Bulletin of Mathematical Biology
, Volume 65, Issue 2, pp 323357
First online:
Stoichiometric design of metabolic networks: Multifunctionality, clusters, optimization, weak and strong robustness
 Oliver EbenhöhAffiliated withDepartment of Theoretical Biophysics, Institute of Biology, HumboldtUniversity
 , Reinhart HeinrichAffiliated withDepartment of Theoretical Biophysics, Institute of Biology, HumboldtUniversity Email author
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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.
 Title
 Stoichiometric design of metabolic networks: Multifunctionality, clusters, optimization, weak and strong robustness
 Journal

Bulletin of Mathematical Biology
Volume 65, Issue 2 , pp 323357
 Cover Date
 200303
 DOI
 10.1016/S00928240(03)000028
 Print ISSN
 00928240
 Online ISSN
 15229602
 Publisher
 SpringerVerlag
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 Authors

 Oliver Ebenhöh ^{(1)}
 Reinhart Heinrich ^{(1)}
 Author Affiliations

 1. Department of Theoretical Biophysics, Institute of Biology, HumboldtUniversity, Invalidenstra×e 42, 10115, Berlin, Germany