The Library

Guided conjugate Bayesian clustering for uncovering rhythmically expressed genes

Tools

Anderson, Paul E., Smith, J. Q., Edwards, Kieron D. and Millar, A. J. (2006) Guided conjugate Bayesian clustering for uncovering rhythmically expressed genes. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2006 (No.7).

Preview

PDF
WRAP_Anderson_06-07w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (9Mb)

Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

Abstract

Background: An increasing number of microarray experiments produce time series of expression levels for many
genes. Some recent clustering algorithms respect the time ordering of the data and are, importantly, extremely
fast. The focus of this paper is the development of such an algorithm on a microarray data set consisting of
22,810 genes of the plant Arabidopsis thaliana measured at 13 time points over two days. Circadian rhythms
control the timing of various physiological and metabolic processes and are regulated by genes acting in
feedback loops. The aim is to cluster and classify the expression profiles in order to identify genes potentially
involved in, and regulated by, the circadian clock.
Results: A greedy search over time series of expression levels (where series are compared pairwise, the two most
similar put in the same cluster and so forth) will get a fast result but will only explore a very limited number of
the possible partitions of the profiles. We propose an improved, deterministic method based on a multi-step
application of a conjugate Bayesian clustering algorithm. It allows the entire space to be searched more fully and
intelligently. The values of the summary statistics are used to not only score clusters of genes, but also to guide
the search of the vast partition space. By following this procedure, we are able to cluster genes that are known
to be rhythmically expressed with genes of previously unknown function; thus suggesting potentially interesting
targets for future experiments.

Item Type:

Working or Discussion Paper (Working Paper)

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Arabidopsis thaliana -- Genetics -- Mathematical models, Time-series analysis, Cluster analysis, Circadian rhythms -- Mathematical models

Series Name:

Working papers

Publisher:

University of Warwick. Centre for Research in Statistical Methodology

Place of Publication:

Coventry

Official Date:

2006

Dates:

Date	Event
2006	Published

Volume:

Vol.2006

Number:

No.7

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

Funder:

Engineering and Physical Sciences Research Council (EPSRC), Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC), BioSim

Grant number:

G19886 (BBSRC)

References:

