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Experimental and Mathematical Approaches to Modeling Plant Metabolic Networks

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Experimental and Mathematical Approaches to Modeling Plant Metabolic Networks PHYTOCHEMISTRY Phytochemistry 68 (2007) 2351–2374 www.elsevier.com/locate/phytochem Review Experimental and mathematical approaches to modeling plant metabolic networks Rigoberto Rios-Estepa a,b, Bernd Markus Lange a,* a Institute of Biological Chemistry, M.J. Murdock Metabolomics Laboratory, Center for Integrated Biotechnology, Washington State University, P.O. Box 646340, Pullman, WA 99164-6340, USA b School of Chemical Engineering and Bioengineering, Washington State University, P.O. Box 642710, Pullman, WA 99164-2710, USA Received 24 January 2007; received in revised form 16 April 2007 Available online 11 June 2007 This article is dedicated to the memory of Reinhart Heinrich, one of the founding fathers of metabolic control theory and a pioneer of systems biology. Abstract To support their sessile and autotrophic lifestyle higher plants have evolved elaborate networks of metabolic pathways. Dynamic changes in these metabolic networks are among the developmental forces underlying the functional differentiation of organs, tissues and specialized cell types. They are also important in the various interactions of a plant with its environment. Further complexity is added by the extensive compartmentation of the various interconnected metabolic pathways in plants. Thus, although being used widely for assessing the control of metabolic flux in microbes, mathematical modeling approaches that require steady-state approximations are of limited utility for understanding complex plant metabolic networks. However, considerable progress has been made when manageable metabolic subsystems were studied. In this article, we will explain in general terms and using simple examples the concepts underlying stoichiometric modeling (metabolic flux analysis and metabolic pathway analysis) and kinetic approaches to modeling (including met- abolic control analysis as a special case). Selected studies demonstrating the prospects of these approaches, or combinations of them, for understanding the control of flux through particular plant pathways are discussed. We argue that iterative cycles of (dry) mathemat- ical modeling and (wet) laboratory testing will become increasingly important for simulating the distribution of flux in plant metabolic networks and deriving rational experimental designs for metabolic engineering efforts. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: BioPathAt; Bondomer; Cumomer; Elementary modes; Flux; Isotopomer; Metabolic control analysis Contents 1. Introduction . 2352 2. Metabolic flux analysis. 2353 2.1. Case study of flux balance analysis . 2356 2.1.1. Limitations of stoichiometric analyses . 2358 2.2. Metabolic pathway analysis . 2358 2.2.1. Elementary modes analysis . 2358 2.2.2. Extreme pathway analysis . 2360 2.3. Case study of isotope labeling-based metabolic flux analysis . 2360 * Corresponding author. Tel.: +1 509 335 3794; fax: +1 509 335 7643. E-mail address: [email protected] (B.M. Lange). URL: http://www.wsu.edu/~lange-m/ (B.M. Lange). 0031-9422/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.phytochem.2007.04.021 2352 R. Rios-Estepa, B.M. Lange / Phytochemistry 68 (2007) 2351–2374 2.3.1. Atom mapping matrices . 2360 2.3.2. Isotopomer balancing . 2362 2.3.3. Cumomer balancing . 2362 2.3.4. Bondomer balancing . 2362 2.4. Metabolic flux analysis for modeling of plant metabolic networks . 2363 2.4.1. Steady-state labeling . 2363 2.4.2. Dynamic labeling . 2364 2.4.3. Highlight: central carbon metabolism in soybean embryos . 2365 3. Kinetic analysis of metabolic networks . 2366 3.1. Case study of kinetic modeling and dynamic simulation . 2366 3.2. Kinetic models of plant metabolic networks . 2367 3.3. Metabolic control analysis . 2367 3.3.1. Case study of metabolic control analysis. 2367 3.3.2. Metabolic control analysis for modeling plant metabolic networks . 2368 4. Conclusions. 2370 Appendix A. Supplementary data . 2370 References . 2370 1. Introduction biochemical engineers but most plant biologists are not familiar with the underlying mathematical framework. Metabolic engineering aims to purposefully alter (using In this article, we are discussing some the most widely genetic engineering techniques) an organism’s metabolic used methods for modeling metabolic networks and illus- pathways in order to better understand how these path- trate their utility in simplified case studies. We are ways work or to redesign them for the production of par- attempting to provide sufficient information for phyto- ticular target metabolites. In 2002, the entire January chemists, biochemists, biophysicists and geneticists to issue of the journal Metabolic Engineering (Metabolic understand the basic