Hierarchical Probabilistic Interaction Modeling for Multiple Gene Expression Replicates.

Microarray technology allows for the collection of multiple replicates of gene expression time course data for hundreds of genes at a handful of time points. Developing hypotheses about a gene transcriptional network, based on time course gene expression data is an important and very challenging problem. In many situations there are similarities which suggest a hierarchical structure between the replicates. This paper develops posterior probabilities for network features based on multiple hierarchical replications. Through Bayesian inference, in conjunction with the Metropolis-Hastings algorithm and model averaging, a hierarchical multiple replicate algorithm is applied to seven sets of simulated data and to a set of Arabidopsis thaliana gene expression data. The models of the simulated data suggest high posterior probabilities for pairs of genes which have at least moderate signal partial correlation. For the Arabidopsis model, many of the highest posterior probability edges agree with the literature.

Bayesian probabilistic network modeling from multiple independent replicates.

Often protein (or gene) time-course data are collected for multiple replicates. Each replicate generally has sparse data with the number of time points being less than the number of proteins. Usually each replicate is modeled separately. However, here all the information in each of the replicates is used to make a composite inference about signal networks. The composite inference comes from combining well structured Bayesian probabilistic modeling with a multi-faceted Markov Chain Monte Carlo algorithm. Based on simulations which investigate many different types of network interactions and experimental variabilities, the composite examination uncovers many important relationships within the networks. In particular, when the edge's partial correlation between two proteins is at least moderate, then the composite's posterior probability is large.

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.

Comparison of Co-Temporal Modeling Algorithms on Sparse Experimental Time Series Data Sets.

Multiple approaches for reverse-engineering biological networks from time-series data have been proposed in the computational biology literature. These approaches can be classified by their underlying mathematical algorithms, such as Bayesian or algebraic techniques, as well as by their time paradigm, which includes next-state and co-temporal modeling. The types of biological relationships, such as parent-child or siblings, discovered by these algorithms are quite varied. It is important to understand the strengths and weaknesses of the various algorithms and time paradigms on actual experimental data. We assess how well the co-temporal implementations of three algorithms, continuous Bayesian, discrete Bayesian, and computational algebraic, can 1) identify two types of entity relationships, parent and sibling, between biological entities, 2) deal with experimental sparse time course data, and 3) handle experimental noise seen in replicate data sets. These algorithms are evaluated, using the shuffle index metric, for how well the resulting models match literature models in terms of siblings and parent relationships. Results indicate that all three co-temporal algorithms perform well, at a statistically significant level, at finding sibling relationships, but perform relatively poorly in finding parent relationships.

Algebraic dependency models of protein signal transduction networks from time-series data.

Signal transduction networks are crucial for inter- and intra-cellular signaling. Signals are often transmitted via covalent modification of protein structure, with phosphorylation/dephosphorylation as the primary example. In this paper, we apply a recently described method of computational algebra to the modeling of signaling networks, based on time-course protein modification data. Computational algebraic techniques are employed to construct next-state functions. A Monte Carlo method is used to approximate the Deegan-Packel Index of Power corresponding to the respective variables. The Deegan-Packel Index of Power is used to conjecture dependencies in the cellular signaling networks. We apply this method to two examples of protein modification time-course data available in the literature. These experiments identified protein carbonylation upon exposure of cells to sub-lethal concentrations of copper. We demonstrate that this method can identify protein dependencies that might correspond to regulatory mechanisms to shut down glycolysis in a reverse, step-wise fashion in response to copper-induced oxidative stress in yeast. These examples show that the computational algebra approach can identify dependencies that may outline signaling networks involved in the response of glycolytic enzymes to the oxidative stress caused by copper.