Bioprocesses are often modeled based only on extracellular measurements. Under this situation, classical lumped models view the cell as a black-box converting substrates into products while neglecting the intracellular metabolism. Recently, there have been attempts to link macroscopic reaction models to the internal flux distribution assuming that intracellular reactions are always in quasi-steady state. Such models are identified based on adapting convex combinations of elementary mode fluxes to experimental data either by free choice as in the case of Provost et al.(2006), Zhou et al. (2006) and Provost and Bastin (2004) or by using cybernetic laws as in so-called hybrid cybernetic models (Kim, 2005).

Since there is often an infinite number of ways of distributing the measured fluxes among the elementary flux modes (EFMs), it is important to develop a consistent way of determining the minimal subset of EFMs necessary for the formulation of such “macro-micro” models. We propose the yield vector analysis (YVA) as a useful tool for designing the minimum structure of metabolic models.

The model reduction strategy of this work, based on YVA, is accomplished in two stages. It is possible to reduce the set of EFMs into a smaller subset, which fully describes all the phenotypic states generated by the original network model. This first stage of reduction is achieved by investigating the volume of the solution domain in the yield vector space, even before experimental measurements are available. The resulting reduced EFM set not only simplifies the model construction, but also facilitates the pathway analysis of the metabolic network. In the second stage, we pick up the minimum number of EFMs best-fitting experimental measurements among the previously reduced EFM set. This final choice defines the minimal subset of EFM for the metabolic model.

YVA also improves our understanding of the model structure. For example, through YVA, the relation between the number of available measurements and the size of the minimal subset of EFMs (Provost et al., 2006) is readily interpreted and the condition where the minimal EFM set is uniquely determined is clearly described.

Metabolism of S. cerevisiae has been chosen as a case study to show how YVA can be effectively used for the reduction of the EFM set and subsequently for a systematic construction of a hybrid cybernetic model.

References

Kim, J. I. (2005) A Hybrid Model of Anaerobic E. coli: Cybernetic Approach and Elementary Mode Analysis. MS Dissertation, Purdue University

Provost, A. and Bastin, G. (2004) Dynamic Metabolic Modelling under the Balanced Growth Condition. Journal of Process Control 14:717-728

Provost, A., Bastin, G., Agathos, S. N., Schneider, Y.-J. (2006) Metabolic Design of Macroscopic Bioreaction Models: Application to Chinese Hamster Ovary Cells. Bioprocess Biosyst Eng 29:349-366

Zhou, F. Bi, J.-X., Zeng, A.-P. and Yuan, J.-Q. (2006) A Macrokinetic and Regulator for Myeloma Cell Culture based on Metabolic Balance of Pathways. Process Biochemistry 41:2207-2217