Dynamics of protein-protein interactions (PPIs) reveals the recondite principles of biological processes inside a cell. Shown in a wealth of study, just a small group of proteins, rather than the majority, play more essential roles at crucial points of biological processes. This present work focuses on identifying these critical proteins exhibiting dramatic structural changes in dynamic PPI networks. First, a comprehensive way of modeling the dynamic PPIs is presented which simultaneously analyzes the activity of proteins and assembles the dynamic coregulation correlation between proteins at each time point. Second, a novel method is proposed, named msiDBN, which models a common representation of multiple PPI networks using a deep belief network framework and analyzes the reconstruction errors and the variabilities across the time courses in the biological process. Experiments were implemented on data of yeast cell cycles. We evaluated our network construction method by comparing the functional representations of the derived networks with two other traditional construction methods. The ranking results of critical proteins in msiDBN were compared with the results from the baseline methods. The results of comparison showed that msiDBN had better reconstruction rate and identified more proteins of critical value to yeast cell cycle process.
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