Abstract
To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a period of time because biologically related gene groups can share the same change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. This work is aimed at discovering gene groups with similar change patterns which share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. We applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cho, R. J., Campbell, M. J., Winzeler, E. A., Steinmetz, L., Conway, A., Wodicka, L., Wolfsberg, T. G., Gabrielian, A. E., Landsman, D., Lockhart, D. J. and Davi, R. W. (1998) A genome-wide transcriptional analysis of the mitotic cell cycle. Mol. Cell 2, 65–73.
Spellman, P. T., Sherlock, G., Zhang, M. Q., Iyer, V. R., Anders, K., Eisen, M. B., Brown, P. O., Botstein, D. and Futcher, B. (1998) Comprehensive identification of cell cycle-regulated genes of the yeast Saccaromyces cerevisiae by microarray hybridization. Mol. Biology of the Cell 9, 3273–3297.
Serban, N. and Wasserman, L. (2005) CATS: Clustering after transformation and smoothing. J. Amer. Statist. Assoc. 471, 990–999.
Ernst, J., Nau, G. J. and Bar-Joseph, Z. (2005) Clustering short time series gene expression data. Bioinformatics 21, 195–168.
Li, J. and Wong, L. (2002) Identifying good diagnostic gene groups from gene expression profiles using the concept of emerging patterns. Bioinformatics 18, 725–34.
Park, T., Yi, S. G., Lee, S., Lee, S. Y., Yoo, D., Ahn, J., and Lee, Y. (2003) Statistical tests for identifying differentially expressed gene in time-course microarray experiments. Bioinformatics 19, 694–703.
Lai, Y., Wu, B., Chen, L. and Zhao, H. (2004) A statistical method for identifying differential gene-gene co-expression patterns. Bioinformatics 20, 3146–55.
Zhang, L., Zhang, A. and Ramanathan, M. (2003) Fourier harmonic approach for visualizing temporal patterns of gene expression data. Proc. IEEE Comp. Sys. Bioinformatics Conf. 2, 137–147.
Murthy, K. R. K. and Hua, L. J. (2004) Improved Fourier transform method for unsupervised cell-cycle regulated gene prediction. Proc. IEEE Comp. Sys. Bioinformatics Conf. 194–203.
Kim, B., Littell, R. C. and Wu, R. (2006) Clustering periodic patterns of gene expression based on Fourier approximations. Current Genomics 7, 197–203.
Kim, J. and Kim, H. (2008) Clustering of change patterns using Fourier coefficients. Bioinformatics 24, 184–191.
Peddada,S., Lobenhofer, E., Li L., Afshari C., Weinberg C. and Umbach D. M. (2003) Gene selection and clustering for time-course and dose response microarray experiments using order-restricted inference. Bioinformatics 19, 834–841.
Johansson, D., Lindgren, P., Berglund, A., (2003) A multivariate approach applied to microarray data for identification of genes with cell cycle-coupled transcription. Bioinformatics 19, 467–473.
Schliep, A., Schōnhuth, A., Steinhoff, C., (2003) Using hidden Markov models to analyze gene expression time course data. Bioinformatics 19 (Suppl.), i255-i263.
Luan and Li (2003) Clustering of time-course gene expression data using a mixed-effects models with B-splines. Bioinformatics 19, 474–482.
Song J. J., Lee, H. J., Morris, J. S. and Kang, S. (2007) Clustering of time-course gene expression data using functional data analysis. Comp. Biol. and Chem. 31, 4, 265–274.
Bar-Joseph, Z. (2004) Analyzing time series gene expression data. Bioinformatics 20, 2493–2503.
Yeung, K. Y., Fraley, C., Murua, A., Raftery, A. E. and Ruzzo, W. L. (2001) Model based clustering and data transformations for gene expression data. Bioinformatics 17, 977–998.
Murtage, C. and Raftery, A. E. (1984) Fitting straight lines to point patterns. Pattern Recognition 17, 479–483.
Fraley, C. and Raftery, A. E. (2002) Model-based clustering, discriminant analysis and Density Estimation. J. Amer. Statist. Assoc. 97, 611–631.
Tolstov, G. P. (1962) Fourier analysis. McGraw-Hill, New York.
Stein, E. M. and Shakarchi, R. (2003) Fourier analysis. Princeton University Press, Princeton.
