Skip to main content
Log in

Time-averaged order parameter restraints in molecular dynamics simulations

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

Abstract

A method is described that allows experimental \(S^2\) order parameters to be enforced as a time-averaged quantity in molecular dynamics simulations. The two parameters that characterize time-averaged restraining, the memory relaxation time and the weight of the restraining potential energy term in the potential energy function used in the simulation, are systematically investigated based on two model systems, a vector with one end restrained in space and a pentapeptide. For the latter it is shown that the backbone N–H order parameter of individual residues can be enforced such that the spatial fluctuations of quantities depending on atomic coordinates are not significantly perturbed. The applicability to realistic systems is illustrated for the B3 domain of protein G in aqueous solution.

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
Fig. 9

Similar content being viewed by others

References

  • Barker JA, Watts RO (1973) Monte Carlo studies of the dielectric properties of water-like models. Mol Phys 26:789–792

    Article  ADS  Google Scholar 

  • Beauchamp KA, Lin YS, Das R, Pande VS (2012) Are protein force fields getting better? A systematic benchmark on 524 diverse NMR measurements. J Chem Theory Comput 8:1409–1414

    Article  Google Scholar 

  • Berendsen HJC (1985) Treatment of long-range forces in molecular dynamics. In: Hermans J (ed) Molecular dynamics and protein structure. Polycrystal Book Service, Western Springs, pp 18–22

    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

    Chapter  Google Scholar 

  • 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 

  • Best RB, Vendruscolo M (2004) Determination of protein structures consistent with NMR order parameters. J Am Chem Soc 126:8090–8091

    Article  Google Scholar 

  • Brainard JR, Szabo A (1981) Theory for nuclear magnetic relaxation of probes in anisotropic systems: application to cholesterol in phospholipid vesicles. Biochemistry 20:4618–4628

    Article  Google Scholar 

  • Braun W, Bösch C, Brown LR, Gō N, Wüthrich K (1981) Combined use of proton–proton Overhauser enhancements and a distance geometry algorithm for determination of polypeptide conformations. Application to micelle-bound glucagon. Biochim Biophys Acta 667:377–396

    Article  Google Scholar 

  • Brüschweiler R, Wright PE (1994) NMR order parameters of biomolecules: a new analytical representation and application to the Gaussian axial fluctuation model. J Am Chem Soc 116:8426–8427

    Article  Google Scholar 

  • Brüschweiler R, Roux B, Blackledge M, Griesinger C, Karplus M, Ernst RR (1992) Influence of rapid intramolecular motion on NMR cross relaxation rates. A molecular dynamics study of antamanide in solution. J Am Chem Soc 114:2289–2302

    Article  Google Scholar 

  • Buck M, Bouguet-Bonnet S, Pastor RW, MacKerell AD (2006) Importance of the CMAP correction to the CHARMM22 protein force field: dynamics of hen lysozyme. Biophys J 90:L36–L38

    Article  Google Scholar 

  • Cavalli A, Camilloni C, Vendruscolo M (2013) Molecular dynamics simulations with replica-averaged structural restraints generate structural ensembles according to the maximum entropy principle. J Chem Phys 138:094112

    Google Scholar 

  • Chandrasekhar I, Clore GM, Szabo A, Gronenborn AM, Brooks BR (1992) A 500 ps molecular dynamics simulation study of interleukin-1\(\beta \) in water. Correlation with nuclear magnetic resonance spectroscopy and crystallography. J Mol Biol 226:239–250

    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 

  • Daura X, Mark AE, van Gunsteren WF (1999) Peptide folding simulations: No solvent required? Comput Phys Commun 123:97–102

    Article  MATH  ADS  Google Scholar 

  • d’Auvergne EJ, Gooley PR (2003) The use of model selection in the model-free analysis of protein dynamics. J Biomol NMR 25:25–39

    Article  Google Scholar 

  • Dolenc J, Missimer JH, Steinmetz MO, van Gunsteren WF (2010) Methods of NMR structure refinement: molecular dynamics simulations improve the agreement with measured NMR data of a C-terminal peptide of GCN4-p1. J Biomol NMR 47:221–235

    Article  Google Scholar 

  • Duan Y, Wu C, Chowdhury S, Lee MC, Xiong G, Zhang W, Yang R, Cieplak P, Luo R, Lee T, Caldwell J, Wang J, Kollman P (2003) A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J Comput Chem 24:1999–2012

