Continuous cotemporal probabilistic modeling of systems biology networks from sparse data

Modeling of biological networks is a difficult endeavor, but exploration of this problem is essential for understanding the systems behavior of biological processes. In this contribution, developed for sparse data, we present a new continuous Bayesian graphical learning algorithm to cotemporally model proteins in signaling networks and genes in transcriptional regulatory networks. In this continuous Bayesian algorithm, the correlation matrix is singular because the number of time points is less than the number of biological entities (genes or proteins). A suitable restriction on the degree of the graph's vertices is applied and a Metropolis-Hastings algorithm is guided by a BIC-based posterior probability score. Ten independent and diverse runs of the algorithm are conducted, so that the probability space is properly well-explored. Diagnostics to test the applicability of the algorithm to the specific data sets are developed; this is a major benefit of the methodology. This novel algorithm is applied to two time course experimental data sets: 1) protein modification data identifying a potential signaling network in chondrocytes, and 2) gene expression data identifying the transcriptional regulatory network underlying dendritic cell maturation. This method gives high estimated posterior probabilities to many of the proteins' directed edges that are predicted by the literature; for the gene study, the method gives high posterior probabilities to many of the literature-predicted sibling edges. In simulations, the method gives substantially higher estimated posterior probabilities for true edges and true subnetworks than for their false counterparts.