform and water to determine the changes in the conformations and the relative stabilities of the prolyl residue by the geometry relaxations in solutions. Vibrational frequencies were calculated for all stationary points at the HF/6-31+G(d) level in the gas phase and used to compute enthalpies and Gibbs free energies with a scale factor 0.8961 at 25 °C and 1 atm.74 A scale factor 0.89 was chosen to reproduce experimental frequencies for the amide I band of N-methylacetamide in Ar and N2 matrixes.61 Each transition state was confirmed by checking whether it has one imaginary

J. Phys. Chem. B, Vol. 110, No. 35, 2006 17647 frequency after frequency calculations at the HF level. The relative total free energy (∆Gtot) for each conformation in solution was computed by the sum of the relative conformational free energy (∆G) in the gas phase and the relative solvation free energy (∆∆Gs). Results and Discussion Conformational Preferences in the Gas Phase. Diproline. Table 1 lists the backbone torsion angles and thermodynamic quantities for the local minima and transition states of the proline and diproline peptides optimized at the HF/6-31+G(d) level of theory in the gas phase. The corresponding endocyclic torsion angles of the prolyl residues are listed in Table S1 of the Supporting Information. The backbone torsion angles and relative electronic energies for Ac-Pro-NMe2 were taken from ref 58. The conformational stabilities of Ac-Pro-NMe2 in the gas phase are calculated to be in the order td > tu > cd > cu by the relative electronic energies (∆Ee) and the relative free energies (∆G). The relative instabilities of the cis conformation to the trans conformation are 2.86 and 2.83 kcal/mol in ∆G for both the down- and the up-puckered conformations, respectively. The backbone torsion angles, endocyclic torsion angles, and thermodynamic quantities for the local minima and transition state ts1 of Ac-Pro-NMe2 optimized at the B3LYP/6-31+G(d) and B3LYP/6-311++G(d,p) levels are listed in Table S2 of the Supporting Information. The backbone torsion angles φ and ψ at these two B3LYP levels move by approximately -3° and -6°, respectively, from those at the HF/6-31+G(d) level. The relative electronic energies and relative free energies decrease by 0.1-0.8 and 0.7-1.7 kcal/mol, respectively, at these two B3LYP levels. However, the conformational stabilities of the local minima for Ac-Pro-NMe2 at these two B3LYP levels show the same order as found at the HF/6-31+G(d) level. In particular, the rotational barriers to the trans-to-cis isomerization of the Ac-Pro peptide bond are calculated to be 21.45 and 21.26 kcal/mol at these two B3LYP levels, respectively, which are higher by 0.45 and 0.26 kcal/mol, respectively, than that at the HF/6-31+G(d) level. These calculated results indicate that the electron correlation estimated at the B3LYP levels even with larger basis sets does not lead to a remarkable change in the conformations and their relative stabilities of the local minima and transition state for Ac-Pro-NMe2. In diproline Ac-(Pro)2-NMe2, the 12 local minima were identified from the 16 initial conformations. The four tc conformations with the trans and cis peptide bonds for the first and second prolines, respectively, disappeared after optimizations. The conformations with all-down puckerings appear to be more preferred by ∆Ee and ∆G than the conformations with the mixed puckerings or all-up puckerings for all conformations with the tt, ct, and cc peptide bonds. The conformational stability is calculated by ∆Ee and ∆G to be in the order tt > ct > cc for all feasible puckerings, which indicates the preference for the PPII-like structure over the PPI-like one in the gas phase. The mean relative instabilities of the cis conformation to the trans conformation are 2.99 kcal/mol in ∆G for the conformations tt and ct and 3.74 kcal/mol in ∆G for the conformations ct and cc. This indicates that the relative stability of the cis conformation is likely to depend on the configuration of the adjacent peptide bonds. From ∆G of conformation cc to conformation tt, the mean instability of the PPI structure relative to the PPII structure can be estimated as 3.37 kcal/mol per proline residue. The prolyl puckerings are found by ∆G to be in the orders dd > ud > du > uu in the PPII-like structures and dd > du > ud > uu in the PPI-like ones.

17648 J. Phys. Chem. B, Vol. 110, No. 35, 2006

Kang et al.

TABLE 1: Backbone Torsion Angles and Thermodynamic Quantities of Local Minima and Transition States for Ac-Pro-NMe2 and Ac-(Pro)2-NMe2 Optimized at the HF/6-31+G(d) Level backbonea Ac conf.c

ω0

Pro1 φ1

ψ1

thermodynamic quantitiesb

Pro2 ω1

ψ2

φ2

ω2

∆Eed

∆He

∆Ge

0.00 0.52 2.95 4.02 20.09

0.00 0.49 2.78 3.85 19.09

0.00 0.91 2.86 3.74 21.00

0.00 0.40 0.91 1.11 2.77 3.47 3.94 4.49 6.31 7.38 7.69 8.75 20.43 24.62

0.00 0.45 0.91 1.14 2.70 3.39 3.86 4.41 6.07 7.15 7.41 8.50 19.55 23.66

0.00 0.61 0.39 1.58 2.82 3.62 3.70 4.43 6.38 7.44 7.29 8.39 21.59 25.73

f

td tu cd cu ts1

176.8 175.7 -2.6 -5.7 120.8

-70.0 -61.0 -75.4 -60.8 -73.7

142.1 137.6 166.4 160.6 -41.8

-178.5 -178.1 -176.6 -177.7 -178.1

tdtd tdtu tutd tutu cdtd cdtu cutd cutu cdcd cucd cdcu cucu ts1 ts2

176.4 178.0 175.7 176.7 -1.5 -4.2 -5.6 -9.8 -3.2 -7.3 -3.6 -6.3 120.9 1.8

-71.1 -70.7 -61.6 -61.2 -75.6 -72.9 -60.6 -61.1 -76.2 -57.0 -76.4 -58.2 -78.3 -78.7

149.6 138.6 141.1 134.3 156.6 162.9 154.2 165.4 164.8 162.8 169.4 165.6 -55.5 154.0

175.3 171.7 177.9 173.6 172.4 168.4 173.1 169.7 -6.7 -6.3 -13.3 -9.1 178.9 113.1

Ac-Pro-NMe2

Ac-(Pro)2-NMe2 -74.1 154.3 -62.1 140.9 -76.5 151.4 -63.6 139.6 -70.2 153.3 -58.6 141.1 -70.2 151.7 -59.1 140.4 -76.1 166.6 -75.7 166.6 -65.0 163.4 -66.5 162.3 -68.4 143.6 -82.3 -48.4

-176.1 -178.4 -176.7 -178.6 -176.4 -178.4 -176.6 -178.3 -177.1 -177.0 -178.3 -178.1 -178.5 -175.3

a Units in degrees. b Units in kcal/mol. c Trans and cis prolyl peptide bonds are represented by “t” and “c”, respectively. Down and up puckerings are denoted by subscripts “d” and “u”, respectively. The conformations tFd, tFu, cFd, and cFu are represented by td, tu, cd, and cu, respectively. d Relative electronic energies. e ∆H and ∆G are relative changes of enthalpy and Gibbs free energy calculated at 25 °C, respectively. f Backbone torsion angles and relative electronic energies were taken from ref 58.

