The Community for Technology Leaders
RSS Icon
Issue No.05 - Sept.-Oct. (2012 vol.9)
pp: 1545-1552
Michael Margaliot , Sch. of Electr. Eng., Tel-Aviv Univ., Tel-Aviv, Israel
Tamir Tuller , Dept. of Biomed. Eng., Tel-Aviv Univ., Tel-Aviv, Israel
Gene translation is a central process in all living organisms. Developing a better understanding of this complex process may have ramifications to almost every biomedical discipline. Recently, Reuveni et al. proposed a new computational model of this process called the ribosome flow model (RFM). In this study, we show that the dynamical behavior of the RFM is relatively simple. There exists a unique equilibrium point e and every trajectory converges to e. Furthermore, convergence is monotone in the sense that the distance to e can never increase. This qualitative behavior is maintained for any feasible set of parameter values, suggesting that the RFM is highly robust. Our analysis is based on a contraction principle and the theory of monotone dynamical systems. These analysis tools may prove useful in studying other properties of the RFM as well as additional intracellular biological processes.
physiological models, cellular biophysics, genetics, intracellular biological process, stability analysis, ribosome flow model, gene translation, living organisms, biomedical discipline, computational model, dynamical behavior, RFM, equilibrium point, contraction principle, monotone dynamical systems, Trajectory, Computational modeling, Mathematical model, Biological system modeling, Indexes, Vectors, Equations, tridiagonal cooperative systems., Gene translation, systems biology, computational models, monotone dynamical systems
Michael Margaliot, Tamir Tuller, "Stability Analysis of the Ribosome Flow Model", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.9, no. 5, pp. 1545-1552, Sept.-Oct. 2012, doi:10.1109/TCBB.2012.88
[1] C. Kimchi-Sarfaty, J. Oh, I. Kim, Z. Sauna, A. Calcagno, S. Ambudkar, and M. Gottesman, "A "Silent" Polymorphism in the Mdr1 Gene Changes Substrate Specificity," Science, vol. 315, pp. 525-528, 2007.
[2] J. Coleman, D. Papamichail, S. Skiena, B. Futcher, E. Wimmer, and S. Mueller, "Virus Attenuation by Genome-Scale Changes in Codon Pair Bias," Science, vol. 320, pp. 1784-1787, 2008.
[3] I. Bahir, Y. Prat, M. Linial, and M. Fromer, "Viral Adaptation to Host: A Proteome-Based Analysis of Codon Usage and Amino Acid Preferences," Molecular Systems Biology, vol. 5, pp. 1-14, 2009.
[4] A. van Weringh, M. Ragonnet-Cronin, E. Pranckeviciene, M. Pavon-Eternod, L. Kleiman, and X. Xia, "Hiv-1 Modulates the Trna Pool to Improve Translation Efficiency," Molecular Biology Evolution, vol. 28, no. 6, pp. 1827-1834, 2011.
[5] C. Vogel, S.A. Rde, D. Ko, S. Le, B. Shapiro, S. Burns, D. Sandhu, D. Boutz, E. Marcotte, and L. Penalva, "Sequence Signatures and Mrna Concentration Can Explain Two-Thirds of Protein Abundance Variation in a Human Cell Line," Molecular Systems Biology, vol. 6, pp. 1-9, 2010.
[6] C. Pearson, "Repeat Associated Non-ATG Translation Initiation: One DNA, Two Transcripts, Seven Reading Frames, Potentially Nine Toxic Entities," PLoS Genetics, vol. 7, p. e1002018, 2011.
[7] J. Comeron, "Weak Selection and Recent Mutational Changes Influence Polymorphic Synonymous Mutations in Humans," Proc. Nat'l Academy Sciences USA, vol. 103, pp. 6940-6945, 2006.
[8] C. Gustafsson, S. Govindarajan, and J. Minshull, "Codon Bias and Heterologous Protein Expression," Trends Biotechnology, vol. 22, pp. 346-353, 2004.
[9] G. Kudla, A. Murray, D. Tollervey, and J. Plotkin, "Coding-Sequence Determinants of Gene Expression in Escherichia Coli," Science, vol. 324, pp. 255-258, 2009.
[10] J. 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.
[11] N. Burgess-Brown, S. Sharma, F. Sobott, C. Loenarz, U. Oppermann, and O. Gileadi, "Codon Optimization Can Improve Expression of Human Genes in Escherichia Coli: A Multi-Gene Study," Protein Expression and Purification, vol. 59, pp. 94-102, 2008.
