Mathematical Modeling Approaches in Plant Metabolomics

  • Lisa Fürtauer
  • Jakob Weiszmann
  • Wolfram Weckwerth
  • Thomas NägeleEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 1778)


The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Key words

Metabolomics Plant biochemistry Mathematical modeling ODE Jacobian matrix Multivariate statistics Time series analysis Granger causality 



This work was supported by the Austrian Science Fund (FWF), Project I 2071, and the Vienna Metabolomics Center ViMe at the University of Vienna.


  1. 1.
    Morgan JA, Rhodes D (2002) Mathematical modeling of plant metabolic pathways. Metab Eng 4:80–89CrossRefPubMedGoogle Scholar
  2. 2.
    Prusinkiewicz P (2004) Modeling plant growth and development. Curr Opin Plant Biol 7:79–83CrossRefPubMedGoogle Scholar
  3. 3.
    Fiehn O (2002) Metabolomics-the link between genotypes and phenotypes. Plant Mol Biol 48:155–171CrossRefPubMedGoogle Scholar
  4. 4.
    Weckwerth W (2011) Unpredictability of metabolism-the key role of metabolomics science in combination with next-generation genome sequencing. Anal Bioanal Chem 400:1967–1978CrossRefPubMedPubMedCentralGoogle Scholar
  5. 5.
    Liberman LM, Sozzani R, Benfey PN (2012) Integrative systems biology: an attempt to describe a simple weed. Curr Opin Plant Biol 15:162–167CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Hoermiller II, Naegele T, Augustin H et al (2017) Subcellular reprogramming of metabolism during cold acclimation in Arabidopsis thaliana. Plant Cell Environ 40:602–610CrossRefPubMedGoogle Scholar
  7. 7.
    Hurry V (2017) Metabolic reprogramming in response to cold stress is like real estate, it’s all about location. Plant Cell Environ 40:599–601CrossRefPubMedGoogle Scholar
  8. 8.
    Fürtauer L, Weckwerth W, Nägele T (2016) A benchtop fractionation procedure for subcellular analysis of the plant metabolome. Front Plant Sci 7:1912CrossRefPubMedPubMedCentralGoogle Scholar
  9. 9.
    Nägele T (2014) Linking metabolomics data to underlying metabolic regulation. Front Mol Biosci 1:22CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Wang Y, Zhang X-S, Chen L (2010) Optimization meets systems biology. BMC Syst Biol 4:S1CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Banga JR (2008) Optimization in computational systems biology. BMC Syst Biol 2:47CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Reali F, Priami C, Marchetti L (2017) Optimization algorithms for computational systems biology. Front Appl Math Stat 3:6CrossRefGoogle Scholar
  13. 13.
    Loomis RS, Rabbinge R, Ng E (1979) Explanatory models in crop physiology. Annu Rev Plant Physiol 30:339–367CrossRefGoogle Scholar
  14. 14.
    Rios-Estepa R, Lange BM (2007) Experimental and mathematical approaches to modeling plant metabolic networks. Phytochemistry 68:2351–2374CrossRefPubMedGoogle Scholar
  15. 15.
    Klipp E, Liebermeister W (2006) Mathematical modeling of intracellular signaling pathways. BMC Neurosci 7(Suppl 1):S10CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Chew YH, Smith RW, Jones HJ et al (2014) Mathematical models light up plant signaling. Plant Cell 26:5–20CrossRefPubMedPubMedCentralGoogle Scholar
  17. 17.
    Rohwer JM (2012) Kinetic modelling of plant metabolic pathways. J Exp Bot 63:2275–2292CrossRefPubMedGoogle Scholar
  18. 18.
    Gombert AK, Nielsen J (2000) Mathematical modelling of metabolism. Curr Opin Biotechnol 11:180–186CrossRefPubMedGoogle Scholar
  19. 19.
    Giersch C (2000) Mathematical modelling of metabolism. Curr Opin Plant Biol 3:249–253CrossRefPubMedGoogle Scholar
  20. 20.
    Pettersson G, Ryde-Pettersson U (1988) A mathematical model of the Calvin photosynthesis cycle. Eur J Biochem 175:661–672CrossRefPubMedGoogle Scholar
