  Messenger RNA translation is often studied by means of statistical-mechanical
models based on the Asymmetric Simple Exclusion Process (ASEP), which considers
hopping particles (the ribosomes) on a lattice (the polynucleotide chain). In
this work we extend this class of models and consider the two fundamental steps
of the ribosome's biochemical cycle following a coarse-grained perspective. In
order to achieve a better understanding of the underlying biological processes
and compare the theoretical predictions with experimental results, we provide a
description lying between the minimal ASEP-like models and the more detailed
models, which are analytically hard to treat. We use a mean-field approach to
study the dynamics of particles associated with an internal stepping cycle. In
this framework it is possible to characterize analytically different phases of
the system (high density, low density or maximal current phase). Crucially, we
show that the transitions between these different phases occur at different
parameter values than the equivalent transitions in a standard ASEP, indicating
the importance of including the two fundamental steps of the ribosome's
biochemical cycle into the model.
