Comment on "Length-dependent translation of messenger RNA by ribosomes"

In the recent paper of Valleriani {\it et al} [Phys. Rev. E {\bf 83}, 042903 (2011)], a simple model for describing the translation of messenger RNA (mRNA) by ribosomes is presented, and an expression of the translational ratio $r$, defined as the ratio of translation rate ${\omega }_{\mathrm{t}\mathrm{l}}$ of protein from mRNA to degradation rate ${\omega }_p$ of protein, is obtained. The key point to get this ratio $r$ is to get the translation rate ${\omega }_{\mathrm{t}\mathrm{l}}$. In the study of Valleriani {\it et al}, ${\omega }_{\mathrm{t}\mathrm{l}}$ is assumed to be the mean value of measured translation rate, i.e. the mean value of ratio of the translation number of protein to the lifetime of mRNA. However, in experiments different methods might be used to get ${\omega }_{\mathrm{t}\mathrm{l}}$. Therefore, for the sake of future application of their model to more experimental data analysis, in this comment three methods to get the translation rate ${\omega }_{\mathrm{t}\mathrm{l}}$, and consequently the translational ratio $r$, are provided. Based on one of the methods which might be employed in most of the experiments, we find that the translational ratio $r$ decays exponentially with the length of mRNA in prokaryotic cells, and decays reciprocally with the length of mRNA in eukaryotic cells. This result is slight different from that obtained in Valleriani’s study.