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.
Unable to display preview. Download preview PDF.
- 4.Chen, W.W., Schoeberl, B., Jasper, P.J., Niepel, M., Nielsen, U.B., Lauffenburger, D.A., Sorger, P.K.: Input-output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data. Mol. Syst. Biol. 5, 239 (2009)Google Scholar
- 8.Hirsch, M., Smith, H.: Monotone dynamical systems. In: Handbook of Differential Equations: Ordinary Differential Equations, vol. 2, pp. 239–357 (2006)Google Scholar
- 14.Li, C., Donizelli, M., Rodriguez, N., Dharuri, H., Endler, L., Chelliah, V., Li, L., He, E., Henry, A., Stefan, M.I., Snoep, J.L., Hucka, M., Le Novère, N., Laibe, C.: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models.. BMC Systems Biology 4, 92 (2010)CrossRefGoogle Scholar
- 17.Sontag, E.: Monotone and near-monotone biochemical networks. LNCIS, vol. 357, pp. 79–122 (2007)Google Scholar
- 18.Soranzo, N., Ramezani, F., Iacono, G., Altafini, C.: Graph-theoretical decompositions of large-scale biological networks. Automatica (2010), conditionally acceptedGoogle Scholar