High-throughput techniques allow to measure hundreds of cell components simultaneously. The inference of interactions between cell components from these experimental data facilitates the understanding of complex cell processes. Differential equations have been established to model the dynamic behavior of these regulatory networks quantitatively. Usually traditional regression methods fail in this setting, since they overfit the data. 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 that are based on chemical reaction kinetics. One property of these systems is that they usually converge to a steady state and a lot 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 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 applied our method to a simulated and a real world dataset and revealed main regulatory interactions. Moreover, we were able to reconstruct the dynamic behavior of the network.