title: Explicit expression for the steady-state translation rate in the infinite-dimensional homogeneous ribosome flow model.
abstract: Gene translation is a central stage in the intracellular process of protein synthesis. Gene translation proceeds in three major stages: initiation, elongation, and termination. During the elongation step, ribosomes (intracellular macromolecules) 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 ordinary differential equations, 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. We also derive bounds that show that the behavior of the HRFM for finite, and relatively small, values of $(n)$ is already in good agreement with the closed-form result in the infinite-dimensional case. For example, for $(n=15)$, the relative error is already less than 4 percent. Our results can, thus, be used in practice for analyzing the behavior of finite-dimensional HRFMs that model translation. To demonstrate this, we apply our approach to estimate the mean initiation rate in M. musculus, finding it to be around 0.17 codons per second.
authors.affiliation: Tel-Aviv University, Tel-Aviv.
authors.forename: Yoram
authors.initials: Y
authors.lastname: Zarai
authors.affiliation: Tel-Aviv University, Tel-Aviv.
authors.forename: Michael
authors.initials: M
authors.lastname: Margaliot
authors.affiliation: Tel-Aviv University, Tel-Aviv.
authors.forename: Tamir
authors.initials: T
authors.lastname: Tuller
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008957:Models, Genetic; D014176:Protein Biosynthesis / Q000235:genetics*; D012270:Ribosomes / Q000235:genetics*