g Jin Byun

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ϕ and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values.

Conformational preference and cis–trans isomerization of 4‐methylproline residues

Conformational preferences and prolyl cis-trans isomerizations of the (2S,4S)-4-methylproline (4S-MePro) and (2S,4R)-4-methylproline (4R-MePro) residues are explored at the M06-2X/cc-pVTZ//M06-2X/6-31+G(d) level of theory in the gas phase and in water, where solvation free energies were calculated using the implicit SMD model. In the gas phase, the down-puckered γ-turn structure with the trans prolyl peptide bond is most preferred for both Ac-4S-MePro-NHMe and Ac-4R-MePro-NHMe, in which the C(7) hydrogen bond between two terminal groups seems to play a role, as found for Ac-Pro-NHMe. Because of the C(7) hydrogen bonds weakened by the favorable direct interactions between the backbone C==O and H--N groups and water molecules, the 4S-MePro residue has a strong preference of the up-puckered polyproline II (PP(II)) structure over the down-puckered PP(II) structure in water, whereas the latter somewhat prevails over the former for the 4R-MePro residue. However, these two structures are nearly equally populated for Ac-Pro-NHMe. The calculated populations for the backbone structures of Ac-4S-MePro-NHMe and Ac-4R-MePro-NHMe in water are reasonably consistent with CD and NMR experiments. In particular, our calculated results on the puckering preference of the 4S-MePro and 4R-MePro residues with the PP(II) structures are in accord with the observed results for the stability of the (X-Y-Gly)(7) triple helix with X = 4R-MePro or Pro and Y = 4S-MePro or Pro. The calculated rotational barriers indicate that the cis-trans isomerization may in common proceed through the anticlockwise rotation for Ac-4S-MePro-NHMe, Ac-4R-MePro-NHMe, and Ac-Pro-NHMe in water. The lowest rotational barriers become higher by 0.24-1.43 kcal/mol for Ac-4S-MePro-NHMe and Ac-4R-MePro-NHMe than those for Ac-Pro-NHMe in water.

Conformational preferences and pKa value of selenocysteine residue

The conformational preferences of the L‐selenocysteine (Sec) dipeptides with selenol and selenolate groups (Ac‐Sec‐NHMe and Ac‐Sec−‐NHMe, respectively) and the apparent (i.e., macroscopic) pKa value of the Sec residue have been studied using the dispersion‐corrected density functionals M06‐2X and B2PLYP‐D with the implicit solvation method in the gas phase and in water. In the gas phase, the backbone‐to‐backbone and/or side chain‐to‐backbone hydrogen bonds are found to contribute in stabilizing the most preferred conformations for the Sec and Sec− residues, as seen for the Cys and Cys− residues. However, the polyproline II‐like conformations prevail over the conformations with the backbone‐to‐backbone hydrogen bonds in water because of the weakened hydrogen bonds by the favorable direct interactions between the backbone CO and HN groups and water molecules. The Sec and Sec− residues are found to adopt more various conformations than the Cys and Cys− residues in water, although the most preferred conformations of the neutral and/or anionic forms of the two residues are similar each other in the gas phase and in water. Using the statistically weighted free energies of the Sec and Sec− dipeptides in the gas phase and their solvation free energies, the pKa value of the Sec residue is estimated to be 5.47 at 25°C, which is in good agreement with the experimental value of 5.43 ± 0.02. It is found that the lower pKa value of the selenol side chain for the Sec residue by ∼3 units than the thiol side chain for the Cys residue is ascribed to the higher gas‐phase acidity of the Sec residue.

Conformational preferences and prolyl cis–trans isomerization of phosphorylated Ser/Thr‐Pro motifs

