Abstract
The presence of cells latently infected with HIV is currently considered to be a major barrier to viral eradication within a patient. Here, we consider birth–death-immigration models for the latent cell population in a single patient, and present analytical results for the size of this population in the absence of treatment. We provide results both at steady state (viral set point), and during the non-equilibrium setting of early infection. We obtain semi-analytic results showing how latency-reversing drugs might be expected to affect the size of the latent pool over time. We also analyze the probability of rare mutant viral strains joining the latent cell population, allowing for steady-state and dynamic viral populations within the host.
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References
Alexander HK, Bonhoeffer S (2012) Pre-existence and emergence of drug resistance in a generalized model of intra-host viral dynamics. Epidemics 4(4):187–202. https://doi.org/10.1016/j.epidem.2012.10.001
Allen L (2010) An introduction to stochastic processes with applications to biology, 2nd edn. Chapman and Hall, Upper Saddle River
Althaus CL, Joos B, Perelson AS, Günthard HF (2014) Quantifying the turnover of transcriptional subclasses of HIV-1-infected cells. PLoS Comput Biol 10(10):e1003,871. https://doi.org/10.1371/journal.pcbi.1003871
Archin NM, Liberty AL, Kashuba AD, Choudhary SK, Kuruc JD, Crooks AM, Parker DC, Anderson EM, Kearney MF, Strain MC, Richman DD, Hudgens MG, Bosch RJ, Coffin JM, Eron JJ, Hazuda DJ, Margolis DM (2012) Administration of vorinostat disrupts HIV-1 latency in patients on antiretroviral therapy. Nature 487(7408):482–5. https://doi.org/10.1038/nature11286
Archin NM, Sung JM, Garrido C, Soriano-Sarabia N, Margolis DM (2014) Eradicating HIV-1 infection: seeking to clear a persistent pathogen. Nat Rev Microbiol 12(11):750–64. https://doi.org/10.1038/nrmicro3352
Bonhoeffer S, Nowak MA (1997) Pre-existence and emergence of drug resistance in HIV-1 infection. Proc Biol Sci 264(1382):631–7. https://doi.org/10.1098/rspb.1997.0089
Bullen CK, Laird GM, Durand CM, Siliciano JD, Siliciano RF (2014) New ex vivo approaches distinguish effective and ineffective single agents for reversing HIV-1 latency in vivo. Nat Med 20(4):425–9. https://doi.org/10.1038/nm.3489
Chomont N, El-Far M, Ancuta P, Trautmann L, Procopio FA, Yassine-Diab B, Boucher G, Boulassel MR, Ghattas G, Brenchley JM, Schacker TW, Hill BJ, Douek DC, Routy JP, Haddad EK, Sékaly RP (2009) HIV reservoir size and persistence are driven by T cell survival and homeostatic proliferation. Nat Med 15(8):893–900. https://doi.org/10.1038/nm.1972
Chun TW, Engel D, Mizell SB, Ehler LA, Fauci AS (1998) Induction of HIV-1 replication in latently infected CD4+ T cells using a combination of cytokines. J Exp Med 188(1):83–91
Conway JM, Coombs D (2011) A stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients. PLoS Comput Biol 7(4):e1002033. https://doi.org/10.1371/journal.pcbi.1002033
Conway JM, Perelson AS (2015) Post-treatment control of HIV infection. Proc Natl Acad Sci USA 112(17):5467–5472. https://doi.org/10.1073/pnas.1419162112
Conway JM, Konrad BP, Coombs D (2013) Stochastic analysis of pre- and postexposure prophylaxis against HIV infection. SIAM J. Appl. Math. 73(2):904–928. https://doi.org/10.1137/120876800
Elliott JH, McMahon JH, Chang CC, Lee SA, Hartogensis W, Bumpus N, Savic R, Roney J, Hoh R, Solomon A, Piatak M, Gorelick RJ, Lifson J, Bacchetti P, Deeks SG, Lewin SR (2015) Short-term administration of disulfiram for reversal of latent HIV infection: a phase 2 dose-escalation study. Lancet HIV 2(12):e520–9. https://doi.org/10.1016/S2352-3018(15)00226-X
