Conformational Preferences of Proline Analogues with Different Ring

3496

J. Phys. Chem. B 2007, 111, 3496-3507

Conformational Preferences of Proline Analogues with Different Ring Size Jong Suk Jhon and Young Kee Kang* Department of Chemistry and Basic Science Research Institute, Chungbuk National UniVersity, Cheongju, Chungbuk 361-763, South Korea ReceiVed: October 18, 2006; In Final Form: January 15, 2007

The conformational study on L-azetidine-2-carboxylic acid (Ac-Aze-NHMe, the Aze dipeptide) and (S)piperidine-2-carboxylic acid (Ac-Pip-NHMe, the Pip dipeptide) is carried out using ab initio HF and density functional methods with the self-consistent reaction field method to explore the differences in conformational preferences and cis-trans isomerization for proline residue and its analogues with different ring size in the gas phase and in solution (chloroform and water). The change of ring size by deleting a CH2 group from or adding a CH2 group to the prolyl ring results the remarkable changes in backbone and ring structures compared with those of the Pro dipeptide, especially in the C′-N imide bond length and the bond angles around the N-CR bond. The four-membered azetidine ring can have either puckered structure depending on the backbone structure because of the less puckered structure. The six-membered piperidine ring can adopt chair and boat conformations, but the chair conformation is more preferred than the boat conformation. These calculated preferences for puckering are consistent with experimental results from analysis of X-ray structures of Azeand Pip-containing peptides. On going from Pro to Aze to Pip, the axiality (i.e., a tendency to adopt the axial orientation) of the NHMe group becomes stronger, which can be ascribed to reduce the steric hindrances between 1,2-substituted Ac and NHMe groups. As the solvent polarity increases, the polyproline II-like conformation becomes more populated and the relative stability of conformation tC with a C7 hydrogen bond between C′dO of the amino group and N-H of the carboxyl group decreases for both the Aze and Pip dipeptides, as seen for the Pro dipeptide. The cis population and rotational barriers for the imide bond increase with the increase of solvent polarity for both the Aze and Pip dipeptides, as seen for the Pro dipeptide. In particular, the cis-trans isomerization proceeds in common through only the clockwise rotation with ω′ ≈ +120° about azetyl and piperidyl peptide bonds in the gas phase and in solution, as seen for alanyl and prolyl peptide bonds. The pertinent distance d(N‚‚‚H-NNHMe) and the pyramidality of imide nitrogen can describe the role of this hydrogen bond in stabilizing the transition state structure, but the lower rotational barriers for the Aze and Pip dipeptides than those for the Pro dipeptide, which is observed from experiments, cannot be rationalized.

Introduction L-Azetidine-2-carboxylic acid (Aze) is a homologue of proline (Pro) with a four-membered azetidine ring instead of a fivemembered pyrrolidine ring of proline. It has been first isolated from the plant ConVallaria majalis L.1 The replacement of Pro with Aze causes to inhibit the growth of Escherichia coli and the seedlings of mung bean (Phaseolus aureus).2 In spite of similar chemical structures, the replacement of Pro with Aze has resulted in remarkable changes in structures and biological properties of polyproline,3,4 collagen,5-8 peptides,9,10 and proteins.11-13 In particular, the addition of Aze to budding yeast cells induces the protein misfolding and selectively activates the heat shock factor that is required for the subsequent G1 arrest of the cell cycle.12 The incorporation of Aze in place of Pro in the C-terminus of YbeL protein from E. coli significantly suppresses tagging by SsrA, an RNA molecule contained in all eubacteria.13 (S)-Piperidine-2-carboxylic acid (L-pipecolic acid, Pip) is also a proline analogue with a six-membered piperidine ring. Pip is a major metabolic intermediate of L-lysine in the mammalian

* To whom correspondence should be addressed. Telephone: +82-43261-2285. Fax: +82-43-273-8328. E-mail: [email protected].

and chick brain.14-16 Pip is known to activate γ-aminobutyric acid receptors and to attenuate feeding and sleeping-like behavior in neonatal chicks.17 In particular, Pip is found in many biologically active compounds such as immunosuppresants18 and antibiotics.19,20 Pip has also been incorporated into several bioactive peptides and used in designing potent inhibitors.10,21,22 Recently, a Pip-containing pentapeptide has been used to determine the thermodynamic properties of the interaction between the peptidyl prolyl cis-trans isomerase Pin1 and its substrate.23 The azetidine ring of peptides has both down- and uppuckered conformations, although the degree of puckering is smaller than that of the pyrrolidine ring.24-28 The down- and up-puckered conformations are defined as those where the Cγ atom and the C′dO group of Aze residue lie on the same and opposite sides, respectively, of the plane defined by the three atoms Cγ, N, and CR, as defined for the Pro residue (Figure 1). The piperidine ring can adopt chair and boat conformations, but only the chair conformation preferentially exists in X-ray structures of peptides.29-34 From NMR experiments in water, the cis populations of the Ac-X peptide bond for Ac-X-OH (X ) Aze, Pip, and Pro) are estimated to in the order Pro > Aze > Pip.35-37 The cis

10.1021/jp066835z CCC: $37.00 © 2007 American Chemical Society Published on Web 03/13/2007

Conformational Preferences of Aze and Pip Dipeptides

J. Phys. Chem. B, Vol. 111, No. 13, 2007 3497 density functional methods with the self-consistent reaction field (SCRF) method to explore the differences in conformational preferences and cis-trans isomerization for the proline residue and its analogues with different ring size in the gas phase and in solution. Computational Methods

Figure 1. Definition of torsion angles and structural parameters for Aze and Pip dipeptides.

populations of the Pip residue are calculated to be quite similar to those of the Pro residue for Ac-X-NHMe,38-40 Ala-X(4-)nitroanilide,41 and Ala-Gly-X-Phe-(4-)nitroanilide41 (hereafter nitroanilide is abbreviated as NA). However, the cis populations of the Aze residue are computed to prevail over those of the Pip and Pro residues for Ala-X-(4-)NA and AlaGly-X-Phe-(4-)NA.41 In particular, the rotational barriers to the cis-to-trans isomerization of the imide peptide bond for Aze and Pip residues are observed to be ∼2 kcal/mol lower than that of the Pro residue in water.39,41 The faster rates for the cistrans isomerization of Pip-containing peptides than the corresponding Pro-containing peptides are ascribed to (a) the destabilization of trans and cis conformations relative to the transition state due to the steric clashes of the larger size of piperidine ring and (b) the greater pyramidality of pipecolyl nitrogen than that of prolyl nitrogen in stabilizing the transition state.42 However, the first factor appears not to work in Azecontaining peptides. Recently, the pyramidality of prolyl nitrogen has been used in explaining the differences in rotational barriers for 4(R)-substituted proline residues43 and for non-prolyl and prolyl residues.44 For Aze residue, Aze-containing dipeptides, and polymers of Aze as well as collagen-like poly(Gly-X-Y) sequences, where X and Y can be Pro or Aze, empirical energy calculations with fixed geometries and planar azetidine ring have been carried out.45-47 The overall conformational preferences of Aze and Pro residues are found to be similar but the collagen-like nearextended conformation is energetically less favorable for the Aze residue than for the Pro residue. All Aze-containing polymer chains are more flexible than the Pro-containing one. This was interpreted as a consequence of an increased number of conformations accessible to the Aze residue as compared to the Pro residue. Empirical conformational energy computations of Ac-Pip-NHMe indicate that (a) the conformations with the trans imide peptide bond are slightly more stable than the cis conformations and (b) the chair conformations of the piperidine ring are appreciably more stable by 3-5 kcal/mol than the boat conformations.48 However, no conformational studies on Aze and Pip residues using quantum-mechanical methods have been reported until now. We report here the results on Ac-AzeNHMe (the Aze dipeptide) and Ac-Pip-NHMe (the Pip dipeptide) calculated using ab initio Hartree-Fock (HF) and

Chemical structures and torsional parameters for Aze and Pip dipeptides are defined in Figure 1. All ab initio HF and density functional calculations were carried out using the Gaussian 9849 and Gaussian 0350 packages. Here, each backbone conformation of the dipeptides is represented by a capital letter depending on its values of φ and ψ for the backbone.51 Conformations C, A, F, and D are equivalent to the γ-turn (C7eq), R-helical (RR), polyproline-like (β or PII), and β2 structures in other works, respectively. Trans and cis conformations for the Ac-X (X ) Aze, Pip, or Pro) imide bond are denoted by “t” and “c”, respectively. Down- and up-puckered conformations for the azetidine ring are represented by “d” and “u”, respectively. The azetidyl puckering is described by the endocyclic torsion angle χ1 for the N-CR-Cβ-Cγ sequence (i.e., positive and negative χ1 for the down- and up-puckered structures, respectively), as defined for the Pro residue.44,52 The piperidine ring can adopt chair- and boat-puckered conformations. Chair conformations have +-+-+ and -+-+- signs for the torsion angles χ1χ5, which are represented by “c” and “c′”, respectively. Boat conformations have +--+- and ++-++ signs for the torsion angles χ1-χ5, which are denoted by “b” and “b′”, respectively. According to the definitions used for the furanoside ring of nucleosides53 and the pyrrolidine ring of proline,54 the piperidyl puckerings c, c′, b, and b′ can be denoted by NCγ, γ β N γ NC , B , and B , respectively. Two local minima tCd and tCu of Ac-Pro-NHMe (the Pro dipeptide) with the trans imide bond optimized at the HF/631+G(d) level44,52 were edited by deleting the CγH2 group from the pyrrolidine ring using the Chem3D program55 to generate starting conformations for optimization of the Aze dipeptide.56 After minimizations at the HF/6-31+G(d) level, two initial conformations of the Aze dipeptide were converged to the identical conformation tCu, which is less up-puckered with the endocyclic torsion angle χ1 of -4.3°. Using the same procedure, the local minimum cAu of the Aze dipeptide with the cis imide bond was located starting from two local minima cAd and cAu of the Pro dipeptide optimized at the HF/6-31+G(d) level,44,52 which is also less up-puckered with the torsion angle χ1 of -5.1°. Using the Chem3D program,55 the local minimum tCd of the Pro dipeptide optimized at the HF/6-31+G(d) level44,52 was edited by adding a CH2 group to the CγH2 group of the pyrrolidine ring to generate two starting conformations with chair and boat puckerings (NCγ and NBγ, respectively) for optimization of the Pip dipeptide with the trans imide bond.56 The piperidine rings of X-ray structures of Pip-containing peptides adopt the NCγ chair conformation.32-34 After minimizations at the HF/6-31+G(d) level, these two starting conformations were converged to the conformations tCc and tCb′, respectively. Two local minima cDc and cAb with chair and boat puckerings (NCγ and βB, respectively) of the Pip dipeptide with the cis imide bond were found by optimizing the conformations obtained from the adiabatic optimization of the conformations tCc and tCb′ with ω′ ) +10° for the Ac-Pip bond, respectively, at the same level. Two local minima tCb′ and tFb′ in chloroform were reoptimized and converged to the conformation tFc′ with another NCγ chair puckering in water,

