Motivation: mRNA transcriptional dynamics is governed by a complex network of transcription factor (TF) proteins. Experimental and theoretical analysis of this process is hindered by the fact that measurements of TF activity in vivo is very challenging. Current models that jointly infer TF activities and model parameters rely on either of the two main simplifying assumptions: either the dynamics is simplified (e.g. assuming quasi-steady state) or the interactions between TFs are ignored, resulting in models accounting for a single TF.
Results: We present a novel approach to reverse engineer the dynamics of multiple TFs jointly regulating the expression of a set of genes. The model relies on a continuous time, differential equation description of transcriptional dynamics where TFs are treated as latent on/off variables and are modelled using a switching stochastic process (telegraph process). The model can not only incorporate both activation and repression, but allows any non-trivial interaction between TFs, including AND and OR gates. By using a factorization assumption within a variational Bayesian treatment we formulate a framework that can reconstruct both the activity profiles of the TFs and the type of regulation from time series gene expression data. We demonstrate the identifiability of the model on a simple but non-trivial synthetic example, and then use it to formulate non-trivial predictions about transcriptional control during yeast metabolism.