  We study a two filament driven lattice gas model with oppositely directed
species of particles moving on two parallel filaments with filament switching
processes and particle inflow and outflow at filament ends. The filament
switching process is {\it correlated} such that particles switch filaments with
finite probability only when oppositely directed particles meet on the same
filament. This model mimics some of the coarse grained features observed in
context of microtubule (MT) based intracellular transport, wherein cellular
cargo loaded and off-loaded at filament ends are transported on multiple
parallel microtubule (MT) filaments and can switch between the parallel
microtubule filaments. We focus on a regime where the filaments are weakly
coupled, such that filament switching rates scale inversely as the length of
the filament. We find that the interplay (off)loading processes at the
boundaries and the filament switching process leads to some distinctive
features of the system. These features includes occurrence of variety of phases
in the system with inhomogeneous density profiles including localized density
shocks, density difference across the filaments and bidirectional current flows
in the system. We analyze the system by developing a mean field (MF) theory and
comparing the results obtained from the MF theory with the Monte Carlo (MC)
simulations of the dynamics of the system. We find that the steady state
density and current profiles of particles and the phase diagram obtained within
the MF picture matches quite well with MC simulation results. These findings
maybe useful for studying multi-filament intracellular transport.
