Skip to main content
SpringerLink
Log in

Asymmetric Karplus curves for the protein side-chain 3 J couplings

  • Article
  • Published:
Journal of Biomolecular NMR Aims and scope Submit manuscript

Abstract

The standard Karplus equation for calculating 3 J coupling constants from any given dihedral angle requires three empirical coefficients be determined that relate to the magnitudes of three modes of the angle dependency of 3 J. Considering cosine modes only (bimodal, unimodal and baseline component), Karplus curves are generally symmetric with respect to the sign of the angle argument. Typically, their primary and secondary maxima differ in amplitude, whereas the two minima are of equal depth. However, chiral molecular topologies, such as those surrounding the main-chain and side-chain torsions in amino-acid residues, preclude, as regards substituent positioning, exact mirror-image conformations from being formed—for any given torsion-angle value. It is therefore unlikely that 3 J couplings assume identical values for the corresponding positive and negative dihedral angles. This suggests that a better empirical fit of the torsion-angle dependency of 3 J could be obtained when removing the constraint of symmetrically identical coupling constants. A sine term added to the Karplus equation allows independent modelling of both curve minima typically located near dihedral-angle values of +90° and −90°. Revisiting an extensive 3 J coupling dataset previously recorded to determine the side-chain torsions χ1 in the protein flavodoxin, the asymmetric Karplus model accomplishes a more accurate fit to the experimental data. Asymmetries revealed in the angle dependencies exceed the experimental precision in determining 3 J. Accounting for these effects helps improve molecular models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Artali, R., Bombieri, G., Meneghetti. F., Gilardi. G., Sadeghi, S.J., Cavazzini, D., Rossi, G.L.: Comparison of the refined crystal structure of wild-type (1.34 Å) flavodoxin from Desulfovibrio vulgaris and the S35C mutant (1.44 Å) at 100 K. Acta. Crystallogr. Sect. D 58, 1787–1792 (2002)

    Article  Google Scholar 

  • Barfield, M., Karplus, M.: Valence-bond bond-order formulation for contact nuclear spin-spin coupling. J. Am. Chem. Soc. 85, 2870–2871 (1969)

    Google Scholar 

  • Bates, D.M., Watts, D.G.: Nonlinear Regression Analysis and its Applications. Wiley, New York (1988)

    MATH  Google Scholar 

  • Blümel, M., Schmidt, J.M., Löhr, F., Rüterjans, H.: Quantitative φ torsion angle analysis in Desulfovibrio vulgaris flavodoxin based on six φ related 3 J couplings. Eur. Biophys. J. 27, 321–334 (1998)

    Article  Google Scholar 

  • Brüschweiler, R., Case, D.A.: Adding harmonic motion to the Karplus relation for spin-spin coupling. J. Am. Chem. Soc. 116, 11199–11200 (1994)

    Article  Google Scholar 

  • Chou, J.J., Case, D.A., Bax, A.: Insights into the mobility of methyl-bearing side chains in proteins from 3 J CC and 3 J CN couplings. J. Am. Chem. Soc. 125, 8959–8966 (2003)

    Article  Google Scholar 

  • Donders, L.A., de Leeuw, F.A.A.M., Altona, C.: Relationship between proton–proton NMR coupling constants and substituent electronegativities. Magn. Res. Chem. 27, 556–563 (1989)

    Article  Google Scholar 

  • Dzakula, Z., Westler, W.M., Markley, J.L.: Continuous probability distribution (CUPID) analysis of potentials for internal rotations. J. Magn. Reson. B 111, 109–126 (1996)

    Article  Google Scholar 

  • Haasnoot, C.A.G., de Leeuw, F.A.A.M., Altona, C.: The relationship between proton–proton NMR coupling constants and substituent electronegativities—I. An empirical generalization of the Karplus equation. Tetrahedron 36, 2783–2792 (1980)

    Article  Google Scholar 

  • Haasnoot, C.A.G., de Leeuw, F.A.A.M., de Leeuw, H.P.M., Altona, C.: The relationship between proton–proton NMR coupling constants and substituent electronegativities. II. Conformational analysis of the sugar ring in nucleosides and nucleotides in solution using a generalized Karplus equation. Org. Magn. Reson. 15, 43–52 (1981a)

    Article  Google Scholar 

  • Haasnoot, C.A.G., de Leeuw, F.A.A.M., de Leeuw, H.P.M., Altona, C.: 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 (1981b)

    Article  Google Scholar 

  • IUPAC-IUB Commision on Biochemical Nomenclature J. Mol. Biol. 52, 1–17 (1970)

    Google Scholar 

  • Janin, J., Wodak, S., Levitt, M., Maigret, B.: Conformation of amino acid side-chains in proteins. J. Mol. Biol. 125, 357–386 (1978)

    Article  Google Scholar 

  • Karimi-Nejad, Y., Schmidt, J.M., Rüterjans, H., Schwalbe, H., Griesinger, C.: Conformation of valine side chains in ribonuclease T1 determined by NMR studies of homonuclear and heteronuclear 3 J coupling constants. Biochemistry 33, 5481–5492 (1994)

