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

In a recent paper by Valleriani et al. [Phys. Rev. E 83, 042903 (2011)], a simple model for the translation of messenger RNA (mRNA) is presented. Using this model, the protein translational ratio r, defined as the ratio of protein translation rate ω(tl) from mRNA to protein degradation rate ω(p), is obtained. The key point in obtaining the translational ratio r is to get the protein translation rate ω(tl). In Valleriani et al.'s paper, ω(tl) is obtained as the mean value of the measured translation rate, which is the ratio of the synthesized protein number to the mRNA lifetime. However, in experiments, different methods might be used to obtain the value of ω(tl). Therefore, to apply Valleriani et al.'s model to more general experiments, in this Comment three methods to obtain the translation rate ω(tl), and consequently the translational ratio r, are presented. 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 mRNA length in prokaryotic cells, and decays reciprocally with mRNA length in eukaryotic cells. This result is slight different from that which was obtained in Valleriani et al.'s paper.