Abstract: Protein function prediction is a fundamental task in the post-genomic era. Available functional annotations of proteins are incomplete and the annotations of two homologous species are complementary to each other. However, how to effectively leverage <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mutually complementary</i> annotations of different species to further boost the prediction performance is still not well studied. In this paper, we propose a cross-species protein function prediction approach by performing Asynchronous Random Walk on a heterogeneous network ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AsyRW</i> ). AsyRW first constructs a heterogeneous network to integrate multiple functional association networks derived from different biological data, established homology-relationships between proteins from different species, known annotations of proteins and Gene Ontology (GO). To account for the intrinsic structures of intra- and inter-species of proteins and that of GO, AsyRW quantifies the individual walk lengths of each network node using the gravity-like theory, and then performs asynchronous-random walk with the individual length to predict associations between proteins and GO terms. Experiments on annotations archived in different years show that individual walk length and asynchronous-random walk can effectively leverage the complementary annotations of different species, AsyRW has a significantly improved performance to other related and competitive methods. The codes of AsyRW are available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">http://mlda.swu.edu.cn/codes.php?name=AsyRW</uri> .
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