Communication: Accurate determination of side-chain torsion angle χ1 in proteins: Phenylalanine residues

R. Suardíaz, R. Crespo-Otero, C. Pérez, J. San Fabián, J. M. García de la Vega
2011 Journal of Chemical Physics  
Quantitative side-chain torsion angle χ 1 determinations of phenylalanine residues in Desulfovibrio vulgaris flavodoxin are carried out using exclusively the correlation between the experimental vicinal coupling constants and theoretically determined Karplus equations. Karplus coefficients for nine vicinal coupling related with the torsion angle χ 1 were calculated using the B3LYP functional and basis sets of different size. Optimized χ 1 angles are in outstanding agreement with those
more » ... reported by employing x ray and NMR measurements. Knowledge on the three-dimensional structure of biological macromolecules is a key factor for understanding molecular processes occurring in living systems. 1 NMR spectroscopy is the only method that allows the determination of 3D-structures of proteins in solution. Measurement of nuclear Overhauser effects complemented with scalar coupling constants and chemical shifts provides the constraints needed for the determination of 3D-structures. Additionally, residual dipolar couplings make it possible to estimate the relative orientation of a number of bond vectors. Three-bond scalar coupling constants ( 3 J ) benefit NMR structure refinements through the well known Karplus equation 2 and have been demonstrated to deliver quantitative constraints on backbone and side-chain torsional angles of proteins. 3, 4 The use of the vicinal coupling constants 3 J XY for obtaining torsional angles relies on the accurate knowledge of the angular dependence on those couplings. A truncated Fourier series is used to describe this relationship, shown here for the couplings related to the side-chain dihedral angle χ 1 , where θ is the dihedral angle between the planes X − C α − C β and C α − C β − Y , which can be related to the χ 1 angle assuming perfect tetrahedral geometries at the C α and C β atoms, θ = χ 1 + θ (see Fig. 1 ). Phase shifts θ for each coupling type are shown in Table I . Equation (1) reduces to the usual Karplus equation 2 when the coefficients C 3 , S 1 , and S 2 are neglected. Here, we report the determination of side-chain torsion angle χ 1 of a well known protein, Desulfovibrio vulgaris flavodoxin, using experimental vicinal coupling constants and theoretical Karplus-like equations. The Fourier coefficients are obtained theoretically. Therefore, none of the a) Electronic mail: garcia.delavega@uam.es. coefficients of Eq. (1) are neglected. We follow a seven steps procedure: (1) An amino acid residue phenylalanine (PHE) from Desulfovibrio vulgaris flavodoxin 3 is chosen. Six PHE residues are found in that protein. Between seven and nine coupling constants 3 J XY related to χ 1 angle are available for each of those residues. A total of 49 experimental 3 J XY values have been reported. 3 (2) The amino acid geometry was fully optimized at the B3LYP/6-31G** level of theory 5, 6 using the GAUSSIAN program. 7 (3) The dihedral angle χ 1 (N − C α − C β − C γ ) is scanned from 0 • to 300 • in 60 • steps with all the remaining degrees of freedom optimized at the same level of theory as described in previous work. 8 A set of six geometries with different torsion angle χ 1 is obtained. (4) For each of these geometries with various values of torsion, nine coupling constants 3 J XY (χ 1 ) related to the side-chain torsion χ 1 are calculated at B3LYP level of theory and the following five basis sets: TZVP, 9 6-31G(d,p), 10 EPR-III, 11 aug-cc-pVTZ-J, 12 and pcJ-2 (Ref. 13) using standard procedure. 14-18 Although these basis sets are of different size and hence require different computational effort, the results are similar (see Tables II and III) . Therefore, the inexpensive TZVP basis set can be an acceptable choice for future calculations. B3LYP/TZVP level of theory has proved to provide similar results to those of ab initio SOPPA and SOPPA(CCSD) methods with larger basis sets 19 and has been used successfully in the calculations of J and hyperfine couplings. 20-24 (5) The nine sets of coupling constants 3 J XY and the angles from geometry optimizations were used to calculate the six corresponding Fourier coefficients in Eq. (1), solving 6 × 6 system of nonhomogeneous linear equations. The Fourier coefficients for the B3LYP/TZVP level and for other levels of theory are shown in Table I and in the supplementary information, 25 respectively. (6) For each amino acid residue, single χ 1 sweep is used to look for the minimum of the root mean square deviation (rmsd) between the calculated couplings 3 J cal X,Y , using the Karplus equation (1) for the angle χ 1 , and the experimental ones 3 J exp X,Y .
doi:10.1063/1.3553204 pmid:21322654 fatcat:pzoszmekorbhlfgdn263zyjgua