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Issue No. 06 - Nov.-Dec. (2012 vol. 9)
ISSN: 1545-5963
pp: 1724-1736
M. Margaliot , Sch. of Electr. Eng.-Syst., Tel-Aviv Univ., Tel-Aviv, Israel
T. Tuller , Dept. of Biomed. Eng., Tel-Aviv Univ., Tel-Aviv, Israel
ABSTRACT
A central biological process in all living organisms is gene translation. Developing a deeper understanding of this complex process may have ramifications to almost every biomedical discipline. Reuveni et al. recently proposed a new computational model of gene translation called the Ribosome Flow Model (RFM). In this paper, we consider a particular case of this model, called the Homogeneous Ribosome Flow Model (HRFM). From a biological viewpoint, this corresponds to the case where the transition rates of all the coding sequence codons are identical. This regime has been suggested recently based on experiments in mouse embryonic cells. We consider the steady-state distribution of the HRFM. We provide formulas that relate the different parameters of the model in steady state. We prove the following properties: 1) the ribosomal density profile is monotonically decreasing along the coding sequence; 2) the ribosomal density at each codon monotonically increases with the initiation rate; and 3) for a constant initiation rate, the translation rate monotonically decreases with the length of the coding sequence. In addition, we analyze the translation rate of the HRFM at the limit of very high and very low initiation rate, and provide explicit formulas for the translation rate in these two cases. We discuss the relationship between these theoretical results and biological findings on the translation process.
INDEX TERMS
Computational modeling, Mathematical model, Biological system modeling, Bioinformatics, Steady-state, Encoding,constant elongation speed, Gene translation, systems biology, continued fractions, tridiagonal matrices, equilibrium point, monotone systems, translation elongation
CITATION
M. Margaliot, T. Tuller, "On the Steady-State Distribution in the Homogeneous Ribosome Flow Model", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. , pp. 1724-1736, Nov.-Dec. 2012, doi:10.1109/TCBB.2012.120
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