FLUX SPECTRUM APPROACH

The intracellular metabolism of living cells is usually represented by a metabolic network. This network encodes a set of elementary biochemical reactions taking place within the cell.

Metabolic flux analysis provides a methodology to determine the actual flux distribution using a metabolic network and a set of measured fluxes. To overcome some of its limitations, the flux spectrum approach has been recently introduced [1, 2, 3].

Thanks to the inclusion of reversibility constraints —based on a priori knowledge— and the consideration of the uncertainty of the measured fluxes, the flux spectrum approach provides two main advantages [1]:
  • a more reliable and richer estimation of the non-measured fluxes when the network is determined.
  • an estimation of the non-measured fluxes even if the network is underdetermined—when metabolic flux analysis cannot be used.

CALCULATION OF THE FLUX SPECTRUM

In [3] we have described a modified algorithm to compute the flux spectrum that overcomes a limitation of the one given in our previous works [1, 2]. The old algorithm can lead to a slight, but unnecessary, magnification of the effect of the uncertainty. We have checked that this effect is negligible in the examples used to illustrate our papers; However, the new algorithm will yield slightly better results in the general case.

B2. The following image summarizes the simplest method to compute the flux spectrum:

fsa

where S is the stoichiometric matrix, v the metabolic fluxes, vi the irreversible fluxes and vm the measured fluxes.

A2. There is another valid method to compute the flux spectrum, which keeps the division between measured and unknown fluxes used in the first proposals [1, 2]. Still not online... (available upon request)


download

SOFTWARE

You can download the matlab files that implement the new method to compute the flux spectrum. The compressed file contains two matlab functions and a simple example that illustrates its use.




RESOURCES

More information about the flux spectrum approach is given in different communications (journal articles, posters, slides, etc.):
  • these slides introduce the flux spectrum approach and its main applications.
  • The poster [3] gives a good summary of the flux spectrum approach.
  • The article in BMC [2] provides a detailed description of the flux spectrum features and its advantages over metabolic flux analysis.
  • The most illustrative application of the flux spectrum approach is given in [2].


REFERENCES

[1] Llaneras F, Picó J. A procedure for the estimation over time of metabolic fluxes in scenarios where measurements are uncertain and/or insufficient. BMC Bioinformatics, 2007, 8:421
[article - free open access]

[2] Llaneras F, Picó J. An interval approach for dealing with flux distributions and elementary modes activity patterns. Journal of Theoretical Biology, 2007, 246(2): 290-308.
[article]

[3] Llaneras F, Bastin G., Picó J: On metabolic flux analysis when measurements are insufficient and/or uncertain: the flux spectrum and the flux space. IAP Dysco workshop, Belgium, 2007.
[poster]

[4] Llaneras F, Tortajada M, Picó J: Structural analysis of metabolic pathways applied to heterologous protein production in P. Pastoris. Journal of Biotechnology. 131(2)S209, 13th European Congress on Biotechnology, 2007.
[reference] [poster]