Skip to main content
Log in

On the use of time-averaging restraints when deriving biomolecular structure from \(^3J\)-coupling values obtained from NMR experiments

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

Abstract

Deriving molecular structure from \(^3J\)-couplings obtained from NMR experiments is a challenge due to (1) the uncertainty in the Karplus relation \(^3J(\theta )\) connecting a \(^3J\)-coupling value to a torsional angle \(\theta \), (2) the need to account for the averaging inherent to the measurement of \(^3J\)-couplings, and (3) the sampling road blocks that may emerge due to the multiple-valuedness of the inverse function \(\theta (^3J)\) of the function \(^3J(\theta )\). Ways to properly handle these issues in structure refinement of biomolecules are discussed and illustrated using the protein hen egg white lysozyme as example.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Abraham RJ, McLauchlan KA (1968) The proton resonance spectra and conformations of the prolines. Mol Phys 5:513–523

    Article  ADS  Google Scholar 

  • Allison JR, van Gunsteren WF (2009) A method to explore protein side chain conformational variability using experimental data. ChemPhysChem 10:3213–3228

    Article  Google Scholar 

  • Artymiuk PJ, Blake CCF, Rice DW, Wilson KS (1982) The structures of the monoclinic and orthorhombic forms of hen egg-white lysozyme at 6 Ångstroms resolution. Acta Crystallogr Sect B 38:778–783

    Article  Google Scholar 

  • Berendsen HJC, Postma JPM, van Gunsteren WF, Hermans J (1981) Interaction models for water in relation to protein hydration. In: Pullmann B (ed) Intermolecular forces. Reidel, Dordrecht, pp 331–342

  • Berendsen HJC, Postma JPM, van Gunsteren WF, DiNola A, Haak JR (1984) Molecular dynamics with coupling to an external bath. J Chem Phys 81:3684–3690

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  • 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 simulation: GROMOS05. J Comput Chem 26:1719–1751

    Article  Google Scholar 

  • Christen M, Keller B, van Gunsteren WF (2007) Biomolecular structure refinement based on adaptive restraints using local-elevation simulation. J Biomol NMR 39:265–273

    Article  Google Scholar 

  • Cung MT, Marraud M (1982) Conformational dependence of the vicinal proton coupling constant for the C\(^\alpha \)-C\(^\beta \) bond in peptides. Biopolymers 21:953–967

    Article  Google Scholar 

  • Daura X, Gademann K, Jaun B, Seebach D, van Gunsteren WF, Mark AE (1999) Peptide folding: when simulation meets experiment. Angew Chem Intl Ed 38:236–240

    Article  Google Scholar 

  • de Vlieg J, Boelens R, Scheek RM, Kaptein R, van Gunsteren WF (1986) Restrained molecular dynamics procedure for protein tertiary structure determination from NMR data: A lac repressor headpiece structure based on information on J-coupling and from presence and absence of NOE’s. Isr J Chem 27:181–188

    Article  Google Scholar 

  • Deber CM, Torchia DA, Blout ER (1971) Cyclic peptides. I. Cyclo(tri-L-propyl) and derivatives. Synthesis and molecular conformation from nuclear magnetic resonance. J Am Chem Soc 93:4893–4897

    Article  Google Scholar 

  • deMarco A, Llinás M, Wüthrich K (1978) Analysis of the \(^1\)H-NMR spectra of ferrichrome peptides. I. The non-amide protons. Biopolymers 17:617–636

    Article  Google Scholar 

  • Drenth J (1994) Principles of protein X-ray crystallography. Springer, New York

    Book  Google Scholar 

  • Fischman AJ, Live DH, Wyssbrod HR, Agosta WC, Cowburn D (1980) Torsion angles in the cystine bridge of oxytocin in aqueous solution. Measurements of circumjacent vicinal couplings between \(^1\)H, \(^{13}\)C, and \(^{15}\)N. J Am Chem Soc 102:2533–2539

    Article  Google Scholar 

  • Gros P, van Gunsteren WF, Hol WG (1990) Inclusion of thermal motion in crystallographic structures by restrained molecular dynamics. Science 249:1149–1152

    Article  ADS  Google Scholar 

  • Hansen N, Heller F, Schmid N, van Gunsteren WF (2014) Time-averaged order parameter restraints in molecular dynamics simulations. J Biomol NMR 60:169–187

    Article  Google Scholar 

  • Harvey TS, van Gunsteren WF (1993) The application of chemical shift calculation to protein structure determination by NMR. In: Angeletti RH (ed) Techniques in protein chemistry IV. Academic Press, San Diego, pp 615–615

