A graph-based method to introduce approximations in kinetic networks

Simplification of models of complex kinetic networks is essential for purposes of optimization and control. A common technique for complexity reduction is to use equilibrium assumptions for reactions and species to eliminate species from the network. For models of larger kinetic networks and multiple equilibrium relations, the manifold that characterizes the response of the model subject to the equilibrium relations can only be approximated. We introduce a greedy-type algorithm to select a set of equilibrium relations in such a manner this manifold can be expressed analytically. This algorithm uses the interaction graph that represents the dependencies between equilibrium relations. If the equilibrium relations are selected such that the interdependency is minimized, analytical expressions for decoupled groups of equilibrium relations can be found. An objective function characterizes the trade-off between the order, the accuracy and the complexity of the reduced model. This objective function is maximized through the selection of equilibrium relations.