State-space model for gene regulatory networks with time delays

This work proposes a state-space model to account for time delays in gene regulatory network. This model views genes as the observation variables, whose expression values depend on the current internal state variables and any external inputs. The Bayesian information criterion (BIC) and probabilistic principal component analysis (PPCA) are used to estimate the number of internal state variables and their expression profiles from gene expression data. By constructing dynamic equations with time delays for the internal state variables and the relationships between them and the observation variables (gene expression profiles), state-space models for gene regulatory networks with time delays are realized. The parameters of the proposed model may be unambiguously identified from time-course gene expression data with low computational cost. The method is applied to one time-course gene expression dataset, and the modes constructed. The results show that not only is the model (almost) stable, but also it has better prediction accuracy than a model without incorporating time delay.