  21. 21.
    Pettersson G (1997) Control properties of the Calvin photosynthesis cycle at physiological carbon dioxide concentrations. Biochim Biophys Acta 1322:173–182CrossRefGoogle Scholar
  22. 22.
    Pokhilko A, Bou-Torrent J, Pulido P et al (2015) Mathematical modelling of the diurnal regulation of the MEP pathway in Arabidopsis. New Phytol 206:1075–1085CrossRefPubMedGoogle Scholar
  23. 23.
    Funahashi A, Morohashi M, Kitano H, Tanimura N (2003) CellDesigner: a process diagram editor for gene-regulatory and biochemical networks. Biosilico 1:159–162CrossRefGoogle Scholar
  24. 24.
    Schomburg I, Hofmann O, Baensch C et al (2000) Enzyme data and metabolic information: BRENDA, a resource for research in biology, biochemistry, and medicine. Gene Funct Dis 1:109–118CrossRefGoogle Scholar
  25. 25.
    Hoops S, Sahle S, Gauges R et al (2006) COPASI – a COmplex PAthway SImulator. Bioinformatics 22:3067–3074CrossRefPubMedGoogle Scholar
  26. 26.
    Schmidt H (2007) SBaddon: high performance simulation for the Systems Biology Toolbox for MATLAB. Bioinformatics 23:646–647CrossRefPubMedGoogle Scholar
  27. 27.
    Steuer R, Gross T, Selbig J, Blasius B (2006) Structural kinetic modeling of metabolic networks. Proc Natl Acad Sci U S A 103:11868–11873CrossRefPubMedPubMedCentralGoogle Scholar
  28. 28.
    Reznik E, Segre D (2010) On the stability of metabolic cycles. J Theor Biol 266:536–549CrossRefPubMedPubMedCentralGoogle Scholar
  29. 29.
    Henkel S, Nägele T, Hörmiller I et al (2011) A systems biology approach to analyse leaf carbohydrate metabolism in Arabidopsis thaliana. EURASIP J Bioinform Syst Biol 2011:2CrossRefPubMedPubMedCentralGoogle Scholar
  30. 30.
    Fürtauer L, Nägele T (2016) Approximating the stabilization of cellular metabolism by compartmentalization. Theory Biosci 135:73CrossRefPubMedPubMedCentralGoogle Scholar
  31. 31.
    Jiao W-B, Schneeberger K (2017) The impact of third generation genomic technologies on plant genome assembly. Curr Opin Plant Biol 36:64–70CrossRefPubMedGoogle Scholar
  32. 32.
    Vivek-Ananth RP, Samal A (2016) Advances in the integration of transcriptional regulatory information into genome-scale metabolic models. Biosystems 147:1–10CrossRefPubMedGoogle Scholar
  33. 33.
    Thiele I, Palsson BO (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction. Nat Protoc 5:93–121CrossRefPubMedPubMedCentralGoogle Scholar
  34. 34.
    Nägele T, Mair A, Sun X et al (2014) Solving the differential biochemical Jacobian from metabolomics covariance data. PLoS One 9:e92299CrossRefPubMedPubMedCentralGoogle Scholar
  35. 35.
    Kügler P, Yang W (2014) Identification of alterations in the Jacobian of biochemical reaction networks from steady state covariance data at two conditions. J Math Biol 68:1757–1783CrossRefPubMedGoogle Scholar
  36. 36.
    Doerfler H, Lyon D, Nägele T et al (2013) Granger causality in integrated GC-MS and LC-MS metabolomics data reveals the interface of primary and secondary metabolism. Metabolomics 9:564–574CrossRefPubMedGoogle Scholar
  37. 37.
    Sun XL, Weckwerth W (2012) COVAIN: a toolbox for uni- and multivariate statistics, time-series and correlation network analysis and inverse estimation of the differential Jacobian from metabolomics covariance data. Metabolomics 8:S81–S93CrossRefGoogle Scholar
  38. 38.
    Nukarinen E, Nägele T, Pedrotti L, Wurzinger B, Mair A, Landgraf R, Börnke F, Hanson J, Teige M, Baena-Gonzalez E, Dröge-Laser W, Weckwerth W (2016) Quantitative phosphoproteomics reveals the role of the AMPK plant ortholog SnRK1 as a metabolic master regulator under energy deprivation. Sci Rep 6(1):31697CrossRefPubMedPubMedCentralGoogle Scholar
