Proximity of intracellular regulatory networks to monotone systems.

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.