Avalanches, branching ratios, and clustering of attractors in Random Boolean Networks and in the segment polarity network of \emph{Drosophila}

Details Avalanches, branching ratios, and clustering of attractors in Random Boolean Networks and in the segment polarity network of \emph{Drosophila} Avalanches, branching ratios, and clustering of attractors in Random Boolean Networks and in the segment polarity network of \emph{Drosophila}

2008-05-02

arxiv.org/abs/0805.0326v1

Physics

Biological Physics

Scientific paper

10.1088/1367-2630/10/6/063002

We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in Random Boolean Networks (RBNs) and in the \emph{Drosophila} polarity network by exact enumeration. A transient time is the duration of the transient from a starting state to an attractor. An avalanche is a special transient which starts as single Boolean element perturbation of an attractor state. Significant differences at short times between the avalanche and the transient times for RBNs with small connectivity $K$ -- compared to the number of elements $N$ -- indicate that attractors tend to cluster in configuration space. In addition, one bit flip has a non-negligible chance to put an attractor state directly onto another attractor. This clustering is also present in the segment polarity gene network of \emph{Drosophila melanogaster}, suggesting that this may be a robust feature of biological regulatory networks. We also define and measure a branching ratio for the state space networks and find evidence for a new time scale that diverges roughly linearly with $N$ for $2\leq K \ll N$. Analytic arguments show that this time scale does not appear in the random map nor can the random map exhibit clustering of attractors. We further show that for K=2 the branching ratio exhibits the largest variation with distance from the attractor compared to other values of $K$ and that the avalanche durations exhibit no characteristic scale within our statistical resolution. Hence, we propose that the branching ratio and the avalanche duration are new indicators for scale-free behavior that may or may not be found simultaneously with other indicators of emergent complexity in extended, deterministic dynamical systems.

Affiliated with

Also associated with

No associations

Rating

Avalanches, branching ratios, and clustering of attractors in Random Boolean Networks and in the segment polarity network of \emph{Drosophila} does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Avalanches, branching ratios, and clustering of attractors in Random Boolean Networks and in the segment polarity network of \emph{Drosophila}, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Avalanches, branching ratios, and clustering of attractors in Random Boolean Networks and in the segment polarity network of \emph{Drosophila} will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-512530