Partially non-homogeneous dynamic Bayesian networks based on Bayesian regression models with partitioned design matrices

Abstract

Motivation: Non-homogeneous dynamic Bayesian networks (NH-DBNs) are a popular modelling tool for learning cellular networks from time series data. In systems biology, time series are often measured under different experimental conditions, and not rarely only some network interaction parameters depend on the condition while the other parameters stay constant across conditions. For this situation, we propose a new partially NH-DBN, based on Bayesian hierarchical regression models with partitioned design matrices. With regard to our main application to semi-quantitative (immunoblot) timecourse data from mammalian target of rapamycin complex 1 (mTORC1) signalling, we also propose a Gaussian process-based method to solve the problem of non-equidistant time series measurements. Results: On synthetic network data and on yeast gene expression data the new model leads to improved network reconstruction accuracies. We then use the new model to reconstruct the topologies of the circadian clock network in Arabidopsis thaliana and the mTORC1 signalling pathway. The inferred network topologies show features that are consistent with the biological literature.