Graph-Based Decomposition of Biochemical Reaction Networks into Monotone Subsystems

Large-scale model development for biochemical reaction networks of living cells is currently possible through qualitative model classes such as graphs, Boolean logic, or Petri nets. However, when it is important to understand quantitative dynamic features of a system, uncertainty about the networks often limits large-scale model development. Recent results, especially from monotone systems theory, suggest that structural network constraints can allow consistent system decompositions, and thus modular solutions to the scaling problem. Here, we propose an algorithm for the decomposition of large networks into monotone subsystems, which is a computationally hard problem. In contrast to prior methods, it employs graph mapping and iterative, randomized refinement of modules to approximate a globally optimal decomposition with homogeneous modules and minimal interfaces between them. Application to a medium-scale model for signaling pathways in yeast demonstrates that our algorithm yields efficient and biologically interpretable modularizations; both aspects are critical for extending the scope of (quantitative) cellular network analysis.