Journal of Biological Physics

, Volume 39, Issue 2, pp 327–342 | Cite as

Complex dynamics of defective interfering baculoviruses during serial passage in insect cells

  • Mark P. ZwartEmail author
  • Gorben P. Pijlman
  • Josep Sardanyés
  • Jorge Duarte
  • Cristina Januário
  • Santiago F. Elena
Original Paper


Defective interfering (DI) viruses are thought to cause oscillations in virus levels, known as the ‘Von Magnus effect’. Interference by DI viruses has been proposed to underlie these dynamics, although experimental tests of this idea have not been forthcoming. For the baculoviruses, insect viruses commonly used for the expression of heterologous proteins in insect cells, the molecular mechanisms underlying DI generation have been investigated. However, the dynamics of baculovirus populations harboring DIs have not been studied in detail. In order to address this issue, we used quantitative real-time PCR to determine the levels of helper and DI viruses during 50 serial passages of Autographa californica multiple nucleopolyhedrovirus (AcMNPV) in Sf21 cells. Unexpectedly, the helper and DI viruses changed levels largely in phase, and oscillations were highly irregular, suggesting the presence of chaos. We therefore developed a simple mathematical model of baculovirus-DI dynamics. This theoretical model reproduced patterns qualitatively similar to the experimental data. Although we cannot exclude that experimental variation (noise) plays an important role in generating the observed patterns, the presence of chaos in the model dynamics was confirmed with the computation of the maximal Lyapunov exponent, and a Ruelle-Takens-Newhouse route to chaos was identified at decreasing production of DI viruses, using mutation as a control parameter. Our results contribute to a better understanding of the dynamics of DI baculoviruses, and suggest that changes in virus levels over passages may exhibit chaos.


Baculovirus Bifurcations Chaos Defective interfering virus Experimental evolution 



The authors thank Javier Carrera, Just Vlak and Lia Hemerik for helpful discussion. MPZ was supported by a Rubicon Grant from the Netherlands Organization for Scientific Research (NWO, and a ‘Juan de la Cierva’ postdoctoral contract (JCI-2011-10379) from the Spanish ‘Secretaría de Estado de Investigación, Desarrollo e Innovación’. JS was supported by the Botín Foundation. SFE was supported by grant BFU2012-30805, also from the Spanish ‘Secretaría de Estado de Investigación, Desarrollo e Innovación’.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Mark P. Zwart
    • 1
    • 2
    Email author
  • Gorben P. Pijlman
    • 3
  • Josep Sardanyés
    • 4
    • 5
  • Jorge Duarte
    • 5
    • 7
  • Cristina Januário
    • 6
  • Santiago F. Elena
    • 1
    • 8
  1. 1.Instituto de Biología Molecular y Celular de PlantasConsejo Superior de Investigaciones Científicas-UPVValènciaSpain
  2. 2.Quantitative Veterinary Epidemiology GroupWageningen UniversityWageningenThe Netherlands
  3. 3.Laboratory of VirologyWageningen UniversityWageningenThe Netherlands
  4. 4.ICREA-Complex Systems LaboratoryUniversitat Pompeu FabraBarcelonaSpain
  5. 5.Institut de Biologia Evolutiva (CSIC-Universitat Pompeu Fabra)BarcelonaSpain
  6. 6.Engineering Superior Institute of LisbonLisboaPortugal
  7. 7.Centro de Análise Matemática, Geometria e Sistemas DinâmicosInstituto Superior TécnicoLisboaPortugal
  8. 8.The Santa Fe InstituteSanta FeUSA

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