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Journal of Computer Science and Technology

, Volume 34, Issue 1, pp 16–34 | Cite as

Controllability and Its Applications to Biological Networks

  • Lin Wu
  • Min Li
  • Jian-Xin Wang
  • Fang-Xiang WuEmail author
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Abstract

Biological elements usually exert their functions through interactions with others to form various types of biological networks. The ability of controlling the dynamics of biological networks is of enormous benefits to pharmaceutical and medical industry as well as scientific research. Though there are many mathematical methods for steering dynamic systems towards desired states, the methods are usually not feasible for applying to complex biological networks. The difficulties come from the lack of accurate model that can capture the dynamics of interactions between biological elements and the fact that many mathematical methods are computationally intractable for large-scale networks. Recently, a concept in control theory — controllability, has been applied to investigate the dynamics of complex networks. In this article, recent advances on the controllability of complex networks and applications to biological networks are reviewed. Developing dynamic models is the prior concern for analyzing dynamics of biological networks. First, we introduce a widely used dynamic model for investigating controllability of complex networks. Then recent studies of theorems and algorithms for having complex biological networks controllable in general or specific application scenarios are reviewed. Finally, applications to real biological networks manifest that investigating the controllability of biological networks can shed lights on many critical physiological or medical problems, such as revealing biological mechanisms and identifying drug targets, from a systematic perspective.

