### 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.

Original language | English |
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Pages (from-to) | 1657-1686 |

Number of pages | 30 |

Journal | Journal of Mathematical Chemistry |

Volume | 53 |

Issue number | 8 |

DOIs | |

Publication status | Published - May 15 2015 |

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### Keywords

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

### ASJC Scopus subject areas

- Chemistry(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Chemistry*,

*53*(8), 1657-1686. https://doi.org/10.1007/s10910-015-0511-9

**Reaction network realizations of rational biochemical systems and their structural properties.** / Gábor, Attila; Hangos, K.; Banga, Julio R.; Szederkényi, G.

Research output: Contribution to journal › Article

*Journal of Mathematical Chemistry*, vol. 53, no. 8, pp. 1657-1686. https://doi.org/10.1007/s10910-015-0511-9

}

TY - JOUR

T1 - Reaction network realizations of rational biochemical systems and their structural properties

AU - Gábor, Attila

AU - Hangos, K.

AU - Banga, Julio R.

AU - Szederkényi, G.

PY - 2015/5/15

Y1 - 2015/5/15

N2 - 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.

AB - 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.

KW - Biochemical reaction graph

KW - Dynamic equivalence

KW - Dynamic models

KW - Parameter-free model analysis

UR - http://www.scopus.com/inward/record.url?scp=84938992980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938992980&partnerID=8YFLogxK

U2 - 10.1007/s10910-015-0511-9

DO - 10.1007/s10910-015-0511-9

M3 - Article

AN - SCOPUS:84938992980

VL - 53

SP - 1657

EP - 1686

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 8

ER -