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Issue No. 05 - Sept.-Oct. (2013 vol. 10)
ISSN: 1545-5963
pp: 1322-1328
Yoram Zarai , Sch. of Electr. Eng., Tel-Aviv Univ., Tel-Aviv, Israel
Michael Margaliot , Sch. of Electr. Eng., Tel-Aviv Univ., Tel-Aviv, Israel
Tamir Tuller , Sch. of Electr. Eng., Tel-Aviv Univ., Tel-Aviv, Israel
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.
Proteins, Steady-state, Mathematical model, Biological system modeling, Genetics, Computational modeling

Y. Zarai, M. Margaliot and T. Tuller, "Explicit Expression for the Steady-State Translation Rate in the Infinite-Dimensional Homogeneous Ribosome Flow Model," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 5, pp. 1322-1328, 2014.
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