Abstract
Structural knowledge about proteins is mainly derived from values of observables, measurable in NMR spectroscopic or X-ray diffraction experiments, i.e. absorbed or scattered intensities, through theoretically derived relationships between structural quantities such as atom positions or torsional angles on the one hand and observable quantities such as squared structure factor amplitudes, NOE intensities or 3 J-coupling constants on the other. The standardly used relation connecting 3 J-couplings to torsional angles is the Karplus relation, which is used in protein structure refinement as well as in the evaluation of simulated properties of proteins. The accuracy of the simple and generalised Karplus relations is investigated using side-chain structural and 3 J αβ-coupling data for three different proteins, Plastocyanin, Lysozyme, and FKBP, for which such data are available. The results show that the widely used Karplus relations are only a rough estimate for the relation between 3 J αβ-couplings and the corresponding χ1-angle in proteins.
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References
IUPAC-IUB (1970) Commission of biochemical nomenclature: abbreviations and symbols for the description of the conformation of polypeptide chains. Biochemistry 9:3471–3479
Abraham RJ, McLauchlan KA (1962) The proton resonance spectra and conformations of the prolines Part II. The conformations of trans hydroxy-L-proline and cis (allo) hydroxy-L-proline in solution. Mol Phys 5:513–523
Allison JR, van Gunsteren WF (2009) A method to explore protein side chain conformational variability using experimental data. ChemPhysChem 10:3213–3228
Artymiuk PJ, Blake CCF, Rice DW, Wilson KS (1982) The structure of the monoclinic and orthorhombic forms of hen egg-white Lysozyme at 6Å resolution. Acta Cryst B 38:778–783
Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE (2000) The Protein Data Bank, www.pdb.org. Nucleic Acids Res 28:235–242
Brüschweiler R, Case DA (1994) Adding harmonic motion to the Karplus relation for spin–spin coupling. J Am Chem Soc 116:11199–11200
Bystrov VF (1976) Spin–spin coupling and the conformational states of peptide systems. Prog Nucl Mag Res Sp 10:41–81
Carter D, He J, Ruble JR, Wright B (1997) The structure of the orthorhombic form of hen egg-white lysozyme at 1.5Å resolution. PDB 1AKI
Christen M, Hünenberger PH, Bakowies D, Baron R, Bürgi R, Geerke DP, Heinz TN, Kastenholz MA, Kräutler V, Oostenbrink C, Peter C, Trzesniak D, van Gunsteren WF (2005) The GROMOS software for biomolecular simulations: GROMOS05. J Comput Chem 26:1719–1751
Deber CM, Torchia DA, Blout ER (1971) Cyclic peptides. I. Cyclo(tri-L-prolyl) and derivatives. Synthesis and molecular conformation from Nuclear Magnetic Resonance. J Am Chem Soc 93:4893–4897
Fischman AJ, Live DH, Wyssbrod HR, Agosta WC, Cowburn D (1980) Torsion angles in the cystine bridge of Oxytocin an aqueous solution. Measurements of circumjacent vicinal couplings between 1H, 13C, and 15N. J Am Chem Soc 102:2533–2539
van Gunsteren WF, Gros P, Torda AE, Berendsen H, van Schaik R (1991) On deriving spatial structure from NMR or X-ray diffraction data. In: Protein conformation Wiley-Interscience, Ciba Foundation symposium, vol 161, pp. 150–166
van Gunsteren WF, Brunne RM, Gros P, van Schaik RC, Schiffer CA, Torda AE (1994) Accounting for molecular mobility in structure determination based on Nuclear Magnetic Resonance spectroscopic and X-ray diffraction data. In: James TL, Oppenheimer NJ (eds) Methods in enzymology: nuclear magnetic resonance, vol 239, Academic Press, New York, pp 619–654
van Gunsteren WF, Bonvin AMJJ, Daura X, Smith L (1999) Aspects of modeling biomolecular structure on the basis of spectroscopic or diffraction data. In: Krishna and Berliner (eds) Structure computation and dynamics in protein NMR, Biol Magnetic Resonance. Plenum Publishers, New York, vol 17, pp 3–35
Haasnoot CAG, de Leeuw FAAM, de Leeuw HPM, Altona C (1979) Interpretation of vicinal proton-proton coupling constants by a generalised Karplus relation. Conformational analysis of the exocyclic C4’-C5’ bond in nucleosides and nucleotides. Rec J Roy Neth Chem Soc 98:576–577
Haasnoot CAG, de Leeuw FAAM, de Leeuw HPM, Altona C (1981) Relationship between proton-proton NMR coupling constants and substituent electronegativities. III. Conformational analysis of proline rings in solution using a generalized Karplus equation. Biopolymers 20:1211–1245
Hendrickson WA, Konnert JH (1981) Stereochemical restrained crystallographic least-squares refinement of macromolecule structures. In: Srimivasan R (eds) Biomolecular structure, conformation, function and evolution, vol 1: diffraction and related studies, Pergamon Press, New York, pp 43–57
Huggins ML (1953) Bond energies and polarities. J Am Chem Soc 75:4123–4126
Imai K, Osawa E (1990) An empirical extension of the Karplus equation. Magn Reson Chem 28:668–674
Karplus M (1959) Contact electron-spin coupling of nuclear magnetic moments. J Chem Phys 30:11–15
