Comparative study of the transcriptional regulatory networks of E. coli and yeast: Structural characteristics leading to marginal dynamic stability

Dynamical properties of the transcriptional regulatory network of Escherichia coli and Saccharomyces cerevisiae are studied within the framework of random Boolean functions. The dynamical response of these networks to a single point mutation is characterized by the number of mutated elements as a function of time and the distribution of the relaxation time to a new stationary state, which turn out to be different in both networks. Comparison with the behavior of randomized networks reveals relevant structural characteristics other than the mean connectivity, namely the organization of circuits and the functional form of the in-degree distribution. The abundance of single-element circuits in E. coli and the broad in-degree distribution of S. cerevisiae shift their dynamics towards marginal stability overcoming the restrictions imposed by their mean connectivities, which is argued to be related to the simultaneous presence of robustness and adaptivity in living organisms.