(132c) Stochastic Events in Protein Synthesis

A mathematical model is presented to describe the stochastic events which occur during protein synthesis. Different outcomes compete, based on kinetic rates, and the desirable (correct) outcome usually has highest probability to realize. Undesirable outcomes are directly related to errors, thus stochastic models afford average translation rates as well as error estimates. A new view towards protein synthesis and synthesis errors is taken in this analysis. The translation of messenger RNA (mRNA) from its 5' end to is 3' end by the ribosome involves two sequential steps: (1) codon interpretation and amino acids insertion and (2) translocation of the ribosome to read the next codon. Previous studies have focused on errors associated with the first step ? misacetylation of transport RNA (tRNA) and mistranslation by near cognate amino-acetylated tRNAs. But incorrect translocation has been limited to mechanistic studies on ribosomal frameshifting. Since the mRNA is translated three nucleic acids at a time (triplets or codons), three reading frames exist: the zero reading frame defines the protein sequence that is intended, the -1 reading frame is defined as the set of codons which are formed by shifting one position in the 5' direction and the +1 reading frame is formed by a shift of one position in the 3' direction. The concept of a tri-frame translational process is introduced. Three different protein sequences are encoded in the three reading frames, and the ribosome can access different reading frames. A stochastic model for frameshifting is presented. Although several factors influence the frameshifting process, a major contributor is the pausing of the ribosome to await the arrival of the cognate aa-tRNA. This mechanism links the frameshifting to the availability of cognate aa-tRNA and thus connects the ribosome kinetics with species transport. The model is illustrated for several genes of E. coli and it is shown that frameshifting becomes a post-transcriptional regulatory mechanism. A very interesting example of autogeneous control is the prfB gene, because an intentional frameshift at the 26th codon is required to synthesize the correct gene. The theory provides exact expressions for translational efficiency.