The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks

Abstract

We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SFin topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SFboth and SFout topologies. The functionality of the SFout topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SFout and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SFout topologies are also more robust to mutations than ER networks. Furthermore, the SFout topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.

16 pages, 15 figures

References in corpus (5)

• On the uniform generation of random graphs with prescribed degree sequences
• Neutral genetic drift can aid functional protein evolution
• Evolution favors protein mutational robustness in sufficiently large populations
• Evolution of a population of random Boolean networks
• Critical Boolean networks with scale-free in-degree distribution

Cited by in corpus (6)

• Algorithmic Networks: central time to trigger expected emergent open-endedness
• Boolean function metrics can assist modelers to check and choose logical rules
• Evolution of regulatory networks towards adaptability and stability in a changing environment
• Network evolution towards optimal dynamical performance
• Symmetry-based coarse-graining of evolved dynamical networks
• Starvation suppression in dense scale-free metabolic networks: Dynamical mean-field analysis of catalytic reaction networks