Flux balance analysis

B. Flux Balance Analysis and Elementary Flux Modes... 

Considering a trade-off between knowledge that is required prior to the analysis and predictive power, stoichiometric network analysis must be regarded as the most successful computational approach to large-scale metabolic networks to date. It is computationally feasible even for large-scale networks, and it is nonetheless far more predictive that a simple graph-based analysis. Stoichiometric analysis has resulted in a vast number of applications [35,67,70 74], including quantitative predictions of metabolic network function [50, 64]. The two most well-known variants of stoichiometric analysis, namely, flux balance analysis and elementary flux modes, constitute the topic of Section V. 

An analysis of the right nullspace K provides the conceptual basis of flux balance analysis and has led to a plethora of highly successful applications in metabolic network analysis. In particular, all steady-state flux vectors v° = v(S°,p) can be written as a linear combination of columns Jfcx- of K, such that... 

Equation (64) justifies the application of flux-balance analysis even in the face of (i) fast short-term fluctuations and (ii) periodic long term for example, circadian variability. The steady state balance condition restricts the feasible steady-state flux distributions to the flux cone P = v° G IRr IVv0 = 0. The reduction of the admissible flux space, with some of its algebraic properties already summarized in Section III.B, is exploited by several computational approaches, most notably Flux Balance Analysis (FBA) [61, 71, 235] and elementary flux modes (EFMs) [96, 236 238],... 

Probably the most prominent approach to large-scale metabolic networks is constraint-based flux balance analysis. The steady-state condition Eq. (63) defines a linear equation with respect to the feasible flux distributions v°. Formulating a set of constraints and a linear objective function, the properties of the solution space P can be exploredusing standard techniques of linear programming (LP). In this case, the flux balance approach takes the form ... 

Despite its widely recognized limitations, flux balance analysis has resulted in a large number of successful applications [35, 67, 72 74], including several extensions and refinements. See Ref. [247] for a recent review. Of particular interest are recent efforts to augment the stoichiometric balance equations with thermodynamic constraints providing a link between concentration and flux in the constraint-based analysis of metabolic networks [74, 149, 150]. For a more comprehensive review, we refer to the very readable monograph of Palsson [50]. 

From a theoretical perspective, and provided that the network structure and some information about input and output fluxes are available, the intracellular steady-state fluxes can be estimated utilizing flux balance analysis. In conjunction with large-scale concentrations measurements, as described in Section IV, this allows, at least in principle, to specify the metabolic state of the system. 

However, FBA in itself is not sufficient to uniquely determine intracellular fluxes. In addition to the ambiguities with respect to the choice of the objective function, flux balance analysis is not able to deal with the following rather common scenarios [248] (i) Parallel metabolic routes cannot be resovled. For example, in the simplest case of two enzymes mediating the same reaction, the optimization procedure can only assign the sum of a flux of both routes, but not the flux of each route, (ii) Reversible reaction steps can not be resolved, only the sum of both directions, that is, the net flux, (iii) Cyclic fluxes cannot be resolved as they have no impact on the overall network flux, (iv) Futile cycles, which are common in many organisms, are not present in the FBA solution, because they are usually not optimal with respect to any optimization criterion. These shortcomings necessitate a direct experimental approach to metabolic fluxes, as detailed in the next section. 

As discussed in Section V.B, flux balance analysis allows to estimate intracellular steady-state fluxes provided the network structure and some information about... 

The first term in Eq. (68) describes the steady-state properties of the system, as exploited by flux balance analysis to constrain the stoichiometrically feasible flux distributions. Since we consider infinitesimal perturbations only, quadratic terms in the expansion are neglected. In this case, the time-dependent behavior of an infinitesimal perturbation AS(t) = S — S° in the vicinity of S° is described by a linear differential equation... 

CONSTRAINT (FLUX-BALANCE) ANALYSIS DETAILED KINETIC MODELS... 

In close analogy to flux-balance analysis, we thus extend the constraint-based description of metabolic networks to incorporate (local) dynamic properties. Recall the expansion of the mass-balance equation into a Taylor series, already given in Eq. (68)... 

A. Hoppe, S. Hoffmann, and H. G. Holzhiitter, Including metabolite concentrations into flux balance analysis Thermodynamic realizability as a constraint on flux distributions in metabolic networks. BMC Syst. Biol. 1, 23 (2007). 

Matlab MathWorks High-level language and interactive environment that enables simulation of biochemical networks using integrated flux balance analysis, regulatory flux balance analysis, and ordinary differential equations (http // www.mathworks. com/products/matlab/)... 

Yices SRI International Constraint solver that can handle flux balance analysis (http // yices.csl.sri.com/)... 

Plata G, Hsiao TL, Olszewski KL et al (2010) Reconstruction and flux-balance analysis of the Plasmodium falciparum metabolic network. Mol Syst Biol 6 408... 

Fig. 2 Simplified workflow for the reconstruction of genome-scale metabolic models and their use in simulating cellular function through flux balance analysis...

Integration of flux balance analysis and physiological of respiration deficient mutants Bioethanol production [234]... 

As we shall see, linear algebraic constraints arising from steady state mass balance form the basis of metabolic flux analysis (MFA) and flux balance analysis (FBA). Thermodynamic laws, while introducing inherent non-linearities into the mathematical description of the feasible flux space, allow determination of feasible reaction directions and facilitate the introduction of reactant concentrations to the constraint-based framework. 

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