Title: Interference of two co-directional exclusion processes in the presence of a static bottleneck: a biologically motivated model,
Abstract: We develope a two-species exclusion process with a distinct pair of entry and
exit sites for each species of rigid rods. The relatively slower forward
stepping of the rods in an extended bottleneck region, located in between the
two entry sites, controls the extent of interference of the co-directional flow
of the two species of rods. The relative positions of the sites of entry of the
two species of rods with respect to the location of the bottleneck are
motivated by a biological phenomenon. However, the primary focus of the study
here is to explore the effects of the interference of the flow of the two
species of rods on their spatio-temporal organization and the regulations of
this interference by the extended bottleneck. By a combination of mean-field
theory and computer simulation we calculate the flux of both species of rods
and their density profiles as well as the composite phase diagrams of the
system. If the bottleneck is sufficiently stringent some of the phases become
practically unrealizable although not ruled out on the basis of any fundamental
physical principle. Moreover the extent of suppression of flow of the
downstream entrants by the flow of the upstream entrants can also be regulated
by the strength of the bottleneck. We speculate on the possible implications of
the results in the context of the biological phenomenon that motivated the
formulation of the theoretical model.