Network-based regulatory pathways analysis

Motivation: A useful approach to unraveling and understanding complex biological networks is to decompose networks into basic functional and structural units. Recent application of convex analysis to metabolic networks leads to the development of network-based metabolic pathway analysis and the decomposition of metabolic networks into metabolic extreme pathways that are true functional units of metabolic systems. Metabolic extreme pathways are derived from limited knowledge of the metabolic networks, but provide an integrated predictive description of metabolic networks. It is important to extend the concept of network-based metabolic pathways to genetic networks and develop mathematical procedures for network-based regulatory pathway analysis. Results: We have established Kirchhoff's first law in genetic networks and introduced a concept of gene flows using matrix decomposition method. The Kirchhoff's first law provides the theoretical foundations for mathematical framework for development defining network-based regulatory pathways, and applying convex analysis in decomposing the genetic networks into regulatory extreme pathways. We presented a new approach to characterize the extreme pathway and developed a new algorithm for identifying a set of extreme pathways. Convex analysis and extreme pathway structure provide a unified framework for functional and structural analysis of metabolic and genetic networks, which will increase our ability to analyze, interpret and predict the function of metabolic and genetic networks. The proposed models for network-based regulatory pathway analysis have been applied to apoptosis regulatory network.