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Based on previous studies related to the yeast cell cycle, it is well known that the underlying cellular network in yeast consists of many interactions between genes that have periodic expression patterns during the cell division cycle. In this study, it is proposed that cell cycle-specific gene expression can be understood as a phenomenon of collective synchronization or, in other words, an ensemble of non-identical oscillating response signals from different systems. Therefore, we aimed to apply the theory of statistical multivariate phase synchronization to understand the cell's cyclic transcriptome as a phenomenon of collective synchronization. To this end, a novel algorithm called Self-Organizing Maps with statistical Phase Synchronization (SOMPS) is proposed and evaluated using yeast cell cycle-specific gene expression data. From the evaluation experiments, we draw the following conclusions: 1) It is possible to find groups of genes that have biological interactions with each other and significantly share gene ontology slim terms of biological processes using the theory of multivariate phase synchronization with cell cycle-specific gene expression signals; 2) Among all output clusters of SOMPS, a relatively large cluster with high periodicity with respect to its trained mean field can be considered a prominent cluster; 3) For each gene, it is possible to identify the degree of the strength of its biological interactions with other genes using the coupling strength of synchronization with its trained mean field; and 4) It is feasible to understand cell cycle-specific expression patterns as a phenomenon of collective synchronization.

Self-Organizing Maps with Statistical Phase Synchronization (SOMPS) for Analyzing Cell Cycle-Specific Gene Expression Data