Abstract
We investigate the sensitivity of Boolean Networks (BNs) to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs). We adopt Ribeiro and Kauffman’s Ergodic Set and use it to study the long term dynamics of a BN. We define the sensitivity of a BN to be the mean change in its Ergodic Set structure under all possible loss of interaction mutations. Insilico experiments were used to selectively evolve BNs for sensitivity to losing interactions. We find that maximum sensitivity was often achievable and resulted in the BNs becoming topologically balanced, i.e. they evolve towards network structures in which they have a similar number of inhibitory and excitatory interactions. In terms of the dynamics, the dominant sensitivity strategy that evolved was to build BNs with Ergodic Sets dominated by a single long limit cycle which is easily destabilised by mutations. We discuss the relevance of our findings in the context of Stem Cell Differentiation and propose a relationship between pluripotent stem cells and our evolved sensitive networks.
Highlights
The robustness of biochemical networks in noisy environments is thought to be a key property of properly functioning cells [1,2,3]
We find that evolving for sensitivity to mutations of this type leads to what we call topologically balanced networks, which have a similar number of excitatory and inhibitory interactions
The first we describe as being topologically balanced, whereas the second relates to the presence of long limit cycles in their Ergodic Set (ES), which collapse under deletion mutations
Summary
The robustness of biochemical networks in noisy environments is thought to be a key property of properly functioning cells [1,2,3]. They differ considerably from the sensitivity measure we employ later, which considers changes in the longterm dynamics of a Boolean Network resulting from permanent interaction losses.
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