About this Journal Submit a Manuscript Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 752631, 34 pages
http://dx.doi.org/10.1155/2012/752631
Research Article

Estimating Network Kinetics of the MAPK/ERK Pathway Using Biochemical Data

1Department of Statistics, Middle East Technical University, 06800 Ankara, Turkey
2Institute of Mathematics and Computing Science, Groningen University, 9747 AG Groningen, The Netherlands

Received 29 June 2012; Revised 11 September 2012; Accepted 12 September 2012

Academic Editor: Ming Li

Copyright © 2012 Vilda Purutçuoğlu and Ernst Wit. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. Kolch, “Meaningful relationships: the regulation of the Ras/Raf/MEK/ERK pathway by protein interactions,” Biochemical Journal, vol. 351, no. 2, pp. 289–305, 2000. View at Publisher · View at Google Scholar · View at Scopus
  2. W. Kolch, M. Calder, and D. Gilbert, “When kinases meet mathematics: the systems biology of MAPK signalling,” FEBS Letters, vol. 579, no. 8, pp. 1891–1895, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Friedman, T. Hastie, and R. Tibshirani, “Sparse inverse covariance estimation with the graphical lasso,” Biostatistics, vol. 9, no. 3, pp. 432–441, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. S. Reinker, R. M. Altman, and J. Timmer, “Parameter estimation in stochastic biochemical reactions,” IEE Proceedings, vol. 153, no. 4, pp. 168–178, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Golightly and D. J. Wilkinson, “Bayesian inference for nonlinear multivariate diffusion models observed with error,” Computational Statistics & Data Analysis, vol. 52, no. 3, pp. 1674–1693, 2008. View at Publisher · View at Google Scholar
  6. R. J. Boys, D. J. Wilkinson, and T. B. L. Kirkwood, “Bayesian inference for a discretely observed stochastic kinetic model,” Statistics and Computing, vol. 18, no. 2, pp. 125–135, 2008. View at Publisher · View at Google Scholar
  7. J. R. Banga, “Optimization in computational systems biology,” BMC Systems Biology, vol. 2, article 47, pp. 1–7, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. J. M. Bower and H. Bolouri, Computational Modelling of Genetic and Biochemical Networks, Massachusetts Institute of Technology, 2nd edition, 2001.
  9. A. Golightly and D. J. Wilkinson, “Bayesian inference for stochastic kinetic models using a diffusion approximation,” Biometrics, vol. 61, no. 3, pp. 781–788, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. D. J. Wilkinson, Stochastic Modelling for Systems Biology, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2006.
  11. N. G. VanKampen, Stochastic Processes in Physics and Chemistry, Elsevier, 1981.
  12. H. Risken, The Fokker-Planck Equation, vol. 18, Springer, Berlin, Germany, 1984. View at Publisher · View at Google Scholar
  13. D. T. Gillespie, “Exact stochastic simulation of coupled chemical reactions,” Journal of Physical Chemistry, vol. 81, no. 25, pp. 2340–2361, 1977. View at Publisher · View at Google Scholar · View at Scopus
  14. D. J. Wilkinson, “Parallel Bayesian computation,” in Handbook of parallel computing and statistics, vol. 184, pp. 477–508, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2006. View at Publisher · View at Google Scholar
  15. R. Khanin, V. Vinciotti, V. Mersinias, C. P. Smith, and E. Wit, “Statistical reconstruction of transcription factor activity using Michaelis-Menten kinetics,” Biometrics, vol. 63, no. 3, pp. 816–823, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. G. Sanguinetti, M. Rattray, and N. D. Lawrence, “A probabilistic dynamical model for quantitative inference of the regulatory mechanism of transcription,” Bioinformatics, vol. 22, no. 14, pp. 1753–1759, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. H. Bolouri, Computational Modelling of Gene Regulatory Networks—A Primer, Imperial College Press, 2008.
  18. V. Vyshemirsky, M. Girolami, A. Gormand, and W. Kolch, “A Bayesian analysis of the ERK signalling pathway,” Tech. Rep. TR-2006-227, University of Glasgow, 2006.
  19. J. Vera, J. Bachmann, A. C. Pfeifer et al., “A systems biology approach to analyse amplification in the JAK2-STAT5 signalling pathway,” BMC Systems Biology, vol. 2, no. 38, pp. 1–13, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. K. Yeung, T. Seitz, S. Li et al., “Suppression of Raf-1 kinase activity and MAP kinase signalling by RKIP,” Nature, vol. 401, pp. 173–177, 1999.
  21. V. Purutçuoğlu and E. Wit, “Bayesian inference for the MAPK/ERK pathway by considering the dependency of the kinetic parameters,” Bayesian Analysis, vol. 3, no. 4, pp. 851–886, 2008. View at Publisher · View at Google Scholar
  22. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, Germany, 3rd edition, 1993.
  23. B. Eraker, “MCMC analysis of diffusion models with application to finance,” Journal of Business & Economic Statistics, vol. 19, no. 2, pp. 177–191, 2001. View at Publisher · View at Google Scholar
  24. B. P. Carlin and T. A. Louis, Bayes and Empirical Bayes Methods for Data Analysis, Chapman & Hall/CRC, 2nd edition, 2000.
