Perturbation propagation in random and evolved Boolean networks

Abstract

We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but non-random networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.

Evolving Boolean Networks on Tunable Fitness Landscapes

“…5 (average of 100 runs). Future work should consider other aspects of structure, such as motif analysis, and heterogeneous B values (e.g., after [21]) which may result in the emergence of small-world or scale-free topologies, for example.…”

“…See [5] for an overview of work evolving the related threshold networks to an attractor). The same approach has been used to explore attractor stability [21] and to model real regulatory network data, see [54] for an example using probabilistic RBN. Sipper and Ruppin [52] evolved RBN for the well-known density task.…”

Evolution of regulatory networks towards adaptability and stability in a changing environment

“…The mean connectivity has been shown to converge to k ∞ = 2 in some evolution models [32,[34][35][36]44], which is the critical point distinguishing the ordered and the chaotic phases in random Boolean networks [45]. Different values of k ∞ have been reported in other models [26,27], where k ∞ > 2, implying a fundamental difference between the evolved networks and random networks. In our model, k ∞ ranges from 1.2 to 1.7 for 30 N 800 and the data are fitted by a logarithmic growth with N as k ∞ ∼ 0.53 + 0.17 ln N [see Fig.…”

“…This model network is supposed to represent the network structure typical of a population. The evolution of Boolean networks towards enhancing adaptability [18][19][20][21][22], stability [23][24][25][26][27][28][29][30][31], or both [32] has been studied, mostly by applying the genetic algorithm or similar ones to a group of small networks. In particular, the model networks which evolve by rewiring links towards local dynamics being neither active nor inactive have been shown to reproduce the critical global connectivity and many of the universal features of real-world biological networks [33][34][35][36], demonstrating the close relation between evolution and the structure of biological networks.…”

On the evolution of Boolean networks for computation: a guide RNA mechanism

“…The same approach has been used to explore attractor stability [15] and to model real regulatory network data, eg, see [16] for an example using probabilistic RBN. Sipper and Ruppin [17] evolved RBN for the well-known density task and Bull [18] has evolved RBN ensembles to solve benchmark machine learning problems.…”