3498 J. Phys. Chem. B, Vol. 111, No. 13, 2007 which was also identified as a local minimum in the gas phase.56 A local minimum cFc′ with the cis imide bond was also found by optimizing the conformation obtained from the adiabatic optimization of the conformation tFc′ with ω′ ) 0°. The 2-D potential energy surfaces (PESs) of the conformations for Aze and Pip dipeptides with trans and cis imide bonds were calculated along the backbone torsion angle ψ at the HF/ 6-31+G(d) level, in which adiabatic optimizations were performed at each value of ψ with an interval of 15° for -180° e ψ e 180°. Two conformations tCu and cAu for the Aze dipeptide and four conformations tCc, tCb′, cDc, and cAb for the Pip dipeptide were used as initial structures of these adiabatic optimizations. In addition, two high-energy conformations tFc′ and cFc′ with the NCγ chair puckering were used as initial structures for another adiabatic optimizations. From these PESs for Aze and Pip dipeptides, the other local minima were identified and reoptimized at the same level. The transition state ts1 for the cis-trans isomerization of the Aze dipeptide was found by optimizing the conformation obtained from the adiabatic optimization of the conformation cAu with ω′ ) +117° for the Ac-Aze bond at the HF/631+G(d) level, as done for the Pro dipeptide in refs 44 and 52. The transition state ts2 of the Aze dipeptide was located starting from the ts1 with ω′ ) -67° at the same level. Four initial conformations for transition states of the Pip dipeptide were generated from conformations cDc and tCb with ω′ ) +117° and -67°. After minimizations at the HF/6-31+G(d) level, the transition states ts1 and ts2 with chair and boat conformations, respectively, were located at ω′ ≈ +114° for the Pip dipeptide. Local minima and transition states for Aze and Pip dipeptides optimized at the HF/6-31+G(d) level were used as initial points for optimizations at the hybrid density functional B3LYP/6311++G(d,p) level of theory. We employed the conductor-like polarizable continuum model (CPCM) SCRF method,58 implemented in the Gaussian 03 package,50 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.59 The solvation free energy is the sum of the electrostatic free energy and the nonelectrostatic energy terms.59 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. Single-point solvation free energy calculations were carried out on each grid point of the PES in the gas phase to get the PESs in chloroform and water. 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) and HF/6-31+G(d)//B3LYP/6-31+G(d) levels provided hydration free energies in agreement with available experimental data.60 All local minima and transition states for Aze and Pip dipeptides optimized at the HF/6-31+G(d) level in the gas phase were used as starting structures for optimizations at the HF/631+G(d) level in chloroform and water. In addition, some local minima found from the PESs in chloroform and water were reoptimized in chloroform and water, respectively. The B3LYP/ 6-311++G(d,p) single-point energies were calculated for all local minima and transition states of Aze and Pip dipeptides located at the CPCM HF/6-31+G(d) level in solution. Vibrational frequencies were calculated for all stationary points at the HF level in the gas phase and in solution, and the

Jhon and Kang B3LYP level in the gas phase, which were used to compute enthalpies and Gibbs free energies with the scale factors of 0.8961 and 0.9862 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.61 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.62 The zero-point energy correction and the thermal energy corrections were used to calculate the enthalpy (H) and entropy (S) of each conformation.59,63 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 solution 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 solution. The relative total free energies are used here to interpret the conformational preferences and cis-trans isomerization in the gas phase and in solution. Results and Discussion Backbone Conformational Preferences. The 2-D PESs of Ac-Aze-NHMe with trans and cis imide bonds calculated along the backbone torsion angle ψ at the HF/6-31+G(d) level in the gas phase are shown in Figure 2. For the trans-Aze dipeptide, the PES show a single minimum tCu at ψ ≈ 60° with up puckering, and two points of reflection tAu at ψ ≈ -15° and tFd at ψ ≈ 135° with up and down puckerings, respectively, whereas the trans-Pro dipeptide has three local minima tCd, tCu, and tAu.52 On the PES of the cis-Aze dipeptide, there are two local minima cAu at ψ ≈ -15° and polyproline I (PPI)-like cFd at ψ ≈ 165° with up and down puckerings, respectively. The barrier at ψ ≈ -105° for the uppuckered cis-Aze dipeptide is similar to that at ψ ≈ 75° for its down-puckered conformation and these two barriers are similar to those for the cis-Pro dipeptide with down and up puckerings.52 In order to examine the change of puckering for the azetidine ring, the endocyclic torsion angles χ1 of Aze dipeptide with trans and cis imide bonds optimized along the backbone torsion angle ψ at the HF/6-31+G(d) level in the gas phase are plotted in Figure 3. The maximum and minimum values of χ1 were calculated to be 10.3° and -10.4° for the trans-Aze dipeptide, respectively, whereas the corresponding values were evaluated to be 31.8° and -25.8° for conformations tCd and tAu of the Pro dipeptide with down and up puckerings, respectively.44,52 This indicates that the four-membered azetidine ring is less puckered than the five-membered pyrrolidine ring, as expected. From the study on the ring flip for the Pro dipeptide with trans and cis imide bonds along the torsion angles χ1 at the HF/631+G(d) level, it has been observed that the prolyl ring has two distinct local minima (i.e., down and up puckerings) and that the barriers to ring flip from a down-puckered conformation to an up-puckered one are estimated to be 2.87 and 3.16 kcal/ mol for trans and cis conformers, respectively.54,64 However, the azetidine ring can have either puckered structure depending on the backbone structure because of the less puckered structure, as shown in Figure 3. The trans-Aze dipeptide has up-puckered structures with negative χ1 values for -165° e ψ < 120°, except at ψ ) -105°, and down-puckered structures with positive χ1 values for 120° e ψ e 180°, which are polyproline-like


Figure 2. Potential energy surfaces of Aze dipeptide at the HF/631+G(d) level with the CPCM method along the backbone torsion angle ψ in the gas phase, chloroform, and water: trans, b; cis, O.

Figure 3. Optimized endocyclic torsion angle χ1 along the backbone torsion angle ψ for Aze dipeptide at the HF/6-31+G(d) level in the gas phase: trans, b; cis, O.

structures. The cis-Aze dipeptide has up-puckered structures for -165° e ψ < 15°, and down-puckered structures for ψ g 15°, except for 90° < ψ < 135°. Both trans and cis conformers have the maximum up and down puckerings at ψ ) -60° and 180°, respectively.

J. Phys. Chem. B, Vol. 111, No. 13, 2007 3499

Figure 4. Potential energy surfaces of Pip dipeptide at the HF/631+G(d) level with the CPCM method along the backbone torsion angle ψ in the gas phase, chloroform, and water: trans-chair, b; trans-boat, O; cis-chair, 1; cis-boat, 3.

The 2-D PESs of Ac-Pip-NHMe with trans and cis imide bonds having chair and boat puckerings calculated along the backbone torsion angle ψ at the HF/6-31+G(d) level in the gas phase are shown in Figure 4. The trans-Pip dipeptide with chair puckering has a single minimum tCc at ψ ≈ 75° and two points of reflection at ψ ≈ 30° and 155°, whereas the trans-Pip dipeptide with boat puckering has two local minima tCb at ψ ≈ 65° and tCb′ at ψ ≈ 80°. The PES of the chair-puckered trans-Pip dipeptide is similar to those of the trans-Aze dipeptide and the down-puckered trans-Pro dipeptide.52 However, the PES of the boat-puckered trans-Pip dipeptide is different from that of the up-puckered trans-Pro dipeptide.52 On the PESs of the cis-Pip dipeptide with chair and boat puckerings, there are four local minima cDc at ψ ≈ 25° and cFc at ψ ≈ 170° for chair puckering, and cAb at ψ ≈ 10° and cFb at ψ ≈ 160° for boat puckering. The two barriers at ψ ≈ -105° and ψ ≈ 90° are similar to those for the cis-Pro dipeptide, though a small shift of the ψ angle is found.52 The PESs of the cis-Pip dipeptide are similar to those of the cis-Aze and trans-Pro dipeptides with down and up puckerings.52 However, the puckering-energy differences between conformations cDc and cBb and between

3500 J. Phys. Chem. B, Vol. 111, No. 13, 2007

Jhon and Kang

TABLE 1: Backbone Torsion Angles, Endocyclic Torsion Angles, and Thermodynamic Properties of Local Minima and Transition States for Aze Dipeptide Optimized at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) Levels in the Gas Phasea backbone torsion angles

endocyclic torsion angles

conformerb

ω′

φ

ψ

ω

χ0

χ1

tCu cAu cFd ts1 ts2

-164.0 25.4 -15.2 127.0 -57.8

-81.5 -94.0 -51.9 -103.1 -92.5

55.3 -12.1 165.5 -8.2 -2.5

178.4 -176.6 175.4 -175.3 -179.5

tCu cAuf cFd ts1 ts2

-166.8 25.8 -8.8 128.7 -56.2

-77.0 -95.9 -53.7 -105.1 -94.7

57.9 -8.5 155.7 -8.1 -3.6

B3LYP/6-311++G(d,p) 179.9 3.3 -3.1 -177.2 3.7 -3.5 175.8 -2.4 2.2 -176.1 16.4 -16.0 -179.8 16.8 -16.2