[12] 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.
[13] D. Drummond and C. Wilke, "Mistranslation-Induced Protein Misfolding as a Dominant Constraint on Coding-Sequence Evolution," Cell, vol. 134, pp. 341-352, 2008.
[14] D.A. Drummond and C.O. Wilke, "The Evolutionary Consequences of Erroneous Protein Synthesis," Nature Rev. Genetics, vol. 10, pp. 715-724, 2009.
[15] P. Shah and M.A. Gilchrist, "Explaining Complex Codon Usage Patterns with Selection for Translational Efficiency, Mutation Bias, and Genetic Drift," Proc. Nat'l Academy Sciences USA, vol. 108, pp. 10231-10236, 2010.
[16] P. Shah and M.A. Gilchrist, "Effect of Correlated Trna Abundances on Translation Errors and Evolution of Codon Usage Bias," PLoS Genetics, vol. 6, p. e1001128, 2010.
[17] G. Plata, M.E. Gottesman, and D. Vitkup, "The Rate of the Molecular Clock and the Cost of Gratuitous Protein Synthesis," Genome Biology, vol. 11, p. R98, 2010.
[18] M. Bulmer, "The Selection-Mutation-Drift Theory of Synonymous Codon Usage," Genetics, vol. 129, pp. 897-907, 1991.
[19] P. Sharp and W. Li, "The Rate of Synonymous Substitution in Enterobacterial Genes Is Inversely Related to Codon Usage Bias," Molecular Biology Evolution, vol. 4, pp. 222-230, 1987.
[20] C. Danpure, "How Can the Products of a Single Gene be Localized to More than One Intracellular Compartment," Trends Cell Biology, vol. 5, pp. 230-238, 1995.
[21] A. Kochetov, "Alternative Translation Start Sites and Their Significance for Eukaryotic Proteomes," Molecular Biology, vol. 40, pp. 705-712, 2006.
[22] T. Schmeing, R. Voorhees, A. Kelley, and V. Ramakrishnan, "How Mutations in tRNA Distant from the Anticodon Affect the Fidelity of Decoding," Nature Structural and Molecular Biology, vol. 18, pp. 432-436, 2011.
[23] T. Warnecke and L. Hurst, "Groel Dependency Affects Codon Usage-Support for a Critical Role of Misfolding in Gene Evolution," Molecular Systems Biology, vol. 6, pp. 1-11, 2010.
[24] T. Zhou, M. Weems, and C. Wilke, "Translationally Optimal Codons Associate with Structurally Sensitive Sites in Proteins," Molecular Biology Evolution, vol. 26, pp. 1571-1580, 2009.
[25] F. Zhang, S. Saha, S. Shabalina, and A. Kashina, "Differential Arginylation of Actin Isoforms Is Regulated by Coding Sequence-Dependent Degradation," Science, vol. 329, pp. 1534-1537, 2010.
[26] K. Fredrick and M. Ibba, "How the Sequence of a Gene Can Tune Its Translation," Cell, vol. 141, pp. 227-229, 2010.
[27] J. Elf, D. Nilsson, T. Tenson, and M. Ehrenberg, "Selective Charging of tRNA Isoacceptors Explains Patterns of Codon Usage," Science, vol. 300, pp. 1718-1722, 2003.
[28] M. Schmidt, A. Houseman, A. Ivanov, and D. Wolf, "Comparative Proteomic and Transcriptomic Profiling of the Fission Yeast Schizosaccharomyces Pombe," Molecular Systems Biology, vol. 3, article 79, 2007.
[29] G. Cannarozzi, N. Schraudolph, M. Faty, P. von Rohr, M. Friberg, A. Roth, P. Gonnet, G. Gonnet, and Y. Barral, "A Role for Codon Order in Translation Dynamics," Cell, vol. 141, pp. 355-367, 2010.
[30] O. Man and Y. Pilpel, "Differential Translation Efficiency of Orthologous Genes Is Involved in Phenotypic Divergence of Yeast Species," Nature Genetics, vol. 39, pp. 415-421, 2007.
[31] Z. Zhang, L. Zhou, L. Hu, Y. Zhu, H. Xu, Y. Liu, X. Chen, X. Yi, X. Kong, and L. Hurst, "Nonsense-Mediated Decay Targets Have Multiple Sequence-Related Features that Can Inhibit Translation," Molecular Systems Biology, vol. 6, pp. 1-9, 2010.
