Proteins with large influence on network dynamics evolve slowly

Studies of protein evolution typically take a coarse view of protein function. Here I take a much finer view, using detailed mechanistic models to measure the influence of each constituent protein on its network’s dynamics. I show that a protein’s dynamical influence and its evolutionary rate are negatively correlated, implying purifying selection on network dynamics. Correlation coefficients are typically of order-0.3, among the strongest known correlates of evolutionary rate. Moreover, this correlation is independent of interaction degree, expression level, and knock-out essentiality. Dynamical influence The inclusive measure of dynamics, χ2, sums over all dynamical species in the network [Gutenkunst (2007)]. The dynamical influence κi of parameter i is (see Figure 1A) The dynamical influence of a protein is the mean influence of parameters governing reactions the protein participates in. For example, in the network shown in Figure 1B the influence of Ras incorporates all the highlighted reactions. Evolutionary rate Maximum-likelihood dN/dS values were inferred with PAML, using alignments and sequences from Homologene an