A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations pp 181-210 | Cite as

# Model Reduction of Genetic-Metabolic Networks via Time Scale Separation

## Abstract

Model reduction techniques often prove indispensable in the analysis of physical and biological phenomena. A succesful reduction technique can substantially simplify a model while retaining all of its pertinent features. In metabolic networks, metabolites evolve on much shorter time scales than the catalytic enzymes. In this chapter, we exploit this discrepancy to justify the reduction via time scale separation of a class of models of metabolic networks under genetic regulation . We formalise the concept of a metabolic network and employ Tikhonov’s Theorem for singularly perturbed systems. We demonstrate the applicability of our result by using it to address a problem in metabolic engineering: the genetic control of branched metabolic pathways. We conclude by providing guidelines on how to generalise our result to larger classes of networks.

## Keywords

Time scale separation Model reduction Genetic-metabolic networks## Notes

### Acknowledgments

We thank Aivar Sootla for very useful discussions about various topics described in this chapter and Alexandros Houssein and Keshava Murthy for their valuable advice regarding how to improve this script.

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