Bayesian deconvolution and quantification of metabolites from \(J\)-resolved NMR spectroscopy. (English) Zbl 1480.62254

Summary: Two-dimensional (2D) nuclear magnetic resonance (NMR) methods have become increasingly popular in metabolomics, since they have considerable potential to accurately identify and quantify metabolites within complex biological samples. 2D \(^1\text{H}\, J\)-resolved (JRES) NMR spectroscopy is a widely used method that expands overlapping resonances into a second dimension. However, existing analytical processing methods do not fully exploit the information in the JRES spectrum and, more importantly, do not provide measures of uncertainty associated with the estimates of quantities of interest, such as metabolite concentration. Combining the data-generating mechanisms and the extensive prior knowledge available in online databases, we develop a Bayesian method to analyse 2D JRES data, which allows for automatic deconvolution, identification and quantification of metabolites. The model extends and improves previous work on one-dimensional nmr spectral data. Our approach is based on a combination of B-spline tight wavelet frames and theoretical templates, and thus enables the automatic incorporation of expert knowledge within the inferential framework. Posterior inference is performed through specially devised Markov chain Monte Carlo methods. We demonstrate the performance of our approach via analyses of datasets from serum and urine, showing the advantages of our proposed approach in terms of identification and quantification of metabolites.


62P35 Applications of statistics to physics
62F15 Bayesian inference
62H35 Image analysis in multivariate analysis
65C05 Monte Carlo methods
65T60 Numerical methods for wavelets
Full Text: DOI


[1] Astle, W., De Iorio, M., Richardson, S., Stephens, D., and Ebbels, T. (2012). “A Bayesian Model of NMR Spectra for the Deconvolution and Quantification of Metabolites in Complex Biological Mixtures.” Journal of the American Statistical Association, 107(500): 1259-1271. · Zbl 1284.62163
[2] Aue, W. P., Bartholdi, E., and Ernst, R. R. (1976a). “Two-dimensional spectroscopy. Application to nuclear magnetic resonance.” The Journal of Chemical Physics, 64(5): 2229-2246. doi: https://doi.org/10.1063/1.432450.
[3] Aue, W. P., Karhan, J., and Ernst, R. R. (1976b). “Homonuclear broad band decoupling and two-dimensional J-resolved NMR spectroscopy.” The Journal of Chemical Physics, 64(10): 4226-4227. doi: https://doi.org/10.1063/1.431994.
[4] Bhadra, A., Datta, J., Polson, N. G., Willard, B., et al. (2019). “Lasso meets horseshoe: A survey.” Statistical Science, 34(3): 405-427. · Zbl 1429.62308
[5] Bhattacharya, A., Pati, D., Pillai, N. S., and Dunson, D. B. (2015). “Dirichlet-Laplace priors for optimal shrinkage.” Journal of the American Statistical Association, 110(512): 1479-1490. · Zbl 1373.62368
[6] Bieleń, A., Mrochem-Kwarciak, J., Skorupa, A., Ciszek, M., Heyda, A., Wygoda, A., Kotylak, A., Składowski, K., Sokół, M., et al. (2019). “NMR-based metabolomics in real-time monitoring of treatment induced toxicity and cachexia in head and neck cancer: a method for early detection of high risk patients.” Metabolomics, 15(8): 110.
[7] Braunschweiler, L. and Ernst, R. (1983). “Coherence transfer by isotropic mixing: Application to proton correlation spectroscopy.” Journal of Magnetic Resonance, 53(3): 521-528. URL http://www.sciencedirect.com/science/article/pii/0022236483902263.
[8] Brindle, J. T., Antti, H., Holmes, E., Tranter, G., Nicholson, J. K., Bethell, H. W. L., Clarke, S., Schofield, P. M., McKilligin, E., Mosedale, D. E., and Grainger, D. J. (2002). “Rapid and noninvasive diagnosis of the presence and severity of coronary heart disease using 1H-NMR-based metabonomics.” Nature Medicine, 8: 1439-1445. doi: https://doi.org/10.1038/nm1202-802.