Keywords

biological network network controllability steering node 

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References

  1. [1]
    Ito T, Chiba T, Ozawa R et al. A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proceedings of the National Academy of Sciences, 2001, 98(8): 4569-4574.CrossRefGoogle Scholar
  2. [2]
    Sprinzak E, Margalit H. Correlated sequence-signatures as markers of protein-protein interaction. Journal of Molecular Biology, 2001, 311(4): 681-692.CrossRefGoogle Scholar
  3. [3]
    Liu L Z, Wu F X, Zhang W J. Reverse engineering of gene regulatory networks from biological data. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 2012, 2(5): 365-385.Google Scholar
  4. [4]
    Gu S, Pasqualetti F, Cieslak M et al. Controllability of structural brain networks. Nature Communications, 2015, 6: Article No. 8414.Google Scholar
  5. [5]
    Csermely P, Agoston V, Pongor S. The efficiency of multitarget drugs: The network approach might help drug design. Trends in Pharmacological Sciences, 2005, 26(4): 178-182.CrossRefGoogle Scholar
  6. [6]
    Dai Y F, Zhao X M. A survey on the computational approaches to identify drug targets in the postgenomic era. BioMed Research International, 2015, 2015: Article No. 239654.Google Scholar
  7. [7]
    Wang X, Gulbahce N, Yu H. Network-based methods for human disease gene prediction. Briefings in Functional Genomics, 2011, 10(5): 280-293.CrossRefGoogle Scholar
  8. [8]
    Chen B, Fan W, Liu J et al. Identifying protein complexes and functional modules — From static PPI networks to dynamic PPI networks. Briefings in Bioinformatics, 2013, 15(2): 177-194.CrossRefGoogle Scholar
  9. [9]
    Kalman R E. Mathematical description of linear dynamical systems. Journal of the Society for Industrial and Applied Mathematics Control, Series A, 1963, 1(2): 152-192.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Lin C T. Structural controllability. IEEE Transactions on Automatic Control, 1974, 19(3): 201-208.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Liu Y Y, Slotine J J, Barabási A L. Controllability of complex networks. Nature, 2011, 473(7346): 167-173.CrossRefGoogle Scholar
  12. [12]
    Wang B, Gao L, Zhang Q et al. Diversified control paths: A significant way disease genes perturb the human regulatory network. PLoS One, 2015, 10(8): Article No. e0135491.Google Scholar
  13. [13]
    Wu L, Shen Y, Li M et al. Network output controllabilitybased method for drug target identification. IEEE Transactions on Nano Bioscience, 2015, 14(2): 184-191.CrossRefGoogle Scholar
  14. [14]
    Yan G, Vértes P E, Towlson E K et al. Network control principles predict neuron function in the caenorhabditis elegans connectome. Nature, 2017, 550(7677): 519-523.CrossRefGoogle Scholar
  15. [15]
    D’haeseleer P, Wen X, Fuhrman S et al. Linear modeling of mRNA expression levels during CNS development and injury. Pacific Symposium on Biocomputing, 1999, 4: 41-52.Google Scholar
  16. [16]
    Slotine J J, Li W. Applied Nonlinear Control. Pearson, 1991.Google Scholar
  17. [17]
    Liu Y Y, Barabási A L. Control principles of complex systems. Reviews of Modern Physics, 2016, 88(3): Article 035006.Google Scholar
  18. [18]
    Shields R, Pearson J. Structural controllability of multiinput linear systems. IEEE Transactions on Automatic Control, 1976, 21(2): 203-212.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Glover K, Silverman L. Characterization of structural controllability. IEEE Transactions on Automatic Control, 1976, 21(4): 534-537.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Hosoe S, Matsumoto K. On the irreducibility condition in the structural controllability theorem. IEEE Transactions on Automatic Control, 1979, 24(6): 963-966.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Linnemann A. A further simplification in the proof of the structural controllability theorem. IEEE Transactions on Automatic Control, 1986, 31(7): 638-639.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    Hosoe S. Determination of generic dimensions of controllable subspaces and its application. IEEE Transactions on Automatic Control, 1980, 25(6): 1192-1196.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Poljak S. On the generic dimension of controllable subspaces. IEEE Transactions on Automatic Control, 1990, 35(3): 367-369.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Murota K, Poljak S. Note on a graph-theoretic criterion for structural output controllability. IEEE Transactions on Automatic Control, 1990, 35(8): 939-942.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    Wu F X,Wu L,Wang J et al. Transittability of complex networks and its applications to regulatory biomolecular networks. Scientific Reports, 2014, 4: Article No. 4819.Google Scholar
  26. [26]
    Mayeda H, Yamada T. Strong structural controllability. SIAM Journal on Control and Optimization, 1979, 17(1): 123-138.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Tu C. Strong structural control centrality of a complex network. Physica Scripta, 2015, 90(3): Article No. 035202.Google Scholar
  28. [28]
    Nepusz T, Vicsek T. Controlling edge dynamics in complex networks. Nature Physics, 2012, 8(7): 568-573.CrossRefGoogle Scholar
  29. [29]
    Cowan N J, Chastain E J, Vilhena D A et al. Nodal dynamics, not degree distributions, determine the structural controllability of complex networks. PLoS One, 2012, 7(6): Article No. e38398.Google Scholar
