Empirical isotropic chemical shift surfaces.

A list of proteins is given for which spatial structures, with a resolution better than 2.5 A, are known from entries in the Protein Data Bank (PDB) and isotropic chemical shift (ICS) values are known from the RefDB database related to the Biological Magnetic Resonance Bank (BMRB) database. The structures chosen provide, with unknown uncertainties, dihedral angles phi and psi characterizing the backbone structure of the residues. The joint use of experimental ICSs of the same residues within the proteins, again with mostly unknown uncertainties, and ab initio ICS(phi,psi) surfaces obtained for the model peptides For-(L-Ala)(n)-NH(2), with n = 1, 3, and 5, resulted in so-called empirical ICS(phi,psi) surfaces for all major nuclei of the 20 naturally occurring alpha-amino acids. Out of the many empirical surfaces determined, it is the 13C(alpha)-1H(alpha) ICS(phi,psi) surface which seems to be most promising for identifying major secondary structure types, alpha-helix, beta-strand, left-handed helix (alpha(D)), and polyproline-II. Detailed tests suggest that Ala is a good model for many naturally occurring alpha-amino acids. Two-dimensional empirical 13C(alpha)-1H(alpha) ICS(phi,psi) correlation plots, obtained so far only from computations on small peptide models, suggest the utility of the experimental information contained therein and thus they should provide useful constraints for structure determinations of proteins.

A combined electronegativity equalization and electrostatic potential fit method for the determination of atomic point charges.

We report an approach for the determination of atomic monopoles of macromolecular systems using connectivity and geometry parameters alone. The method is appropriate also for the calculation of charge distributions based on the quantum mechanically determined wave function and does not suffer from the mathematical instability of other electrostatic potential fit methods.

Molecular structures of the two most stable conformers of free glycine.

The equilibrium molecular structures of the two lowest-energy conformers of glycine, Gly-Ip and Gly-IIn, have been characterized by high-level ab initio electronic structure computations, including all-electron cc-pVTZ CCSD(T) geometry optimizations and 6-31G* MP2 quartic force fields, the latter to account for anharmonic zero-point vibrational effects to isotopologic rotational constants. Based on experimentally measured vibrationally averaged effective rotational constant sets of several isotopologues and our ab initio data for structural constraints and zero-point vibrational shifts, least-squares structural refinements were performed to determine improved Born-Oppenheimer equilibrium (r(e)) structures of Gly-Ip and Gly-IIn. Without the ab initio constraints even the extensive set of empirical rotational constants available for 5 and 10 isotopologues of Gly-Ip and Gly-IIn, respectively, cannot satisfactorily fix their molecular structure. Excellent agreement between theory and experiment is found for the rotational constants of both conformers, the rms residual of the final fits being 7.8 and 51.6 kHz for Gly-Ip and Gly-IIn, respectively. High-level ab initio computations with focal point extrapolations determine the barrier to planarity separating Gly-IIp and Gly-IIn to be 20.5 +/- 5.0 cm(-1). The equilibrium torsion angle tau(NCCO) of Gly-IIn, characterizing the deviation of its heavy-atom framework from planarity, is (11 +/- 2) degrees. Nevertheless, in the ground vibrational state the effective structure of Gly-IIn has a plane of symmetry.

Secondary structures of peptides and proteins via NMR chemical-shielding anisotropy (CSA) parameters.

Complete nuclear magnetic resonance (NMR) chemical-shielding tensors, sigma, have been computed at different levels of density-functional theory (DFT), within the gauge-including atomic orbital (GIAO) formalism, for the atoms of the peptide model For-L-Ala-NH2 as a function of the backbone dihedral angles phi and psi by employing a dense grid of 10 degrees. A complete set of rigorously orthogonal symmetric tensor invariants, {sigma iso, rho, tau}, is introduced, where sigma iso is the usual isotropic chemical shielding, while the newly introduced rho and tau parameters describe the magnitude and the orientation/shape of the chemical-shielding anisotropy (CSA), respectively. The set {sigma iso, rho, tau} is unaffected by unitary transformations of the symmetric part of the shielding tensor. The mathematically and physically motivated {rho, tau} anisotropy pair is easily connected to more traditional shielding anisotropy measures, like span (Omega) and skew (kappa). The effectiveness of the different partitions of the CSA information in predicting conformations of peptides and proteins has been tested throughout the Ramachandran space by generating theoretical NMR anisotropy surfaces for our For-L-Ala-NH2 model. The CSA surfaces, including Omega(phi, psi), kappa(phi, psi), rho(phi, psi), and tau(phi, psi) are highly structured. Individually, none of these surfaces is able to distinguish unequivocally between the alpha-helix and beta-strand secondary structural types of proteins. However, two- and three-dimensional correlated plots, including Omega versus kappa, rho versus tau, and sigma iso versus rho versus tau, especially for 13Calpha, have considerable promise in distinguishing among all four of the major secondary structural elements.

