Skip to main content
SpringerLink
Log in

Spatial Aspects of HIV Infection

  • Chapter
  • First Online:
Mathematical Methods and Models in Biomedicine

Abstract

Human immunodeficiency virus type 1 (HIV-1) is one of the most and intensely studied viral pathogens in the history of science. However, despite the huge scientific effort, many aspects of HIV infection dynamics and disease pathogenesis within a host are still not understood. Mathematical modeling has helped to improve our understanding of the infection as well as the dynamics of the immune response. Fitting models to clinical data has provided estimates for the turnover rate of target cells [82, 83,111], the lifetime of infected cells and viral particles [104, 109], as well as for the rate of viral production by infected cells [21, 44]. Most mathematical models applied to experimental data on viral infections have been formulated as systems of ordinary differential equations (ODE) [91, 101, 104].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Allen, C.D., Okada, T., Tang, H.L., Cyster, J.G.: Imaging of germinal center selection events during affinity maturation. Science 315, 528–531 (2007)

    Google Scholar 

  2. Althaus, C.L., De Vos, A.S., De Boer, R.J.: Reassessing the human immunodeficiency virus type 1 life cycle through age-structured modeling: Life span of infected cells, viral generation time, and basic reproductive number, R0. J. Virol. 83, 7659–7667 (2009)

    Google Scholar 

  3. Bajenoff, M., Egen, J.G., Koo, L.Y., Laugier, J.P., Brau, F., Glaichenhaus, N., Germain, R.N.: Stromal cell networks regulate lymphocyte entry, migration, and territoriality in lymph nodes. Immunity 25, 989–1001 (2006)

    Google Scholar 

  4. Bajenoff, M., Glaichenhaus, N., Germain, R.N.: Fibroblastic reticular cells guide T lymphocyte entry into and migration within the splenic T cell zone. J. Immunol. 181, 3947–3954 (2008)

    Google Scholar 

  5. Balagopalan, L., Sherman, E., Barr, V.A., Samelson, L.E.: Imaging techniques for assaying lymphocyte activation in action. Nat. Rev. Immunol. 11, 21–33 (2011)

    Google Scholar 

  6. Baldazzi, V., Castiglione, F., Bernaschi, M.: An enhanced agent based model of the immune system response. Cell. Immunol. 244, 77–79 (2006)

    Google Scholar 

  7. Bauer, A.L., Beauchemin, C.A., Perelson, A.S.: Agent-based modeling of host-pathogen systems: The successes and challenges. Inf. Sci. 179, 1379–1389 (2009)

    Google Scholar 

  8. Beauchemin, C.: Probing the effects of the well-mixed assumption on viral infection dynamics. J. Theor. Biol. 242, 464–477 (2006)

    MathSciNet  Google Scholar 

  9. Beauchemin, C., Samuel, J., Tuszynski, J.: A simple cellular automaton model for influenza A viral infections. J. Theor. Biol. 232, 223–234 (2005)

    MathSciNet  Google Scholar 

  10. Beltman, J.B., Maree, A.F., Lynch, J.N., Miller, M.J., de Boer, R.J.: Lymph node topology dictates T cell migration behavior. J. Exp. Med. 204, 771–780 (2007)

    Google Scholar 

  11. Beltman, J.B., Maree, A.F., de Boer, R.J.: Analysing immune cell migration. Nat. Rev. Immunol. 9, 789–798 (2009)

    Google Scholar 

  12. Bernaschi, M., Castiglione, F.: Selection of escape mutants from immune recognition during HIV infection. Immunol. Cell Biol. 80, 307–313 (2002)

    Google Scholar 

  13. Betts, M.R., Nason, M.C., West, S.M., De Rosa, S.C., Migueles, S.A., Abraham, J., Lederman, M.M., Benito, J.M., Goepfert, P.A., Connors, M., Roederer, M., Koup, R.A.: HIV nonprogressors preferentially maintain highly functional HIV-specific CD8+ T cells. Blood 107, 4781–4789 (2006)

    Google Scholar 

  14. Bocharov, G.A., Romanyukha, A.A.: Mathematical model of antiviral immune response. III. Influenza A virus infection. J. Theor. Biol. 167, 323–360 (1994)

    Google Scholar 

  15. Bogle, G., Dunbar, P.R.: Simulating T-cell motility in the lymph node paracortex with a packed lattice geometry. Immunol. Cell Biol. 86, 676–687 (2008)

    Google Scholar 

  16. Bogle, G., Dunbar, P.R.: Agent-based simulation of T-cell activation and proliferation within a lymph node. Immunol. Cell Biol. 88, 172–179 (2010)