HF/6-31+G(d) 4.5 -4.3 5.4 -5.1 -6.3 5.9 16.6 -16.1 16.9 -16.2

thermodynamic properties

χ2

χ3

∆Eec

∆Hd

∆Ge

4.3 5.1 -5.9 16.1 16.1

-4.5 -5.4 6.4 -16.7 -16.9

0.00 2.59 5.44 15.70 18.89

0.00 2.50 5.25 14.82 17.96

0.00 2.34 4.49 16.33 18.81

3.1 3.5 -2.2 16.0 16.2

-3.3 -3.7 2.4 -16.5 -16.9

0.00 3.33 6.15 17.65 20.20

0.00 3.23 5.96 16.60 19.09

0.00 3.08 4.94 18.31 20.23

a Torsion angles are defined in Figure 1; units in degrees. b See the text for definition. For example, the first letter code tCu is the backbone conformation C with the trans peptide bond and the up-puckered structure. c Relative electronic energies in kcal/mol. d Relative enthalpy changes in kcal/mol at T ) 25 °C. e Relative Gibbs free energies in kcal/mol at T ) 25 °C. f The backbone conformation should be B according to the definition of Zimmerman et al. (ref 51), but it is represented as A in this work because the value of ψ is just beyond the boundary ψ ) -10° for the backbone conformation A.

conformations cFc and cFb for the cis-Pip dipeptide are larger than those between conformations cAd and cAu and between conformations cFd and cFu for the cis-Pro dipeptide, respectively.52 In particular, the boat-puckered Pip dipeptide prefers the b (βB) conformation for its trans and cis conformers but the b′ (NBγ) conformation for trans conformers with -180° e ψ e -135° or 60° e ψ e 180°. In the PESs of the Pip dipeptide started from tFc′ and cFc′ with the NCγ chair puckering (data not drawn separately), the third local minimum cAc′ is located at ψ ) -35°. However, these three local minima tFc′, cAc′, and cFc′ have relatively higher conformational energies of 5.56, 8.00, and 11.26 kcal/ mol to the global minimum tCc, respectively. It should be noted that the NCγ chair puckering is allowed at 120° e ψ e 180° for trans conformers and at -165° e ψ e -30° or 120° e ψ e 150° for cis conformers. In other regions of ψ, the b or b′ boat puckerings are preferred to the c′ puckering. In particular, these NCγ chair-puckered conformations have the values of χ0 ) +24° to +67°.56 The PESs of Aze and Pip dipeptides along the angle ψ at the HF/6-31+G(d) level with the CPCM method in chloroform and water are shown in Figures 2 and 4, respectively. In chloroform, there are no significant changes in PESs for both dipeptides compared with those in the gas phase, except for the appearance of local minima tAu and tFd for the Aze dipeptide and local minima tFc, tDc, tAb, and tFb′ for the Pip dipeptide, which are points of reflection in the gas phase. The PESs of both the dipeptides in water are similar to those in chloroform. However, four local minima tCc, tCb, tCb′, and tFb′ for the Pip dipeptide in chloroform are no longer local minima in water. The barrier height at ψ ≈ -105° become more lowered form the gas phase to chloroform to water for both dipeptides. However, the relative stabilities of local minima are affected with the increase of solvent polarity. In particular, the polyproline II (PPII)-like conformation tF becomes more preferred for both dipeptides and the relative stability of the conformation tC decreases as the solvent polarity increases. This may be caused by weakening a C7 hydrogen bond between C′dO of the amino group and N-H of the carboxyl group that plays a role in stabilizing the conformation tC in the gas phase, as seen for the Pro dipeptide.44,52 Preferred Conformations of Azetidine Dipeptide. In the Gas Phase. Table 1 lists the backbone torsion angles, endocyclic torsion angles, and thermodynamic properties of local minima

and transition states for Ac-Aze-NHMe optimized at the HF/ 6-31+G(d) and B3LYP/6-311++G(d,p) levels in the gas phase. The conformations and thermodynamic properties of local minima and transition states optimized at both the levels are quite similar, although the relative values of thermodynamic properties are larger at the B3LYP level than those at the HF level. The conformational stabilities of the Aze dipeptide are calculated to be in the order tCu > cAu > cFd at the both levels in the gas phase. The global minimum tCu has a C7 hydrogen bond between C′dO of the amino group and N-H of the carboxyl group, which plays a role in determining the lowest energy conformations for N-acetyl-N′-methylamides of alanine,44 proline,44,52,65-68 4(R)-substituted prolines,43,69 pseudoprolines,70 and 5-methylated prolines.71 The distances of this hydrogen bond for the Aze dipeptide are calculated to be 2.08 and 1.97 Å at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels, respectively, which are somewhat shorter than the values of 2.13 and 1.99 Å for the conformation tCu of the Pro dipeptide at the HF and B3LYP levels, respectively.44 The calculated thermodynamic properties indicate that relative conformational free energy (∆G) is governed by relative conformational electronic energy (∆Ee) for each conformation at both HF and B3LYP levels. The ∆G’s of conformations cAu and cFd to the most preferred conformation tCu are calculated to be 2.34 and 4.49 kcal/mol at the HF/6-31+G(d) level, respectively, and 3.08 and 4.94 kcal/mol at the B3LYP/6311++G(d,p) level, respectively, which are ∼0.6 kcal/mol higher than the ∆G’s of conformations cAd and cFd for the Pro dipeptide at both levels.44,52 Scheraga and his co-workers45 have carried out empirical energy calculations on the Aze dipeptide with the fixed geometries using the ECEPP/2 force field,72 where the azetidine ring was assumed to be planar based on X-ray structures for t-Boc-Aze-OH26 and NMR experiments for Ac-Aze-OH.36 According to their calculations, the overall conformational preferences of the Aze and Pro residues were found to be similar, but the near-extended conformation tF was energetically less favorable for the Aze residue than for the Pro residue. However, the appearance of local minima tA and tF for the Aze dipeptide by the ECEPP/2 force field seems to be caused by the fixed geometries and/or potential parameters used, because they are not local minima but points of reflection from HF/6-31+G(d) calculations, as described above. The relative stabilities for conformations cA and cF to the lowest-energy conformation



TABLE 2: Backbone Torsion Angles, Endocyclic Torsion Angles, and Thermodynamic Properties of Local Minima and Transition States for Aze Dipeptide Optimized at the CPCM HF/6-31+G(d) Level in Solutiona backbone torsion angles


conformerb

ω′

φ

ψ

ω

tCuf tAug cAu tFd cFd ts1 ts2

-163.8 -161.1 22.9 172.8 -8.9 126.1 -57.1

-79.7 -88.3 -92.3 -60.3 -58.4 -102.7 -94.2

47.2 -8.6 -12.3 145.6 164.6 -10.8 -4.4

176.6 -179.9 -176.5 178.8 175.6 -176.0 -178.4

tAu cAu tFd cFd ts1 ts2

-163.5 20.5 177.5 0.8 126.9 -54.8

-86.8 -92.0 -64.8 -67.6 -102.8 -96.5

-12.0 -10.9 152.5 164.8 -12.4 -8.6

-177.6 -177.1 176.7 175.5 -176.4 -177.4

χ0

χ1


χ2

χ3

∆Eec

∆Hd

∆Ge

chloroform 4.8 -4.6 5.7 -5.4 4.4 -4.2 -5.0 4.7 -4.3 4.0 16.5 -16.0 16.7 -16.0

4.5 5.3 4.2 -4.6 -4.0 15.9 16.0

-4.8 -5.7 -4.4 5.0 4.3 -16.6 -16.7

0.00 0.71 1.31 1.69 2.29 16.19 18.86

0.00 0.61 1.23 1.57 2.14 15.31 17.98

0.00 0.41 1.17 0.76 1.42 16.79 18.75

water 3.7 -3.5 2.4 -2.3 -2.2 2.1 -1.6 1.5 16.5 -16.1 17.2 -16.7

3.5 2.3 -2.1 -1.5 16.0 16.5

-3.8 -2.5 2.2 1.6 -16.6 -17.3

0.00 0.75 0.33 0.70 17.51 19.06

0.00 0.77 0.31 0.01 16.86 18.46

0.56 1.36 0.00 1.60 19.12 20.12

a,b,d,e See footnotes a, b, d, and e of Table 1. c The relative conformational free energy (∆Ee) is the sum of the conformational electronic energy (∆Ee,s) and the relative solvation free energy (∆∆Gsolv) in solution; units in kcal/mol. f The backbone conformation should be B according to the definition of Zimmerman et al. (ref 51), but it is represented as C in this work because the value of ψ is just beyond the boundary ψ ) 50° for the backbone conformation C. g See footnote f of Table 1.

