### Abstract

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

Pages (from-to) | 323-357 |

Number of pages | 35 |

Journal | Bulletin of Mathematical Biology |

Volume | 65 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Mar 2003 |

### Fingerprint

### Keywords

- Algorithms
- Animals
- Carbon
- Cluster Analysis
- Computational Biology
- Computer Simulation
- Computer-Aided Design
- Metabolism
- Models, Biological
- Mutation
- Statistical Distributions

### Cite this

*Bulletin of Mathematical Biology*,

*65*(2), 323-357. https://doi.org/10.1016/S0092-8240(03)00002-8

**Stoichiometric design of metabolic networks : multifunctionality,clusters, optimization, weak and strong robustness.** / Ebenhoeh, Oliver; Heinrich, Reinhart.

Research output: Contribution to journal › Article

*Bulletin of Mathematical Biology*, vol. 65, no. 2, pp. 323-357. https://doi.org/10.1016/S0092-8240(03)00002-8

}

TY - JOUR

T1 - Stoichiometric design of metabolic networks

T2 - multifunctionality,clusters, optimization, weak and strong robustness

AU - Ebenhoeh, Oliver

AU - Heinrich, Reinhart

PY - 2003/3/1

Y1 - 2003/3/1

N2 - Starting from a limited set of reactions describing changes in the carbon skeleton of biochemical compounds complete sets of metabolic networks are constructed. The networks are characterized by the number and types of participating reactions. Elementary networks are defined by the condition that a specific chemical conversion can be performed by a set of given reactions and that this ability will be lost by elimination of any of these reactions. Groups of networks are identified with respect to their ability to perform a certain number of metabolic conversions in an elementary way which are called the network's functions. The number of the network functions defines the degree of multifunctionality. Transitions between networks and mutations of networks are defined by exchanges of single reactions. Different mutations exist such as gain or loss of function mutations and neutral mutations. Based on these mutations neighbourhood relations between networks are established which are described in a graph theoretical way. Basic properties of these graphs are determined such as diameter, connectedness, distance distribution of pairs of vertices. A concept is developed to quantify the robustness of networks against changes in their stoichiometry where we distinguish between strong and weak robustness. Evolutionary algorithms are applied to study the development of network populations under constant and time dependent environmental conditions. It is shown that the populations evolve toward clusters of networks performing a common function and which are closely neighboured. Under changing environmental conditions multifunctional networks prove to be optimal and will be selected.

AB - Starting from a limited set of reactions describing changes in the carbon skeleton of biochemical compounds complete sets of metabolic networks are constructed. The networks are characterized by the number and types of participating reactions. Elementary networks are defined by the condition that a specific chemical conversion can be performed by a set of given reactions and that this ability will be lost by elimination of any of these reactions. Groups of networks are identified with respect to their ability to perform a certain number of metabolic conversions in an elementary way which are called the network's functions. The number of the network functions defines the degree of multifunctionality. Transitions between networks and mutations of networks are defined by exchanges of single reactions. Different mutations exist such as gain or loss of function mutations and neutral mutations. Based on these mutations neighbourhood relations between networks are established which are described in a graph theoretical way. Basic properties of these graphs are determined such as diameter, connectedness, distance distribution of pairs of vertices. A concept is developed to quantify the robustness of networks against changes in their stoichiometry where we distinguish between strong and weak robustness. Evolutionary algorithms are applied to study the development of network populations under constant and time dependent environmental conditions. It is shown that the populations evolve toward clusters of networks performing a common function and which are closely neighboured. Under changing environmental conditions multifunctional networks prove to be optimal and will be selected.

KW - Algorithms

KW - Animals

KW - Carbon

KW - Cluster Analysis

KW - Computational Biology

KW - Computer Simulation

KW - Computer-Aided Design

KW - Metabolism

KW - Models, Biological

KW - Mutation

KW - Statistical Distributions

U2 - 10.1016/S0092-8240(03)00002-8

DO - 10.1016/S0092-8240(03)00002-8

M3 - Article

VL - 65

SP - 323

EP - 357

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 2

ER -