Karplus M (1963) Vicinal proton coupling in Nuclear Magnetic Resonance. J Am Chem Soc 85:2870–2871
Kopple KD, Wiley GR, Tauke R (1973) A dihedral angle-vicinal proton coupling constant correlation for the α-β bond of amino acid residues. Biopolymers 12:627–636
Lindorff-Larsen K, Best RB, Vendruscolo M (2005) Interpreting dynamically-averaged scalar couplings in proteins. J Biomol NMR 32:273–280
Mádi ZL, Griesinger C, Ernst RR (1990) Conformational dynamics of proline residues in Antamadine. J coupling analysis of strongly coupled spin systems based on E.COSY spectra. J Am Chem Soc 112:2908–2914
de Marco A, Llinás M, Wüthrich K (1978) Analysis of the 1H-NMR spectra of Ferrichrome peptides. I. The non-amide protons. Biopolymers 17:617–636
Moore JM, Lepre CA, Gippler GP, Chazin WJ, Case DA, Wright PE (1991) High-resolution solution structure of reduced french bean Plastocyanin and comparison with the crystal structure of poplar Plastocyanin. J Mol Biol 221:533–555
Oostenbrink C, Villa A, Mark AE, van Gunsteren WF (2004) A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6. J Comput Chem 25:1656–1676
Pardi A, Billeter M, Wüthrich K (1984) Calibration of the angular dependence of the amide proton-Cα proton coupling constants, \(^{3}J_{{HN}_{\alpha}}\), in a globular protein: use of \(^{3}J_{{HN}_{\alpha}}\) for identification of helical secondary structure. J Mol Biol 180:741–751
Pérez C, Löhr F, Rüterjans H, Schmidt JM (2001) Self-consistent Karplus parametrization of 3 J couplings depending on the polypeptide side-chain torsion χ1. J Am Chem Soc 123:7081–7093
Salmon L, Bouvignies G, Markwick P, Blackledge M (2011) Nuclear Magnetic Resonance provides a quantitative description of protein conformational flexibility on physiologically important time scales. Biochemistry 50:2735–2747
Schmid N, Allison JR, Dolenc J, Eichenberger AP, Kunz AP, van Gunsteren WF (2011) Biomolecular structure refinement using the GROMOS simulation software. J Biomol NMR 51:265–281
Schmid N, Eichenberger AP, Choutko A, Riniker S, Winiger M, Mark AE, van Gunsteren WF (2011) Definition and testing of the GROMOS force-field versions 54A7 and 54B7. Eur Biophys J 40:843–856
Schmidt JM (2007) Asymmetric Karplus curves for the protein side-chain 3 J couplings. J Biomol NMR 37:287–301
Schmidt JM, Blümel M, Löhr F, Rüterjans H (1999) Self-consistent 3 J coupling analysis for the joint calibration of Karplus coefficients and evaluation of torsional angles. J Biomol NMR 14:1–12
Schuler LD, Daura X, van Gunsteren WF (2001) An improved GROMOS96 force field for aliphatic hydrocarbons in the condensed phase. J Comput Chem 22:1205–1218
Schwalbe H, Grimshaw SB, Spencer A, Buck M, Boyd J, Dobson CM, Redfield C, Smith LJ (2001) A refined solution structure of hen Lysozyme determined using residual dipolar couling data. Protein Sci 10:677–688
Smith LJ, Sutcliffe MJ, Redfield C, Dobson CM (1991) Analysis of \(\varphi\) and χ1 torsion angles from hen Lysozyme in solution from 1H NMR spin-spin coupling constants. Biochemistry 30:986–996
Steiner D, van Gunsteren WF (2012) An improved structural characterisation of reduced french bean Plastocyanin based on NMR data and local-elevation molecular dynamics simulation. Eur Biophys J (accepted)
Suardíaz R, Pérez C, de la Vega JMG, Fabián JS, Contreras RH (2007) Theoretical Karplus relationships for vicinal coupling constants around χ1 in valine. Chem Phys Lett 442:119–123
Vaney MC, Maignan S, Riès-Kautt M, Ducruix A (1996) High-resolution structure (1.33Å) of a HEW Lysozyme tetragonal crystal grown in the APCF apparatus. Data and structural comparison with a crystal grown under microgravity from SpaceHab-01 mission. Acta Cryst D 52:505–517
Vögeli B, Ying J, Grishaev A, Bax A (2007) Limits on variations in protein backbone dynamics from precise measurements of scalar couplings. J Am Chem Soc 129:9377–9385
Wang AC, Bax A (1996) Determination of the backbone dihedral angles ϕ in human Ubiquitin from reparameterized empirical Karplus equations. J Am Chem Soc 118:2483–2494
Wüthrich K (1986) NMR of proteins and nucleic acids. Wiley, New York
Xu RX, Olejniczak ET, Fesik SW (1992) Stereospecific assignment and χ1 rotamers for FKBP when bound to Ascomycin from \({^{3}J_{H_\alpha\, H_\beta}}\) and \({^{3}J_{N\, H_\beta}}\) coupling constants. FEBS Lett 305:137–143
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This work was financially supported by the National Center of Competence in Research (NCCR) in Structural Biology and by grant number 200020-137827 of the Swiss National Science Foundation, and by grant number 228076 of the European Research Council, which is gratefully acknowledged.
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Steiner, D., Allison, J.R., Eichenberger, A.P. et al. On the calculation of 3 J αβ-coupling constants for side chains in proteins. J Biomol NMR 53, 223–246 (2012). https://doi.org/10.1007/s10858-012-9634-5
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DOI: https://doi.org/10.1007/s10858-012-9634-5