Mathematical models of in vitro viral kinetics help us understand and quantify the main determinants underlying the virus-host cell interactions. We aimed to provide a numerical characterization of the Zika virus (ZIKV) in vitro infection kinetics, an arthropod-borne emerging virus that has gained public recognition due to its association with microcephaly in newborns. The mathematical model of in vitro viral infection typically assumes that degradation of extracellular infectious virus proceeds in an exponential manner, that is, each viral particle has the same probability of losing infectivity at any given time. We incubated ZIKV stock in the cell culture media and sampled with high frequency for quantification over the course of 96 h. The data showed a delay in the virus degradation in the first 24 h followed by a decline, which could not be captured by the model with exponentially distributed decay time of infectious virus. Thus, we proposed a model, in which inactivation of infectious ZIKV is gamma distributed and fit the model to the temporal measurements of infectious virus remaining in the media. The model was able to reproduce the data well and yielded the decay time of infectious ZIKV to be 40 h. We studied the in vitro ZIKV infection kinetics by conducting cell infection at two distinct multiplicity of infection and measuring viral loads over time. We fit the mathematical model of in vitro viral infection with gamma distributed degradation time of infectious virus to the viral growth data and identified the timespans and rates involved within the ZIKV-host cell interplay. Our mathematical analysis combined with the data provides a well-described example of non-exponential viral decay dynamics and presents numerical characterization of in vitro infection with ZIKV.

Department of Biophysics and Physical Chemistry Faculty of Pharmacy Charles University Heyrovského 1203 500 05 Hradec Králové Czech Republic

Viral Populations and Pathogenesis Unit Department of Virology Institut Pasteur CNRS UMR 3569 F 75015 Paris France

Zobrazit více v PubMed

Dick G.W., Kitchen S.F., Haddow A.J. Zika virus (I). Isolations and serological specificity. Trans. R. Soc. Trop. Med. Hyg. 1952;46:509–520. doi: 10.1016/0035-9203(52)90042-4. PubMed DOI

Lanciotti R.S., Kosoy O.L., Laven J.J., Velez J.O., Lambert A.J., Johnson A.J., Stanfield S.M., Duffy M.R. Genetic and serologic properties of Zika virus associated with an epidemic, Yap State, Micronesia, 2007. Emerg. Infect. Dis. 2008;14:1232. doi: 10.3201/eid1408.080287. PubMed DOI PMC

Oehler E., Watrin L., Larre P., Leparc-Goffart I., Lastere S., Valour F., Baudouin L., Mallet H.P., Musso D., Ghawche F. Zika virus infection complicated by Guillain-Barre syndrome—Case report, French Polynesia, December 2013. Eurosurveillance. 2014;19:20720. doi: 10.2807/1560-7917.ES2014.19.9.20720. PubMed DOI

Dyer O. Zika virus spreads across Americas as concerns mount over birth defects. BMJ. 2015;351:h6983. doi: 10.1136/bmj.h6983. PubMed DOI

Parra B., Lizarazo J., Jiménez-Arango J.A., Zea-Vera A.F., González-Manrique G., Vargas J., Angarita J.A., Zuñiga G., Lopez-Gonzalez R., Beltran C.L., et al. Guillain–Barré syndrome associated with Zika virus infection in Colombia. N. Engl. J. Med. 2016;375:1513–1523. doi: 10.1056/NEJMoa1605564. PubMed DOI

Mlakar J., Korva M., Tul N., Popović M., Poljšak-Prijatelj M., Mraz J., Kolenc M., Resman Rus K., Vesnaver Vipotnik T., Fabjan Vodušek V., et al. Zika virus associated with microcephaly. N. Engl. J. Med. 2016;374:951–958. doi: 10.1056/NEJMoa1600651. PubMed DOI

European Centre for Disease Prevention and Control . Rapid Risk Assessment: Zika Virus Epidemic in the Americas: Potential Association with Microcephaly and Guillain-Barré Syndrome. European Centre for Disease Prevention and Control; Solna, Sweden: 2015.

Ioos S., Malletm H.P., Goffartm I.L., Gauthier V., Cardoso T., Herida M. Current Zika virus epidemiology and recent epidemics. Med. Maladies Infect. 2014;44:302–307. doi: 10.1016/j.medmal.2014.04.008. PubMed DOI

Hiatt C.W. Kinetics of the inactivation of viruses. Bacteriol. Rev. 1964;2:150–163. doi: 10.1128/MMBR.28.2.150-163.1964. PubMed DOI PMC

Beauchemin C.A.A., Kim Y.I., Yu Q., Ciaramella G., DeVincenzo J.P. Uncovering critical properties of the human respiratory syncytial virus by combining in vitro assays and in silico analyses. PLoS ONE. 2019;14:e0214708. doi: 10.1371/journal.pone.0214708. PubMed DOI PMC