    Google Scholar 

  17. Bousso, P., Bhakta, N.R., Lewis, R.S., Robey, E.: Dynamics of thymocyte-stromal cell interactions visualized by two-photon microscopy. Science 296, 1876–1880 (2002)

    Google Scholar 

  18. Burkhead, E.G., Hawkins, J.M., Molinek, D.K.: A dynamical study of a cellular automata model of the spread of HIV in a lymph node. Bull. Math. Biol. 71, 25–74 (2009)

    MathSciNet  MATH  Google Scholar 

  19. Castiglione, F., Poccia, F., D’Offizi, G., Bernaschi, M.: Mutation, fitness, viral diversity, and predictive markers of disease progression in a computational model of HIV type 1 infection. AIDS Res. Hum. Retroviruses 20, 1314–1323 (2004)

    Google Scholar 

  20. Castiglione, F., Pappalardo, F., Bernaschi, M., Motta, S.: Optimization of HAART with genetic algorithms and agent-based models of HIV infection. Bioinformatics 23, 3350–3355 (2007)

    Google Scholar 

  21. Chen, H.Y., Di Mascio, M., Perelson, A.S., Ho, D.D., Zhang, L.: Determination of virus burst size in vivo using a single-cycle SIV in rhesus macaques. Proc. Natl. Acad. Sci. U.S.A. 104, 19079–19084 (2007)

    Google Scholar 

  22. Chen, P., Hubner, W., Spinelli, M.A., Chen, B.K.: Predominant mode of human immunodeficiency virus transfer between T cells is mediated by sustained Env-dependent neutralization-resistant virological synapses. J. Virol. 81, 12582–12595 (2007)

    Google Scholar 

  23. Cheynier, R., Henrichwark, S., Hadida, F., Pelletier, E., Oksenhendler, E., Autran, B., Wain-Hobson, S.: HIV and T cell expansion in splenic white pulps is accompanied by infiltration of HIV-specific cytotoxic T lymphocytes. Cell 78, 373–387 (1994)

    Google Scholar 

  24. Coombes, J.L., Robey, E.A.: Dynamic imaging of host-pathogen interactions in vivo. Nat. Rev. Immunol. 10, 353–364 (2010)

    Google Scholar 

  25. Danielson, C.M., Hope, T.J.: Imaging of HIV/host protein interactions. Curr. Top. Microbiol. Immunol. 339, 103–123 (2009)

    Google Scholar 

  26. Davenport, M.P., Ribeiro, R.M., Perelson, A.S.: Kinetics of virus-specific CD8+ T cells and the control of human immunodeficiency virus infection. J. Virol. 78, 10096–10103 (2004)

    Google Scholar 

  27. De Boer, R.J., Ribeiro, R.M., Perelson, A.S.: Current estimates for HIV-1 production imply rapid viral clearance in lymphoid tissues. PLoS Comput. Biol. 6, e1000906 (2010)

    Google Scholar 

  28. Dieckmann, U., Law, R., Metz, J. (eds.): The Geometry of Ecological Interactions: Simplifying Spatial Complexity. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  29. Dimitrov, D.S., Hillman, K., Manischewitz, J., Blumenthal, R., Golding, H.: Kinetics of soluble CD4 binding to cells expressing human immunodeficiency virus type 1 envelope glycoprotein. J. Virol. 66, 132–138 (1992)

    Google Scholar 

  30. Durrett, R.: Stochastic spatial models. SIAM Rev. 41, 677–718 (1999)

    MathSciNet  MATH  Google Scholar 

  31. Emery, V.C., Cope, A.V., Bowen, E.F., Gor, D., Griffiths, P.D.: The dynamics of human cytomegalovirus replication in vivo. J. Exp. Med. 190, 177–182 (1999)

    Google Scholar 

  32. Frank, S.A.: Within-host spatial dynamics of viruses and defective interfering particles. J. Theor. Biol. 206, 279–290 (2000)

    Google Scholar 

  33. Fraser, C., Hollingsworth, T.D., Chapman, R., de Wolf, F., Hanage, W.P.: Variation in HIV-1 set-point viral load: Epidemiological analysis and an evolutionary hypothesis. Proc. Natl. Acad. Sci. U.S.A. 104, 17441–17446 (2007)

    Google Scholar 

  34. Funk, G.A., Jansen, V.A., Bonhoeffer, S., Killingback, T.: Spatial models of virus-immune dynamics. J. Theor. Biol. 233, 221–236 (2005)

