### Abstract

We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and hyperedges to reactions. Pathways are modelled as integer hyperflows and we expand the network model by detailed routing constraints. In contrast to the more traditional approaches like Flux Balance Analysis or Elementary Mode analysis we insist on integer-valued flows. While this choice makes it necessary to solve possibly hard integer linear programs, it has the advantage that more detailed mechanistic questions can be formulated. It is thus possible to query networks for general transformation motifs, and to automatically enumerate optimal and near-optimal pathways. Similarities and differences between our work and traditional approaches in metabolic network analysis are discussed in detail. To demonstrate the applicability of the mathematical framework to real-life problems we first explore the design space of possible non-oxidative glycolysis pathways and show that recent manually designed pathways can be further optimized. We then use a model of sugar chemistry to investigate pathways in the autocatalytic formose process. A graph transformation-based approach is used to automatically generate the reaction networks of interest.

Original language | English |
---|---|

Journal | IEEE/ACM Transactions on Computational Biology and Bioinformatics |

Volume | 16 |

Issue number | 2 |

Pages (from-to) | 510-523 |

ISSN | 1545-5963 |

DOIs | |

Publication status | Published - 1. Mar 2019 |

### Fingerprint

### Keywords

- autocatalysis
- Biological system modeling
- Chemicals
- chemistry
- Computational modeling
- Computer science
- formose
- hyperflow
- integer linear programming
- Mathematical model
- network flow
- non-oxidative glycolysis pathway
- Pathway
- reaction network
- Visualization

### Cite this

*IEEE/ACM Transactions on Computational Biology and Bioinformatics*,

*16*(2), 510-523. https://doi.org/10.1109/TCBB.2017.2781724

}

*IEEE/ACM Transactions on Computational Biology and Bioinformatics*, vol. 16, no. 2, pp. 510-523. https://doi.org/10.1109/TCBB.2017.2781724

**Chemical transformation motifs : modelling pathways as integer hyperflows.** / Andersen, Jakob L.; Flamm, Christoph; Merkle, Daniel; Stadler, Peter F.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Chemical transformation motifs

T2 - modelling pathways as integer hyperflows

AU - Andersen, Jakob L.

AU - Flamm, Christoph

AU - Merkle, Daniel

AU - Stadler, Peter F.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and hyperedges to reactions. Pathways are modelled as integer hyperflows and we expand the network model by detailed routing constraints. In contrast to the more traditional approaches like Flux Balance Analysis or Elementary Mode analysis we insist on integer-valued flows. While this choice makes it necessary to solve possibly hard integer linear programs, it has the advantage that more detailed mechanistic questions can be formulated. It is thus possible to query networks for general transformation motifs, and to automatically enumerate optimal and near-optimal pathways. Similarities and differences between our work and traditional approaches in metabolic network analysis are discussed in detail. To demonstrate the applicability of the mathematical framework to real-life problems we first explore the design space of possible non-oxidative glycolysis pathways and show that recent manually designed pathways can be further optimized. We then use a model of sugar chemistry to investigate pathways in the autocatalytic formose process. A graph transformation-based approach is used to automatically generate the reaction networks of interest.

AB - We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and hyperedges to reactions. Pathways are modelled as integer hyperflows and we expand the network model by detailed routing constraints. In contrast to the more traditional approaches like Flux Balance Analysis or Elementary Mode analysis we insist on integer-valued flows. While this choice makes it necessary to solve possibly hard integer linear programs, it has the advantage that more detailed mechanistic questions can be formulated. It is thus possible to query networks for general transformation motifs, and to automatically enumerate optimal and near-optimal pathways. Similarities and differences between our work and traditional approaches in metabolic network analysis are discussed in detail. To demonstrate the applicability of the mathematical framework to real-life problems we first explore the design space of possible non-oxidative glycolysis pathways and show that recent manually designed pathways can be further optimized. We then use a model of sugar chemistry to investigate pathways in the autocatalytic formose process. A graph transformation-based approach is used to automatically generate the reaction networks of interest.

KW - autocatalysis

KW - Biological system modeling

KW - Chemicals

KW - chemistry

KW - Computational modeling

KW - Computer science

KW - formose

KW - hyperflow

KW - integer linear programming

KW - Mathematical model

KW - network flow

KW - non-oxidative glycolysis pathway

KW - Pathway

KW - reaction network

KW - Visualization

U2 - 10.1109/TCBB.2017.2781724

DO - 10.1109/TCBB.2017.2781724

M3 - Journal article

C2 - 29990045

AN - SCOPUS:85039800502

VL - 16

SP - 510

EP - 523

JO - I E E E - A C M Transactions on Computational Biology and Bioinformatics

JF - I E E E - A C M Transactions on Computational Biology and Bioinformatics

SN - 1545-5963

IS - 2

ER -