Advertisement

Target Controllability of Linear Networks

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9859)

Abstract

Computational analysis of the structure of intra-cellular molecular interaction networks can suggest novel therapeutic approaches for systemic diseases like cancer. Recent research in the area of network science has shown that network control theory can be a powerful tool in the understanding and manipulation of such bio-medical networks. In 2011, Liu et al. developed a polynomial time optimization algorithm for computing the size of the minimal set of nodes controlling a given linear network. In 2014, Gao et al. generalized the problem for target structural control, where the objective is to optimize the size of the minimal set of nodes controlling a given target within a linear network. The working hypothesis in this case is that partial control might be “cheaper” (in the size of the controlling set) than the full control of a network. The authors developed a Greedy algorithm searching for the minimal solution of the structural target control problem, however, no suggestions were given over the actual complexity of the optimization problem. In here we prove that the structural target controllability problem is NP-hard when looking to minimize the number of driven nodes within the network, i.e., the first set of nodes which need to be directly controlled in order to structurally control the target. We also show that the Greedy algorithm provided by Gao et al. in 2014 might in some special cases fail to provide a valid solution, and a subsequent validation step is required. Also, we improve their search algorithm using several heuristics, obtaining in the end up to a 10-fold decrease in running time and also a significant decrease of the size of the minimal solution found by the algorithms.

Keywords

Bipartite Graph Greedy Algorithm Essential Gene Target Node Target Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Ashworth, A., Lord, C.J., Reis-Filho, J.S.: Genetic interactions in cancer progression and treatment. Cell 145(1), 30–38 (2011)CrossRefGoogle Scholar
  2. 2.
    Blomen, V.A., et al.: Gene essentiality and synthetic lethality in haploid human cells. Science 350(6264), 1092–1096 (2015)CrossRefGoogle Scholar
  3. 3.
    Brough, R., et al.: Searching for synthetic lethality in cancer. Curr. Opin. Genet. Dev. 21, 34–41 (2011)CrossRefGoogle Scholar
  4. 4.
    Gao, J., Liu, Y., D’Souza, M.R., Barabsi, L.A.: Target control of complex networks. Nat Comm., Article no. 5415 (2014)Google Scholar
  5. 5.
    Hopkins, A.L.: Network pharmacology: the next paradigm in drug discovery. Nat. Chem. Biol. 4, 682–690 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kalman, R.E.: Mathematical description of linear dynamical systems. J. Soc. Indus. Appl. Math. Ser. A 1, 152–192 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Koh, Y.L.J., Brown, R.K., Sayad, A., Kasimer, D., Ketela, T., Moffat, J.: COLT-Cancer: functional genetic screening resource for essential genes in human cancer cell lines. Nucl. Acids Res. 40(Database issue), D957–D963 (2012). doi: 10.1093/nar/gkr959 CrossRefGoogle Scholar
  8. 8.
    Kolch, W., et al.: The dynamic control of signal transduction networks in cancer cells. Nat. Rev. 15, 515–525 (2015)CrossRefGoogle Scholar
  9. 9.
    Lin, C.-T.: Structural controllability. IEEE Trans. Autom. Control 19, 201–208 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Liu, Y., Slotine, J.J., Barabsi, L.A.: Controllability of complex networks. Nature 473, 167–173 (2011)CrossRefGoogle Scholar
  11. 11.
    Marcotte, R., Brown, R.K., Suarez, F., et al.: Essential gene profiles in breast, pancreatic, and ovarian cancer cells. Cancer Discov. 2(2), 172–189 (2012). doi: 10.1158/2159-8290 CrossRefGoogle Scholar
  12. 12.
    Perfetto, L., Briganti, L., Calderone, A.: SIGNOR: a database of causal relationships between biological entities. Nucl. Acids Res. 44(D1), D548–554 (2016). doi: 10.1093/nar/gkv1048 CrossRefGoogle Scholar
  13. 13.
    Poljak, S.: On the generic dimension of controllable subspaces. IEEE Trans. Autom. Control 35(3), 367–369 (1990). doi: 10.1109/9.50361 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Poljak, S., Murota, K.: Note on a graph-theoretic criterion for structural output controllability. IEEE Trans. Autom. Control 35, 939–942 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Shields, R.W., Pearson, J.B.: Structural controllability of multi-input linear systems. IEEE Trans. Autom. Control 21, 203–212 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Wang, T., et al.: Identification and characterization of essential genes in the human genome. Science 350(6264), 1096–1101 (2015)CrossRefGoogle Scholar
  17. 17.
    Zañudo, J.G.T., Albert, R.: Cell fate reprogramming by control of intracellular network dynamics. PLoS Comput. Biol. 11(4), e1004193 (2015)CrossRefGoogle Scholar
  18. 18.
    Zhan, T., Boutros, M.: Towards a compendium of essential genes - from model organisms to synthetic lethality in cancer cells. Crit. Rev. Biochem. Mol. Biol. 51(2), 74–85 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Computational Biomodeling Laboratory, Department of Computer Science and Turku Centre for Computer ScienceÅbo Akademi UniversityTurkuFinland

Personalised recommendations