TABLE 3: Thermodynamic Properties of Aze Dipeptide Computed at the B3LYP/6-311++G(d,p)//CPCM HF/ 6-31+G(d) Level in Solutiona chloroform b

conformer

∆Ee

∆Hd

tCu tAu cAu tFd cFd ts1 ts2

0.00 1.57 1.96 2.31 2.69 18.26 20.16

0.00 1.47 1.88 2.19 2.54 17.38 19.28

c

water ∆Ge

∆Ee

∆Hd

∆Ge

0.00 1.27 1.83 1.38 1.82 18.85 20.06

0.07 0.69 0.00 0.15 19.02 19.64

0.62 1.25 0.53 0.00 18.92 19.58

0.96 1.63 0.00 1.38 20.97 21.02

c

a Units in kcal/mol. b-e See footnotes b-e of Table 1. 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.

tC by the ECEPP/2 calculations are consistent with our HF/631+G(d) results, but their relative energies are underestimated by 0.8 and 2.4 kcal/mol from HF values, respectively. In Solution. Table 2 lists the backbone torsion angles, endocyclic torsion angles, and thermodynamic properties of local minima and transition states for the Aze dipeptide optimized at the CPCM HF/6-31+G(d) level in chloroform and water. The conformational stabilities of the Aze dipeptide by ∆G are calculated to be in the order tCu > tAu > tFd > cAu > cFd in chloroform, which is the same as that in the gas phase, except that the R-helical conformation tAu and PPII-like conformation tFd become preferred in chloroform. In particular, the conformation tFd becomes most preferred and is followed by the conformation tAu in water. The thermodynamic properties of the Aze dipeptide corrected by the single-point energies at the B3LYP/6-311++G(d,p)// CPCM HF/6-31+G(d) level in chloroform and water are listed in Table 3, which are used in the analysis of the conformational populations and the cis-trans isomerization below. The representative conformations tFd and cFd and the transition state ts1 for the Aze dipeptide at this corrected level in water are presented in Figure 5. The conformational stabilities by ∆G at this corrected level are similar to the orders by ∆G at the CPCM HF/6-31+G(d) level in chloroform and water, as described above. However, the relative stabilities of conformations cAu

Figure 5. Preferred conformations tFd and cFd and transition state ts1 of Aze dipeptide at the B3LYP/6-311++G(d,p)//CPCM HF/631+G(d) level in water. Hydrogen bond is represented by a broken line.

and cFd with the cis peptide bond become comparable in chloroform and the PPI-like structure cFd becomes more populated in water. Preferred Conformations of Piperidine Dipeptide. In the Gas Phase. The backbone torsion angles, endocyclic torsion angles, and thermodynamic properties of local minima and transition states for Ac-Pip-NHMe optimized at the HF/631+G(d) and B3LYP/6-311++G(d,p) levels in the gas phase are listed in Table 4. The conformations and thermodynamic properties of local minima and transition states optimized at both the levels are quite similar, and the relative values of thermodynamic properties at the B3LYP level are somewhat larger than those at the HF level. The conformational stabilities of the Pip dipeptide by ∆G are calculated to be in the orders tCc > cDc > tCb > cFc > tCb′ > cAb > tFc′ > cAc′ ≈ cFb > cFc′ at the HF level and tCc > cDc > tCb > tCb′ > cAb > cFc > tFc′ ≈ cAc′ > cFb > cFc′ at the B3LYP level. The global minimum tCc has a chair-puckered conformation with a C7 hydrogen bond between C′dO of amino group and N-H of the carboxyl group, as seen for the global minima tCd of the Pro dipeptide44,52 and tCu of the Aze dipeptide. The dis-

3502 J. Phys. Chem. B, Vol. 111, No. 13, 2007

Jhon and Kang

TABLE 4: Backbone Torsion Angles, Endocyclic Torsion Angles, and Thermodynamic Properties of Local Minima and Transition States for Pip Dipeptide Optimized at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) Levels in the Gas Phasea backbone torsion angles


conformerb

ω′

φ

ψ

ω

χ0

tCc cDc tCb tCb′ cFc tFc′ cAbf cAc′ cFb cFc′ ts1 ts2

-178.1 6.4 -171.5 -178.3 -11.5 -178.6 12.5 13.2 3.6 13.7 114.2 113.5

-91.3 -115.1 -90.4 -91.8 -83.0 -52.5 -99.5 -65.7 -80.5 -56.2 -146.6 -116.7

72.0 23.4 65.2 77.5 171.7 132.0 7.1 -35.2 161.1 143.6 22.1 1.0

-178.6 177.7 179.1 -175.9 -177.8 -175.4 179.4 -176.5 178.4 174.6 176.4 179.7

-49.5 -52.0 -28.0 -48.5 -49.7 41.7 -28.0 26.3 -22.9 35.7 -46.1 -10.4

tCc cDc tCb tCb′ cFc tFc′ cAbf cAc′ cFb cFc′ ts1 ts2

-177.8 5.7 -171.8 -177.6 -5.5 -177.9 10.5 11.9 2.2 13.0 115.2 114.7

-89.0 -113.5 -87.5 -89.7 -93.3 -51.0 -95.2 -64.8 -77.2 -41.8 -147.8 -117.1

73.5 22.0 66.6 76.1 140.8 129.3 3.9 -34.9 153.2 132.8 20.5 0.2

-177.1 177.3 -179.6 -175.8 177.2 -176.1 179.6 -177.2 177.7 175.2 176.4 179.5

χ1

χ2


χ3

χ4

χ5

∆Eec

∆Hd

∆Ge

54.5 54.6 -33.2 -66.9 55.9 -59.1 -27.2 -62.7 -21.2 -60.2 55.4 -16.5

-55.9 -54.8 61.3 38.5 -52.8 53.6 58.7 49.2 57.4 51.9 -52.9 61.5

54.7 54.7 -28.5 19.1 51.2 -45.6 -29.1 -31.4 -33.8 -40.0 48.4 -47.0

0.00 2.21 3.35 4.75 5.31 5.56 5.75 8.00 8.97 11.26 16.58 20.02

0.00 2.01 3.36 4.88 5.02 5.30 5.61 7.80 8.70 10.91 15.30 18.87

0.00 1.68 3.42 4.44 4.03 5.69 5.03 7.56 7.62 10.25 16.42 19.11

B3LYP/6-311++G(d,p) -48.0 47.5 -52.4 55.2 -50.8 49.8 -52.8 54.9 -27.7 56.5 -25.0 -32.5 -45.8 18.0 35.3 -67.2 -47.7 49.1 -54.5 56.3 38.9 -45.6 56.6 -59.4 -24.9 59.3 -32.8 -24.4 25.4 -39.5 58.3 -62.5 -20.4 58.8 -36.4 -20.8 46.8 -49.8 55.0 -56.6 -45.2 49.1 -54.2 55.6 -8.6 55.1 -41.2 -14.9

-55.3 -54.6 61.2 41.7 -53.5 53.2 58.5 48.9 58.4 55.7 -53.1 61.3

52.8 53.7 -28.9 14.6 50.7 -43.7 -32.1 -30.7 -36.5 -51.4 47.8 -48.6

0.00 2.28 3.18 4.16 5.62 6.56 6.10 8.22 9.12 10.66 18.93 22.08

0.00 1.48 3.12 4.20 4.81 6.30 5.93 7.95 8.19 10.25 16.88 20.76

0.00 2.67 3.05 3.80 5.14 6.79 5.05 6.92 8.69 9.66 19.49 21.11

HF/6-31+G(d) 47.6 -51.3 50.6 -52.9 56.1 -24.0 17.3 37.0 51.5 -55.7 -47.4 56.8 59.6 -30.0 -40.1 58.6 59.8 -35.8 -45.2 57.8 49.6 -54.3 55.6 -39.8

a Torsion angles are defined in Figure 1; units in degrees. b See the text for definition. For example, the first letter code tCc is the backbone conformation C with the trans peptide bond and the chair-form structure. c-e See footnotes c-e of Table 1. f See footnote f of Table 1.

tances of this hydrogen bond for the Pip dipeptide are calculated to be 2.22 and 2.10 Å at the HF/6-31+G(d) and B3LYP/6311++G(d,p) levels, respectively, which are somewhat longer than the values of 2.11 and 1.98 Å for the conformation tCd of the Pro dipeptide at the HF and B3LYP levels, respectively.44 The calculated thermodynamic properties indicate that ∆G is governed by ∆Ee for each conformation at both HF and B3LYP levels, as seen for the Aze dipeptide. The values of ∆G for the second preferred conformation cDc with the cis imide bond to the most preferred conformation tCc are calculated to be 1.68 and 2.67 kcal/mol at the HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels, respectively. The ∆G’s of the boat-puckered conformation tCb from the chair-puckered conformation tCc for the Pip dipeptide are estimated to be 3.42 and 3.05 kcal/mol at the HF/6-31+G(d) and B3LYP/6311++G(d,p) levels, respectively, which are ∼1.8 kcal/mol higher than those of the up-puckered conformation tCu from the down-puckered conformation tCd for the Pro dipeptide at both levels.54 The conformation tFc′ with the NCγ chair puckering is ∼6 kcal/mol higher in ∆G than the most preferred conformation tCc with the NCγ chair puckering at both levels. In particular, it should be noted that the PPII-like conformation tF is not a local minimum for the Pro dipeptide in the gas phase.44,52 The conformation cAc′ is 2.7 kcal/mol more stable in ∆G than the conformation cFc′ at both levels. However, the conformation cFc′ is ∼5 kcal/mol higher in ∆G than the conformation tFc′ at both levels. The torsion angles φ and ψ of the conformations tFc′ and cFc′ with χ0 ≈ +40°56 are shifted by about +30° and -20° from those of the conformations tCc and cFc, respectively, at both levels. The conformation tCb′ with the NBγ boat puckering is ∼1 kcal/mol higher in ∆Ee and ∆G than the conformation tCb with the βB boat puckering, and there is a shift in ψ by ∼+10° in the conformation tCb′ from the conformation tCb at both levels.

