Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network

We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for mutations. When link addition is dominant, an infinite-order percolation transition arises as a function of the addition rate. In the opposite limit of high duplication rate, the network exhibits giant structural fluctuations in different realizations. For biologically-relevant growth rates, the node degree distribution has an algebraic tail with a peculiar rate dependence for the associated exponent.