[9] Bruce, S. D., Higinbotham, J., Marshall, I., and Beswick, P. H. (2000). “An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra.” Journal of Magnetic Resonance, 142(1): 57-63.
[10] Bundy, J. G., Spurgeon, D. J., Svendsen, C., Hankard, P. K., Osborn, D., Lindon, J. C., and Nicholson, J. K. (2002). “Earthworm species of the genus Eisenia can be phenotypically differentiated by metabolic profiling.” FEBS Letters, 521(1): 115-120. URL http://www.sciencedirect.com/science/article/pii/S0014579302028545.
[11] Carvalho, C. M., Polson, N. G., and Scott, J. G. (2010). “The horseshoe estimator for sparse signals.” Biometrika, 97(2): 465-480. URL http://www.jstor.org/stable/25734098. · Zbl 1406.62021
[12] Casazza, P. G. and Kutyniok, G. (2012). Finite Frames: Theory and Applications. Birkhäuser Basel.
[13] Cavanagh, J., Skelton, N., Fairbrother, W., Rance, M., Palmer, A., Skelton, N., and Rance, M. (2007). Protein NMR Spectroscopy: Principles and Practice. Academic Press.
[14] Christen, J. A. and Fox, C. (2010). “A general purpose sampling algorithm for continuous distributions (the \(t\)-walk).” Bayesian Analysis, 5(2): 263-281. · Zbl 1330.62007
[15] Craig, A., Cloarec, O., Holmes, E., Nicholson, J., and Lindon, J. (2006). “Scaling and normalization effects in NMR spectroscopic metabonomic data sets.” Analytical Chemistry, 78(7): 2262-2267.
[16] Daubechies, I., Grossmann, A., and Meyer, Y. (1986). “Painless Nonorthogonal Expansions.” Journal of Mathematical Physics, 27. · Zbl 0608.46014
[17] Davis, D. G. and Bax, A. (1985). “Assignment of complex proton NMR spectra via two-dimensional homonuclear Hartmann-Hahn spectroscopy.” Journal of the American Chemical Society, 107(9): 2820-2821. doi: https://doi.org/10.1021/ja00295a052.
[18] Dehghan, A. (2019). “Linking Metabolic Phenotyping and Genomic Information.” In The Handbook of Metabolic Phenotyping, 561-569. Elsevier.
[19] Dona, A. C., Jiménez, B., Schäfer, H., Humpfer, E., Spraul, M., Lewis, M. R., Pearce, J. T. M., Holmes, E., Lindon, J. C., and Nicholson, J. K. (2014). “Precision High-Throughput Proton NMR Spectroscopy of Human Urine, Serum, and Plasma for Large-Scale Metabolic Phenotyping.” Analytical Chemistry, 86(19): 9887-9894. doi: https://doi.org/10.1021/ac5025039.
[20] Dong, B. and Shen, Z. (2010). “MRA-based wavelet frames and applications.” IAS/Park City Mathematics Series, 19. · Zbl 1344.94009
[21] Dong, B. and Shen, Z. (2015). “Image restoration: a data-driven perspective.” In Proceedings of the International Congress on Industrial and Applied Mathematics (ICIAM), 65-108. Beijing, China: High Education Press.
[22] Duffin, R. and Schaeffer, A. (1952). “A class of nonharmonic Fourier series.” Transactions of the American Mathematical Society, 72: 341-366. · Zbl 0049.32401
[23] Elliott, P., Vergnaud, A.-C., Singh, D., Neasham, D., Spear, J., and Heard, A. (2014). “The Airwave Health Monitoring Study of police officers and staff in Great Britain: Rationale, design and methods.” Environmental Research, 134: 280-285. Linking Exposure and Health in Environmental Public Health Tracking. URL http://www.sciencedirect.com/science/article/pii/S0013935114002564.
