Bulletin of Mathematical Biology

, Volume 75, Issue 6, pp 988–1011 | Cite as

Dynamics of Influenza Virus and Human Host Interactions During Infection and Replication Cycle

  • Alex Madrahimov
  • Tomáš Helikar
  • Bryan Kowal
  • Guoqing Lu
  • Jim Rogers
Original Article


The replication and life cycle of the influenza virus is governed by an intricate network of intracellular regulatory events during infection, including interactions with an even more complex system of biochemical interactions of the host cell. Computational modeling and systems biology have been successfully employed to further the understanding of various biological systems, however, computational studies of the complexity of intracellular interactions during influenza infection is lacking. In this work, we present the first large-scale dynamical model of the infection and replication cycle of influenza, as well as some of its interactions with the host’s signaling machinery. Specifically, we focus on and visualize the dynamics of the internalization and endocytosis of the virus, replication and translation of its genomic components, as well as the assembly of progeny virions. Simulations and analyses of the models dynamics qualitatively reproduced numerous biological phenomena discovered in the laboratory. Finally, comparisons of the dynamics of existing and proposed drugs, our results suggest that a drug targeting PB1:PA would be more efficient than existing Amantadin/Rimantaine or Zanamivir/Oseltamivir.


Influenza A Systems biology Dynamical model Computational modeling Probabilistic Boolean network 

Supplementary material

11538_2012_9777_MOESM1_ESM.pdf (120 kb)
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  1. Abdi, A., Tahoori, M. B., & Emamian, E. S. (2008). Fault diagnosis engineering of digital circuits can identify vulnerable molecules in complex cellular pathways. Sci. Signal., 1(42), ra10. CrossRefGoogle Scholar
  2. Alon, U. (2007). Network motifs: theory and experimental approaches. Nat. Rev. Genet., 8(6), 450–461. CrossRefGoogle Scholar
  3. Bagowski, C. P., & Ferrell, J. E. (2001). Bistability in the JNK cascade. Curr. Biol., CB, 11(15), 1176–1182. CrossRefGoogle Scholar
  4. Bagowski, C. P., Besser, J., Frey, C. R., & Ferrell, J. E. (2003). The JNK cascade as a biochemical switch in mammalian cells: ultrasensitive and all-or-none responses. Curr. Biol., CB, 13(4), 315–320. CrossRefGoogle Scholar
  5. Beauchemin, C., Samuel, J., & Tuszynski, J. (2005). A simple cellular automaton model for influenza A viral infections. J. Theor. Biol., 232(2), 223–234. MathSciNetCrossRefGoogle Scholar
  6. Beyer, T., Busse, M., Hristov, K., Gurbiel, S., Smida, M., Haus, U.-U., Ballerstein, K., Pfeuffer, F., Weismantel, R., Schraven, B., & Lindquist, J. A. (2011). Integrating signals from the T-cell receptor and the interleukin-2 receptor. PLoS Comput. Biol., 7(8), e1002121. CrossRefGoogle Scholar
  7. Biswas, S. K., & Nayak, D. P. (1996). Influenza virus polymerase basic protein 1 interacts with influenza virus polymerase basic protein 2 at multiple sites. J. Virol., 70(10), 6716–6722. Google Scholar
  8. Boivin, S., Cusack, S., Ruigrok, R. W. H., & Hart, D. J. (2010). Influenza A virus polymerase: structural insights into replication and host adaptation mechanisms. J. Biol. Chem., 285(37), 28411–28417. CrossRefGoogle Scholar