    MathSciNet  Google Scholar 

  35. Germain, R.N., Bajenoff, M., Castellino, F., Chieppa, M., Egen, J.G., Huang, A.Y., Ishii, M., Koo, L.Y., Qi, H.: Making friends in out-of-the-way places: How cells of the immune system get together and how they conduct their business as revealed by intravital imaging. Immunol. Rev. 221, 163–181 (2008)

    Google Scholar 

  36. Gratton, S., Cheynier, R., Dumaurier, M.J., Oksenhendler, E., Wain-Hobson, S.: Highly restricted spread of HIV-1 and multiply infected cells within splenic germinal centers. Proc. Natl. Acad. Sci. U.S.A. 97, 14566–14571 (2000)

    Google Scholar 

  37. Graw, F., Regoes, R.R.: Investigating CTL mediated killing with a 3D cellular automaton. PLoS Comput. Biol. 5, e1000466 (2009)

    Google Scholar 

  38. Graziano, F.M., Kettoola, S.Y., Munshower, J.M., Stapleton, J.T., Towfic, G.J.: Effect of spatial distribution of T-Cells and HIV load on HIV progression. Bioinformatics 24, 855–860 (2008)

    Google Scholar 

  39. Grenfell, B.T., Bolker, B.M., Kleczkowski, A.: Seasonality and extinction in chaotic metapopulations. Proc. Sci. Bio 259, 97–103 (1995)

    Google Scholar 

  40. Grossman, Z., Meier-Schellersheim, M., Paul, W.E., Picker, L.J.: Pathogenesis of HIV infection: What the virus spares is as important as what it destroys. Nat. Med. 12, 289–295 (2006)

    Google Scholar 

  41. Groux, H., Torpier, G., Monte, D., Mouton, Y., Capron, A., Ameisen, J.C.: Activation-induced death by apoptosis in CD4+ T cells from human immunodeficiency virus-infected asymptomatic individuals. J. Exp. Med. 175, 331–340 (1992)

    Google Scholar 

  42. Haase, A.T.: Perils at mucosal front lines for HIV and SIV and their hosts. Nat. Rev. Immunol. 5, 783–792 (2005)

    Google Scholar 

  43. Haase, A.T.: Targeting early infection to prevent HIV-1 mucosal transmission. Nature 464, 217–223 (2010)

    Google Scholar 

  44. Haase, A.T., Henry, K., Zupancic, M., Sedgewick, G., Faust, R.A., Melroe, H., Cavert, W., Gebhard, K., Staskus, K., Zhang, Z.Q., Dailey, P.J., Balfour, H.H., Erice, A., Perelson, A.S.: Quantitative image analysis of HIV-1 infection in lymphoid tissue. Science 274, 985–989 (1996)

    Google Scholar 

  45. Halling-Brown, M., Pappalardo, F., Rapin, N., Zhang, P., Alemani, D., Emerson, A., Castiglione, F., Duroux, P., Pennisi, M., Miotto, O., Churchill, D., Rossi, E., Moss, D.S., Sansom, C.E., Bernaschi, M., Lefranc, M.P., Brunak, S., Lund, O., Motta, S., Lollini, P.L., Murgo, A., Palladini, A., Basford, K.E., Brusic, V., Shepherd, A.J.: ImmunoGrid: Towards agent-based simulations of the human immune system at a natural scale. Philos. Transact. A Math. Phys. Eng. Sci. 368, 2799–2815 (2010)

    Google Scholar 

  46. Heath, S.L., Tew, J.G., Tew, J.G., Szakal, A.K., Burton, G.F.: Follicular dendritic cells and human immunodeficiency virus infectivity. Nature 377, 740–744 (1995)

    Google Scholar 

  47. Hladik, F., McElrath, M.J.: Setting the stage: Host invasion by HIV. Nat. Rev. Immunol. 8, 447–457 (2008)

    Google Scholar 

  48. Hlavacek, W.S., Wofsy, C., Perelson, A.S.: Dissociation of HIV-1 from follicular dendritic cells during HAART: Mathematical analysis. Proc. Natl. Acad. Sci. U.S.A. 96, 14681–14686 (1999)

    Google Scholar 

  49. Hlavacek, W.S., Stilianakis, N.I., Notermans, D.W., Danner, S.A., Perelson, A.S.: Influence of follicular dendritic cells on decay of HIV during antiretroviral therapy. Proc. Natl. Acad. Sci. U.S.A. 97, 10966–10971 (2000)

    Google Scholar 

  50. Hlavacek, W.S., Stilianakis, N.I., Perelson, A.S.: Influence of follicular dendritic cells on HIV dynamics. Philos. Trans. R. Soc. Lond. B Biol. Sci. 355, 1051–1058 (2000)

