A model for mis-sense error in protein synthesis: mis-charged cognate tRNA versus mis-reading of codon

The sequence of amino acid monomers in the primary structure of protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by incorporation of the successive amino acid monomers, is carried out by a molecular machine called ribosome. Transfer RNA (tRNA) molecules, each species of which is "charged" with a specific amino acid, enters the ribosome and participates in the reading of the codon by the ribosome. Both mis-reading of mRNA codon and prior mis-charging of a tRNA can lead to "mis-sense" error, i.e,. erroneous substitution of a correct amino acid monomer by an incorrect one during the synthesis of a protein. We develop a theoretical model of protein synthesis that allows for both types of contributions to the "mis-sense" error. We report exact analytical formulae for several quantities that characterize the interplay of mis-charging of tRNA and mis-reading of mRNA. The average rate of elongation of a protein is given by a generalized Michaelis-Menten-like formula. We discuss the main implications of these results. These formulae will be very useful in future in analyzing the data collected during experimental investigations of this phenomenon.