Analysis of the steady state translation rate in the infinite-dimensional homogeneous ribosomeflowmodel ?

Gene translation is a central stage in the intra-cellular process of protein synthesis. Gene translation proceeds in three major stages: initiation, elongation, and termination. During the elongation step ribosomes (intra cellular macro-molecules) link amino acids together in the order specified by messenger RNA (mRNA) molecules. The homogeneous ribosome flow model (HRFM) is a mathematical model of translation elongation under the assumption of constant elongation rate along the mRNA sequence. The HRFM includes n first-order nonlinear ODEs, where n represents the length of the mRNA sequence, and two positive parameters: ribosomal initiation rate and the (constant) elongation rate. Here we analyze the HRFM when n goes to infinity and derive a simple expression for the steady-state protein synthesis rate. Simulations suggest that the behavior of the HRFM for n ≥ 15 is already in good agreement with the behavior in the case of infinite n studied here. Thus, our result may be used in practice for estimating the translation rates of different genes or for engineering genes to produce a desired translation rate.