[24] Féraud, B., Govaerts, B., Verleysen, M., and Tullio, P. (2015). “Statistical treatment of 2D NMR COSY spectra in metabolomics: data preparation, clustering-based evaluation of the Metabolomic Informative Content and comparison with H-NMR.” Metabolomics, 11(6): 1756-1768. URL http://libproxy1.nus.edu.sg/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=110339434&site=ehost-live.
[25] Fonville, J. M., Maher, A. D., Coen, M., Holmes, E., Lindon, J. C., and Nicholson, J. K. (2010). “Evaluation of Full-Resolution J-Resolved 1H NMR Projections of Biofluids for Metabonomics Information Retrieval and Biomarker Identification.” Analytical Chemistry, 82(5): 1811-1821. PMID: 20131799. doi: https://doi.org/10.1021/ac902443k.
[26] Forgacs, A. L., Kent, M. N., Makley, M. K., Mets, B., DelRaso, N., Jahns, G. L., Burgoon, L. D., Zacharewski, T. R., and Reo, N. V. (2011). “Comparative metabolomic and genomic analyses of TCDD-elicited metabolic disruption in mouse and rat liver.” Toxicological Sciences, 125(1): 41-55.
[27] Gelman, A. (2006). “Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper).” Bayesian Analysis, 1(3): 515-534. · Zbl 1331.62139
[28] George, E. I. and McCulloch, R. E. (1993). “Variable selection via Gibbs sampling.” Journal of the American Statistical Association, 88(423): 881-889.
[29] Goldman, M. (1992). Quantum description of high-resolution NMR in liquids. Oxford University Press.
[30] Gómez, J., Brezmes, J., Mallol, R., Rodríguez, M. A., Vinaixa, M., Salek, R. M., Correig, X., and Cañellas, N. (2014). “Dolphin: a tool for automatic targeted metabolite profiling using 1D and 2D 1H-NMR data.” Analytical and Bioanalytical Chemistry, 406(30): 7967-7976. doi: https://doi.org/10.1007/s00216-014-8225-6.
[31] Griffiths, J. R., McSheehy, P. M. J., Robinson, S. P., Troy, H., Chung, Y. L., Leek, R., Williams, K. J., Stratford, I. J., Harris, A. L., and Stubbs, M. (2002). “Metabolic changes detected by in vivo magnetic resonance studies of HEPA-1 wild-type tumors and tumors deficient in hypoxia-inducible factor-1beta (HIF-1beta): evidence of an anabolic role for the HIF-1 pathway.” Cancer research, 62 3: 688-95.
[32] Hajduk, A., Mrochem-Kwarciak, J., Skorupa, A., Ciszek, M., Heyda, A., Składowski, K., Sokół, M., et al. (2016). “1 H NMR based metabolomic approach to monitoring of the head and neck cancer treatment toxicity.” Metabolomics, 12(6): 102.
[33] Hao, J., Astle, W., De Iorio, M., and Ebbels, T. M. D. (2012). “BATMAN: an R package for the automated quantification of metabolites from nuclear magnetic resonance spectra using a Bayesian model.” Bioinformatics, 28(15): 2088-2090. doi: http://dx.doi.org/10.1093/bioinformatics/bts308.
[34] Hao, J., Liebeke, M., Astle, W., De Iorio, M., Bundy, J., and Ebbels, T. M. D. (2014). “Bayesina deconvolution and quantification of metabolites in compex 1D NMR spectra using Batman.” Nature Protocols, 9(6): 1416.
[35] Heinecke, A., Ye, L., De Iorio, M., and Ebbels, T. (2020). “Supplementary Materials.” Bayesian Analysis.
[36] Helmus, J. J. and Jaroniec, C. P. (2013). “Nmrglue: an open source Python package for the analysis of multidimensional NMR data.” Journal of biomolecular NMR, 55(4): 355-367.
[37] Hollinshead, K. E., Williams, D. S., Tennant, D. A., and Ludwig, C. (2016). “Probing cancer cell metabolism using NMR spectroscopy.” In Tumor Microenvironment, 89-111. Springer.
