Optimal Reconstruction of Graph Evolution Dynamics for Duplication-Based Models

Emre Sefer, Samuel Gilmour

Abstract: The research on biological network evolution and graph growth models, such as the Duplication-Mutation with Random Mutation (DMR) model, enable us to characterize the protein interaction network’s evolutionary dynamics founded on duplication and divergence via mutation in a principled way. The existing approaches to reconstruct historical ancestral graphs for DMR model mainly focus on greedy approaches and results in suboptimal solutions. In this study, we come up with ILP-DMR, a novel Integer Linear Programming (ILP)-based formulation, to reconstruct historical PPI graphs by likelihood maximization over DMR model. We assess the effectiveness of our approach in reconstructing the history of synthetic as well as optimal history of the proteins from the families of bZIP transcription factors. In comparison to the existing techniques, solutions returned by our ILP-DMR have a higher likelihood and are more robust to model mismatch and noise in the data. Solutions extracted by ILP-DMR have a higher likelihood than the existing methods, and our solutions better agree with the biological findings of different studies. Our datasets and code are available at https://github.com/seferlab/dmrhistory.