Biochemical reaction systems – system theory and decomposition

Biochemical reaction networks may be modeled as biochemical reaction systems consisting of differential equations with rational functions. Biochemical reaction systems are defined as rational positive dynamic systems with inputs and outputs, and illustrated by examples. This formulation makes available the results from algebraic system theory for rational systems and a relation with computer algebra. It is shown how to decompose networks into subsystems and how to relate them to graphs. The realization problem for this class of systems is briefly discussed. Finally, control problems for biochemical reaction networks are formulated.