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Genome‐scale metabolic networks

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Abstract 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 Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under: Models of Systems Properties and Processes > Cellular Models

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(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.

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Models have been constructed which build on the constraint‐based framework to integrate metabolic, transcriptional regulatory, and signal transduction networks (each represented using different mathematics) into a single model.

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Schematic representation of regulated flux balance analysis (rFBA) using Boolean expressions to simulate regulatory elements. The concept is generalized to integrated FBA (iFBA), also incorporating ordinary differential equations (ODEs) to simulate regulation. The algorithm is an iterative procedure, generating time series output at each iteration.

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Ethanol excretion rate related to biomass yield for 178,575 elementary modes (EMs) of an Escherichia coli central metabolism network with 97 metabolites and 120 reactions; only growth on glucose (Glc) was considered. Ethanol production is possible only for suboptimal growth.

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Network inconsistencies due to dead‐end metabolites (a) or reaction couplings (b). Nodes correspond to metabolites and arrows denote reactions.

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(a) Nullspace (blue hyperplane) and the two‐dimensional cone as intersection of the nullspace with the positive orthant. (b) Additional boundary constraints (dotted lines) shape a bounded convex region. The flux balance analysis (FBA) objective function (blue solid line) touches the region in the optimal point (blue circle). (c) The same cone, now in a two‐dimensional view, with feasible regions for wild‐type (red area) and mutant (yellow). The FBA objective function touches the regions at the optimal points (blue circles). If Minimization of metabolic adjustment (MoMA) is used instead, the distance to the best wild‐type value is minimized, resulting in a different optimal value for the mutant (green triangle). (d) As a third alternative, regulatory on/off minimization (ROOM) minimizes the number of necessary changes. The brown lines indicate that one variable is kept constant, implying a minimal number of changes for this example. Here, two alternative optimal values are possible (brown squares).

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