Collocation-based sparse estimation for constructing dynamic gene networks.

One of the open problems in systems biology is to infer dynamic gene networks describing the underlying biological process with mathematical, statistical and computational methods. The first-order difference equation-based models such as dynamic Bayesian networks and vector autoregressive models were used to infer time-lagged relationships between genes from time-series microarray data. However, two primary problems greatly reduce the effectiveness of current approaches. The first problem is the tacit assumption that time lag is stationary. The second is the inseparability between measurement noise and process noise (unmeasured disturbances that pass through time process). To address these problems, we propose a stochastic differential equation model for inferring continuous-time dynamic gene networks under the situation in which both of the process noise and the observation noise exist. We present a collocation-based sparse estimation for simultaneous parameter estimation and model selection in the model. The collocation-based approach requires considerably less computational effort than traditional methods in ordinary stochastic differential equation models. We also incorporate various biological knowledge easily to refine the estimation accuracy with the proposed method. The results using simulated data and real time-series expression data of human primary small airway epithelial cells demonstrate that the proposed approach outperforms competing approaches and can provide significant genes influenced by gefitinib.