Skip to main content

Use of Inverse Theory Algorithms in the Analysis of Biomembrane NMR Data

  • Protocol
Methods in Membrane Lipids

Part of the book series: Methods in Molecular Biology™ ((MIMB,volume 400))

Abstract

Treating the analysis of experimental spectroscopic data as an inverse problem and using regularization techniques to obtain stable pseudoinverse solutions, allows access to previously unavailable level of spectroscopic detail. The data is mapped into an appropriate physically relevant parameter space, leading to better qualitative and quantitative understanding of the underlying physics, and in turn, to better and more detailed models. A brief survey of relevant inverse methods is illustrated by several successful applications to the analysis of nuclear magnetic resonance data, yielding new insight into the structure and dynamics of biomembrane lipids.

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

Access this chapter

Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    *

    When the limits of integration are fixed as appropriate for the majority of problems of practical interest, this is the so-called Fredholm integral equation (FIE) of the first kind.

  2. 2.

    ?

    Eqs. 4 and 5, and covers all forms of the regularization functional.

  3. 3.

    *

    1-steroyl-2-docosahexaenoyl-sn-glycero-3-phosphocholine.

References

  1. Hadamard, J. (1923) Lectures on the Cauchy problem in linear partial differential equations. Yale University Press, New Haven, USA.

    Google Scholar 

  2. Santamarina, J. C. and Fratta, D. (2005) Discrete signals and inverse problems. An Introduction for Engineers and Scientists. p. 276, John Wiley & Sons Ltd., Chichester, England.

    Book  Google Scholar 

  3. Lawson, C. L. and Hanson, R. J. (1974) Solving linear least squares problems. Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  4. Hansen, P. C. (1998) Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion, in Monographs on Mathematical Modeling and Computation, vol. 4, Society for Industrial and Applied Mathematics Philadelphia PA.

    Google Scholar 

  5. Tikhonov, A. N. and Arsenin, V. Y. (1977) Solutions of Ill-Posed Problems. John Wiley & Sons, New York.

    Google Scholar 

  6. Schäfer, H., Albrecht, U., and Richert, R. (1994) Dispersive first-order reactions I: Data analysis. J. Chem. Phys. 182, 53.

    Article  Google Scholar 

  7. Honerkamp, J. and Weese, J. (1990) Tikhonov’s regularization method for ill-posed problems. A comparison of different methods for the determination of the regularization parameter. Contin. Mech. Thermodyn. 2, 17–30.

    Article  Google Scholar 

  8. Weese, J. (1992) A reliable and fast method for the solution of Fredholm integral equations of the first kind based on Tikhonov regularization. Comput. Phys. Commun. 69, 99–111.

    Article  Google Scholar 

  9. Bloom, M., Davis, J. H., and MacKay, A. L. (1981) Direct determination of the oriented sample NMR spectrum from the powder spectrum for systems with local axial symmetry. Chem. Phys. Lett. 80, 198–202.

    Article  CAS  Google Scholar 

  10. Sternin, E., Bloom, M., and MacKay, A. L. (1983) De-Pake-ing of NMR spectra. J. Magn. Reson. 55, 274–282.

    CAS  Google Scholar 

  11. Whittall, K., Sternin, E., Bloom, M., and MacKay, A. L. (1989) Time-and frequency-domain “dePakeing“ using inverse theory. J. Mag. Res. 84, 64–71.

    Google Scholar 

  12. Davis, J. H. (1991) Deuterium nuclear magnetic resonance spectroscopy in partially ordered systems, in Isotopes in the Physical and Biomedical Sciences, vol. 2, (Buncel, E. and Jones, J. R., eds.), Elsevier, Amsterdam, pp. 99–157.

    Google Scholar 

  13. Schäfer, H. and Stannarius, R. (1995) Calculation of orientational distributions of partially ordered samples from NMR spectra. J. Magn. Reson. B 106, 14–23.

    Article  Google Scholar 

  14. Schäfer, H. Madler, B., and Sternin, E. (1998) Determination of Orientational Order Parameters from 2H NMR Spectra of Magnetically Partially Oriented Lipid Bilayers. Biophys. J. 74(2), 1007–1014.

    Article  PubMed  Google Scholar 

  15. Sternin, E., Schäfer, H. Polozov, I., and Gawrisch, K. (2001) Simultaneous determination of orientational and order parameter distributions from NMR spectra of partially oriented model membranes. J. Magn. Reson. 149, 110–113.

