Modeling Gene Regulation Networks Using Ordinary Differential Equations

Gene regulation networks are composed of transcription factors, their interactions, and targets. It is of great interest to reconstruct and study these regulatory networks from genomics data. Ordinary differential equations (ODEs) are popular tools to model the dynamic system of gene regulation networks. Although the form of ODEs is often provided based on expert knowledge, the values for ODE parameters are seldom known. It is a challenging problem to infer ODE parameters from gene expression data, because the ODEs do not have analytic solutions and the time-course gene expression data are usually sparse and associated with large noise. In this chapter, we review how the generalized profiling method can be applied to obtain estimates for ODE parameters from the time-course gene expression data. We also summarize the consistency and asymptotic normality results for the generalized profiling estimates.