    Article  Google Scholar 

  • Eichenberger AP, Allison JR, Dolenc J, Geerke DP, Horta BAC, Meier K, Oostenbrink C, Schmid N, Steiner D, Wang D, van Gunsteren WF (2011) The GROMOS++ software for the analysis of biomolecular simulation trajectories. J Chem Theory Comput 7:3379–3390

    Article  Google Scholar 

  • Evenäs J, Forsén S, Malmendal A, Akke M (1999) Backbone dynamics and energetics of a calmodulin domain mutant exchanging between closed and open conformations. J Mol Biol 289:603–617

    Article  Google Scholar 

  • Feenstra KA, Peter C, Scheek RM, van Gunsteren WF, Mark AE (2002) A comparison of methods for calculating NMR cross-relaxation rates (NOESY and ROESY intensities) in small peptides. J Biomol NMR 23:181–194

    Article  Google Scholar 

  • Fennen J, Torda AE, van Gunsteren WF (1995) Structure refinement with molecular dynamics and a Boltzmann-weighted ensemble. J Biomol NMR 6:163–170

    Article  Google Scholar 

  • Fukunishi H, Watanabe O, Takada S (2002) On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: application to protein structure prediction. J Chem Phys 116:9058–9067

    Article  ADS  Google Scholar 

  • Gapsys V, de Groot BL (2013) Optimal superpositioning of flexible molecule ensembles. Biophys J 104:196–207

    Article  Google Scholar 

  • Gáspári Z, Perczel A (2010) Protein dynamics as reported by NMR. Annu Rep NMR Spectrosc 71:35–75

    Article  Google Scholar 

  • Gattin Z, Schwartz J, Mathad RI, Jaun B, van Gunsteren WF (2009) Interpreting experimental data by using molecular simulation instead of model building. Chem Eur J 15:6389–6398

    Article  Google Scholar 

  • Gniewek P, Kolinski A, Jernigan RL, Kloczkowski A (2012) How noise in force fields can affect the structural refinement of protein models. Proteins Struct Funct Bioinf 80:335–341

    Article  Google Scholar 

  • Gros P, van Gunsteren WF (1993) Crystallographic refinement and structure-factor time-averaging by molecular dynamics in the absence of a physical force field. Mol Sim 10:377–395

    Article  Google Scholar 

  • Hall JB, Fushman D (2003) Characterization of the overall and local dynamics of a protein with intermediate rotational anisotropy: differentiating between conformational exchange and anisotropic diffusion in the B3 domain of protein G. J Biomol NMR 27:261–275

    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) Tech Protein Chem, vol 4. Academic Press, New York, pp 615–622

    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 

  • Henry ER, Szabo A (1985) Influence of vibrational motion on solid state line shapes and NMR relaxation. J Chem Phys 82:4753–4761

    Article  ADS  Google Scholar 

  • Hess B, Scheek RM (2003) Orientation restraints in molecular dynamics simulations using time and ensemble averaging. J Magn Reson 164:19–27

    Article  ADS  Google Scholar 

  • Hockney RW (1970) The potential calculation and some applications. Methods Comput Phys 9:136–211

    Google Scholar 

  • Hornak V, Abel R, Okur A, Strockbine B, Roitberg A, Simmerling C (2006) Comparison of multiple Amber force fields and development of improved protein backbone parameters. Proteins Struct Funct Bioinf 65:712–725

    Article  Google Scholar 

  • Huber T, van Gunsteren WF (1998) SWARM-MD: searching conformational space by cooperative molecular dynamics. J Phys Chem A 102:5937–5943

    Article  Google Scholar 

  • Huber T, Torda AE, van Gunsteren WF (1996) Optimization methods for conformational sampling using a Boltzmann-weighted mean field approach. Biopolymers 39:103–114

    Article  Google Scholar 

  • Jardetzky O (1980) On the nature of molecular conformations inferred from high-resolution NMR. Biochim Biophys Acta 621:227–232

    Article  Google Scholar 

  • Jarymowycz VA, Stone MJ (2006) Fast time scale dynamics of protein backbones: NMR relaxation methods, applications, and functional consequences. Chem Rev 106:1624–1671

    Article  Google Scholar 

  • Johnson E (2012) Separability between overall and internal motion: a protein folding problem. Proteins Struct Funct Bioinf 80:2645–2651

