Abstract
Complex mixtures are at the heart of biology, and biomacromolecules almost always exhibit their function in a mixture, e.g., the mode of action for a spider venom is typically dependent on a cocktail of compounds, not just the protein. Information about diseases is encoded in body fluids such as urine and plasma in the form of metabolite concentrations determined by the actions of enzymes. To understand better what is happening in real living systems we urgently need better methods to characterize such mixtures. In this paper we describe a potent way to disentangle the NMR spectra of mixture components, by exploiting data that vary independently in three or more dimensions, allowing the use of powerful algorithms to decompose the data to extract the information sought. The particular focus of this paper is on NMR diffusion data, which are typically bilinear but can be extended by a third dimension to give the desired data structure.
Similar content being viewed by others
References
Adams RW, Aguilar JA, Cassani J, Morris GA, Nilsson M (2011) Resolving natural product epimer spectra by matrix-assisted DOSY. Org Biomol Chem 9(20):7062–7064
Andersson CA, Bro R (2000) The N-way Toolbox for MATLAB. Chemom Intell Lab Syst 52(1):1–4
Appellof CJ, Davidson ER (1981) Strategies for analyzing data from video fluorometric monitoring of liquid chromatographic effluents. Anal Chem 53(13):2053–2056. doi:10.1021/ac00236a025
Barbe L, Lundberg E, Oksvold P, Stenius A, Lewin E, Björling E, Asplund A, Pontén F, Brismar H, Uhlén M, Andersson-Svahn H (2008) Toward a confocal subcellular atlas of the human proteome. Mol Cell Proteomics 7(3):499–508. doi:10.1074/mcp.M700325-MCP200
Barjat H, Morris GA, Smart S, Swanson AG, Williams SCR (1995) High-resolution diffusion-ordered 2D spectroscopy (HR-DOSY): a new tool for the analysis of complex mixtures. J Magn Reson B 108(2):170–172
Botana A, Aguilar JA, Nilsson M, Morris GA (2011) J-modulation effects in DOSY experiments and their suppression: the Oneshot45 experiment. J Magn Reson 208(2):270–278. doi:10.1016/j.jmr.2010.11.012
Bowyer PJ, Swanson AG, Morris GA (2001) Analyzing and correcting spectrometer temperature sensitivity. J Magn Reson 152(2):234–246
Bro R (1997) PARAFAC. Tutorial and applications. Chemom Intell Lab Syst 38(2):149–171
Bro R, Viereck N, Toft M, Toft H, Hansen PI, Engelsen SB (2010) Mathematical chromatography solves the cocktail party effect in mixtures using 2D spectra and PARAFAC. Trends Analyt Chem 29(4):281–284. doi:10.1016/j.trac.2010.01.008
Cassani J, Nilsson M, Morris GA (2012) Flavonoid mixture analysis by matrix-assisted diffusion-ordered spectroscopy. J Nat Prod 75(2):131–134
Cattell R (1944) “Parallel proportional profiles” and other principles for determining the choice of factors by rotation. Psychometrika 9(4):267–283. doi:10.1007/bf02288739
Colbourne AA, Morris GA, Nilsson M (2011) Local covariance order diffusion-ordered spectroscopy: a powerful tool for mixture analysis. J Am Chem Soc 133(20):7640–7643. doi:10.1021/ja2004895
Day IJ (2011) On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter. J Magn Reson 211(2):178–185
Delsuc MA, Malliavin TE (1998) Maximum entropy processing of DOSY NMR spectra. Anal Chem 70(10):2146–2148
Dyrby M, Petersen M, Whittaker AK, Lambert L, Nørgaard L, Bro R, Engelsen SB (2005) Analysis of lipoproteins using 2D diffusion-edited NMR spectroscopy and multi-way chemometrics. Anal Chim Acta 531(2):209–216. doi:10.1016/j.aca.2004.10.052
