Computational Modeling of Biochemical Networks Using COPASI

  • Pedro Mendes
  • Stefan Hoops
  • Sven Sahle
  • Ralph Gauges
  • Joseph Dada
  • Ursula Kummer
Part of the Methods in Molecular Biology book series (MIMB, volume 500)

Summary

Computational modeling and simulation of biochemical networks is at the core of systems biology and this includes many types of analyses that can aid understanding of how these systems work. COPASI is a generic software package for modeling and simulation of biochemical networks which provides many of these analyses in convenient ways that do not require the user to program or to have deep knowledge of the numerical algorithms. Here we provide a description of how these modeling techniques can be applied to biochemical models using COPASI. The focus is both on practical aspects of software usage as well as on the utility of these analyses in aiding biological understanding. Practical examples are described for steady-state and time-course simulations, stoichiometric analyses, parameter scanning, sensitivity analysis (including metabolic control analysis), global optimization, parameter estimation, and stochastic simulation. The examples used are all published models that are available in the BioModels database in SBML format.

Keywords

Simulation Modeling Systems biology Optimization Stochastic simulation Sensitivity analysis Parameter estimation SBML Stoichiometric analysis 

References

  1. 1.
    Garfinkel, D., Marbach, C. B., and Shapiro, N. Z. (1977) Stiff differential equations. Ann. Rev. Biophys. Bioeng. 6, 525–542.CrossRefGoogle Scholar
  2. 2.
    Petzold, L. (1983) Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM J. Sci. Stat. Comput. 4, 136–148.CrossRefGoogle Scholar
  3. 3.
    Gillespie, D. T. (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434.CrossRefGoogle Scholar
  4. 4.
    Gillespie, D. T. (1977) Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361.CrossRefGoogle Scholar
  5. 5.
    Gillespie, D. T. (2007) Stochastic simulation of chemical kinetics. Ann. Rev. Phys. Chem. 58, 35–55.CrossRefGoogle Scholar
  6. 6.
    Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes, P., and Kummer, U. (2006) COPASI – a COmplex PAthway SImulator. Bioinformatics 22, 3067–3074.PubMedCrossRefGoogle Scholar
  7. 7.
    Le Novere, N., Bornstein, B., Broicher, A., Courtot, M., Donizelli, M., Dharuri, H., Li, L., Sauro, H., Schilstra, M., Shapiro, B., Snoep, J. L., and Hucka, M. (2006) BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Res. 34, D689–D691.PubMedCrossRefGoogle Scholar
  8. 8.
    Kholodenko, B. N. (2000) Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. Eur. J. Biochem. 267, 1583–1588.PubMedCrossRefGoogle Scholar
  9. 9.
    Curien, G., Ravanel, S., and Dumas, R. (2003) A kinetic model of the branch-point between the methionine and threonine biosynthesis pathways in Arabidopsis thaliana. Eur. J. Biochem. 270, 4615–4627.PubMedCrossRefGoogle Scholar
  10. 10.
    Schuster, S. and Hilgetag, C. (1994) On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2, 165–182.CrossRefGoogle Scholar
  11. 11.
    Schuster, S., Fell, D. A., and Dandekar, T. (2000) A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat. Biotechnol. 18, 326–332.PubMedCrossRefGoogle Scholar
  12. 12.
    Reder, C. (1988) Metabolic control theory. A structural approach. J. Theor. Biol. 135, 175–201.PubMedCrossRefGoogle Scholar
  13. 13.
    Holzhütter, H. G. (2004) The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks. Eur. J. Biochem. 271, 2905–2922.PubMedCrossRefGoogle Scholar
  14. 14.
    Kacser, H. and Burns, J. A. (1973) The control of flux. Symp. Soc. Exp. Biol. 27, 65–104.PubMedGoogle Scholar
  15. 15.
    Heinrich, R. and Rapoport, T. A. (1974) A linear steady-state treatment of enzymatic chains. General properties, control and effector strength. Eur. J. Biochem. 42, 89–95.PubMedCrossRefGoogle Scholar
  16. 16.
    Fell, D. A. (1992) Metabolic control analysis – a survey of its theoretical and experimental development. Biochem. J. 286, 313–330.PubMedGoogle Scholar
  17. 17.
    Heinrich, R. and Schuster, S. (1996) The Regulation of Cellular Systems. Chapman & Hall, New York, NY.Google Scholar
  18. 18.
    Fell, D. A. (1996) Understanding the Control of Metabolism. Portland Press, London.Google Scholar
  19. 19.