    Article  Google Scholar 

  • Johnson E, Showalter SA, Brüschweiler R (2008) A multifaceted approach to the interpretation of NMR order parameters: a case study of a dynamic \(\alpha \)-helix. J Phys Chem B 112:6203–6210

    Article  Google Scholar 

  • Kim DE, Blum B, Bradley P, Baker D (2009) Sampling bottlenecks in de novo protein structure prediction. J Mol Biol 393:249–260

    Article  Google Scholar 

  • Lipari G, Szabo A (1982) Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. 1. Theory and range of validity. J Am Chem Soc 104:4546–4559

    Article  Google Scholar 

  • Luginbühl P, Wüthrich K (2002) Semi-classical nuclear spin relaxation theory revisited for use with biological macromolecules. Prog Nucl Magn Reson Spectrosc 40:199–247

    Article  Google Scholar 

  • MacKerell AD (2004) Empirical force fields for biological macromolecules: overview and issues. J Comput Chem 25:1584–1604

    Article  Google Scholar 

  • MacKerell AD, Feig M, Brooks CL (2004) Improved treatment of the protein backbone in empirical force fields. J Am Chem Soc 126:698–699

    Article  Google Scholar 

  • Marchand S, Roux B (1998) Molecular dynamics study of calbindin \(\text{D}_{\rm 9k}\) in the apo and singly and doubly calcium-loaded state. Proteins Struct Funct Bioinf 33:265–284

    Article  Google Scholar 

  • Misura KMS, Baker D (2005) Progress and challenges in high-resolution refinement of protein structure models. Proteins Struct Funct Bioinf 59:15–29

    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 simulations. J Mol Biol 267:1012–1025

    Article  Google Scholar 

  • Olsson S, Frellsen J, Boomsma W, Mardia KV, Hamelryck T (2013) Inference of structure ensembles of flexible biomolecules from sparse, averaged data. PLoS One 8:e79439

    Google Scholar 

  • Olsson S, Vögeli BR, Cavalli A, Boomsma W, Ferkinghoff-Borg J, Lindorff-Larsen K, Hamelryck T (2014) Probabilistic determination of native state ensembles of proteins. J Chem Theory Comput 10:3484–3491

    Article  Google Scholar 

  • Palmer AG III, Williams J, McDermott A (1996) Nuclear magnetic resonance studies of biopolymer dynamics. J Phys Chem 100:13,293–13,310

    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 NMR refinement? A model study for DNA. J Mol Biol 220:457–479

    Article  Google Scholar 

  • Pepermans H, Tourwé D, van Binst G, Boelens R, Scheek RM, van Gunsteren WF, Kaptein R (1988) The combined use of NMR, distance geometry, and restrained molecular dynamics for the conformational study of a cyclic somatostatin analogue. Biopolymers 27:323–338

    Article  Google Scholar 

  • Peter C, Daura X, van Gunsteren WF (2001) Calculation of NMR-relaxation parameters for flexible molecules from molecular dynamics simulations. J Biomol NMR 20:297–310

    Article  Google Scholar 

  • Pfeiffer S, Fushman D, Cowburn D (2001) Simulated and NMR-derived backbone dynamics of a protein with significant flexibility: a comparison of spectral densities for the \(\beta \)ARK1 PH domain. J Am Chem Soc 123:3021–3036

    Article  Google Scholar 

  • Pitera JW, Chodera JD (2012) On the use of experimental observations to bias simulated ensembles. J Chem Theory Comput 8:4335–3451

    Article  Google Scholar 

  • Raval A, Piana S, Eastwood MP, Dror RO, Shaw DE (2012) Refinement of protein structure homology models via long, all-atom molecular dynamics simulations. Proteins 80:2071–2079

    Google Scholar 

  • Richter B, Gsponer J, Várnai P, Salvatella X, Vendruscolo M (2007) The mumo (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins. J Biomol NMR 37:117–135

    Article  Google Scholar 

  • Roux B, Weare J (2013) On the statistical equivalence of restrained-ensemble simulations with the maximum entropy method. J Chem Phys 138:084107

    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 

  • Sapienza PJ, Lee AL (2010) Using NMR to study fast dynamics in proteins: methods and applications. Curr Opin Pharmacol 10:723–730

