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Open Access Open Badges Research article

A phase synchronization clustering algorithm for identifying interesting groups of genes from cell cycle expression data

Chang Sik Kim1*, Cheol Soo Bae2 and Hong Joon Tcha3

Author Affiliations

1 Institute of Animal Resources Research, Kangwon National University, Chuncheon, Republic of Korea

2 Department of Biomedical Engineering, Kwandong University, Kangnung, Republic of Korea

3 Department of Information Technology, Kangwon National University, Chuncheon, Republic of Korea

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BMC Bioinformatics 2008, 9:56  doi:10.1186/1471-2105-9-56

Published: 28 January 2008



The previous studies of genome-wide expression patterns show that a certain percentage of genes are cell cycle regulated. The expression data has been analyzed in a number of different ways to identify cell cycle dependent genes. In this study, we pose the hypothesis that cell cycle dependent genes are considered as oscillating systems with a rhythm, i.e. systems producing response signals with period and frequency. Therefore, we are motivated to apply the theory of multivariate phase synchronization for clustering cell cycle specific genome-wide expression data.


We propose the strategy to find groups of genes according to the specific biological process by analyzing cell cycle specific gene expression data. To evaluate the propose method, we use the modified Kuramoto model, which is a phase governing equation that provides the long-term dynamics of globally coupled oscillators. With this equation, we simulate two groups of expression signals, and the simulated signals from each group shares their own common rhythm. Then, the simulated expression data are mixed with randomly generated expression data to be used as input data set to the algorithm. Using these simulated expression data, it is shown that the algorithm is able to identify expression signals that are involved in the same oscillating process. We also evaluate the method with yeast cell cycle expression data. It is shown that the output clusters by the proposed algorithm include genes, which are closely associated with each other by sharing significant Gene Ontology terms of biological process and/or having relatively many known biological interactions. Therefore, the evaluation analysis indicates that the method is able to identify expression signals according to the specific biological process. Our evaluation analysis also indicates that some portion of output by the proposed algorithm is not obtainable by the traditional clustering algorithm with Euclidean distance or linear correlation.


Based on the evaluation experiments, we draw the conclusion as follows: 1) Based on the theory of multivariate phase synchronization, it is feasible to find groups of genes, which have relevant biological interactions and/or significantly shared GO slim terms of biological process, using cell cycle specific gene expression signals. 2) Among all the output clusters by the proposed algorithm, the cluster with relatively large size has a tendency to include more known interactions than the one with relatively small size. 3) It is feasible to understand the cell cycle specific gene expression patterns as the phenomenon of collective synchronization. 4) The proposed algorithm is able to find prominent groups of genes, which are not obtainable by traditional clustering algorithm.