  We develop a stochastic model for the programmed frameshift of ribosomes
synthesizing a protein while moving along a mRNA template. Normally the reading
frame of a ribosome decodes successive triplets of nucleotides on the mRNA in a
step-by-step manner. We focus on the programmed shift of the ribosomal reading
frame, forward or backward, by only one nucleotide which results in a fusion
protein; it occurs when a ribosome temporarily loses its grip to its mRNA
track. Special "slippery" sequences of nucleotides and also downstream
secondary structures of the mRNA strand are believed to play key roles in
programmed frameshift. Here we explore the role of an hitherto neglected
parameter in regulating -1 programmed frameshift. Specifically, we demonstrate
that the frameshift frequency can be strongly regulated also by the density of
the ribosomes, all of which are engaged in simultaneous translation of the same
mRNA, at and around the slippery sequence. Monte Carlo simulations support the
analytical predictions obtained from a mean-field analysis of the stochastic
dynamics.
