  The process of protein synthesis in biological systems resembles a one
dimensional driven lattice gas in which the particles have spatial extent,
covering more than one lattice site. We expand the well studied Totally
Asymmetric Exclusion Process (TASEP), in which particles typically cover a
single lattice site, to include cases with extended objects. Exact solutions
can be determined for a uniform closed system. We analyze the uniform open
system through two approaches. First, a continuum limit produces a modified
diffusion equation for particle density profiles. Second, an extremal principle
based on domain wall theory accurately predicts the phase diagram and currents
in each phase. Finally, we briefly consider approximate approaches to a
non-uniform open system with quenched disorder in the particle hopping rates
and compare these approaches with Monte Carlo simulations.
