Structurally robust biological networks
1 Dipartimento di Matematica ed Informatica, Universitá degli Studi di Udine, Via delle Scienze 206, 33100 Udine, Italy
2 Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd. Pasadena, CA 91125, USA
BMC Systems Biology 2011, 5:74 doi:10.1186/1752-0509-5-74Published: 17 May 2011
The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation.
In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature.
The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters.