On the Difficulty of Inferring Gene Regulatory Networks: A Study of the Fitness Landscape Generated by Relative Squared Error

  • Francesco Sambo
  • Marco A. Montes de Oca
  • Barbara Di Camillo
  • Thomas Stützle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5975)

Abstract

Inferring gene regulatory networks from expression profiles is a challenging problem that has been tackled using many different approaches. When posed as an optimization problem, the typical goal is to minimize the value of an error measure, such as the relative squared error, between the real profiles and those generated with a model whose parameters are to be optimized. In this paper, we use dynamic recurrent neural networks to model regulatory interactions and study systematically the “fitness landscape” that results from measuring the relative squared error. Although the results of the study indicate that the generated landscapes have a positive fitness-distance correlation, the error values span several orders of magnitude over very short distance variations. This suggests that the fitness landscape has extremely deep valleys, which can make general-purpose state-of-the-art continuous optimization algorithms exhibit a very poor performance. Further results, obtained from an analysis based on perturbations of the optimal network topology, support approaches in which the spaces of network topologies and of network parameters are decoupled.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bansal, M., Belcastro, V., Ambesi-Impiombato, A., di Bernardo, D.: How to infer gene networks from expression profiles. Mol. Syst. Biol. 3(78) (February 2007)Google Scholar
  2. 2.
    Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods. MPS-SIAM Series in Optimization. SIAM, Philadelphia (2000)MATHGoogle Scholar
  3. 3.
    Di Camillo, B., Toffolo, G., Cobelli, C.: A gene network simulator to assess reverse engineering algorithms. Annals of the New York Academy of Sciences 1158(1), 125–142 (2009)CrossRefGoogle Scholar
  4. 4.
    Fehlberg, E.: Low-order classical runge-kutta formulas with step size control and their application to some heat transfer problems. Technical Report 315, NASA (1969)Google Scholar
  5. 5.
    Ferrazzi, F., Sebastiani, P., Ramoni, M.F., Bellazzi, R.: Bayesian approaches to reverse engineer cellular systems: a simulation study on nonlinear gaussian networks. BMC Bioinformatics 8(suppl. 5) (2007)Google Scholar
  6. 6.
    Gennemark, P., Wedelin, D.: Benchmarks for identification of ordinary differential equations from time series data. Bioinformatics 25(6), 780–786 (2009)CrossRefGoogle Scholar
  7. 7.
    Hunter, L.: Life and its molecules: A brief introduction. AI Magazine - Special issue on AI and Bioinformatics 25(1), 9–22 (2004)Google Scholar
  8. 8.
    Ideker, T., Ozier, O., Schwikowski, B., Siegel, A.F.: Discovering regulatory and signalling circuits in molecular interaction networks. Bioinformatics 18(suppl. 1), 233–240 (2002)Google Scholar
  9. 9.
    Jones, T.: Evolutionary algorithms, fitness landscapes and search. Working Papers 95-05-048, Santa Fe Institute (1995)Google Scholar
  10. 10.
    Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of the 6th International Conference on Genetic Algorithms, pp. 184–192. Morgan Kaufmann, San Francisco (1995)Google Scholar
  11. 11.
    de Jong, H.: Modeling and simulation of genetic regulatory systems: A literature review. Journal of Computational Biology 9(1), 67–103 (2002)CrossRefGoogle Scholar
  12. 12.
    Kennedy, J., Eberhart, R., Shi, Y.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)Google Scholar
  13. 13.
