Issue No. 05 - Sept.-Oct. (2013 vol. 10)

ISSN: 1545-5963

pp: 1322-1328

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TCBB.2013.120

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

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.

INDEX TERMS

Proteins, Steady-state, Mathematical model, Biological system modeling, Genetics, Computational modeling,periodic continued fractions, Gene translation, systems biology, computational models, monotone dynamical systems

CITATION

Yoram Zarai, Michael Margaliot, Tamir Tuller, "Explicit Expression for the Steady-State Translation Rate in the Infinite-Dimensional Homogeneous Ribosome Flow Model",

*IEEE/ACM Transactions on Computational Biology and Bioinformatics*, vol. 10, no. , pp. 1322-1328, Sept.-Oct. 2013, doi:10.1109/TCBB.2013.120