A 3-species Exclusion Process: a model motivated by Leaky Initiation and Interference in Protein Synthesis

The totally asymmetric simple exclusion process (TASEP) was originally introduced fifty years ago as a model for the synthesis of biopolymers, called protein, by macromolecular machines called ribosome. In that formulation, the mRNA template for protein synthesis, that also serves as the track for the motor-like movement of the ribosomes, is represented by a lattice. We introduce a 3-species exclusion model that captures some of the hitherto neglected, but crucially important, details of the initiation of protein synthesis. We study the interference of the synthesis of two different proteins, the templates for which are encoded on two different, but overlapping, segments of the same lattice. We formulate the process of search for the start sites for protein synthesis as first-passage problems and calculate the mean initiation times for the synthesis of the two species of proteins. We show how the mean initiation times get affected by ``leaky scanning’’ and the interference of the three exclusion processes.