Abstract
This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Levy JA (2007) HIV and the pathogenesis of AIDS. ASM press, Washington, DC
Moir S, Chun TW, Fauci AS (2011) Pathogenic mechanisms of HIV disease. (Translated from eng). Annu Rev Pathol 6:223–248
Lackner A, Lederman MM, Rodriguez B (2012) HIV pathogenesis: the host. Cold Spring Harbor Perspectives in Medicine 2(9)
Coffin JM (1995) HIV population dynamics in vivo: implications for genetic variation, pathogenesis, and therapy. Science 267(5197):483–489
Nowak MA, May RM (2000) Virus dynamics. Mathematical principles of immunology and virology. Oxford University Press, Oxford
Perelson AS (2002) Modelling viral and immune system dynamics. Nature Rev Immunol 2(1):28–36
Perelson AS, Ribeiro RM (2013) Modeling the within-host dynamics of HIV infection. (Translated from Eng). BMC Biol 11(1):96
Wodarz D, Nowak MA (2002) Mathematical models of HIV pathogenesis and treatment. Bioessays 24(12):1178–1187
Nowak MA (2006) Evolutionary dynamics: exploring the equations of life. Harvard University Press, Cambridge, MA
McLean AR (2013) Infectious disease modeling. Infectious diseases. Springer, New York, pp 99–115
Nowak MA, Bangham CR (1996) Population dynamics of immune responses to persistent viruses. Science 272(5258):74–79
Anderson RM, May RM (1991) Infectious diseases of humans. Oxfors University Press, Oxofrd, England
Bonhoeffer S, May RM, Shaw GM, Nowak MA (1997) Virus dynamics and drug therapy. Proc Natl Acad Sci U S A 94(13):6971–6976
Ho DD et al (1995) Rapid turnover of plasma virions and Cd4 lymphocytes in HIV-1 infection. Nature 373(6510):123–126
Wei XP et al (1995) Viral dynamics in human-immunodeficiency-virus type-1 infection. Nature 373(6510):117–122
Perelson AS et al (1997) Decay characteristics of HIV-1-infected compartments during combination therapy. Nature 387(6629):188–191
Perelson AS, Neumann AU, Markowitz M, Leonard JM, Ho DD (1996) HIV-1 dynamics in-vivo – virion clearance rate, infected cell life-span, and viral generation time. Science 271(5255):1582–1586
Perelson AS, Essunger P, Ho DD (1997) Dynamics of HIV-1 and CD4+ lymphocytes in vivo. AIDS 11(SA):S17–S24
De Boer RJ, Ribeiro RM, Perelson AS (2010) Current estimates for HIV-1 production imply rapid viral clearance in lymphoid tissues. PLoS Comput Biol 6(9):e1000906
Finzi D et al (1997) Identification of a reservoir for HIV-1 in patients on highly active antiretroviral therapy [see comments]. Science 278(5341):1295–1300
Finzi D et al (1999) Latent infection of CD4+ T cells provides a mechanism for lifelong persistence of HIV-1, even in patients on effective combination therapy. (Translated from Eng). Nat Med 5(5):512–517 (in Eng)
Eisele E, Siliciano RF (2012) Redefining the viral reservoirs that prevent HIV-1 eradication. (Translated from eng). Immunity 37(3):377–388 (in eng)
Nowak MA et al (1997) Viral dynamics of primary viremia and antiretroviral therapy in simian immunodeficiency virus infection. J Virol 71(10):7518–7525
Little SJ, McLean AR, Spina CA, Richman DD, Havlir DV (1999) Viral dynamics of acute HIV-1 infection. J Exp Med 190(6):841–850
Ribeiro RM et al (2010) Estimation of the initial viral growth rate and basic reproductive number during acute HIV-1 infection. (Translated from eng). J Virol 84(12):6096–6102 (in eng)
Asquith B, Edwards CT, Lipsitch M, McLean AR (2006) Inefficient cytotoxic T lymphocyte-mediated killing of HIV-1-infected cells in vivo. PLoS Biol 4(4):e90
Wick WD, Yang OO, Corey L, Self SG (2005) How many human immunodeficiency virus type 1-infected target cells can a cytotoxic. T-lymphocyte kill? (Translated from eng). J Virol 79(21):13579–13586 (in eng)
Nowak MA (1996) Immune-responses against multiple epitopes – a theory for immunodominance and antigenic variation. Semin Virol 7(1):83–92
Nowak MA et al (1991) Antigenic diversity thresholds and the development of AIDS. Science 254(5034):963–969
