The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks
- How life both diversifies and maintains its function in the face of random mutation is an open question: we model the networks describing interactions between genes to explore this evolutionary tradeoff
To explore this question, we consider a class of key players in biological functionality: gene regulatory networks (GRNs), which describe how genes regulate each others' production in our cells. The products of one gene may lead to increased or decreased expression of another gene's products; this regulation is used by the cell to control its contents in response to signalling and sensory inputs.
In this paper, in the Journal of Theoretical Biology here (free here), we investigate the effects of mutations on the functions of model GRNs. Specifically, we calculate the different types of behaviour that a model GRN can show -- some of these involve a fixed state where every gene is either on or off, and some involve a cycling process where genes periodically switch on then off in a fixed pattern. We modelled mutations by randomly removing parts of the network, and explored how these mutations changed the GRN behaviour. If a random mutation changed the behaviour of the GRN (for example, changing the switching patterns of a gene), it is more evolvable; if the behaviour stays the same after a mutation, it is more robust.
(top) Several model GRNs: dots are genes, arrows describe one gene enhancing the production of another; flat ends describe one gene decreasing the production of another. (bottom) The gene states that each network can experience. Each point is a different on/off pattern of genes; the loops in the centre of the "flowers" are cycles of gene states that all connected states eventually collapse down to over time.
We found that the structure of a GRN dramatically affects the influence of mutations. We investigated so-called "Erdos-Renyi" (ER) structures, where nodes are connected randomly, and "scale-free" (SF) structures, where some "hub" nodes are connected to lots of others, but many more nodes connect only to very few neighbours. Social networks are often SF, with a small number of highly connected people and a large number of less connected one. SF networks were both more evolvable and more robust in the face of random mutations than ER ones: fewer mutations changed their behaviour, but those mutations that did have an effect gave rise to a more diverse set of new behaviours. We also found that SF networks were more robust to changes in environment (random changes to individual gene states). In biology we often observe that GRNs are scale-free: this work suggests the evolutionary advantages enjoyed by this class of networks, and thus a possible explanation for their appearance in biology. Iain