CSDL Home IEEE/ACM Transactions on Computational Biology and Bioinformatics 2013 vol.10 Issue No.05 - Sept.-Oct.

Subscribe

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

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

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

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. 5, pp. 1322-1328, Sept.-Oct. 2013, doi:10.1109/TCBB.2013.120REFERENCES

- [1] B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter,
Molecular Biology of the Cell. Garland Science, 2002.- [2] S. Zhang, E. Goldman, and G. Zubay, "Clustering of Low Usage Codons and Ribosome Movement,"
J. Theoretical Biology, vol. 170, pp. 339-354, 1994.- [3] A. Dana and T. Tuller, "Efficient Manipulations of Synonymous Mutations for Controlling Translation Rate: An Analytical Approach,"
J. Computational Biology, vol. 19, pp. 200-231, 2012.- [4] R. Heinrich and T. Rapoport, "Mathematical Modelling of Translation of mRNA in Eucaryotes; Steady State, Time-Dependent Processes and Application to Reticulocytes,"
J. Theoretical Biology, vol. 86, pp. 279-313, 1980.- [5] C.T. MacDonald, J.H. Gibbs, and A.C. Pipkin, "Kinetics of Biopolymerization on Nucleic Acid Templates,"
Biopolymers, vol. 6, pp. 1-25, 1968.- [6] T. Tuller, I. Veksler, N. Gazit, M. Kupiec, E. Ruppin, and M. Ziv, "Composite Effects of the Coding Sequences Determinants on the Speed and Density of Ribosomes,"
Genome Biology, vol. 12, no. 11,article R110, 2011.- [7] T. Tuller, M. Kupiec, and E. Ruppin, "Determinants of Protein Abundance and Translation Efficiency in S. cerevisiae,"
PLoS Computational Biology, vol. 3, no. 12, article e248, 2007.- [8] L.B. Shaw, R.K. Zia, and K.H. Lee, "Totally Asymmetric Exclusion Process with Extended Objects: A Model for Protein Synthesis,"
Phys. Rev. E, vol. 68, article 021910, 2003.- [9] R. Zia, J. Dong, and B. Schmittmann, "Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments,"
J. Statistical Physics, vol. 144, pp. 405-428, 2011.- [10] A. Schadschneider, D. Chowdhury, and K. Nishinari,
Stochastic Transport in Complex Systems: From Molecules to Vehicles. Elsevier, 2011.- [11] S. Reuveni, I. Meilijson, M. Kupiec, E. Ruppin, and T. Tuller, "Genome-Scale Analysis of Translation Elongation with a Ribosome Flow Model,"
PLoS Computational Biology, vol. 7, article e1002127, 2011.- [12] J.B. Plotkin and G. Kudla, "Synonymous But Not the Same: The Causes and Consequences of Codon Bias,"
Nature Rev. Genetics, vol. 12, pp. 32-42, 2010.- [13] M. Kozak, "Point Mutations Define a Sequence Flanking the Aug Initiator Codon that Modulates Translation by Eukaryotic Ribosomes,"
Cell, vol. 44, no. 2, pp. 283-292, 1986.- [14] M. Margaliot and T. Tuller, "Stability Analysis of the Ribosome Flow Model,"
IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 9, no. 5, pp. 1545-1552, Sep./Oct. 2012.- [15] N.T. Ingolia, L. Lareau, and J. Weissman, "Ribosome Profiling of Mouse Embryonic Stem Cells Reveals the Complexity and Dynamics of Mammalian Proteomes,"
Cell, vol. 147, no. 4, pp. 789-802, 2011.- [16] M. Margaliot and T. Tuller, "On the Steady-State Distribution in the Homogeneous Ribosome Flow Model,"
IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 9, no. 6, pp. 1724-1736, Nov./Dec. 2012.- [17] M. Margaliot and T. Tuller, "Ribosome Flow Model with Positive Feedback,"
J. Royal Soc. Interface, vol. 10, article 20130267, 2013.- [18] W.B. Jones and W.J. Thron,
Continued Fractions: Analytic Theory and Applications. Addison-Wesley, 1980.- [19] G. Kudla, A.W. Murray, D. Tollervey, and J.B. Plotkin, "Coding-Sequence Determinants of Gene Expression in Escherichia coli,"
Science, vol. 324, pp. 255-258, 2009.- [20] F. Supek and T. Smuc, "On Relevance of Codon Usage to Expression of Synthetic and Natural Genes in Escherichia coli,"
Genetics, vol. 185, pp. 1129-1134, 2010.- [21] T. Tuller, Y.Y. Waldman, M. Kupiec, and E. Ruppin, "Translation Efficiency Is Determined by Both Codon Bias and Folding Energy,"
