Understanding the evolution and structure of protein-protein interaction (PPI) networks is a central problem of systems biology. Since most processes in the cell are carried out by groups of proteins acting together, a theoretical model of how PPI networks develop based on duplications and mutations is an essential ingredient for understanding the complex wiring of the cell. Many different network models have been proposed, from those that follow power-law degree distributions and those that model complementarity of protein binding domains, to those that have geometric properties. Here, we introduce a new model for PPI network (and thus gene) evolution that produces well-fitting network models for currently available PPI networks. The model integrates geometric network properties with evolutionary dynamics of PPI network evolution.