10550
J. Phys. Chem. B 2007, 111, 10550-10556
Puckering Transition of Proline Residue in Water Young Kee Kang* Department of Chemistry, Chungbuk National UniVersity, Cheongju, Chungbuk 361-763, Republic of Korea ReceiVed: May 4, 2007; In Final Form: June 28, 2007
The puckering transition of the proline residue with trans and cis prolyl peptide bonds was explored by optimizations along the torsion angle χ1 of the prolyl ring using quantum-chemical methods in water. By analyzing the potential energy surfaces and local minima in water, it is observed that the puckering transition of the proline residue proceeds from a down-puckered conformation to an up-puckered one and vice versa through the transition state with an envelope form having the N atom at the top of the envelope and not a planar one, as seen in the gas phase, although the backbone conformations are different in the gas phase and in water. The barriers to the puckering transition ∆Gqupfdown are estimated to be 3.12 and 3.00 kcal/mol for trans and cis conformers at the B3LYP/6-311++G(d,p) level of theory in water, respectively, which are about 1.7 kcal/mol higher than those in the gas phase. Out of 2197 prolines from the 241 high-resolution PDB chains, four transition-state-like structures with the envelope ring puckering are identified. Three of them have the trans prolyl peptide bonds and one has the cis one. The favorable or steric interactions by neighboring residues may be responsible for the stabilization of these transition-state-like ring structures in the proteins.
Introduction The Pro residue is unique in that its side chain is covalently bonded to the nitrogen atom of the peptide backbone. This leads the backbone to not form a hydrogen bond and the N-CR rotation (φ) to be restrained to about -60°. The pyrrolidine of the Pro residue is a five-membered ring that may adopt two distinct down-puckered (or Cγ-endo) and up-puckered (or Cγexo) conformations,1 which have been known to be almost equally probable from analysis of X-ray structures of peptides2-4 and proteins.5-7 The down- and up-puckered conformations are defined as those where the Cγ atom and the C′dO group of Pro residue lie on the same and opposite sides, respectively, of the plane defined by the three atoms Cδ, N, and CR (Figure 1), which have positive and negative values of the torsion angle χ1, respectively. 13C NMR relaxation measurements have provided abundant evidence for the interconversion between two puckerings in peptides in solution and in the solid state, whose relaxation time was estimated to be about 1-30 ps8-10 and the apparent barrier was estimated to be about 1.3 kcal/mol for DL-proline in the solid state.9 From Raman spectroscopic experiments on the proline zwitterion in water, the frequency for puckering was estimated to be ∼260 cm-1 (∼0.7 kcal/mol), and the puckering was suggested to be coupled with the rotation of the CO2- group.11 Considerable empirical and quantum mechanical calculations have been carried out on various model compounds of the Pro residue, but only a few works have focused on the transition of prolyl puckering. From empirical force field calculations on N-acetylproline methyl ester, the conversion of ring puckering was found to proceed through a flat saddle with a barrier of 3.6 kcal/mol and a planar transition state with a barrier of 2.0 kcal/ mol above the global minima, respectively.3 At Hartee-Fock * Tel.: +82-43-261-2285. Fax: +82-43-273-8328. E-mail: ykkang@ chungbuk.ac.kr.
Figure 1. Definition of torsion angles and structural parameters for the proline dipeptide. The torsion angle χ1 is defined for the N-CR-CβCγ sequence.
(HF) and hybrid density functional B3LYP levels of theory with various basis sets, it was reported that the barriers to the downto-up and up-to-down puckering transitions are 2.2-2.9 and 1.1-2.1 kcal/mol, respectively, depending on the amino and carboxylic end groups in the gas phase (see Table 1 of ref 16).12-17 The corresponding barriers are calculated to be 3.0 and 2.0 kcal/mol for the 4(R)-hydroxyproline (Hyp) residue, respectively, and 1.4 and 1.7 kcal/mol for the 4(R)-fluoroproline (Flp) residue, respectively.16 Recently, the relative energies for the transition states ts1 and ts2 and the planar conformation to the up-puckered conformation of the proline zwitterion are estimated to be 1.72, 2.08, and 4.10 kcal/mol at the B3LYP/ 6-31++G(d,p) level with the conductor-like screening model (COSMO)18 in water.11 Although the correlations of the cis/trans population and the prolyl puckering were suggested by analyzing X-ray structures of peptides and proteins,5-7 it was known that the cis-trans isomerization and the puckering transition were not coupled and that the prolyl ring could flip between the down- and uppuckered conformations either with the trans or with the cis peptide bond.19 By analyzing the potential energy surfaces (PESs) and local minima of Pro, Hyp, and Flp residues, it is observed that the prolyl ring flips through the transition state with an envelope form having the N atom at the top of the
10.1021/jp073411b CCC: $37.00 © 2007 American Chemical Society Published on Web 08/16/2007
Puckering Transition of Pro Residue in Water envelope and not a planar one for both trans and cis conformers in the gas phase.14-16 This transition state with an envelope structure is quite similar to the transition state ts2 of the proline zwitterion optimized in water.11 Recently, Ho et al.20 derived an analytical equation for the coupling between torsion angles φ and χ1 of the proline ring with fixed bond lengths and three fixed bond angles, which gives two symmetric conformations corresponding to the up and down puckerings for each φ value and correlates well with the observed results from X-ray structures of proteins in the Protein Data Bank21 (PDB). They also suggested that the strain in the Cγ-Cδ-N angle appears to be the principal barrier between the up and down puckerings. They reported that 216 trans-Pro (4.8%) and 19 cis-Pro (0.4%) residues out of the 4525 prolines from 500 nonhomologous proteins with a resolution of >1.8 Å have the planar structure. Juffer and his co-workers have carried out the quantum mechanics/molecular mechanics (QM/MM) energy