Abstract
Existing evidence such as codon usage bias suggests that protein translation of fast-growing organisms has been optimised for accuracy and better yield. One possibility for optimisation stems from the fact that different codons are translated at different rates. Common measures for optimal codon choice, which ignore the dynamics of this process, have so far had mixed success in predicting protein levels. Recent advances in experimental techniques such as ribosome profiling allow us to study dynamical details of this intricate process and theoretical modelling is required to interpret the new data. In this work we study a kinetic model for translation that takes into account stochastic movement of individual ribosomes along the mRNA molecule. Unlike previous studies of this and similar models that were limited to numerical simulations, we develop a novel mathematical method to find the steady state solution when the translation initiation is a rate-limiting step. This allows us, for the first time, to find an analytic prediction for the translation rate and ribosome density. We use these predictions to address some of the long-standing controversies surrounding the determinants of translation efficiency.