Reduction techniques for network validation in systems biology.

The rapidly increasing amount of experimental biological data enables the development of large and complex, often genome-scale models of molecular systems. The simulation and analysis of these computer models of metabolism, signal transduction, and gene regulation are standard applications in systems biology, but size and complexity of the networks limit the feasibility of many methods. Reduction of networks provides a hierarchical view of complex networks and gives insight knowledge into their coarse-grained structural properties. Although network reduction has been extensively studied in computer science, adaptation and exploration of these concepts are still lacking for the analysis of biochemical reaction systems. Using the Petri net formalism, we describe two local network structures, common transition pairs and minimal transition invariants. We apply these two structural elements for network reduction. The reduction preserves the CTI-property (covered by transition invariants), which is an important feature for completeness of biological models. We demonstrate this concept for a selection of metabolic networks including a benchmark network of Saccharomyces cerevisiae whose straightforward treatment is not yet feasible even on modern supercomputers.