    Cascante, M., Boros, L. G., Comin-Anduix, B., de Atauri, P., Centelles, J. J., and Lee, P. W. (2002) Metabolic control analysis in drug discovery and disease. Nat. Biotechnol. 20, 243–249.PubMedCrossRefGoogle Scholar
  20. 20.
    Rohwer, J. M. and Botha, F. C. (2001) Analysis of sucrose accumulation in the sugar cane culm on the basis of in vitro kinetic data. Biochem. J. 358, 437–445.PubMedCrossRefGoogle Scholar
  21. 21.
    Höfer, T. and Heinrich, R. (1993) A second-order approach to metabolic control analysis. J. Theor. Biol. 164, 85–102.PubMedCrossRefGoogle Scholar
  22. 22.
    Mendes, P. and Kell, D. B. (1998) Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 14, 869–883.PubMedCrossRefGoogle Scholar
  23. 23.
    Wolpert, D. H. and Macready, W. G. (1997) No free lunch theorems for optimization. IEEE Trans. Evolut. Comput. 1, 67–82.CrossRefGoogle Scholar
  24. 24.
    Fogel, D. B., Fogel, L. J., and Atmar, J. W. (1992) Meta-evolutionary programming, in 25th Asilomar Conference on Signals, Systems & Computers (Chen, R. R., ed.). IEEE Computer Society, Asilomar, CA, pp. 540–545.Google Scholar
  25. 25.
    Runarsson, T. and Yao, X. (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evolut. Comput. 4, 284–294.CrossRefGoogle Scholar
  26. 26.
    Michalewicz, Z. (1994) Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin.Google Scholar
  27. 27.
    Hooke, R. and Jeeves, T. A. (1961) “Direct search” solution of numerical and statistical problems. J. ACM 8, 212–229.CrossRefGoogle Scholar
  28. 28.
    Levenberg, K. (1944) A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math. 2, 164–168.Google Scholar
  29. 29.
    Goldfeld, S. M., Quant, R. E., and Trotter, H. F. (1966) Maximisation by quadratic hill-climbing. Econometrica 34, 541–555.CrossRefGoogle Scholar
  30. 30.
    Marquardt, D. W. (1963) An algorithm for least squares estimation of nonlinear parameters. SIAM J. 11, 431–441.Google Scholar
  31. 31.
    Nelder, J. A. and Mead, R. (1965) A simplex method for function minimization. Comput. J. 7, 308–313.Google Scholar
  32. 32.
    Kennedy, J. and Eberhart, R. (1995) Particle swarm optimization. Proc. IEEE Int. Conf. Neural Netw. 4, 1942–1948.CrossRefGoogle Scholar
  33. 33.
    Brent, P. R. (1973) A new algorithm for minimizing a function of several variables without calculating derivatives, in Algorithms for Minimization Without Derivatives (Brent, P. R., ed.). Prentice-Hall, Englewood Cliffs, NJ, pp. 117–167.Google Scholar
  34. 34.
    Corana, A., Marchesi, M., Martini, C., and Ridella, S. (1987) Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm. ACM Trans. Math. Softw. 13, 262–280.CrossRefGoogle Scholar
  35. 35.
    Nash, S. G. (1984) Newton-type minimization via the Lanczos method. SIAM J. Numer. Anal. 21, 770–788.CrossRefGoogle Scholar
  36. 36.
    Johnson, M. L. and Faunt, L. M. (1992) Parameter estimation by least-squares methods. Methods Enzymol. 210, 1–37.PubMedCrossRefGoogle Scholar
  37. 37.
    Gibson, M. A. and Bruck, J. (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 104, 1876–1889.CrossRefGoogle Scholar
  38. 38.
    Goldbeter, A., Dupont, G., and Berridge, M. J. (1990) Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc. Natl Acad. Sci. USA 87, 1461–1465.PubMedCrossRefGoogle Scholar
  39. 39.
    Rao, C. V. and Arkin, A. P. (2003) Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm. J. Chem. Phys. 118, 4999–5010.CrossRefGoogle Scholar
  40. 40.
    Cao, Y., Gillespie, D., and Petzold, L. (2005) Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems. J. Comput. Phys. 206, 395–411.CrossRefGoogle Scholar
  41. 41.
    Acerenza, L., Sauro, H. M., and Kacser, H. (1989) Control analysis of time dependent metabolic systems. J. Theor. Biol. 137, 423–444.PubMedCrossRefGoogle Scholar
  42. 42.
    Ingalls, B. P. and Sauro, H. M. (2003) Sensitivity analysis of stoichiometric networks: an extension of metabolic control analysis to non-steady state trajectories. J. Theor. Biol. 222, 23–36.PubMedCrossRefGoogle Scholar

Copyright information

© Humana Press 2009

Authors and Affiliations

  • Pedro Mendes
    • 1
  • Stefan Hoops
  • Sven Sahle
  • Ralph Gauges
  • Joseph Dada
  • Ursula Kummer
  1. 1.School of Computer Science and Manchester Centre for Integrative Systems BiologyUniversity of ManchesterManchesterUK

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