Self-consistent Karplus parametrization of 3J couplings depending on the polypeptide side-chain torsion chi1

Recently proposed self-consistent 3J coupling analysis (Schmidt, J. M.; Blümel, M.; Löhr, F.; Rüterjans, H. J. Biomol. NMR 1999, 14, 1-12) has been carried out to calibrate Karplus parameters constituting the empirical dependence of 3J coupling constants on the chi1 dihedral angle in amino acid side chains. The procedure involves simultaneous least-squares optimization of six sets of three Karplus coefficients related to all six 3J coupling types accessible in 15N,13C-labeled proteins. A simple concept of fundamental and incremental component couplings is proposed to account for substituent effects, eventually yielding amino acid topology-specific Karplus parameters. The method is exemplified with recombinant Desulfovibrio vulgaris flavodoxin (147 amino acids, 16 kDa) with reference to a total of 749 experimental 3JHalpha,Hbeta, 3JN',Hbeta, 3JC',Hbeta, 3JHalpha,Cgamma, 3JN',Cgamma, and 3JC',Cgamma coupling constants. Unlike other parametrizations, the present method does not make reference to X-ray coordinates, so that the Karplus coefficients obtained are not influenced by differences between solution and crystal states. Cross validation using X-ray torsion angles demonstrates the improvement relative to previous parametrizations. The Karplus coefficients derived are applicable to other proteins, too. Parameter refinement also yields a series of chi1 torsion angles, providing valuable constraints for protein structure determination, as well as optional parameters of local angular mobility in the contexts of Gaussian random fluctuation or a three-site jump model. The procedure permits automatic stereospecific assignments of Hbeta and Cgamma chemical shifts. The majority of the flavodoxin side-chain conformations agrees with high-resolution X-ray structures of the protein. Marked deviations between NMR and X-ray datasets are attributed to different rotameric states due to crystal-packing effects and to conformational equilibria between multiple chi1 rotamers.