    Article  Google Scholar 

  • Karplus, M.: Contact electron-spin coupling of nuclear magnetic resonance. J. Chem. Phys. 30, 11–15 (1959)

    Article  Google Scholar 

  • Karplus, M.: Vicinal proton coupling in nuclear magnetic resonance. J. Am. Chem. Soc. 85, 2870–2871 (1963)

    Article  Google Scholar 

  • Knauf, M.A., Löhr, F., Blümel, M., Mayhews, S.G., Rüterjans, H.: NMR Investigation of the solution conformation of oxidized flavodoxin from Desulfovibrio vulgaris: determination of the tertiary structure and detection of protein-bound water molecules. Eur. J. Biochem. 238, 423–434 (1996)

    Article  Google Scholar 

  • Pachler, K.G.R.: Nuclear magnetic resonance study of some a-amino acids—I. Coupling constants in alkaline and acidic medium. Spectrochim. Acta 19, 2085–2092 (1963)

    Article  Google Scholar 

  • Pachler, K.G.R.: Nuclear magnetic resonance study of some a-amino acids—II. Rotational isomerism. Spectrochim. Acta 20, 581–587 (1964)

    Article  Google Scholar 

  • Pachler, K.G.R.: Extended Hückel theory MO calculations of proton–proton coupling constants. The substituent effect in fluoroethane. Tetrahedron Lett. 22, 1955–1958 (1970)

    Article  Google Scholar 

  • Pachler, K.G.R.: Extended Hückel theory MO calculations of proton–proton coupling constants—II. The effect of substituents on vicinal couplings in monosubstituted ethanes. Tetrahedron 27, 187–199 (1971)

    Article  Google Scholar 

  • Pachler, K.G.R.: The dependence of vicinal proton–proton coupling constants on dihedral angle and substituents. J. Chem. Soc. Perkin Trans. II, 1936–1940 (1972)

    Google Scholar 

  • Pérez, C., Löhr, F., Rüterjans, H., Schmidt, J.M.: Self-consistent Karplus parametrization of 3 J couplings depending on the polypeptide sidechain torsion χ1. J. Am. Chem. Soc. 123, 7081–7093 (2001)

    Article  Google Scholar 

  • Ponder, J.W., Richards, F.M.: Tertiary templates for proteins—Use of packing criteria in the emmeration of allowed sequences for different structural chesses. J. Mol. Biol. 193, 775–791 (1987)

    Article  Google Scholar 

  • Sarkar, S.K., Young, P.E., Torchia, D.A.: Ring dynamics of d,l-proline and d,l-proline hydrochloride in the solid state: a 2H nuclear magnetic resonance study. J. Am. Chem. Soc. 108, 6459–6464 (1986)

    Article  Google Scholar 

  • Schmidt, J.M., Brüschweiler, R., Ernst, R.R., Dunbrack, R.L. Jr, Joseph, D., Karplus, M.: Molecular dynamics simulation of the proline conformational equilibrium and dynamics in antamanide using the CHARMM force field. J. Am. Chem. Soc. 115, 8747–8756 (1993)

    Article  Google Scholar 

  • Schmidt, J.M.: Conformational equilibria in polypeptides. II. Dihedral-angle distribution in antamanide based on three-bond coupling information. J. Magn. Reson. 124, 310–322 (1997)

    Article  Google Scholar 

  • Schmidt, J.M., Blümel, M., Löhr, F., Rüterjans, H.: Self-consistent 3 J coupling analysis for the joint calibration of Karplus coefficients and φ-torsion angles. J. Biomol. NMR 14, 1–12 (1999)

    Article  Google Scholar 

  • Walsh, M.A.: Structural studies on a genetically engineered flavodoxin. Dissertation, National University of Ireland (1994)

  • Walsh, M.A., McCarthy, A., O’Farrell, P.A., McArdle, P., Cunningham, P.D., Mayhew, S.G., Higgins, T.M.: X-ray crystal structure of the Desulfovibrio vulgaris (Hildenborough) apoflavodoxin–riboflavin complex. Eur. J. Biochem. 258, 362–371 (1998)

    Article  Google Scholar 

  • Watt, W., Tulinsky, A., Swenson, R.P., Watenpaugh, K.D.: Comparison of the crystal structures of a flavodoxin in its three oxidation states at cryogenic temperatures. J. Mol. Biol. 218, 195–208 (1991)

    Article  Google Scholar 

Download references

Acknowledgements

Frank Löhr is thanked for stimulating discussion and his continual interest in this J-coupling study.

Author information

Authors and Affiliations

  1. Biosciences Department, University of Kent, Canterbury, Kent, CT2 7NJ, UK

    Jürgen M. Schmidt

Authors
  1. Jürgen M. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jürgen M. Schmidt.

Electronic supplementary material

Below is the link to the electronic supplementary material

ESM 1 (PDF 61 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schmidt, J.M. Asymmetric Karplus curves for the protein side-chain 3 J couplings. J Biomol NMR 37, 287–301 (2007). https://doi.org/10.1007/s10858-006-9140-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10858-006-9140-8

Keywords

Search

Navigation