These calculated conformational preferences generally accord with those of Ac-(Pro)2-OMe calculated using the ECEPP force field,46 except for that the tc conformations are no longer local minima at the HF/6-31+G(d) level, as mentioned above. In addition, our calculated preferences for PPII- and PPI-like structures at the HF/6-31+G(d) level are consistent with those of Ac-(Pro)2-OMe at the HF/6-31G(d) level,53 except the relative energies of the PPI-like structures are increased by about 1 kcal/mol at the HF/6-31+G(d) level. The mean values of the backbone torsion angles (φ, ψ) for the diproline are estimated to be (-66°, 141°) for the PPII-like structures and (-67°, 163°) for the PPI-like structures at the first proline residue, whereas the corresponding values are (-67°, 147°) and (-71°, 165°) at the second proline residue, respectively. These values are similar to those of Ac-ProNMe2, except that the value of ψ at the first proline residue becomes larger by about 7°. The calculated mean values of (φ, ψ) for the diproline with the trans peptide bonds at the HF/631+G(d) level are consistent with the values from X-ray diffraction for t-Boc-(Pro)2-OH39,41 and t-Boc-(Pro)2-NHMe.40 Triproline. Table 2 lists the backbone torsion angles and thermodynamic quantities for the local minima of the triproline peptide Ac-(Pro)3-NMe2 optimized at the HF/6-31+G(d) level in the gas phase. The corresponding endocyclic torsion angles of the prolyl residues are listed in Table S1 of the Supporting Information. The 54 local minima were identified from the 64 initial conformations, which were generated by all possible combinations of the peptide bonds and puckerings. Several conformations with a specific combination of the trans and cis peptide bonds are found not to be local minima depending on the puckerings, except for the conformations with the ddd and udd puckerings. In triproline, the conformations with all-down puckerings are found by ∆Ee and ∆G to be more preferred than the conformations with the mixed puckerings or all-up puckerings for all conformations generated by the combination of the trans and

cis peptide bonds, although the dud puckering is more favorable by about 0.2 kcal/mol in ∆G than the ddd puckering for the ttt (i.e., PPII-like) conformation. The conformational stability in the order ttt > ctt > cct > ccc calculated by ∆Ee and ∆G for all feasible puckerings indicates that the PPII-like structure is more preferred than the PPI-like one in the gas phase, as found for the diproline. From ∆G of conformation ccc to conformation ttt, the PPI structure is known to be less stable by 2.95 kcal/ mol per proline residue than the PPII structure, which is similar to that of the diproline, as discussed above. The optimized values of the backbone torsion angles (φ, ψ) for each proline of the triproline are similar to those of the diproline, except that the values of ψ2 at the second proline residue for the conformations ttc and ctc are calculated to be 113°-123°. The calculated mean values of (φ, ψ) ) (-73°, 151°) for the first two proline residues of the triproline in the PPII-like structure at the HF/6-31+G(d) level are consistent with the values of (-79°, 147°) from X-ray diffraction for tertamyloxycarbonyl-(Pro)3-OH.42 In addition, for the all-downpuckered conformations of Ac-(Pro)3-NMe2, the conformational stability is calculated to be by ∆Ee in the order ttt > ctt > ttc ≈ tct > cct > ctc > ccc > tcc at the HF/6-31+G(d) level, whereas it was reported to be ttt > ttc > tct > ctt > cct for Ac-(Pro)3-OMe from the conformational energy calculations using the ECEPP force field.46 Tetraproline and Pentaproline. The backbone torsion angles and thermodynamic quantities for the local minima of tetraproline Ac-(Pro)4-NMe2 and pentaproline Ac-(Pro)5-NMe2 optimized at the HF/6-31+G(d) level in the gas phase are listed in Tables 3 and 4, respectively. The corresponding endocyclic torsion angles of the prolyl residues are listed in Table S1 of the Supporting Information. Because the conformations with all-down puckerings are found by ∆Ee and ∆G to be more preferred than the conformations with the mixed puckerings or all-up puckerings for diproline and triproline, as described above,

Conformational Preferences of Pro Peptides

J. Phys. Chem. B, Vol. 110, No. 35, 2006 17649

TABLE 2: Backbone Torsion Angles and Thermodynamic Quantities of Ac-(Pro)3-NMe2 Optimized at the HF/6-31+G(d) Level backbonea Ac

Pro1

Pro2

thermodynamic quantitiesb

Pro3

conf.c

ω0

φ1

ψ1

ω1

φ2

ψ2

ω2

φ3

ψ3

ω3

∆Eed

∆He

∆Ge

tdtdtd cdtdtd tdtdcd tdcdtd cdcdtd cdtdcd cdcdcd tdcdcd tdtdtu cdtdtu tdcdtu cdcdtu cdcdcu tdcdcu tdtutd cdtutd tdtucd tdcutd cdcutd cdcucd tdcucd tutdtd cutdtd tutdcd tucdtd cucdtd cutdcd cucdcd tucdcd tdtutu cdtutu tdcutu cdcutu cdcucu tutdtu cutdtu tucdtu cucdtu cucdcu tucdcu tututd cututd tutucd tucutd cucutd cucucd tucucd tututu cututu cutucu cucutu tucutu cucucu tucucu

176.2 -1.7 177.2 177.7 -2.9 -4.0 -1.4 176.0 176.4 -1.7 178.1 -3.0 -1.3 175.7 177.8 -2.6 178.0 178.0 -3.5 -2.0 176.3 175.5 -5.7 177.1 175.0 -4.7 -7.1 -4.1 174.0 178.0 -2.7 178.2 -3.5 -1.8 176.0 -5.6 175.3 -4.9 -4.2 173.5 176.5 -7.2 177.3 174.9 -5.4 -4.8 173.9 176.7 -7.2 -7.2 -5.8 174.9 -4.7 173.4

-71.3 -75.4 -70.9 -84.6 -76.0 -74.3 -80.6 -76.2 -70.9 -75.4 -85.5 -76.1 -80.7 -76.1 -70.8 -75.1 -69.5 -88.0 -76.3 -80.4 -79.5 -61.8 -60.2 -60.6 -71.8 -58.0 -59.2 -61.0 -66.5 -70.5 -75.3 -88.8 -76.4 -80.6 -61.2 -60.2 -72.3 -58.0 -62.1 -66.2 -61.3 -62.2 -60.1 -74.2 -57.9 -60.2 -68.7 -60.9 -62.2 -59.1 -58.1 -74.5 -61.5 -68.0

150.1 157.1 153.5 151.2 162.8 166.5 164.5 162.0 149.9 157.2 148.6 163.9 164.8 163.0 138.2 163.3 142.9 155.0 168.2 169.7 165.2 141.6 154.5 141.3 150.3 159.2 161.8 162.1 159.3 138.2 163.5 153.7 169.7 170.2 140.8 154.5 148.5 160.3 162.8 160.5 134.1 164.4 137.8 153.9 164.1 166.9 162.5 134.4 164.2 161.8 165.7 153.1 167.7 163.8

175.9 172.8 176.7 -15.2 -5.5 175.3 -9.2 -6.5 177.2 173.5 -16.3 -6.4 -9.8 -6.6 171.8 170.5 170.8 -21.3 -13.3 -16.9 -14.7 178.3 173.6 177.5 -14.9 -2.6 173.7 -5.5 -4.7 172.7 171.4 -22.3 -14.0 -17.8 180.0 174.4 -16.1 -3.2 -6.4 -4.1 173.9 170.9 172.2 -20.5 -9.1 -13.0 -12.0 174.4 171.5 173.7 -9.8 -21.3 -14.4 -11.1

