Before revision:  In this preprint we provide 1) detailed mechanistic description of the translationprocess with explicit representation of every state of translating mRNA, followed by 2) deriving the simplest and basic ODE model of coupled transcription, translation and degradation , and 3) developing a model suitable for describing all known mechanisms of miRNA action on translation. The basic model is constructed by correct lumping of the detailed model states and by separating the description of ribosomal turnover. It remains linear under assumption of that the translation is not limited by availability of ribosomal subunits or initiation factors. The only serious limitation of this type of translation modeling is in that it does not take into account possible interactions between ribosomes.
After revision:  In this preprint we provide 1) detailed mechanistic description of the translationprocess with explicit representation of every state of translating mRNA, followed by 2) deriving the simplest and basic ODE model of coupled transcription, translation and degradation ) exists. We build such a model by lumping multiple states of translated mRNA into few dynamical variables and introducing a pool of translating ribosomes. The basic and simple model can be extended, if necessary, to take into account possible interactions between ribosomes.