  Recent advances in DNA sequencing and fluorescence imaging have made it
possible to monitor the dynamics of ribosomes actively engaged in messenger RNA
(mRNA) translation. Here, we model these experiments within the inhomogeneous
totally asymmetric simple exclusion process (TASEP) using realistic kinetic
parameters. In particular we present analytic expressions to describe the
following three cases: (a) translation of a newly transcribed mRNA, (b)
translation in the steady state and, specifically the dynamics of individual
(tagged) ribosomes and (c) run-off translation after inhibition of translation
initiation. In the cases (b) and (c) we develop an effective medium
approximation to describe many-ribosome dynamics in terms of a single tagged
ribosome in an effective medium. The predictions are in good agreement with
stochastic simulations.