concepts of mathematical modeling Engineering, Volume 4, Issue 1, Pages 1–106, January and to allow them to evaluate the available literature. It 2002) was devoted to highlighting the progress, problems is our hope that this article will serve as a primer for read- and prospects of plant metabolic engineering. Undoubt- ers to think about how mathematical modeling can be uti- edly, the plant metabolic engineering community has lized in providing quantitative descriptions of metabolic made considerable progress, which is attested by highly network behavior. Of course, we cannot cover the issue publicized success stories such as the development of pro- in-depth and the reader is referred to the primary litera- vitamin A-producing grains of ‘golden rice’ (Ye et al., ture and several excellent books for further perusal (Hein- 2000) or the production of thermoplastic polyhydroxyalk- rich and Schuster, 1996; Fell, 1997; Stephanopoulos et al., anoate polymers in transgenic oilseed rape (Slater et al., 1998). 1999). However, further success of plant metabolic engi- Various bioinformatic tools are available to compute the neering at a commercial scale, besides suffering from lack topology of genome-scale metabolic networks from exper- of public acceptance in some parts of the world, has been imental data (reviewed in Xia et al., 2004). However, the hampered by an insufficient understanding of the mecha- mathematical modeling methods used today for estimating nisms controlling flux through plant metabolic pathways, flux through metabolic pathways (or networks of path- and the outcome of metabolic engineering attempts can- ways) require an in-depth knowledge of one or more of not yet be predicted with satisfactory accuracy (DellaP- the following input data: the (assumed) stoichiometry of enna, 2001). With the advent of ‘omics’ technologies (in all biochemical reactions, reversibility of enzymatic steps, particular transcriptomics, proteomics, and metabolo- branching patterns of (sub)pathways, uptake rates of a mics), which allow the global profiling of the abundance metabolic substrate and conversion rate into end products, of constituents involved in metabolic pathways, our abil- subcellular compartmentation, the kinetic constants of the ity to document changes brought about by metabolic enzymes involved, and possibly profiles of transcript, pro- engineering is greatly enhanced. However, it has been tein and/or metabolite abundance. Thus, although gen- argued that these approaches have to be augmented by ome-scale reconstructions have been attempted for quantitative mathematical modeling, combined in an iter- microbes (reviewed in Price et al., 2004), the majority of ative cycle with experimental testing of model predictions, flux modeling efforts in plants has been restricted to one to enable a rational design of metabolic engineering strat- pathway or a small set of pathways. Mathematical model- egies (Sweetlove and Fernie, 2005; Fernie et al., 2005; ing approaches for flux determination can be categorized Lange, 2006; Ratcliffe and Shachar-Hill, 2006). Pathway based on the algorithms, constraints and data types that modeling has been an area of strength for chemical and are utilized, and their selection for a particular project will R. Rios-Estepa, B.M. Lange / Phytochemistry 68 (2007) 2351–2374 2353 Table 1 its conversion rate into products, and the production of Overview of freely available software packages and online tools for biomass are considered. Further developments of this mathematical modeling of plant metabolism concept, which are based on the use of different algo- Modeling method Software tool References rithms and constraints, are flux balance analysis (FBA), Isotope labeling- 13C-Flux Wiechert et al. (2001) extreme pathway analysis (EPA) and elementary modes based FiatFlux Zamboni et al. (2005) analysis (EMA). Because of the limitations of stoichiome- metabolic flux Mathematica-based Selivanov et al. (2006) tric modeling, an experimental approach was developed program (no name given) that is based on labeling experiments with stable isotopes 13 NMR2Flux Sriram et al. (2004) (primarily C) and subsequent analysis of the distribution Elementary modes FluxAnalyzer Klamt et al. (2003) of label in different carbon atoms of the target metabo- analysis SNA Urbanczik (2006) lites. Mechanistic (kinetic) models incorporate knowledge YANA Schwarz et al. (2005) regarding the kinetic properties of enzymes involved in a Extreme pathway FluxAnalyzer Klamt et al. (2003) metabolic network and can be used to simulate how intra- analysis Expa Bell and Palsson (2005) cellular fluxes will change when the experimental system is perturbed. Metabolic control analysis (MCA) has become Kinetic modeling CellDesigner (latest Funahashi et al. (2003) the most widely used kinetics-based tool to gain a quan- version is 3.5.1) titative understanding
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