The conformational study on Ac-pSer-Pro-NHMe and Ac-pThr-Pro-NHMe peptides has been carried out using hybrid density functional methods with the implicit solvation reaction field theory at the B3LYP/ 6-311++G(d,p)//B3LYP/6-31+G(d) level of theory in the gas phase and in solution (chloroform and water). For both pSer-Pro and pThr-Pro peptides in the gas phase and in chloroform, the most preferred conformation has the alpha-helical structure for the pSer/pThr residue, the down-puckered polyproline I structure for the Pro residue, and the cis prolyl peptide bond between the two residues, in which two hydrogen bonds between the phosphate oxygens with the backbone N--H groups seem to play a role. However, the trans conformations that have a single hydrogen bond of the phosphate oxygen with either of two backbone N--H groups become most preferred for both peptides in water. This is because the hydration free energy of the anionic oxygen of the phosphate group is expected to dramatically decrease for the cis conformation upon formation of the hydrogen bond with the backbone N--H groups. These calculated results are consistent with the observations by NMR and IR experiments, suggesting the existence of hydrogen bonds between the charged phosphoryl group and the backbone amide protons in solution. The calculated cis populations of 14.7 and 14.2% and rotational barriers of 19.87 and 20.57 kcal/mol to the cis-to-trans isomerization for pSer-Pro and pThr-Pro peptides in water, respectively, are consistent with the observed values for pSer-Pro and pThr-Pro containing peptides from NMR experiments. However, the hydrogen bond between the prolyl nitrogen and the following amide N--H group, which was suggested to be capable of catalyzing the prolyl isomerization, does not play a role in stabilizing the preferred transition state for the pSer/pThr-Pro peptides in water. Instead, the amide hydrogen of the NHMe group is involved in a bifurcated hydrogen bond with the anionic oxygen and phosphoester oxygen of the phosphate group.

Local Control of the Cis–Trans Isomerization and Backbone Dihedral Angles in Peptides Using Trifluoromethylated Pseudoprolines

NMR studies and theoretical calculations have been performed on model peptides Ac-Ser(ΨPro)-NHMe, (S,S)Ac-Ser(Ψ(H,CF3)Pro)-NHMe, and (R,S)Ac-Ser(Ψ(CF3,H)Pro)-NHMe. Their thermodynamic and kinetic features have been analyzed in chloroform, DMSO, and water, allowing a precise description of their conformational properties. We found that trifluoromethyl C(δ)-substitutions of oxazolidine-based pseudoprolines can strongly influence the cis-trans rotational barriers with only moderate effects on the cis/trans population ratio. In CHCl(3), the configuration of the CF(3)-C(δ) entirely controls the ψ-dihedral angle, allowing the stabilization of γ-turn-like or PPI/PPII-like backbone conformations. Moreover, in water and DMSO, this C(δ)-configuration can be used to efficiently constrain the ring puckering without affecting the cis/trans population ratio. Theoretical calculations have ascertained the electronic and geometric properties induced by the trifluoromethyl substituent and provided a rational understanding of the NMR observations.

Strength of CH···π interactions in the C-terminal subdomain of villin headpiece.

The relative free energies of the folded structures of the seven model peptides with PLX (X = W, Y, F, H, and A) and ALX (X = W and A) sequences to the corresponding extended structures are calculated using the density functional methods in water to evaluate the relative strengths of CH···π interactions, especially proline···aromatic interactions for the PLX motif of the C-terminal subdomain of villin headpiece. It has been found that the Pro···π contacts for the folded structures of the PLW, PLY, PLF, and PLH peptides have in common a geometric pattern having the edge of the Pro ring interacting with the face of the aromatic ring, as found for functionally important Pro residues in proteins. At the M06-2X/cc-pVTZ//SMD M06-2X/6-31+G(d) level of theory, the relative stabilities of the folded structures to the extended structures are obtained in the order PLW > ALW > PLA > PLH > PLY > ALA > PLF by the conformational Gibbs free energies in water, which is reasonably consistent with the observed results from the CD thermal analysis for wild-type and mutants of the C-terminal subdomains of villin headpieces. Although the interaction energies excluding the solvation free energies play a role in determining the relative stabilities of the PLX and ALX peptides, the solvation and entropic terms are found to be of consequence, too. In particular, it has been known that ∼40% of the total interaction energy of the PLW peptide is ascribed to the CH···π interactions of the contacting side chains for Pro and Trp residues, in which the dispersion terms play a role.

Puckering transitions of pseudoproline residues

The puckering transitions of pesudoprolines such as oxazolidine and thiazolidine residues (Oxa and Thz dipeptides) with trans and cis prolyl peptide bonds were explored by optimizations along the endocyclic torsion angle χ1 using quantum‐chemical methods in the gas phase and in water. The overall shapes of the potential energy surfaces for Oxa and Thz dipeptides in the gas phase and in water are similar to those for the Pro dipeptide, although there are some differences in relative stabilities of local minima and in barriers to puckering transition. On the whole, the barriers to puckering transition for Oxa and Thz dipeptides are computed to be 0.8–3.2 kcal/mol at the B3LYP/6‐311++G(d,p) level in the gas phase and in water, which are lower by 0.5–1.9 kcal/mol than those for the Pro dipeptide. The n → σ* interactions for the delocalization of the lone pair of the prolyl amide nitrogen into the antibonding orbitals that are anti to the lone pair appear to play a role in stabilizing the nonplanar puckered transition states over the corresponding planar structures. The calculated barriers indicate that the down‐to‐up puckering transition can proceed in the orders Pro < Oxa < Thz in the gas phase and Pro ≈ Oxa < Thz in water.