Schmid B., Rinas M., Ruggieri A., Acosta E.G., Bartenschlager M., Reuter A., Fischl W., Harder N., Bergeest J.P., Flossdorf M., et al. Live cell analysis and mathematical modeling identify determinants of attenuation of dengue virus 2’-O-methylation mutant. PLoS Pathog. 2015;11 doi: 10.1371/journal.ppat.1005345. PubMed DOI PMC

Kostyuchenko V.A., Lim E.X., Zhang S., Fibriansah G., Ng T.S., Ooi J.S., Shi J., Lok S.M. Structure of the thermally stable Zika virus. Nature. 2016;533:425–428. doi: 10.1038/nature17994. PubMed DOI

Goo L., Dowd K.A., Smith A.R., Pelc R.S., DeMaso C.R., Pierson T.C. Zika virus is not uniquely stable at physiological temperatures compared to other flaviviruses. mBio. 2016;7:e01396-16. doi: 10.1128/mBio.01396-16. PubMed DOI PMC

Ansarah-Sobrinho C., Nelson S., Jost C.A., Whitehead S.S., Pierson T.C. Temperature-dependent production of pseudoinfectious dengue reporter virus particles by complementation. Virology. 2008;381:67–74. doi: 10.1016/j.virol.2008.08.021. PubMed DOI PMC

Dowd K.A., Jost C.A., Durbin A.P., Whitehead S.S., Pierson T.C. A dynamic landscape for antibody binding modulates antibody-mediated neutralization of West Nile virus. PLoS Pathog. 2011;7 doi: 10.1371/journal.ppat.1002111. PubMed DOI PMC

Manning J.S., Collins J.K. Effects of cell culture and laboratory conditions on type 2 dengue virus infectivity. J. Clin. Microbiol. 1979;10:235–239. doi: 10.1128/JCM.10.2.235-239.1979. PubMed DOI PMC

Wu H., Zhu H., Miao H., Perelson A.S. Parameter identifiability and estimation of HIV/AIDS dynamic models. Bull. Math. Biol. 2008;70:785–799. doi: 10.1007/s11538-007-9279-9. PubMed DOI

Verotta D. Models and estimation methods for clinical HIV-1 data. J. Comput. Appl. Math. 2005;184:275–300. doi: 10.1016/j.cam.2004.08.017. DOI

Miao H., Dykes C., Demeter L.M., Cavenaugh J., Park S.Y., Perelson A.S., Wu H. Modeling and estimation of kinetic parameters and replicative fitness of HIV-1 from flow-cytometry-based growth competition experiments. Bull. Math. Biol. 2008;70:1749–1771. doi: 10.1007/s11538-008-9323-4. PubMed DOI PMC

Kakizoe Y., Nakaoka S., Beauchemin C.A., Morita S., Mori H., Igarashi T., Aihara K., Miura T., Iwami S. A method to determine the duration of the eclipse phase for in vitro infection with a highly pathogenic SHIV strain. Sci. Rep. 2015;5:10371. doi: 10.1038/srep10371. PubMed DOI PMC

Beauchemin C.A., Miura T., Iwami S. Duration of SHIV production by infected cells is not exponentially distributed: Implications for estimates of infection parameters and antiviral efficacy. Sci. Rep. 2017;7:42765. doi: 10.1038/srep42765. PubMed DOI PMC

Perelson A.S., Ribeiro R.M. Modeling the within-host dynamics of HIV infection. BMC Biol. 2013;11:96. doi: 10.1186/1741-7007-11-96. PubMed DOI PMC

Chatterjee A., Guedj J., Perelson A.S. Mathematical modeling of HCV infection: What can it teach us in the era of direct antiviral agents? Antivir. Ther. 2012;17:1171. doi: 10.3851/IMP2428. PubMed DOI PMC

Aston P. A new model for the dynamics of hepatitis C infection: Derivation, analysis and implications. Viruses. 2018;10:195. doi: 10.3390/v10040195. PubMed DOI PMC

Rihan F.A., Sheek-Hussein M., Tridane A., Yafia R. Dynamics of hepatitis C virus infection: Mathematical modeling and parameter estimation. Math. Model. Nat. Phenom. 2017;12:33–47. doi: 10.1051/mmnp/201712503. DOI

Arthur J.G., Tran H.T., Aston P. Feasibility of parameter estimation in hepatitis C viral dynamics models. J. Inverse Ill-Posed Probl. 2017;25:69–80. doi: 10.1515/jiip-2014-0048. DOI

Perelson A.S., Ribeiro R.M. Estimating drug efficacy and viral dynamic parameters: HIV and HCV. Stat. Med. 2008;27:4647–4657. doi: 10.1002/sim.3116. PubMed DOI

