Protein-protein interaction network inference from multiple kernels with optimization based on random walk by linear programming

Reconstruction of PPI networks is a central task in systems biology, and inference from multiple heterogeneous data sources offers a promising computational approach to making de novo PPI prediction by leveraging complementary information and the partial network structure. However, how to quickly learn weights for heterogeneous data sources remains a challenge. In this work, we developed a method to infer de novo PPIs by combining multiple data sources represented in kernel format and obtaining optimal weights based on random walk over the existing partial network. Our proposed method utilizes Baker algorithm and the training data to construct a transition matrix which constrains how a random walk would traverse the partial network. Multiple heterogeneous features for the proteins in the network, including gene expression and Pfam domain profiles, are then combined into the form of a weighted kernel, which provides a new adjacency matrix for the whole network but is required to comply with the transition matrix on the part of the training subnetwork. This requirement is met by adjusting the weights to minimize the element-wise difference between the transition matrix and the weighted kernel. The minimization problem is solved by linear programming. The weighted kernel is then transformed to regularized Laplacian (RL) kernel to infer missing or new edges in the PPI network. The results on synthetic data and real data from Yeast show that the accuracy of PPI prediction measured by AUC is increased by up to 19% as compared to a control method without using optimal weights. Moreover, the weights learned by our method Weight Optimization by Linear Programming (WOLP) are very consistent with that learned by sampling, and can provide insights into the relations between PPIs and various feature kernels, thereby improving PPI prediction.