  9. Boulo, S., Akarsu, H., Ruigrok, R. W. H., & Baudin, F. (2007). Nuclear traffic of influenza virus proteins and ribonucleoprotein complexes. Virus Res., 124(1–2), 12–21. CrossRefGoogle Scholar
  10. Boyer, L. A., Lee, T. I., Cole, M. F., Johnstone, S. E., Levine, S. S., Zucker, J. P., Guenther, M. G., Kumar, R. M., Murray, H. L., Jenner, R. G., Gifford, D. K., Melton, D. A., Jaenisch, R., & Young, R. A. (2005). Core transcriptional regulatory circuitry in human embryonic stem cells. Cell, 122(6), 947–956. CrossRefGoogle Scholar
  11. Brandman, O., & Meyer, T. (2008). Feedback loops shape cellular signals in space and time. Science (New York, NY), 322(5900), 390–395. MathSciNetMATHCrossRefGoogle Scholar
  12. Broadbent, A. J., & Subbarao, K. (2011). Influenza virus vaccines: lessons from the 2009 H1N1 pandemic. Curr. Opin. Virol., 1(4), 254–262. CrossRefGoogle Scholar
  13. Chaves, M., Albert, R., & Sontag, E. D. (2005). Robustness and fragility of Boolean models for genetic regulatory networks. J. Theor. Biol., 235(3), 431–449. MathSciNetCrossRefGoogle Scholar
  14. Chaves, M., Sontag, E. D., & Albert, R. (2006). Methods of robustness analysis for Boolean models of gene control networks. Syst. Biol., 153(4), 154–167. CrossRefGoogle Scholar
  15. Cheng, D., & Qi, H. (2010). State-space analysis of Boolean networks. IEEE Trans. Neural Netw., 21(4), 584–594. A publication of the IEEE Neural Networks Council MathSciNetCrossRefGoogle Scholar
  16. Daum, G., Eisenmann-Tappe, I., Fries, H. W., Troppmair, J., & Rapp, U. R. (1994). The ins and outs of Raf kinases. Trends Biochem. Sci., 19(11), 474–480. CrossRefGoogle Scholar
  17. De Clercq, E. (2006). Antiviral agents active against influenza A viruses. Nat. Rev. Drug Discov., 5(12), 1015–1025. CrossRefGoogle Scholar
  18. Detjen, B. M., St Angelo, C., Katze, M. G., & Krug, R. M. (1987). The three influenza virus polymerase (P) proteins not associated with viral nucleocapsids in the infected cell are in the form of a complex. J. Virol., 61(1), 16–22. Google Scholar
  19. Ehrhardt, C., Marjuki, H., Wolff, T., Nürnberg, B., Planz, O., Pleschka, S., & Ludwig, S. (2006). Bivalent role of the phosphatidylinositol-3-kinase (PI3K) during influenza virus infection and host cell defence. Cell. Microbiol., 8(8), 1336–1348. CrossRefGoogle Scholar
  20. Ehrhardt, C., Wolff, T., Pleschka, S., Planz, O., Beermann, W., Bode, J. G., Schmolke, M., & Ludwig, S. (2007). Influenza A virus NS1 protein activates the PI3K/Akt pathway to mediate antiapoptotic signaling responses. J. Virol., 81(7), 3058–3067. CrossRefGoogle Scholar
  21. Eierhoff, T., Hrincius, E. R., Rescher, U., Ludwig, S., & Ehrhardt, C. (2010). The epidermal growth factor receptor (EGFR) promotes uptake of influenza A viruses (IAV) into host cells. PLoS Pathog., 6(9), e1001099. CrossRefGoogle Scholar
  22. Emmert-Streib, F., & Dehmer, M. (2009). Information processing in the transcriptional regulatory network of yeast: functional robustness. BMC Syst. Biol., 3(35). Google Scholar
  23. Engelhardt, O. G., & Fodor, E. (2006). Functional association between viral and cellular transcription during influenza virus infection. Reviews in medical virology, 16(5), 329–345. CrossRefGoogle Scholar
  24. Ferrell, J. E. (2011). Simple rules for complex processes: new lessons from the budding yeast cell cycle. Mol. Cell, 43(4), 497–500. CrossRefGoogle Scholar