    Article  Google Scholar 

  • Scheek RM, Torda AE, Kemmink J, van Gunsteren WF (1991) Structure determination by NMR: the modelling of NMR parameters as ensemble averages. In: Hoch JC, Poulsen FM, Redfield C (eds) Computational aspects of the study of biological macromolecules by nuclear magnetic resonance spectroscopy, NATO ASI Series A225. Plenum Press, New York, pp 209–217

    Chapter  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, Gros P, van Gunsteren WF (1995) Time-averaging crystallographic refinement: possibilities and limitations using alpha-cyclodextrin as a test system. Acta Cryst D51:85–92

    Google Scholar 

  • Schmid N, Allison JR, Dolenc J, Eichenberger AP, Kunz APE, 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 

  • Schmid N, Christ CD, Christen M, Eichenberger AP, van Gunsteren WF (2012) Architecture, implementation and parallelisation of the GROMOS software for biomolecular simulation. Comput Phys Commun 183:890–903

    Article  ADS  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 114:10,654–10,656

    Article  Google Scholar 

  • Schmitz U, Ulyanov B, Kumar A, James TL (1993) Molecular dynamics with weighted time-averaged restraints for a DNA octamer: dynamic interpretation of NMR 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 simulations. J Biomol NMR 12:501–508

    Article  Google Scholar 

  • Showalter SA, Brüschweiler R (2007) Validation of molecular dynamics simulations of biomolecules. J Chem Theory Comput 3:961–975

    Article  Google Scholar 

  • Smith LJ, Mark AE, Dobson CM, van Gunsteren WF (1995a) Comparison of MD simulations and NMR experiments for hen lysozyme: analysis of local fluctuations, cooperative motions and global changes. Biochemistry 34:10918–10931

    Article  Google Scholar 

  • Smith PE, van Schaik RC, Szyperski T, Wüthrich K, van Gunsteren WF (1995b) Internal mobility of the basic pancreatic trypsin inhibitor in solution: a comparison of NMR spin relaxation measurements and molecular dynamics. J Mol Biol 246:356–365

    Article  Google Scholar 

  • Stocker U, van Gunsteren WF (2000) Molecular dynamics simulation of hen egg white lysozyme: a test of the GROMOS96 force field against nuclear magnetic resonance data. Proteins Struct Funct Bioinf 40:145–153

    Article  Google Scholar 

  • Sugita Y, Okamoto Y (1999) Replica-exchange molecular dynamics method for protein folding. Chem Phys Lett 314:141–151

    Article  ADS  Google Scholar 

  • Sugita Y, Kitao A, Okamoto Y (2000) Multidimensional replica-exchange method for free-energy calculations. J Chem Phys 113:6042–6051

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

    Article  Google Scholar 

  • Trbovic N, Kim B, Friesner RA, Palmer AG (2008) Structural analysis of protein dynamics by MD simulations and NMR spin-relaxation. Proteins Struct Funct Bioinf 71:684–694

    Article  Google Scholar 

  • van Gunsteren WF, Berendsen HJC (1988) A leap-frog algorithm for stochastic dynamics. Mol Sim 1:173–185

    Article  Google Scholar 

  • van Gunsteren WF, Berendsen HJC, Rullmann JAC (1981) Stochastic dynamics for molecules with constraints. Brownian dynamics of n-alkanes. Mol Phys 44:69–95

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • van Gunsteren WF, Dolenc J, Mark AE (2008) Molecular simulation as an aid to experimentalists. Curr Opin Struct Biol 18:149–153

    Article  Google Scholar 

  • White AD, Voth GA (2014) Efficient and minimal method to bias molecular simulations with experimental data. J Chem Theory Comput 10:3023–3030

    Article  Google Scholar 

  • Wong V, Case DA (2008) Evaluating rotational diffusion from protein MD simulation. J Phys Chem B 112:6013–6024

    Article  Google Scholar 

  • Yun-Yu S, Lu W, van Gunsteren WF (1988) On the approximation of solvent effects on the conformation and dynamics of cyclosporin A by stochastic dynamics simulation techniques. Mol Sim 1:369–383

    Article  Google Scholar 

Download references

Acknowledgments

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. N.H. thanks the German Research Foundation (DFG) for financial support within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Niels Hansen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hansen, N., Heller, F., Schmid, N. et al. Time-averaged order parameter restraints in molecular dynamics simulations. J Biomol NMR 60, 169–187 (2014). https://doi.org/10.1007/s10858-014-9866-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10858-014-9866-7

Keywords

Navigation