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Fluxomers: a new approach for 13C metabolic flux analysis.

Srour O, Young JD, Eldar YC - BMC Syst Biol (2011)

Bottom Line: These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization.Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models.We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept. of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.

ABSTRACT

Background: The ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.

Results: This article addresses the mathematical and computational formulation of (13)C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.

Conclusions: Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.

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Simple metabolic network. (a) Standard network representation. Carbon atoms are drawn explicitly with arrows to indicate atom transitions. Unidirectional arrows represent unidirectional fluxes while bidirectional fluxes (such as flux 5) are represented by bidirectional arrows. (b) Fluxomers representation. Each arrow is a group of fluxomers. X's appear on the appropriate atom positions to indicate summation of divergent fluxomers.
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Figure 3: Simple metabolic network. (a) Standard network representation. Carbon atoms are drawn explicitly with arrows to indicate atom transitions. Unidirectional arrows represent unidirectional fluxes while bidirectional fluxes (such as flux 5) are represented by bidirectional arrows. (b) Fluxomers representation. Each arrow is a group of fluxomers. X's appear on the appropriate atom positions to indicate summation of divergent fluxomers.

Mentions: In the following, we show how to construct and solve MFA problems using fluxomer variables. First we define and explain the basic properties of fluxomers. Then we show how to express MFA balance equations and measurements in terms of fluxomers. Finally, we formulate the MFA optimization problem and present the FIA algorithm for solving it. Throughout this section we use boldface uppercase letters A to denote matrices, lowercase boldface letters x to denote vectors, and lowercase letters u for scalars. We use the <○ >product z = x○y to represent the element-wise product vector, i.e. zi = xiyi. The model formulation will be illustrated using the simple metabolic network shown in Figure 3.


Fluxomers: a new approach for 13C metabolic flux analysis.

Srour O, Young JD, Eldar YC - BMC Syst Biol (2011)

Simple metabolic network. (a) Standard network representation. Carbon atoms are drawn explicitly with arrows to indicate atom transitions. Unidirectional arrows represent unidirectional fluxes while bidirectional fluxes (such as flux 5) are represented by bidirectional arrows. (b) Fluxomers representation. Each arrow is a group of fluxomers. X's appear on the appropriate atom positions to indicate summation of divergent fluxomers.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750106&req=5

Figure 3: Simple metabolic network. (a) Standard network representation. Carbon atoms are drawn explicitly with arrows to indicate atom transitions. Unidirectional arrows represent unidirectional fluxes while bidirectional fluxes (such as flux 5) are represented by bidirectional arrows. (b) Fluxomers representation. Each arrow is a group of fluxomers. X's appear on the appropriate atom positions to indicate summation of divergent fluxomers.
Mentions: In the following, we show how to construct and solve MFA problems using fluxomer variables. First we define and explain the basic properties of fluxomers. Then we show how to express MFA balance equations and measurements in terms of fluxomers. Finally, we formulate the MFA optimization problem and present the FIA algorithm for solving it. Throughout this section we use boldface uppercase letters A to denote matrices, lowercase boldface letters x to denote vectors, and lowercase letters u for scalars. We use the <○ >product z = x○y to represent the element-wise product vector, i.e. zi = xiyi. The model formulation will be illustrated using the simple metabolic network shown in Figure 3.

Bottom Line: These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization.Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models.We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept. of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.

ABSTRACT

Background: The ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.

Results: This article addresses the mathematical and computational formulation of (13)C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.

Conclusions: Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.

Show MeSH
Related in: MedlinePlus