Abstract
Residual dipolar couplings, chemical shift anisotropies and quadrupolar couplings provide information about the orientation of inter-spin vectors and the anisotropic contribution of the local environment to the chemical shifts of nuclei, respectively. Structural interpretation of these observables requires parameterization of their angular dependence in terms of an alignment tensor. We compare and evaluate two algorithms for generating the optimal alignment tensor for a given molecular structure and set of experimental data, namely SVD (Losonczi et al. in J Magn Reson 138(2):334–342, 1999), which scales as \({{\mathcal {O}}(n^2)}\), and the linear least squares algorithm (Press et al. in Numerical recipes in C. The art of scientific computing, 2nd edn. Cambridge University Press, Cambridge, 1997), which scales as \({{\mathcal {O}}(n)}\).
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References
Blackledge M (2005) Recent progress in the study of biomolecular structure and dynamics in solution from residual dipolar couplings. Prog Nucl Magn Reson Spectrosc 46(1):23–61. doi:10.1016/j.pnmrs.2004.11.002
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. doi:10.1021/ct2003622
Galassi M, Davies J, Theiler J, Gough B, Jungman G, Alken P, Booth M, Rossi F, Ulerich R (2009) GNU scientific library reference manual, 3rd edn. Network Theory Ltd
Golub GH, van Loan CF (2012) Matrix computations, 4th edn. Johns Hopkins University Press, Baltimore
Hess B, Scheek RM (2003) Orientation restraints in molecular dynamics simulations using time and ensemble averaging. J Magn Reson 164(1):19–27. doi:10.1016/S1090-7807(03)00178-2
Kunz APE, Allison JR, Geerke DP, Horta BAC, Hünenberger PH, Riniker S, Schmid N (2012) New functionalities in the gromos biomolecular simulation software. J Comput Chem 33:340–353. doi:10.1002/jcc.21954
Lipsitz RS, Tjandra N (2004) Residual dipolar couplings in nmr structure analysis. Ann Rev Biophys Biomol Struct 33(1):387–413. doi:10.1146/annurev.biophys.33.110502.140306
Losonczi JA, Andrec M, Fischer MW, Prestegard JH (1999) Order matrix analysis of residual dipolar couplings using singular value decomposition. J Magn Reson 138(2):334–342. doi:10.1006/jmre.1999.1754
Mason J (1993) Conventions for the reporting of nuclear magnetic shielding (or shift) tensors suggested by participants in the NATO ARW on NMR shielding constants at the university of maryland, college park, July 1992. Solid State Nucl Magn Reson 2(5):285–288. doi:10.1016/0926-2040(93)90010-K
Mehring M (1983) Principles of high resolution NMR in solids, 2nd edn. Springer, Berlin. doi:10.1007/978-3-642-68756-3
Moltke S, Grzesiek S (1999) Structural constraints from residual tensorial couplings in high resolution NMR without an explicit term for the alignment tensor. J Biomol NMR doi:10.1023/A:1008309630377
Ottiger M, Bax A (1998) Determination of relative N–\({\text{ H }}^{\rm N}\), N–C′, C\(^\alpha \)–C′, and C\(^\alpha \)–H\(^\alpha \) effective bond lengths in a protein by NMR in a dilute liquid crystalline phase. J Am Chem Soc 120(12):334–341. doi:10.1021/ja9826791
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1997) Numerical recipes in C. The art of scientific computing, 2nd edn. Cambridge, Cambridge University Press
Prestegard JH, Bougault CM, Kishore AI (2004) Residual dipolar couplings in structure determination of biomolecules. Chem Rev 104(8):3519–3540. doi:10.1021/cr030419i
Sass J, Cordier F, Hoffmann A, Rogowski M, Cousin A, Omichinski JG, Löwen H, Grzesiek S (1999) Purple membrane induced alignment of biological macromolecules in the magnetic field. J Am Chem Soc 121(10):2047–2055. doi:10.1021/ja983887w
Saupe A (1964) Kernresonanzen in kristallinen Flüssigkeiten und in kristallinflüssigen Lösungen. Zeitung für Naturforschung 19a:161–171
Schmid N, Allison JR, Dolenc J, Eichenberger AP, Kunz APE, van Gunsteren WF (2011) Biomolecular structure refinement using the gromos simulation software. J Biomol NMR 51:265–281. doi:10.1007/s10858-011-9534-0
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
Acknowledgments
The authors wish to thank Wilfred van Gunsteren for very helpful discussions on the calculation and interpretation of RDCs. This work was financially supported by a Marsden Fast-Start Award (13-MAU-039, J.R.A.) and a Massey University Doctoral Scholarship (L.N.W.).
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Wirz, L.N., Allison, J.R. Fitting alignment tensor components to experimental RDCs, CSAs and RQCs. J Biomol NMR 62, 25–29 (2015). https://doi.org/10.1007/s10858-015-9907-x
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DOI: https://doi.org/10.1007/s10858-015-9907-x