  30. [30]
    Nie S, Wang X, Zhang H et al. Robustness of controllability for networks based on edge-attack. PLoS One, 2014, 9(2): Article No. e89066.Google Scholar
  31. [31]
    Wang W X, Ni X, Lai Y C et al. Optimizing controllability of complex networks by minimum structural perturbations. Physical Review E, 2012, 85(2): Article No. 026115.Google Scholar
  32. [32]
    Wu L, Li M, Wang J et al. CytoCtrlAnalyser: A cytoscape app for biomolecular network controllability analysis. Bioinformatics, 2018, 34(8): 1428-1430.CrossRefGoogle Scholar
  33. [33]
    Wu L, Li M, Wang J et al. Minimum steering node set of complex networks and its applications to biomolecular networks. IET Systems Biology, 2016, 10(3): 116-123.CrossRefGoogle Scholar
  34. [34]
    Liu Y Y, Slotine J J, Barab´asi A L. Control centrality and hierarchical structure in complex networks. PLoS One, 2012, 7(9): Article No. e44459.Google Scholar
  35. [35]
    Iudice F L, Garofalo F, Sorrentino F. Structural permeability of complex networks to control signals. Nature Communications, 2015, 6: Article No. 8349.Google Scholar
  36. [36]
    Liu X, Pan L. Controllability of the better chosen partial networks. Physica A: Statistical Mechanics and Its Applications, 2016, 456: 120-127.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    Commault C, van der Woude J, Boukhobza T. On the fixed controllable subspace in linear structured systems. Systems & Control Letters, 2017, 102: 42-47.MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    Wu L, Shen Y, Li M et al. Drug target identification based on structural output controllability of complex networks. In Proc. the 10th International Symposium Bioinformatics Research and Applications, June 2014, pp.188-199.Google Scholar
  39. [39]
    Gao J, Liu Y Y, D’Souza R M et al. Target control of complex networks. Nature Communications, 2014, 5: Article No. 5415.Google Scholar
  40. [40]
    Ogata K. Modern Control Engineering (3rd edition). Prentice Hall, 1996.Google Scholar
  41. [41]
    Hopcroft J E, Karp R M. An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing, 1973, 2(4): 225-231.MathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    Zhang X, Lv T, Yang X et al. Structural controllability of complex networks based on preferential matching. PLoS One, 2014, 9(11): Article No. e112039.Google Scholar
  43. [43]
    Goodrich M T, Tamassia R. Algorithm Design: Foundation, Analysis and Internet Examples. John Wiley & Sons, 2006.Google Scholar
  44. [44]
    Wu L, Tang L, Li M et al. The MSS of complex networks with centrality based preference and its application to biomolecular networks. In Proc. the 2016 IEEE International Conference on Bioinformatics and Biomedicine, December 2016, pp.229-234.Google Scholar
  45. [45]
    Pequito S, Kar S, Aguiar A P. On the complexity of the constrained input selection problem for structural linear systems. Automatica, 2015, 62: 193-199.MathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    Lindmark G, Altafini C. Controllability of complex networks with unilateral inputs. Scientific Reports, 2017, 7: Article No. 1824.Google Scholar
  47. [47]
    Rugh W J, Kailath T. Linear System Theory (2nd edition). Pearson, 1995.Google Scholar
  48. [48]
    Wang L Z, Chen Y Z, Wang W X et al. Physical controllability of complex networks. Scientific Reports, 2017, 7: Article No. 40198.Google Scholar
  49. [49]
    Li G, Tang P, Wen C et al. Boundary constraints for minimum cost control of directed networks. IEEE Transactions on Cybernetics, 2017, 47(12): 4196-4207.CrossRefGoogle Scholar
  50. [50]
    Czeizler E, Gratie C, Chiu W K et al. Target controllability of linear networks. In Proc. the 14th International Conference on Computational Methods in Systems Biology, September 2016, pp.67-81.Google Scholar
  51. [51]
    Kuhn H W. The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 1955, 2(1/2): 83-97.MathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    Zhang X, Wang H, Lv T. Efficient target control of complex networks based on preferential matching. PLoS One, 2017, 12(4): Article No. e0175375.Google Scholar
  53. [53]
    Liu X, Pan L, Stanley H E et al. Controllability of giant connected components in a directed network. Physical Review E, 2017, 95(4): Article No. 042318.Google Scholar
  54. [54]
    Piao X, Lv T, Zhang X et al. Strategy for community control of complex networks. Physica A: Statistical Mechanics and Its Applications, 2015, 421: 98-108.CrossRefGoogle Scholar
  55. [55]
    Guo W F, Zhang S W, Wei Z G et al. Constrained target controllability of complex networks. Journal of Statistical Mechanics: Theory and Experiment, 2017, 2017(6): Article No. 063402.Google Scholar
  56. [56]
    Khazanchi R, Dempsey K, Thapa I et al. On identifying and analyzing significant nodes in protein-protein interaction networks. In Proc. the 23rd IEEE International Conference on Data Mining Workshops, December 2013, pp.343-348.Google Scholar
  57. [57]
    Badhwar R, Bagler G. Control of neuronal network in caenorhabditis elegans. PLoS One, 2015, 10(9): Article No. e0139204.Google Scholar
  58. [58]
    Noori H R, Schöttler J, Ercsey-Ravasz M et al. A multiscale cerebral neurochemical connectome of the rat brain. PLoS Biology, 2017, 15(7): Article No. e2002612.Google Scholar
  59. [59]
