Refined mean-field approaches to ``edge-effects'' in open TASEP's

We study the totally asymmetric simple exclusion process (TASEP) with a defect site, hopping rate $q <$ 1, at the edge of the system and particles occupying $\ell$ lattice sites. Using two different mean-field approximations, we analyze the behavior of the steady state current $J$ in the presence of the defect as a function of entry rate $\alpha $ and $q.$ In good agreement with Monte Carlo simulations, these two methods bring insight to understanding the significance of having one or a cluster of slow codons (unit of messenger RNA, template of protein synthesis) immediately after initiation during protein synthesis. Related work is published in Journal of Physics A, vol. 41 (2008).