Conformational preferences and pKa value of cysteine residue.

The conformational preferences of the Cys dipeptides with thiol and thiolate groups (Ac-Cys-NHMe and Ac-Cys (-)-NHMe, respectively) and the apparent (i.e., macroscopic) p K a value of the Cys dipeptide have been studied at the hybrid density functional B3LYP/6-311++G(d,p)//B3LYP/6-31+G(d) level with the conductor-like polarizable continuum model in the gas phase and in water. The hydrogen bonds and/or favorable interactions between the backbone and the thiol group of the side chain resulted in the different conformational preferences of the Cys and Cys (-) dipeptides from those of the Ala dipeptide in the gas phase and in water, although the preferred conformations of the Cys dipeptide are in part similar to those of the Ala dipeptide. In particular, the interactions between the thiolate group and the backbone amide groups appear to play a role in stabilizing the alpha- or 3 10-helical conformations for the Cys (-) dipeptide in the gas phase and in water. The p K a value of the Cys residue is estimated to be 8.58 at 25 degrees C using the statistically weighted free energies of all feasible conformations for the Cys and Cys (-) dipeptides in the gas phase and solvation free energies, which is consistent with the observed values of 8.3 and 8.22 +/- 0.16.

Conformational Preferences of X-Pro Sequences: Ala-Pro and Aib-Pro Motifs

Conformational preferences and prolyl cis-trans isomerizations of the X-Pro motifs (Ac-X-Pro-NHMe, X = Ala and Aib) are explored using the meta-hybrid functional M06-2X and the double-hybrid functional B2PLYP-D with empirical dispersion corrections in the gas phase and in water, where solvation free energies were calculated using the implicit SMD model. Ac-Ala-Pro-NHMe favors the type VI β-turns in the gas phase and the open conformations in water. The populations of type VI β-turns decrease from 71% in the gas phase to 21% in water, which is reasonably consistent with IR and NMR experimental results on tBoc-Ala-Pro-NHMe. However, Ac-Aib-Pro-NHMe prefers the type I β-turns with α-helical structures for both residues in the gas phase and in water, whose populations are estimated to be 66% in both phases. These calculated results may rationalize why most of the peptaibiotics containing the Aib-Pro sequence have a regular α-helical conformation at the N- or C-terminus but a kinked α-helical structure in the middle of the helix. The cis-trans isomerizations of the Ala-Pro and Aib-Pro peptide bonds proceed via the clockwise rotation with the different backbone conformations. The rotational barriers to cis-to-trans isomerization are estimated to be 19.73 kcal/mol for the Ala-Pro tripeptide and 16.64 kcal/mol for the Aib-Pro tripeptide in water, which indicates that the rotational barrier becomes lower by ~3 kcal/mol for the Aib-Pro peptide bond. The calculated rotational barrier for Ac-Ala-Pro-NHMe is consistent with the observed value of 19.3 kcal/mol for Suc-Ala-Ala-Pro-Phe-pNA from NMR experiments in a buffered solution.

Conformational preferences of helix foldamers of γ‐peptides based on 2‐(aminomethyl)cyclohexanecarboxylic acid

The conformational preferences of helix foldamers having different sizes of the H-bonded pseudocycles have been studied for di- to octa-γ(2,3)-peptides based on 2-(aminomethyl)cyclohexanecarboxylic acid (γAmc6) with a cyclohexyl constraint on the C(α)-C(β) bond using density functional methods. The helical structures of the γAmc6 oligopeptides with homochiral configurations are known to be much stable than those with heterochiral configurations in the gas phase and in solution (chloroform and water). In particular, it is found that the (P/M)-2.5(14)-helices are most preferred in the gas phase and in chloroform, whereas the (P/M)-2.3(12)-helices become most populated in water due to the larger helix dipole moments. As the peptide sequence becomes longer, the helix propensities of 14- and 12-helices are found to increase both in the gas phase and in solution. The γAmc6 peptides longer than octapeptide are expected to exist as a mixture of 12- and 14-helices with the similar populations in water. The mean backbone torsion angles and helical parameters of the 14-helix foldamers of γAmc6 oligopeptides are quite similar to those of 2-aminocyclohexylacetic acid oligopeptides and γ(2,3,4)-aminobutyric acid tetrapeptide in the solid state, despite the different substituents on the backbone.