On the stationary frequency of programmed ribosomal-1 frameshift

We present a stochastic model for programmed ribosomal -1 frameshift, triggered by a slippery sequence and a following pseudoknot on the mRNA template, that allows for the exact derivation of the stationary distribution of ribosome positions and for exact analytical calculations of the stationary rate of frameshift, its efficiency and other quantities of interest. We also present the stationary phase diagram as a function of the initiation rate and the density ribosomes that the pseudoknot can support. These observations provide mathematically rigorous evidence for the notion that the density of molecular motors is an important control parameter for the elongation rate in the presence of slippery sequences both in transcription of RNA and translation of proteins.