TASEP with extended particles and local inhomogeneities

Though much is known about the totally asymmetric simple exclusion process (TASEP), there are still non-trivial characteristics worthy of further exploration. In particular, in TASEPs with extended particles that ``cover'' $\ell >1$ lattice sites, non-trivial correlations between the particles exist, even for a case with a trivial distribution for the microscopic configurations. Further, $\xi $, the characteristic length of these correlations can be extremely long, e.g., $O\left( 10^{2}\right) $. They set up interesting structures in the density profile behind ``bottlenecks'' (localized inhomogeneities, with hopping rates $q$ smaller than those in the rest of the lattice: $q<1$) in the system. For TASEPs with open boundaries, we study how one or more such bottlenecks affect both the profiles and the overall current. Using simulations, we present results for a range of $% q,\ell ,$ and the {\em locations }of the inhomogeneities: $x_{i}$. For example, the current is somewhat enhanced if a single bottleneck is located close to either system boundary. But it is reduced significantly if two bottlenecks are present and closely spaced, i.e., provided $\left| x_{1}-x_{2}\right| $$\leq$ $\xi .$ We also discuss the possible impact of these findings on ribosome queueing and codon optimization in protein production.