- Flux balance analysis
**Introduction****Flux balance analysis**(**FBA**) has been shown to be a very useful technique for analysis of metabolic capabilities of cellularsystem s. Living organisms survive, grow or strive with the help of the available nutrients they find in their environment. They transform the nutrients into molecules they can use through a complex set of chemical reactions called metabolism. About organisms for which the whole metabolism is approximately known, (for instance the bacterium "E. coli") one can address the following problem: given some known available nutrients, which set of metabolic fluxes maximizes the growth rate of the organism? The aim of metabolic flux balance analysis, which is a mathematical analysis of the metabolism, is to solve this problem.Organisms like E. coli can be cultivated in mediums with defined concentrations of nutrients, and their growth rate can be measured, so that results of FBA can be compared with experiments.

A good description of the basic concepts of FBA can be found at http://www.nature.com/nbt/web_extras/supp_info/nbt0201_125/info_frame.html

**Overview**A chemical system can be described by a set of differential equations. For instance, suppose a chemical system has two reactions: A + B -> C at rate V1 and C -> A at rate V2. This system can be described by the differential equations: d(A)/dt = V2 - V1, d(B)/dt = -V1, and d(C)/dt = V1 - V2. A system is at steady state when all three derivatives (rates of change) are 0. FBA involves carrying out a steady state analysis, using the stoichiometric matrix for the system in question.

The system is assumed to be optimized with respect to functions such as maximization of biomass production or minimization of nutrient utilization, following which it is solved to obtain a steady state flux distribution. This flux distribution is then used to interpret the metabolic capabilities of the system. The dynamic mass balance of the metabolic system is described using the stoichiometric matrix, relating the flux rates of enzymatic reactions, $mathbf\{v\}\_\{n\; imes\; 1\}$ to time derivatives of metabolite concentrations, $mathbf\{x\}\_\{m\; imes\; 1\}$ as

:$frac\{dmathbf\{x\{dt\}\; =\; mathbf\{N\},mathbf\{v\}$

:$mathbf\{v\}=\; [v\_1\; v\_2\; ...\; v\_\{n\}\; b\_1\; b\_2\; ...\; b\_\{n\_\{ext\; ]\; ^T$

where $v\_i$ signifies the internal fluxes, $b\_i$ represents the exchange fluxes in the system and $n\_\{ext\}$ is the number of external metabolites in the system. At steady state,

:$frac\{dmathbf\{x\{dt\}\; =\; mathbf\{N\},mathbf\{v\}\; =\; 0$

Therefore, the required flux distribution belongs to the null space of $mathbf\{N\}$ . Since $m\; <\; n$ , the system is under-determined and may be solved for $mathbf\{v\}$ fixing an optimisation criterion, following which, the system translates into a linear programming problem:

:$min\_\{mathbf\{v\; mathbf\{c\}^Tmathbf\{v\}\; qquad\; extrm\{s.\; t.\}\; quad\; mathbf\{N\},mathbf\{v\}=0$

where $c$ represents the objective function composition, in terms of the fluxes. Further, we can constrain:

:$0\; <\; v\_i\; <\; infty$

$-infty\; <\; b\_i\; <\; infty$

which necessitates all internal irreversible reactions to have a flux in the positive direction and allows exchange fluxes to be in either direction. Practically, a finite upper bound can be imposed, so that the problem does not become unbounded. This upper bound may also be decided based on the knowledge of cellular physiology.

**Perturbations**FBA also has the capabilities to address effect of gene deletions and other types of perturbations on the system. Gene deletion studies can be performed by constraining the reaction flux(es) corresponding to the gene(s) (and therefore, of their corresponding proteins(s)), to zero. Effects of inhibitors of particular proteins can also be studied in a similar way, by constraining the upper bounds of their fluxes to any defined fraction of the normal flux, corresponding to the extents of inhibition.

**References*** Bonarius HPJ, Schmid G, Tramper J (1997) Flux analysis of underdetermined metabolic networks: The quest for the missing constraints. "Trends Biotech"

**15**: 308–314.

* Forster J, Famili I, Fu P, Palsson BO, Nielsen J (2003) Genome-scale reconstruction of the "Saccharomyces cerevisiae" metabolic network. "Genome Res"**13**: 244–253.

* Edwards JS, Palsson BO (2000) The "Escherichia coli" MG1655 in silico metabolic genotype: Its definition, characteristics, and capabilities. "Proc Natl Acad Sci U S A"**97**: 5528–5533.

* Edwards JS, Covert M, Palsson BO (2002) Metabolic modelling of microbes: The flux-balance approach. "Environ Microbiol"**4**: 133–133.

* Kauffman KJ, Prakash P, Edwards JS (2003) Advances in flux balance analysis. "Curr Opin Biotech"**14**: 491–496.

* Alvarez-Vasquez F, Sims K, Cowart L, Okamoto Y, Voit E, et al. (2005) Simulation and validation of modelled sphingolipid metabolism in Saccharomyces cerevisiae. "Nature"**433**: 425–430.

* Edwards JS, Ibarra RU, Palsson BO (2001) "In silico" predictions of Escherichia coli metabolic capabilities are consistent with experimental data. "Nat Biotechnol"**19**: 125–130.

* Raman K, Rajagopalan P, Chandra N (2005) Flux Balance Analysis of Mycolic Acid Pathway: Targets for Anti-Tubercular Drugs. "PLoS Comput Biol"**1(5)**: e46

*Wikimedia Foundation.
2010.*

### См. также в других словарях:

**Flux (metabolism)**— Flux, or metabolic flux is the rate of turnover of molecules through a metabolic pathway. Flux is regulated by the enzymes involved in a pathway. Within cells, regulation of flux is vital for all metabolic pathways to regulate the metabolic… … Wikipedia**Flux (biochemistry)**— Flux, or metabolic flux is the rate of turnover of molecules through a metabolic pathway or an enzyme. Within cells regulation of flux is vital for all metabolic pathways to regulate the metabolic pathway s activity under different conditions.… … Wikipedia**Flux**— This article is about the concept of flux in science and mathematics. For other uses of the word, see Flux (disambiguation). In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical… … Wikipedia**Balance of trade**— Cumulative Current Account Balance 1980–2008 based on the International Monetary Fund data … Wikipedia**Metabolic flux analysis**— is an analysis technique similar to Flux Balance Analysis used to determine the rate at which a metabolite is produced during a bioprocess. This bioinformatics related … Wikipedia**Mass balance**— A mass balance (also called a material balance) is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown,… … Wikipedia**Metabolic network modelling**— Metabolic network showing interactions between enzymes and metabolites in the Arabidopsis thaliana citric acid cycle. Enzymes and metabolites are the red dots and interactions between them are the lines … Wikipedia**Computational systems biology**— is the algorithm and application development arm of systems biology. It is also directly associated with bioinformatics and computational biology. Computational systems biology aims to develop and use efficient algorithms, data structures and… … Wikipedia**Modelling biological systems**— Modeling biological systems is a significant task of systems biology and mathematical biology. Computational systems biology aims to develop and use efficient algorithms, data structures, visualization and communication tools with the goal of… … Wikipedia**Fluxome**— is the totality of quantified flux amount of all the metabolites in cells. In FBA(Flux Balance Analysis), the fluctuations of metabolites and proteins are the key elements. The omics concept of fluxome is useful in quantitating all the… … Wikipedia