-74.0 -70.3 -90.5 -75.9 -76.3 -90.9 -76.1 -80.1 -73.6 -70.1 -77.1 -76.2 -76.7 -80.9 -63.1 -61.1 -71.0 -65.8 -65.5 -65.2 -69.6 -76.6 -70.4 -97.6 -79.1 -77.6 -94.7 -77.0 -82.5 -62.2 -60.0 -66.1 -65.8 -65.5 -76.3 -70.1 -80.2 -77.8 -77.6 -84.2 -64.3 -60.9 -90.1 -70.0 -66.5 -65.4 -73.4 -63.6 -59.9 -94.7 -67.5 -70.7 -66.2 -75.7

152.1 152.3 123.3 141.8 156.7 119.6 165.5 156.6 146.1 149.2 144.2 162.9 170.8 161.9 144.9 146.6 137.2 140.2 156.9 165.2 154.8 151.2 151.7 113.4 139.5 157.0 113.3 165.7 156.2 136.9 139.4 142.7 166.2 170.4 140.3 146.8 141.7 162.9 170.8 162.4 143.4 145.7 118.9 136.7 155.8 164.7 154.6 135.6 139.0 113.3 165.3 138.9 170.0 161.5

174.7 174.1 -18.0 -177.8 171.5 -18.8 -7.9 6.0 170.4 169.7 177.1 169.8 -15.7 -0.8 177.2 175.7 -20.4 -177.0 171.9 -7.4 8.3 174.9 174.2 -13.9 -178.5 171.7 -16.2 -6.6 6.2 172.7 172.1 178.5 170.2 -13.8 171.2 169.8 176.3 170.0 -14.2 -2.5 178.2 176.1 -16.1 -176.9 172.4 -5.7 8.7 173.0 172.3 -16.3 170.6 178.6 -12.7 0.7

-73.7 -73.8 -84.8 -72.0 -69.9 -83.7 -74.2 -81.3 -60.8 -60.6 -63.0 -59.6 -63.8 -70.5 -75.4 -75.3 -84.5 -71.9 -69.7 -74.8 -82.5 -73.6 -73.9 -86.0 -71.2 -69.9 -84.0 -74.7 -81.9 -63.3 -62.7 -62.9 -59.7 -64.5 -61.5 -60.9 -62.2 -59.7 -64.0 -71.5 -75.3 -75.6 -86.9 -71.1 -69.8 -75.6 -83.3 -63.5 -62.8 -84.0 -59.9 -62.5 -64.8 -73.1

154.5 156.4 164.9 142.7 155.2 168.6 171.4 168.9 140.7 142.9 139.1 143.7 168.4 165.6 148.9 155.4 148.1 141.7 154.7 170.8 168.4 153.8 156.3 170.8 142.0 155.0 172.1 171.5 168.7 139.2 141.5 138.5 143.3 167.2 140.2 142.8 138.7 143.7 167.7 165.8 143.3 155.3 167.2 140.9 154.3 170.7 168.4 138.9 141.5 172.1 143.4 138.1 166.8 165.1

-176.1 -176.0 -176.4 -178.3 -176.2 -176.3 -178.9 -177.8 -178.3 -178.2 -178.1 -178.0 173.0 -179.6 -177.1 -176.1 -176.1 -178.4 -176.3 -178.4 -177.5 -176.1 -176.0 -176.7 -178.5 -176.3 -176.6 -179.4 -178.3 -178.5 -178.4 -177.9 -177.8 173.1 -178.4 -178.2 -178.2 -177.9 172.7 172.1 -178.6 -176.1 -176.2 -178.6 -176.3 -178.8 -178.0 -178.5 -178.4 -176.6 -177.7 -178.2 172.9 172.4

0.00 2.44 5.04 5.08 5.65 7.66 8.44 10.83 0.56 3.07 5.96 6.39 9.49 12.50 0.81 3.56 6.41 6.54 7.12 9.86 12.53 0.91 3.60 5.33 6.44 6.69 8.53 9.79 11.97 1.13 4.01 7.44 7.64 10.89 1.37 4.20 7.31 7.44 10.81 13.43 1.53 4.57 6.94 8.01 8.16 11.16 13.76 1.77 5.01 8.53 8.70 8.92 12.18 15.22

0.00 2.37 5.10 5.09 5.47 7.65 8.15 10.47 0.59 3.01 5.97 6.20 9.18 12.13 0.85 3.44 6.46 6.52 6.92 9.52 12.14 0.91 3.51 5.44 6.44 6.52 8.53 9.50 11.61 1.19 3.92 7.42 7.43 10.53 1.42 4.13 7.31 7.26 10.50 13.05 1.57 4.44 7.00 8.00 7.97 10.84 13.38 1.81 4.91 8.53 8.51 8.90 11.83 14.83

0.00 2.62 6.27 4.70 6.02 9.40 8.85 11.16 0.33 2.87 5.52 6.59 10.18 12.35 -0.15 3.23 6.54 6.34 7.10 9.99 12.31 0.62 3.58 7.37 6.04 7.08 10.18 9.57 12.05 1.40 3.89 7.24 7.78 11.17 1.25 3.84 6.84 7.69 11.17 13.62 1.28 3.99 8.39 7.76 8.17 10.93 13.36 2.34 4.65 10.18 8.79 8.60 12.21 14.90

a

Units in degrees. b Units in kcal/mol.

c-e

See footnotes c-e of Table 1.

the all-down-puckered conformations are only considered in analyzing the conformational preferences of tetraproline and pentaproline. In a recent work on Ac-(Pro)6-OMe at the HF/ 6-31G(d) and B3LYP/6-31G(d) levels, the all-down-puckered structures are found to be energetically more stable than other puckered structures for the PPII- and PPI-like conformations.53 The relative stabilities are calculated by ∆Ee and ∆G in the order tttt > cttt > cctt > tttc > ccct > cccc > ttcc > tccc for the tetraproline and ttttt > ctttt > ccttt > ttttc > ccctt > tttcc > cccct > ccccc > ttccc > tcccc for the pentaproline, which indicates that the PPII-like structure is more preferred than the

PPI-like one in the gas phase, as found for diproline and triproline. The possible intermediates during the PPII-to-PPI conformational transition of the pentaproline optimized at the HF/6-31+G(d) level of theory in the gas phase are depicted in Figure 2. In particular, the conformational stability order ttt‚‚ ‚ttt > ctt‚‚‚ttt > cct‚‚‚ttt > ccc‚‚‚ttt > ‚‚‚ > ccc‚‚‚ctt > ccc‚‚ ‚cct > ccc‚‚‚ccc found for triproline to pentaproline indicates that the intermediates for the trans-to-cis or cis-to-trans isomerization of polyproline have the H2N-cis-cis‚‚‚trans-transCOOH configuration in the gas phase. From the previous ECEPP calculations, it was confirmed that the relative stabilities

17650 J. Phys. Chem. B, Vol. 110, No. 35, 2006

Kang et al.