Molecular structure of proline.

The molecular structures of the two lowest-energy conformers of proline, Pro-I and Pro-II, have been characterized by ab initio electronic structure computations. An extensive MP2/6-31G* quartic force field for Pro-I, containing 62,835 unique elements in the internal coordinate space, was computed to account for anharmonic vibrational effects, including total zero-point contributions to isotopomeric rotational constants. New re and improved r0 least-squares structural refinements were performed to determine the heavy-atom framework of Pro-I, based on experimentally measured (A. Lesarri, S. Mata, E. J. Cocinero, S. Blanco, J. C. Lopez, J. L. Alonso, Angew. Chem. 2002, 114, 4867; Angew. Chem. Int. Ed. 2002, 41, 4673) rotational constant sets of nine isotopomers and our ab initio data for structural constraints and zero-point vibrational (ZPV) shifts. Without the ab initio constraints, even the extensive set of empirical rotational constants cannot satisfactorily fix the molecular structure of the most stable conformer of proline, a 17-atom molecule with no symmetry. After imposing the ab initio constraints, excellent agreement between theory and experiment is found for the heavy-atom geometric framework, the root-mean-square (rms) residual of the empirical rotational constant fit being cut in half by adding ZPV corrections. The most significant disparity, about 0.07 A, between the empirical and the best ab initio structures, concerns the r(N...H) distance of the intramolecular hydrogen bond. Some of the experimental quartic centrifugal distortion constants assigned to Pro-II have been corrected based on data obtained from a theoretical force field.

A theoretical case study of type I and type II beta-turns.

NMR chemical shielding anisotropy tensors have been computed by employing a medium size basis set and the GIAO-DFT(B3LYP) formalism of electronic structure theory for all of the atoms of type I and type II beta-turn models. The models contain all possible combinations of the amino acid residues Gly, Ala, Val, and Ser, with all possible side-chain orientations where applicable in a dipeptide. The several hundred structures investigated contain either constrained or optimized phi, psi, and chi dihedral angles. A statistical analysis of the resulting large database was performed and multidimensional (2D and 3D) chemical-shift/chemical-shift plots were generated. The (1)H(alpha-13)C(alpha), (13)C(alpha-1)H(alpha-13)C(beta), and (13)C(alpha-1)H(alpha-13)C' 2D and 3D plots have the notable feature that the conformers clearly cluster in distinct regions. This allows straightforward identification of the backbone and side-chain conformations of the residues forming beta-turns. Chemical shift calculations on larger For-(L-Ala)(n)-NH(2) (n=4, 6, 8) models, containing a single type I or type II beta-turn, prove that the simple models employed are adequate. A limited number of chemical shift calculations performed at the highly correlated CCSD(T) level prove the adequacy of the computational method chosen. For all nuclei, statistically averaged theoretical and experimental shifts taken from the BioMagnetic Resonance Bank (BMRB) exhibit good correlation. These results confirm and extend our previous findings that chemical shift information from selected multiple-pulse NMR experiments could be employed directly to extract folding information for polypeptides and proteins.

Conformers of gaseous proline.

Accurate geometries, relative energies, rotational and quartic centrifugal distortion constants, dipole moments, harmonic vibrational frequencies, and infrared intensities were determined from ab initio electronic structure calculations for eighteen conformers of the neutral form of the amino acid L-proline. Only four conformers have notable population at low and moderate temperature. The second most stable conformer is only 2+/-2 kJ mol(-1) above the global minimum, while the third and fourth conformers are nearly degenerate and have an excess energy of 7+/-2 kJ mol(-1) relative to the global minimum. All four conformers have one hydrogen bond: N.HO in the lower energy pair of conformers, and NH.O in the higher energy pair of conformers. The conformer pairs differ only in their ring puckering. The relative energies of the conformers include corrections for valence electron correlation, extrapolated to the complete basis set limit, as well as core correlation and relativistic effects. Structural features of the pyrrolidine ring of proline are discussed by using the concept of pseudorotation. The accurate rotational and quartic centrifugal distortion constants as well as the vibrational frequencies and infrared intensities should aid identification and characterization of the conformers of L-proline by rotational and vibrational spectroscopy, respectively. Bonding features of L-proline, especially intramolecular hydrogen bonds, were investigated by the atoms-in-molecules (AIM) technique.