  We construct an algorithm that generates large, band-diagonal transition
matrices for a totally asymmetric exclusion process (TASEP) with local hopping
rate inhomogeneities. The matrices are diagonalized numerically to find
steady-state currents of TASEPs with local variations in hopping rate. The
results are then used to investigate clustering of slow codons along mRNA.
Ribosome density profiles near neighboring clusters of slow codons interact,
enhancing suppression of ribosome throughput when such bottlenecks are closely
spaced. Increasing the slow codon cluster size, beyond $\approx 3-4$, does not
significantly reduce ribosome current. Our results are verified by extensive
Monte-Carlo simulations and provide a biologically-motivated explanation for
the experimentally-observed clustering of low-usage codons.

Statistical Mechanics;Soft Condensed Matter;Subcellular Processes