Self-organized critical random Boolean networks

Physical Review E, 2010

We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical connectivity kc = 2. Also, we show that both, pairwise correlation and complexity measures are maximized in dynamically critical networks. These results are in good agreement with the previously reported studies on random Boolean networks and random threshold networks, and show once again that critical networks provide an optimal coordination of diverse behavior.

2008

Abstract Random Boolean Networks (RBNs) are discrete dynamical systems which have been used to model Gene Regulatory Networks. We investigate the well-known phase transition between ordered and chaotic behavior in RBNs from the perspective of the distributed computation conducted by their nodes. We use a recently published framework to characterize the distributed computation in terms of its underlying information dynamics: information storage, information transfer and information modification.

2006

The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between topology and dynamics during the evolution. The final evolved state is shown to be independent of initial conditions. The network appears to be driven to a random Boolean network with uniform in-degree of two in the large network limit. However, for biologically realized network sizes, significant finite-size effects are observed including a broad in-degree distribution and an average in-degree connection between two and three. These results may be important for explaining properties of gene regulatory networks.

Physical Review Letters, 2003

Physical Review E, 2005

In this paper we study in detail the behavior of random-walk networks ͑RWN's͒. These networks are a generalization of the well-known random Boolean networks ͑RBN's͒, a classical approach to the study of the genome. RWN's are also discrete networks, but their response is defined by small variations in the state of each gene, thus being a more realistic representation of the genome and a natural bridge between discrete and continuous models. RWN's show a clear transition between order and disorder. Here we explicitly deduce the formula of the critical line for the annealed model and compute numerically the transition points for quenched and annealed models. We show that RBN's and the annealed model of RWN's act as an upper and a lower limit for the quenched model of RWN's. Finally we calculate the limit of the annealed model for the continuous case.

2010

Random Boolean networks (RBNs) are models of genetic regulatory networks. It is useful to describe RBNs as self-organizing systems to study how changes in the nodes and connections affect the global network dynamics. This article reviews eight different methods for guiding the self-organization of RBNs. In particular, the article is focussed on guiding RBNs towards the critical dynamical regime, which is near the phase transition between the ordered and dynamical phases. The properties and advantages of the critical regime for life, computation, adaptability, evolvability, and robustness are reviewed. The guidance methods of RBNs can be used for engineering systems with the features of the critical regime, as well as for studying how natural selection evolved living systems, which are also critical.

Working Papers, 1997

A new order parameter approximation to Random Boolean Networks (RBN) is introduced, based on the concept of Boolean derivative. A statistical argument involving an annealed approximation is used, allowing to measure the order parameter in terms of the statistical properties of a random matrix. Using the same formalism, a Lyapunov exponent is calculated, allowing to provide the onset of damage spreading through the network and how sensitive it is to single ips. Finnally, these measures are used in order to estimate the critical boundaries for chaos control in RBN.

Journal of Physics A: Mathematical and …, 1998

A variant of a simple method for chaos control is applied to achieve control in random Boolean networks (RBNs). It is shown that a RBN in the chaotic phase can be forced to behave periodically if a certain quenched fraction γ of the automata is given a fixed state (the system variables) every T time-steps. An analytic relationship between γ and T is derived using the size of the stable core as an order parameter.

Journal de Physique, 1987

2014 Nous avons étudié par simulation sur ordinateur l'apparition de structures spatiales dans les cycles limites des réseaux aléatoires d'automates cellulaires Booléens. Ces mesures ont porté sur les périodes locales des automates comparées à la période globale du réseau et sur la percolation des structures oscillantes. Le seuil de percolation de ces structures est le même que celui observé par Derrida et Stauffer pour le comportement des distances entre configurations initialement différentes.

Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a theoretical viewpoint, since it is possible to tune their asymptotic behaviour from order to disorder. The usual approach characterizes network families as a whole, either by means of static or dynamic measures. We show here that a more detailed study, based on the properties of system's attractors, can provide information that makes it possible to predict with higher precision important properties, such as system's response to gene knock-out. A new set of principled measures is introduced, that explains some puzzling behaviours of these networks. These results are not limited to random Boolean network models, but they are general and hold for any discrete model exhibiting similar dynamical characteristics.