    Google Scholar 

  51. Ho, D.D., Neumann, A.U., Perelson, A.S., Chen, W., Leonard, J.M., Markowitz, M.: Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature 373, 123–126 (1995)

    Google Scholar 

  52. Hübner, W., McNerney, G.P., Chen, P., Dale, B.M., Gordon, R.E., Chuang, F.Y., Li, X.D., Asmuth, D.M., Huser, T., Chen, B.K.: Quantitative 3D video microscopy of HIV transfer across T cell virological synapses. Science 323, 1743–1747 (2009)

    Google Scholar 

  53. Jolly, C., Kashefi, K., Hollinshead, M., Sattentau, Q.J.: HIV-1 cell to cell transfer across an Env-induced, actin-dependent synapse. J. Exp. Med. 199, 283–293 (2004)

    Google Scholar 

  54. Joo, J., Lebowitz, J.L.: Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 036114 (2004)

    Google Scholar 

  55. Kaul, R., Plummer, F.A., Kimani, J., Dong, T., Kiama, P., Rostron, T., Njagi, E., MacDonald, K.S., Bwayo, J.J., McMichael, A.J., Rowland-Jones, S.L.: HIV-1-specific mucosal CD8+ lymphocyte responses in the cervix of HIV-1-resistant prostitutes in Nairobi. J. Immunol. 164, 1602–1611 (2000)

    Google Scholar 

  56. Keele, B.F., Li, H., Learn, G.H., Hraber, P., Giorgi, E.E., Grayson, T., Sun, C., Chen, Y., Yeh, W.W., Letvin, N.L., Mascola, J.R., Nabel, G.J., Haynes, B.F., Bhattacharya, T., Perelson, A.S., Korber, B.T., Hahn, B.H., Shaw, G.M.: Low-dose rectal inoculation of rhesus macaques by SIVsmE660 or SIVmac251 recapitulates human mucosal infection by HIV-1. J. Exp. Med. 206, 1117–1134 (2009)

    Google Scholar 

  57. Keeling, M.J., Rohani, P.: Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton (2008)

    MATH  Google Scholar 

  58. Keeling, M.J., Rand, D.A., Morris, A.J.: Correlation models for childhood epidemics. Proc. Biol. Sci. 264, 1149–1156 (1997)

    Google Scholar 

  59. Keeling, M.J., Woolhouse, M.E., May, R.M., Davies, G., Grenfell, B.T.: Modelling vaccination strategies against foot-and-mouth disease. Nature 421, 136–142 (2003)

    Google Scholar 

  60. Kepler, T.B., Perelson, A.S.: Drug concentration heterogeneity facilitates the evolution of drug resistance. Proc. Natl. Acad. Sci. U.S.A. 95, 11514–11519 (1998)

    MATH  Google Scholar 

  61. Kirschner, D., Webb, G.F.: A model for treatment strategy in the chemotherapy of AIDS. Bull. Math. Biol. 58, 376–390 (1996)

    Google Scholar 

  62. Korber, B.T., Letvin, N.L., Haynes, B.F.: T-cell vaccine strategies for human immunodeficiency virus, the virus with a thousand faces. J. Virol. 83, 8300–8314 (2009)

    Google Scholar 

  63. Ladi, E., Herzmark, P., Robey, E.: In situ imaging of the mouse thymus using 2-photon microscopy. J. Vis. Exp.11 e652. doi:10.3791/652 (2008)

    Google Scholar 

  64. Levin, S.A., Durrett, R.: From individuals to epidemics. Philos. Trans. R. Soc. Lond. B Biol. Sci. 351, 1615–1621 (1996)

    Google Scholar 

  65. Lin, H., Shuai, J.W.: A stochastic spatial model of HIV dynamics with an asymmetric battle between the virus and the immune system. New J. Phy. 12, 043051 (2010)

    Google Scholar 

  66. Linderman, J.J., Riggs, T., Pande, M., Miller, M., Marino, S., Kirschner, D.E.: Characterizing the dynamics of CD4+ T cell priming within a lymph node. J. Immunol. 184, 2873–2885 (2010)

    Google Scholar 

  67. Lindquist, R.L., Shakhar, G., Dudziak, D., Wardemann, H., Eisenreich, T., Dustin, M.L., Nussenzweig, M.C.: Visualizing dendritic cell networks in vivo. Nat. Immunol. 5, 1243–1250 (2004)

    Google Scholar 

  68. Louzoun, Y., Solomon, S., Atlan, H., Cohen, I.R.: Modeling complexity in biology. Physica A. 297, 242–252 (2001)

    MATH  Google Scholar 

  69. Markowitz, M., Louie, M., Hurley, A., Sun, E., Di Mascio, M., Perelson, A.S., Ho, D.D.: A novel antiviral intervention results in more accurate assessment of human immunodeficiency virus type 1 replication dynamics and T-cell decay in vivo. J. Virol. 77, 5037–5038 (2003)