  25. S. Chib, F. Nardari, and N. Shephard, “Analysis of high dimensional multivariate stochastic volatility models,” Journal of Econometrics, vol. 134, no. 2, pp. 341–371, 2006. View at Publisher · View at Google Scholar
  26. D. Hames and N. Hooper, Instant Notes: Biochemistry, BIOS Scientific Publishers, 2000.
  27. R. L. Switzer and L. F. Garrity, Experimental Biochemistry, W.H. Freeman and Company, New York, NY, USA, 3rd edition, 2003.
  28. N. Fedoroff and W. Fontana, “Genetic networks: small numbers of big molecules,” Science, vol. 297, no. 5584, pp. 1129–1131, 2002. View at Publisher · View at Google Scholar · View at Scopus
  29. D. A. Hume, “Probability in transcriptional regulation and its implications for leukocyte differentiation and inducible gene expression,” Blood, vol. 96, no. 7, pp. 2323–2328, 2000. View at Scopus
  30. L. Kaufman and P. J. Rousseeuw, Finding Groups in Data, John Wiley & Sons, New York, NY, USA, 1990. View at Publisher · View at Google Scholar
  31. A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis, Chapman & Hall/CRC, 2nd edition, 2004.
  32. S. Park, O. Rath, S. Beach et al., “Regulation of RKIP binding to the N-region of the Raf-1 kinase,” FEBS Letters, vol. 580, no. 27, pp. 6405–6412, 2006. View at Publisher · View at Google Scholar · View at Scopus
  33. W. Kolch, “MAPK signalling networks,” Oncogene Course Notes, 2005.
  34. W. Kolch, “MAPK signalling networks,” RTK Consortium Presentation, 2005.
  35. R. J. Orton, O. E. Sturm, V. Vyshemirsky, M. Calder, D. R. Gilbert, and W. Kolch, “Computational modelling of the receptor-tyrosine-kinase-activated MAPK pathway,” Biochemical Journal, vol. 392, no. 2, pp. 249–261, 2005. View at Publisher · View at Google Scholar · View at Scopus
  36. B. Schoeberl, C. Eichler-Jonsson, E. D. Gilles, and G. Müller, “Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors,” Nature Biotechnology, vol. 20, no. 4, pp. 370–375, 2002. View at Publisher · View at Google Scholar · View at Scopus
  37. B. N. Kholodenko, O. V. Demin, G. Moehren, and J. B. Hoek, “Quantification of short term signaling by the epidermal growth factor receptor,” Journal of Biological Chemistry, vol. 274, no. 42, pp. 30169–30181, 1999. View at Publisher · View at Google Scholar · View at Scopus
  38. F. A. Brightman and D. A. Fell, “Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells,” FEBS Letters, vol. 482, no. 3, pp. 169–174, 2000. View at Publisher · View at Google Scholar · View at Scopus
  39. O. Elerian, S. Chib, and N. Shephard, “Likelihood inference for discretely observed nonlinear diffusions,” Econometrica, vol. 69, no. 4, pp. 959–993, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  40. A. Golightly and D. J. Wilkinson, “Bayesian sequential inference for stochastic kinetic biochemical network models,” Journal of Computational Biology, vol. 13, no. 3, pp. 838–851, 2006. View at Publisher · View at Google Scholar
  41. V. Purutçuoglu, “Inference of the stochastic MAPK pathway by modified diffusion bridge method,” Central European Journal of Operations Research, pp. 1–15, 2012. View at Publisher · View at Google Scholar
  42. M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  43. S. Havlin, S. V. Buldyrev, A. L. Goldberger et al., “Fractals in biology and medicine,” Chaos, Solitons and Fractals, vol. 6, pp. 171–201, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  44. D. Craciun, A. Isvoran, and N. M. Avram, “Long range correlation of hydrophilicity and flexibility along the calcium binding protein chains,” Physica A, vol. 388, no. 21, pp. 4609–4618, 2009. View at Publisher · View at Google Scholar · View at Scopus
  45. S. C. Lim and S. V. Muniandy, “On some possible generalizations of fractional Brownian motion,” Physics Letters. A, vol. 266, no. 2-3, pp. 140–145, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  46. S. C. Kou and X. S. Xie, “Generalized langevin equation with fractional gaussian noise: subdiffusion within a single protein molecule,” Physical Review Letters, vol. 93, no. 18, pp. 180603–4, 2004. View at Publisher · View at Google Scholar · View at Scopus
  47. M. Li, W. Zhao, and S. Chen, “Mbm-based scalings of traffic propagated in internet,” Mathematical Problems in Engineering, vol. 2011, Article ID 389803, 21 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  48. M. Li and W. Zhao, “Quantitatively investigating the locally weak stationarity of modified multifractional gaussian noise,” Physics A, vol. 391, no. 24, pp. 6268–6278, 2012.
  49. R. F. Peltier and J. Levy-Vehel, “A new method for estimating the parameter of fractional brownian motion,” Tech. Rep. RR, 2696:1–4, INRIA, 1994.
  50. J.-P. Bouchaud and A. Georges, “Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications,” Physics Reports, vol. 195, no. 4-5, pp. 127–293, 1990. View at Publisher · View at Google Scholar
  51. D. Gamerman and H. F. Lopes, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2nd edition, 2006.