    Chapter  Google Scholar 

  • Heinz TN, van Gunsteren WF, Hünenberger PH (2001) Comparison of four methods to compute the dielectric permittivity of liquids from molecular dynamics simulations. J Chem Phys 115:1125–1136

    Article  ADS  Google Scholar 

  • Huber T, Torda AE, van Gunsteren WF (1994) Local elevation: a method for improving the searching properties of molecular dynamics simulation. J Comput Aided Mol Des 8:695–708

    Article  ADS  Google Scholar 

  • Kaptein R, Zuiderweg ERP, Scheek RM, Boelens R, van Gunsteren WF (1985) A protein structure from nuclear magnetic resonance data: lac repressor headpiece. J Mol Biol 182:179–182

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Keller B, Christen M, Oostenbrink C, van Gunsteren WF (2007) On using oscillating time-dependent restraints in MD simulation. J Biomol NMR 37:1–14

    Article  Google Scholar 

  • Nanzer AP, Poulsen FM, van Gunsteren WF, Torda AE (1994) Reassessment of the structure of chymotrypsin inhibitor 2 (CI-2) using time-averaged NMR restraints. Biochemistry 33:14503–14511

    Article  Google Scholar 

  • Nanzer AP, van Gunsteren WF, Torda AE (1995) Parametrisation of time-averaged distance restraints in MD simulations. J Biomol NMR 6:313–320

    Article  Google Scholar 

  • Nanzer AP, Torda AE, Bisang C, Weber C, Robinson JA, van Gunsteren WF (1997) Dynamical studies of peptide motifs in the plasmodium falciparum circumsporozoite surface protein by restrained and unrestrained MD. J Mol Biol 267:1012–1025

    Article  Google Scholar 

  • Pardi A, Billeter M, Wüthrich K (1984) Calibration of the angular dependence of the amide proton-C\(^\alpha \) proton coupling constants, \(^3{J}_{{{\rm HN}}_\alpha} \), in a globular protein. Use of \(^3{J}_{{{\rm HN}}_\alpha} \) for identification of helical secondary structure. J Mol Biol 180:741–751

    Article  Google Scholar 

  • Pearlman DA (1994a) How is an NMR structure best defined? an analysis of molecular dynamics distance-based approaches. J Biomol NMR 4:1–16

    Google Scholar 

  • Pearlman DA (1994b) How well do time-averaged J-coupling restraints work? J Biomol NMR 4:279–299

    Google Scholar 

  • Pearlman DA, Kollman PA (1991) Are time-averaged restraints necessary for nuclear magnetic resonance refinement? A model study for DNA. J Mol Biol 220:457–479

    Article  Google Scholar 

  • Pérez C, Löhr F, Rüterjans H, Schmidt JM (2001) Self-consistent Karplus parametrization of \(^3{J}\) couplings depending on the polypeptide side-chain torsion \(\chi _1\). J Am Chem Soc 123:7081–7093

    Article  Google Scholar 

  • Ryckaert JP, Ciccotti G, Berendsen HJC (1977) Numerical integration of the Cartesian equations of motion of a system with constraints: Molecular dynamics of \(n\)-alkanes. J Comput Phys 23:327–341

    Article  ADS  Google Scholar 

  • Schiffer CA, van Gunsteren WF (1999) Accessibility and order of water sites in and around proteins: a crystallographic time-averaging study. Proteins 36:501–511

    Article  Google Scholar 

  • Schiffer CA, Huber R, Wüthrich K, van Gunsteren WF (1994) Simultaneous refinement of the structure of BPTI against NMR data measured in solution and X-ray diffraction data measured in single crystals. J Mol Biol 241:588–599

    Article  Google Scholar 

  • Schiffer CA, Gros P, van Gunsteren WF (1995) Time-averaging crystallographic refinement: possibilities and limitations using alpha-cyclodextrin as a test system. Acta Cryst D51:82–92

    Google Scholar 

  • Schmid N, Allison JR, Dolenc J, Eichenberger AP, Kunz AP, van Gunsteren WF (2011a) Biomolecular structure refinement using the GROMOS simulation software. J Biomol NMR 51:265–281

    Article  Google Scholar 

  • Schmid N, Eichenberger A, Choutko A, Riniker S, Winger M, Mark AE, van Gunsteren WF (2011b) Definition and testing of the GROMOS force-field versions: 54A7 and 54B7. Eur Biophys J 40:843–856

    Article  Google Scholar 

  • 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 torsion angles. J Biomol NMR 14:1–12

    Article  Google Scholar 

  • Schmitz U, Kumar A, James TL (1992) Dynamic interpretation of NMR data: molecular dynamics with weighted time-averaged restraints and ensemble R-factor. J Am Chem Soc 114:10654–10656