  25. Forst, C. V. (2006). Host-pathogen systems biology. Drug Discov. Today, 11(5–6), 220–227. CrossRefGoogle Scholar
  26. Fry, A. M., & Gubareva, L. V. (2012). Understanding influenza virus resistance to antiviral agents; early warning signs for wider community circulation. J. Inf. Dis. Google Scholar
  27. Ghanem, A., Mayer, D., Chase, G., Tegge, W., Frank, R., Kochs, G., García-Sastre, A., & Schwemmle, M. (2007). Peptide-mediated interference with influenza A virus polymerase. J. Virol., 81(14), 7801–7804. CrossRefGoogle Scholar
  28. Gillis, J. S. (2006). An avian influenza vaccine for humans targeting the polymerase B2 protein inside the capsid instead of hemagglutinin or neuramidase on the virus surface. Med. Hypotheses, 66(5), 975–977. MathSciNetCrossRefGoogle Scholar
  29. Gong, J., Xu, W., & Zhang, J. (2007). Structure and functions of influenza virus neuraminidase. Curr. Med. Chem., 14(1), 113–122. CrossRefGoogle Scholar
  30. González, S., Zürcher, T., & Ortín, J. (1996). Identification of two separate domains in the influenza virus PB1 protein involved in the interaction with the PB2 and PA subunits: a model for the viral RNA polymerase structure. Nucleic Acids Res., 24(22), 4456–4463. CrossRefGoogle Scholar
  31. Gubareva, L. V., Kaiser, L., & Hayden, F. G. (2000). Influenza virus neuraminidase inhibitors. Lancet, 355(9206), 827–835. CrossRefGoogle Scholar
  32. Hancioglu, B., Swigon, D., & Clermont, G. (2007). A dynamical model of human immune response to influenza A virus infection. J. Theor. Biol., 246(1), 70–86. MathSciNetCrossRefGoogle Scholar
  33. Helikar, T., & Rogers, J. A. (2009). ChemChains: a platform for simulation and analysis of biochemical networks aimed to laboratory scientists. BMC Syst. Biol., 3, 58. CrossRefGoogle Scholar
  34. Helikar, T., Konvalina, J., Heidel, J., & Rogers, J. A. (2008). Emergent decision-making in biological signal transduction networks. Proc. Natl. Acad. Sci. USA, 105(6), 1913–1918. CrossRefGoogle Scholar
  35. Helikar, T. T., Kochi, N., Konvalina, J., & Rogers, J. A. (2011). Boolean modeling of biochemical networks. Open Bioinforma. J., 4(5), 16–25. MathSciNetGoogle Scholar
  36. Helikar, T., Kowal, B., McClenathan, S., Bruckner, M., Rowley, T., Madrahimov, A., Wicks, B., Shrestha, M., Limbu, K., & Rogers, J. A. (2012a). The cell collective: toward an open and collaborative approach to systems biology. BMC Syst. Biol., 6(1), 96. CrossRefGoogle Scholar
  37. Helikar, T., Kowal, B., Madrahimov, A., Shrestha, M., Pedersen, J., Konvalina, J., & Rogers, J. A. (2012b). Bio-Logic Builder: a non-technical tool for building dynamical, qualitative models. PLoS ONE, 7(10), e46417. CrossRefGoogle Scholar
  38. Herz, C., Stavnezer, E., Krug, R., & Gurney, T. (1981). Influenza virus, an RNA virus, synthesizes its messenger RNA in the nucleus of infected cells. Cell, 26(3 Pt 1), 391–400. CrossRefGoogle Scholar
  39. Ison, M. G. (2011). Antivirals and resistance: influenza virus. Curr. Opin. Virol., 1(6), 563–573. CrossRefGoogle Scholar
  40. Kitano, H. (2002). Systems biology: a brief overview. Science, 295(5560), 1662–1664. CrossRefGoogle Scholar
  41. König, R., Stertz, S., Zhou, Y., Inoue, A., Hoffmann, H.-H., Bhattacharyya, S., Alamares, J. G., Tscherne, D. M., Ortigoza, M. B., Liang, Y., Gao, Q., Andrews, S. E., Bandyopadhyay, S., De Jesus, P., Tu, B. P., Pache, L., Shih, C., Orth, A., Bonamy, G., Miraglia, L., Ideker, T., García-Sastre, A., Young, J. A. T., Palese, P., Shaw, M. L., & Chanda, S. K. (2010). Human host factors required for influenza virus replication. Nature, 463(7282), 813–817. CrossRefGoogle Scholar
  42. Krumbholz, A., Philipps, A., Oehring, H., Schwarzer, K., Eitner, A., Wutzler, P., & Zell, R. (2011). Current knowledge on PB1-F2 of influenza A viruses. Med. Microbiol. Immunol., 200(2), 69–75. CrossRefGoogle Scholar
  43. Lee, T. I., Rinaldi, N. J., Robert, F., Odom, D. T., Bar-Joseph, Z., Gerber, G. K., Hannett, N. M., Harbison, C. T., Thompson, C. M., Simon, I., Zeitlinger, J., Jennings, E. G., Murray, H. L., Gordon, D. B., Ren, B., Wyrick, J. J., Tagne, J.-B., Volkert, T. L., Fraenkel, E., Gifford, D. K., & Young, R. A. (2002). Transcriptional regulatory networks in saccharomyces cerevisiae. Science (New York, NY), 298(5594), 799–804. CrossRefGoogle Scholar
  44. Ludwig, S., Pleschka, S., Planz, O., & Wolff, T. (2006). Ringing the alarm bells: signalling and apoptosis in influenza virus infected cells. Cell. Microbiol., 8(3), 375–386. CrossRefGoogle Scholar
  45. Ma’ayan, A., Jenkins, S. L., Neves, S., Hasseldine, A., Grace, E., Dubin-Thaler, B., Eungdamrong, N. J., Weng, G., Ram, P. T., Rice, J. J., Kershenbaum, A., Stolovitzky, G. A., Blitzer, R. D., & Iyengar, R. (2005). Formation of regulatory patterns during signal propagation in a Mammalian cellular network. Science (New York, NY), 309(5737), 1078–1083. CrossRefGoogle Scholar
  46. Mangan, S., & Alon, U. (2003). Structure and function of the feed-forward loop network motif. Proc. Natl. Acad. Sci. USA, 100(21), 11980–11985. CrossRefGoogle Scholar
  47. Mangan, S., Zaslaver, A., & Alon, U. (2003). The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks. J. Mol. Biol., 334(2), 197–204. CrossRefGoogle Scholar
  48. Matallanas, D., Birtwistle, M., Romano, D., Zebisch, A., Rauch, J., von Kriegsheim, A., & Kolch, W. (2011). Raf family kinases: old dogs have learned new tricks. Genes Cancer, 2(3), 232–260. CrossRefGoogle Scholar
  49. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., & Alon, U. (2002). Network motifs: simple building blocks of complex networks. Science (New York, NY), 298(5594), 824–827. CrossRefGoogle Scholar
  50. Morris, M. K., Saez-Rodriguez, J., Sorger, P. K., & Lauffenburger, D. A. (2010). Logic-based models for the analysis of cell signaling networks. Biochemistry, 49(15), 3216–3224. CrossRefGoogle Scholar
  51. Nakazawa, M., Kadowaki, S., Watanabe, I., Kadowaki, Y., Takei, M., & Fukuda, H. (2008). PA subunit of RNA polymerase as a promising target for anti-influenza virus agents. Antivir. Res., 78(3), 194–201. CrossRefGoogle Scholar
  52. Naldi, A., Carneiro, J., Chaouiya, C., & Thieffry, D. (2010). Diversity and plasticity of Th cell types predicted from regulatory network modelling. PLoS Comput. Biol., 6(9), e1000912. CrossRefGoogle Scholar
  53. Odom, D. T., Zizlsperger, N., Gordon, D. B., Bell, G. W., Rinaldi, N. J., Murray, H. L., Volkert, T. L., Schreiber, J., Rolfe, P. A., Gifford, D. K., Fraenkel, E., Bell, G. I., & Young, R. A. (2004). Control of pancreas and liver gene expression by HNF transcription factors. Science (New York, NY), 303(5662), 1378–1381. CrossRefGoogle Scholar
  54. Ohtsu, Y., Honda, Y., Sakata, Y., Kato, H., & Toyoda, T. (2002). Fine mapping of the subunit binding sites of influenza virus RNA polymerase. Microbiol. Immunol., 46(3), 167–175. Google Scholar
  55. O’Neill, R. E., Talon, J., & Palese, P. (1998). The influenza virus NEP (NS2 protein) mediates the nuclear export of viral ribonucleoproteins. EMBO J., 17(1), 288–296. CrossRefGoogle Scholar
  56. Oslund, K. L., & Baumgarth, N. (2011). Influenza-induced innate immunity: regulators of viral replication, respiratory tract pathology & adaptive immunity. Future Virol., 6(8), 951–962. CrossRefGoogle Scholar
  57. Payungporn, S., Panjaworayan, N., Makkoch, J., & Poovorawan, Y. (2010). Molecular characteristics of the human pandemic influenza A virus (H1N1). Acta Virol., 54(3), 155–163. CrossRefGoogle Scholar
  58. Pérez, D. R., & Donis, R. O. (1995). A 48-amino-acid region of influenza A virus PB1 protein is sufficient for complex formation with PA. J. Virol., 69(11), 6932–6939. Google Scholar
  59. Pinto, L. H., Holsinger, L. J., & Lamb, R. A. (1992). Influenza virus M2 protein has ion channel activity. Cell, 69(3), 517–528. CrossRefGoogle Scholar
  60. Pleschka, S., Wolff, T., Ehrhardt, C., Hobom, G., Planz, O., Rapp, U. R., & Ludwig, S. (2001). Influenza virus propagation is impaired by inhibition of the Raf/MEK/ERK signalling cascade. Nat. Cell Biol., 3(3), 301–305. CrossRefGoogle Scholar
  61. Poole, E. L., Medcalf, L., Elton, D., & Digard, P. (2007). Evidence that the C-terminal PB2-binding region of the influenza A virus PB1 protein is a discrete alpha-helical domain. FEBS Lett., 581(27), 5300–5306. CrossRefGoogle Scholar
  62. Rodríguez, A., Sosa, D., Torres, L., Molina, B., Frías, S., & Mendoza, L. (2012). A Boolean network model of the FA/BRCA pathway. Bioinformatics (Oxford, England), 28(6), 858–866. CrossRefGoogle Scholar
  63. Root, C. N., Wills, E. G., McNair, L. L., & Whittaker, G. R. (2000). Entry of influenza viruses into cells is inhibited by a highly specific protein kinase C inhibitor. J. Gen. Virol., 81(Pt 11), 2697–2705. Google Scholar
  64. Rossman, J. S., & Lamb, R. A. (2011). Influenza virus assembly and budding. Virology, 411(2), 229–236. CrossRefGoogle Scholar
  65. Saez-Rodriguez, J., Simeoni, L., Lindquist, J. A., Hemenway, R., Bommhardt, U., Arndt, B., Haus, U.-U., Weismantel, R., Gilles, E. D., Klamt, S., & Schraven, B. (2007). A logical model provides insights into T cell receptor signaling. PLoS Comput. Biol., 3(8), e163. MathSciNetCrossRefGoogle Scholar
  66. Shapira, S. D., Gat-Viks, I., Shum, B. O. V., Dricot, A., de Grace, M. M., Wu, L., Gupta, P. B., Hao, T., Silver, S. J., Root, D. E., Hill, D. E., Regev, A., & Hacohen, N. (2009). A physical and regulatory map of host-influenza interactions reveals pathways in H1N1 infection. Cell, 139(7), 1255–1267. CrossRefGoogle Scholar
  67. Shen-Orr, S. S., Milo, R., Mangan, S., & Alon, U. (2002). Network motifs in the transcriptional regulation network of Escherichia coli. Nat. Genet., 31(1), 64–68. CrossRefGoogle Scholar
  68. Siciliano, V., Menolascina, F., Marucci, L., Fracassi, C., Garzilli, I., Moretti, M. N., & di Bernardo, D. (2011). Construction and modelling of an inducible positive feedback loop stably integrated in a mammalian cell-line. PLoS Comput. Biol., 7(6), e1002074. CrossRefGoogle Scholar
  69. Sidorenko, Y., & Reichl, U. (2004). Structured model of influenza virus replication in MDCK cells. Biotechnol. Bioeng., 88(1), 1–14. CrossRefGoogle Scholar
  70. Sieczkarski, S. B., Brown, H. A., & Whittaker, G. R. (2003). Role of protein kinase C betaII in influenza virus entry via late endosomes. J. Virol., 77(1), 460–469. CrossRefGoogle Scholar
  71. Skehel, J. (2009). An overview of influenza haemagglutinin and neuraminidase. Biol., J. Int. Assoc. Biol. Stand., 37(3), 177–178. Google Scholar
  72. Song, B. M., Kang, Y. M., Kim, H. S., & Seo, S. H. (2011). Induction of inflammatory cytokines and toll-like receptors in human normal respiratory epithelial cells infected with seasonal H1N1, 2009 pandemic H1N1, seasonal H3N2, and highly pathogenic H5N1 influenza virus. Viral Immunol., 24(3), 179–187. CrossRefGoogle Scholar
  73. Takeda, M., Pekosz, A., Shuck, K., Pinto, L. H., & Lamb, R. A. (2002). Influenza a virus M2 ion channel activity is essential for efficient replication in tissue culture. J. Virol., 76(3), 1391–1399. CrossRefGoogle Scholar
  74. Trautmann, L., & Sekaly, R.-P. (2011). Solving vaccine mysteries: a systems biology perspective. Nat. Immunol., 12(8), 729–731. CrossRefGoogle Scholar
  75. Turan, K., Mibayashi, M., Sugiyama, K., Saito, S., Numajiri, A., & Nagata, K. (2004). Nuclear MxA proteins form a complex with influenza virus NP and inhibit the transcription of the engineered influenza virus genome. Nucleic Acids Res., 32(2), 643–652. CrossRefGoogle Scholar
  76. Umezawa, T. (2011). Systems biology approaches to abscisic acid signaling. J. Plant Res., 124(4), 539–548. CrossRefGoogle Scholar
  77. Watanabe, T., Watanabe, S., & Kawaoka, Y. (2010). Cellular networks involved in the influenza virus life cycle. Cell Host Microbe, 7(6), 427–439. CrossRefGoogle Scholar
  78. Webster, R. G., Bean, W. J., Gorman, O. T., Chambers, T. M., & Kawaoka, Y. (1992). Evolution and ecology of influenza A viruses. Microbiol. Rev., 56(1), 152–179. Google Scholar
  79. Wilkinson, T. M., Li, C. K. F., Chui, C. S. C., Huang, A. K. Y., Perkins, M., Liebner, J. C., Lambkin-Williams, R., Gilbert, A., Oxford, J., Nicholas, B., Staples, K. J., Dong, T., Douek, D. C., McMichael, A. J., & Xu, X.-N. (2012). Preexisting influenza-specific CD4+ T cells correlate with disease protection against influenza challenge in humans. Nat. Med., 18(2), 274–280. CrossRefGoogle Scholar
  80. Wunderlich, K., Mayer, D., Ranadheera, C., Holler, A.-S., Mänz, B., Martin, A., Chase, G., Tegge, W., Frank, R., Kessler, U., & Schwemmle, M. (2009). Identification of a PA-binding peptide with inhibitory activity against influenza A and B virus replication. PLoS ONE, 4(10), e7517. CrossRefGoogle Scholar
  81. Yan, Q. (2010). Systems biology of influenza: understanding multidimensional interactions for personalized prevention and treatment. Methods Mol. Biol., 662, 285–302. CrossRefGoogle Scholar
  82. Zheng, J., Zhang, D., Przytycki, P. F., Zielinski, R., Capala, J., & Przytycka, T. M. (2010). SimBoolNet—a cytoscape plugin for dynamic simulation of signaling networks. Bioinformatics (Oxford, England), 26(1), 141–142. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  • Alex Madrahimov
    • 1
    • 2
  • Tomáš Helikar
    • 2
  • Bryan Kowal
    • 3
  • Guoqing Lu
    • 1
  • Jim Rogers
    • 2
    • 4
  1. 1.Department of BiologyUniversity of Nebraska at OmahaOmahaUSA
  2. 2.Department of MathematicsUniversity of Nebraska at OmahaOmahaUSA
  3. 3.College of Information TechnologyUniversity of Nebraska at OmahaOmahaUSA
  4. 4.Department of Pathology and MicrobiologyUniversity of Nebraska Medical CenterOmahaUSA

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