Genome-Scale Metabolic Networks Marco Terzer1 Nathaniel D

Advanced Review Genome-scale metabolic networks Marco Terzer1 Nathaniel D. Maynard2 Markus W. Covert2 and Jorg¨ Stelling1∗ During the last decade, models have been developed to characterize cellular metabolism at the level of an entire metabolic network. The main concept that underlies whole-network metabolic modeling is the identification and mathematical definition of constraints. Here, we review large-scale metabolic network modeling, in particular, stoichiometric- and constraint-based approaches. Although many such models have been reconstructed, few networks have been extensively validated and tested experimentally, and we focus on these. We describe how metabolic networks can be represented using stoichiometric matrices and well-defined constraints on metabolic fluxes. We then discuss relatively successful approaches, including flux balance analysis (FBA), pathway analysis, and common extensions or modifications to these approaches. Finally, we describe techniques for integrating these approaches with models of other biological processes. 2009 John Wiley & Sons, Inc. WIREsSystBiolMed LARGE-SCALE NETWORK ANALYSIS Most analysis techniques in this area employ up to three types of constraints.1 Physico-chemical etabolic networks are well-enough character- constraints are defined by conservation laws for Mized that it is now possible to construct and mass and energy, dependency of reaction rates on analyze mathematical models of their behavior at metabolite concentrations, and negative free energy a whole-genome level.1,2 This is not due to rich, change for spontaneous reactions. Environmental extensive datasets—in fact, the existing data are far constraints are imposed as a result of specific from comprehensive.3 Even in the best-understood conditions, such as the availability of nutrients organisms, the majority of kinetic parameters remain or electron acceptors. Finally, the effects of gene undetermined. Instead, whole-network modeling of expression may result in regulatory constraints as metabolism has largely been enabled by the develop- the cell adapts to environmental changes. ment of new computational methods that are able to Here, we review large-scale metabolic net- make compelling and testable predictions even with- work modeling, focusing on stoichiometric-and out many parameters. As a result, metabolic modeling constraint-based approaches. After discussing how has become a bellwether, leading the way toward a these approaches work, we will highlight common fundamental goal in biology: a computational model and relatively successful approaches as well as exist- of an entire cell. ing models. Finally, we will comment on the possibility The main concept that underlies whole-network of integrating these models with models of other bio- metabolic modeling is the identification and math- logical processes, such as transcriptional regulation ematical definition of constraints. These constraints and signal transduction, as another step toward true then separate feasible and infeasible metabolic behav- whole-cell modeling. iors. Importantly, the constraints are often much easier to identify than kinetic parameters, making large-scale model building possible. MODEL DEVELOPMENT ∗Correspondence to: [email protected] The Stoichiometric Matrix 1Department of Biosystems Science and Engineering, ETH Zurich, Although there are a variety of metabolic model- Switzerland ing approaches, all of them share a fundamental 2Department of Bioengineering, Stanford University, Stanford, CA, requirement: a stoichiometric matrix based on a USA reconstructed metabolic network. Each column of the DOI: 10.1002/wsbm.037 stoichiometric matrix corresponds to a chemical or 2009 John Wiley & Sons, Inc. Advanced Review www.wiley.com/wires/sysbio (a) (c) d A v1 d t v2 b v b 1 1 2 –1–1 0 1 0 0 v A B d B 3 = 1 0 1 0–10 b v2 v3 d t 1 C 0–100–11 d C b2 b b3 d t 3 (b) (d) Material Balances Reaction stoichiometry Kinetic Subject to: Steady-state dA pH Thermodynamic = –v1 –v2 + b1 dt ∞ ≤ ≤∞ ≤ ≤ 0 = S·v – v1 0 b1 10 dB ∞ ≤ ≤∞ ≤ ≤ = v1 + v3 – b2 v2 0 b2 10 dt ∞ ≤ ≤∞ ≤ ≤ ∞ v3 0 b3 dC = v2 –v3 – b3 dt Objective: maximize b2 FIGURE 1| (a) A small reaction network consisting of three metabolites (A, B, and C), three transport reactions, and three enzymatic reactions is constructed. vi indicates the flux through reaction i and bj represents the flux through transport protein j. (b) Material balance equations are shown for each metabolite. (c) A stoichiometric matrix is populated according to Eq. 1. (d) Assumptions, constraints, and an objective are listed for the system. transport reaction, with non-zero values that identify Equation (2) is a homogeneous system of linear the metabolites which participate in the reaction as equations. It requires that each