Empirical conformational energy computations of the Pip dipeptide indicate that (a) the conformations with the trans imide peptide bond are slightly more stable than the cis conformations and (b) the chair conformations of the piperidine ring are appreciably more stable by 3-5 kcal/mol than the boat conformations.48 In Solution. The backbone torsion angles, endocyclic torsion angles, and thermodynamic properties of local minima and transition states for the Pip dipeptide optimized at the CPCM HF/6-31+G(d) level in chloroform and water are listed in Table 5. The conformational stabilities of the Pip dipeptide by ∆G are calculated to be in the orders tFc > tCc ≈ tDc > cDc > cFc > tFc′ ≈ tCb ≈ tAb > tFb′ ≈ cAb > tCb′ > cFb > cAc′ > cFc′ in chloroform and tFc > tDc > tFc′ ≈ cFc > cDc ≈ tAb > cFb > cAb > cFc′ > cAc′ in water. The PPII-like conformation tFc becomes feasible in chloroform and water and the ∆G’s of all conformations relative to the global minimum tFc become more elevated. On going from gas phase to chloroform to water, the conformations tFc′ and cFc′ with the γ NC chair puckering become more preferred. The value of ∆G for the most preferred cis conformation cDc to the most preferred conformation tFc for the Pip dipeptide are calculated to be 1.27 and 4.01 kcal/mol in chloroform and water, respectively. The ∆G of the most preferred boat-puckered conformation tCb from the most preferred chair-puckered conformation tFc for the Pip dipeptide is estimated to be 3.30 kcal/mol in chloroform and the corresponding value for conformations tAb and tFc is calculated to be 4.22 kcal/mol in water. This indicates that instability of boat-puckered conformation relative to the chair-puckered conformation is similar in the gas phase and chloroform but increases in water. However, the ∆G’s of the most preferred up-puckered conformation tFu from the most preferred down-puckered conformation tFd for



TABLE 5: Backbone Torsion Angles, Endocyclic Torsion Angles, and Thermodynamic Properties of Local Minima and Transition States for Pip Dipeptide Optimized at the CPCM HF/6-31+G(d) Level in Solutiona backbone torsion angles


conformerb

ω′

φ

ψ

ω

χ0

tCc tFc tDc cDc cFc tCb tFc′ tAbf cAbf tCb′ tFb′ cFb cAc′ cFc′ ts1 ts2

-177.4 175.0 -172.6 7.9 -12.1 -170.9 -176.4 -169.7 12.6 -178.3 177.6 3.2 11.1 8.5 113.8 112.8

-93.4 -79.7 -118.1 -116.7 -83.1 -90.8 -51.9 -89.2 -97.8 -93.3 -85.3 -81.1 -67.0 -61.3 -145.5 -112.9

64.8 154.5 28.1 22.0 172.7 57.9 136.6 -4.0 3.5 73.1 152.8 162.7 -33.5 146.9 19.4 -4.7

179.6 179.8 174.2 176.7 -178.0 177.7 -178.3 176.5 179.1 -177.1 178.5 178.8 -175.0 174.7 176.1 179.9

-50.1 -44.6 -53.5 -52.3 -48.8 -29.1 42.4 -18.6 -27.0 -49.0 -44.0 -22.8 18.9 22.3 -45.6 -6.8

tFc tDc cDc cFc tFc′ tAb cAbf cFb cAc′ cFc′ ts1 ts2

176.2 -174.0 9.6 -13.6 -174.7 -169.5 12.6 4.9 9.8 6.6 114.8 112.8

-80.5 -116.0 -121.3 -77.4 -53.2 -84.8 -90.1 -79.4 -65.8 -64.2 -143.8 -113.5

161.5 24.6 25.9 166.3 141.3 -10.0 -4.6 160.3 -33.5 147.1 14.8 -7.5

179.0 175.3 176.3 179.9 176.6 179.5 179.3 177.8 -175.5 175.5 176.5 0.2

-44.2 -53.6 -54.3 -43.8 41.4 -15.3 -20.4 -18.5 18.8 15.3 -44.7 -7.3

a,b

χ1


χ3

χ4

χ5

∆Eec

∆Hd

∆Ge

chloroform 48.0 -51.5 48.1 -55.4 51.4 -52.8 50.8 -53.1 51.2 -55.9 56.9 -24.1 -48.0 56.8 58.4 -37.4 59.8 -31.5 18.9 35.5 10.2 42.4 59.8 -36.1 -36.3 59.1 -38.8 59.4 49.4 -54.5 54.2 -42.5

54.4 57.4 53.8 54.6 56.1 -33.7 -58.8 -19.6 -25.7 -66.6 -68.0 -20.9 -64.1 -63.0 55.5 -12.8

-55.9 -52.9 -55.0 -55.0 -52.7 61.5 53.7 58.4 58.2 39.3 37.0 57.2 46.9 47.0 -52.6 59.6

55.1 47.6 56.2 55.3 50.4 -27.9 -46.1 -38.0 -29.9 18.3 19.2 -33.9 -24.6 -26.9 47.9 -49.4

0.00 0.04 0.37 1.14 2.03 2.90 2.96 3.62 4.35 4.85 4.89 5.53 6.17 7.23 16.23 19.57

0.03 0.00 0.26 1.09 1.92 2.97 2.76 3.62 4.37 5.03 4.93 5.44 6.14 7.14 15.04 18.52

0.27 0.00 0.33 1.27 1.67 3.30 3.19 3.42 4.33 4.66 4.08 5.06 6.03 7.00 16.50 19.21

water 48.5 -56.0 51.5 -53.1 51.4 -52.5 49.2 -56.9 -47.7 57.1 57.7 -40.2 59.4 -37.6 58.7 -38.6 -37.7 60.3 -35.7 60.2 48.8 -54.7 54.5 -42.6

57.4 54.1 53.8 57.4 -59.3 -16.2 -19.4 -18.0 -63.9 -64.2 55.8 -12.9

-52.5 -55.3 -56.1 -52.2 53.5 57.2 57.4 57.0 45.4 44.2 -52.4 59.5

47.0 56.6 58.0 46.4 -45.2 -40.6 -36.0 -37.4 -23.1 -19.9 47.2 -49.0

0.00 1.06 2.26 2.40 2.18 3.49 5.23 5.08 6.22 5.85 18.04 21.28

0.00 1.40 2.16 2.78 2.01 3.73 5.76 5.32 6.50 6.03 16.91 20.35

0.00 1.96 4.01 2.78 2.50 4.22 6.19 5.20 6.72 6.37 18.61 21.49

See footnotes a and b of Table 4. c See footnote c of Table 2.

d,e

χ2

See footnotes d and e of Table 1.

f

See footnote f of Table 1.

TABLE 6: Thermodynamic Properties of Pip Dipeptide Computed at the B3LYP/6-311++G(d,p)//CPCM HF/ 6-31+G(d) Level in Solutiona chloroform

water

conformerb

∆Eec

∆Hd

∆Ge

tCc tFc tDc cDc cFc tCb tFc′ tAbf cAbf tCb′ tFb′ cFb cAc′ cFc′ ts1 ts2

0.00 0.97 0.39 1.09 2.13 2.76 3.58 3.96 4.65 4.25 5.49 5.43 6.28 6.62 18.47 21.70

0.00 0.90 0.25 1.01 1.98 2.79 3.35 3.93 4.63 4.40 5.50 5.30 6.23 6.50 17.24 20.61

0.00 0.66 0.08 0.95 1.50 2.88 3.54 3.49 4.35 3.79 4.41 4.69 5.88 6.13 18.46 21.06

∆Eec

∆Hd

∆Ge

0.00 0.35 1.58 1.76

0.00 0.68 1.48 2.14

0.00 1.24 3.33 2.13

1.70 3.02 4.71

1.53 3.27 5.24

2.02 3.75 5.67

4.07 5.48 4.30 19.62 22.72

4.31 5.75 4.48 18.49 21.79

4.19 5.97 4.83 20.20 22.93

a Units in kcal/mol. b See footnote b of Table 4. c-e See footnotes c-e of Table 1. The B3LYP/6-311++G(d,p) single-point energies were replaced for the conformational HF/6-31+G(d) electronic energies of Table 5. The vibrational and thermal contributions used are those obtained at the CPCM HF/6-31+G(d) level in Table 5. f See footnote f of Table 1.

the Pro dipeptide in chloroform and water are estimated to be 0.42 and 0.01 kcal/mol, respectively.44 The thermodynamic properties of the Pip dipeptide corrected by the single-point energies as the B3LYP/6-311++G(d,p)// CPCM HF/6-31+G(d) level in chloroform and water are listed in Table 6. The representative conformations tFc and cFc and the transition state ts1 for the Pip dipeptide at this corrected

Figure 6. Preferred conformations tFc and cFc and transition state ts1 of Pip dipeptide at the B3LYP/6-311++G(d,p)//CPCM HF/631+G(d) level in water. Hydrogen bond is represented by a broken line.

level in water are presented in Figure 6. The conformational stabilities by ∆G at this corrected level are similar to the orders by ∆G at the CPCM HF/6-31+G(d) level in chloroform and water, as described above. However, conformations tCc and tDc become equally most preferred and are followed by the conformation tFc in chloroform. Comparison of Structural Parameters for Preferred Conformations. The structural parameters of the most preferred