  39. 39.
    Wang L, Nägele T, Doerfler H, Fragner L, Chaturvedi P, Nukarinen E, Bellaire A, Huber W, Weiszmann J, Engelmeier D, Ramsak Z, Gruden K, Weckwerth W (2016) System level analysis of cacao seed ripening reveals a sequential interplay of primary and secondary metabolism leading to polyphenol accumulation and preparation of stress resistance. Plant J 87(3):318–332CrossRefPubMedGoogle Scholar
  40. 40.
    Schelter B (2006) Handbook of time series analysis recent theoretical developments and applications. Weinheim, Wiley-VCHCrossRefGoogle Scholar
  41. 41.
    Derryberry DR (2014) Basic data analysis for time series with R. Wiley, Hoboken, NJCrossRefGoogle Scholar
  42. 42.
    Smilde AK, Westerhuis JA, Hoefsloot HCJ et al (2010) Dynamic metabolomic data analysis: a tutorial review. Metabolomics 6:3–17CrossRefPubMedGoogle Scholar
  43. 43.
    Xia J, Sinelnikov IV, Wishart DS (2011) MetATT: a web-based metabolomics tool for analyzing time-series and two-factor datasets. Bioinformatics 27:2455–2456CrossRefPubMedGoogle Scholar
  44. 44.
    Xia J, Wishart DS (2016) Using MetaboAnalyst 3.0 for comprehensive metabolomics data analysis. Curr Protoc Bioinformatics 55:14.10.1–14.10.91CrossRefGoogle Scholar
  45. 45.
    Girbig D, Selbig J, Grimbs S (2012) A MATLAB toolbox for structural kinetic modeling. Bioinformatics 28:2546–2547CrossRefPubMedGoogle Scholar
  46. 46.
    Schmidt H, Jirstrand M (2006) Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22:514–515CrossRefPubMedGoogle Scholar
  47. 47.
    Aurich MK, Fleming RMT, Thiele I (2016) MetaboTools: a comprehensive toolbox for analysis of genome-scale metabolic models. Front Physiol 7:327CrossRefPubMedPubMedCentralGoogle Scholar
  48. 48.
    Fitzpatrick MA, McGrath CM, Young SP (2014) Pathomx: an interactive workflow-based tool for the analysis of metabolomic data. BMC Bioinformatics 15:396CrossRefPubMedPubMedCentralGoogle Scholar
  49. 49.
    Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:414–426Google Scholar
  50. 50.
    van den Berg RA, Hoefsloot HC, Westerhuis JA et al (2006) Centering, scaling, and transformations: improving the biological information content of metabolomics data. BMC Genomics 7:142CrossRefPubMedPubMedCentralGoogle Scholar
  51. 51.
    Mintz-Oron S, Meir S, Malitsky S et al (2012) Reconstruction of Arabidopsis metabolic network models accounting for subcellular compartmentalization and tissue-specificity. Proc Natl Acad Sci U S A 109:339–344CrossRefPubMedGoogle Scholar
  52. 52.
    Bogart E, Myers CR (2016) Multiscale metabolic modeling of C4 plants: connecting nonlinear genome-scale models to leaf-scale metabolism in developing maize leaves. PLoS One 11:e0151722CrossRefPubMedPubMedCentralGoogle Scholar
  53. 53.
    Shaw R, Kundu S (2015) Flux balance analysis of genome-scale metabolic model of rice (Oryza sativa): aiming to increase biomass. J Biosci 40:819–828CrossRefPubMedGoogle Scholar
  54. 54.
    Nägele T, Fürtauer L, Nagler M et al (2016) A strategy for functional interpretation of metabolomic time series data in context of metabolic network information. Front Mol Biosci 3:6CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Lisa Fürtauer
    • 1
  • Jakob Weiszmann
    • 1
    • 2
  • Wolfram Weckwerth
    • 1
    • 2
  • Thomas Nägele
    • 1
    • 2
    • 3
    Email author
  1. 1.Department of Ecogenomics and Systems Biology, Faculty of Life SciencesUniversity of ViennaViennaAustria
  2. 2.Vienna Metabolomics CenterUniversity of ViennaViennaAustria
  3. 3.Department Biology ILudwig-Maximilians-Universität MünchenPlanegg-MartinsriedAustria

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