Exclusion model of mRNA translation with collision-induced ribosome drop-off

The translation of messenger RNA transcripts to proteins is commonly modeled as a one-dimensional totally asymmetric exclusion process with extended particles. Here we focus on the effects of premature termination of translation through the irreversible detachment of ribosomes. We consider a model where the detachment is induced by the unsuccessful attempt to move to an occupied site. The model is exactly solvable in a simplified geometry consisting of the translation initiation region followed by a single slow site representing a translation bottleneck. In agreement with recent experimental and computational studies we find a non-monotonic dependence of the ribosome current on the initiation rate, but only if the leading particle in a colliding pair detaches. Simulations show that the effect persists for larger lattices and extended bottlenecks. In the homogeneous system the ribosome density decays asymptotically as the inverse square root of the distance to the initiation site.