TABLE 3: Backbone Torsion Angles and Thermodynamic Quantities of Ac-(Pro)4-NMe2 with Down Puckerings Optimized at the HF/6-31+G(d) Level backbonea Ac conf.c

Pro1

ω0

Pro2

ψ1

φ1

tttt 176.1 -71.3 cttt -1.6 -75.4 cctt -3.1 -76.0 tttc 176.3 -70.7 ccct -1.0 -81.2 cccc -1.5 -80.5 ttcc 175.3 -73.8 tccc 175.7 -75.8

ω1

φ2

ψ2

150.0 175.7 -74.3 152.4 157.0 172.5 -70.5 152.7 163.0 -5.8 -76.0 157.2 148.2 178.0 -75.3 155.1 164.2 -10.1 -76.3 163.7 163.5 -7.8 -78.3 165.5 151.5 172.1 -78.9 164.0 161.9 -4.4 -82.4 157.0

Pro3 ω2

φ3

ψ3

175.4 174.9 172.1 176.2 -7.4 -8.6 -7.6 4.2

-73.6 -73.6 -69.8 -91.5 -74.2 -74.5 -79.8 -81.5

thermodynamic quantitiesb

Pro4 ω3

ψ4

φ4

ω4

152.1 174.5 -73.5 154.2 -176.1 153.3 173.9 -73.3 155.5 -176.1 153.3 173.5 -73.4 157.3 -176.1 121.6 -17.8 -84.7 166.4 -176.4 160.6 170.2 -69.8 155.7 -176.3 168.2 -9.9 -72.5 173.0 -179.9 158.9 3.4 -79.1 170.6 -178.0 166.5 -8.8 -74.6 170.7 -178.3

∆Eed

∆He

∆Ge

0.00 2.48 5.33 5.45 7.83 10.16 10.50 12.79

0.00 2.40 5.14 5.51 7.58 9.81 10.17 12.37

0.00 2.68 5.84 6.78 8.73 10.56 10.82 13.59

a Units in degrees. b Units in kcal/mol. c See footnote c of Table 1. Because all proline residues have the down puckerings, each conformation is represented by only the trans (t) or cis (c) peptide bonds. d,eSee footnotes d and e of Table 1.

TABLE 4: Backbone Torsion Angles and Thermodynamic Quantities of Ac-(Pro)5-NMe2 with Down Puckerings Optimized at the HF/6-31+G(d) Level backbonea Ac

Pro1

conf.c

ω0

φ1

ttttt ctttt ccttt ttttc ccctt cccct tttcc ccccc ttccc tcccc

176.1 -1.6 -3.0 176.3 -0.5 -1.6 175.6 -1.5 175.1 175.4

-71.3 -75.4 -76.1 -71.0 -81.7 -80.6 -72.2 -80.5 -74.4 -75.9

a

ψ1

Pro2 ω1

φ2

ψ2

150.2 175.5 -74.2 152.4 156.9 172.4 -70.5 152.6 163.0 -5.7 -76.1 157.0 149.2 176.2 -74.3 150.9 164.1 -10.4 -76.4 163.8 163.5 -7.7 -78.3 165.5 152.7 172.8 -74.4 153.7 163.4 -7.8 -78.1 164.6 152.4 171.2 -78.1 163.9 162.4 -4.0 -82.7 156.3

Pro3 ω2

φ3

175.1 174.7 171.8 177.2 -7.8 -8.9 172.4 -6.9 -5.7 5.5

-73.8 -73.8 -69.9 -74.7 -73.7 -74.0 -77.8 -76.3 -82.1 -83.3

ψ3

Pro4 ω3

φ4

ψ4

thermodynamic quantitiesb

Pro5 ω4

φ5

ψ5

ω5

∆Eed

∆He

∆Ge

152.4 175.2 -73.5 152.0 174.5 -73.5 154.6 -176.1 0.00 0.00 0.00 153.5 174.7 -73.3 152.7 174.1 -73.3 154.9 -176.1 2.46 2.38 2.62 153.6 174.4 -73.2 153.9 173.5 -73.1 156.0 -176.1 5.38 5.19 5.85 155.0 176.1 -91.8 121.5 -17.7 -84.7 166.6 -176.5 5.39 5.46 6.71 161.2 170.9 -69.4 153.5 173.2 -73.3 158.2 -176.1 7.36 7.10 8.36 166.4 -8.4 -72.6 161.0 169.9 -70.1 157.3 -176.3 9.73 9.40 11.21 163.8 -6.5 -80.8 159.3 2.4 -79.5 169.4 -178.0 10.36 10.02 10.70 167.9 -10.5 -73.1 168.6 -10.7 -72.0 171.9 176.8 11.50 11.10 12.90 159.2 1.5 -79.2 167.1 -9.2 -74.0 171.2 -178.4 12.56 12.16 13.19 166.7 -9.4 -75.1 168.0 -9.9 -72.9 172.7 180.0 14.60 14.13 15.09

Units in degrees. b Units in kcal/mol. c See footnote c of Table 3.

d,eSee

footnotes d and e of Table 1.

Figure 2. Possible intermediates during the PPII-to-PPI conformational transition of pentaproline Ac-(Pro)5-NMe2 optimized at the HF/6-31+G(d) level of theory in the gas phase. Side and axial views are presented at the top and bottom, respectively. Relative conformational free energies (∆G) in the gas phase are shown below the axial views, units in kcal/mol. The values in parentheses correspond to the relative free energies in water.

are in the orders tttt > tttc > cttt for Ac-(Pro)4-OMe and ttttt > ttttc > ccccc for Ac-(Pro)5-OMe.46 In particular, the relative instability of the conformation with the cis peptide bonds is likely to be affected by the configuration

of the adjacent peptide bonds, which can be deduced from the calculated results that the conformations with the same number of cis peptide bonds have different values of ∆Ee and ∆G, as found for diproline and triproline above. From ∆G of the PPI-

Conformational Preferences of Pro Peptides like conformation to the PPII-like conformation, the PPI-like structure is calculated to be less stable by 2.64 and 2.58 kcal/ mol per proline residue for the tetraproline and pentaproline, respectively, than the PPII-like structure, whereas the corresponding values are 3.37 and 2.95 kcal/mol for diproline and triproline, respectively, as shown above. This indicates that the free energy difference per proline residue between the PPIIand the PPI-like structures decreases as the proline chain becomes longer in the gas phase. This increase in the relative stability of the PPI-like structure was ascribed to the more favorable long-range nonbonded interactions for the compact structures of the PPI-like conformation.47 The optimized mean values of the backbone torsion angles (φ, ψ) for the proline residues are (-73°, 152°) and (-77°, 168°) for the PPII- and PPI-like structures of tetraproline, respectively. The corresponding values are (-73°, 152°) and (-76°, 167°) for pentaproline, respectively. Our optimized values are reasonably consistent with the values of (-76°, 145°) and (-83°, 158°) for the PPII and PPI structures of polyprolines deduced from X-ray diffraction.16 In addition, the calculated mean values for the PPII-like structure of tetraproline are consistent with those from X-ray diffraction for t-Boc-(Pro)4OBzl.43 Our optimized mean values of φ and ψ for the PPIIlike structures of tetraproline and pentaproline are identical with those of Ac-(Pro)6-OMe optimized at the B3LYP/6-31G(d) level.53 In particular, the mean unit heights are computed to be 3.08 and 1.97 Å for the PPII- and PPI-like structures of pentaproline optimized at the HF/6-31+G(d) level, respectively, using the helical axis defined as a least-squares line computed from the Cartesian coordinates of all CR atoms for each conformation,76 which are in good agreement with the values of 3.12 and 1.90 Å for the PPII and PPI structures of polyprolines deduced from X-ray diffraction.16 Conformational Preferences in Solution. Diproline. Table 5 lists the relative solvation free energies and relative total free energies for the local minima and transition states of the proline and diproline peptides in chloroform, 1-propanol, and water. The conformational stabilities of Ac-Pro-NMe2 in chloroform are calculated to be in the order td > tu > cd > cu, the same as in the gas phase. This indicates that the PPII-like conformations with the trans peptide bond prevail over the PPI-like conformations with the cis peptide bond in the gas phase and in chloroform. However, the PPII- and PPI-like conformations become comparable in 1-propanol, and the PPI-like conformations become a little favored in water. To determine the changes in the conformations and the relative stabilities of the prolyl residue by the geometry relaxations in solution, the local minima and transition state ts1 of Ac-Pro-NMe2 optimized at the HF/6-31+G(d) level in the gas phase were reoptimized at the CPCM HF/6-31+G(d) level in chloroform and water. The backbone torsion angles, endocyclic torsion angles, and thermodynamic quantities for the local minima and transition states of Ac-Pro-NMe2 optimized in chloroform and water are listed in Table S3 of the Supporting Information. In chloroform, the optimized conformations of all local minima and transition state ts1 are changed slightly from those in the gas phase, except for the backbone torsion angle ψ for the optimized conformations td and tu with shifts by +16° and +11°, respectively. The geometry relaxations in chloroform result in changes of the relative free energies by -0.4 to +0.4 kcal/mol. However, the conformational stabilities remain the same with and without the geometry relaxations in chloroform. However, the conformations tu and td become more preferred

