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Translation is an important process for prokaryotic and eukaryotic cells toproduce necessary proteins for cell growth. Numerious experiments have beenperformed to explore the translational properties. Diverse models have alsobeen developed to determine the biochemical mechanism of translation. However,to simplify the majority of the existing models, the frameshifting of ribosomealong the mRNA transcript is neglected, which actually occurs in real cells andhas been extensively experimentally studied. The frameshifting of ribosomeevidently influences the efficiency and speed of translation, considering thatthe peptide chains synthesized by shifted ribosomes will not fold intofunctional proteins and will degrade rapidly. In this study, a theoreticalmodel is presented to describe the translational process based on the model fortotally asymmetric simple exclusion process. In this model, the frameshiftingof the ribosome along the mRNA transcript and the attachment/detachment of theribosome to/from the main body of mRNA codons during translation elongationprocess, are explicitly included. The results show that, with ribosomeframeshifing, the speed of correctly synthesized peptide chains may increasefirst and then decrease with both the translation initiation rate $\alpha$ andthe ribosome detachment rate $\omega_d$. This results indicates that regulatingthe translation process to reach maximal synthesized speed of proteins istheoretically feasible. Traffic-related problems of ribosome motion along themRNA transcript are also addressed theoretically. Depending on parametervalues, shock wave (or domain wall) may exist for ribosome probabilities alongthe mRNA.

Translation with frameshifting of ribosome along mRNA transcript