Metabolic Flux Analysis

  • Tae Hoon YangEmail author
Part of the Methods in Pharmacology and Toxicology book series (MIPT)


In modern metabolomics, cellular reactions are observed as an integrated and networked system, termed as the metabolic network, instead of individual enzymatic reactions. Based on the metabolic network quantitated in terms of fluxes which are the rates at which materials are processed through the metabolic pathways, functional and regulatory activities of cells can be understood in its entirety. Typically, a realistic metabolic network which comprises catabolic and anabolic pathway fluxes of cells represents an underdetermined system from a stoichiometric viewpoint. This yields the intracellular fluxes that cannot be calculated from other fluxes measured. In order to determine those fluxes, 13C labeling information is most frequently applied. This involves mathematical models that compute distributions of fluxes together with experimental tools for 13C labeling analysis.

In this regard, understating the modeling techniques that aim the metabolic flux analysis using 13C isotopomer analysis is one central issue of metabolomics. Therefore, we describe the principle of different modeling strategies of the metabolic flux analysis in this chapter. First, we introduce the stoichiometry-based approach which is the foundation of the 13C-based approaches. Further to this, the modeling aspect of 13C-based approaches and related tools such as computer-aided optimal design of 13C labeling experiments and numerical computation of fluxes from measured 13C labeling states of metabolic products are treated. Also, the mathematical and statistical background is provided, which are relevant to the modeling of 13C-based metabolic flux analysis.

Key words

Metabolic Flux Analysis Isotopic Labeling Modeling 



Cumomers (cumulated isotopomers)

A set of one or more isotopomers whose particular carbon positions are labeled


A vector field whose components are the partial derivatives of a scalar function f

Hessian matrix

The square matrix of second-order partial derivatives of a function

Isotopologues (isotopic homologues)

Molecular species having identical elemental and chemical compositions but differ in isotopic content

Isotopomers (isotopic isomers)

Molecular species that differ by the location of isotopes on a compound

Jacobian matrix

The matrix of all first-order partial derivatives of a vector-valued function

Least-squares minimization

Numerical estimation of regression parameters by minimizing the sum of the squared residuals resulting from the difference between the model-predicted and measured values

Mass isotopomers

Groups of isotopomers classified in accordance with their nominal mass

Metabolic flux

The rate at which material is processed through a metabolic pathway defined in a metabolic network

Metabolic flux analysis

Quantification of metabolic fluxes in a metabolic network

Nonlinear programming

A numerical process of solving a system containing nonlinear nature

Null space of a matrix A

The set of all vectors x for which Ax = 0. The null space of a matrix with n columns is a linear subspace of n-dimensional Euclidean space


A process writing a function so that all the variables depend on the same variable (parameter)

Rank of a matrix

Maximal number of linearly independent rows (columns) in a matrix

Reduced row echelon form

A matrix obtained using Gauss–Jordan elimination with partial pivoting of its parent matrix


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Genomatica, Inc.San DiegoUSA

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