AF:III: small: Convex optimization for protein-protein interaction network alignment

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High-throughput experimental techniques have been producing a large amount of protein-protein interaction (PPI) data. Comparative analysis (e.g., alignment) of PPI networks greatly benefits the understanding of evolutionary relationship among species, helps identify functional modules and provides information for protein function annotations. The research goal of this proposal is to study optimization methods that can align PPI networks much more accurately than existing methods. This proposal will apply several elegant and powerful optimization techniques to understand the mathematical structure of the problem and develop efficient alignment algorithms. This proposal will also develop software implementing the proposed algorithms. The proposed algorithms will be implemented as both a standalone program and Cytoscape plugin so that they can be easily used by biologists. The resultant software and plugin shall benefit a broad range of biological and biomedical applications, such as protein functional annotation, understanding of disease processes, design of novel diagnostics and drugs, and precision medicine. The research results will be disseminated to the optimization, computer vision/graphics and biology communities through a variety of venues. The source code will be released so that it can be useful to other network analysis researchers who want to adapt the code for their own research projects and to other optimization method researchers who want to work on biological network analysis. This project will train a few PhD students and summer interns, who will receive training in the intersection of optimization techniques, network biology and programming. Undergraduate and underrepresented students will be recruited through our summer intern program, CRA-W and collaborators. The research results will be integrated into course materials and used in an Illinois online bioinformatics program that has trained many underrepresented students. This proposal will study a novel convex optimization algorithm for the alignment of two or multiple PPI networks. This convex method distinguishes itself from the widely-used seed-and-extension or progressive alignment strategy in that it simultaneously aligns all the input networks and proteins while the latter methods use a greedy strategy to build an alignment. A greedy strategy may introduce alignment errors at an early stage that cannot be fixed later, but this convex method can avoid this. Due to its simultaneous alignment strategy, this convex method shall detect many more proteins that are functionally conserved across all input PPI networks than existing methods and produce more accurate pairwise alignments of multiple networks. This proposal will also study a few methods to speed up the proposed convex alignment method, by making use of special topology properties of PPI networks and exploring low-rank representation of proteins. Finally, this proposal will implement the proposed algorithms as a standalone software package and Cytoscape plugin to greatly facilitate the application of comparative network analysis to biological and biomedical science discovery.