Evans R, Haiber S, Nilsson M, Morris GA (2009) Isomer resolution by micelle-assisted diffusion-ordered spectroscopy. Anal Chem 81(11):4548–4550. doi:10.1021/ac9005777
Geiger T, Wehner A, Schaab C, Cox J, Mann M (2012) Comparative proteomic analysis of eleven common cell lines reveals ubiquitous but varying expression of most proteins. Mol Cell Proteomics 11(3). doi:10.1074/mcp.M111.014050
Harshman R (1970) Foundations of the PARAFAC procedure. UCLA Work Papers Phon 16:1–84
Hoffman RE, Arzuan H, Pemberton C, Aserin A, Garti N (2008) High-resolution NMR “chromatography” using a liquids spectrometer. J Magn Reson 194(2):295–299
Istratov AA, Vyvenko OF (1999) Exponential analysis in physical phenomena. Rev Sci Instrum 70(2):1233–1257
Johnson CS Jr (1999) Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications. Prog Nucl Magn Reson Spectrosc 34(3–4):203–256
Kavakka JS, Parviainen V, Wähälä K, Kilpeläinen I, Heikkinen S (2010) Enhanced chromatographic NMR with polyethyleneglycol. A novel resolving agent for diffusion ordered spectroscopy. Magn Reson Chem 48(10):777–781. doi:10.1002/mrc.2660
Khajeh M, Botana A, Bernstein MA, Nilsson M, Morris GA (2010) Reaction kinetics studied using diffusion-ordered spectroscopy and multiway chemometrics. Anal Chem 82(5):2102–2108. doi:10.1021/ac100110m
Morris GA (2007) Diffusion-ordered spectroscopy. In: Harris RK, Wasylishen RE (eds) Encyclopedia of magnetic resonance. Wiley, Chichester. doi:10.1002/9780470034590.emrstm0119.pub2
Morris KF, Johnson CS (1993) Resolution of discrete and continuous molecular size distributions by means of diffusion-ordered 2D NMR spectroscopy. J Am Chem Soc 115(10):4291–4299
Morris KF, Stilbs P, Johnson CS (1994) Analysis of mixtures based on molecular-size and hydrophobicity by means of diffusion-ordered 2D NMR. Anal Chem 66(2):211–215. doi:10.1021/ac00074a006
Morris GA, Barjat H, Home TJ (1997) Reference deconvolution methods. Prog Nucl Magn Reson Spectrosc 31(2–3):197–257
Nilsson M (2009) The DOSY toolbox: a new tool for processing PFG NMR diffusion data. J Magn Reson 200(2):296–302
Nilsson M, Morris GA (2006) Correction of systematic errors in CORE processing of DOSY data. Magn Reson Chem 44(7):655–660. doi:10.1002/mrc.1805
Nilsson M, Morris GA (2007) Improved DECRA processing of DOSY data: correcting for non-uniform field gradients. Magn Reson Chem 45(8):656–660. doi:10.1002/mrc.2023
Nilsson M, Morris GA (2008) Speedy component resolution: an improved tool for processing diffusion-ordered spectroscopy data. Anal Chem 80(10):3777–3782. doi:10.1021/ac7025833
Nilsson M, Connell MA, Davis AL, Morris GA (2006) Biexponential fitting of diffusion-ordered NMR data: practicalities and limitations. Anal Chem 78(9):3040–3045
Nilsson M, Botana A, Morris GA (2009a) T1-diffusion-ordered spectroscopy: nuclear magnetic resonance mixture analysis using parallel factor analysis. Anal Chem 81(19):8119–8125. doi:10.1021/ac901321w
Nilsson M, Khajeh M, Botana A, Bernstein MA, Morris GA (2009b) Diffusion NMR and trilinear analysis in the study of reaction kinetics. Chem Commun 10:1252–1254. doi:10.1039/b820813a
Pedersen HT, Dyrby M, Engelsen SB, Bro R, Webb GA (2006) Application of multi-way analysis to 2D NMR data. In: Webb G (ed) Annual reports on NMR spectroscopy, vol 59, Academic Press, New York, pp 207–233
