13C-FLUX Web Page

 

Contents

Metabolic Flux Analysis

Carbon Labeling Experiments (CLEs)

Evaluation of CLEs

Statistical Analysis

Features of 13C-FLUX

System Requirements

Availability

Documentation and Further Reading

Software Download

Full Version for Academic Usage

Metabolic Flux Analysis

    In recent years, metabolic flux analysis (MFA) has become one of the major tools in metabolic engineering. The aim of MFA is the detailed quantification of all metabolic fluxes in the central metabolism of a microorganism. The result is a flux map that shows the distribution of anabolic and catabolic fluxes over the metabolic network (Figure 1). Based on such a flux map or a comparison of different flux maps, possible targets for genetic modifications might be identified, the result of an already performed genetic manipulation can be judged or conclusions about the cellular energy metabolism can be drawn.

    Figure 1: Two flux maps from Corynebacterium glutamicum under growth and lysine producing conditions. The pathways are abbreviated by: emp - Embden Meyerhof Parnas Pathway, ppp - Pentose Phosphate Pathway, tca - Tricarboxylic Acid Cycle, ana – Anaplerosis. Adapted from XXX.

Carbon Labeling Experiments (CLEs)

    13C MFA is based on a carbon labeling experiment (CLE). In such an experiment a specifically 13C labeled substrate like e.g. [1-13C]-glucose is fed to the biological system. The labeled carbon atoms are then distributed all over the metabolic network until finally the isotopic enrichment in the intracellular metabolite pools can be measured by NMR or MS instruments. The resulting data provide a large amount of information to quantitate the intracellular fluxes. Figure 2 summarizes the principle of 13C MFA: From measured extracellular fluxes and measured intracellular labeling information the intracellular fluxes have to be computed.

    Figure 2: Principle of 13C metabolic flux analysis: The intracellular forward and backward fluxes have to be determined from the measured extracellular fluxes and the measured intracellular labeling information.

Evaluation of CLEs

The evaluation of a CLE is based on a rather complicated mathematical model that describes how the labeled material distributes over the metabolic network. The centerpiece of data evaluation is a simulation of the CLE. In this simulation it is assumed that the intracellular fluxes are already known. Based on guessed flux values and the known input substrate composition the stationary distribution of 13C labeled molecules over the network can be computed.
Having established a simulator for CLEs, the most widely applied evaluation algorithm proceeds as follows (Figure 3):
  1. Guess some flux distribution over the metabolic network which fulfills the stoichiometric balance equations.
  2. Simulate a CLE based on this flux distribution and the known labeling state of the input substrate.
  3. From the outcoming isotopomer distribution compute the measured values that would come out if the guessed fluxes were present in system.
  4. Compute the difference between the measurements predicted by the simulation and those measurements which were really obtained. The discrepancy is usually measured by a sum of squares where each single residual value is weighted by the corresponding measurement standard deviation.
  5. Based on the computed discrepancy a systematic variation of the guessed fluxes is performed by applying an optimization algorithm. This implies an iteration of the steps 2-4.
Figure 3: Evaluation algorithm for MFA.

Statistical Analysis

After termination of the parameter fitting procedure a detailed statistical analysis of the estimated fluxes is necessary because biological systems and measurements are usually extremely noisy and thus the error propagation from the measurements to the estimated fluxes may lead to seemingly precise but statistically worthless results. The following statistical techniques for MFA have been established in recent years:
  1. The sensitivities of the measured values with respect to the estimated fluxes are collected in the output sensitivity matrix. This matrix shows which of the fluxes have the strongest influence on which of the measurements.
  2. From the output sensitivity matrix the flux covariance matrix of the estimated parameters can be immediately computed. From this covariance matrix a confidence region for fluxes can be derived. In particular a confidence interval can be assigned to each single estimated flux value.
  3. As a routine procedure a chi-square test is applied to the obtained minimal sum of squares. By this test the goodness of fit can be judged and possible gross measurement errors can be detected and excluded from the data set.