calculations on the liganded trisephosphate isomerase (TIM) that has an active site proline (Pro168) in a planar conformation.17 The planarity of this proline was ascribed to the steric interactions between Pro168 and neighboring residues Tyr166 and Ala171. By comparison of the proline conformations in the X-ray structures of a liganded TIM (PDB entry 1N5522) and an unliganded TIM (PDB entry 1NEY23), the planarity of Pro168 was suggested to play a role in the overall catalytic cycle of TIM. In particular, they calculated the energy profile for the down-to-up puckering transition of Ac-Pro-NHMe (the proline dipeptide) at the B3LYP/6-31G(d) level in the gas phase, in which the starting coordinates for the down, up, and planar conformations were taken from the X-ray structures of Pro58, Pro49, and Pro168 residues of the liganded TIM (PDB entry 1N55), respectively. They interpreted the transition state for the puckering transition with the relative energy of 2.2 kcal/mol as a nearly planar conformation close to the conformation of Pro168 in 1N55. However, their transition state is a downpuckered conformation and not a nearly planar one. In this work, we report the puckering transition of the proline dipeptide with trans and cis prolyl peptide bonds studied by optimizations along the torsion angle χ1 of the prolyl ring using quantum-chemical methods in water. In particular, we discuss the conformation and thermodynamic properties of the transition state in water and its relevant structures found in X-ray structures of proteins. Computational Methods Chemical structures and torsional parameters for the proline dipeptide are defined in Figure 1. All ab initio HF and hybrid density functional B3LYP calculations were carried out using the Gaussian 03 package.24 Here, each backbone conformation of the proline dipeptide is represented by a capital letter depending on its values of φ and ψ for the backbone.25 Conformations C, A, and F are equivalent to the γ-turn (C7eq), R-helical (RR), and polyproline-like (PII and PI) structures in other works, respectively. Trans and cis conformations for the Ac-Pro peptide bond are defined by the orientation of the methyl carbon of the acetyl group and the CR of the Pro residue, which are denoted by “t” and “c”, respectively. Down- and up-puckered conformations of the proline dipeptide are represented by “d” and “u”, respectively. Usually, the down- and up-puckered conformations have positive and negative values of the endocyclic torsion angle χ1, respectively.2 The planar structure of the prolyl ring is denoted by “p”. We employed the conductor-like polarizable continuum model (CPCM),26,27 implemented in the Gaussian 03 package,24 to
J. Phys. Chem. B, Vol. 111, No. 35, 2007 10551 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.28,29 The solvation free energy is the sum of the electrostatic free energy and the nonelectrostatic energy terms.30 The latter is composed of the cavitation, dispersion, and repulsion energy terms. For CPCMUAKS calculations, the default average areas of 0.2 Å2 for tesserae were used. The dielectric constant of water used here is 78.4 at 25 °C. Recently, the CPCM-UAKS calculations for a number of neutral and charged organic molecules at the HF/631+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.31 Because of the higher barrier to rotation of the Ac-Pro peptide bond (∼13-19 kcal/mol) than the barrier to ring flip,19 calculations were carried out only for trans and cis conformers. Because the prolyl puckering was successively described by an endocyclic torsion angle χ1,2,14-16 the CPCM HF/6-31+G(d) energies were optimized along the torsion angle χ1 starting from the up-puckered minimum to the down-puckered one for each χ1 between -20° and +25° with a step of 5° for both trans and cis conformers in water. The local minima tFu, tFd, cFu, and cFd identified for the proline dipeptide at the CPCM HF/631+G(d) level in water32 were used as starting points for these optimizations in water. The two conformations with the highest energies for trans and cis conformers at χ1 ) +10° on the PES were reoptimized to locate the transition states ts1 and ts2 in water, respectively. In addition, X-ray structures for Pro168 in a liganded TIM (PDB entry 1N5522) and for Pro166 in an unliganded TIM (PDB entry 1NEYB23) were optimized with all backbone torsion angles and endocyclic torsion angles χ1 and χ3 fixed at the values of X-ray structures. The B3LYP/6311++G(d,p) single-point energies were calculated for all local minima and transition states of the proline dipeptide located at the CPCM HF/6-31+G(d) level in water. Vibrational frequencies were calculated for all stationary points at the CPCM HF/6-31+G(d) level in water, which were used to compute enthalpies and Gibbs free energies with a scale factor of 0.89 for corrections of vibrational frequencies at 25 °C and 1 atm. A scale factor of 0.89 was chosen to reproduce experimental frequencies for the amide I band of N-methylacetamide in Ar and N2 matrixes.33 The zero-point energy correction and the thermal energy corrections were used to calculate the enthalpy (H) and entropy (S) of each conformation.34,35 The analysis uses the standard thermodynamic expressions for an ideal gas in the canonical ensemble. Each transition state was confirmed by checking whether it has one imaginary frequency after frequency calculations. The relative total free energy (∆G) for each conformation in water was computed by the sum of the relative conformational energy (∆E), the thermal contributions, and the entropic contribution. The relative conformational energy (∆E) was taken as the sum of the conformational electronic energy (∆Ee) and the relative solvation free energy (∆∆Gsolv) in solution. The relative total free energies are used here to interpret the conformational preferences in water. Recently, the conformational preferences and cis-trans isomerization of the alanine and proline dipeptides in water were satisfactorily described at the B3LYP/6-311++G(d,p)//CPCM HF/6-31+G(d) level.32 To investigate the planar and transition-state-like conformations of proline rings in X-ray structures of proteins, we used 241 polypeptide chains with 30% sequence identity threshold, R-factors of