Krakauer D.C., Komarova N.L. Levels of selection in positive-strand virus dynamics. J. Evol. Biol. 2003;16:64–73. doi: 10.1046/j.1420-9101.2003.00481.x. PubMed DOI

Regoes R.R., Crotty S., Antia R., Tanaka M.M. Optimal replication of poliovirus within cells. Am. Nat. 2005;165:364–373. doi: 10.1086/428295. PubMed DOI

Schulte M.B., Draghi J.A., Plotkin J.B., Andino R. Experimentally guided models reveal replication principles that shape the mutation distribution of RNA viruses. Elife. 2015;4:e03753. doi: 10.7554/eLife.03753. PubMed DOI PMC

Boianelli A., Nguyen V., Ebensen T., Schulze K., Wilk E., Sharma N., Stegemann-Koniszewski S., Bruder D., Toapanta F., Guzmán C., et al. Modeling influenza virus infection: A roadmap for influenza research. Viruses. 2015;7:5274–5304. doi: 10.3390/v7102875. PubMed DOI PMC

Pinilla L.T., Holder B.P., Abed Y., Boivin G., Beauchemin C.A. The H275Y neuraminidase mutation of the pandemic A/H1N1 influenza virus lengthens the eclipse phase and reduces viral output of infected cells, potentially compromising fitness in ferrets. J. Virol. 2012;86:10651–10660. doi: 10.1128/JVI.07244-11. PubMed DOI PMC

Holder B.P., Beauchemin C.A. Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture. BMC Public Health. 2011;11:S10. doi: 10.1186/1471-2458-11-S1-S10. PubMed DOI PMC

Holder B.P., Liao L.E., Simon P., Boivin G., Beauchemin C.A. Design considerations in building in silico equivalents of common experimental influenza virus assays. Autoimmunity. 2011;44:282–293. doi: 10.3109/08916934.2011.523267. PubMed DOI

Simon P.F., de La Vega M.A., Paradis É., Mendoza E., Coombs K.M., Kobasa D., Beauchemin C.A. Avian influenza viruses that cause highly virulent infections in humans exhibit distinct replicative properties in contrast to human H1N1 viruses. Sci. Rep. 2016;6:24154. doi: 10.1038/srep24154. PubMed DOI PMC

Paradis E.G., Pinilla L.T., Holder B.P., Abed Y., Boivin G., Beauchemin C.A. Impact of the H275Y and I223V mutations in the neuraminidase of the 2009 pandemic influenza virus in vitro and evaluating experimental reproducibility. PLoS ONE. 2015;10:e0126115. doi: 10.1371/journal.pone.0126115. PubMed DOI PMC

Iwami S., Holder B.P., Beauchemin C.A.A., Morita S., Tada T., Sato K., Igarashi T., Miura T. Quantification system for the viral dynamics of a highly pathogenic simian/human immunodeficiency virus based on an in vitro experiment and a mathematical model. Retrovirology. 2012;9:18. doi: 10.1186/1742-4690-9-18. PubMed DOI PMC

Banerjee S., Guedj J., Ribeiro R.M., Moses M., Perelson A.S. Estimating biologically relevant parameters under uncertainty for experimental within-host murine West Nile virus infection. J. R. Soc. Interface. 2016;13:20160130. doi: 10.1098/rsif.2016.0130. PubMed DOI PMC

Nguyen V.K., Binder S.C., Boianelli A., Meyer-Hermann M., Hernandez-Vargas E.A. Ebola virus infection modeling and identifiability problems. Front. Microbiol. 2015;6:257. doi: 10.3389/fmicb.2015.00257. PubMed DOI PMC

Nguyen V.K., Hernandez-Vargas E.A. Windows of opportunity for Ebola virus infection treatment and vaccination. Sci. Rep. 2017;7:8975. doi: 10.1038/s41598-017-08884-0. PubMed DOI PMC

Desmyter J., Melnick J.L., Rawls W.E. Defectiveness of interferon production and of rubella virus interference in a line of African green monkey kidney cells (Vero) J. Virol. 1968;2:955–961. doi: 10.1128/JVI.2.10.955-961.1968. PubMed DOI PMC

Osada N., Kohara A., Yamaji T., Hirayama N., Kasai F., Sekizuka T., Kuroda M., Hanada K. The genome landscape of the African green monkey kidney-derived Vero cell line. DNA Res. 2014;21:673–683. doi: 10.1093/dnares/dsu029. PubMed DOI PMC

Pastorino B., Bessaud M., Grandadam M., Murri S., Tolou H.J., Peyrefitte C.N. Development of a TaqMan® RT-PCR assay without RNA extraction step for the detection and quantification of African Chikungunya viruses. J. Virol. Methods. 2005;124:65–71. doi: 10.1016/j.jviromet.2004.11.002. PubMed DOI

