Determining and analyzing differentially expressed genes from cDNA microarray experiments with complementary designs

Bayesian meta-analysis models for microarray data: a comparative study

Background

With the growing abundance of microarray data, statistical methods are increasingly needed to integrate results across studies. Two common approaches for meta-analysis of microarrays include either combining gene expression measures across studies or combining summaries such as p-values, probabilities or ranks. Here, we compare two Bayesian meta-analysis models that are analogous to these methods.

Results

Two Bayesian meta-analysis models for microarray data have recently been introduced. The first model combines standardized gene expression measures across studies into an overall mean, accounting for inter-study variability, while the second combines probabilities of differential expression without combining expression values. Both models produce the gene-specific posterior probability of differential expression, which is the basis for inference. Since the standardized expression integration model includes inter-study variability, it may improve accuracy of results versus the probability integration model. However, due to the small number of studies typical in microarray meta-analyses, the variability between studies is challenging to estimate. The probability integration model eliminates the need to model variability between studies, and thus its implementation is more straightforward. We found in simulations of two and five studies that combining probabilities outperformed combining standardized gene expression measures for three comparison values: the percent of true discovered genes in meta-analysis versus individual studies; the percent of true genes omitted in meta-analysis versus separate studies, and the number of true discovered genes for fixed levels of Bayesian false discovery. We identified similar results when pooling two independent studies of Bacillus subtilis. We assumed that each study was produced from the same microarray platform with only two conditions: a treatment and control, and that the data sets were pre-scaled.

Conclusion

The Bayesian meta-analysis model that combines probabilities across studies does not aggregate gene expression measures, thus an inter-study variability parameter is not included in the model. This results in a simpler modeling approach than aggregating expression measures, which accounts for variability across studies. The probability integration model identified more true discovered genes and fewer true omitted genes than combining expression measures, for our data sets.

Bayesian models for pooling microarray studies with multiple sources of replications

Background

Biologists often conduct multiple but different cDNA microarray studies that all target the same biological system or pathway. Within each study, replicate slides within repeated identical experiments are often produced. Pooling information across studies can help more accurately identify true target genes. Here, we introduce a method to integrate multiple independent studies efficiently.

Results

We introduce a Bayesian hierarchical model to pool cDNA microarray data across multiple independent studies to identify highly expressed genes. Each study has multiple sources of variation, i.e. replicate slides within repeated identical experiments. Our model produces the gene-specific posterior probability of differential expression, which provides a direct method for ranking genes, and provides Bayesian estimates of false discovery rates (FDR). In simulations combining two and five independent studies, with fixed FDR levels, we observed large increases in the number of discovered genes in pooled versus individual analyses. When the number of output genes is fixed (e.g., top 100), the pooled model found appreciably more truly differentially expressed genes than the individual studies. We were also able to identify more differentially expressed genes from pooling two independent studies in Bacillus subtilis than from each individual data set. Finally, we observed that in our simulation studies our Bayesian FDR estimates tracked the true FDRs very well.

Conclusion

Our method provides a cohesive framework for combining multiple but not identical microarray studies with several sources of replication, with data produced from the same platform. We assume that each study contains only two conditions: an experimental and a control sample. We demonstrated our model's suitability for a small number of studies that have been either pre-scaled or have no outliers.

The program of gene transcription for a single differentiating cell type during sporulation in Bacillus subtilis

Asymmetric division during sporulation by Bacillus subtilis generates a mother cell that undergoes a 5-h program of differentiation. The program is governed by a hierarchical cascade consisting of the transcription factors: σ^E, σ^K, GerE, GerR, and SpoIIID. The program consists of the activation and repression of 383 genes. The σ^E factor turns on 262 genes, including those for GerR and SpoIIID. These DNA-binding proteins downregulate almost half of the genes in the σ^E regulon. In addition, SpoIIID turns on ten genes, including genes involved in the appearance of σ^K_. Next, σ^K activates 75 additional genes, including that for GerE. This DNA-binding protein, in turn, represses half of the genes that had been activated by σ^K while switching on a final set of 36 genes. Evidence is presented that repression and activation contribute to proper morphogenesis. The program of gene expression is driven forward by its hierarchical organization and by the repressive effects of the DNA-binding proteins. The logic of the program is that of a linked series of feed-forward loops, which generate successive pulses of gene transcription. Similar regulatory circuits could be a common feature of other systems of cellular differentiation.

A comprehensive genomic analysis of sporulation in Bacillus subtilis reveals a coordinated program of gene activation and repression, which involves 383 genes