    Article  Google Scholar 

  • Schmitz U, Ulyanov NB, Kumar A, James TL (1993) Molecular dynamics with weighted time-averaged restraints for a DNA octamer: dynamic interpretation of nuclear magnetic resonance data. J Mol Biol 234:373–389

    Article  Google Scholar 

  • Scott WRP, Mark AE, van Gunsteren WF (1998) On using time-averaging restraints in molecular dynamics simulation. J Biomol NMR 12:501–508

    Article  Google Scholar 

  • Smith LJ, Sutcliffe MJ, Redfield C, Dobson CM (1991) Analysis of \(\phi \) and \(\chi _1\) torsion angles for hen lysozyme in solution from \(^1\)H NMR spin-spin coupling constants. Biochemistry 30:986–996

    Article  Google Scholar 

  • Smith LJ, Rought Whitta G, Dolenc J, Wang D, van Gunsteren WF (2016) A molecular dynamics simulation investigation of the relative stability of the cyclic peptide octreotide and its deprotonated and its (CF\(_3\))-Trp substituted analogs in different solvents. Bioorg Med Chem. doi:10.1016/j.bmc.2016.08.001

    Google Scholar 

  • Tironi IG, Sperb R, Smith PE, van Gunsteren WF (1995) A generalized reaction field method for molecular dynamics simulations. J Chem Phys 102:5451–5459

    Article  ADS  Google Scholar 

  • Torda AE, Scheek RM, van Gunsteren WF (1989) Time-dependent distance restraints in molecular dynamics simulations. Chem Phys Lett 157:289–294

    Article  ADS  Google Scholar 

  • Torda AE, Scheek RM, van Gunsteren WF (1990) Time-averaged nuclear Overhauser effect distance restraints applied to tendamistat. J Mol Biol 214:223–235

    Article  Google Scholar 

  • Torda AE, Brunne RM, Huber T, Kessler H, van Gunsteren WF (1993) Structure refinement using time-averaged J-coupling constant restraints. J Biomol NMR 3:55–66

    Article  Google Scholar 

  • van Gunsteren WF (1990) On testing theoretical models by comparison of calculated with experimental data. In: Rivail JL (ed) Studies in physical and theoretical chemistry, modelling of molecular structures and properties, vol 71. Elsevier, Amsterdam, pp 463–478

    Google Scholar 

  • van Gunsteren WF (2016) http://www.gromos.net. Accessed 13 May 2016

  • van Gunsteren WF, Kaptein R, Zuiderweg ERP (1984) Use of molecular dynamics computer simulations when determining protein structure by 2D NMR. In: Olsen WK (ed) Proceedings of the NATO/CECAM workshop on nucleic acid conformation and dynamics, Orsay, pp 79–82

  • van Gunsteren WF, Boelens R, Kaptein R, Scheek RM, Zuiderweg ERP (1985) An improved restrained molecular dynamics technique to obtain protein tertiary structure from nuclear magnetic resonance data. In: Molecular dynamics and protein structure, polycrystal book service, Western Springs. IL, USA, pp 92–99

  • van Gunsteren WF, Billeter SR, Eising AA, Hünenberger PH, Krüger P, Mark AE, Scott WRP, Tironi IG (1996) Biomolecular simulation: the GROMOS96 manual and user guide. Vdf Hochschulverlag AG an der ETH Zürich, Zürich, Groningen

  • van Schaik RC, Berendsen HJC, Torda AE, van Gunsteren WF (1993) A structure refinement method based on molecular dynamics in four spatial dimensions. J Mol Biol 234:751–762

    Article  Google Scholar 

  • Wang AC, Bax A (1996) Determination of the backbone dihedral angles \(\phi \) in human ubiquitin from reparametrized empirical Karplus equations. J Am Chem Soc 118:2483–2494

    Article  Google Scholar 

  • Wüthrich K (1986) NMR of proteins and nucleic acids. Wiley, New York

    Google Scholar 

Download references

Acknowledgments

L.J.S. would like to acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out some of this work. http://dx.doi.org/10.5281/zenodo.22558. W.F.vG. thanks the Swiss National Science Foundation, Grant Number 200020-137827, and the European Research Council, Grant Number 228076, for financial support. N.H. thanks the German Research Foundation (DFG) for financial support within the Cluster of Excellence in Simulation Technology (EXC 310/2) at the University of Stuttgart.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Niels Hansen.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 183 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Smith, L.J., van Gunsteren, W.F. & Hansen, N. On the use of time-averaging restraints when deriving biomolecular structure from \(^3J\)-coupling values obtained from NMR experiments. J Biomol NMR 66, 69–83 (2016). https://doi.org/10.1007/s10858-016-0058-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10858-016-0058-5

Keywords

Navigation