J. Phys. Chem. B, Vol. 110, No. 35, 2006 17651 TABLE 5: Relative Solvation Free Energies and Relative Total Free Energies of Ac-Pro-NMe2 and Ac-(Pro)2-NMe2 at the CPCM HF/6-31+G(d) Level in Solutiona chloroform conf.b

c

∆∆Gs

∆Gtotd

1-propanol ∆∆Gs

c

∆Gtotd

water ∆∆Gsc

∆Gtotd

e

td tu cd cu ts1

0.00 -0.22 -1.66 -2.04 0.20

Ac-Pro-NMe2 0.00 0.03 0.03 0.69 -0.62 0.29 1.20 -2.86 0.00 1.70 -3.35 0.39 21.20 0.50 21.50

0.21 -0.48 -2.86 -3.37 0.66

0.21 0.43 0.00 0.37 21.66

tdtd tdtu tutd tutu cdtd cdtu cutd cutu cdcd cucd cdcu cucu ts1 ts2

0.00 0.63 -0.36 0.18 -0.69 -0.87 -1.45 -1.44 -1.87 -2.11 -2.01 -2.26 1.28 -0.70

Ac-(Pro)2-NMe2 0.00 0.00 0.00 1.24 1.57 2.18 0.02 -0.17 0.22 1.76 0.66 2.24 2.12 -0.41 2.40 2.75 -0.85 2.77 2.25 -1.90 1.80 2.99 -1.86 2.58 4.51 -0.26 6.12 5.33 -0.78 6.66 5.28 -0.55 6.74 6.13 -1.03 7.37 22.87 3.78 25.38 25.03 -0.24 25.50

0.00 1.64 -0.18 0.69 -0.49 -0.94 -2.03 -1.99 -0.36 -0.89 -0.67 -1.15 3.91 -0.32

0.00 2.25 0.21 2.27 2.32 2.68 1.67 2.45 6.01 6.55 6.62 7.25 25.50 25.41

a Energies in kcal/mol. Solvation free energies were calculated for stationary structures optimized at the HF/6-31+G(d) level in the gas phase using the CPCM-UAKS method of Gaussian 03 (ref 56) with the default area of tesserae equal to 0.2 Å2 if not specified. b See footnote c of Table 1 for the definition of conformational letter codes. c Relative solvation free energy; ∆∆G ) ∆G - ∆G , where ∆G s,i s,i s,0 s,0 ) -4.34, -10.26, and -11.06 kcal/mol for Ac-Pro-NMe2, and ∆Gs,0 ) -4.31, -14.26, and -15.19 kcal/mol for Ac-(Pro)2-NMe2, in chloroform, 1-propanol, and water, respectively. d Relative total free energy computed by the sum of the relative Gibbs free energy (∆G) and relative solvation free energy (∆∆Gs). e Conformations of AcPro-NMe2 optimized at the HF/6-31+G(d) level were taken from ref 58.

than the conformations cd and cu after the optimization in water, which may be mainly due to the larger shifts in the backbone torsion angle ψ for the optimized conformations td and tu by approximately +23° from those optimized in the gas phase. The geometry relaxations in water result in changes of the relative free energies by -0.4 to +2.5 kcal/mol, and the conformational stabilities become in the order tu > td > cu > cd. The latter indicates the preference for the PPII-like conformations over the PPI-like conformations after the geometry relaxations in water, as found for the proline oligopeptides described below. The rotational barrier to the trans-to-cis isomerization of the Ac-Pro peptide bond becomes higher by 1.85 kcal/mol after the geometry relaxations in water. However, the larger shifts in the backbone torsion angle ψ for the proline residues in the oligopeptides are not expected; for example, there are only the shifts in the ψ by approximately +3° for the two prolines of Ac-Gly-Pro-Pro-Gly-NHMe after the geometry relaxations at the CPCM HF/6-31G(d) level in water.77 In diproline Ac-(Pro)2-NMe2, the PPII-like conformations with the tt peptide bonds are the most preferred in all the solutions as in the gas phase. However, in all the solutions, the population of the conformation tdtu decreases, whereas the population of the conformation tutd increases. The conformational populations estimated from the relative free energies in the gas phase and in solutions are listed in Table S4 of the Supporting Information. The conformational stability is calculated by ∆G to be in the order tt > ct > cc for all feasible puckerings, which indicates the preference of the PPII-like

