Abstract
The innate immune response is recognized as a key driver in controlling an influenza virus infection in a host. However, the mechanistic action of such innate response is not fully understood. Infection experiments on ex vivo explants from swine trachea represent an efficient alternative to animal experiments, as the explants conserved key characteristics of an organ from an animal. In the present work we compare three cellular automata models of influenza virus dynamics. The models are fitted to free virus and infected cells data from ex vivo swine trachea experiments. Our findings suggest that the presence of an immune response is necessary to explain the observed dynamics in ex vivo organ culture. Moreover, such immune response should include a refractory state for epithelial cells, and not just a reduced infection rate. Our results may shed light on how the immune system responds to an infection event.
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Data availability
The codes (in Matlab) and data employed for the current study are available at https://github.com/olmosliceaga/influenza_virus_spread.
References
Aponte-Serrano JO, Weaver JJA, Sego TJ et al (2021) Multicellular spatial model of RNA virus replication and interferon responses reveals factors controlling plaque growth dynamics. PLoS Comput Biol 17(10):e1008874. https://doi.org/10.1371/journal.pcbi.1008874
Baccam P, Beauchemin C, Macken CA et al (2006) Kinetics of influenza A virus infection in humans. J Virol 80:7590–7599. https://doi.org/10.1128/JVI.01623-05
Barnard D (2009) Animal models for the study of influenza pathogenesis and therapy. Antivir Res 82:A110–A122. https://doi.org/10.1016/j.antiviral.2008.12.014
Beauchemin CA, Handel A (2011) A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead. BMC Public Health 11(Suppl 1:S7):1–15. https://doi.org/10.1186/1471-2458-11-S1-S7
Beauchemin C, Samuel J, Tuszynski J (2005) A simple cellular automaton model for influenza A viral infections. J Theor Biol 232:223–234. https://doi.org/10.1016/j.jtbi.2004.08.001
Beauchemin C, Forrest S, Koster F (2006) Modeling influenza viral dynamics in tissue. In: Bersini H, Carneiro J (eds) International conference on artificial immune systems: artificial immune systems. Springer, Berlin p 4163 (23–36). https://doi.org/10.1007/11823940_3
Boianelli A, Nguyen VK, Ebensen T et al (2015) Modeling influenza virus infection: a roadmap for influenza research. Viruses 7:5274–5304. https://doi.org/10.3390/v7102875
Borkenhagen LK, Salman MD, Ma MJ et al (2019) Animal influenza virus infections in humans: a commentary. Int J Infect Dis 88:113–119. https://doi.org/10.1016/j.ijid.2019.08.002
Cao P, McCaw JM (2017) The mechanisms for within-host influenza virus control affect model-based assessment and prediction of antiviral treatment. Viruses 9(197):1–20. https://doi.org/10.3390/v9080197
Carrat F, Vergu E, Ferguson NM et al (2008) Time lines of infection and disease in human influenza: a review of volunteer challenge studies. Am J Epidemiol 167(7):775–785. https://doi.org/10.3390/mps1020012
de Vries RD, Rennick LJ, Duprex WP et al (2018) Paramyxovirus infections in ex vivo lung slice cultures of different host species. Methods Protoc 1(12):1–9. https://doi.org/10.3390/mps1020012
Delgado-Ortega M, Melo S, Punyadarsaniya D et al (2014) Innate immune response to a H3N2 subtype swine influenza virus in newborn porcine trachea cells, alveolar macrophages, and precision-cut lung slices. Vet Res 45:42. https://doi.org/10.1186/1297-9716-45-42
Gregg RW, Shabnam F, Shoemaker JE (2021) Agent-based modeling reveals benefits of heterogeneous and stochastic cell populations during cGAS-mediated IFN\(\beta \) production. Bioinformatics 37(10):1428–1434. https://doi.org/10.1093/bioinformatics/btaa969
Grimm V, Revilla E, Berger U et al (2005) Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310(5750):987–991. https://doi.org/10.1126/science.1116681
