A statistical analysis of memory CD8 T cell differentiation: An application of a hierarchical state space model to a short time course microarray experiment

In this CD8 T-cell experiment, acute lymphocytic choriomeningitis virus Armstrong (LCMV) infection of mice was used as a model system to study memory CD8 T cell differentiation. Genetically identical, uninfected mice were sacrificed on the baseline day (naïve) to obtain naïve CD8 T cells. Other genetically identical mice were infected with LCMV on the baseline day. Then mice were sacrificed at day 8 (d8) and day 15 (d15) to obtain effector CD8 T cells, and at greater than day 30 (Imm) to obtain memory CD8 T cells. Affymetrix MG-U74AV2 arrays were used to measure 12, 488 genes in P14 CD8 T cells from mouse spleens at these four time points. For each chip, cells from at least three mice were pooled to obtain sufficient RNA for MG-U74AV2 hybridization. Structurally, this CD8 T-cell experiment is similar to many in that it involves measurements taken on different mice (independent sampling), in one biological group, at a small number of irregularly spaced time points, and exhibiting patterns of temporal nonstationarity. The goal of the analysis is to assist investigators in understanding the underlying system biology by identifying temporally differentially expressed (TDE) genes and characterizing temporal changes involved in memory CD8 T cell differentiation.

In the original analysis, Kaech et al. (2002a) selected genes based on whether their average gene expression levels changed (decreased or increased) at any time point by at least 1.7 fold (original linear scale) compared to the first time point, generating a set of 431 genes. They applied a K-means clustering algorithm on the selected genes and found six major patterns out of 10 clusters. In this original analysis, the temporal aspects of the data were ignored and both the fold change cutoff in the selection method and the number of clusters in K-means clustering were chosen arbitrarily. Although they identified several individual genes known to be important in differentiating naïve, effector and memory CD8 T cells, the biological meaning of the obtained clusters is not clear and the interpretation of clustering results is not straightforward. To improve interpretation, we re-analyzed this CD8 Tcell experiment by focusing on the direction (upregulation, downregulation and no change) and the magnitude of the gene-specific successive differences (changes) in the mean gene expression levels (log base 2 scale) over time.

1.2. Analysis of time course microarray data. Methods up to now for time course microarray experiments can be divided into two classes: (1) methods extended from those for static microarray experiments, and (2) methods extended from time series analysis. Examples of the first type of methods include hierarchical clustering [Eisen et al. (1998) and Spellman et al. (1998)], K-means clustering [Tavazoie et al. (1999), Kaech et al. (2002a) and Bar-Joseph et al. (2002)], self-organizing maps [Tamayo et al. (1999)], singular value decomposition [Alter, Brown and Botstein (2000) and Wall, Dyck and Brettin (2001)], ANOVA-based analysis [Park et al. (2003)] and pairwise analysis. Ignoring the temporal aspects of data, these types of methods have the potential to suffer from low sensitivity. Examples of methods inspired by time series analysis include Auto-Regression (AR) based models, multivariate Normal models, B-splines based models, and hidden Markov models (HMMs). Ramoni, Sebastiani and Cohen (2002) represented gene expression sequences as stationary series produced from a finite number of AR processes and applied an agglomerative Bayes clustering algorithm to search gene clusters. Using the multivariate Normal distribution, Tai and Speed (2006) developed a multivariate hierarchical empirical Bayes model to i

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