MOTIVATION: Time-course gene expression datasets provide important insights into dynamic aspects of biological processes, such as circadian rhythms, cell cycle and organ development. In a typical microarray time-course experiment, measurements are obtained at each time point from multiple replicate samples. Accurately recovering the gene expression patterns from experimental observations is made challenging by both measurement noise and variation among replicates' rates of development. Prior work on this topic has focused on inference of expression patterns assuming that the replicate times are synchronized. We develop a statistical approach that simultaneously infers both (i) the underlying (hidden) expression profile for each gene, as well as (ii) the biological time for each individual replicate. Our approach is based on Gaussian process regression (GPR) combined with a probabilistic model that accounts for uncertainty about the biological development time of each replicate. RESULTS: We apply GPR with uncertain measurement times to a microarray dataset of mRNA expression for the hair-growth cycle in mouse back skin, predicting both profile shapes and biological times for each replicate. The predicted time shifts show high consistency with independently obtained morphological estimates of relative development. We also show that the method systematically reduces prediction error on out-of-sample data, significantly reducing the mean squared error in a cross-validation study. AVAILABILITY: Matlab code for GPR with uncertain time shifts is available at http://sli.ics.uci.edu/Code/GPRTimeshift/ CONTACT: [email protected].

MOTIVATION: Cyclical biological processes such as cell division and circadian regulation produce coordinated periodic expression of thousands of genes. Identification of such genes and their expression patterns is a crucial step in discovering underlying regulatory mechanisms. Existing computational methods are biased toward discovering genes that follow sine-wave patterns. RESULTS: We present an analysis of variance (ANOVA) periodicity detector and its Bayesian extension that can be used to discover periodic transcripts of arbitrary shapes from replicated gene expression profiles. The models are applicable when the profiles are collected at comparable time points for at least two cycles. We provide an empirical Bayes procedure for estimating parameters of the prior distributions and derive closed-form expressions for the posterior probability of periodicity, enabling efficient computation. The model is applied to two datasets profiling circadian regulation in murine liver and skeletal muscle, revealing a substantial number of previously undetected non-sinusoidal periodic transcripts in each. We also apply quantitative real-time PCR to several highly ranked non-sinusoidal transcripts in liver tissue found by the model, providing independent evidence of circadian regulation of these genes. AVAILABILITY: Matlab software for estimating prior distributions and performing inference is available for download from http://www.datalab.uci.edu/resources/periodicity/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Clustering is an important analysis performed on microarray gene expression data since it groups genes which have similar expression patterns and enables the exploration of unknown gene functions. Microarray experiments are associated with many sources of experimental and biological variation and the resulting gene expression data are therefore very noisy. Many heuristic and model-based clustering approaches have been developed to cluster this noisy data. However, few of them include consideration of probe-level measurement error which provides rich information about technical variability. RESULTS: We augment a standard model-based clustering method to incorporate probe-level measurement error. Using probe-level measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we include the probe-level measurement error directly into the standard Gaussian mixture model. Our augmented model is shown to provide improved clustering performance on simulated datasets and a real mouse time-course dataset. CONCLUSION: The performance of model-based clustering of gene expression data is improved by including probe-level measurement error and more biologically meaningful clustering results are obtained.