Molecular traffic control in single-file networks with fast catalysts

As a model for molecular traffic control we investigate the diffusion of hard core particles in crossed single-file systems. We consider a square lattice of single-files being connected to external reservoirs. The (vertical) alpha channels, carrying only A particles, are connected to reservoirs with constant density rho(A). B particles move along the (horizontal) beta channels, which are connected to reservoirs of density rho(B). We allow the irreversible transition A-->B at intersections. We are interested in the stationary density profile in the alpha and beta channels, which is the distribution of the occupation probabilities over the lattice. We calculate the stationary currents of the system and show that for sufficiently long channels the currents (as a function of the reservoir densities) show in the limit of large transition rates nonanalytic behavior. The results obtained by direct solution of the master equation are verified by kinetic Monte Carlo simulations.