Identifying the genes of interest

There have been many published studies involving developmental time course experiments. As indicated above, experimenters' aims vary, but we can categorize them broadly as: (i) one-sample, where the aim is to identify genes which change over time, perhaps in some specific way; (ii) two-sample, where in addition to identifying temporally varying gene expression, interest is in comparisons across two biological conditions; and (iii) D > two-sample experiments, which are as in (ii), with D > three biological conditions. These categories apply equally to longitudinal and cross-sectional studies. Before we go on to the analysis methods, we illustrate the foregoing by assigning some of the case studies cited above to their category.

The study in Himanen et al. (9) on a lateral root induction system of A. thaliana to characterize the early molecular regulation induced by auxin is an example of a one-sample problem: only a single treatment (i.e. NPA followed by NAA) was applied to the same type of cells, and the genes whose expression levels change over time were of interest. Examples in the two-sample category include the study of Schwamborn et al. (11), who compared the temporal profiles between the TNFa-treated and untreated human astrocytoma cells U373, in order to elucidate the post-treatment transcriptional response. Similarly, Tepperman et al. (12) compared the temporal profiles of genes in wild type (wt) and phytochrome B (phyB) null mutant A. thaliana, to identify genes regulated by phyB in response to continuous monochromatic red light (Rc) during the induction of seedling de-etiolation. Both of these studies involved just two different biological conditions: treated versus control cells, and wild type versus mutant organ isms. In this type of problem, identifying all the genes with different temporal profiles between the two biological conditions was usually of interest, although sometimes only genes with different shapes were of interest, with those having similar shapes but different magnitude across the two conditions not being of interest. An example in category (iii) is the study of transcriptional response to CRF described in Peeters et al. (13). There gene expression levels were measured at 0, 0.5, 1, 2, 4, 8, 24 h after four different treatments are applied to mouse AtT-20 cells. As in the two-sample problem, genes of interest are those which have different gene expression profiles over time, either in shape and magnitude, or in magnitude only, between the four treatments.

The identification of temporally changing or differentially changing genes not only gives insight into the biological processes under study, it also provides a way of selecting a subset of genes from the entire gene set for further analysis such as clustering. As yet there are relatively few methods available for identifying the genes of interest in this context. The approaches most widely used are those for identifying differentially expressed genes for replicated microarray experiments across two or more independent sample groups (20-29). The idea here is the simple one of testing whether there are changes in a gene's expression across time by making comparisons between times, for example between all consecutive pairs of time points, or all possible pairs of time points (85). It is reasonable though not ideal to analyze time course data with these approaches, as they assume independence of the samples across different times, which is not true for longitudinal time course data. We will give some solutions to these problems for both longitudinal and cross-sectional data in the following subsections.

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