First and second order Markov posterior probabilities on multiple time-course data sets

Development of models that explain relationships between changes in gene products often involve multiple replications of transcript abundance measurements across time courses. This paper develops a composite probabilistic analysis using a next-state paradigm. We not only consider the usual first-order Markov (next time step) setting but we also introduce a combined first-order and second-order Markov process which allows modeling of downstream relationships that show a one or two point time lag response. This is especially important to identify transcripts which change as a result of changes in earlier transcriptional events. As well, composite replicate next-state models are developed separately for independently and hierarchically related replications. Our Bayesian models produce rigorous posterior probabilities of relationships between genes. Multiple and varied simulations are conducted to verify the utility of our next-state composite models. We also make important practical biological inferences about transcriptional signaling networks in roots. These Bayesian methods are applied to an experimentally generated data set to validate our methods and to correlate the results from this analysis with other coexpression relationships predicted by other algorithms. This experimental data set examined the changes in transcript abundance in the roots of the model plant, Arabidopsis thaliana, whose synthesis was induced by a hormone. This modeling identified novel relationships and those predicated by other methods, both of which can be experimentally tested.