Neutral evolution of proteins: The superfunnel in sequence space and its relation to mutational robustness

Following Kimura's neutral theory of molecular evolution [M. Kimura, The Neutral Theory of Molecular Evolution (Cambridge University Press, Cambridge, 1983) (reprinted in 1986)], it has become common to assume that the vast majority of viable mutations of a gene confer little or no functional advantage. Yet, in silico models of protein evolution have shown that mutational robustness of sequences could be selected for, even in the context of neutral evolution. The evolution of a biological population can be seen as a diffusion on the network of viable sequences. This network is called a "neutral network." Depending on the mutation rate μ and the population size N, the biological population can evolve purely randomly (μN1) or it can evolve in such a way as to select for sequences of higher mutational robustness (μN1). The stringency of the selection depends not only on the product μN but also on the exact topology of the neutral network, the special arrangement of which was named "superfunnel." Even though the relation between mutation rate, population size, and selection was thoroughly investigated, a study of the salient topological features of the superfunnel that could affect the strength of the selection was wanting. This question is addressed in this study. We use two different models of proteins: on lattice and off lattice. We compare neutral networks computed using these models to random networks. From this, we identify two important factors of the topology that determine the stringency of the selection for mutationally robust sequences. First, the presence of highly connected nodes ("hubs") in the network increases the selection for mutationally robust sequences. Second, the stringency of the selection increases when the correlation between a sequence's mutational robustness and its neighbors' increases. The latter finding relates a global characteristic of the neutral network to a local one, which is attainable through experiments or molecular modeling.