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. We find maximizations in information storage and coherent information transfer on either side of the critical point, allowing us to explain the phase transition in RBNs in terms of the intrinsic distributed computations they are undertaking.

In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the complexity reduction related to different updating schemes. We also report that all updating schemes yield very similar critical stability values, meaning that the “edge of chaos ” does not depend much on the updating scheme. After discussion, we conclude that synchonous RBNs are justifiable theoretical models of biological networks.

Background: A logical model of the known metabolic processes in S. cerevisiae was constructed from iFF708, an existing Flux Balance Analysis (FBA) model, and augmented with information from the KEGG online pathway database. The use of predicate logic as the knowledge representation for modelling enables an explicit representation of the structure of the metabolic network, and enables logical inference techniques to be used for model identification/improvement. Results: Compared to the FBA model, the logical model has information on an additional 263 putative genes and 247 additional reactions. The correctness of this model was evaluated by comparison with iND750 (an updated FBA model closely related to iFF708) by evaluating the performance of both models on predicting empirical minimal medium growth data/essential gene listings. Conclusion: ROC analysis and other statistical studies revealed that use of the simpler logical form and larger coverage results in no significant degradation of performance compared to iND750.

Evolution depends on the possibility of successfully exploring fitness landscapes via mutation and recombination. With these search procedures, exploration is difficult in ”rugged” fitness landscapes, where small mutations can drastically change functionalities in an organism. Random Boolean networks (RBNs), being general models, can be used to explore theories of how evolution can take place in rugged landscapes; or even change the landscapes. In this paper, we study the effect that redundant nodes have on the robustness of RBNs. Using computer simulations, we have found that the addition of redundant nodes to RBNs increases their robustness. We conjecture that redundancy is a way of ”smoothing ” fitness landscapes. Therefore, redundancy can facilitate evolutionary searches. However, too much robustness could reduce the rate of adaptation of an evolutionary process.

In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown that the statistical properties of Random Boolean networks change considerable according to the updating scheme. We study with computer simulations sensitivity to initial conditions as a measure of order/chaos. We find that independently of their updating scheme, all network types have very similar phase transitions, namely when the average number of connections of nodes is between one and three. This critical value depends more on the size of the network than on the updating scheme.

Abstract. We present and discuss the results of an experimental analysis in the design of Boolean networks by means of genetic algorithms. A population of networks is evolved with the aim of finding a network such that the attractor it reaches is of required length l. In general, any target can be defined, provided that it is possible to model the task as an optimisation problem over the space of networks. We experiment with different initial conditions for the networks, namely in ordered, chaotic and critical regions, and also with different target length values. Results show that all kinds of initial networks can attain the desired goal, but with different success ratios: initial populations composed of critical or chaotic networks are more likely to reach the target. Moreover, the evolution starting from critical networks achieves the best overall performance. This study is the first step toward the use of search algorithms as tools for automatically design Boolean networks with required properties. 1

This paper presents a conceptual framework for speaking about self-organizing systems. The aim is to provide a methodology useful for designing and controlling systems developed to solve complex problems. A brief introduction to complexity and selforganization is given before introducing the conceptual framework and the methodology. A case study on self-organizing traffic lights illustrates the ideas presented in the paper.

Abstract This paper considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number k of parent nodes, which is fixed for all nodes. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. We make use of a Boolean rule that is a generalization of rule 126 of elementary cellular automata. We provide formulae for the probability of finding a node in state 1 at a time t for the class of Asynchronous Random Boolean Networks (ARBN) in which only one node is updated at every time step, and for the class of Generalized ARBNs (GARBN) in which a random number of nodes can be updated at each time point. We use simulation methods to generate consecutive states of the network for both the real system and the models under the various schemes. The results match well. We study the dynamics of the models through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show, both theoretically and by example, that the ARBNs generate an ordered behavior regardless of the updating scheme used, whereas the GARBNs have behaviors that range from order to chaos depending on the type of random variable used to determine the number of nodes to be updated and the parameter combinations. 1.

In order to understand complex genetic regulatory networks researchers require automated formal modelling techniques that provide appropriate analysis tools. In this paper we propose a new qualitative model for genetic regulatory networks based on Petri nets and detail a process for automatically constructing these models using logic minimization. We take as our starting point the Boolean network approach in which regulatory entities are viewed abstractly as binary switches. The idea is to extract terms representing a Boolean network using logic minimization and to then directly translate these terms into appropriate Petri net control structures. The resulting compact Petri net model addresses a number of shortcomings associated with Boolean networks and is particularly suited to analysis using the wide range of Petri net tools. We demonstrate our approach by presenting a detailed case study in which the genetic regulatory network underlying the nutritional stress response in Escherichia coli is modelled and analysed.

Randomly connecting networks have proven to be universal computing machines. By interconnecting a set of nodes in a random way one can model very complicated non-linear dynamic systems. Although random Boolean networks (RBN) use Boolean functions as their basic component, there are not hardware implementations of such systems. The absence of implementations is mainly due to the arbitrary connectionism exhibited by the network, and connection flexibility use to be very expensive in terms of hardware resources. In this paper we present an onchip self-reconfigurable approach for providing a flexible connectionism at very low resource cost by partially reconfiguring Virtex II FPGAs. 1.