R. Porreca, E. Cinquemani, J. Lygeros, and G. Ferrari-Trecate. Invalidation of the structure of genetic network dynamics: a geometric approach. International Journal of Robust and Nonlinear Control - Special Issue on System Identification for Biological Systems , 22(10):1140--1156, 2012.
This work concerns the identification of the structure of a genetic network model from measurements of geneproduct concentrations and synthesis rates. In earlier work, we developed a data preprocessing algorithmthat is able to reject many hypotheses on the network structure by testing certain monotonicity propertiesfor a wide family of network models. Here we develop a geometric interpretation of the method. Then,for a relevant subclass of genetic network models, we extend our approach to the combined testing ofmonotonicity and convexity-like properties associated with the network structures. The theoretical aspectsand practical performance of the enhanced methods are illustrated by way of numerical results.