[38] Holmes, E., Loo, R. L., Stamler, J., Bictash, M., Yap, I. K. S., Chan, Q., Ebbels, T., De Iorio, M., Brown, I. J., Veselkov, K. A., Daviglus, M. L., Kesteloot, H., Ueshima, H., Zhao, L., Nicholson, J. K., and Elliott, P. (2008). “Human metabolic phenotype diversity and its association with diet and blood pressure.” Nature, 453: 396-400. doi: https://doi.org/10.1038/nature06882.
[39] Hore, P. (2015). Nuclear Magnetic Resonance. Oxford chemistry primers. Oxford University Press. URL https://books.google.com.sg/books?id=L9umCAAAQBAJ.
[40] Illig, T., Gieger, C., Zhai, G., Römisch-Margl, W., Wang-Sattler, R., Prehn, C., Altmaier, E., Kastenmüller, G., Kato, B. S., Mewes, H.-W., Meitinger, T., de Angelis, M. H., Kronenberg, F., Soranzo, N., Wichmann, H.-E., Spector, T. D., Adamski, J., and Suhre, K. (2009). “A genome-wide perspective of genetic variation in human metabolism.” Nature Genetics, 42: 137-141. doi: https://doi.org/10.1038/ng.507.
[41] Kalli, M., Griffin, J. E., and Walker, S. G. (2011). “Slice Sampling Mixture Models.” Statistics and Computing, 21: 93-105. · Zbl 1256.65006
[42] Kikuchi, J., Tsuboi, Y., Komatsu, K., Gomi, M., Chikayama, E., and Date, Y. (2016). “SpinCouple: Development of a Web Tool for Analyzing Metabolite Mixtures via Two-Dimensional J-Resolved NMR Database.” Analytical Chemistry, 88(1): 659-665. PMID: 26624790. doi: https://doi.org/10.1021/acs.analchem.5b02311.
[43] Lindon, J. C., Nicholson, J. K., Holmes, E., Antti, H., Bollard, M. E., Keun, H., Beckonert, O., Ebbels, T. M., Reily, M. D., Robertson, D., Stevens, G. J., Luke, P., Breau, A. P., Cantor, G. H., Bible, R. H., Niederhauser, U., Senn, H., Schlotterbeck, G., Sidelmann, U. G., Laursen, S. M., Tymiak, A., Car, B. D., Lehman-McKeeman, L., Colet, J.-M., Loukaci, A., and Thomas, C. (2003). “Contemporary issues in toxicology the role of metabonomics in toxicology and its evaluation by the COMET project.” Toxicology and Applied Pharmacology, 187(3): 137-146. URL http://www.sciencedirect.com/science/article/pii/S0041008X02000790.
[44] Ludwig, C. and Viant, M. R. (2010). “Two-dimensional J-resolved NMR spectroscopy: review of a key methodology in the metabolomics toolbox.” Phytochemical Analysis, 21(1): 22-32. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/pca.1186.
[45] Mahrous, E. A. and Farag, M. A. (2015). “Two dimensional NMR spectroscopic approaches for exploring plant metabolome: a review.” Journal of Advanced Research, 6(1): 3-15.
[46] Mallat, S. (2008). A Wavelet Tour of Signal Processing: The Sparse Way. Academic Press, Inc. · Zbl 1170.94003
[47] Mitchell, T. J. and Beauchamp, J. J. (1988). “Bayesian variable selection in linear regression.” Journal of the American Statistical Association, 83(404): 1023-1032. · Zbl 0673.62051
[48] Moore, G. J. and Sillerud, L. O. (1994). “The pH Dependence of Chemical Shift and Spin-Spin Coupling for Citrate.” Journal of Magnetic Resonance, 103: 87-88.
[49] Palaric, C., Pilard, S., Fontaine, J.-X., Boccard, J., Mathiron, D., Rigaud, S., Cailleu, D., Mesnard, F., Gut, Y., Renaud, T., et al. (2019). “Processing of NMR and MS metabolomics data using chemometrics methods: a global tool for fungi biotransformation reactions monitoring.” Metabolomics, 15(8): 107.
