Simplified stochastic models with time delay for studying the degradation process of mRNA molecules.

Message RNA (mRNA) is the template for protein synthesis. It carries information from DNA in the nucleus to the ribosome sites of protein synthesis in the cell. The turnover process of mRNA is a chemical event with multiple small step reactions and the degradation of mRNA molecules is an important step in gene expression. A number of mathematical models have been proposed to study the dynamics of mRNA turnover, ranging from a one-step first order reaction model to the linear multi-component models. Although the linear multi-component models provide detailed dynamics of mRNA degradation, the simple first-order reaction model has been widely used in mathematical modelling of genetic regulatory networks. To illustrate the difference between these models, we first considered a stochastic model based on the multi-component model. Then a simpler stochastic model was proposed to approximate the linear multi-component model. We also discussed the delayed one-step reaction models with different types of time delay, including the constant delay, exponentially distributed delay and Erlang distributed delay. The comparison study suggested that the one-step reaction models failed to realise the dynamics of mRNA turnover accurately. Therefore, more sophisticated one-step reaction models are needed to study the dynamics of mRNA degradation.