TY - JOUR

T1 - Explicit Expression for the steady-state translation rate in the infinite-dimensional homogeneous Ribosome Flow Model

AU - Zarai, Yoram

AU - Margaliot, Michael

AU - Tuller, Tamir

PY - 2013/9

Y1 - 2013/9

N2 - 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.

AB - 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.

KW - Gene translation

KW - computational models

KW - monotone dynamical systems

KW - periodic continued fractions

KW - systems biology

UR - http://www.scopus.com/inward/record.url?scp=84894598328&partnerID=8YFLogxK

U2 - 10.1109/TCBB.2013.120

DO - 10.1109/TCBB.2013.120

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AN - SCOPUS:84894598328

SN - 1545-5963

VL - 10

SP - 1322

EP - 1328

JO - IEEE/ACM Transactions on Computational Biology and Bioinformatics

JF - IEEE/ACM Transactions on Computational Biology and Bioinformatics

IS - 5

M1 - 6731359

ER -