no. 3
Infection spreading in cell culture as a reaction-diffusion wave
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 791-814

Infection spreading in cell culture occurs due to virus replication in infected cells and its random motion in the extracellular space. Multiplicity of infection experiments in cell cultures are conventionally used for the characterization of viral infection by the number of viral plaques and the rate of their growth. We describe this process with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells, virus, and interferon. Time delay corresponds to the duration of viral replication inside infected cells. We show that infection propagates in cell culture as a reaction-diffusion wave, we determine the wave speed and prove its existence. Next, we carry out numerical simulations and identify three stages of infection progression: infection decay during time delay due to virus replication, explosive growth of viral load when infected cells begin to reproduce it, and finally, wave-like infection progression in cell culture characterized by a constant or slowly growing total viral load. The modelling results are in agreement with the experimental data for the coronavirus infection in a culture of epithelial cells and for some other experiments. The presence of interferon produced by infected cells decreases the viral load but does not change the speed of infection progression in cell culture. In the 2D modelling, the total viral load grows faster than in the 1D case due to the increase of plaque perimeter.

DOI : 10.1051/m2an/2022019
Classification : 35K52, 92C30
Keywords: Viral infection, cell culture, reaction-diffusion equations, time delay 
@article{M2AN_2022__56_3_791_0,
     author = {Ait Mahiout, Latifa and Bessonov, Nikolai and Kazmierczak, Bogdan and Sadaka, Georges and Volpert, Vitaly},
     title = {Infection spreading in cell culture as a reaction-diffusion wave},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {791--814},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {3},
     doi = {10.1051/m2an/2022019},
     mrnumber = {4411480},
     zbl = {1492.35373},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2022019/}
}
TY  - JOUR
AU  - Ait Mahiout, Latifa
AU  - Bessonov, Nikolai
AU  - Kazmierczak, Bogdan
AU  - Sadaka, Georges
AU  - Volpert, Vitaly
TI  - Infection spreading in cell culture as a reaction-diffusion wave
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2022
SP  - 791
EP  - 814
VL  - 56
IS  - 3
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/m2an/2022019/
DO  - 10.1051/m2an/2022019
LA  - en
ID  - M2AN_2022__56_3_791_0
ER  - 
%0 Journal Article
%A Ait Mahiout, Latifa
%A Bessonov, Nikolai
%A Kazmierczak, Bogdan
%A Sadaka, Georges
%A Volpert, Vitaly
%T Infection spreading in cell culture as a reaction-diffusion wave
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2022
%P 791-814
%V 56
%N 3
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/m2an/2022019/
%R 10.1051/m2an/2022019
%G en
%F M2AN_2022__56_3_791_0
Ait Mahiout, Latifa; Bessonov, Nikolai; Kazmierczak, Bogdan; Sadaka, Georges; Volpert, Vitaly. Infection spreading in cell culture as a reaction-diffusion wave. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 791-814. doi: 10.1051/m2an/2022019

[1] F. Akpinar, B. Inankur and J. Yin, Spatial-temporal patterns of viral amplification and interference initiated by a single infected cell. J. Virol. 90 (2016) 7552–7566. | DOI

[2] G. Bocharov, A. Meyerhans, N. Bessonov, S. Trofimchuk and V. Volpert, Spatiotemporal dynamics of virus infection spreading in tissues, PLoS One 11 (2016) e0168576. | DOI

[3] G. Bocharov, V. Volpert, B. Ludewig and A. Meyerhans, Mathematical Immunology of Virus Infections. Springer, Cham (2018). | MR | DOI

[4] G. Bocharov, A. Meyerhans, N. Bessonov, S. Trofimchuk and V. Volpert, Interplay between reaction and diffusion processes in governing the dynamics of virus infections. J. Theor. Biol. 457 (2018) 221–236. | MR | Zbl | DOI

[5] A. Bouchnita, A. Tokarev and V. Volpert, A multiscale model suggests that a moderately weak inhibition of SARS-CoV-2 replication by type I IFN could accelerate the clearance of the virus. bioRxiv (2021). DOI: . | DOI

