Metabolic flux balance analysis

Recently, genome-scale cellular metabolic networks have been reconstructed and metabolic flux balance analysis (FBA) has been conducted using reconstructed... 

Barrera-Martinez, L, Gonzalez-Garcla, R. A., Salgado-Manjarrez, E., Aranda-Barradas, J. S. A simple metabolic flux balance analysis of biomass and bioethanol production in5ac-charomyces cerevisiae fed-batch cultures. Biotech Bioprocess Eng. 2011, 16,13-22. 

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... 

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. 

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). 

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...

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. 

The concept that modules comprise the traditional pathways is gaining more focus as basic functional building blocks (20). Gene expression patterns in pathways and their formation of modules has been an intense topic of study (21, 22). These pathways combined with flux balance analysis have also provided interesting results about the metabolic pathway of yeast (23) and Escherichia coli (24). The latter involves steady-state analysis using reaction stoichiometry information, such as those stored in the KEGG REACTION database, and it is gaining renewed interest for systematic analysis of metabolic networks (6). 

We note that metabolic systems are studied often in systems biology using dynamics analysis such as flux balance analysis and differential equations. However, discussion regarding systems dynamics is beyond the scope of this current manuscript, and we refer the interested reader to the relevant literature (37, 38). This limitation, however, does not preclude these analyses from the standpoint of integrated systems analysis for understanding the metabolic pathway. 

Metabolic networks can be quantitatively and qualitatively studied without enzyme kinetic parameters by using a constraints-based approach. Metabolic networks must obey the fundamental physicochemical laws, such as mass, energy, redox balances, diffusion, and thermodynamics. Therefore, when kinetic constants are unavailable, cellular function can still be mathematically constrained based on the mass and energy balance. Flux balance analysis (FBA) is a mathematical modeling framework that can be used to study the steady-state metabolic capabilities of cell-based physicochemical constraints. ... 

Flux balance analysis has been used for over 15 yr to study the metabolic flux distribution. Initially, the applications of FBA were primarily educational however, recently, the utility has grown. The FBA has been applied to study the effect of gene deletions, the design of bacterial metabolism for industrial and environmental applications, or for the computational exploration of cellular physiology. Metabolic engineering has been successfully applied to engineer micro-organisms to produce valuable biochemicals... 

Whereas detailed dynamic models can precisely answer questions on cellular behavior, the widespread application of such approaches has been hampered by the lack of kinetic information. In the absence of kinetic information, a method known as flux balance analysis (FBA) has been developed to analyze the metabolic capabilities of a cellular system based on mass balance constraints [Varma and Palsson 1994 Edwards et al. 1999 Edwards and Palsson 2000],... 

Boyle NR, Morgan JA Flux balance analysis of primary metabolism in Chlamydomonas reinhardtii, BMC Syst Biol 3 4, 2009. 

Due to lack of kinetic parameters, structural metabolic network modeling has been widely applied for analyzing cellular metabolism under steady-state. Depending on what assumptions are made and whether experimental data are required, different techniques have been developed to analyze the invariant of metabohc networks such as metabolic flux analysis (MFA), flux balance analysis (FBA), and metabolic pathway analysis (MPA) including elementary mode and extreme pathway analyses (Lewis et al. 2012 Stephanopoulos et al. 1998 Trinh et al. 2(X)9). 

Similar to MFA, flux balance analysis (FBA) determines a metabolic flux vector r corresponding to a physiological state for the cell under a given condition but can... 

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