In Silico Modelling and Analysis of Ribosome Kinetics and aa-tRNA Competition

  • D. Bošnački
  • T. E. Pronk
  • E. P. de Vink
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5750)

Abstract

We present a formal analysis of ribosome kinetics using probabilistic model checking and the tool Prism. We compute different parameters of the model, like probabilities of translation errors and average insertion times per codon. The model predicts strong correlation to the quotient of the concentrations of the so-called cognate and near-cognate tRNAs, in accord with experimental findings and other studies. Using piecewise analysis of the model, we are able to give an analytical explanation of this observation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arkin, A., Ross, J., McAdams, H.H.: Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected. Escherichia coli cells. Genetics 149, 1633–1648 (1998)Google Scholar
  2. 2.
    Baier, C., Katoen, J.-P., Hermanns, H.: Approximate symbolic model checking of continuous-time Markov chains. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 146–161. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  3. 3.
    Bošnački, D., ten Eikelder, H.M.M., Steijaert, M.N., de Vink, E.P.: Stochastic analysis of amino acid substitution in protein synthesis. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 367–386. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of signalling pathways using continuous time Markov chains. In: Priami, C., Plotkin, G. (eds.) Transactions on Computational Systems Biology VI. LNCS (LNBI), vol. 4220, pp. 44–67. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Chabrier, N., Fages, F.: Symbolic model checking of biochemical networks. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 149–162. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Rule-based modelling of cellular signalling. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 17–41. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Dong, H., Nilsson, L., Kurland, C.G.: Co-variation of tRNA abundance and codon usage in Escherichia coli at different growth rates. Journal of Molecular Biology 260, 649–663 (1996)CrossRefGoogle Scholar
  8. 8.
    Nureki, O., et al.: Enzyme structure with two catalytic sites for double-sieve selection of substrate. Science 280, 578–582 (1998)CrossRefGoogle Scholar
  9. 9.
    Fluitt, A., Pienaar, E., Viljoen, H.: Ribosome kinetics and aa-tRNA competition determine rate and fidelity of peptide synthesis. Computational Biology and Chemistry 31, 335–346 (2007)CrossRefMATHGoogle Scholar
  10. 10.
    Gilchrist, M.A., Wagner, A.: A model of protein translation including codon bias, nonsense errors, and ribosome recycling. Journal of Theoretical Biology 239, 417–434 (2006)CrossRefGoogle Scholar
  11. 11.
    Goodman, M.F.: Coping with replication ‘train wrecks’ in Escherichia coli using Pol V, Pol II and RecA proteins. Trends in Biochemical Sciences 25, 189–195 (2000)CrossRefGoogle Scholar
  12. 12.
    Gromadski, K.B., Rodnina, M.V.: Kinetic determinants of high-fidelity tRNA discrimination on the ribosome. Molecular Cell 13(2), 191–200 (2004)CrossRefGoogle Scholar
  13. 13.
    Heath, J., Kwiatkowska, M., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. In: Priami, C. (ed.) CMSB 2006. LNCS (LNBI), vol. 4210, pp. 32–47. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Heyd, A.W., Drew, D.A.: A mathematical model for elongation of a peptide chain. Bulletin of Mathematical Biology 65, 1095–1109 (2003)CrossRefMATHGoogle Scholar
  15. 15.
    Ibba, M., Söll, D.: Aminoacyl-tRNAs: setting the limits of the genetic code. Genes & Development 18, 731–738 (2004)CrossRefGoogle Scholar
  16. 16.
    Johnson, K.A.: Conformational coupling in DNA polymerase fidelity. Annual Reviews in Biochemistry 62, 685–713 (1993)CrossRefGoogle Scholar
  17. 17.
    Karp, G.: Cell and Molecular Biology, 5th edn. Wiley, Chichester (2008)Google Scholar
  18. 18.
    Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model cheking with Prism: a hybrid approach. Journal on Software Tools for Technology Transfer 6, 128–142 (2004), http://www.prismmodelchecker.org/ CrossRefGoogle Scholar
  19. 19.
    Martomo, S.A., Mathews, C.K.: Effects of biological DNA precursor pool asymmetry upon accuracy of DNA replication in vitro. Mutation Research 499, 197–211 (2002)CrossRefGoogle Scholar
  20. 20.
    Ni, M., Wang, S.-Y., Li, J.-K., Ouyang, Q.: Simulating the temporal modulation of inducible DNA damage response in Escherichia coli. Biophysical Journal 93, 62–73 (2007)CrossRefGoogle Scholar
  21. 21.
    Pape, T., Wintermeyer, W., Rodnina, M.: Complete kinetic mechanism of elongation factor Tu-dependent binding of aa-tRNA to the A-site of E. coli. EMBO Journal 17, 7490–7497 (1998)CrossRefGoogle Scholar
  22. 22.
    Priami, C., Regev, A., Shapiro, E., Silverman, W.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Information Processing Letters 80, 25–31 (2001)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Rodnina, M.V., Wintermeyer, W.: Ribosome fidelity: tRNA discrimination, proofreading and induced fit. Trends in Biochemical Sciences 26(2), 124–130 (2001)CrossRefGoogle Scholar
  24. 24.
    Savelsbergh, A., et al.: An elongation factor G-induced ribosome rearrangement precedes tRNA–mRNA translocation. Molecular Cell 11, 1517–1523 (2003)CrossRefGoogle Scholar
  25. 25.
    Sørensen, M.A., Kurland, C.G., Pedersen, S.: Codon usage determines translation rate in Escherichia coli. Journal of Molecular Biology 207, 365–377 (1989)CrossRefGoogle Scholar
  26. 26.
    Viljoen, H.: Private communication (2008)Google Scholar
  27. 27.
    Wahab, S.Z., Rowley, K.O., Holmes, W.M.: Effects of \(tRNA^{Leu}_1\) overproduction in Escherichia coli. Molecular Microbiology 7, 253–263 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • D. Bošnački
    • 1
  • T. E. Pronk
    • 2
  • E. P. de Vink
    • 3
  1. 1.Dept. of Biomedical EngineeringEindhoven University of TechnologyNetherlands
  2. 2.Swammerdam Institute for Life SciencesUniversity of AmsterdamNetherlands
  3. 3.Dept. of Mathematics and Computer ScienceEindhoven University of TechnologyNetherlands

Personalised recommendations