Finzi D, Blankson J, Siliciano JD, Margolick JB, Chadwick K, Pierson T, Smith K, Lisziewicz J, Lori F, Flexner C, Quinn TC, Chaisson RE, Rosenberg E, Walker B, Gange S, Gallant J, Siliciano RF (1999) Latent infection of CD4+ T cells provides a mechanism for lifelong persistence of HIV-1, even in patients on effective combination therapy. Nat Med 5(5):512–7. https://doi.org/10.1038/8394
Gadhamsetty S, Dixit NM (2010) Estimating frequencies of minority nevirapine-resistant strains in chronically HIV-1-infected individuals naive to nevirapine by using stochastic simulations and a mathematical model. J Virol 84(19):10,230–40. https://doi.org/10.1128/JVI.01010-10
Gutiérrez C, Serrano-Villar S, Madrid-Elena N, Pérez-Elías MJ, Martín ME, Barbas C, Ruipérez J, Muñoz E, Muñoz-Fernández MA, Castor T, Moreno S (2016) Bryostatin-1 for latent virus reactivation in HIV-infected patients on antiretroviral therapy. AIDS 30(9):1385–92. https://doi.org/10.1097/QAD.0000000000001064
Hill AL, Rosenbloom DIS, Fu F, Nowak MA, Siliciano RF (2014) Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1. Proc Natl Acad Sci USA 111(37):13475–13480. https://doi.org/10.1073/pnas.1406663111
Hill AL, Rosenbloom DIS, Goldstein E, Hanhauser E, Kuritzkes DR, Siliciano RF, Henrich TJ (2016a) Real-time predictions of reservoir size and rebound time during antiretroviral therapy interruption trials for HIV. PLoS Pathog 12(4):e1005,535. https://doi.org/10.1371/journal.ppat.1005535
Hill AL, Rosenbloom DIS, Siliciano JD, Siliciano RF (2016b) Insufficient evidence for rare activation of latent HIV in the absence of reservoir-reducing interventions. PLoS Pathog 12(8):e1005,679. https://doi.org/10.1371/journal.ppat.1005679
Ho YC, Shan L, Hosmane NN, Wang J, Laskey SB, Rosenbloom DIS, Lai J, Blankson JN, Siliciano JD, Siliciano RF (2013) Replication-competent noninduced proviruses in the latent reservoir increase barrier to HIV-1 cure. Cell 155(3):540–51. https://doi.org/10.1016/j.cell.2013.09.020
Hosmane NN, Kwon KJ, Bruner KM, Capoferri AA, Beg S, Rosenbloom DIS, Keele BF, Ho YC, Siliciano JD, Siliciano RF (2017) Proliferation of latently infected CD4+ T cells carrying replication-competent HIV-1: Potential role in latent reservoir dynamics. J Exp Med 214(4):959–972. https://doi.org/10.1084/jem.20170193
Joos B, Fischer M, Kuster H, Pillai SK, Wong JK, Böni J, Hirschel B, Weber R, Trkola A, Günthard HF, Swiss HIV Cohort Study (2008) HIV rebounds from latently infected cells, rather than from continuing low-level replication. Proc Natl Acad Sci USA 105(43):16,725–30, DOIurl10.1073/pnas.0804192105
Karlin S, Taylor H (1974) A first course in stochastic processes, 2nd edn. Academic Press Inc, London
Kendall D (1957) On the generalized birth-and-death process. Ann Math Stat 19:1–15
Kim H, Perelson AS (2006) Viral and latent reservoir persistence in HIV-1-infected patients on therapy. PLoS Comput Biol 2(10):e135. https://doi.org/10.1371/journal.pcbi.0020135
Konrad BP, Taylor D, Conway JM, Ogilvie GS, Coombs D (2017) On the duration of the period between exposure to HIV and detectable infection. Epidemics 20:73–83. https://doi.org/10.1016/j.epidem.2017.03.002
Margolis DM, Garcia JV, Hazuda DJ, Haynes BF (2016) Latency reversal and viral clearance to cure HIV-1. Science 353(6297):aaf6517, https://doi.org/10.1126/science.aaf6517