3504 J. Phys. Chem. B, Vol. 111, No. 13, 2007 trans and cis conformations by ∆G for Aze and Pip dipeptides are compared to those of the Pro dipeptide in the gas phase and in water. The structural parameters for the Pro dipeptide are taken from ref 44. In the gas phase, there are shifts of +11°, +1°, and -29° in backbone torsion angles ω′, φ, and ψ, respectively, for the conformation tCu of the Aze dipeptide from those of the Pro dipeptide and the corresponding shifts for the conformation cAu are +20°, -17°, and +10°, respectively, at the HF/6-31+G(d) level. The similar amounts of shift are found at the B3LYP/6-311++G(d,p) level in the gas phase. However, the corresponding shifts are +5°, +9°, and +1° for the conformation tFd, respectively, and -1°, +9°, and +7° for the conformation cFd, respectively, at the CPCM HF/6-31+G(d) level in water. There are some small shifts of -5° to +2° in backbone torsion angles ω', φ, and ψ for the conformation tCc for the Pip dipeptide from those of the conformation tCd for the Pro dipeptide at both HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels in the gas phase. However, the relatively larger shifts of -26° and +33° in torsion angles φ and ψ, respectively, are found for the conformation cDc of the Pip dipeptide from those of the conformation cAd for the Pro dipeptide at the HF/631+G(d) level and the corresponding shifts of -22° and +27° are found at the B3LYP/6-311++G(d,p) level, respectively. At the CPCM HF/6-31+G(d) level in water, there are shifts of +6°, -7°, and +10° in torsion angles ω′, φ, and ψ, respectively, for the conformation tFc of the Pip dipeptide from those of the conformation tFd for the Pro dipeptide and the corresponding shifts for the conformation cFc of the Pip dipeptide are +20°, -17°, and +10°, respectively, from those of the conformation cFd for the Pro dipeptide. There are no significant changes in bond lengths for the most preferred trans and cis conformations of Aze and Pip dipeptides compared with those of the Pro dipeptide at both HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels in the gas phase and at the CPCM HF/6-31+G(d) level in water. However, the C′-N, N-CR, and CR-C′ bonds for the Aze dipeptide become shorter by 0.003-0.015 Å in both the gas phase and water, whereas the C′-N bond in the gas phase and the C′-N, N-CR, and CR-C′ bonds in water become longer by 0.005-0.009 and 0.006-0.017 Å, respectively, for the Pip dipeptide. In particular, there are remarkable changes in the bond angles around the N-CR bond for both Aze and Pip dipeptides in the gas phase and in water. The bond angles of Cγ-N-CR, N-CRCβ, and N-Cγ-Cβ for the azetidine ring of the Aze dipeptide are decreased by 14-19° from those for the pyrrolidine ring of the Pro dipeptide. The bond angles of C′-N-CR, C′-N-Cγ, N-CR-C′, and Cβ-CR-C′ for the Aze dipeptide are increased by 2-9° from those of the Pro dipeptide. However, only the bond angles of N-CR-Cβ, CR-Cβ-Cγ, and N-C-Cδ for the Pip dipeptide are increased by 8-11° from those of the Pro dipeptide. Recently, 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 Cγ-N-CR for prolyl ring) around the nitrogen.43,44,56 As the quantity δ becomes more negative, the degree of nonplanarity of the nitrogen increases more. The calculated values of the quantity δ are -6° and -11° at the HF/6-31+G(d) level and -3° and -12° at the B3LYP/ 6-311++G(d,p) level for conformations tCu and cAu of the Aze dipeptide, respectively, in the gas phase. The corresponding values are -1° for conformations tCc and cDc of the Pip dipeptide at both levels. These results indicate that the imide

Jhon and Kang nitrogens of local minima for the Aze dipeptide have more the pyramidal character than those for the Pro dipeptide, because the values of δ are -1° and -3° for the same conformations of the Pro dipeptide at both levels.44 In water, the nonplanarity of the imide nitrogen, however, is negligible (i.e., δ ≈ 0°) for both Aze and Pro dipeptides, whereas the values of δ are estimated to be -3° for conformations tFc and cFc of the Pip dipeptide. Orientation of NHMe Group at CR. It has been found that monosubstituted cyclohexanes exhibit a preference to adopt an equatorial orientation, whereas the steric hindrance between adjacent equatorial groups can provoke a tendency of the substituents to adopt axial orientations for 1,2-disubstituted cyclohexanes.73 In the case of the prolyl ring and its analogues, the backbone torsion angle φ is calculated to be -60° to -90°, -80° to -96°, and -80° to -121° for local minima of Pro, Aze, and Pip dipeptides, respectively, at both HF and B3LYP levels in the gas phase and in solution, except for the conformations tFd and cFd for the Aze dipeptide and the conformations tFc′, cAc′, and cFc′ for the Pip dipeptide (see Tables 5 and 6 of ref 44 and Tables 1, 2, 4, and 5). On going from Pro to Aze to Pip, the axiality (i.e., a tendency to adopt the axial orientation) of the NHMe group becomes stronger, which can be ascribed to reduce the steric hindrances between 1,2-substituted Ac and NHMe groups. In particular, the conformations tFc′, cAc′, and cFc′ for the Pip dipeptide have a very small value of φ ≈ -50°, which seems to result in the puckering change from c (NCγ) to c′ (NCγ) and the shift in the torsion angle ψ by about -20°, compared to those of the conformations tFc and cFc. It should be noted that the transition state structures have a stronger axiality than local minima for all three dipeptides. Comparison with X-Ray structures. The azetidine rings in X-ray structures of Aze-containing peptides t-Boc-Aze-OH26 and Z-Pro-Aze-OH27 are slightly up-puckered, whereas the preferred conformations calculated in this work are up-, up-, and down-puckered in the gas phase, chloroform, and water, respectively. In addition, the values of torsion angles φ and ψ for X-ray structures of these two peptides are different from our calculated ones in the gas phase and in solution. The piperidine ring can adopt chair and boat conformations but only the chair conformation preferentially exists in X-ray structures of Pip-containing peptides,32-34 which is consistent with our calculated results for the Pip dipeptide. The backbone torsion angles φ and ψ of an X-ray structure for t-Boc-Pip-NHMe33 are quite similar to those of a preferred conformation tDc for the Pip dipeptide in chloroform and water. However, the backbone conformations of X-ray structures for t-Boc-AibPip-Aib-OMe32 and t-Boc-D-Ala-Pip-NHiPr34 are distorted left- and right-handed R-helices, respectively, which are not identified as local minima for the Pip dipeptide in the gas phase and in solution. These conformational differences may be ascribed to the different terminal groups as well as the packing and intermolecular hydrogen bonds in crystal that cannot be considered in the isolated Aze and Pip dipeptides. Population of Backbone Conformations. The populations of the backbone conformations for Aze and Pip dipeptides are listed in Table 7. Each population was computed using the normalized Boltzmann weight by the relative free energy at the B3LYP/6-311++G(d,p) level in the gas phase and at the B3LYP/6-311++G(d,p)//CPCM HF/6-31+G(d) level in chloroform and water. In the gas phase, the populations of the conformation tCu for the Aze dipeptide and the conformation tCc for the Pip dipeptide with C7 intramolecular hydrogen bonds are found to



TABLE 7: Populations of Backbone Conformations, Rotational Barriers, and Relative Energies of Cis Conformers for Aze, Pip, and Pro Dipeptides Calculated at the B3LYP/6-311++G(d,p) Level in the Gas Phase and in Solution backbone populationsa solvent

C

gas phase chloroform water

99.4 76.5 0.0


98.9 40.4 0.0


97.4 54.9 0.0

D

A

F

cise

0.6 12.5 19.2

0.0 11.0 80.8

0.6 7.0 11.8

0.0 0.1 0.2

0.0 16.5 89.3

1.1 11.3 2.7

2.5 12.2 10.1

0.0 32.9 89.9

2.5 9.0 23.3

rotational barrierb,c exptl cise

∆Gqtc

∆Gqct

relative energyb,d ∆Gc/t

Ac-Aze-NHMe 10f 42,f 45,g 20,h 40i

18.31 18.85 20.97

15.23 17.02 19.58 (17.1,f 17.7,h 17.3i)

3.08 1.83 1.38

19.49 18.46 20.20 (17.8j)

16.82 17.51 18.07 (17.0,h 17.2j)

2.67 0.95 2.13 (0.6j)

19.15 19.32 21.61 (20.4j)

16.99 17.68 20.93 (19.3,h 19.6,i 19.8j)

2.16 1.64 0.68 (0.6j,o)

Ac-Pip-NHMe 1.1 43.0 10.6

38,g 13,h 21,i 28,j 25k Ac-Pro-NHMel 14,m 15n 6,h 23,i 27,j 24,n 28o

a Units in %. The populations were computed using total free energies of Tables 1 and 3 for Ac-Aze-NHMe, and Tables 4 and 6 for AcPip-NHMe at 25 °C, respectively. b Energies in kcal/mol. The lowest total energy for each of trans, cis, and transition state conformations was used for these calculations. Experimental values are listed in parentheses. c ∆Gqtc and ∆Gqct represent the barriers for the trans-to-cis and cis-totrans rotations for the Ac-X (X ) Aze, Pip, or Pro) peptide bond, respectively. d ∆Gc/t is the relative total energy of the cis conformer to the trans conformer. e Cis Ac-X (X ) Aze, Pip, or Pro) peptide bonds. f For Ac-Aze-OH; from ref 36. g For Ac-Aze-OH and Ac-Pip-OH; from ref 37. h For Ala-X-(4-)NA; from ref 41. iFor Ala-Gly-X-Phe-(4-)NA; from ref 41. j From ref 39. k For Ac-Gly-Ala-Pip-Gly-NH2; from ref 42. l Calculated values for Ac-Pro-NHMe; from ref 44. m From ref 35. n From ref 38. o From ref 40.

be dominant. Populations of R-helical (i.e., tA) and polyproline II-like (i.e., tF) structures are computed to be negligible. The cis populations are calculated to be 0.6% and 1.1% for Aze and Pip dipeptides, which are due to conformations cAu and cDc for Aze and Pip dipeptides, respectively. The calculated populations of backbone and cis conformations for Aze and Pip dipeptides are quite similar to those of the Pro dipeptide.44 In chloroform, the conformation tCu for the Aze dipeptide is found to be most preferred as in the gas phase, followed by R-helical conformations tAu and cAu and polyproline-like conformations tFd and cFd. In the case of the Pip dipeptide, conformations tCc and tDc become most populated and are followed by the PPII-like conformation tFc. The populations for these two dipeptides are different from those for the Pro dipeptide.44 The cis populations for Aze and Pip dipeptides are calculated to be 7.0% and 11.3%, respectively, in chloroform, which are ascribed to the conformations cFd and cAu for the Aze dipeptide and the conformations cDc and cFc for the Pip dipeptide. In water, the PPII-like conformations tFd and tFc for Aze and Pip dipeptides, respectively, become most populated, as seen for the Pro dipeptide.44 However, the next preferred conformations are tAu, tDc, and tAd for Aze, Pip, and Pro dipeptides, respectively. The cis populations are calculated to be 11.8% and 2.7% for Aze and Pip dipeptides in water, respectively, which are due to the conformations cFd and cAu for the Aze dipeptide and the conformation cFc for the Pip dipeptide. The cis population increases as the solvent polarity increases for both Aze and Pip dipeptides, as seen for the Pro dipeptide,44 except for the decrease of cis population for the Pip dipeptide on going from chloroform to water. From NMR experiments in water, the cis populations of the Ac-X peptide bond for AcX-OH (X ) Aze, Pip, and Pro) are estimated to in the order Pro > Aze > Pip.35-37 The cis populations of the Pip residue are calculated to be quite similar to those of the Pro residue for Ac-X-NHMe,38-40 Ala-X-(4-)NA,41 and Ala-Gly-XPhe-(4-)NA.41 However, the cis populations of the Aze residue are computed to prevail over those of the Pip and Pro residues for Ala-X-(4-)NA and Ala-Gly-X-Phe-(4-)NA.41 Based on these experimental results, the cis populations can be estimated to be 20-45% and 21-38% for Aze and Pip residues in water, respectively, which are larger than those for Aze and

