Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming
ACM Transactions on Mathematical Software (TOMS)
Systematic component selection for gene-network refinement
Bioinformatics
Bayesian inference of gene regulatory networks using gene expression time series data
BIRD'07 Proceedings of the 1st international conference on Bioinformatics research and development
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High-throughput techniques allow measurement of hundreds of cell components simultaneously. The inference of interactions between cell components from these experimental data facilitates the understanding of complex regulatory processes. Differential equations have been established to model the dynamic behavior of these regulatory networks quantitatively. Usually traditional regression methods for estimating model parameters fail in this setting, since they overfit the data. This is even the case, if the focus is on modeling subnetworks of, at most, a few tens of components. In a Bayesian learning approach, this problem is avoided by a restriction of the search space with prior probability distributions over model parameters. This paper combines both differential equation models and a Bayesian approach. We model the periodic behavior of proteins involved in the cell cycle of the budding yeast Saccharomyces cerevisiae, with differential equations, which are based on chemical reaction kinetics. One property of these systems is that they usually converge to a steady state, and lots of efforts have been made to explain the observed periodic behavior. We introduce an approach to infer an oscillating network from experimental data. First, an oscillating core network is learned. This is extended by further components by using a Bayesian approach in a second step. A specifically designed hierarchical prior distribution over interaction strengths prevents overfitting, and drives the solutions to sparse networks with only a few significant interactions. We apply our method to a simulated and a real world dataset and reveal main regulatory interactions. Moreover, we are able to reconstruct the dynamic behavior of the network.