    Google Scholar 

  70. Martin, N., Welsch, S., Jolly, C., Briggs, J.A., Vaux, D., Sattentau, Q.J.: Virological synapse-mediated spread of human immunodeficiency virus type 1 between T cells is sensitive to entry inhibition. J. Virol. 84, 3516–3527 (2010)

    Google Scholar 

  71. McDonald, D., Vodicka, M.A., Lucero, G., Svitkina, T.M., Borisy, G.G., Emerman, M., Hope, T.J.: Visualization of the intracellular behavior of HIV in living cells. J. Cell Biol. 159, 441–452 (2002)

    Google Scholar 

  72. McDonald, D., Wu, L., Bohks, S.M., KewalRamani, V.N., Unutmaz, D., Hope, T.J.: Recruitment of HIV and its receptors to dendritic cell-T cell junctions. Science 300, 1295–1297 (2003)

    Google Scholar 

  73. Mempel, T.R., Henrickson, S.E., Von Andrian, U.H.: T-cell priming by dendritic cells in lymph nodes occurs in three distinct phases. Nature 427, 154–159 (2004)

    Google Scholar 

  74. Meyers, L.A., Pourbohloul, B., Newman, M.E., Skowronski, D.M., Brunham, R.C.: Network theory and SARS: Predicting outbreak diversity. J. Theor. Biol. 232, 71–81 (2005)

    MathSciNet  Google Scholar 

  75. Mielke, A., Pandey, R.B.: A computer simulation study of cell population in a fuzzy interaction model for mutating HIV. Physica A 251, 430–438 (1998)

    Google Scholar 

  76. Miller, S.E., Levenson, R.M., Aldridge, C., Hester, S., Kenan, D.J., Howell, D.N.: Identification of focal viral infections by confocal microscopy for subsequent ultrastructural analysis. Ultrastruct. Pathol. 21, 183–193 (1997)

    Google Scholar 

  77. Miller, M.J., Wei, S.H., Parker, I., Cahalan, M.D.: Two-photon imaging of lymphocyte motility and antigen response in intact lymph node. Science 296, 1869–1873 (2002)

    Google Scholar 

  78. Miller, M.J., Wei, S.H., Cahalan, M.D., Parker, I.: Autonomous T cell trafficking examined in vivo with intravital two-photon microscopy. Proc. Natl. Acad. Sci. U.S.A. 100, 2604–2609 (2003)

    Google Scholar 

  79. Miller, M.J., Hejazi, A.S., Wei, S.H., Cahalan, M.D., Parker, I.: T cell repertoire scanning is promoted by dynamic dendritic cell behavior and random T cell motility in the lymph node. Proc. Natl. Acad. Sci. U.S.A. 101, 998–1003 (2004)

    Google Scholar 

  80. Miller, M.J., Safrina, O., Parker, I., Cahalan, M.D.: Imaging the single cell dynamics of CD4+ T cell activation by dendritic cells in lymph nodes. J. Exp. Med. 200, 847–856 (2004)

    Google Scholar 

  81. Miller, C.J., Li, Q., Abel, K., Kim, E.Y., Ma, Z.M., Wietgrefe, S., La Franco-Scheuch, L., Compton, L., Duan, L., Shore, M.D., Zupancic, M., Busch, M., Carlis, J., Wolinsky, S., Wolinksy, S., Haase, A.T.: Propagation and dissemination of infection after vaginal transmission of simian immunodeficiency virus. J. Virol. 79, 9217–9227 (2005)

    Google Scholar 

  82. Mohri, H., Bonhoeffer, S., Monard, S., Perelson, A.S., Ho, D.D.: Rapid turnover of T lymphocytes in SIV-infected rhesus macaques. Science 279, 1223–1227 (1998)

    Google Scholar 

  83. Mohri, H., Perelson, A.S., Tung, K., Ribeiro, R.M., Ramratnam, B., Markowitz, M., Kost, R., Hurley, A., Weinberger, L., Cesar, D., Hellerstein, M.K., Ho, D.D.: Increased turnover of T lymphocytes in HIV-1 infection and its reduction by antiretroviral therapy. J. Exp. Med. 194, 1277–1287 (2001)

    Google Scholar 

  84. Mueller, S.N., Germain, R.N.: Stromal cell contributions to the homeostasis and functionality of the immune system. Nat. Rev. Immunol. 9, 618–629 (2009)

