Résumé
Gene expression consists in the synthesis of proteins from the information
encoded on DNA. One of the two main steps of gene expression is the translation
of messenger RNA (mRNA) into polypeptide sequences of amino acids. Here, by
taking into account mRNA degradation, we model the motion of ribosomes along
mRNA with a ballistic model where particles advance along a filament without
excluded volume interactions. Unidirectional models of transport have
previously been used to fit the average density of ribosomes obtained by the
experimental ribo-sequencing (Ribo-seq) technique. In this case an inverse fit
gives access to the kinetic rates: the position-dependent speeds and the entry
rate of ribosomes onto mRNA. The degradation rate is not, however, accounted
for and experimental data from different experiments are needed to have enough
parameters for the fit. Here, we propose an entirely novel experimental setup
and theoretical framework consisting in splitting the mRNAs into categories
depending on the number of ribosomes from one to four. We solve analytically
the ballistic model for a fixed number of ribosomes per mRNA, study the
different regimes of degradation, and propose a criteria for the quality of the
inverse fit. The proposed method provides a high sensitivity to the mRNA
degradation rate. The additional equations coming from using the monosome
(single ribosome) and polysome (arbitrary number) ribo-seq profiles enable us
to determine all the kinetic rates in terms of the experimentally accessible
mRNA degradation rate.