[50] Parsons, H. M., Ludwig, C., Günther, U. L., and Viant, M. R. (2007). “Improved classification accuracy in 1-and 2-dimensional NMR metabolomics data using the variance stabilising generalised logarithm transformation.” BMC Bioinformatics, 8(1): 234.
[51] Piironen, J., Vehtari, A., et al. (2017). “Sparsity information and regularization in the horseshoe and other shrinkage priors.” Electronic Journal of Statistics, 11(2): 5018-5051. · Zbl 1459.62141
[52] Polson, N. G., Scott, J. G., et al. (2012). “On the half-Cauchy prior for a global scale parameter.” Bayesian Analysis, 7(4): 887-902. · Zbl 1330.62148
[53] Raamsdonk, L. M., Teusink, B., Broadhurst, D., Zhang, N., Hayes, A., Walsh, M. C., Berden, J. A., Brindle, K. M., Kell, D. B., Rowland, J. J., Westerhoff, H. V., van Dam, K., and Oliver, S. G. (2001). “A functional genomics strategy that uses metabolome data to reveal the phenotype of silent mutations.” Nature Biotechnology, 19: 45-50. doi: https://doi.org/10.1038/83496.
[54] Ripley, B. (2009). Stochastic Simulation. Wiley Series in Probability and Statistics. Wiley. URL https://books.google.co.uk/books?id=rmGfsJxRDqgC.
[55] Robert, C. and Casella, G. (2013). Monte Carlo statistical methods. Springer Science & Business Media. · Zbl 1096.62003
[56] Roberts, G. O. and Rosenthal, J. S. (2009). “Examples of adaptive MCMC.” Journal of Computational and Graphical Statistics, 18(2): 349-367.
[57] Ron, A. and Shen, Z. (1997). “Affine systems in \[{L_2}({\mathbb{R}^d})\]: the analysis of the analysis operator.” Journal of Functional Analysis, 148: 408-447. · Zbl 0891.42018
[58] Sousa, S., Magalhães, A., and Ferreira, M. M. C. (2013). “Optimized bucketing for NMR spectra: Three case studies.” Chemometrics and Intelligent Laboratory Systems, 122: 93-102.
[59] Tibshirani, R. (1996). “Regression Shrinkage and Selection via the Lasso.” Journal of the Royal Statistical Society. Series B (Methodological), 58(1): 267-288. URL http://www.jstor.org/stable/2346178. · Zbl 0850.62538
[60] Tipping, M. E. (2001). “Sparse Bayesian learning and the relevance vector machine.” Journal of Machine Learning Research, 1: 211-244. · Zbl 0997.68109
[61] Ulrich, E. L., Akutsu, H., Doreleijers, J. F., Harano, Y., Ioannidis, Y. E., Lin, J., Livny, M., Mading, S., Maziuk, D., Miller, Z., Nakatani, E., Schulte, C. F., Tolmie, D. E., Kent Wenger, R., Yao, H., and Markley, J. L. (2007). “BioMagResBank.” Nucleic Acids Research, 36(suppl-1): D402-D408. doi: https://doi.org/10.1093/nar/gkm957.
[62] Viant, M. R. (2003). “Improved methods for the acquisition and interpretation of NMR metabolomic data.” Biochemical and Biophysical Research Communications, 310(3): 943-948. URL http://www.sciencedirect.com/science/article/pii/S0006291X03018618.
[63] Viswan, A., Singh, C., Kayastha, A. M., Azim, A., and Sinha, N. (2019). “An NMR based panorama of the heterogeneous biology of acute respiratory distress syndrome (ARDS) from the standpoint of metabolic biomarkers.” NMR in Biomedicine. doi: https://doi.org/10.1002/nbm.4192.
[64] Weljie, A. M., Newton, J., Mercier, P., Carlson, E., and Slupsky, C. M. (2006). “Targeted Profiling: Quantitative Analysis of 1H NMR Metabolomics Data.” Analytical Chemistry, 78(13): 4430-4442. doi: https://doi.org/10.1021/ac060209g.
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