[6] M. Czerkies, Z. Korwek, W. Prus, M. Kochańczyk, J. Jaruszewicz-Błońska, K. Tudelska, S. Błoński, M. Kimmel, A. R. Brasier and T. Lipniacki, Cell fate in antiviral response arises in the crosstalk of IRF, NF-B and JAK/STAT pathways. Nat. Commun. 9 (2018) 493. | DOI

[7] C. Dykes, J. Wang, X. Jin, V. Planelles, D. Sung An, A. Tallo, Y. Huang, H. Wu and L. M. Demeter, Evaluation of a multiple-cycle, recombinant virus, growth competition assay that uses flow cytometry to measure replication efficiency of human immunodeficiency virus type 1 in cell culture. J. Clin. Microbiol. 44 (2006) 1930–1943. | DOI

[8] K. Haye, S. Burmakina, T. Moran, A. GarcíA-Sastre and A. Fernandez-Sesma, The NS1 protein of a human influenza virus inhibits Type I Interferon production and the induction of antiviral responses in primary human dendritic and respiratory epithelial cells. J. Virol. 83 (2009) 6849–6862. | DOI

[9] F. Hecht, S. Auliac, O. Pironneau, J. Morice, A. Le Hyaric and K. Ohtsuka, FreeFem++ (manual) (2007) www.freefem.org.

[10] B. P. Holder, P. Simon, L. E. Liao, Y. Abed, X. Bouhy, C. A. A. Beauchemin and G. Boivin, Assessing the in vitro fitness of an Oseltamivir-resistant seasonal A/H1N1 influenza strain using a mathematical model. PLoS One 6 (2011) e14767. | DOI

[11] S. Jegouic, I. Pelletier, F. B. Riquet and R. Andrianarivelo Mala, Recombination between polioviruses and co-circulating coxsackie A viruses: role in the emergence of pathogenic vaccine-derived polioviruses. PloS Pathogens 5 (2009) e1000412. | DOI

[12] M. Labadie and A. Marciniak-Czochra, A reaction-diffusion model for viral infection and immune response. (2011) hal-00546034v2

[13] G. Li, Y. Fan, Y. Lai, T. Han, Z. Li, P. Zhou, P. Pan, W. Wang, D. Hu, X. Liu, Q. Zhang and J. Wu, Coronavirus infections and immune responses. J. Med. Virol. 92 (2020) 424–432. | DOI

[14] S. M. Lindsay, A. Timm and J. Yin, A quantitative comet infection assay for influenza virus. J. Virol. Methods 179 (2012) 351–358. | DOI

[15] I. A. Rodriguez-Brenes, A. Hofacre, H. Fan and D. Wodarz, Complex dynamics of virus spread from low infection multiplicities: implications for the spread of oncolytic viruses. PLoS Comput. Biol. 13 (2017) e1005241. | DOI

[16] A. C. Sims, R. S. Baric, B. Yount, S. E. Burkett, P. L. Collins and R. J. Pickles, Severe acute respiratory syndrome coronavirus infection of human ciliated airway epithelia: role of ciliated cells in viral spread in the conducting airways of the lungs. J. Virol. 79 (2005) 15511–15524. | DOI

[17] M. Su, Y. Chen, S. Qi, D. Shi, L. Feng and D. Sun, A mini-review on cell cycle regulation of coronavirus infection Front. Veterinary Sci. 7 (2020) 586826.

[18] S. Trofimchuk and V. Volpert, Traveling waves in delayed reaction-diffusion equations in biology. Math. Biosci. Eng. 17 (2020) 6487–6514. | MR | Zbl | DOI

[19] V. Volpert, Elliptic Partial Differential Equations. Volume 1. Fredholm Property of Elliptic Problems in Unbounded Domains. Birkhauser, Basel (2011). | MR | Zbl | DOI

[20] V. Volpert, Elliptic Partial Differential Equations. Volume 2. Reaction-Diffusion Equations. Birkhauser, Basel (2014). | MR | Zbl | DOI

[21] A. Volpert and V. Volpert, Formally adjoint problems and solvability conditions for elliptic operators. Russ. J. Math. Phys. 11 (2004) 474–497. | MR | Zbl

[22] J. Yin and J. S. Mccaskill, Replication of viruses in a growing plaque: a reaction-diffusion model. Biophys. J. 61 (1992) 1540–1549. | DOI

Cité par Sources :