17652 J. Phys. Chem. B, Vol. 110, No. 35, 2006 structure over the PPI-like one in all the solutions, as found in the gas phase. However, from ∆G of conformation cc to conformation tt, the instabilities of the PPI structure relative to the PPII structure can be estimated as 2.26, 3.06, and 3.01 kcal/ mol per proline residue in chloroform, 1-propanol, and water, respectively. This indicates that the PPI-like structures of diproline become more populated in solution. Although the dd puckering is most preferred for the PPI-like conformation with all cis peptide bonds in the gas phase and in all the solutions, the dd puckering is most preferred for the conformation with the ct peptide bond in the gas phase and in chloroform, whereas the ud puckering is most preferred in 1-propanol and water. In particular, the relative free energies of 1.80 and 1.67 kcal/mol for the conformation cutd in 1-propanol and water are lower by 0.3 and 0.5 kcal/mol than that of the conformation cdtd in chloroform and play a role in elevating the rotational barriers ∆Gctq to the cis-to-trans isomerization for the first prolyl peptide bond and ∆Gtcq to the trans-to-cis isomerization for the second prolyl peptide bond in 1-propanol and water over that in chloroform, which is discussed in the following section. Triproline. In Table 6, the relative solvation free energies and relative total free energies for the local minima of the triproline peptide Ac-(Pro)3-NMe2 in solutions are listed. In chloroform, 1-propanol, and water, the conformations with alldown puckerings are found by ∆G to be more preferred than the conformations with the mixed puckerings or all-up puckerings for all conformations generated by the combination of the trans and cis peptide bonds, except for conformation cct with udd puckering and conformation ctc with uuu puckering in water. The estimated populations for the PPII-like conformations with all-down puckerings are 35.4%, 43.9%, and 43.0% in chloroform, 1-propanol, and water, respectively, as shown in Table S4 of the Supporting Information. The populations for the following preferred PPII-like conformations with udd puckerings are 28.9%, 32.9%, and 33.4% in chloroform, 1-propanol, and water, respectively. The conformational stability in the order ttt > ctt > cct > ccc calculated by ∆G for all feasible puckerings indicates that the PPII-like structure is more preferred than the PPI-like one in solutions, as found for diproline. From ∆G of conformation ccc to conformation ttt, the instabilities of the PPI structure relative to the PPII structure can be estimated as 2.43, 3.93, and 3.92 kcal/mol per proline residue in chloroform, 1-propanol, and water, respectively. This indicates that the PPI-like structures of triproline become less populated in 1-propanol and water, contrary to the results for diproline discussed above. Tetraproline and Pentaproline. The relative solvation free energies and relative total free energies for the local minima of the tetraproline peptide Ac-(Pro)4-NMe2 and pentaproline Ac-(Pro)5-NMe2 in solutions are listed in Tables 7 and 8, respectively. The relative stabilities of tetraproline are calculated by ∆G in the order tttt > cttt > cctt > tttc > ccct > cccc > ttcc > tccc in chloroform, the same as in the gas phase, but tttt > cttt > cctt > tttc ≈ ttcc > ccct > cccc > tccc in 1-propanol and water. For pentaproline, the order is calculated to be ttttt > ctttt > ccttt > ttttc > ccctt > tttcc > cccct > ccccc > ttccc > tcccc in chloroform, as found in the gas phase, but ttttt > ctttt > ccttt > ttttc > tttcc > ccctt > ttccc > tcccc ≈ cccct > ccccc in 1-propanol and water. These calculated results indicate that the PPII-like structure is more preferred than the PPI-like one in solution, as found for diproline and triproline. In particular, the conformational stability order ttt‚‚‚ttt > ctt‚‚‚ttt > cct‚‚‚ttt

Kang et al. TABLE 6: Relative Solvation Free Energies and Relative Total Free Energies of Ac-(Pro)3-NMe2 at the CPCM HF/6-31+G(d) Level in Solutiona chloroform

1-propanol

water

conf.b

∆∆Gsc

∆Gtotd

∆∆Gsc

∆Gtotd

∆∆Gsc

∆Gtotd

tdtdtd cdtdtd tdtdcd tdcdtd cdcdtd cdtdcd cdcdcd tdcdcd tdtdtu cdtdtu tdcdtu cdcdtu cdcdcu tdcdcu tdtutd cdtutd tdtucd tdcutd cdcutd cdcucd tdcucd tutdtd cutdtd tutdcd tucdtd cucdtd cutdcd cucdcd tucdcd tdtutu cdtutu tdcutu cdcutu cdcucu tutdtu cutdtu tucdtu cucdtu cucdcu tucdcu tututd cututd tutucd tucutd cucutd cucucd tucucd tututu cututu cutucu cucutu tucutu cucucu tucucu

0.00 -0.64 1.99 1.48 -0.73 1.20 -1.54 -2.57 0.78 -0.20 1.62 -0.53 -2.02 -2.90 0.49 -0.88 2.27 1.59 -0.98 -1.67 -2.38 -0.50 -1.34 1.83 1.00 -0.72 1.13 -1.85 -2.71 1.01 -0.38 1.76 -1.02 -2.17 0.28 -0.80 1.09 -0.92 -2.23 -3.38 0.17 -1.59 2.03 1.31 -1.36 -1.76 -2.46 0.50 -1.00 1.12 -1.43 1.42 -2.33 -3.16

0.00 1.98 8.26 6.18 5.29 10.59 7.30 8.59 1.11 2.68 7.14 6.06 8.15 9.45 0.35 2.35 8.81 7.93 6.12 8.32 9.93 0.12 2.25 9.21 7.04 6.36 11.31 7.72 9.34 2.42 3.51 8.99 6.77 9.00 1.53 3.04 7.92 6.77 8.94 10.24 1.45 2.39 10.43 9.07 6.81 9.17 10.90 2.84 3.65 11.30 7.37 10.03 9.87 11.74

0.00 -0.95 5.04 5.19 2.82 3.35 2.95 0.82 1.69 0.06 5.45 2.60 1.99 0.08 1.06 -1.41e 6.67 5.07 2.32 2.98 1.11 -0.45 -1.85 4.48 4.40 1.75 3.45 2.52 0.41 2.06 -0.32 5.09 1.38 2.05 1.30 -0.96 4.40 1.04 1.71 -0.62 0.73 -2.22 4.82 4.78 0.87 2.42e 0.77 1.25 -1.35 3.45 0.61 4.91 1.54 -0.36

0.00 1.67 11.32 9.89 8.84 12.74 11.79 11.98 2.02 2.94 10.97 9.19 12.17 12.43 0.92 1.82 13.21 11.41 9.42 12.98 13.43 0.17 1.74 11.85 10.43 8.83 13.63 12.08 12.46 3.47 3.57 12.33 9.16 13.23 2.55 2.88 11.24 8.72 12.89 13.00 2.01 1.76 13.21 12.54 9.04 13.35 14.13 3.58 3.30 13.63 9.41 13.52 13.75 14.54

0.00 -1.04 5.18 5.34 2.84 3.37 2.92 0.66 1.76 0.02 5.61 2.60 1.93 -0.11 1.12 -1.52e 6.86 5.20 2.32 2.96 0.97 -0.47 -1.97 4.60 4.51 1.73 3.48 2.49 0.23 5.13 -0.39 5.22 1.33 2.01 1.36 -1.05 4.51 0.99 1.66 -0.85 0.76 -2.37 4.95 4.89 0.83 2.77 0.60 1.30 -1.46 3.48 0.56 5.01 1.48 -0.58

0.00 1.58 11.45 10.04 8.87 12.76 11.77 11.82 2.08 2.89 11.13 9.19 12.11 12.23 0.97 1.71 13.40 11.54 9.42 12.95 13.28 0.15 1.62 11.97 10.54 8.81 13.66 12.05 12.27 6.54 3.49 12.46 9.11 13.18 2.61 2.80 11.35 8.67 12.83 12.77 2.04 1.62 13.35 12.64 8.99 13.70 13.96 3.64 3.19 11.66 9.35 13.62 13.69 14.33

a

Energies in kcal/mol. See footnote a of Table 5. b See footnote c of Table 1 for the definition of conformational letter codes. c Relative solvation free energy; ∆∆Gs,i ) ∆Gs,i - ∆Gs,0, where ∆Gs,0 ) -4.05, -17.64, and -18.86 kcal/mol for the conformation tdtdtd in chloroform, 1-propanol, and water, respectively. d Relative total free energy; see footnote d of Table 5. e Calculated with the area of tesserae equal to 0.1 Å2.

