Modeling Gene Expression from Microarray Expression Data with State-Space Equations

We describe a new method to model gene expression from time-course gene expression data. The modelling is in terms of state-space descriptions of linear systems. A cell can be considered to be a system where the behaviours (responses) of the cell depend completely on the current internal state plus any external inputs. The gene expression levels in the cell provide information about the behaviours of the cell. In previously proposed methods, genes were viewed as internal state variables of a cellular system and their expression levels were the values of the intemal state variables. This viewpoint has suffered from the underestimation of the model parameters. Instead, we view genes as the observation variables, whose expression values depend on the current intemal state variables and any external input. Factor analysis is used to identify the internal state variables, and Bayesian Information Criterion (BIC) is used to determine the number of the internal state variables. By building dynamic equations of the internal state variables and the relationships between the internal state variables and the observation variables (gene expression profiles), we get state-space descriptions of gene expression model. In the present method, model parameters may be unambiguously identified from time-course gene expression data. We apply the method to two time-course gene expression datasets to illustrate it.