    Kentzoglanakis, K., Poole, M.J., Adams, C.: Incorporating heuristics in a swarm intelligence framework for inferring gene regulatory networks from gene expression time series. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds.) ANTS 2008. LNCS, vol. 5217, pp. 323–330. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Kimura, S., Ide, K., Kashihara, A., Kano, M., Hatakeyama, M., Masui, R., Nakagawa, N., Yokoyama, S., Kuramitsu, S., Konagaya, A.: Inference of S-system models of genetic networks using a cooperative coevolutionary algorithm. Bioinformatics 21(7), 1154–1163 (2005)CrossRefGoogle Scholar
  15. 15.
    Kremer, S.C.: Field Guide to Dynamical Recurrent Networks. Wiley-IEEE Press, Chichester (2001)Google Scholar
  16. 16.
    Liang, S., Fuhrman, S., Somogyi, R.: Reveal: a general reverse engineering algorithm for inference of genetic network architectures. In: Pacific Symposium on Biocomputing, pp. 18–29 (1998)Google Scholar
  17. 17.
    Margolin, A.A., Nemenman, I., Basso, K., Wiggins, C., Stolovitzky, G., Dalla Favera, R., Califano, A.: Aracne: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context. BMC Bioinformatics 7(suppl. 1) (2006)Google Scholar
  18. 18.
    Merz, P., Freisleben, B.: Fitness landscapes and memetic algorithm design. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 244–260. McGraw Hill, London (1999)Google Scholar
  19. 19.
    Molla, M., Waddell, M., Page, D., Shavlik, J.: Using machine learning to design and interpret gene-expression microarrays. AI Magazine - Special issue on AI and Bioinformatics 25(1), 23–44 (2004)Google Scholar
  20. 20.
    Moré, J.J., Wild, S.M.: Benchmarking derivative-free optimization algorithms. SIAM Journal on Optimization 20(1), 172–191 (2009)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Noman, N., Iba, I.: Reverse engineering genetic networks using evolutionary computation. Genome Informatics 16(2), 205–214 (2005)Google Scholar
  22. 22.
    Powell, M.J.D.: The NEWUOA software for unconstrained optimization. In: Large-Scale Nonlinear Optimization, Nonconvex Optimization and Its Applications, vol. 83, pp. 255–297. Springer, Berlin (2006)Google Scholar
  23. 23.
    Ressom, H.W., Zhang, Y., Xuan, J., Wang, Y., Clarke, R.: Inference of gene regulatory networks from time course gene expression data using neural networks and swarm intelligence. In: IEEE Symposium on Computational Intelligence and Bioinformatics and Computational Biology, pp. 1–8. IEEE, Los Alamitos (2006)Google Scholar
  24. 24.
    Spieth, C., Worzischek, R., Streichert, F., Supper, J., Speer, N., Zell, A.: Comparing evolutionary algorithms on the problem of network inference. In: Cattolico, M. (ed.) Genetic and Evolutionary Computation Conference, GECCO 2006, Proceedings, Seattle, Washington, USA, July 8-12, pp. 305–306. ACM, New York (2006)CrossRefGoogle Scholar
  25. 25.
    Vu, T.T., Vohradsky, J.: Nonlinear differential equation model for quantification of transcriptional regulation applied to microarray data of saccharomyces cerevisiae. Nucleic Acids Research 35(1), 279–287 (2007)CrossRefGoogle Scholar
  26. 26.
    Xu, R., Hu, X., Wunsch II, D.: Inference of genetic regulatory networks from time series gene expression data. In: Proceedings of the International Joint Conference on Neural Networks, vol. 2, pp. 1215–1220. IEEE Press, Los Alamitos (2004)Google Scholar
  27. 27.
    Xu, R., Venayagamoorthy, G.K., Wunsch II, D.C.: Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization. Neural Networks 20(8), 917–927 (2007)MATHCrossRefGoogle Scholar
  28. 28.
    Xu, R., Wunsch II, D., Frank, R.: Inference of genetic regulatory networks with recurrent neural network models using particle swarm optimization. IEEE/ACM Trans. Comput. Biol. Bioinformatics 4(4), 681–692 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Francesco Sambo
    • 1
  • Marco A. Montes de Oca
    • 2
  • Barbara Di Camillo
    • 1
  • Thomas Stützle
    • 2
  1. 1.Dipartimento di Ingegneria dell’InformazioneUniversità di PadovaPaduaItaly
  2. 2.IRIDIA-CoDE, Université Libre de BruxellesBrusselsBelgium

Personalised recommendations