Monie D, Simmons RP, Nettles RE, Kieffer TL, Zhou Y, Zhang H, Karmon S, Ingersoll R, Chadwick K, Zhang H, Margolick JB, Quinn TC, Ray SC, Wind-Rotolo M, Miller M, Persaud D, Siliciano RF (2005) A novel assay allows genotyping of the latent reservoir for human immunodeficiency virus type 1 in the resting CD4+ T cells of viremic patients. J Virol 79(8):5185–202. https://doi.org/10.1128/JVI.79.8.5185-5202.2005
Müller V, Vigueras-Gómez JF, Bonhoeffer S (2002) Decelerating decay of latently infected cells during prolonged therapy for human immunodeficiency virus type 1 infection. J Virol 76(17):8963–5
Perelson A, Nelson P (1999) Mathematical models of HIV-1 dynamics in vivo. SIAM Rev 41:3–44
Perelson AS, Essunger P, Cao Y, Vesanen M, Hurley A, Saksela K, Markowitz M, Ho DD (1997) Decay characteristics of HIV-1-infected compartments during combination therapy. Nature 387(6629):188–91. https://doi.org/10.1038/387188a0
Pinkevych M, Cromer D, Tolstrup M, Grimm AJ, Cooper DA, Lewin SR, Søgaard OS, Rasmussen TA, Kent SJ, Kelleher AD, Davenport MP (2015) HIV reactivation from latency after treatment interruption occurs on average every 5-8 days–implications for HIV remission. PLoS Pathog 11(7):e1005,000. https://doi.org/10.1371/journal.ppat.1005000
Rasmussen TA, Tolstrup M, Søgaard OS (2016) Reversal of latency as part of a cure for HIV-1. Trends Microbiol 24(2):90–97. https://doi.org/10.1016/j.tim.2015.11.003
Renshaw E (2011) Stochastic population processes: analysis, approximations, simulations. Oxford University Press, Oxford
Ribeiro RM, Bonhoeffer S (2000) Production of resistant HIV mutants during antiretroviral therapy. Proc Natl Acad Sci USA 97(14):7681–6
Ribeiro RM, Bonhoeffer S, Nowak MA (1998) The frequency of resistant mutant virus before antiviral therapy. AIDS 12(5):461–5
Richman DD, Margolis DM, Delaney M, Greene WC, Hazuda D, Pomerantz RJ (2009) The challenge of finding a cure for HIV infection. Science 323(5919):1304–7. https://doi.org/10.1126/science.1165706
Ruelas DS, Greene WC (2013) An integrated overview of HIV-1 latency. Cell 155(3):519–29. https://doi.org/10.1016/j.cell.2013.09.044
Siliciano JD, Kajdas J, Finzi D, Quinn TC, Chadwick K, Margolick JB, Kovacs C, Gange SJ, Siliciano RF (2003) Long-term follow-up studies confirm the stability of the latent reservoir for HIV-1 in resting CD4+ T cells. Nat Med 9(6):727–8. https://doi.org/10.1038/nm880
Sultan B, Benn P, Waters L (2014) Current perspectives in HIV post-exposure prophylaxis. HIV AIDS (Auckl) 6:147–58. https://doi.org/10.2147/HIV.S46585
Whitney JB, Hill AL, Sanisetty S, Penaloza-MacMaster P, Liu J, Shetty M, Parenteau L, Cabral C, Shields J, Blackmore S, Smith JY, Brinkman AL, Peter LE, Mathew SI, Smith KM, Borducchi EN, Rosenbloom DIS, Lewis MG, Hattersley J, Li B, Hesselgesser J, Geleziunas R, Robb ML, Kim JH, Michael NL, Barouch DH (2014) Rapid seeding of the viral reservoir prior to SIV viraemia in rhesus monkeys. Nature 512(7512):74–7. https://doi.org/10.1038/nature13594
Acknowledgements
We thank Jessica M. Conway and Alejandra D. Herrera for helpful discussions and references.
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This work was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant number 04611 to DC) and by a scholarship from the Government of Egypt (to SAA).
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Azoz, S.A., Coombs, D. Stochastic Dynamics of the Latently Infected Cell Reservoir During HIV Infection. Bull Math Biol 81, 131–154 (2019). https://doi.org/10.1007/s11538-018-0520-5
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DOI: https://doi.org/10.1007/s11538-018-0520-5