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An Approach for Dividing Models of Biological Reaction Networks into Functional Units

Michael Ederer

Institute of System Dynamics and Control Engineering, University of Stuttgart Pfaffenwaldring 9 70569 Stuttgart, Germany, ederer{at}isr.uni-stuttgart.de

Thomas Sauter

Institute of System Dynamics and Control Engineering, University of Stuttgart Pfaffenwaldring 9 70569 Stuttgart, Germany

Eric Bullinger

Institute for Systems Theory in Engineering, University of Stuttgart Pfaffenwaldring 9 70569 Stuttgart, Germany

Ernst-Dieter Gilles

Max Planck Institute, Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg, Germany

Frank Allgöwer

Institute for Systems Theory in Engineering, University of Stuttgart Pfaffenwaldring 9 70569 Stuttgart, Germany

Biological reaction networks consist of many substances and reactions between them. Like many other biological systems, they have a modular structure. Therefore, a division of a biological reaction network into smaller units highly facilitates its investigation. The authors propose an algorithm to divide an ordinary differential equation (ODE) model of a biological reaction network hierarchically into functional units. For every compound, an activity function dependent on concentration or concentration change rate is defined. After performing suitable simulations, distances between the compounds are computed by comparing the activities along the trajectories of the simulation. The distance information is used to generate a dendrogram revealing the internal structure of the reaction network. The algorithm identifies functional units in two models of different networks: catabolite repression in Escherichia coli and epidermal growth factor (EGF) signal transduction in mammalian cells.

Key Words: Systems biology • functional units • biochemical reaction networks • systems analysis • cluster analysis

SIMULATION, Vol. 79, No. 12, 703-716 (2003)
DOI: 10.1177/0037549703040940
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