We adapt a network simulation algorithm called quantitative simulation (QSim) for use in the alignment of biological networks. Unlike most network alignment methods, QSim finds local matches for one network in another, making it asymmetric, and takes full advantage of different edge types. We use QSim to simulate a protein-protein interaction (PPI) network from D. melanogaster using a PPI network from S. cerevisiae, and compare QSim's alignment to those from other methods using Gene Ontology (GO) biological process annotations as proxies for correct alignment matches. The best cross-species protein matches obtained from QSim have a higher agreement in GO biological process annotations than those from either BLAST or an alternative network alignment algorithm.