- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 752631, 34 pages
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.
- 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.
- 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.
- J. Friedman, T. Hastie, and R. Tibshirani, “Sparse inverse covariance estimation with the graphical lasso,” Biostatistics, vol. 9, no. 3, pp. 432–441, 2008.
- S. Reinker, R. M. Altman, and J. Timmer, “Parameter estimation in stochastic biochemical reactions,” IEE Proceedings, vol. 153, no. 4, pp. 168–178, 2006.
- 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.
- 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.
- J. R. Banga, “Optimization in computational systems biology,” BMC Systems Biology, vol. 2, article 47, pp. 1–7, 2008.
- J. M. Bower and H. Bolouri, Computational Modelling of Genetic and Biochemical Networks, Massachusetts Institute of Technology, 2nd edition, 2001.
- 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.
- D. J. Wilkinson, Stochastic Modelling for Systems Biology, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2006.
- N. G. VanKampen, Stochastic Processes in Physics and Chemistry, Elsevier, 1981.
- H. Risken, The Fokker-Planck Equation, vol. 18, Springer, Berlin, Germany, 1984.
- D. T. Gillespie, “Exact stochastic simulation of coupled chemical reactions,” Journal of Physical Chemistry, vol. 81, no. 25, pp. 2340–2361, 1977.
- 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.
- 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.
- 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.
- H. Bolouri, Computational Modelling of Gene Regulatory Networks—A Primer, Imperial College Press, 2008.
- 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.
- 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.
- 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.
- 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.
- P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, Germany, 3rd edition, 1993.
- B. Eraker, “MCMC analysis of diffusion models with application to finance,” Journal of Business & Economic Statistics, vol. 19, no. 2, pp. 177–191, 2001.
- B. P. Carlin and T. A. Louis, Bayes and Empirical Bayes Methods for Data Analysis, Chapman & Hall/CRC, 2nd edition, 2000.
- 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.
- D. Hames and N. Hooper, Instant Notes: Biochemistry, BIOS Scientific Publishers, 2000.
- R. L. Switzer and L. F. Garrity, Experimental Biochemistry, W.H. Freeman and Company, New York, NY, USA, 3rd edition, 2003.
- N. Fedoroff and W. Fontana, “Genetic networks: small numbers of big molecules,” Science, vol. 297, no. 5584, pp. 1129–1131, 2002.
- 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.
- L. Kaufman and P. J. Rousseeuw, Finding Groups in Data, John Wiley & Sons, New York, NY, USA, 1990.
- A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis, Chapman & Hall/CRC, 2nd edition, 2004.
- 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.
- W. Kolch, “MAPK signalling networks,” Oncogene Course Notes, 2005.
- W. Kolch, “MAPK signalling networks,” RTK Consortium Presentation, 2005.
- 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.
- 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.
- 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.
- 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.
- O. Elerian, S. Chib, and N. Shephard, “Likelihood inference for discretely observed nonlinear diffusions,” Econometrica, vol. 69, no. 4, pp. 959–993, 2001.
- 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.
- V. Purutçuoglu, “Inference of the stochastic MAPK pathway by modified diffusion bridge method,” Central European Journal of Operations Research, pp. 1–15, 2012.
- M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.