Building on the linear matrix inequality (LMI) formulation developed recently by Zavlanos et al. (Automatica: Special Issue Syst Biol 47(6):1113–1122, 2011), we present a theoretical framework and algorithms to derive a class of ordinary differential equation (ODE) models of gene regulatory networks using literature curated data and microarray data. The solution proposed by Zavlanos et al. (Automatica: Special Issue Syst Biol 47(6):1113–1122, 2011) requires that the microarray data be obtained as the outcome of a series of controlled experiments in which the network is perturbed by over-expressing one gene at a time. We note that this constraint may be relaxed for some applications and, in addition, demonstrate how the conservatism in these algorithms may be reduced by using the Perron–Frobenius diagonal dominance conditions as the stability constraints. Due to the LMI formulation, it follows that the bounded real lemma may easily be used to make use of additional information. We present case studies that illustrate how these algorithms can be used on datasets to derive ODE models of the underlying regulatory networks.
Linear models Gene regulatory networks Ordinary differential equations Linear matrix inequalities Convex optimization High throughput data