Nowak MA et al (1995) Antigenic oscillations and shifting immunodominance in HIV-1 infections. Nature 375(6532):606–611
Wodarz D, Nowak MA (1998) The effect of different immune responses on the evolution of virulent CXCR4 tropic HIV. Proc R Soc Lond B 265(1411):2149–2158
Regoes RR, Bonhoeffer S (2005) The HIV coreceptor switch: a population dynamical perspective. Trends Microbiol 13(6):269–277
Ball CL, Gilchrist MA, Coombs D (2007) Modeling within-host evolution of HIV: mutation, competition and strain replacement. Bull Math Biol 69(7):2361–2385
Stilianakis NI, Schenzle D (2006) On the intra-host dynamics of HIV-1 infections. Math Biosci 199(1):1–25
Rouzine IM, Weinberger LS (2013) The quantitative theory of within-host viral evolution. J Stat Mech Theory Exp 2013(01), P01009
Lee HY, Perelson AS, Park S-C, Leitner T (2008) Dynamic correlation between intrahost HIV-1 quasispecies evolution and disease progression. PLoS Comput Biol 4(12):e1000240
Kimata JT, Kuller L, Anderson DB, Dailey P, Overbaugh J (1999) Emerging cytopathic and antigenic simian immunodeficiency virus variants influence AIDS progression. Nat Med 5(5):535–541
Wei X et al (2003) Antibody neutralization and escape by HIV-1. Nature 422(6929):307–312
Ganusov VV, De Boer RJ (2006) Estimating costs and benefits of CTL escape mutations in SIV/HIV infection. (Translated from eng). PLoS Comput Biol 2(3):e24
Ganusov VV et al (2011) Fitness costs and diversity of the cytotoxic T lymphocyte (CTL) response determine the rate of CTL escape during acute and chronic phases of HIV infection. (Translated from eng). J Virol 85(20):10518–10528 (in eng)
Fryer HR et al (2010) Modelling the evolution and spread of HIV immune escape mutants. PLoS Pathog 6(11):e1001196
Kadolsky UD, Asquith B (2010) Quantifying the impact of human immunodeficiency virus-1 escape from cytotoxic T-lymphocytes. PLoS Comput Biol 6(11):e1000981
Mostowy R et al (2012) Estimating the fitness cost of escape from HLA presentation in HIV-1 protease and reverse transcriptase. PLoS Comput Biol 8(5):e1002525
Ganusov VV, Neher RA, Perelson AS (2013) Mathematical modeling of escape of HIV from cytotoxic T lymphocyte responses. J Stat Mech Theory Exp 2013(01), P01010
Lama J (2003) The physiological relevance of CD4 receptor down-modulation during HIV infection. Curr HIV Res 1(2):167–184
Levesque K, Finzi A, Binette J, Cohen EA (2004) Role of CD4 receptor down-regulation during HIV-1 infection. Curr HIV Res 2(1):51–59
Michel N, Allespach I, Venzke S, Fackler OT, Keppler OT (2005) The Nef protein of human immunodeficiency virus establishes super infection immunity by a dual strategy to downregulate cell-surface CCR5 and CD4. Curr Biol 15(8):714–723
Chen BK, Gandhi RT, Baltimore D (1996) CD4 down-modulation during infection of human T cells with human immunodeficiency virus type 1 involves independent activities of vpu, env, and nef. J Virol 70(9):6044–6053
Wildum S, Schindler M, Munch J, Kirchhoff F (2006) Contribution of Vpu, Env, and Nef to CD4 down-modulation and resistance of human immunodeficiency virus type 1-infected T cells to superinfection. J Virol 80(16):8047–8059
Gratton S, Cheynier R, Dumaurier MJ, Oksenhendler E, Wain-Hobson S (2000) Highly restricted spread of HIV-1 and multiply infected cells within splenic germinal centers. Proc Natl Acad Sci U S A 97(26):14566–14571
Jung A et al (2002) Multiply infected spleen cells in HIV patients. Nature 418(6894):144
Mattapallil JJ et al (2005) Massive infection and loss of memory CD4+ T cells in multiple tissues during acute SIV infection. Nature 434(7037):1093–1097
Hubner W et al (2009) Quantitative 3D video microscopy of HIV transfer across T cell virological synapses. Science 323(5922):1743–1747
Jolly C, Sattentau QJ (2004) Retroviral spread by induction of virological synapses. Traffic 5(9):643–650
McDonald D et al (2003) Recruitment of HIV and its receptors to dendritic cell–T cell junctions. Science 300(5623):1295–1297
