Development and Application of a Modified Genetic Algorithm for Estimating Parameters in GMA Models

  1. Hormiga, José A.
  2. Torres, Néstor V. 1
  3. González-Alcón, Carlos 1
  1. 1 Universidad de La Laguna

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    GRID grid.10041.34

Applied Mathematics

ISSN: 2152-7385

Year of publication: 2014

Volume: 05

Issue: 16

Pages: 2447-2457

Type: Article

Export: RIS
DOI: 10.4236/am.2014.516236 GOOGLE SCHOLAR lock_openOpen access editor
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In this work we introduce a modified version of the simple genetic algorithm (MGA) and will show the results of its application to two GMA power law models (a general theoretical branched pathway system and a mathematical model of the amplification and responsiveness of the JAK2/STAT5 pathway representing an actual, experimentally studied system). The two case studies serve to illustrate the utility and potentialities of the MGA method for concerning parameter estimation in complex models of biological significance. The analysis of the results obtained from the application of the MGA algorithm allows an evaluation of the potentialities and shortcomings of the proposed algorithm when compared with other parameter estimation algorithm such as the simple genetic algorithm (SGA) and the simulated annealing (SA). MGA shows better performance in both studied cases than SGA and SA, either in the presence or absence of noise. It is suggested that these advantages are due to the fact that the objective function definition in the MGA could include the experimental error as a weight factor, thus minimizing the distance between the data and the predicted value. Actually, MGA is slightly slower that the SGA and the SA, but this limitation is compensated by its greater efficiency in finding objective values closer to the global optimum. Finally, MGA can lead to an early local optimum, but this shortcoming may be prevented by providing a great population diversity through the insertion of different selection processes.

Bibliographic References

  • [1] Michaelis, L. and Menten, M. (1913) Die kinetik der invertinwirkung. Biochemistry Zeitung, 79, 333-369.
  • [2] Briggs, G.E. and Haldane, J.B. (1925) A Note on the Kinetics of Enzyme Action. Biochemical Journal, 19, 338- 339.
  • [3] Cornish-Bowden, A. (2004) Fundamentals of Enzyme Kinetics. 3rd Edition, Portland Press, Lon-don.
  • [4] Savageau, M.A. (1976) Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology. Addison-Wesley, Reading.
  • [5] Voit, E.O. (2000) Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists. Cambridge University Press, Cambridge.
  • [6] Sorribas, A., Hernandez-Bermejo, B., Vilaprinyo, E. and Alves, R. (2007) Cooperativity and Saturation in Biochemical Networks: A Saturable Formalism Using Taylor Series Approximations. Biotechnology and Bioengineering, 97, 1259- 1277.
  • [7] Vera, J., Balsa-Canto, E., Wellstead, P., Banga, J.R. and Wolkenhauer, O. (2007) Power-Law Models of Signal Transduction Pathways. Cellular Signalling, 19, 1531-1541.
  • [8] Torres, N.V. and Voit, E.O. (2002) Pathway Analysis and Optimization in Metabolic Engineering. Cambridge University Press, Cambridge.
  • [9] Park, L.J., Park, C.H., Park, C. and Lee, T. (1997) Application of Genetic Algorithms to Parameter Estimation of Bioprocesses. Medical Biological Engineering Computing, 35, 47-49.
  • [10] Polisety, P.K. and Voit, E.O. (2006) Identification of Metabolic System Parameters Using Global Optimization Methods. Theoretical Biology and Medical Modelling, 3, 4.
  • [11] Ashyraliyev, M., Fomekong-Nanfack, Y., Kaandorp, J.A. and Blom, J.G. (2009) Systems Biology: Parameter Estimation for Biochemical Model. FEBS Journal, 276, 886-902.
  • [12] Swartz, J. and Bremermann, H. (1975) Discussion of Parameter Estimation in Biological Modelling: Algorithms for Estimation and Evaluation of the Estimates. Journal of Mathematical Biology, 1, 241-257.
  • [13] Chou, I.C. and Voit, E.O. (2008) Recent Developments in Parameter Estimation and Structure Identification of Biochemical and Genomic Systems. Mathematical Biosciences, 219, 57-83.
  • [14] Holland, J.H. (1976) Adaptation. In: Rosen, R. and Snell, F.M., Eds., Progress in Theoretical Biology IV, Academic Press, New York, 263-293.
  • [15] Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Read- ing.
  • [16] Fogel, D.B. (1997) Review of an Introduction to Genetic Algorithms. Bulletin of Mathematical Biology, 59, 199-204.
  • [17] Fogel, D.B. (1997) Evolutionary Algorithms in Theory and Practice. Complexity, 2, 26-27.<26::AID-CPLX6>3.0.CO;2-7
  • [18] Vera, J., González-Alcón, C., Marín-Sanguino, A. and Torres, N. (2010) Optimization of Biochemical Systems through Mathematical Programming: Methods and Applications. Computers & Operations Research, 37, 1427-1438.
  • [19] Granville, V., Krivanek, M. and Rasson, J.P. (1994) Simulated Annealing: A Proof of Convergence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16, 652-656.
  • [20] Vera, J., Bachmann, J., Pfeifer, A.C., Becker, V., Hormiga, J.A., Torres Darias, N., Timmer, J., Klingmüller, U. and Wolkenhauer, O. (2008) A Systems Biology Approach to Analyse Amplification in the JAK2-STAT5 Signalling Pathway. BMC Systems Biology, 2, 38.