Bayesian Clustering of Replicated Time-course Gene Expression Data with Weak Signals

To identify novel dynamic patterns of gene expression, we develop a statistical method to cluster noisy measurements of gene expression collected from multiple replicates at multiple time points, with an unknown number of clusters. We propose a random-effects mixture model coupled with a Dirichlet-process prior for clustering. The mixture model formulation allows for probabilistic cluster assignments. The random-effects formulation allows for attributing the total variability in the data to the sources that are consistent with the experimental design, particularly when the noise level is high and the temporal dependence is not strong. The Dirichlet-process prior induces a prior distribution on partitions and helps to estimate the number of clusters (or mixture components) from the data. We further tackle two challenges associated with Dirichlet-process prior-based methods. One is efficient sampling. We develop a novel Metropolis-Hastings Markov Chain Monte Carlo (MCMC) procedure to sample the partitions. The other is efficient use of the MCMC samples in forming clusters. We propose a two-step procedure for posterior inference, which involves resampling and relabeling, to estimate the posterior allocation probability matrix. This matrix can be directly used in cluster assignments, while describing the uncertainty in clustering. We demonstrate the effectiveness of our model and sampling procedure through simulated data. Applying our method to a real data set collected from Drosophila adult muscle cells after five-minute Notch activation, we identify 14 clusters of different transcriptional responses among 163 differentially expressed genes, which provides novel insights into underlying transcriptional mechanisms in the Notch signaling pathway. The algorithm developed here is implemented in the R package DIRECT, available on CRAN.