    Deisseroth K. Circuit dynamics of adaptive and maladaptive behaviour. Nature, 2014, 505(7483): 309-317.CrossRefGoogle Scholar
  60. [60]
    Kringelbach M L, Jenkinson N, Owen S L et al. Translational principles of deep brain stimulation. Nature Reviews Neuroscience, 2007, 8(8): 623-635.CrossRefGoogle Scholar
  61. [61]
    Li F, Long T, Lu Y et al. The yeast cell-cycle network is robustly designed. Proceedings of the National Academy of Sciences of the United States of America, 2004, 101(14): 4781-4786.CrossRefGoogle Scholar
  62. [62]
    Davidich M I, Bornholdt S. Boolean network model predicts cell cycle sequence of fission yeast. PLoS One, 2008, 3(2): Article No. e1672.Google Scholar
  63. [63]
    Moes M, Le Béchec A, Crespo I et al. A novel network integrating a miRNA-203/SNAI1 feedback loop which regulates epithelial to mesenchymal transition. PLoS One, 2012, 7(4): Article No. e35440.Google Scholar
  64. [64]
    Krumsiek J, Marr C, Schroeder T et al. Hierarchical differentiation of myeloid progenitors is encoded in the transcription factor network. PLoS One, 2011, 6(8): Article No. e22649.Google Scholar
  65. [65]
    Mendoza L. A network model for the control of the differentiation process in Th cells. Biosystems, 2006, 84(2): 101-114.CrossRefGoogle Scholar
  66. [66]
    Lee H J, Takemoto N, Kurata H et al. Gata-3 induces T helper cell type 2 (Th2) cytokine expression and chromatin remodeling in committed Th1 cells. Journal of Experimental Medicine, 2000, 192(1): 105-116.CrossRefGoogle Scholar
  67. [67]
    Szabo S J, Kim S T, Costa G L et al. A novel transcription factor, T-bet, directs Th1 lineage commitment. Cell, 2000, 100(6): 655-669.CrossRefGoogle Scholar
  68. [68]
    Hwang E S, Szabo S J, Schwartzberg P L et al. T helper cell fate specified by kinase-mediated interaction of T-bet with GATA-3. Science, 2005, 307(5708): 430-433.CrossRefGoogle Scholar
  69. [69]
    Kanhaiya K, Czeizler E, Gratie C et al. Controlling directed protein interaction networks in cancer. Technical Report, Turku Centre for Computer Science, 2017. http://tucs.fi/publications/attachment.php?fname=tKaCzGrPe16a.full.pdf, Nov. 2018.
  70. [70]
    Wu L, Tang L, Li M et al. Biomolecular network controllability with drug binding information. IEEE Transactions on Nano Bioscience, 2017, 16(5): 326-332.CrossRefGoogle Scholar
  71. [71]
    Jia T, Liu Y Y, Csóka E et al. Emergence of bimodality in controlling complex networks. Nature Communications, 2013, 4: Article No. 2002.Google Scholar
  72. [72]
    Liu X, Pan L. Identifying driver nodes in the human signaling network using structural controllability analysis. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2015, 12(2): 467-472.CrossRefGoogle Scholar
  73. [73]
    Jia T, Barabási A L. Control capacity and a random sampling method in exploring controllability of complex networks. Scientific Reports, 2013, 3: Article No. 2354.Google Scholar
  74. [74]
    Liu X, Pan L. Detection of driver metabolites in the human liver metabolic network using structural controllability analysis. BMC Systems Biology, 2014, 8(1): Article No. 51.Google Scholar
  75. [75]
    Vinayagam A, Gibson T E, Lee H J et al. Controllability analysis of the directed human protein interaction network identifies disease genes and drug targets. Proceedings of the National Academy of Sciences of the United States of America, 2016, 113(18): 4976-4981.CrossRefGoogle Scholar
  76. [76]
    Matsuoka Y, Matsumae H, Katoh M et al. A comprehensive map of the influenza A virus replication cycle. BMC Systems Biology, 2013, 7(1): Article No. 97.Google Scholar
  77. [77]
    Uhart M, Flores G, Bustos D. M. Controllability of proteinprotein interaction phosphorylation-based networks: Participation of the hub 14-3-3 protein family. Scientific Reports, 2016, 6: Article No. 26234.Google Scholar
  78. [78]
    Ravindran V, Sunitha V, Bagler G. Identification of critical regulatory genes in cancer signaling network using controllability analysis. Physica A: Statistical Mechanics and Its Applications, 2017, 474: 134-143.CrossRefGoogle Scholar
  79. [79]
    Ruths J, Ruths D. Control profiles of complex networks. Science, 2014, 343(6177): 1373-1376.MathSciNetCrossRefzbMATHGoogle Scholar
  80. [80]
    Tu C, Rocha R P, Corbetta M et al. Warnings and caveats in brain controllability. Neuroimage, 2017, 176: 83-91.CrossRefGoogle Scholar
  81. [81]
    Vanunu O, Magger O, Ruppin E et al. Associating genes and protein complexes with disease via network propagation. PLoS Computational Biology, 2010, 6(1): Article No. e1000641.Google Scholar
  82. [82]
    Wang B, Gao L, Gao Y. Control range: A controllabilitybased index for node significance in directed networks. Journal of Statistical Mechanics: Theory and Experiment, 2012, 2012(04): Article No. P04011.Google Scholar
  83. [83]
    Wang B, Gao L, Gao Y et al. Controllability and observability analysis for vertex domination centrality in directed networks. Scientific Reports, 2014, 4: Article No. 5399.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Lin Wu
    • 1
  • Min Li
    • 2
  • Jian-Xin Wang
    • 2
  • Fang-Xiang Wu
    • 1
    • 2
    • 3
    Email author
  1. 1.Division of Biomedical EngineeringUniversity of SaskatchewanSaskatoonCanada
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaChina
  3. 3.Department of Mechanical EngineeringUniversity of SaskatchewanSaskatoonCanada

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