# Reaction network realizations of rational biochemical systems and their structural properties

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## Abstract

In this paper, a frequently used representation of mass-action type reaction networks is extended to a more general system class where the reaction rates are in rational function form. An algorithm is given to compute a possible reaction graph from the kinetic differential equations. However, this structure is generally non-unique, as it is illustrated through the phenomenon of dynamical equivalence, when different reaction network structures correspond to exactly the same dynamics. It is shown that under some technical assumptions, the so-called dense realization containing the maximal number of reactions, forms a super-structure in the sense that the reaction graph of any dynamically equivalent reaction network is the sub-graph of the dense realization. Additionally, optimization based methods are given to find dynamically equivalent realizations with preferred properties, such as dense realizations or sparse realizations. The introduced concepts are illustrated by examples.

## Keywords

Dynamic models Biochemical reaction graph Dynamic equivalence Parameter-free model analysis## Notes

### Acknowledgments

AG and JRB are supported by the funding from EU FP7 ITN “NICHE”, Project No. 289384. KMH is thankful for the funding from the Hungarian Scientific Research Fund through Grant K83440. GSz acknowledges the support of the Hungarian Scientific Research Fund through Grant NF104706.

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