### Abstract

Weak reversibility is a crucial structural property of chemical reaction networks (CRNs) with mass action kinetics, because it has major implications related to the existence, uniqueness and stability of equilibrium points and to the boundedness of solutions. In this paper, we present two new algorithms to find dynamically equivalent weakly reversible realizations of a given CRN. They are based on linear programming and thus have polynomial time-complexity. Hence, these algorithms can deal with large-scale biochemical reaction networks, too. Furthermore, one of the methods is able to deal with linearly conjugate networks, too.

Original language | English |
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Pages (from-to) | 1386-1404 |

Number of pages | 19 |

Journal | Journal of Mathematical Chemistry |

Volume | 52 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Chemical reaction networks
- Dynamical equivalence
- Linear conjugacy
- Optimization
- Weak reversibility

### ASJC Scopus subject areas

- Chemistry(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Chemistry*,

*52*(5), 1386-1404. https://doi.org/10.1007/s10910-014-0318-0

**Polynomial time algorithms to determine weakly reversible realizations of chemical reaction networks.** / Rudan, János; Szederkényi, G.; Hangos, K.; Péni, Tamás.

Research output: Contribution to journal › Article

*Journal of Mathematical Chemistry*, vol. 52, no. 5, pp. 1386-1404. https://doi.org/10.1007/s10910-014-0318-0

}

TY - JOUR

T1 - Polynomial time algorithms to determine weakly reversible realizations of chemical reaction networks

AU - Rudan, János

AU - Szederkényi, G.

AU - Hangos, K.

AU - Péni, Tamás

PY - 2014

Y1 - 2014

N2 - Weak reversibility is a crucial structural property of chemical reaction networks (CRNs) with mass action kinetics, because it has major implications related to the existence, uniqueness and stability of equilibrium points and to the boundedness of solutions. In this paper, we present two new algorithms to find dynamically equivalent weakly reversible realizations of a given CRN. They are based on linear programming and thus have polynomial time-complexity. Hence, these algorithms can deal with large-scale biochemical reaction networks, too. Furthermore, one of the methods is able to deal with linearly conjugate networks, too.

AB - Weak reversibility is a crucial structural property of chemical reaction networks (CRNs) with mass action kinetics, because it has major implications related to the existence, uniqueness and stability of equilibrium points and to the boundedness of solutions. In this paper, we present two new algorithms to find dynamically equivalent weakly reversible realizations of a given CRN. They are based on linear programming and thus have polynomial time-complexity. Hence, these algorithms can deal with large-scale biochemical reaction networks, too. Furthermore, one of the methods is able to deal with linearly conjugate networks, too.

KW - Chemical reaction networks

KW - Dynamical equivalence

KW - Linear conjugacy

KW - Optimization

KW - Weak reversibility

UR - http://www.scopus.com/inward/record.url?scp=84897429614&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897429614&partnerID=8YFLogxK

U2 - 10.1007/s10910-014-0318-0

DO - 10.1007/s10910-014-0318-0

M3 - Article

VL - 52

SP - 1386

EP - 1404

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 5

ER -