    Google Scholar 

  85. Müller, V., Maree, A.F., De Boer, R.J.: Release of virus from lymphoid tissue affects human immunodeficiency virus type 1 and hepatitis C virus kinetics in the blood. J. Virol. 75, 2597–2603 (2001)

    Google Scholar 

  86. Nelson, P.W., Gilchrist, M.A., Coombs, D., Hyman, J.M., Perelson, A.S.: An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. Math. Biosci. Eng. 1, 267–288 (2004)

    MathSciNet  MATH  Google Scholar 

  87. Neumann, A.U., Lam, N.P., Dahari, H., Gretch, D.R., Wiley, T.E., Layden, T.J., Perelson, A.S.: Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science 282, 103–107 (1998)

    Google Scholar 

  88. Newman, M.E.: Threshold effects for two pathogens spreading on a network. Phys. Rev. Lett. 95, 108701 (2005)

    Google Scholar 

  89. Nowak, M.A., Bangham, C.R.: Population dynamics of immune responses to persistent viruses. Science 272, 74–79 (1996)

    Google Scholar 

  90. Nowak, M.A., May, R.M.: Mathematical biology of HIV infections: Antigenic variation and diversity threshold. Math. Biosci. 106, 1–21 (1991)

    MATH  Google Scholar 

  91. Nowak, M.A., May, R.M.: Virus dynamics: Mathematical Principles of Immunology and Virology. Oxford University Press, Oxford (2000)

    MATH  Google Scholar 

  92. Nowak, M.A., Anderson, R.M., McLean, A.R., Wolfs, T.F., Goudsmit, J., May, R.M.: Antigenic diversity thresholds and the development of AIDS. Science 254, 963–969 (1991)

    Google Scholar 

  93. Nowak, M.A., Bonhoeffer, S., Hill, A.M., Boehme, R., Thomas, H.C., McDade, H.: Viral dynamics in hepatitis B virus infection. Proc. Natl. Acad. Sci. U.S.A. 93, 4398–4402 (1996)

    Google Scholar 

  94. Ostrowski, M.A., Krakauer, D.C., Li, Y., Justement, S.J., Learn, G., Ehler, L.A., Stanley, S.K., Nowak, M., Fauci, A.S.: Effect of immune activation on the dynamics of human immunodeficiency virus replication and on the distribution of viral quasispecies. J. Virol. 72, 7772–7784 (1998)

    Google Scholar 

  95. Ovaskainen, O., Cornell, S.J.: Asymptotically exact analysis of stochastic metapopulation dynamics with explicit spatial structure. Theor. Popul. Biol. 69, 13–33 (2006)

    MATH  Google Scholar 

  96. Pandey, R.B.: Cellular automata approach to interacting cellular network models for the dynamics of cell population in an early HIV infection. Physica A 179, 442–470 (1991)

    Google Scholar 

  97. Pandey, R.B., Stauffer, D.: Metastability with probabilistic cellular automata in an HIV infection. J. Stat. Phys. 61, 235–240 (1990)

    Google Scholar 

  98. Pantaleo, G., Graziosi, C., Fauci, A.S.: The role of lymphoid organs in the pathogenesis of HIV infection. Semin. Immunol. 5, 157–163 (1993)

    Google Scholar 

  99. Pappalardo, F., Halling-Brown, M.D., Rapin, N., Zhang, P., Alemani, D., Emerson, A., Paci, P., Duroux, P., Pennisi, M., Palladini, A., Miotto, O., Churchill, D., Rossi, E., Shepherd, A.J., Moss, D.S., Castiglione, F., Bernaschi, M., Lefranc, M.P., Brunak, S., Motta, S., Lollini, P.L., Basford, K.E., Brusic, V.: ImmunoGrid, an integrative environment for large-scale simulation of the immune system for vaccine discovery, design and optimization. Brief. Bioinformatics 10, 330–340 (2009)

    Google Scholar 

  100. Pearson, J.E., Krapivsky, P., Perelson, A.S.: Stochastic theory of early viral infection: Continuous versus burst production of virions. PLoS Comput. Biol. 7, e1001058 (2011)

    MathSciNet  Google Scholar 

  101. Perelson, A.S.: Modelling viral and immune system dynamics. Nat. Rev. Immunol. 2, 28–36 (2002)

    Google Scholar 

  102. Perelson, A.S., Ribeiro, R.M.: Estimating drug efficacy and viral dynamic parameters: HIV and HCV. Stat. Med. 27, 4647–4657 (2008)

