Abstract
Sample correlations between gene pairs within expression profiles are potentially informative regarding gene regulatory pathway structure. However, as is the case with other statistical summaries, observed correlation may be induced or suppressed by factors which are unrelated to gene functionality. In this paper, we consider the effect of heterogeneity on observed correlations, both at the tissue and subject level. Using gene expression profiles from highly enriched samples of three distinct embryonic glial cell types of the rodent neural tube, the effect of tissue heterogeneity on correlations is directly estimated for a simple two component model. Then, a stochastic model of cell population kinetics is used to assess correlation effects for more complex mixtures. Finally, a mathematical model for correlation effects of subject-level heterogeneity is developed. Although decomposition of correlation into functional and nonfunctional sources will generally not be possible, since this depends on nonobservable parameters, reasonable bounds on the size of such effects can be made using the methods proposed here.
On February 27, 2008, Dr. Andrei Yakovlev tragically passed away. We deeply grieve the loss of our colleague, advisor, and friend who was a source of inspiration for all around him.
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References
Berger, S. L. (2007). The complex language of chromatin regulation during transcription. Nature, 447, 407–412.
Braun, R., Cope, L., & Parmigiani, G. (2008). Identifying differential correlation in gene/pathway combinations. BMC Bioinformatics, 9, 1.
Chen, L., Almudevar, A., & Klebanov, L. (2013). Aggregation effect in microarray data analysis. In A. Y. Yakovlev, L. Klebanov, D. Gaile (Eds.), Statistical methods for microarray data analysis. Methods in Molecular Biology (Vol. 972, pp. 177–191). New York: Springer.
Davies, J., Proschel, C., Zhang, N., Mayer-Proschel, M., & Davies, S. (2008). Transplanted astrocytes derived from BMP- or CNTF-treated glial-restricted precursors have opposite effects on recovery and allodynia after spinal cord injury. Brazilian Journal of Biology, 7, 24.
Dulac, C. (2010). Brain function and chromatin plasticity. Nature, 465, 728–35.
Fraser, P., & Bickmore, W. (2007). Nuclear organization of the genome and the potential for gene regulation. Nature, 447, 413–417.
Friedman, N. (2004). Inferring cellular networks using probabilistic graphical models. Science, 303, 799–805.
Grewal, S. I., & Moazed, D. (2003). Heterochromatin and epigenetic control of gene expression. Science, 301, 798–802.
Hyrien, O., Mayer-Proschel, M., Noble, M., & Yakovlev, A. (2005). A stochastic model to analyze clonal data on multi-type cell populations. Biometrics, 61, 199–207.
Klebanov, L., Jordan, C., & Yakovlev, A. (2006). A new type of stochastic dependence revealed in gene expression data. Statistical Applications in Genetics and Molecular Biology, 5, Article 7.
Klebanov, L., & Yakovlev, A. (2007). Diverse correlation structures in microarray gene expression data and their utility in improving statistical inference. The Annals of Applied Statistics, 1, 538–559.
Li, E. (2002). Chromatin modification and epigenetic reprogramming in mammalian development. Nature Reviews Genetics, 3, 662–673.
Li, G., & Reinberg, D. (2011). Chromatin higher-order structures and gene regulation. Current Opinion in Genetics & Development, 21, 175–186.
Numata, K., Kanai, A., Saito, R., Kondo, S., Adachi, J., Wilming, L. G., et al. (2003). Identification of putative noncoding RNAs among the RIKEN mouse full-length cDNA collection. Genome Research, 13, 1301–1306.
Ponjavic, J., Ponting, C. P., & Lunter, G. (2007). Functionality or transcriptional noise? Evidence for selection within long noncoding RNAs. Genome Research, 17, 556–565.
Qiu, X., Brooks, A., Klebanov, L., & Yakovlev, A. (2005). The effects of normalization on the correlation structure of microarray data. BMC Bioinformatics, 6, 120.
Rao, M., Tanksale, A., Ghatge, M., & Deshpande, V. (1998). Molecular and biotechnological aspects of microbial proteases. Microbiology and Molecular Biology Reviews, 62, 597–635.
Ravasi, T., Suzuki, H., Pang, K. C., Katayama, S., Furuno, M., Okunishi, R., et al. (2006). Experimental validation of the regulated expression of large numbers of non-coding RNA from the mouse genome. Genome Research, 16, 11–19.
Saxena, A., & Carninci, P. (2011). Long non-coding RNA modifies chromatin: Epigenetic silencing by long non-coding RNAs. Bioessays, 33, 830–839.
Soares, L., & Valcarcel, J. (2006). The expanding transcriptome: The genome as the “Book of Sand”. The EMBO Journal, 25, 923–931.
Vogelmann, J., Valeri, A., Guillou, E., Cuvier, O., & Nollmann, M. (2011). Roles of chromatin insulator proteins in higher-order chromatin organization and transcription regulation. Nucleus, 2, 358–369.
Werhli, A. V., Grzegorczyk, M., & Husmeier, D. (2006). Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical Gaussian models and Bayesian networks. Bioinformatics, 22, 2523–2531.
Zhou, X., Kao, M., & Wong, W. (2002). Transitive functional annotation by shortest-path analysis of gene expression data. Proceedings of the National Academy of Sciences of the United States of America, 99, 12783–12788.
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Chen, L., Klebanov, L., Almudevar, A., Proschel, C., Yakovlev, A. (2020). A Study of the Correlation Structure of Microarray Gene Expression Data Based on Mechanistic Modeling of Cell Population Kinetics. In: Almudevar, A., Oakes, D., Hall, J. (eds) Statistical Modeling for Biological Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-34675-1_3
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