> ccc‚‚‚ttt > ‚‚‚ > ccc‚‚‚ctt > ccc‚‚‚cct > ccc‚‚‚ccc found for tetraproline and pentaproline indicates that the intermediates for the trans-to-cis or cis-to-trans isomerization of polyproline have the H2N-cis-cis‚‚‚trans-trans-COOH configuration in solutions, as seen in the gas phase. From ∆G of the PPI-like conformation to the PPII-like conformation, the PPI-like structure is known to be less stable

Conformational Preferences of Pro Peptides

J. Phys. Chem. B, Vol. 110, No. 35, 2006 17653

TABLE 7: Relative Solvation Free Energies and Relative Total Free Energies of Ac-(Pro)4-NMe2 at the CPCM HF/6-31+G(d) Level in Solutiona chloroform

1-propanol

water

conf.b

∆∆Gsc

∆Gtotd

∆∆Gsc

∆Gtotd

∆∆Gsc

∆Gtotd

tttt cttt cctt tttc ccct cccc ttcc tccc

0.00 -0.60 -0.47 1.98 0.56 -0.99 -0.72 -2.00

0.00 2.08 5.37 8.76 9.30 9.57 10.11 11.59

0.00 -1.05 2.79 5.58 6.97 6.32 1.66 3.79

0.00 1.64 8.63 12.35 15.70 16.88 12.48 17.38

0.00 -1.14 2.82 5.70 7.07 6.39 1.53 3.69

0.00 1.55 8.66 12.48 15.80 16.95 12.35 17.28

a Energies in kcal/mol. See footnote a of Table 5. b See footnote c of Table 1 for the definition of conformational letter codes. c Relative solvation free energy; ∆∆Gs,i ) ∆Gs,i - ∆Gs,0, where ∆Gs,0 ) -3.49, -20.68, and -22.17 kcal/mol for the conformation tttt in chloroform, 1-propanol, and water, respectively. d Relative total free energy; see footnote d of Table 5.

TABLE 8: Relative Solvation Free Energies and Relative Total Free Energies of Ac-(Pro)5-NMe2 at the CPCM HF/6-31+G(d) Level in Solutiona chloroform b

c

1-propanol d

c

water d

conf.

∆∆Gs

∆Gtot

∆∆Gs

∆Gtot

∆∆Gsc

∆Gtotd

ttttt ctttt ccttt ttttc ccctt cccct tttcc ccccc ttccc tcccc

0.00 -0.83 -0.62 2.01 0.91 1.24 -0.15 -0.31 -0.47 -1.65

0.00 1.79 5.24 8.72 9.28 12.44 10.55 12.59 12.73 13.44

0.00 -0.90 2.81 5.98 7.67 11.13 3.72 9.96 4.95 7.14

0.00 1.72 8.66 12.69 16.03 22.33 14.42 22.86 18.15 22.23

0.00 -0.97 2.84 6.13 7.81 11.34 3.67 10.14 4.89 7.14

0.00 1.65 8.70 12.83 16.17 22.54 14.37 23.04 18.09 22.23

a Energies in kcal/mol. See footnote a of Table 5. b See footnote c of Table 1 for the definition of conformational letter codes. c Relative solvation free energy; ∆∆Gs,i ) ∆Gs,i - ∆Gs,0, where ∆Gs,0 ) -2.78, -23.94, and -25.73 kcal/mol for the conformation ttttt in chloroform, 1-propanol, and water, respectively. d Relative total free energy; see footnote d of Table 5.

by 2.39, 4.22, and 4.24 kcal/mol per proline residue than the PPII-like structure for the tetraproline in chloroform, 1-propanol, and water, respectively, whereas the corresponding values are 2.52, 4.57, and 4.61 kcal/mol for pentaproline, respectively. This indicates that the free energy difference per proline residue between the PPII- and PPI-like structures increases as the solvent polarity increases and the proline chain becomes longer. Relative Stability of Puckerings. In the gas phase, the difference in ∆G between the up- and the down-puckered conformations for Ac-Pro-NMe2, which is denoted by ∆∆Gu/d hereafter, becomes ∼0.9 kcal/mol for both the trans and the cis structures (Table 1). The mean ∆∆Gu/d per proline is calculated to be 0.90 and 1.08 kcal/mol in diproline and 0.79 and 1.85 kcal/mol in triproline for PPII- and PPI-like structures, respectively (Tables 1 and 2). The small changes in ∆G for the d f u puckering transition indicate that the PPII- or PPI-like structures have preferentially all-down puckerings or partially mixed puckerings, although the value of ∆∆Gu/d for the PPIlike structure of triproline becomes double that of the diproline. The mean ∆∆Gu/d per proline for diproline increases for the PPII-like conformations and decreases for the PPI-like conformations as the solvent polarity increases, although the values are almost the same in 1-propanol and water. The mean ∆∆Gu/d values per proline for triproline are calculated to be 0.78 and 0.83 kcal/mol in chloroform, 1.19 and 0.65 kcal/mol in 1-propanol, and 1.38 and 0.66 kcal/mol in water for PPII- and

Figure 3. Free energy profiles for the cis-trans isomerization of diproline Ac-(Pro)2-NMe2 in the gas phase and in solution.

PPI-like structures, respectively, which shows the increase and decrease in the ∆∆Gu/d per proline, respectively, as the solvent polarity increases. In particular, ∆∆Gu/d per proline for the PPIIlike conformations decreases more in triproline than diproline, whereas that for the PPI-like conformations is nearly the same in both triproline and diproline. This indicates that the downand up-puckered conformations become equally probable in the PPII- and PPI-like conformations as the proline chain becomes longer in solutions. Our calculated results are accord with the NMR19 and Raman optical activity20 experiments that the prolyl ring of PPII has two puckered conformations in water. The puckerings of PPII-like structures of HCO-(Pro)3-NH2 were explored at the B3LYP/6-31G(d,p) level using the COSMO in water, and the differences in energies for down- and up-puckered conformations are calculated to be ∼0.6 kcal/mol, although the conformation with all-down puckerings is the most preferred.20 When ∆G values of the conformations with the same number of down and up puckerings in solution are compared, the up puckering is more favored at the N-termini than the C-termini of the PPII-like conformations. For example, the relative stabilities are found to be in the orders udd > dud > ddu and uud > udu > duu for the PPII-like conformations in water. However, the up puckering is favored at the N- or C-terminus of the PPI-like conformations with a single up puckering, but the preference of the up puckering is found at the N- and C-termini of the PPI-like conformations with two up puckerings. For example, the relative stabilities are calculated to be in the orders udd > ddu > dud and udu > duu > uud for the PPIIlike conformations in water. Conformational Transitions between PPII and PPI Structures. Through the use of the free energies of the most preferred conformations with the tt, ct, and cc peptide bonds (e.g., the conformations tdtd, cdtd, and cdcd in the gas phase) and the transition states ts1 and ts2 shown in Tables 1 and 5, the rotational barriers for the cis-trans isomerization of diproline can be estimated. The ts1 and ts2 are the transition states for the first and second prolyl peptide bonds, respectively. Free energy profiles for the cis-trans isomerization of diproline are depicted in Figure 3. When the contributions to rotational barriers are analyzed, the cis-trans isomerization of diproline is proven to be entirely enthalpy-driven in the gas phase and in solution, to which the electronic energies have considerably contributed, as seen for proline Ac-Pro-NMe2 (Table 1). This is consistent with the experimental results on proline-containing peptides, determined kinetically as a function of temperature.78 In the gas phase, the rotational barriers (∆Gtcq and ∆Gctq) for the trans-to-cis and cis-to-trans isomerizations for the first