Kirkwood T.B., Bangham C.R. Cycles, chaos, and evolution in virus cultures: A model of defective interfering particles. Proc. Natl. Acad. Sci. USA. 1994;91:8685–8689. doi: 10.1073/pnas.91.18.8685. PubMed DOI PMC

Liao L.E., Iwami S., Beauchemin C.A.A. (In)validating experimentally derived knowledge about influenza A defective interfering particles. J. R. Soc. Interface. 2016;13:20160412. doi: 10.1098/rsif.2016.0412. PubMed DOI PMC

Smith J.M. Mathematical Ideas in Biology. Volume 550 Cambridge University Press; Cambridge, UK: 1968.

Macdonald R.D., Yamamoto T., Fedorak P. Statistical prediction of the number of cells surviving infection by an autointerfering virus using the Poisson distribution. J. Theor. Biol. 1977;68:355–363. doi: 10.1016/0022-5193(77)90065-0. PubMed DOI

Foreman-Mackey D., Hogg D.W., Lang D., Goodman J. emcee: The MCMC hammer. Publ. Astron. Soc. Pac. 2013;125:306–312. doi: 10.1086/670067. DOI

Goodman J., Weare J. Ensemble samplers with affine invariance. Commun. Appl. Math. Comput. Sci. 2010;5:65–80. doi: 10.2140/camcos.2010.5.65. DOI

Lloyd A.L. The dependence of viral parameter estimates on the assumed viral life cycle: Limitations of studies of viral load data. Proc. R. Soc. B. 2001;268:847–854. doi: 10.1098/rspb.2000.1572. PubMed DOI PMC

Mittler J.E., Sulzer B., Neumann A.U., Perelson A.S. Influence of delayed viral production on viral dynamics in HIV-1 infected patients. Math. Biosci. 1998;152:143–163. doi: 10.1016/S0025-5564(98)10027-5. PubMed DOI

Hamel R., Dejarnac O., Wichit S., Ekchariyawat P., Neyret A., Luplertlop N., Perera-Lecoin M., Surasombatpattana P., Talignani L., Thomas F., et al. Biology of Zika virus infection in human skin cells. J. Virol. 2015;89:8880–8896. doi: 10.1128/JVI.00354-15. PubMed DOI PMC

Turpin J., Frumence E., Desprès P., Viranaicken W., Krejbich-Trotot P. The Zika virus delays cell death through the anti-apoptotic Bcl-2 family proteins. Cells. 2019;8:1338. doi: 10.3390/cells8111338. PubMed DOI PMC

Dixit N.M., Perelson A.S. HIV dynamics with multiple infections of target cells. Proc. Natl. Acad. Sci. USA. 2005;102:8198–8203. doi: 10.1073/pnas.0407498102. PubMed DOI PMC

Cummings K.W., Levy D.N., Wodarz D. Increased burst size in multiply infected cells can alter basic virus dynamics. Biol. Direct. 2012;7:16. doi: 10.1186/1745-6150-7-16. PubMed DOI PMC

Heldt F.S., Frensing T., Pflugmacher A., Gröpler R., Peschel B., Reichl U. Multiscale modeling of influenza A virus infection supports the development of direct-acting antivirals. PLoS Comput. Biol. 2013;9:e1003372. doi: 10.1371/journal.pcbi.1003372. PubMed DOI PMC

Moser L.A., Boylan B.T., Moreira F.R., Myers L.J., Svenson E.L., Fedorova N.B., Pickett B.E., Bernard K.A. Growth and adaptation of Zika virus in mammalian and mosquito cells. PLoS Negl. Trop. Dis. 2018;12:e0006880. doi: 10.1371/journal.pntd.0006880. PubMed DOI PMC

Willard K.A., Demakovsky L., Tesla B., Goodfellow F.T., Stice S.L., Murdock C.C., Brindley M.A. Zika virus exhibits lineage-specific phenotypes in cell culture, in Aedes aegypti mosquitoes, and in an embryo model. Viruses. 2017;9:383. doi: 10.3390/v9120383. PubMed DOI PMC

Smith D.R., Sprague T.R., Hollidge B.S., Valdez S.M., Padilla S.L., Bellanca S.A., Golden J.W., Coyne S.R., Kulesh D.A., Miller L.J., et al. African and Asian Zika virus isolates display phenotypic differences both in vitro and in vivo. Am. J. Trop. Med. Hyg. 2018;98:432–444. doi: 10.4269/ajtmh.17-0685. PubMed DOI PMC

Mathematical modelling of SARS-CoV-2 infection of human and animal host cells reveals differences in the infection rates and delays in viral particle production by infected cells