Handel A, Akin V, Pilyugin S et al (2014) How sticky should a virus be? The impact of virus binding and release on transmission fitness using influenza as an example. J R Soc Interface 11(20131):083. https://doi.org/10.1098/rsif.2013.1083
Handel A, Liao L, Beauchemin C (2018) Progress and trends in mathematical modelling of influenza A virus infections. Curr Opin Syst Biol 12:30–36. https://doi.org/10.1016/j.coisb.2018.08.009
Heldt FS, Frensing T, Pflugmacher A et al (2013) Multiscale modeling of influenza A virus infection supports the development of direct-acting antivirals. PLOS Comp Biol 9(11):e1003372. https://doi.org/10.1371/journal.pcbi.1003372
Hocke AC, Suttorp N, Hippenstiel S (2017) Human lung ex vivo infection models. Cell Tissue Res 367:511–524. https://doi.org/10.1007/s00441-016-2546-z
Holder BP, Simon P, Liao LL et al (2011) Assessing the in vitro fitness of an oseltamivir-resistant seasonal A/H1N1 influenza strain using a mathematical model. PLoS ONE 6(3):e14767. https://doi.org/10.1371/journal.pone.0014767
Jhutty SS, Boehme JD, Jeron A et al (2022) Predicting influenza A virus infection in the lung from hematological data with machine learning. mSystems. https://doi.org/10.1128/msystems.00459-22
Jones J, Baranovich T, Zaraket H et al (2013) Human H7N9 influenza A viruses replicate in swine respiratory tissue explants. J Virol 87(22):12496–12498. https://doi.org/10.1128/JVI.02499-13
Kang Y, Shen X, Yuan R et al (2018) Pathogenicity and transmissibility of three avian influenza A (H5N6) viruses isolated from wild birds. J Infect 76(3):286–294. https://doi.org/10.1016/j.jinf.2017.12.012
Lange E, Kalthoff D, Blohm U et al (2009) Pathogenesis and transmission of the novel swine-origin influenza virus A/H1N1 after experimental infection of pigs. J Gen Virol 90:2119–2123. https://doi.org/10.1099/vir.0.014480-0
Lavigne GM, Russell H, Sherry B et al (2021) Autocrine and paracrine interferon signalling as ‘ring vaccination’ and ‘contact tracing’ strategies to suppress virus infection in a host. Proc R Soc B 288:1–8. https://doi.org/10.1098/rspb.2020.3002
Leviyang S, Griva I (2018) Investigating functional roles for positive feedback and cellular heterogeneity in the type I interferon response to viral infection. Viruses 10(517):1–29. https://doi.org/10.3390/v10100517
Lin D, Sun S, Du L et al (2012) Natural and experimental infection of dogs with pandemic H1N1/2009 influenza virus. J Gen Virol 93:119–123. https://doi.org/10.1099/vir.0.037358-0
Löndt B, Brookes S, Nash B et al (2013) The infectivity of pandemic 2009 H1N1 and avian influenza viruses for pigs: an assessment by ex vivo respiratory tract organ culture. Influenza Other Respir Viruses 7(3):393–402. https://doi.org/10.1111/j.1750-2659.2012.00397.x
Mitchell H, Levin D, Forrest S et al (2011) Higher level of replication efficiency of 2009 (H1N1) pandemic influenza virus than those of seasonal and avian strains: Kinetics from epithelial cell culture and computational modeling. J Virol 85(2):1125–1135. https://doi.org/10.1128/JVI.01722-10
Mochan E, Ackerman EE, Shoemaker JE (2018) A systems and treatment perspective of models of influenza virus-induced host responses. Processes. https://doi.org/10.3390/pr6090138
Moore JR, Ahmed H, Manicassamy B et al (2020) Varying inoculum dose to assess the roles of the immune response and target cell depletion by the pathogen in control of acute viral infections. Bull Math Biol 82(3):1–35. https://doi.org/10.1007/s11538-020-00711-4
Nunes SF (2011) Influenza A infection dynamics in an ex vivo organ culture of pig trachea. Ph.D. Thesis, University of Cambridge, UK. https://doi.org/10.13140/RG.2.2.16357.58083
Nunes SF, Murcia PR, Tiley LS et al (2009) An ex vivo swine tracheal organ culture for the study of influenza infection. Influenza Other Respir Viruses 4(1):7–15. https://doi.org/10.1111/j.1750-2659.2009.00119.x
Ólafsson S (2006) Metaheuristics. In: Henderson SG, Nelson BL (eds) Handbook in operations research and management science: simulation. Elsevier, Amsterdam, pp 633–654