    MathSciNet  Google Scholar 

  103. Perelson, A.S., Kirschner, D.E., De Boer, R.: Dynamics of HIV infection of CD4+ T cells. Math. Biosci. 114, 81–125 (1993)

    MATH  Google Scholar 

  104. Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M., Ho, D.D.: HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time. Science 271, 1582–1586 (1996)

    Google Scholar 

  105. Perelson, A.S., Essunger, P., Cao, Y., Vesanen, M., Hurley, A., Saksela, K., Markowitz, M., Ho, D.D.: Decay characteristics of HIV-1-infected compartments during combination therapy. Nature 387, 188–191 (1997)

    Google Scholar 

  106. Phee, H., Dzhagalov, I., Mollenauer, M., Wang, Y., Irvine, D.J., Robey, E., Weiss, A.: Regulation of thymocyte positive selection and motility by GIT2. Nat. Immunol. 11, 503–511 (2010)

    Google Scholar 

  107. Picker, L.J., Watkins, D.I.: HIV pathogenesis: The first cut is the deepest. Nat. Immunol. 6, 430–432 (2005)

    Google Scholar 

  108. Pope, M., Haase, A.T.: Transmission, acute HIV-1 infection and the quest for strategies to prevent infection. Nat. Med. 9, 847–852 (2003)

    Google Scholar 

  109. Ramratnam, B., Bonhoeffer, S., Binley, J., Hurley, A., Zhang, L., Mittler, J.E., Markowitz, M., Moore, J.P., Perelson, A.S., Ho, D.D.: Rapid production and clearance of HIV-1 and hepatitis C virus assessed by large volume plasma apheresis. Lancet 354, 1782–1785 (1999)

    Google Scholar 

  110. Reilly, C., Wietgrefe, S., Sedgewick, G., Haase, A.: Determination of simian immunodeficiency virus production by infected activated and resting cells. AIDS 21, 163–168 (2007)

    Google Scholar 

  111. Ribeiro, R.M., Mohri, H., Ho, D.D., Perelson, A.S.: In vivo dynamics of T cell activation, proliferation and death in HIV-1 infection: Why are CD4+ but not CD8+ T cells depleted? Proc. Natl. Acad. Sci. U.S.A. 99, 15572–15577 (2002)

    Google Scholar 

  112. Salazar-Gonzalez, J.F., Salazar, M.G., Keele, B.F., Learn, G.H., Giorgi, E.E., Li, H., Decker, J.M., Wang, S., Baalwa, J., Kraus, M.H., Parrish, N.F., Shaw, K.S., Guffey, M.B., Bar, K.J., Davis, K.L., Ochsenbauer-Jambor, C., Kappes, J.C., Saag, M.S., Cohen, M.S., Mulenga, J., Derdeyn, C.A., Allen, S., Hunter, E., Markowitz, M., Hraber, P., Perelson, A.S., Bhattacharya, T., Haynes, B.F., Korber, B.T., Hahn, B.H., Shaw, G.M.: Genetic identity, biological phenotype, and evolutionary pathways of transmitted/founder viruses in acute and early HIV-1 infection. J. Exp. Med. 206, 1273–1289 (2009)

    Google Scholar 

  113. Sato, H., Orenstein, J., Dimitrov, D., Martin, M.: Cell-to-cell spread of HIV-1 occurs within minutes and may not involve the participation of virus particles. Virology 186, 712–724 (1992)

    Google Scholar 

  114. Sattentau, Q.: Avoiding the void: Cell-to-cell spread of human viruses. Nat. Rev. Microbiol. 6, 815–826 (2008)

    Google Scholar 

  115. Schacker, T., Little, S., Connick, E., Gebhard-Mitchell, K., Zhang, Z.Q., Krieger, J., Pryor, J., Havlir, D., Wong, J.K., Richman, D., Corey, L., Haase, A.T.: Rapid accumulation of human immunodeficiency virus (HIV) in lymphatic tissue reservoirs during acute and early HIV infection: Implications for timing of antiretroviral therapy. J. Infect. Dis. 181, 354–357 (2000)

    Google Scholar 

  116. Schacker, T., Little, S., Connick, E., Gebhard, K., Zhang, Z.Q., Krieger, J., Pryor, J., Havlir, D., Wong, J.K., Schooley, R.T., Richman, D., Corey, L., Haase, A.T.: Productive infection of T cells in lymphoid tissues during primary and early human immunodeficiency virus infection. J. Infect. Dis. 183, 555–562 (2001)

    Google Scholar 

  117. Sourisseau, M., Sol-Foulon, N., Porrot, F., Blanchet, F., Schwartz, O.: Inefficient human immunodeficiency virus replication in mobile lymphocytes. J. Virol. 81, 1000–1012 (2007)