Features of 13C-FLUX

13C-FLUX is a universal software system for the modeling, simulation and evaluation of CLEs. Features of the software system are:
  1. Modeling of CLEs
    1. Fielded spread sheet (Network, Susbtrate, Mesurements)
    2. Syntax test on spread sheet
    3. Consistency test
    4. Detailed model analysing output-file (fdb-file)
    5. Procariontic detailed central metabolism model
  2. Simulation of CLEs
    1. Carbon labeling distribution for user given fluxes
  3. Flux Estimation - Parameter Fitting
    1. Simplex (Nelder-Mead)
    2. Evolutionary algorithm
    3. BFGS (gradient method)
    4. CFSQP (need additional licence agreement - free for academic)
  4. Statistical Analysis
    1. Deviations of fitted fluxes
    2. experimental design (a priori)

System Requirements

The 13C-Flux Toolkit is developed under Linux. Because the binaries (x86) are statically linked, there is a high probability that the software work under any newer Linux operating system on a intel compatible system. However some minimal requirements should be met.
Requirements for 13C-Flux:
Requirements for Helper-Tools:

Availability

13C-FLUX can be obtained in three different ways:
  1. A trial version with a restricted number of fluxes and isotopomers is available from this internet server (see Download) together with the first version of the reference manual. Currently, a tutorial is worked out in which a medium sized example is carried out step by step.
  2. For non-commercial usage at universities and research institutes the fully functioning system can be obtained for free from the authors provided that a contract is signed which excludes commercial usage. See Academic Usage.
  3. For commercial usage the software will be sold by
    METabolic EXplorer GmbH
    Karl-Heinz-Beckurtz-Straße 13
    D-52428 Jülich, Germany
    http://www.metabolic-explorer.com/

Documentation and Further Reading

    Downloads:

    Reference Manual, Version xyz (Link)

    Tutorial, Version xyz (Link)

    Installation Guide (Link)

    ME01-Mini Review

    A universal framework ...

    A gentle Introduction ...

    1997
    W. Wiechert, A.A. de Graaf.
    Bidirectional Reaction Steps in Metabolic Networks. Part I: Modeling and Simulation of Carbon Isotope Labeling
    Experiments.
    Biotechnology and Bioengineering, Vol. 55(1), pp. 101-117. (BB_Bidirectional_Reaction_Steps_Part_1.pdf)

    1997
    W. Wiechert, C. Siefke, A.A. de Graaf, A. Marx.
    Bidirectional Reaction Steps in Metabolic Networks. Part II: Flux Estimation and Statistical Analysis.
    Biotechnology and Bioengineering, Vol. 55(1), pp. 118-135. (BB_Bidirectional_Reaction_Steps_Part_2.pdf)

    1996
    W. Wiechert, A.A. de Graaf.
    In Vivo Stationary Flux Analysis by 13C Labeling Experiments.
    Advances in Biochemical Engineering / Biotechnology, Vol. 54, pp. 109-154.
    (In_Vivo_Stat_Flux_Ana_by_CLE.pdf)

    1995
    W. Wiechert, A.A. de Graaf, A. Marx.
    In vivo stationary flux determination using 13C NMR isotope labelling experiments.
    In: K. Schügerl, A. Munack (Eds.), IFAC CAB 6, Computer Applications in Biotechnology, Pergamon (In_Vivo_Stat_Flux_Det_using_CLE.pdf)

    1999
    Wiechert, M. Möllney, N. Isermann, M. Wurzel, A.A. de Graaf.
    Bidirectional Reaction Steps in Metabolic Networks. Part III: Explicit Solution and Analysis of Isotopomer Labeling Systems.
    Biotechnology and Bioengineering, Vol. 66(2), pp. 69-85. (BB_Bidirectional_Reaction_Steps_Part_3.pdf)

    1999
    M. Möllney, W. Wiechert, D. Kownatzki, A.A. de Graaf.
    Bidirectional Reaction Steps in Metabolic Networks. Part IV: Optimal Design of Isotopomer Labeling Experiments.
    Biotechnology and Bioengineering, Vol. 66(2), pp. 86-103. (BB_Bidirectional_Reaction_Steps_Part_4.pdf)

Software Download

    Trial version restricted to 17 fluxes.

    Online-Documentation (is also included in the Tar Archive):

    Download from this page

Full Version for Academic Usage

Download of Agreement:
Please download and send three signed copies of the agreement (PDF) and your E-Mail address to the following address
Prof. Wolfgang Wiechert
Abteilung Simulationstechnik, IMR, FB11
Paul-Bonatz-Str. 9-11
Universität Siegen
57068 Siegen
Germany
It will be signed by MetEx and Abteilung Simulationstechnik and one copy will be send back to you. The executable files will be sent to your E-Mail (approx. 12MB) address mentioned above.