Arganaraz ER, Schindler M, Kirchhoff F, Cortes MJ, Lama J (2003) Enhanced CD4 down-modulation by late stage HIV-1 nef alleles is associated with increased Env incorporation and viral replication. J Biol Chem 278(36):33912–33919
Lama J, Mangasarian A, Trono D (1999) Cell-surface expression of CD4 reduces HIV-1 infectivity by blocking Env incorporation in a Nef- and Vpu-inhibitable manner. Curr Biol 9(12):622–631
Stoddart CA et al (2003) Human immunodeficiency virus type 1 Nef-mediated downregulation of CD4 correlates with Nef enhancement of viral pathogenesis. J Virol 77(3):2124–2133
Nethe M, Berkhout B, van der Kuyl AC (2005) Retroviral superinfection resistance. Retrovirology 2:52
Chen J et al (2005) Mechanisms of nonrandom human immunodeficiency virus type 1 infection and double infection: preference in virus entry is important but is not the sole factor. J Virol 79(7):4140–4149
Gelderblom HC et al (2008) Viral complementation allows HIV-1 replication without integration. Retrovirology 5:60
Levy DN, Aldrovandi GM, Kutsch O, Shaw GM (2004) Dynamics of HIV-1 recombination in its natural target cells. Proc Natl Acad Sci U S A 101(12):4204–4209
Bonhoeffer S, Chappey C, Parkin NT, Whitcomb JM, Petropoulos CJ (2004) Evidence for positive epistasis in HIV-1. Science 306(5701):1547–1550
Fraser C (2005) HIV recombination: what is the impact on antiretroviral therapy? J R Soc Interface 2(5):489–503
Vijay NNV, Ajmani VR, Perelson AS, Dixit NM (2008) Recombination increases human immunodeficiency virus fitness, but not necessarily diversity. J Gen Virol 89(Pt 6):1467–1477
Althaus CL, Bonhoeffer S (2005) Stochastic interplay between mutation and recombination during the acquisition of drug resistance mutations in human immunodeficiency virus type 1. J Virol 79(21):13572–13578
Kouyos RD, Althaus CL, Bonhoeffer S (2006) Stochastic or deterministic: what is the effective population size of HIV-1? (Translated from eng). Trends Microbiol 14(12):507–511 (in eng)
Kouyos RD, Silander OK, Bonhoeffer S (2007) Epistasis between deleterious mutations and the evolution of recombination. (Translated from eng). Trends Ecol Evol 22(6):308–315 (in eng)
Iwabu Y et al (2008) Superinfection of defective human immunodeficiency virus type 1 with different subtypes of wild-type virus efficiently produces infectious variants with the initial viral phenotypes by complementation followed by recombination. Microbes Infect 10(5):504–513
Wodarz D, Levy DN (2007) Human immunodeficiency virus evolution towards reduced replicative fitness in vivo and the development of AIDS. Proc Biol Sci 274(1624):2481–2490
Wodarz D, Levy DN (2009) Multiple HIV-1 infection of cells and the evolutionary dynamics of cytotoxic T lymphocyte escape mutants. Evolution 63(9):2326–2339
Wodarz D, Levy DN (2011) Effect of different modes of viral spread on the dynamics of multiply infected cells in human immunodeficiency virus infection. (Translated from eng). J R Soc Interface 8(55):289–300 (in eng)
Wodarz D, Levy DN (2011) Effect of multiple infection of cells on the evolutionary dynamics of HIV in vivo: implications for host adaptation mechanisms. (Translated from eng). Exp Biol Med (Maywood) 236(8):926–937 (in eng)
Dixit NM, Perelson AS (2005) HIV dynamics with multiple infections of target cells. Proc Natl Acad Sci U S A 102(23):8198–8203
Cummings KW, Levy DN, Wodarz D (2012) Increased burst size in multiply infected cells can alter basic virus dynamics. (Translated from eng). Biol Direct 7:16
Hofacre A, Wodarz D, Komarova NL, Fan H (2012) Early infection and spread of a conditionally replicating adenovirus under conditions of plaque formation. (Translated from eng). Virology 423(1):89–96 (in eng)
Lifson JD et al (1997) The extent of early viral replication is a critical determinant of the natural history of simian immunodeficiency virus infection. J Virol 71(12):9508–9514
