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Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell
Mathematics, Volume: 9, Issue: 17, Start page: 2025
Swansea University Author: Igor Sazonov
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DOI (Published version): 10.3390/math9172025
Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4+ T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity ca...
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Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4+ T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected cells as well as from random effects and fluctuations in the kinetics of biochemical reactions underlying the virus replication cycle. To quantify the contribution of stochastic effects to the variability of HIV life cycle kinetics, we propose a high-resolution mathematical model formulated as a Markov chain jump process. The model is applied to generate the statistical characteristics of the (i) cell infection multiplicity, (ii) cooperative nature of viral replication, and (iii) variability in virus secretion by phenotypically identical cells. We show that the infection with a fixed number of viruses per CD4+ T cell leads to some heterogeneity of infected cells with respect to the number of integrated proviral genomes. The bottleneck factors in the virus production are identified, including the Gag-Pol proteins. Sensitivity analysis enables ranking of the model parameters with respect to the strength of their impact on the size of viral progeny. The first three globally influential parameters are the transport of genomic mRNA to membrane, the tolerance of transcription activation to Tat-mediated regulation, and the degradation of free and mature virions. These can be considered as potential therapeutical targets.
HIV life cycle; mathematical model; stochastic processes; Markov chain; heterogeneity; sensitivity analysis
Faculty of Science and Engineering
The reported study was funded by the Russian Science Foundation (grant number 18-11-00171), the Russian Foundation for Basic Research (grant number 20-01-00352) and the Moscow Center for Fundamental and Applied Mathematics at INM RAS (agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2019-1624). AM is also supported by the Spanish Ministry of Science and Innovation grant no. PID2019-106323RB-I00(AEI/MINEICO/FEDER, UE), and “Unidad de Excelencia María de Maeztu”, funded by the AEI (CEX2018-000792-M).