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Totally asymmetric simple exclusion process (TASEP) was originally introducedas a model for the traffic-like collective movement of ribosomes on a messengerRNA (mRNA) that serves as the track for the motor-like forward stepping ofindividual ribosomes. In each step, a ribosome elongates a protein by a singleunit using the track also as a template for protein synthesis. But,pre-fabricated, functionally competent, ribosomes are not available to beginsynthesis of protein; a subunit directionally scans the mRNA in search of thepre-designated site where it is supposed to bind with the other subunit andbegin the synthesis of the corresponding protein. However, because of `leaky'scanning, a fraction of the scanning subunits miss the target site and continuetheir search beyond the first target. Sometimes such scanners successfullyidentify the site that marks the site for initiation of the synthesis of adifferent protein. In this paper, we develop an exclusion model, with threeinterconvertible species of hard rods, to capture some of the key features ofthese biological phenomena and study the effects of the interference of theflow of the different species of rods on the same lattice. More specifically,we identify the meantime for the initiation of protein synthesis as appropriatemean {\it first-passage} time that we calculate analytically using theformalism of backward master equations. In spite of the approximations made,our analytical predictions are in reasonably good agreement with the numericaldata that we obtain by performing Monte Carlo simulations. We also compare ourresults with a few experimental facts reported in the literature and proposenew experiments for testing some of our new quantitative predictions.

A biologically motivated three-species exclusion model: effects of leaky scanning and overlapping genes on initiation of protein synthesis