Proc. Nat'l Academy of Sciences USA, vol. 107, no. 8, pp. 3645-3650, 2010.- [22] H. Zur and T. Tuller, "New Universal Rules of Eukaryotic Translation Initiation Fidelity,"
PLoS Computational Biology, vol. 9, no. 7, article e1003136, 2013.- [23] T. Tuller, A. Carmi, K. Vestsigian, S. Navon, Y. Dorfan, J. Zaborske, T. Pan, O. Dahan, I. Furman, and Y. Pilpel, "An Evolutionarily Conserved Mechanism for Controlling the Efficiency of Protein Translation,"
Cell, vol. 141, no. 2, pp. 344-354, 2010.- [24] S. Lee, B. Liu, S. Lee, S. Huang, B. Shen, and S. Qian, "Global Mapping of Translation Initiation Sites in Mammalian Cells at Single-Nucleotide Resolution,"
Proc. Nat'l Academy of Sciences USA, vol. 109, no. 37, pp. E2424-E2432, 2012.- [25] N.T. Ingolia, S. Ghaemmaghami, J.R. Newman, and J.S. Weissman, "Genome-Wide Analysis In Vivo of Translation with Nucleotide Resolution Using Ribosome Profiling,"
Science, vol. 324, no. 5924, pp. 218-223, 2009.- [26] B. Schwanhausser, D. Busse, N. Li, G. Dittmar, J. Schuchhardt, J. Wolf, W. Chen, and M. Selbach, "Global Quantification of Mammalian Gene Expression Control,"
Nature, vol. 473, no. 7347, pp. 337-342, 2011.- [27] L. Lorentzen and H. Waadeland,
Continued Fractions: Convergence Theory, second ed., Atlantis Press, vol. 1, 2008.- [28] D. Angeli and E.D. Sontag, "Monotone Control Systems,"
IEEE Trans. Automatic Control, vol. 48, no. 10, pp. 1684-1698, Oct. 2003.- [29] P.D. Leenheer, D. Angeli, and E.D. Sontag, "Monotone Chemical Reaction Networks,"
J. Math. Chemistry, vol. 41, pp. 295-314, 2007.- [30] G. Enciso and E.D. Sontag, "Monotone Systems under Positive Feedback: Multistability and a Reduction Theorem,"
Systems and Control Letters, vol. 54, pp. 159-168, 2005.- [31] D. Angeli and E.D. Sontag, "Oscillations in I/O Monotone Systems under Negative Feedback,"
IEEE Trans. Automatic Control, vol. 53, no. Special Issue, pp. 166-176, Jan. 2008.- [32] L. Wang, P. de Leenheer, and E.D. Sontag, "Conditions for Global Stability of Monotone Tridiagonal Systems with Negative Feedback,"
Systems Control Letters, vol. 59, pp. 130-138, 2010.- [33] A.W. Craig, A. Haghighat, A.T. Yu, and N. Sonenberg, "Interaction of Polyadenylate-Binding Protein with the eIF4G Homologue PAIP Enhances Translation,"
Nature, vol. 392, no. 6675, pp. 520-523, 1998.- [34] S.Z. Tarun and A.B. Sachs, "Binding of Eukaryotic Translation Initiation Factor 4E (eIF4E) to eIF4G Represses Translation of Uncapped mRNA,"
Molecular and Cellular Biology, vol. 17, pp. 6876-6886, 1997.- [35] M. Margaliot, E.D. Sontag, and T. Tuller, "Entrainment to Periodic Initiation and Transition Rates in the Ribosome Flow Model," http://www.eng.tau.ac.il/~michaelmRFM_entrain.pdf , 2013.
- [36] M. Frenkel-Morgenstern, T. Danon, T. Christian, T. Igarashi, L. Cohen, Y.M. Hou, and L.J. Jensen, "Genes Adopt Non-Optimal Codon Usage to Generate Cell Cycle-Dependent Oscillations in Protein Levels,"
Molecular Systems Biology, vol. 8, article 572, 2012.- [37] Y. Xu, P. Ma, P. Shah, A. Rokas, Y. Liu, and C.H. Johnson, "Non-Optimal Codon Usage is a Mechanism to Achieve Circadian Clock Conditionality,"
Nature, vol. 495, pp. 116-120, 2013.- [38] M. Zhou, J. Guo, J. Cha, M. Chae, S. Chen, J.M. Barral, M.S. Sachs, and Y. Liu, "Non-Optimal Codon Usage Affects Expression, Structure and Function of Clock Protein FRQ,"
Nature, vol. 495, pp. 111-115, 2013.- [39] K. Kruse and F. Julicher, "Oscillations in Cell Biology,"
Current Opinion in Cell Biology, vol. 17, no. 1, pp. 20-26, 2005.- [40] S. Srinivasa and M. Haenggi, "A Statistical Mechanics-Based Framework to Analyze Ad Hoc Networks with Random Access,"
IEEE Trans. Mobile Computing, vol. 11, no. 4, pp. 618-630, Apr. 2012.- [41] D. Chowdhury, A. Schadschneider, and K. Nishinari, "Physics of Transport and Traffic Phenomena in Biology: From Molecular Motors and Cells to Organisms,"
Physics of Life Rev., vol. 2, pp. 318-352, 2005. |