1. Draghici S: Data Analysis Tools for DNA Microarrays. Chapman and Hall 2003.
2. Heard NA, Holmes CC, Stephens DA: A Quantitative Study of Gene Regulation Involved in the
Immune Response of Anopheline Mosquitoes: An Applictaion of Bayesian Hierarchical
Clustering of Curves. J. Amer. Statist. Assoc. 2006, 101(473):18{29.
3. Ceriani MF, Hogenesch JB, Yanovsky M, Panda S, Straume M, Kay SA: Genome-wide expression analysis
in Drosophila reveals genes controlling circadian behavior. J Neurosci 2002, 22:9305{9319.
4. Panda S, Antoch MP, Miller BH, Su AI, Schook AB, Straume M, Schultz PG, Kay SA, Takahashi JS,
Hogenesch JB: Coordinated transcription of key pathways in the mouse by the circadian clock. Cell
2002, 109:307{320.
5. Straume M: DNA microarray time series analysis: automated statistical assessment of circadian
rhythms in gene expression patterning. Methods Enzymol 2004, 383:149{166.
6. Andersson CR, Isaksson A, Gustafsson MG: Bayesian detection of periodic mRNA time profiles
without use of training examples. BMC Bioinformatics 2006, 7(63). [Published online on 9th Feb 2006.
doi:10.1186/1471-2105-7-63].
7. Andesmaki M, L'ahdesmaki H, Pearson R, Huttunen H, Yli-Harja O: Robust detection of periodic time
series measured from biological systems. BMC Bioinformatics 2005, 6(117).
8. Heard NA, Holmes CC, Stephens DA, Hand DJ, Dimopoulos G: Bayesian co-clustering of Anopheles
gene expression time series: a study of immune defense responses to multiple experimental
challenges. Proc. Nat. Acad. Sci. 2005. [Doi:10.1073/pnas.0408393102].
9. Denison DGT, Holmes CC, Mallick BK, Smith AFM: Bayesian Methods for Nonlinear Classification and
Regression. Wiley Series in Probability and Statistics, John Wiley and Sons 2002.
10. Edwards KD, Anderson PE, Hall A, Salathia NS, Locke JCW, Lynn JR, Straume M, Smith JQ, Millar AJ:
FLOWERING LOCUS C mediates natural variation in the high temperature response of the
Arabidopsis circadian clock. The Plant Cell (in press) 2006. [Published online on 10th Feb 2006.
doi:10.1104/tpc.105.038315].
11. Locke JC, Southern MM, Kozma-Bognar L, Hibberd V, Brown PE, Turner MS, Millar AJ: Extension of a
genetic network model by iterative experimentation and mathematical analysis. Mol Sys Biol 1
2005. [Doi:10.1038/msb4100018].
12. Brockwell PJ, Davis RA: Introduction to Time Series and Forecasting. Springer 1996.
13. Hannan EJ: Multiple Time Series. John Wiley and Sons 1970.
14. Banfield JD, Raftery AE: Model-based gaussian and non-gaussian clustering. Biometrics 1993,
49:803{821.
15. Fraley C, Raftery AE: Model-based clustering, discriminant analysis, and density estimation. J.
Amer. Statist. Assoc. 2002, 97:611{631.
16. Luan Y, Li H: Clustering of time-course gene expression data using a mixed-effects model with
B-splines. Bioinformatics 2003, 19:474{482.
17. Ramoni M, Sebastiani P, Kohane PR: Cluster analysis of gene expression dynamics. Proc. Nat. Acad.
Sci. 2002, 99:9121{9126.
18. Wakefield J, Zhou C, Self S: Modelling gene expression over time: curve clustering with informative
prior distributions. In Bayesian Statistics 7. Edited by Bernardo JM, Bayarri MJ, Berger JO, Dawid AP,
Heckerman D, Smith AFM, West M, Oxford University Press 2003.
19. Yeung KY, Fraley C, Murua A, Raftery AE, Ruzzo WL: Model-based clustering and data
transformations for gene expression data. Bioinformatics 2001, 17:977{987.
20. Boucheron S, Bousquet O, Lugosi G: Theory of Classification: A Survey of Recent Advances. ESAIM:
Probability and Statistics 2005, 9:323{375.
21. Chipman H, George E, McCullough R: Bayesian CART Model Search. J. Amer. Statist. Assoc. 1998,
93:935{960.
22. Chipman HA, George EI, McCulloch RE: Bayesian treed models. Machine Learning 2002, 48(1{3):299{320.
23. Doyle MR, Davis SJ, Bastow RM, McWatters HG, Kozma-Bognar L, Nagy F, Millar AJ, Amasino RM: The
ELF4 gene controls circadian rhythms and
owering time in Arabidopsis thaliana. Nature 2002,
419:74{77.
24. Alabadi D, Oyama T, Yanovsky MJ, Harmon FG, Mas P, Kay SA: Reciprocal regulation between TOC1
and LHY/CCA1 within the Arabidopsis circadian clock. Science 2001, 293:880{883.
25. Hazen SP, Schultz TF, Pruneda-Paz JL, Borevitz JO, Ecker JR, Kay SA: LUX ARRHYTHMO encodes a
Myb domain protein essential for circadian rhythms. Proc. Nat. Acad. Sci. 2005, 102:10387{10392.
26. Kuno N, Moller SG, Shinomura T, Xu X, Chua NH, Furuya M: The Novel MYB Protein
EARLY-PHYTOCHROME-RESPONSIVE1 is a Component of a Slave Circadian Oscillator in
Arabidopsis. The Plant Cell 2003, 15:2476{2488.
27. Heintzen C, Nater M, Apel K, Staiger D: AtGRP7, a nuclear RNA-binding protein as a component of
a circadian-regulated negative feedback loop in Arabidopsis thaliana. Proc. Nat. Acad. Sci. 1997,
94:8515{8520.
28. Alabadi D, Yanovsky MJ, Mas P, Harmer SL, Kay SA: Critical role for CCA1 and LHY in maintaining
circadian rhythmicity in Arabidopsis. Curr. Biol. 2002, 12:757{761.
29. Mizoguchi T, Wheatley K, Hanzawa Y, Wright L, Mizoguchi M, Song HR, Carre IA, Coupland G: LHY and
CCA1 are partially redundant genes required to maintain circadian rhythms in Arabidopsis. Dev.
Cell 2002, 2:629{641.
30. Aguilar O, West M: Bayesian dynamic factor models and portfolio allocation. Journal of Business and
Economic Statistics 2000, 18:338{357.
31. George EI, Clyde M: Model uncertainty. Statistical Science 2004, 19:81{94.
32. Heard NA: Code for the algorithm described in Heard et al, J. Amer. Statist. Assoc., 2006.
http://stats.ma.imperial.ac.uk/naheard/public html 2006.