Pip dipeptides computed in the present work. The discrepancy between calculated and observed cis populations could be ascribed to the different length of peptides and end groups employed in calculations and experiments. Cis-Trans Isomerization. We located two transition states ts1 and ts2 for the cis-trans isomerization of each Ac-X peptide bond for Aze and Pip dipeptides in the gas phase and in solution. Transition states ts1 and ts2 for the Aze dipeptide have both up puckering and correspond to transition states ts2 and ts4 for the Pro dipeptide, respectively.44,52 They also correspond to syn/exo and anti/exo conformations according to the definition in ref 74, respectively. However, transition states ts1 and ts2 for the Pip dipeptide have chair and boat puckerings, respectively, and correspond to transition state ts1 (i.e., syn/ exo) for the Pro dipeptide. In particular, transition state ts1 has a lower free energy than ts2 for both Aze and Pip dipeptides in the gas phase and in solution. This indicates that the cis-trans isomerization proceeds in common through only the clockwise rotation with ω′ ≈ +120° about azetyl and piperidyl peptide bonds in the gas phase and in solution, as seen for alanyl and prolyl peptide bonds.44 At the B3LYP/6-311++G(d,p) level in the gas phase, the rotational barriers (∆Gqtc and ∆Gqct) to the trans-to-cis and cisto-trans isomerizations for azetidyl and piperidyl peptide bonds are estimated to be 18.31 and 15.23 kcal/mol for the Aze dipeptide and 19.49 and 16.82 kcal/mol for the Pip dipeptide, respectively. At the B3LYP/6-311++G(d,p)//CPCM HF/631+G(d) level, the values of ∆Gqtc and ∆Gqct are calculated to be 18.85 and 17.02 kcal/mol for the Aze dipeptide and 18.46 and 17.51 kcal/mol for the Pip dipeptide in chloroform, respectively. The corresponding values are computed to be 20.97 and 19.58 kcal/mol for the Aze dipeptide and 20.20 and 18.07 kcal/mol for the Pip dipeptide in water, respectively. Thus, the values of ∆Gqtc and ∆Gqct are lowered by 1-2 kcal/mol for the Aze dipeptide and 1-3 kcal/mol for the Pip dipeptide from those of the Pro dipeptide in the gas phase and in solution, except that the value of ∆Gqtc for the Pip dipeptide is elevated by 0.3 kcal/mol in the gas phase.44 These calculated results are consistent with those from experiments that the rotational barriers to the cis-to-trans isomerization of Aze and Pip residues are ∼2 kcal/mol lower than that of the Pro residue in water.39,41 In particular, the rotational barriers for Aze and Pip dipeptides

3506 J. Phys. Chem. B, Vol. 111, No. 13, 2007 increase as the solvent polarity increases, as seen for the Pro dipeptide, except for the Pip dipeptide on going from gas phase to chloroform. By analysis of the contributions to rotational barriers, cistrans isomerizations for azetidyl and piperidyl bonds are proven to be entirely enthalpy driven in the gas phase and in solution, to which the electronic energies have contributed considerably, as seen for the Ala dipeptide,44 Pro dipeptide,44,52,66 and Pro derivatives.43,70,71 This is consistent with the experimental results on proline-containing peptides, kinetically determined as a function of temperature.75 The kinetic and spectroscopic results have been interpreted as the evidence that indicates the existence of an intramolecular hydrogen bond between the prolyl nitrogen and the following amide N-H group for the transition state structure, which is capable of catalyzing the prolyl isomerization by up to 260fold in model peptides.76 The strength of this hydrogen bond is explained in terms of the hydrogen-bond distance and the pyramidality of imide nitrogen in the gas phase and in water.43,44 The hydrogen-bond distances d(N‚‚‚H-NNHMe) between the imide nitrogen and the following hydrogen of NHMe group for the ts1 structures of Aze, Pip, and Pro dipeptides are computed to be 2.24, 2.20, and 2.1744 Å at the B3LYP/6-311++G(d,p) level in the gas phase, respectively.77 The corresponding distances for Aze, Pip, and Pro dipeptides are computed to be 2.38, 2.27, and 2.3244 Å at the CPCM HF/6-31+G(d) level in water, respectively. We described the degree of nonplanarity (i.e., the pyramidal sp3 character) of the imide nitrogen by the quantity δ computed from three bond angles around the nitrogen above. As the magnitude of δ becomes bigger, the imide nitrogen has more the pyramidal sp3 character and the potency to form the hydrogen bond. In the gas phase, the calculated values of δ for the ts1 structures of Aze, Pip, and Pro dipeptides are -39°, -21°, and -26°44 at the B3LYP/6-311++G(d,p) level, respectively. The calculated value of δ for the Pro dipeptide is similar to the experimental value of -27° for trimethylamine.80 The corresponding values for Aze, Pip, and Pro dipeptides are computed to be -35°, -18°, and -22°44 at the CPCM HF/631+G(d) level in water, respectively. These results indicate that the imide nitrogens of the ts1 structures for Aze and Pip dipeptides have more and less the pyramidal character than that for the Pro dipeptide, respectively. From these analyses of two structural quantities for the imide cis-trans isomerization, the pertinent distance d(N‚‚‚H-NNHMe) and the pyramidality of imide nitrogen can describe the role of this hydrogen bond in stabilizing the transition state structure but the lower rotational barriers for Aze and Pip dipeptides than those for the Pro dipeptide, which is observed from experiments, cannot be rationalized. Conclusions The change of ring size by deleting a CH2 group from or adding a CH2 group to the prolyl ring results the remarkable changes in backbone and ring structures compared with those of the Pro dipeptide. Although there are no significant changes in bond lengths, the C′-N imide bonds for Aze and Pip dipeptides become somewhat shorter and longer than those for the Pro dipeptide, respectively. There are remarkable changes in the bond angles around the N-CR bond for both Aze and Pip dipeptides. The four-membered azetidine ring can have either puckered structure depending on the backbone structure because of the less puckered structure. The six-membered piperidine ring can

Jhon and Kang adopt chair and boat conformations, but the chair conformation is more preferred than the boat conformation. These calculated preferences for puckering are consistent with experimental results from analysis of X-ray structures of Aze- and Pipcontaining peptides. On going from Pro to Aze to Pip, the axiality (i.e., a tendency to adopt the axial orientation) of the NHMe group becomes stronger, which can be ascribed to reduce the steric hindrances between 1,2-substituted Ac and NHMe groups. The relative stabilities of local minima are affected with the increase of solvent polarity. As the solvent polarity increases, the polyproline II-like conformation becomes more populated and the relative stability of conformation tC decreases for both Aze and Pip dipeptides, as seen for the Pro dipeptide. This may be caused by weakening a C7 hydrogen bond between C′dO of the amino group and N-H of the carboxyl group that plays a role in stabilizing the conformation tC in the gas phase. The cis population and rotational barriers for the imide bond increase with the increase of solvent polarity for both Aze and Pip dipeptides, as seen for the Pro dipeptide. In particular, the cis-trans isomerization proceeds in common through only the clockwise rotation with ω′ ≈ +120° about azetyl and piperidyl peptide bonds in the gas phase and in solution, as seen for alanyl and prolyl peptide bonds. The pertinent distance d(N‚‚‚HNNHMe) and the pyramidality of imide nitrogen can describe the role of this hydrogen bond in stabilizing the transition state structure, but the lower rotational barriers for Aze and Pip dipeptides than those for the Pro dipeptide, which is observed from experiments, cannot be rationalized. Acknowledgment. This work is supported by a grant from Chungbuk National University in 2006. Supporting Information Available: Relationships between torsion angles about the N-CR bond and pyramidality at prolyl nitrogen for local minima and transition states of Pro, Aze, and Pip dipeptides. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Fowden, L. Nature 1955, 176, 347. (2) Fowden, L.; Richmond, M. H. Biochim. Biophys. Acta 1963, 71, 459. (3) Boni, R.; Verdini, A. S. Macromolecules 1973, 6, 517. (4) Boni, R.; Di Blasi, R.; Verdini, A. S. Macromolecules 1975, 8, 140. (5) Takeuchi, T.; Rosenbloom, J.; Prockop, D. J. Biochim. Biophys. Acta 1969, 175, 156. (6) Lane, J. M.; Dehm, P.; Prockop, D. J. Biochim. Biophys. Acta 1971, 236, 517. (7) Uitto, J.; Prockop, D. J. Biochim. Biophys. Acta 1974, 336, 234. (8) Boni, R.; Di Blasi, R.; Farina, A.; Verdini, A. S. Biopolymers 1976, 15, 1233. (9) Tsai, F.-H.; Overberger, C. G.; Zand, R. Biopolymers 1990, 30, 1039. (10) Matsoukas, J. M.; Agelis, G.; Hondrelis, J.; Yamdagni, R.; Wu, Q.; Ganter, R.; Smith, J. R.; Moore, D.; Moore, G. J. J. Med. Chem. 1993, 36, 904. (11) Baum, B. J.; Troxler, R. F.; Kagan, H. M.; Grasso, J. A.; Faris, B.; Franzblau, C. Biochem. Biophys. Res. Commun. 1973, 53, 1350. (12) Trotter, E. W.; Berenfeld, L.; Krause, S. A.; Petsko, G. A.; Gray, J. V. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 7313. (13) Hayes, C. S.; B. Bose; Sauer, R. T. J. Biol. Chem. 2002, 277, 33825. (14) Schmidt-Glenewinkel, T.; Nomura, Y.; Giacobini, E. Neurochem. Res. 1977, 2, 619. (15) Nomura, Y.; Schmidt-Glenewinkel, T.; Giacobini, E. DeV. Neurosci. 1978, 1, 239. (16) Giacobini, E.; Nomura, Y.; Schmidt-Glenewinkel, T. Cell. Mol. Biol. 1980, 26, 135.