Lestrel, P. E. (1997) Fourier descriptors and their applications in biology. Cambridge University Press, London.
Eubank, R. and Hart, J. D. (1992) Testing goodness-of-fit via order selection criteria. Ann. Stat. 20, 3, 1412–1425.
Simon, R. M., Korn, E. L., McShane, L. M., Radmacher, M. D., Wright, G. W. and Zhao, Y. (2003) Design and analysis of DNA microarray investigations. Springer, New York.
Yeung, K. Y. and Ruzzo,W. L. (2001) An empirical study on principal component analysis for clustering gene expression data. Bioinformatics 17, 763–774.
Banfield, J. D., and Raftery, A. E. (1993) Model-based Gaussian and non-Gaussian clustering Biometrics 49, 803–821.
Beran, R. and Dumbgen, L. (1998) Modulation of estimators and confidence Sets. Ann. Stat. 26, 1826–1856.
Fraley, C. and Raftery, A.E. (1999) MCLUST: software for Model-based cluster analysis. J. Classif. 16, 297–306.
Freedman, D. and Lane, D. (1980) The Empirical distribution of Fourier coefficients. Ann. Stat. 8, 1244–1251.
Rousseeuw, P. J. (1987) Silhouettes: graphical aid to the interpretation and validation of cluster analysis. J. Comp. and Appl. Math 20, 53–65.
Kaufman, L. and Rousseeuw, P. J. (1990) Finding groups in data: An introduction to cluster analysis. Wiley, New York.
Ajuaje, F. (2002) A cluster validity framework for genome expression data. Biometrics 18, 319–320.
Beissbarth, T. and Speed, T. P. (2004) GOstat: Find statistically overrepresented Gene Ontologies within a group of genes. Bioinformatics 6, 20(9), 1464–1465.
MacQueen, J. B. (1967) Some Methods for classification and Analysis of Multivariate Observations, Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability. Berkeley. University of California Press, 1, 281–297.
Rowen, D. W., Meinke, M. and LaPorte, D. C. (1992) GLC3 and GHA1 of Saccharomyces cerevisiae are allelic and encode the glycogen branching enzyme. Mol. Cell. Biol. Jan;12(1), 22–29.
Haselbeck, R. J. and McAlister-Henn, L. (1993) Function and expression of yeast mitochondrial NAD- and NADP-specific isocitrate dehydrogenases. J. Biol. Chem. 268(16), 12116–12122.
Valenzuela, L., Ballario, P., Aranda, C., Filetici, P. and A. Gonzalez, A. (1998) Regulation of expression of GLT1, the gene encoding glutamate synthase in Saccharomyces cerevisiae. J. Bacteriol. 180(14), 3533–3540.
Jauniaux, J. C., Urrestarazu, L. A., and Wiame, J. M. (1978) Arginine metabolism in Saccharomyces cerevisiae: subcellular localization of the enzymes. J. Bacteriol. 133(3), 1096–1107.
Crabeel, M., Seneca, S., Devos, K. and Glansdorff, N. (1988) Arginine repression of the Saccharomyces cerevisiae ARG1 gene comparison of the ARG1 and ARG3 control regions. Curr. Gen. 3(2), 113–124.
Masselot M. and De Robichon-Szulmajster, H. (1975) Methionine biosynthesis in Saccharomyces cerevisiae. I. Genetical analysis of auxotrophic mutants. Mol. Gen. Genet. 139(2):121–132.
Thomas, D. and Surdin-Kerjan, Y. (1997) Metabolism of sulfur amino acids in Saccharomyces cerevisiae. Microbiol. Mol. Biol. Rev. 61(4), 503–532.
Acknowledgments
We thank Dr. Carroll for giving motivation and Haseong Kim for providing gene ontology results.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this protocol
Cite this protocol
Kim, J. (2011). Clustering Change Patterns Using Fourier Transformation with Time-Course Gene Expression Data. In: Becskei, A. (eds) Yeast Genetic Networks. Methods in Molecular Biology, vol 734. Humana Press. https://doi.org/10.1007/978-1-61779-086-7_10
Download citation
DOI: https://doi.org/10.1007/978-1-61779-086-7_10
Published:
Publisher Name: Humana Press
Print ISBN: 978-1-61779-085-0
Online ISBN: 978-1-61779-086-7
eBook Packages: Springer Protocols