Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Morgan JA, Rhodes D (2002) Mathematical modeling of plant metabolic pathways. Metab Eng 4:80–89
Prusinkiewicz P (2004) Modeling plant growth and development. Curr Opin Plant Biol 7:79–83
Fiehn O (2002) Metabolomics-the link between genotypes and phenotypes. Plant Mol Biol 48:155–171
Weckwerth W (2011) Unpredictability of metabolism-the key role of metabolomics science in combination with next-generation genome sequencing. Anal Bioanal Chem 400:1967–1978
Liberman LM, Sozzani R, Benfey PN (2012) Integrative systems biology: an attempt to describe a simple weed. Curr Opin Plant Biol 15:162–167
Hoermiller II, Naegele T, Augustin H et al (2017) Subcellular reprogramming of metabolism during cold acclimation in Arabidopsis thaliana. Plant Cell Environ 40:602–610
Hurry V (2017) Metabolic reprogramming in response to cold stress is like real estate, it’s all about location. Plant Cell Environ 40:599–601
Fürtauer L, Weckwerth W, Nägele T (2016) A benchtop fractionation procedure for subcellular analysis of the plant metabolome. Front Plant Sci 7:1912
Nägele T (2014) Linking metabolomics data to underlying metabolic regulation. Front Mol Biosci 1:22
Wang Y, Zhang X-S, Chen L (2010) Optimization meets systems biology. BMC Syst Biol 4:S1
Banga JR (2008) Optimization in computational systems biology. BMC Syst Biol 2:47
Reali F, Priami C, Marchetti L (2017) Optimization algorithms for computational systems biology. Front Appl Math Stat 3:6
Loomis RS, Rabbinge R, Ng E (1979) Explanatory models in crop physiology. Annu Rev Plant Physiol 30:339–367
Rios-Estepa R, Lange BM (2007) Experimental and mathematical approaches to modeling plant metabolic networks. Phytochemistry 68:2351–2374
Klipp E, Liebermeister W (2006) Mathematical modeling of intracellular signaling pathways. BMC Neurosci 7(Suppl 1):S10
Chew YH, Smith RW, Jones HJ et al (2014) Mathematical models light up plant signaling. Plant Cell 26:5–20
Rohwer JM (2012) Kinetic modelling of plant metabolic pathways. J Exp Bot 63:2275–2292
Gombert AK, Nielsen J (2000) Mathematical modelling of metabolism. Curr Opin Biotechnol 11:180–186
Giersch C (2000) Mathematical modelling of metabolism. Curr Opin Plant Biol 3:249–253
Pettersson G, Ryde-Pettersson U (1988) A mathematical model of the Calvin photosynthesis cycle. Eur J Biochem 175:661–672
Pettersson G (1997) Control properties of the Calvin photosynthesis cycle at physiological carbon dioxide concentrations. Biochim Biophys Acta 1322:173–182
Pokhilko A, Bou-Torrent J, Pulido P et al (2015) Mathematical modelling of the diurnal regulation of the MEP pathway in Arabidopsis. New Phytol 206:1075–1085
Funahashi A, Morohashi M, Kitano H, Tanimura N (2003) CellDesigner: a process diagram editor for gene-regulatory and biochemical networks. Biosilico 1:159–162
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 1:109–118
Hoops S, Sahle S, Gauges R et al (2006) COPASI – a COmplex PAthway SImulator. Bioinformatics 22:3067–3074
Schmidt H (2007) SBaddon: high performance simulation for the Systems Biology Toolbox for MATLAB. Bioinformatics 23:646–647
Steuer R, Gross T, Selbig J, Blasius B (2006) Structural kinetic modeling of metabolic networks. Proc Natl Acad Sci U S A 103:11868–11873
Reznik E, Segre D (2010) On the stability of metabolic cycles. J Theor Biol 266:536–549
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 2011:2
Fürtauer L, Nägele T (2016) Approximating the stabilization of cellular metabolism by compartmentalization. Theory Biosci 135:73
Jiao W-B, Schneeberger K (2017) The impact of third generation genomic technologies on plant genome assembly. Curr Opin Plant Biol 36:64–70
Vivek-Ananth RP, Samal A (2016) Advances in the integration of transcriptional regulatory information into genome-scale metabolic models. Biosystems 147:1–10
Thiele I, Palsson BO (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction. Nat Protoc 5:93–121
Nägele T, Mair A, Sun X et al (2014) Solving the differential biochemical Jacobian from metabolomics covariance data. PLoS One 9:e92299
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 68:1757–1783
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 9:564–574
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–S93
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):31697
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):318–332
Schelter B (2006) Handbook of time series analysis recent theoretical developments and applications. Weinheim, Wiley-VCH
Derryberry DR (2014) Basic data analysis for time series with R. Wiley, Hoboken, NJ
Smilde AK, Westerhuis JA, Hoefsloot HCJ et al (2010) Dynamic metabolomic data analysis: a tutorial review. Metabolomics 6:3–17
Xia J, Sinelnikov IV, Wishart DS (2011) MetATT: a web-based metabolomics tool for analyzing time-series and two-factor datasets. Bioinformatics 27:2455–2456
Xia J, Wishart DS (2016) Using MetaboAnalyst 3.0 for comprehensive metabolomics data analysis. Curr Protoc Bioinformatics 55:14.10.1–14.10.91
Girbig D, Selbig J, Grimbs S (2012) A MATLAB toolbox for structural kinetic modeling. Bioinformatics 28:2546–2547
Schmidt H, Jirstrand M (2006) Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22:514–515
Aurich MK, Fleming RMT, Thiele I (2016) MetaboTools: a comprehensive toolbox for analysis of genome-scale metabolic models. Front Physiol 7:327
Fitzpatrick MA, McGrath CM, Young SP (2014) Pathomx: an interactive workflow-based tool for the analysis of metabolomic data. BMC Bioinformatics 15:396
Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:414–426
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 7:142
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 109:339–344
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:e0151722
Shaw R, Kundu S (2015) Flux balance analysis of genome-scale metabolic model of rice (Oryza sativa): aiming to increase biomass. J Biosci 40:819–828
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 3:6
Acknowledgments
This work was supported by the Austrian Science Fund (FWF), Project I 2071, and the Vienna Metabolomics Center ViMe at the University of Vienna.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media, LLC, part of Springer Nature
About this protocol
Cite this protocol
Fürtauer, L., Weiszmann, J., Weckwerth, W., Nägele, T. (2018). Mathematical Modeling Approaches in Plant Metabolomics. In: António, C. (eds) Plant Metabolomics. Methods in Molecular Biology, vol 1778. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-7819-9_24
Download citation
DOI: https://doi.org/10.1007/978-1-4939-7819-9_24
Published:
Publisher Name: Humana Press, New York, NY
Print ISBN: 978-1-4939-7818-2
Online ISBN: 978-1-4939-7819-9
eBook Packages: Springer Protocols