Rudensey LM, Kimata JT, Benveniste RE, Overbaugh J (1995) Progression to AIDS in macaques is associated with changes in the replication, tropism, and cytopathic properties of the simian immunodeficiency virus variant population. Virology 207(2):528–542
Chen P, Hubner W, Spinelli MA, Chen BK (2007) Predominant mode of human immunodeficiency virus transfer between T cells is mediated by sustained Env-dependent neutralization-resistant virological synapses. (Translated from eng). J Virol 81(22):12582–12595 (in eng)
Feldmann J, Schwartz O (2010) HIV-1 virological synapse: live imaging of transmission. (Translated from eng). Viruses 2(8):1666–1680, www.mdpi.com/journals/viruses (in eng)
Martin N, Sattentau Q (2009) Cell-to-cell HIV-1 spread and its implications for immune evasion. (Translated from eng). Curr Opin HIV AIDS 4(2):143–149 (in eng)
Sattentau Q (2008) Avoiding the void: cell-to-cell spread of human viruses. Nat Rev Microbiol 6(11):815–826
Sattentau QJ (2010) Cell-to-cell spread of retroviruses. (Translated from eng). Viruses 2(6):1306–1321, www.mdpi.com/journals/viruses (in eng)
Sourisseau M, Sol-Foulon N, Porrot F, Blanchet F, Schwartz O (2007) Inefficient human immunodeficiency virus replication in mobile lymphocytes. (Translated from eng). J Virol 81(2):1000–1012 (in eng)
Sigal A et al (2011) Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy. (Translated from eng). Nature 477(7362):95–98 (in eng)
Del Portillo A et al (2011) Multiploid inheritance of HIV-1 during cell-to-cell infection. (Translated from eng). J Virol 85(14):7169–7176 (in eng)
Josefsson L et al (2011) Majority of CD4+ T cells from peripheral blood of HIV-1-infected individuals contain only one HIV DNA molecule. (Translated from eng). Proc Natl Acad Sci U S A 108(27):11199–11204 (in eng)
Komarova NL et al (2013) Relative contribution of free-virus and synaptic transmission to the spread of HIV-1 through target cell populations. (Translated from eng). Biol Lett 9(1):20121049
Komarova NL, Levy DN, Wodarz D (2012) Effect of synaptic transmission on viral fitness in HIV infection. (Translated from eng). PLoS One 7(11):e48361
Komarova NL, Wodarz D (2013) Virus dynamics in the presence of synaptic transmission. (Translated from eng). Math Biosci 242(2):161–171 (in eng)
Doceul V, Hollinshead M, van der Linden L, Smith GL (2010) Repulsion of superinfecting virions: a mechanism for rapid virus spread. (Translated from eng). Science 327(5967):873–876 (in eng)
Jolly C (2011) Cell-to-cell transmission of retroviruses: Innate immunity and interferon-induced restriction factors. (Translated from eng). Virology 411(2):251–259 (in eng)
Bieniasz PD (2004) Intrinsic immunity: a front-line defense against viral attack. (Translated from eng). Nat Immunol 5(11):1109–1115 (in eng)
Sakuma R, Noser JA, Ohmine S, Ikeda Y (2007) Inhibition of HIV-1 replication by simian restriction factors, TRIM5alpha and APOBEC3G. (Translated from eng). Gene Ther 14(2):185–189 (in eng)
Stremlau M et al (2004) The cytoplasmic body component TRIM5alpha restricts HIV-1 infection in old world monkeys. (Translated from eng). Nature 427(6977):848–853 (in eng)
Yan N, Chen ZJ (2012) Intrinsic antiviral immunity. (Translated from eng). Nat Immunol 13(3):214–222 (in eng)
Sokolskaja E, Luban J (2006) Cyclophilin, TRIM5, and innate immunity to HIV-1. (Translated from eng). Curr Opin Microbiol 9(4):404–408 (in eng)
Wodarz D (2007) Killer cell dynamics: mathematical and computational approaches to immunology. Springer, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this protocol
Cite this protocol
Wodarz, D. (2014). Mathematical Models of HIV Replication and Pathogenesis. In: De, R., Tomar, N. (eds) Immunoinformatics. Methods in Molecular Biology, vol 1184. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-1115-8_30
Download citation
DOI: https://doi.org/10.1007/978-1-4939-1115-8_30
Published:
Publisher Name: Humana Press, New York, NY
Print ISBN: 978-1-4939-1114-1
Online ISBN: 978-1-4939-1115-8
eBook Packages: Springer Protocols