  Protein translation is one of the most important processes in cell life but,
despite being well understood biochemically, the implications of its intrinsic
stochastic nature have not been fully elucidated. In this paper we develop a
microscopic and stochastic model which describes a crucial step in protein
translation, namely the binding of the tRNA to the ribosome. Our model
explicitly takes into consideration tRNA recharging dynamics, spatial
inhomogeneity and stochastic fluctuations in the number of charged tRNAs around
the ribosome. By analyzing this non-equilibrium system we are able to derive
the statistical distribution of the times needed by the tRNAs to bind to the
ribosome, and to show that it deviates from an exponential due to the coupling
between the fluctuations of charged and uncharged populations of tRNA.
