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.
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Acknowledgments Data on malaria was collected at the laboratory of Prof. Sanjeeva Srivastava, Department of Biosciences and Bioengineering, Indian Institute of Technology Bombay, Mumbai, India (IIT Bombay). The malaria data was cured, in parts, by Prof. Sanjeeva Srivastava at IIT Bombay and by Dr. Jyoti Dixit, Prateek Singh, and Ankit Potla at Strand Life Sciences, Bangalore, India. This research is supported, in parts, by NSF CAREER Award 0845650, NSF CCF 0946601, NSF CCF 1117168, NSF CDI Award EECS 0835632, and by Strand Life Sciences, Bangalore, India.
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- Convex optimization
- Gene regulatory networks
- High throughput data
- Linear matrix inequalities
- Linear models
- Ordinary differential equations