Proximity of Intracellular Regulatory Networks to Monotone

Mount Sinai School of Medicine, Department of Pharmacology and Systems Therapeutics, USA.
IET Systems Biology (Impact Factor: 1.06). 06/2008; 2(3):103-12. DOI: 10.1049/iet-syb:20070036
Source: PubMed


Networks that contain only sign-consistent loops, such as positive feedforward and feedback loops, function as monotone systems. Simulated using differential equations, monotone systems display well-ordered behaviour that excludes the possibility for chaotic dynamics. Perturbations of such systems have unambiguous global effects and a predictability characteristic that confers robustness and adaptability. The authors assess whether the topology of biological regulatory networks is similar to the topology of monotone systems. For this, three intracellular regulatory networks are analysed where links are specified for the directionality and the effects of interactions. These networks were assembled from functional studies in the experimental literature. It is found that the three biological networks contain far more positive 'sign-consistent' feedback and feedforward loops than negative loops. Negative loops can be 'eliminated' from the real networks by the removal of fewer links as compared with the corresponding shuffled networks. The abundance of positive feedforward and feedback loops in real networks emerges from the presence of hubs that are enriched with either negative or positive links. These observations suggest that intracellular regulatory networks are 'close-to-monotone', a characteristic that could contribute to the dynamical stability observed in cellular behaviour.

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    • "They conclude that uniform random graphs perform the best. In the field of biology, the Erd˝ os-Rényi model is accepted as a basic model to study biological networks; [28] assesses the similarity of the topologies between biological regulatory networks and monotone systems, and uses the Erd˝ os-Rényi model is used as a model to compare against, when studying the properties of loops in three intracellular regulatory networks. In [30] this model is again applied to explore how activating and inhibiting connections influence network dynamics. "
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    • "An influence graph is a signed graph where the signs may have the already mentioned meaning of activatory/inhibitory action, or may simply represent the signature of the Jacobian linearization of a nonlinear vector field which is unknown but sign constant over the entire state space (common forms of the kinetics , such as mass-action and Michaelis-Menten, normally obey to this condition), see [3] [5]. In choosing this level of detail for our networks, we are guided by an abundant literature [5] [9] [15] [18] [22] [23] [30], and inspired in particular by a series of papers by E. Sontag and colleagues [1] [3] [17] [28] who showed monotone subsystems are obtained in one case, and a single large strongly monotone subnetwork in the other. Depending on the context, each of these approaches may be of help in better understanding the global structure of large systems and in investigating more properly their dynamical properties. "
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    • "The first three of these networks are considered also in [8] (the first is also in [4] and the third also in [10]). As for the E.coli transcriptional network, our version is almost double in size with respect to the other three (and with respect also to the version considered in [10]). "
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