In systems biology, nonhomogeneous dynamic Bayesian networks (NH-DBNs) have become a popular modeling tool for reconstructing cellular regulatory networks from postgenomic data. In this paper, we focus our attention on NH-DBNs that are based on Bayesian piecewise linear regression models. The new NH-DBN model, proposed here, is a generalization of an earlier proposed model with sequentially coupled network interaction parameters. Unlike the original model, our novel model possesses segment-specific coupling parameters, so that the coupling strengths between parameters can vary over time. Thereby, to avoid model overflexibility and to allow for some information exchange among time segments, we globally couple the segment-specific coupling (strength) parameters by a hyperprior. Our empirical results on synthetic and on real biological network data show that the new model yields better network reconstruction accuracies than the original model.

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. Availability and implementation All datasets have been made available with earlier publications. Our Matlab code is available upon request. Supplementary information Supplementary data are available at Bioinformatics online.

Motivation Non-homogeneous dynamic Bayesian networks (NH-DBNs) are a popular tool for learning networks with time-varying interaction parameters. A multiple changepoint process is used to divide the data into disjoint segments and the network interaction parameters are assumed to be segment-specific. The objective is to infer the network structure along with the segmentation and the segment-specific parameters from the data. The conventional (uncoupled) NH-DBNs do not allow for information exchange among segments, and the interaction parameters have to be learned separately for each segment. More advanced coupled NH-DBN models allow the interaction parameters to vary but enforce them to stay similar over time. As the enforced similarity of the network parameters can have counter-productive effects, we propose a new consensus NH-DBN model that combines features of the uncoupled and the coupled NH-DBN. The new model infers for each individual edge whether its interaction parameter stays similar over time (and should be coupled) or if it changes from segment to segment (and should stay uncoupled). Results Our new model yields higher network reconstruction accuracies than state-of-the-art models for synthetic and yeast network data. For gene expression data from A. thaliana our new model infers a plausible network topology and yields hypotheses about the light-dependencies of the gene interactions. Availability Data are available from earlier publications. Matlab code is available at Bioinformatics online. Supplementary information A supplementary paper is available at Bioinformatics online.

Background Linear regression models are important tools for learning regulatory networks from gene expression time series. A conventional assumption for non-homogeneous regulatory processes on a short time scale is that the network structure stays constant across time, while the network parameters are time-dependent. The objective is then to learn the network structure along with changepoints that divide the time series into time segments. An uncoupled model learns the parameters separately for each segment, while a coupled model enforces the parameters of any segment to stay similar to those of the previous segment. In this paper, we propose a new consensus model that infers for each individual time segment whether it is coupled to (or uncoupled from) the previous segment. Results The results show that the new consensus model is superior to the uncoupled and the coupled model, as well as superior to a recently proposed generalized coupled model. Conclusions The newly proposed model has the uncoupled and the coupled model as limiting cases, and it is able to infer the best trade-off between them from the data.