The evolutionary history of biological networks enables deep functional and evolutionary understanding of various bio-molecular processes. Network growth models, such as the Duplication-Mutation with Complementarity (DMC) model, provide a principled approach to characterizing the evolution of protein-protein interactions (PPI) based on duplication and divergence. Current methods for model-based ancestral network reconstruction, primarily use greedy heuristics and yield sub-optimal solutions.
We present a new Integer Linear Programming (ILP) solution for maximum likelihood reconstruction of ancestral PPI networks using the DMC model. By construction, our model is designed to find the optimal solution. It can also use efficient heuristics from general-purpose ILP solvers to obtain multiple optimal and near-optimal solutions that may be useful in many applications. Experiments on synthetic and real data show that our ILP obtains solutions with higher likelihood than those from previous methods. We evaluate our algorithm on two real PPI networks, with proteins from the families of bZIP transcription factors and Commander complex. On both the networks, solutions from our ILP has higher likelihood and are in better agreement with independent biological evidence from other studies. Availability A Python implementation is available at https://bitbucket.org/cdal/.