    Article  PubMed  CAS  Google Scholar 

  16. Sternin, E., Nizza, D., and Gawrisch, K. (2001) Temperature dependence of DMPC/DHPC mixing in bicelles and its structural implications. Langmuir 17, 2610–2616.

    Article  CAS  Google Scholar 

  17. Sternin, E., Fine, B., Bloom, M., Tilcock, C. P., Wong, K.F., and Cullis, P. R. (1988) Acyl chain orientational order in the hexagonal H II phase of phospholipid-water dispersions. Biophys. J. 54(4), 689–694.

    Article  PubMed  CAS  Google Scholar 

  18. Sternin, E., Zaraiskaya, T., Razavi, R., and Epand, R.M. (2006) Changes in molecular order across the lamellar-to-inverted hexagonal phase transition depend on the position of the double-bond in monounsaturated phospholipid dispersions. Chem. Phys. Lipids 140, 98–108.

    Article  PubMed  CAS  Google Scholar 

  19. Sanders, C. R. and Schwonek, J. P. (1992) Characterization of magnetically orientable bilayers in mixtures of dihexanoylphosphatidylcholine and dimyristoylphosphatidylcholine by solid-state NMR. Biochemistry 31, 8898–8905.

    Article  PubMed  CAS  Google Scholar 

  20. Triba, M. N., Warschawski, D. E., and Devaux, P. F. (2005) Reinvestigation by phosphorus NMR of lipid distribution in bicelles. Biophys. J. 88, 1887–1901.

    Article  PubMed  CAS  Google Scholar 

  21. van Beek, J. D., Beaulieu, L., Schfer, H., Demura, M., Asakura, T., and Meier, B. H. (2000) Solid-state NMR determination of the secondary structure of Samia cynthia ricini silk. Nature 405, 1077–1079.

    Article  PubMed  Google Scholar 

  22. van Beek, J. D., Meier, B. H., and Schäfer, H. (2003) Inverse methods in two-dimensional NMR spectral analysis. J. Magn. Reson. 162, 141–157.

    Article  PubMed  Google Scholar 

  23. Tycko, R., Weliky, D. P., and Berger, A. E. (1996) Investigation of molecular structure in solids by two-dimensional NMR exchange spectroscopy with magic angle spinning. J. Chem. Phys. 105, 7915–7930.

    Article  CAS  Google Scholar 

  24. Bennett, A. E., Weliky, D. P., and Tycko, R. (1998) Quantitative conformational measurements in solid state NMR by constant-time homonuclear dipolar recoupling. J. Am. Chem. Soc. 120, 4897–4898.

    Article  CAS  Google Scholar 

  25. Petkova, A. T., Ishii, Y., Balbach, J. J., et al. (2002) A structural model for Alzheimer’s β-amyloid fibrils based on experimental constraints from solid state NMR. PNAS 99, 16742–16747.

    Article  PubMed  CAS  Google Scholar 

  26. Chan, J. C. C. and Tycko, R. (2003) Solid-state NMR spectroscopy method for determination of the backbone torsion angle psi in peptides with isolated uniformly labeled residues. J. Am. Chem. Soc. 125, 11,828–11,829.

    Article  PubMed  CAS  Google Scholar 

  27. Roths, T. Marth, M., Weese, J., and Honerkamp, J. (2001) A generalized regularization method for nonlinear ill-posed problems enhanced for nonlinear regularization terms. Comput. Phys. Commun. 139, 279–296.

    Article  CAS  Google Scholar 

  28. Hansen, P. C. (1994) Regularization Tools: A Matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms 6, 1–35.

    Article  Google Scholar 

  29. Keyvanloo, A. (2004). Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization. M.Sc. thesis, Brock University, St. Catharines, Ontario.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Humana Press Inc.

About this protocol

Cite this protocol

Sternin, E. (2007). Use of Inverse Theory Algorithms in the Analysis of Biomembrane NMR Data. In: Dopico, A.M. (eds) Methods in Membrane Lipids. Methods in Molecular Biology™, vol 400. Humana Press. https://doi.org/10.1007/978-1-59745-519-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-59745-519-0_8

  • Publisher Name: Humana Press

  • Print ISBN: 978-1-58829-662-7

  • Online ISBN: 978-1-59745-519-0

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics