Bulletin of Mathematical Biology

, Volume 74, Issue 8, pp 1789–1817 | Cite as

Modeling Quasispecies and Drug Resistance in Hepatitis C Patients Treated with a Protease Inhibitor

Original Article


Telaprevir, a novel hepatitis C virus (HCV) NS3-4A serine protease inhibitor, has demonstrated substantial antiviral activity in patients infected with HCV. However, drug-resistant HCV variants were detected in vivo at relatively high frequency a few days after drug administration. Here we use a two-strain mathematical model to explain the rapid emergence of drug resistance in HCV patients treated with telaprevir monotherapy. We examine the effects of backward mutation and liver cell proliferation on the preexistence of the mutant virus and the competition between wild-type and drug-resistant virus during therapy. We also extend the two-strain model to a general model with multiple viral strains. Mutations during therapy only have a minor effect on the dynamics of various viral strains, although they are capable of generating low levels of HCV variants that would otherwise be completely suppressed because of fitness disadvantages. Liver cell proliferation may not affect the pretreatment frequency of mutant variants, but is able to influence the quasispecies dynamics during therapy. It is the relative fitness of each mutant strain compared with wild-type that determines which strain(s) will dominate the virus population. This study provides a theoretical framework for exploring the prevalence of preexisting mutant variants and the evolution of drug resistance during treatment with other HCV protease inhibitors or polymerase inhibitors.


Telaprevir Mutation Fitness Quasispecies Direct-acting antiviral agents Mathematical model 


  1. Adiwijaya, B. S., Herrmann, E., Hare, B., Kieffer, T., Lin, C., et al. (2010). A multi-variant, viral dynamic model of genotype 1 HCV to assess the in vivo evolution of protease-inhibitor resistant variants. PLoS Comput. Biol., 6, e1000745. CrossRefGoogle Scholar
  2. Bacon, B. R., Gordon, S. C., Lawitz, E., Marcellin, P., Vierling, J. M., et al. (2011). Boceprevir for previously treated chronic HCV genotype 1 infection. N. Engl. J. Med., 364, 1207–1217. CrossRefGoogle Scholar
  3. Bartels, D. J., Zhou, Y., Zhang, E. Z., Marcial, M., Byrn, R. A., et al. (2008). Natural prevalence of hepatitis C virus variants with decreased sensitivity to NS3.4A protease inhibitors in treatment-naive subjects. J. Infect. Dis., 198, 800–807. CrossRefGoogle Scholar
  4. Bartenschlager, R., Frese, M., & Pietschmann, T. (2004). Novel insights into hepatitis C virus replication and persistence. Adv. Virus Res., 63, 71–180. CrossRefGoogle Scholar
  5. Chayama, K., Takahashi, S., Toyota, J., Karino, Y., Ikeda, K., et al. (2012). Dual therapy with the nonstructural protein 5A inhibitor, daclatasvir, and the nonstructural protein 3 protease inhibitor, asunaprevir, in hepatitis C virus genotype 1b-infected null responders. Hepatology, 55, 742–748. CrossRefGoogle Scholar
  6. Chu, H., Herrmann, E., Reesink, H., Forestier, N., Weegink, C., et al. (2005). Pharmacokinetics of VX-950, and its effect on hepatitis C viral dynamics. Hepatology, 42 Suppl 1, S694. Google Scholar
  7. Cubero, M., Esteban, J. I., Otero, T., Sauleda, S., Bes, M., et al. (2008). Naturally occurring NS3-protease-inhibitor resistant mutant A156T in the liver of an untreated chronic hepatitis C patient. Virology, 370, 237–245. CrossRefGoogle Scholar
  8. Dahari, H., Ribeiro, R. M., & Perelson, A. S. (2007). Triphasic decline of hepatitis C virus RNA during antiviral therapy. Hepatology, 46, 16–21. CrossRefGoogle Scholar
  9. Davis, G. L., Esteban-Mur, R., Rustgi, V., Hoefs, J., Gordon, S. C., et al. (1998). Interferon alfa-2b alone or in combination with ribavirin for the treatment of relapse of chronic hepatitis C. International Hepatitis Interventional Therapy Group. N. Engl. J. Med., 339, 1493–1499. CrossRefGoogle Scholar
  10. De Leenheer, P., & Pilyugin, S. S. (2008). Multistrain virus dynamics with mutations: a global analysis. Math. Med. Biol., 25, 285–322. CrossRefMATHGoogle Scholar
  11. Domingo, E. (1996). Biological significance of viral quasispecies. Viral Hepat. Rev., 2, 247–261. Google Scholar
  12. Dore, G. J., Matthews, G. V., & Rockstroh, J. (2011). Future of hepatitis C therapy: development of direct-acting antivirals. Curr. Opin. HIV AIDS, 6, 508–513. CrossRefGoogle Scholar
  13. Duffy, S., Shackelton, L. A., & Holmes, E. C. (2008). Rates of evolutionary change in viruses: patterns and determinants. Nat. Rev. Genet., 9, 267–276. CrossRefGoogle Scholar
  14. Egger, D., Wolk, B., Gosert, R., Bianchi, L., Blum, H. E., et al. (2002). Expression of hepatitis C virus proteins induces distinct membrane alterations including a candidate viral replication complex. J. Virol., 76, 5974–5984. CrossRefGoogle Scholar
  15. Elahi, E., & Ronaghi, M. (2004). Pyrosequencing: A tool for DNA sequencing analysis. Methods Mol. Biol., 255, 211–219. Google Scholar
  16. Evans, M. J., von Hahn, T., Tscherne, D. M., Syder, A. J., Panis, M., et al. (2007). Claudin-1 is a hepatitis C virus co-receptor required for a late step in entry. Nature, 446, 801–805. CrossRefGoogle Scholar
  17. Forestier, N., Reesink, H. W., Weegink, C. J., McNair, L., Kieffer, T. L., et al. (2007). Antiviral activity of telaprevir (VX-950) and peginterferon alfa-2a in patients with hepatitis C. Hepatology, 46, 640–648. CrossRefGoogle Scholar
  18. Foster, G. R. (2004). Past, present, and future hepatitis C treatments. Semin. Liver Dis., 24 Suppl 2, 97–104. CrossRefGoogle Scholar
  19. Foy, E., Li, K., Wang, C., Sumpter, J. R., Ikeda, M., et al. (2003). Regulation of interferon regulatory factor-3 by the hepatitis C virus serine protease. Science, 300, 1145–1148. CrossRefGoogle Scholar
  20. Fusco, D. N., & Chung, R. T. (2012). Novel therapies for hepatitis C: insights from the structure of the virus. Annu. Rev. Med., 63, 373–387. CrossRefGoogle Scholar
  21. Gillespie, J. (1998). Population genetics: a concise guide. Baltimore: Johns Hopkins University Press. Google Scholar
  22. Handel, A., Regoes, R. R., & Antia, R. (2006). The role of compensatory mutations in the emergence of drug resistance. PLoS Comput. Biol., 2, e137. CrossRefGoogle Scholar
  23. Hezode, C., Forestier, N., Dusheiko, G., Ferenci, P., Pol, S., et al. (2009). Telaprevir and peginterferon with or without ribavirin for chronic HCV infection. N. Engl. J. Med., 360, 1839–1850. CrossRefGoogle Scholar
  24. Jazwinski, A. B. & Muir, A. J. (2011). Direct-acting antiviral medications for chronic hepatitis C virus infection. Gastroenterol. Hepatol. 7, 154–162. Google Scholar
  25. Keeffe, E. B., Dieterich, D. T., Pawlotsky, J. M., & Benhamou, Y. (2008). Chronic hepatitis B: preventing, detecting, and managing viral resistance. Clín. Gastroenterol. Hepatol., 6, 268–274. CrossRefGoogle Scholar
  26. Khunvichai, A., Chu, H., Garg, V., McHutchison, J., Lawitz, E., et al. (2007). Predicting HCV treatment duration with an HCV protease inhibitor co-administered with PEG-IFN/RBV by modeling both wild-type virus and low level resistant variant dynamics. In Digestive disease week 2007. Washington, D.C., May 19–24, 2007. Google Scholar
  27. Kieffer, T. L., Sarrazin, C., Miller, J. S., Welker, M. W., Forestier, N., et al. (2007). Telaprevir and pegylated interferon-alpha-2a inhibit wild-type and resistant genotype 1 hepatitis C virus replication in patients. Hepatology, 46, 631–639. CrossRefGoogle Scholar
  28. Lamarre, D., Anderson, P. C., Bailey, M., Beaulieu, P., Bolger, G., et al. (2003). An NS3 protease inhibitor with antiviral effects in humans infected with hepatitis C virus. Nature, 426, 186–189. CrossRefGoogle Scholar
  29. Lawitz, E., Rodriguez-Torres, M., Muir, A. J., Kieffer, T. L., McNair, L., et al. (2008). Antiviral effects and safety of telaprevir, peginterferon alfa-2a, and ribavirin for 28 days in hepatitis C patients. J. Hepatol., 49, 163–169. CrossRefGoogle Scholar
  30. Lin, K., Kwong, A. D., & Lin, C. (2004). Combination of a hepatitis C virus NS3-NS4A protease inhibitor and alpha interferon synergistically inhibits viral RNA replication and facilitates viral RNA clearance in replicon cells. Antimicrob. Agents Chemother., 48, 4784–4792. CrossRefGoogle Scholar
  31. Lin, C., Gates, C. A., Rao, B. G., Brennan, D. L., Fulghum, J. R., et al. (2005). In vitro studies of cross-resistance mutations against two hepatitis C virus serine protease inhibitors, VX-950 and BILN 2061. J. Biol. Chem., 280, 36784–36791. CrossRefGoogle Scholar
  32. Lin, K., Perni, R. B., Kwong, A. D., & Lin, C. (2006). VX-950, a novel hepatitis C virus (HCV) NS3-4A protease inhibitor, exhibits potent antiviral activities in HCV replicon cells. Antimicrob. Agents Chemother., 50, 1813–1822. CrossRefGoogle Scholar
  33. Lok, A. S., Gardiner, D. F., Lawitz, E., Martorell, C., Everson, G. T., et al. (2012). Preliminary study of two antiviral agents for hepatitis C genotype 1. N. Engl. J. Med., 366, 216–224. CrossRefGoogle Scholar
  34. Lu, L., Pilot-Matias, T. J., Stewart, K. D., Randolph, J. T., Pithawalla, R., et al. (2004). Mutations conferring resistance to a potent hepatitis C virus serine protease inhibitor in vitro. Antimicrob. Agents Chemother., 48, 2260–2266. CrossRefGoogle Scholar
  35. McCown, M. F., Rajyaguru, S., Le Pogam, S., Ali, S., Jiang, W. R., et al. (2008). The hepatitis C virus replicon presents a higher barrier to resistance to nucleoside analogs than to nonnucleoside polymerase or protease inhibitors. Antimicrob. Agents Chemother., 52, 1604–1612. CrossRefGoogle Scholar
  36. McHutchison, J. G., Gordon, S. C., Schiff, E. R., Shiffman, M. L., Lee, W. M., et al. (1998). Interferon alfa-2b alone or in combination with ribavirin as initial treatment for chronic hepatitis C. Hepatitis Interventional Therapy Group. N. Engl. J. Med., 339, 1485–1492. CrossRefGoogle Scholar
  37. McHutchison, J. G., Everson, G. T., Gordon, S. C., Jacobson, I. M., Sulkowski, M., et al. (2009). Telaprevir with peginterferon and ribavirin for chronic HCV genotype 1 infection. N. Engl. J. Med., 360, 1827–1838. CrossRefGoogle Scholar
  38. McPhee, F., Hernandez, D., Zhai, G., Friborg, J., Yu, F., et al. (2006). Pre-existence of substitutions conferring resistance to HCV NS3 protease inhibitors. In 1st international workshop on hepatitis C resistance and new compounds. Boston, MA, October 25–26, 2006. Google Scholar
  39. Meylan, E., Curran, J., Hofmann, K., Moradpour, D., Binder, M., et al. (2005). Cardif is an adaptor protein in the RIG-I antiviral pathway and is targeted by hepatitis C virus. Nature, 437, 1167–1172. CrossRefGoogle Scholar
  40. Michalopoulos, G. K., & DeFrances, M. C. (1997). Liver regeneration. Science, 276, 60–66. CrossRefGoogle Scholar
  41. Neumann, A. U., Lam, N. P., Dahari, H., Gretch, D. R., Wiley, T. E., et al. (1998). Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science, 282, 103–107. CrossRefGoogle Scholar
  42. Olsen, D. B., Davies, M. E., Handt, L., Koeplinger, K., Zhang, N. R., et al. (2011). Sustained viral response in a hepatitis C virus-infected chimpanzee via a combination of direct-acting antiviral agents. Antimicrob. Agents Chemother., 55, 937–939. CrossRefGoogle Scholar
  43. Pawlotsky, J. M. (2006). Hepatitis C virus population dynamics during infection. Curr. Top. Microbiol. Immunol., 299, 261–284. CrossRefGoogle Scholar
  44. Perni, R. B., Almquist, S. J., Byrn, R. A., Chandorkar, G., Chaturvedi, P. R., et al. (2006). Preclinical profile of VX-950, a potent, selective, and orally bioavailable inhibitor of hepatitis C virus NS3-4A serine protease. Antimicrob. Agents Chemother., 50, 899–909. CrossRefGoogle Scholar
  45. Pileri, P., Uematsu, Y., Campagnoli, S., Galli, G., Falugi, F., et al. (1998). Binding of hepatitis C virus to CD81. Science, 282, 938–941. CrossRefGoogle Scholar
  46. Ploss, A., Evans, M. J., Gaysinskaya, VA, Panis, M., You, H., et al. (2009). Human occludin is a hepatitis C virus entry factor required for infection of mouse cells. Nature, 457, 882–886. CrossRefGoogle Scholar
  47. Poordad, F., McCone, J. J., Bacon, B. R., Bruno, S., Manns, M. P., et al. (2011). Boceprevir for untreated chronic HCV genotype 1 infection. N. Engl. J. Med., 364, 1195–1206. CrossRefGoogle Scholar
  48. Powdrill, M. H., Tchesnokov, E. P., Kozak, R. A., Russell, R. S., Martin, R., et al. (2011). Contribution of a mutational bias in hepatitis C virus replication to the genetic barrier in the development of drug resistance. Proc. Natl. Acad. Sci. USA, 108, 20509–20513. CrossRefGoogle Scholar
  49. Powers, K. A., Dixit, N. M., Ribeiro, R. M., Golia, P., Talal, A. H., et al. (2003). Modeling viral and drug kinetics: Hepatitis C virus treatment with pegylated interferon alfa-2b. Semin. Liver Dis., 23 Suppl 1, 13–18. Google Scholar
  50. Reesink, H. W., Zeuzem, S., Weegink, C. J., Forestier, N., van Vliet, A., et al. (2006). Rapid decline of viral RNA in hepatitis C patients treated with VX-950: a phase Ib, placebo-controlled, randomized study. Gastroenterology, 131, 997–1002. CrossRefGoogle Scholar
  51. Reluga, T. C., Dahari, H., & Perelson, A. S. (2009). Analysis of hepatitis C virus infection models with hepatocyte homeostasis. SIAM J. Appl. Math., 69, 999–1023. MathSciNetCrossRefMATHGoogle Scholar
  52. Rong, L., Feng, Z., & Perelson, A. S. (2007). Emergence of HIV-1 drug resistance during antiretroviral treatment. Bull. Math. Biol., 69, 2027–2060. MathSciNetCrossRefMATHGoogle Scholar
  53. Rong, L., Dahari, H., Ribeiro, R. M., & Perelson, A. S. (2010). Rapid emergence of protease inhibitor resistance in hepatitis C virus. Sci. Transl. Med., 2, 30ra32. CrossRefGoogle Scholar
  54. Sanjuan, R., Nebot, M. R., Chirico, N., Mansky, L. M., & Belshaw, R. (2010). Viral mutation rates. J. Virol., 84, 9733–9748. CrossRefGoogle Scholar
  55. Sarrazin, C., Kieffer, T. L., Bartels, D., Hanzelka, B., Muh, U., et al. (2007). Dynamic hepatitis C virus genotypic and phenotypic changes in patients treated with the protease inhibitor telaprevir. Gastroenterology, 132, 1767–1777. CrossRefGoogle Scholar
  56. Sarrazin, C., Rouzier, R., Wagner, F., Forestier, N., Larrey, D., et al. (2007). SCH 503034, a novel hepatitis C virus protease inhibitor, plus pegylated interferon alpha-2b for genotype 1 nonresponders. Gastroenterology, 132, 1270–1278. CrossRefGoogle Scholar
  57. Scarselli, E., Ansuini, H., Cerino, R., Roccasecca, R. M., Acali, S., et al. (2002). The human scavenger receptor class B type I is a novel candidate receptor for the hepatitis C virus. EMBO J., 21, 5017–5025. CrossRefGoogle Scholar
  58. Shen, L., Peterson, S., Sedaghat, A. R., McMahon, M. A., Callender, M., et al. (2008). Dose-response curve slope sets class-specific limits on inhibitory potential of anti-HIV drugs. Nat. Med., 14, 762–766. CrossRefGoogle Scholar
  59. Sherman, K. E., Flamm, S. L., Afdhal, N. H., Nelson, D. R., Sulkowski, M. S., et al. (2011). Response-guided telaprevir combination treatment for hepatitis C virus infection. N. Engl. J. Med., 365, 1014–1024. CrossRefGoogle Scholar
  60. Soriano, V., Perelson, A. S., & Zoulim, F. (2008). Why are there different dynamics in the selection of drug resistance in HIV and hepatitis B and C viruses? J. Antimicrob. Chemother., 62, 1–4. CrossRefGoogle Scholar
  61. Tong, X., Chase, R., Skelton, A., Chen, T., Wright-Minogue, J., et al. (2006). Identification and analysis of fitness of resistance mutations against the HCV protease inhibitor SCH 503034. Antivir. Res., 70, 28–38. CrossRefGoogle Scholar
  62. Vanwolleghem, T., Meuleman, P., Libbrecht, L., Roskams, T., De Vos, R., et al. (2007). Ultra-rapid cardiotoxicity of the hepatitis C virus protease inhibitor BILN 2061 in the urokinase-type plasminogen activator mouse. Gastroenterology, 133, 1144–1155. CrossRefGoogle Scholar
  63. Wang, L., & Li, M. Y. (2006). Mathematical analysis of the global dynamics of a model for HIV infection of CD4+T cells. Math. Biosci., 200, 44–57. MathSciNetCrossRefMATHGoogle Scholar
  64. World Health Organization (2011) Hepatitis C. Fact sheet No. 164. Revised June 2011. http://www.who.int/mediacentre/factsheets/fs164/en/index.html.
  65. Wyles, D. L., Kaihara, K. A., Vaida, F., & Schooley, R. T. (2007). Synergy of small molecular inhibitors of hepatitis C virus replication directed at multiple viral targets. J. Virol., 81, 3005–3008. CrossRefGoogle Scholar
  66. Wyles, D. L., Kaihara, K. A., & Schooley, R. T. (2008). Synergy of a hepatitis C virus (HCV) NS4A antagonist in combination with HCV protease and polymerase inhibitors. Antimicrob. Agents Chemother., 52, 1862–1864. CrossRefGoogle Scholar
  67. Yeni, P. G., Hammer, S. M., Carpenter, C. C., Cooper, D. A., Fischl, M. A., et al. (2002). Antiretroviral treatment for adult HIV infection in 2002: updated recommendations of the international AIDS society-USA panel. JAMA, 288, 222–235. CrossRefGoogle Scholar
  68. Yi, M., Tong, X., Skelton, A., Chase, R., Chen, T., et al. (2006). Mutations conferring resistance to SCH6, a novel hepatitis C virus NS3/4A protease inhibitor. Reduced RNA replication fitness and partial rescue by second-site mutations. J. Biol. Chem., 281, 8205–8215. CrossRefGoogle Scholar
  69. Zhou, Y., Bartels, D. J., Hanzelka, B. L., Muh, U., Wei, Y., et al. (2008). Phenotypic characterization of resistant Val36 variants of hepatitis C virus NS3-4A serine protease. Antimicrob. Agents Chemother., 52, 110–120. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  • Libin Rong
    • 1
    • 2
  • Ruy M. Ribeiro
    • 2
  • Alan S. Perelson
    • 2
  1. 1.Department of Mathematics and Statistics and Center for Biomedical ResearchOakland UniversityRochesterUSA
  2. 2.Theoretical Biology and BiophysicsLos Alamos National LaboratoryLos AlamosUSA

Personalised recommendations