metabolite is consumed well as the stoichiometric coefficients that correspond in the same quantity as it is produced, and is the basis to each metabolite (Figure 1). The matrix also con- for further analysis of metabolic fluxes based on the tains directionality: substrate and product metabolites stoichiometric matrix. in the matrix have negative and positive coefficients, The process of building stoichiometric matrices respectively. By considering the matrix rows instead has been amply described and reviewed elsewhere.4 of the columns, the stoichiometric matrix can also be Briefly, this process involves gathering a variety of thought of as the list of reactions in which a given genomic, biochemical, and physiological data from metabolite participates. This interpretation is useful the primary literature as well as databases, such 5 6 7 8 when defining mass balances for each metabolite in as Uniprot, BRENDA, BioCyc, KEGG, and the 9 the network. Enzyme Commission database. This information is These mass balances are expressed by a system used to synthesize a list of chemical and transport of differential equations written for all the metabolite reactions together with their metabolite participants concentrations c as follows: for a given cell. In addition, the chemical formula and charge of each metabolite should be inspected to verify dc(t) that the chemical reaction is balanced. A reconstructed = S · v(t)(1)network model is only as good as its corresponding dt stoichiometric matrix, and the amount and quality of experimental evidence supporting the inclusion where S is the stoichiometric matrix and v(t) the vector of a reaction in the matrix can vary significantly. of reaction rates. Note that metabolism operates Therefore, careful curation and continual updates to on a much faster time-scale than regulatory or cell the matrix are critical. division events. It is thus often reasonable to assume that metabolic dynamics have reached a quasi-or pseudo-steady state, where metabolite concentrations Constraints on Reaction Rates do not change. This leads to the metabolite balancing The stoichiometric matrix can be annotated by equation including further important information about either the reactions or the metabolites. The most common matrix annotations include the reversibility of each · = S v(t) 0(2)reaction and the cellular compartment in which 2009 John Wiley & Sons, Inc. WIREs Systems Biology and Medicine Genome-scale metabolic networks each reaction occurs. More generally, reaction rates reaction thermodynamics, energetic requirements for are bounded as a consequence of kinetic constants, maintenance, and known kinetic effects. The model measured or estimated concentration ratios or to has been used for a variety of applications, including reflect the experimental setup. Upper and lower limits the prediction of growth rates, substrate uptake, and can apply to fluxes of individual reactions (vmin ≤ v ≤ by-product secretion for thousands of combinations 17 vmax), and reaction directions can be defined by simply of knockout strains and culture conditions. setting vmin = 0orvmax = 0 for forward or backward Geobacter species network reconstructions have irreversible reactions, respectively. Additional matrix also been developed due to their remarkable bioreme- annotation might include more detailed information diative potential.18 These organisms have somewhat about reaction kinetics. For example, it is possible unique metabolic properties enabling them to oxi- to calculate metabolite uptake or secretion rates dize organic compounds using a variety of toxic without difficulty in several cases; these can be or radioactive metals as electron acceptors. The G. used as a part of the metabolic model. In addition, sulferreducens metabolic model of metabolism14 has 13C chase experiments measure concentrations of been used to engineer a potentially useful strain with internal metabolites, from which enzymatic fluxes can high respiration capacity and low growth rate.19 often be inferred.10,11 At the present such ‘fluxomic’ The S. cerevisiae model is notable, in particular, approaches can only be applied to highly reduced for the recent efforts by the yeast community to metabolic networks, although substantial progress has develop a consensus network. Several reconstructions been made in recent years. had previously been made and varied significantly in their content.20–22 As a result, leading researchers in the yeast field along with metabolic modeling experts Links to Genomic Information were brought together for a weekend ‘jamboree’ The stoichiometric matrix can also be linked explic- to agree on the specifics of yeast metabolism. The itly to the genome and gene expression data for use resulting consensus metabolic network reconstruction

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