Critical Dynamics in Genetic Regulatory Networks: Examples from Four Kingdoms

Enrique Balleza,Maximino Aldana,Alvaro Chaos,Ilya Shmulevich,Elena R. Alvarez-Buylla,Stuart Kauffman,Sui Huang

doi:10.1371/journal.pone.0002456

Abstract

The coordinated expression of the different genes in an organism is essential to sustain functionality under the random external perturbations to which the organism might be subjected. To cope with such external variability, the global dynamics of the genetic network must possess two central properties. (a) It must be robust enough as to guarantee stability under a broad range of external conditions, and (b) it must be flexible enough to recognize and integrate specific external signals that may help the organism to change and adapt to different environments. This compromise between robustness and adaptability has been observed in dynamical systems operating at the brink of a phase transition between order and chaos. Such systems are termed critical. Thus, criticality, a precise, measurable, and well characterized property of dynamical systems, makes it possible for robustness and adaptability to coexist in living organisms. In this work we investigate the dynamical properties of the gene transcription networks reported for S. cerevisiae, E. coli, and B. subtilis, as well as the network of segment polarity genes of D. melanogaster, and the network of flower development of A. thaliana. We use hundreds of microarray experiments to infer the nature of the regulatory interactions among genes, and implement these data into the Boolean models of the genetic networks. Our results show that, to the best of the current experimental data available, the five networks under study indeed operate close to criticality. The generality of this result suggests that criticality at the genetic level might constitute a fundamental evolutionary mechanism that generates the great diversity of dynamically robust living forms that we observe around us.

Highlights

There is evidence that many complex dynamical systems found in nature are critical; namely, they operate close to a phase transition between two different dynamical regimes [1]
Boolean Models of Genetic Networks Several models have been proposed to analyze the dynamics of genetic regulatory networks (GRN) [32,33,34,35]
The overwhelming majority of regulatory phrases for the gene transcription networks of E. coli, S. cerevisiae and B. subtilis are still unknown. Due to this lack of information, to implement the Boolean dynamics on the GRN of these three organisms we used biased random Boolean functions generated with a gene expression probability p inferred from microarray experiments. ( we show that the map M(x) does not change significantly for networks with a large fraction of canalizing functions.) Given the network topology, p can be estimated from microarray experiments by standard Bayessian parametric inference with two states

Summary

Introduction

There is evidence that many complex dynamical systems found in nature are critical; namely, they operate close to a phase transition between two different dynamical regimes [1]. Critical systems exhibit remarkable properties which would be difficult to explain without the assumption of criticality They can integrate, process and transfer information faster and more reliably than non critical systems [13]. They can detect and respond to external stimuli whose intensities span several orders of magnitude, like the brain [11]. These remarkable properties are mainly a consequence of the long-range correlations that emerge close to the critical point, producing collective behaviors and coordinated responses of the entire system. Criticality confers on the system the ability to collectively respond and adapt to an often rapidly changing environment

Methods

Results

Conclusion