Parrish CR, Murcia PR, Holmes EC (2015) Influenza virus reservoirs and intermediate hosts: dogs, horses, and new possibilities for influenza virus exposure of humans. J Virol 89(6):2990–2994. https://doi.org/10.1128/JVI.03146-14
Pawelek KA, Huynh GT, Quinlivan M et al (2012) Modeling within-host dynamics of influenza virus infection including immune responses. PLoS Comp Biol 8(6):e1002588. https://doi.org/10.1371/journal.pcbi.1002588
Petrie SM, Butler J, Barr IG et al (2015) Quantifying relative within-host replication fitness in influenza virus competition experiments. J Theor Biol 382:259–271. https://doi.org/10.1016/j.jtbi.2015.07.003
Rajao DS, Vincent AL (2015) Swine as a model for influenza A virus infection and immunity. ILAR J 56(1):44–52. https://doi.org/10.1093/ilar/ilv002
Randall RE, Goodbourn S (2008) Interferons and viruses: an interplay between induction, signalling, antiviral responses and virus countermeasures. J Gen Virol 89:1–47. https://doi.org/10.1099/vir.0.83391-0
Saenz RA, Quinlivan M, Elton D et al (2010) Dynamics of influenza virus infection and pathology. J Virol 84(8):3974–3983. https://doi.org/10.1128/JVI.02078-09
Starbæk S, Andersen M, Brogaard L et al (2022) Innate antiviral responses in porcine nasal mucosal explants inoculated with influenza A virus are comparable with responses in respiratory tissues after viral infection. Immunobiology 227(3):152192. https://doi.org/10.1016/j.imbio.2022.152192
Sweet C, Smith H (1980) Pathogenicity of influenza virus. Microbiol Rev 44(2):303–330. https://doi.org/10.1128/mr.44.2.303-330.1980
Tamura S, Kurata T (2004) Defense mechanisms against influenza virus infection in the respiratory tract mucosa. Jpn J Infect Dis 57(6):236–47
Van Eyndhoven LC, Singh A, Tel J (2021) Decoding the dynamics of multilayered stochastic antiviral IFN-I responses. Trends Immunol 42(9):1–16. https://doi.org/10.1016/j.it.2021.07.004
World Health Organization (2017) Up to 650 000 people die of respiratory diseases linked to seasonal flu each year. https://www.who.int/news/item/13-12-2017-up-to-650-000-people-die-of-respiratory-diseases-linked-to-sea/sonal-flu-each-year. Accessed 4 Nov 2021
Yan A, Zhou J, Beauchemin C et al (2020) Quantifying mechanistic traits of influenza viral dynamics using in vitro data. Epidemics 33(100):406. https://doi.org/10.1016/j.epidem.2020.100406
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The authors would like to acknowledge ACARUS at the University of Sonora, for lending their facilities for numerical computations.
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Appendix A: Pseudocodes for Simulations
Appendix A: Pseudocodes for Simulations
In this section we present the pseudocodes for the three models used to describe the influenza virus infection in an ex vivo organ culture using a cellular automata (CA) setting (Algorithms 1-3). Each iteration of our CA code simulation accounts for 2 min on the actual experiment. The experiments are registered for four days which corresponds to 2880 iterations.
To initiate the simulations we set all cells into their healthy stage. For each simulation run, all the parameters values are given (Table 2). An initial amount of virus is uniformly distributed over the whole domain. At each time step, virus and interferon (if it applies) diffuse to neighboring cells and cells change status (if appropriate). Table 6 shows the length of each of the stages, both in hours and in number of iterations. Table 7 shows the variables used in each of the models.
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Olmos Liceaga, D., Nunes, S.F. & Saenz, R.A. Ex Vivo Experiments Shed Light on the Innate Immune Response from Influenza Virus. Bull Math Biol 85, 115 (2023). https://doi.org/10.1007/s11538-023-01217-5
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DOI: https://doi.org/10.1007/s11538-023-01217-5