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Non-equilibrium, stochastic model for tRNA binding time statistics

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.