Pelta MD, Morris GA, Stchedroff MJ, Hammond SJ (2002) A one-shot sequence for high-resolution diffusion-ordered spectroscopy. Magn Reson Chem 40(13):S147–S152
Rogerson AK, Aguilar JA, Nilsson M, Morris GA (2011) Simultaneous enhancement of chemical shift dispersion and diffusion resolution in mixture analysis by diffusion-ordered NMR spectroscopy. Chem Commun 47. doi:10.1039/c1cc12456k
Sinnaeve D (2012) The Stejskal–Tanner equation generalized for any gradient shape-an overview of most pulse sequences measuring free diffusion. Concepts Magn Reson Part A 40A(2):39–65. doi:10.1002/cmr.a.21223
Stegeman A, ten Berge JMF, De Lathauwer L (2006) Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices. Psychometrika 71(2):219–229. doi:10.1007/11336-006-1278-2
Stejskal EO, Tanner JE (1965) Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J Chem Phys 42(1):288–292
Stilbs P (1982) Fourier-transform NMR pulsed-gradient spin–echo (FT-PGSE) self-diffusion measurements of solubilization equilibria in SDS solutions. J Colloid Interface Sci 87(2):385–394. doi:10.1016/0021-9797(82)90335-6
Stilbs P (2010) RECORD processing: a robust pathway to component-resolved HR-PGSE NMR diffusometry. J Magn Reson 207(2):332–336. doi:10.1016/j.jmr.2010.09.019
Stilbs P (2013) Automated CORE, RECORD, and GRECORD processing of multi-component PGSE NMR diffusometry data. Eur Biophys J Biophys Lett 42(1):25–32. doi:10.1007/s00249-012-0794-8
Stilbs P, Paulsen K (1996) Global least-squares analysis of large, correlated spectral data sets and application to chemical kinetics and time-resolved fluorescence. Rev Sci Instrum 67(12):4380–4386
Stilbs P, Paulsen K, Griffiths PC (1996) Global least-squares analysis of large, correlated spectral data sets: application to component-resolved FT-PGSE NMR spectroscopy. J Phys Chem 100(20):8180–8189
Tormena CF, Evans R, Haiber S, Nilsson M, Morris GA (2010) Matrix-assisted diffusion-ordered spectroscopy: mixture resolution by NMR using SDS micelles. Magn Reson Chem 48(7):550–553. doi:10.1002/mrc.2621
Tormena CF, Evans R, Haiber S, Nilsson M, Morris GA (2012) Matrix-assisted diffusion-ordered spectroscopy: application of surfactant solutions to the resolution of isomer spectra. Magn Reson Chem 50(6):458–465. doi:10.1002/mrc.3822
Van Gorkom LCM, Hancewicz TM (1998) Analysis of DOSY and GPC-NMR experiments on polymers by multivariate curve resolution. J Magn Reson 130(1):125–130
Viel S, Ziarelli F, Caldarelli S (2003) Enhanced diffusion-edited NMR spectroscopy of mixtures using chromatographic stationary phases. Proc Natl Acad Sci USA 100(17):9696–9698
Windig W, Antalek B (1997) Direct exponential curve resolution algorithm (DECRA): a novel application of the generalized rank annihilation method for a single spectral mixture data set with exponentially decaying contribution profiles. Chemom Intell Lab Syst 37(2):241–254
Zielinski ME, Morris KF (2009) Using perdeuterated surfactant micelles to resolve mixture components in diffusion-ordered NMR spectroscopy. Magn Reson Chem 47(1):53–56
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Björnerås, J., Botana, A., Morris, G.A. et al. Resolving complex mixtures: trilinear diffusion data. J Biomol NMR 58, 251–257 (2014). https://doi.org/10.1007/s10858-013-9752-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10858-013-9752-8