[32] J. Chamary and J.P.L. Hurst, "Hearing Silence: Non-Neutral Evolution at Synonymous Sites in Mammals," Nature Rev. Genetics, vol. 7, pp. 98-108, 2006.
[33] S. Zhang, E. Goldman, and G. Zubay, "Clustering of Low Usage Codons and Ribosome Movement," J. Theoretical Biology, vol. 170, pp. 339-54, 1994.
[34] 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, 2011.
[35] 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.
[36] C. MacDonald and J.G.A. Pipkin, "Kinetics of Biopolymerization on Nucleic Acid Templates," Biopolymers, vol. 6, pp. 1-25, 1968.
[37] 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, p. R110, 2011.
[38] T. Tuller, M. Kupiec, and E. Ruppin, "Determinants of Protein Abundance and Translation Efficiency in s. Cerevisiae," PLoS Computational Biology, vol. 3, pp. 2510-2519, 2007.
[39] 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, p. e1002127, 2011.
[40] H.L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, series Mathematical Surveys and Monographs, vol. 41. Am. Math. Soc., 1995.
[41] E.D. Sontag, "Monotone and Near-Monotone Biochemical Networks," Systems and Synthetic Biology, vol. 1, pp. 59-87, 2007.
[42] J. Smillie, "Competitive and Cooperative Tridiagonal Systems of Differential Equations," SIAM J. Math. Analysis, vol. 15, pp. 530-534, 1984.
[43] L. Shaw, R. Zia, and K. Lee, "Totally Asymmetric Exclusion Process with Extended Objects: A Model for Protein Synthesis," Physical Rev. E, vol. 68, p. 021910, 2003.
[44] 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.
[45] J.E. Marsden and A. Tromba, Vector Calculus, fifth ed. W.H. Freeman, 2003.
[46] M. Vidyasagar, Nonlinear Systems Analysis. Prentice Hall, 1978.
[47] G. Russo, M. di Bernardo, and E.D. Sontag, "Global Entrainment of Transcriptional Systems to Periodic Inputs," PLoS Computational Biology, vol. 6, p. e1000739, 2010.
[48] W. Lohmiller and J.-J. E. Slotine, "On Contraction Analysis for Non-Linear Systems," Automatica, vol. 34, no. 6, pp. 683-696, 1998.
[49] B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell. Garland Science, 2002.
[50] L.S. Churchman and J.S. Weissman, "Nascent Transcript Sequencing Visualizes Transcription at Nucleotide Resolution," Nature, vol. 469, no. 7330, pp. 368-373, 2011.
[51] J.J. Slotine and W. Li, Applied Nonlinear Control. Prentice Hall, 1991.
[52] B. Fiedler and T. Gedeon, "A Lyapunov Function for Tridiagonal Competitive-Cooperative Systems," SIAM J. Math. Analysis, vol. 30, pp. 469-478, 1999.
[53] G. Lakatos and T. Chou, "Totally Asymmetric Exclusion Processes with Particles of Arbitrary Size," J. Physics A: Math. Genetics, vol. 36, pp. 2027-2041, 2003.
[54] D. Angeli and E.D. Sontag, "Oscillations in I/O Monotone Systems under Negative Feedback," IEEE Trans. Automatic Control, vol. 53, no. SI, pp. 166-176, Jan. 2008.
[55] L. Wang, P. de Leenheer, and E. Sontag, "Conditions for Global Stability of Monotone Tridiagonal Systems with Negative Feedback," Systems Control Letters, vol. 59, pp. 130-138, 2010.
[56] P.J. Farabaugh, "Programmed Translational Frameshifting," Ann. Rev. Genetics, vol. 30, pp. 507-528, 1996.
[57] P.V. Baranov, R.F. Gesteland, and J.F. Atkins, "Recoding: Translational Bifurcations in Gene Expression," Gene, vol. 286, no. 5, pp. 187-201, 2002.
[58] A.E. Firth, M. Bekaert, and P.V. Baranov, "Computational Resources for Studying Recoding," Recoding: Expansion of Decoding Rules Enriches Gene Expression, ser. Nucleic Acids and Molecular Biology, J.F. Atkins and R.F. Gesteland, eds., vol. 24, pp. 435-461, Springer, 2010.
[59] 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., pp. 318-352, vol. 2, no. 4, 2005.
7 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool