Inferring latent gene regulatory network kinetics

Regulatory networks consist of genes encoding transcription factors (TFs) and the genes they activate or repress. Various types of systems of ordinary differential equations (ODE) have been proposed to model these networks, ranging from linear to Michaelis-Menten approaches. In practice, a serious drawback to estimate these models is that the TFs are generally unobserved. The reason is the actual lack of high-throughput techniques to measure abundance of proteins in the cell. The challenge is to infer their activity profile together with the kinetic parameters of the ODE using level expression measurements of the genes they regulate. In this work we propose general statistical framework to infer the kinetic parameters of regulatory networks with one or more TFs using time course gene expression data. Our approach is also able to predict the activity levels of the TF. We use a penalized likelihood approach where the ODE is used as a penalty. The main advantage is that the solution of the ODE is not required explicitly as it is common in most proposed methods. This makes our approach computationally efficient and suitable for large systems with many components. We use the proposed method to study a SOS repair system in Escherichia coli. The reconstructed TF exhibits a similar behavior to experimentally measured profiles and the genetic expression data are fitted properly.