Exploring the Dynamic Organization of Random and Evolved Boolean Networks

Abstract

The properties of most systems composed of many interacting elements are neither determined by the topology of the interaction network alone, nor by the dynamical laws in isolation. Rather, they are the outcome of the interplay between topology and dynamics. In this paper, we consider four different types of systems with critical dynamic regime and with increasingly complex dynamical organization (loosely defined as the emergent property of the interactions between topology and dynamics) and analyze them from a structural and dynamic point of view. A first noteworthy result, previously hypothesized but never quantified so far, is that the topology per se induces a notable increase in dynamic organization. A second observation is that evolution does not change dramatically the size distribution of the present dynamic groups, so it seems that it keeps track of the already present organization induced by the topology. Finally, and similarly to what happens in other applications of evolutionary algorithms, the types of dynamic changes strongly depend upon the used fitness function.

A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems

“…Note that the method can be applied to numerous other situations. Limiting ourselves to applications most connected to biological systems, it has already been used for the analysis of autocatalytic organizations, metabolic pathways, genetic network models, [13,15,53] while analyses of cancer progression from individual patient mutation data (first results are available in [20]) and reconstructions of dynamic organizations from single cell data are underway.…”