Maximum Likelihood Estimation for a Gene Regulatory Network Defined by Differential Equations

Gene regulation may be described by a set of deterministic differential equations describing the time rate evolution of the gene product concentrations, and containing parameters accounting for the regulatory relationships occurring in the gene network. We will present maximum likelihood based estimators of the parameters arising in this formalism and we will prove that they have desirable properties. Our results may be applied to a gene regulation model yielding the early Drosophila segments formation relying on a statistical modelling of gene expression data obtained by confocal laser scanning microscopy. The proposed statistical model accounts for the uncertainty in the measurement of gene expression and the uncertainty in the time at which the measurements are performed.