Monte Carlo-based Mouse Nuclear Receptor Superfamily Gene Regulatory Network Prediction: Stochastic Dynamical System on Graph with Zipf Prior

A Monte Carlo based algorithm is proposed to predict gene regulatory network structure of mouse nuclear receptor superfamily, about which little is known although those genes are believed to be related with several difficult diseases. The gene expression data is regarded as sample vector trajectories from a stochastic dynamical system on a graph. The problem is formulated within a Bayesian framework where the graph prior distribution is assumed to follow a Zipf distribution. Appropriateness of a graph is evaluated by the graph posterior mean. The algorithm is implemented with the Exchange Monte Carlo method. After validation against synthesized data, an attempt is made to use the algorithm for predicting network structure of the target, the mouse nuclear receptor superfamily. Several remarks are made on the feasibility of the predicted network from a biological viewpoint.