A simple physical model for scaling in protein-protein interaction networks

It has recently been demonstrated that many biological networks exhibit a scale-free topology where the probability of observing a node with a certain number of edges (k) follows a power law: i.e. p(k) ~ k^-g. This observation has been reproduced by evolutionary models. Here we consider the network of protein-protein interactions and demonstrate that two published independent measurements of these interactions produce graphs that are only weakly correlated with one another despite their strikingly similar topology. We then propose a physical model based on the fundamental principle that (de)solvation is a major physical factor in protein-protein interactions. This model reproduces not only the scale-free nature of such graphs but also a number of higher-order correlations in these networks. A key support of the model is provided by the discovery of a significant correlation between number of interactions made by a protein and the fraction of hydrophobic residues on its surface. The model presented in this paper represents the first physical model for experimentally determined protein-protein interactions that comprehensively reproduces the topological features of interaction networks. These results have profound implications for understanding not only protein-protein interactions but also other types of scale-free networks.