Conformational Preferences of Aze and Pip Dipeptides (17) Takagi, T.; Bungo, T.; Tachibana, T.; Saito, E.-S.; Saito, S.; Yamasaki, I.; Tomonaga, S.; Denbow, D. M.; Furuse, M. J. Neurosci. Res. 2003, 73, 270. (18) Tanaka, H.; Kuroda, A.; Marusawa, H.; Hatanaka, H.; Kino, T.; Goto, T.; Hashimoto, M. J. Am. Chem. Soc. 1987, 109, 5031. (19) Boger, D. L.; Chen, J.-H.; Saionz, K. W. J. Am. Chem. Soc. 1996, 118, 1629. (20) Gupta, S.; Krasnoff, S. B.; Roberts, D. W.; Renwick, J. A. A. J. Am. Chem. Soc. 1991, 113, 707. (21) Copeland, T. D.; Wondrak, E. M.; Tozser, J.; Roberts, M. M.; Oroszlan, S. Biochem. Biophys. Res. Commun. 1990, 169, 310. (22) Tsuda, Y.; Cygler, M.; Gibbs, B. F.; Pedyczak, A.; Fe´thie`re, J.; Yue, S. Y.; Konishi, Y. Biochemistry 1994, 33, 14443. (23) Daum, S.; Fangha¨nel, J.; Wildemann, D.; Schiene-Fischer, C. Biochemistry 2006, 45, 12125. (24) Berman, H. M.; McGandy, E. L.; Burgner, J. W., II; VanEtten, R. L. J. Am. Chem. Soc. 1969, 91, 6177. (25) Inagaki, F.; Takahashi, S.; Tasumi, M.; Miyazawa, T. Bull. Chem. Soc. Jpn. 1975, 48, 1590. (26) Cesari, M.; D’Ilario, L.; Giglio, E.; Rerego, G. Acta Crystallogr., Sect. B 1975, 31, 49. (27) Blessing, R. H.; Smith, G. D. Acta Crystallogr., Sect. B 1982, 38, 1203. (28) Gdaniec, M.; Milewska, M. J.; Polonski, T. Acta Crystallogr., Sect. E 2004, 60, o181. (29) Bhattacharjee, S. K.; Chacko, K. K. Acta Crystallogr., Sect. B 1979, 35, 396. (30) Rae, I. D.; Raston, C. L.; White, A. H. Aust. J. Chem. 1980, 33, 215. (31) Taga, T.; Tanaka, H.; Goto, T.; Tada, S. Acta Crystallogr., Sect. C 1987, 43, 751. (32) Bardi, R.; Piazzesi, A. M.; Crisma, M.; Toniolo, C.; Sukumar, M.; Balaram, P. Acta Crystallogr., Sect. C 1992, 48, 1645. (33) Didierjean, C.; Aubry, A.; Wyckaert, F.; Boussard, G. J. Pept. Res. 2000, 55, 308. (34) Didierjean, C.; Boussard, G.; Aubry, A. Acta Crystallogr., Sect. C 2002, 58, o394. (35) Madison, V.; Schellman, J. Biopolymers 1970, 9, 511. (36) Thomas, W. A.; Williams, M. K. Org. Magn. Reson. 1972, 4, 145. (37) Galardy, R. E.; Alger, J. R.; Liakopoulou-Kyriakides, M. Int. J. Pept. Protein Res. 1982, 19, 123. (38) Delaney, N. G.; Madison, V. J. Am. Chem. Soc. 1982, 104, 6635. (39) Swarbrick, M. E.; Gosselin, F.; Lubell, W. D. J. Org. Chem. 1999, 64, 1993. (40) Taylor, C. M.; Hardre´, R.; Edwards, P. J. B.; Park, J. H. Org. Lett. 2003, 5, 4413. (41) Kern, D.; Schutkowski, M.; Drakenberg, T. J. Am. Chem. Soc. 1997, 119, 8403. (42) Wu, W.-J.; Raleigh, D. P. J. Org. Chem. 1998, 63, 6689. (43) Song, I. K.; Kang, Y. K. J. Phys. Chem. B 2006, 110, 1915. (44) Kang, Y. K. J. Phys. Chem. B 2006, 110, 21338. (45) Zagari, A.; Ne´methy, G.; Scheraga, H. A. Biopolymers 1990, 30, 951. (46) Zagari, A.; Ne´methy, G.; Scheraga, H. A. Biopolymers 1990, 30, 961. (47) Zagari, A.; Ne´methy, G.; Scheraga, H. A. Biopolymers 1990, 30, 967. (48) Toniolo, C.; Bardi, R.; Piazzesi, A. M.; Crisma, M.; Balaram, P.; Sukumar, M.; Paul, P. K. C. In Peptides 1988; Jung, G., Bayer, E. Eds.; Walter de Gruyter: Berlin, 1989; pp 477-479. (49) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; AlLaham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. (50) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;

J. Phys. Chem. B, Vol. 111, No. 13, 2007 3507 Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (51) Zimmerman, S. S.; Pottle, M. S.; Ne´methy, G.; Scheraga, H. A. Macromolecules 1977, 10, 1. Conformations A, C, and F are defined by the backbone torsion angle ψ with the backbone torsion angle φ in the range of -110° < φ < -40°: conformation A, -90° < ψ < -10°; conformation C, 50° < ψ < 130°; conformation F, 130° < ψ < 180° or -180° < ψ < -140°. Conformation D is defined by -180° < φ < -110° and 20° < ψ < 110°. (52) Kang, Y. K. THEOCHEM 2004, 675, 37. (53) Sundaralingam, M. J. Am. Chem. Soc. 1971, 93, 6644. (54) Kang, Y. K. J. Phys. Chem. B 2004, 108, 5463. (55) CS Chem3D, revision 5.0; CambridgeSoft Co.: Cambridge, MA, 1998. (56) Relationships between torsion angles about the N-CR bond from simple geometric considerations57 and pyramidality at prolyl nitrogen for local minima and transition states of Pro, Aze, and Pip dipeptides are discussed in the Supporting Information. (57) Ho, B. K.; Coutsias, E. A.; Seok, C.; Dill, K. A. Protein Sci. 2005, 14, 1011. (58) Barone, V.; Cossi, M. J. Phys. Chem. A 1998, 102, 1995. (59) Frisch, A.; Frisch, M. J.; Trucks, G. W. Gaussian 03 User’s Reference, version 7.0; Gaussian, Inc.: Pittsburgh, PA, 2003. (60) Takano, Y.; Houk, K. N. J. Chem. Theory Comput. 2005, 1, 70. (61) Kang, Y. K. THEOCHEM 2001, 546, 183. (62) Csa´sza´r, A. G.; Perczel, A. Prog. Biophys. Mol. Biol. 1999, 71, 243. (63) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986; Chapter 6. (64) Kang, Y. K.; Choi, H. Y. Biophys. Chem. 2004, 111, 135. (65) Kang, Y. K. J. Phys. Chem. 1996, 100, 11589. (66) Jhon, J. S.; Kang, Y. K. J. Phys. Chem. A 1999, 103, 5436. (67) Benzi, C.; Improta, R.; Scalmani, G.; Barone, V. J. Comput. Chem. 2002, 23, 341. (68) Rankin, K. N.; Boyd, R. J. J. Phys. Chem. A 2002, 106, 11168. (69) Song, I. K.; Kang, Y. K. J. Phys. Chem. B 2005, 109, 16982. (70) Kang, Y. K. J. Phys. Chem. B 2002, 106, 2074. (71) Kang, Y. K. THEOCHEM 2002, 585, 209. (72) Ne´methy, G.; Pottle, M. S.; Scheraga, H. A. J. Phys. Chem. 1983, 87, 1883. (73) Juaristi, E. Introduction to Stereochemistry and Conformational Analysis; John Wiley & Sons: New York, 1991; Chapter 14. (74) Fischer, S.; Dunbrack, R. L., Jr.; Karplus, M. J. Am. Chem. Soc. 1994, 116, 11931. (75) Stein, R. L. AdV. Protein Chem. 1993, 44, 1 and references therein. (76) Cox, C.; Lectka, T. J. Am. Chem. Soc. 1998, 120, 10660. (77) It has been reported that the hydrogen bond distance between N-H and OdC of amides increases as the angle R(N-H‚‚‚O) decreases.78 This may imply that the strength of a hydrogen bond becomes weaker as the angle R(N-H‚‚‚O) becomes decreased from its linearity. In particular, the mean value of R(N-H‚‚‚O) is appreciably smaller for the intramolecular hydrogen bonds (132.5°(15°) than for the intermolecular hydrogen bonds (161.2°(3°).78 However, the distance between the proton and its acceptor has been widely chosen as a criterion of hydrogen bonding.79 Although the angle R(N-H‚‚‚N) for the transition states of Aze, Pro, and Pip dipeptides is calculated to be ∼108°, the distance r(H‚‚‚N) is in the range of 2.25 Å to 2.32 Å, which can be classified as a weak hydrogen bond.79 (78) Taylor, R.; Kennard, O.; Versichel, W. Acta Crystallogr., Sect. B 1984, 40, 280. (79) Jeffrey, G. A. An Introduction to Hydrogen Bonding; Oxford University Press: New York, 1997. (80) Harmony, M. D.; Laurie, V. W.; Kuczkowski, R. L.; Schwendeman, R. H.; Ramsay, D. A.; Lovas, F. J.; Lafferty, W. J.; Maki, A. G. J. Phys. Chem. Ref. Data 1979, 8, 619.

Conformational Preferences of Proline Analogues with Different Ring

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