17654 J. Phys. Chem. B, Vol. 110, No. 35, 2006 prolyl peptide bond (i.e., the conformations tdtd and cdtd) are estimated to be 21.59 and 18.77 kcal/mol at the HF/6-31+G(d) level, respectively, whereas the corresponding values are 22.91 and 19.35 kcal/mol for the second prolyl peptide bond (i.e., the conformations cdtd and cdcd), respectively. The rotational barriers for the first prolyl peptide bond are quite similar to those of Ac-Pro-NMe2 in Table 1 but higher by ∼5 kcal/mol than those of Ac-Pro-NHMe.66 The higher rotational barriers for AcPro-NMe2 and Ac-(Pro)2-NMe2 could be due to the lack of an intramolecular hydrogen bond between the prolyl nitrogen and the following amide N-H group in the transition state,58 which was suggested as an important factor to stabilize the transition state and accelerate the prolyl cis-trans isomerization of proline-containing peptides with the secondary amide group.79 In chloroform, ∆Gtcq and ∆Gctq are computed as 22.87 and 20.75 kcal/mol for the first prolyl peptide bond, respectively, and 22.91 and 20.52 kcal/mol for the second prolyl peptide bond, respectively. In 1-propanol, they are computed as 25.38 and 23.58 kcal/mol for the first prolyl peptide bond, respectively, and 23.70 and 19.38 kcal/mol for the second prolyl peptide bond, respectively. In water, they are computed as 25.50 and 23.83 kcal/mol for the first prolyl peptide bond, respectively, and 23.74 and 19.40 kcal/mol for the second prolyl peptide bond, respectively. The rotational barriers (∆Gtcq) to the trans-to-cis isomerization for both the prolyl peptide bonds increase as the solvent polarity increases, as found for proline Ac-Pro-NMe2.58 However, the rotational barrier (∆Gctq) to the cis-to-trans isomerization for the first prolyl peptide bond increases as the solvent polarity increases, whereas the rotational barrier for the second prolyl peptide bond does not show the monotonic increase as the solvent polarity increases. This is because the preferred conformation with the ct peptide bond is cdtd in the gas phase and in chloroform but cutd in 1-propanol and water and because the relative free energy of the conformation with the ct peptide bond becomes lower as the solvent polarity increases. As a result, the rotational barrier ∆Gtcq for the first peptide bond is somewhat lower than that for the second peptide bond in the gas phase and in chloroform, whereas the rotational barrier ∆Gtcq for the second peptide bond becomes lower than that for the first peptide bond in 1-propanol and water. This indicates that the conformational transition from PPI with the cis peptide bond to PPII with the trans peptide bond is initiated at the C-terminus and proceeds to the N-terminus in 1-propanol and water. This is consistent with the results from NMR experiments on polyproline in D2O24 but opposite to the enzymatic hydrolysis kinetics experiments on polyproline. From our calculations, the free energy difference per proline residue between the PPII- and PPI-like structures decreases as the proline chain becomes longer in the gas phase but increases as the proline chain becomes longer in solution and the solvent polarity increases. In particular, our calculated results in Tables 5-8 indicate that each of the proline oligopeptides can exist as an ensemble of conformations with the trans and cis peptide bonds in solution, although the PPII-like structure with all-trans peptide bonds is dominantly preferred, which is reasonably consistent with the previous observed results. However, the difference in the conformational preferences of the proline oligopeptides in 1-propanol and water is not reflected by our calculations, and an improvement in computing the solvation free energies is required. Conclusions The mean differences in the free energy per proline of the up-puckered conformations relative to the down-puckered

Kang et al. conformations for both diproline and triproline increases for the PPII-like conformations and decreases for the PPI-like conformations as the solvent polarity increases. These calculated results indicate that the PPII-like structures have preferentially all-down puckerings in solutions, whereas the PPI-like structures have partially mixed puckerings. In addition, this indicates that the down- and up-puckered conformations become equally probable in the PPII- and PPI-like conformations as the proline chain becomes longer in solutions. The free energy difference per proline residue between the PPII- and PPI-like structures decreases as the proline chain becomes longer in the gas phase but increases as the proline chain becomes longer in solutions and the solvent polarity increases. In particular, our calculated results indicate that each of the proline oligopeptides can exist as an ensemble of conformations with the trans and cis peptide bonds in solution, although the PPII-like structure with all-trans peptide bonds is dominantly preferred, which is reasonably consistent with the previously observed results. In diproline Ac-(Pro)2-NMe2, the rotational barrier to the cis-to-trans isomerization for the first prolyl peptide bond increases as the solvent polarity increases, whereas the rotational barrier for the second prolyl peptide bond does not show the monotonic increase as the solvent polarity increases. When the rotational barriers for these two prolyl peptide bonds are compared, it could be deduced that the conformational transition from PPI with the cis peptide bond to PPII with the trans peptide bond is initiated at the C-terminus and proceeds to the N-terminus in water. This is consistent with the results from NMR experiments on polyproline in D2O but opposite to the results from enzymatic hydrolysis kinetics experiments on polyproline. Acknowledgment. This work was supported by a grant from the Korea Research Foundation (KRF-2003-041-C20129). Supporting Information Available: Endocyclic torsion angles of prolyl residues for the proline oligopeptides at the HF/6-31+G(d) level in the gas phase, backbone torsion angles, endocyclic torsion angles, and thermodynamic quantities of AcPro-NMe2 at the B3LYP/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 chloroform and water, and their populations in the gas phase, chloroform, 1-propanol, and water. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Momany, F. A.; McGuire, R. F.; Burgess, A. W.; Scheraga, H. A. J. Phys. Chem. 1975, 79, 2361. (2) Balasubramanian, R.; Lakshminarayanan, A. V.; Sabesan, M. N.; Tegoni, G.; Venkatesan, K.; Ramachandran, G. N. Int. J. Protein Res. 1971, 3, 25. (3) DeTar, D. F.; Luthra, N. P. J. Am. Chem. Soc. 1977, 99, 1232. (4) Madison, V. Biopolymers 1977, 16, 2671. (5) Milner-White, E. J.; Bell, L. H.; Maccallum, P. H. J. Mol. Biol. 1992, 228, 725. (6) Pal, D.; Chakrabarti, P. J. Mol. Biol. 1999, 294, 271. (7) Vitagliano, L.; Berisio, R.; Mastrangelo, A.; Mazzarella, L.; Zagari, A. Protein Sci. 2001, 10, 2627. (8) Jabs, A.; Weiss, M. S.; Hilgenfeld, R. J. Mol. Biol. 1999, 286, 291. (9) Schmid, F. X.; Mayr, L. M.; Mu¨cke, M.; Scho¨nbrunner, E. R. AdV. Protein Chem. 1993, 44, 25. (10) Balbach, J.; Schmid, F. X. In Mechanisms of Protein Folding, 2nd ed.; Pain, R. H., Ed.; Oxford University Press: New York, 2000; Chapter 8. (11) Wedemeyer, W. J.; Welker, E.; Scheraga, H. A. Biochemistry 2002, 41, 14637. (12) Dugave, C.; Demange, L. Chem. ReV. 2003, 103, 2475.

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