Translation is a central cellular process and the complexity of its mechanism necessitates mathematical frameworks to better understand system properties and make quantitative predictions for many problems in medicine and biotechnology. Translation is essentially a polymerization process facilitated by the ribosome on an mRNA template consisting of initiation, elongation, and termination phases. Initiation occurs with binding of the ribosome to the ribosomal binding site near the 5' end of the mRNA. During elongation the ribosome facilitates assembly of the polypeptide chain with one amino acid added at each codon along the length of the mRNA. Amino acids are delivered to the ribosome by tRNAs, in the form of ternary complexes, that serve as adapter molecules between the amino acid and the codon occupying the ribosomal A site. Termination involves release of the completed peptide from the ribosome near the 3' end of the mRNA. Several ribosomes can simultaneously translate the same mRNA, forming a structure called a polysome.

We have developed a gene sequence specific mechanistic model for translation which accounts for all the elementary steps of translation elongation. Included in our model is the non-specific binding of tRNAs to the ribosomal A site, and we find that the competitive, non-specific binding of the tRNAs is the rate limiting step in the elongation cycle for every codon. By introducing our model in terms of the Michaelis – Menten kinetic framework, we determine that these results are due to the tRNAs that do not recognize the ribosomal A site codon acting as competitive inhibitors to the tRNAs that do recognize the ribosomal A site codon.

We present the results of a sensitivity analysis to determine the contribution of elongation cycle kinetic parameters of each codon on the overall translation rate. Our sensitivity analysis predicts that at low polysome sizes the codons near the 5' end of the mRNA control the rate, at intermediate polysome sizes different configurations of codons along the length of the mRNA control the rate, and at high polysome sizes the codons near the 3' end of the mRNA control the rate. We observe that the relative position of codons along the mRNA determines the optimal protein synthesis rate and the rate limiting effect of the individual codons. Our results have implications in design of rational protein production systems, wherein quantitative knowledge of responses of protein expression to genetic or environmental perturbations can be used to optimize a cellular system towards the production of a protein of interest.