    Google Scholar 

  118. Sowinski, S., Jolly, C., Berninghausen, O., Purbhoo, M.A., Chauveau, A., Kohler, K., Oddos, S., Eissmann, P., Brodsky, F.M., Hopkins, C., Onfelt, B., Sattentau, Q., Davis, D.M.: Membrane nanotubes physically connect T cells over long distances presenting a novel route for HIV-1 transmission. Nat. Cell Biol. 10, 211–219 (2008)

    Google Scholar 

  119. Stoll, S., Delon, J., Brotz, T.M., Germain, R.N.: Dynamic imaging of T cell-dendritic cell interactions in lymph nodes. Science 296, 1873–1876 (2002)

    Google Scholar 

  120. Strain, M.C., Richman, D.D., Wong, J.K., Levine, H.: Spatiotemporal dynamics of HIV propagation. J. Theor. Biol. 218, 85–96 (2002)

    MathSciNet  Google Scholar 

  121. Tilman, D., Kareiva, P.: Spatial Ecology. Princeton University Press, Princeton, NJ (1997)

    Google Scholar 

  122. Virgin, H.W., Walker, B.D.: Immunology and the elusive AIDS vaccine. Nature 464, 224–231 (2010)

    Google Scholar 

  123. von Neumann, J., Burks, A.W.: Theory of Self Reproducing Cellular Automata. University of Illinois Press, Urbana and London (1966)

    Google Scholar 

  124. Webb, S.D., Keeling, M.J., Boots, M.: Host-parasite interactions between the local and the mean-field: How and when does spatial population structure matter? J. Theor. Biol. 249, 140–152 (2007)

    MathSciNet  Google Scholar 

  125. Wei, X., Ghosh, S.K., Taylor, M.E., Johnson, V.A., Emini, E.A., Deutsch, P., Lifson, J.D., Bonhoeffer, S., Nowak, M.A., Hahn, B.H.: Viral dynamics in human immunodeficiency virus type 1 infection. Nature 373, 117–122 (1995)

    Google Scholar 

  126. Wolfram, S.: Theory and applications of cellular automata. Advanced Series on Complex Systems. World Scientific Publication, Singapore (1986)

    MATH  Google Scholar 

  127. Zhang, L., Dailey, P.J., He, T., Gettie, A., Bonhoeffer, S., Perelson, A.S., Ho, D.D.: Rapid clearance of simian immunodeficiency virus particles from plasma of rhesus macaques. J. Virol. 73, 855–860 (1999)

    Google Scholar 

  128. Zhang, L., Dailey, P.J., Gettie, A., Blanchard, J., Ho, D.D.: The liver is a major organ for clearing simian immunodeficiency virus in rhesus monkeys. J. Virol. 76, 5271–5273 (2002)

    Google Scholar 

  129. Zhu, P., Chertova, E., Bess, J., Lifson, J.D., Arthur, L.O., Liu, J., Taylor, K.A., Roux, K.H.: Electron tomography analysis of envelope glycoprotein trimers on HIV and simian immunodeficiency virus virions. Proc. Natl. Acad. Sci. U.S.A. 100, 15812–15817 (2003)

    Google Scholar 

  130. Zorzenon dos Santos, R.M., Coutinho, S.: Dynamics of HIV infection: A cellular automata approach. Phys. Rev. Lett. 87, 168102 (2001)

    Google Scholar 

Download references

Acknowledgements

Portions of this work were done under the auspices of the U.S. Department of Energy under contract DE-AC52-06NA25396 and supported by the Center for HIV/AIDS Vaccine Immunology and NIH grants AI028433 and OD010095.

Author information

Authors and Affiliations

  1. Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Frederik Graw & Alan S. Perelson

Authors
  1. Frederik Graw
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan S. Perelson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alan S. Perelson .

Editor information

Editors and Affiliations

  1. , Mathematics and Statistics, Southern Illinois University Edwardsvill, Edwardsville, 62026, Illinois, USA

    Urszula Ledzewicz

  2. , Electrical and Systems Engineering, Washington University, Brookings Drive 1, Saint Louis, 63130, Missouri, USA

    Heinz Schättler

  3. Mathematical Biosciences Institute, Ohio State University, W. 18th Avenue 231, Columbus, 43210-1292, Ohio, USA

    Avner Friedman

  4. Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Eugene Kashdan

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Graw, F., Perelson, A.S. (2013). Spatial Aspects of HIV Infection. In: Ledzewicz, U., Schättler, H., Friedman, A., Kashdan, E. (eds) Mathematical Methods and Models in Biomedicine. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4178-6_1

Download citation

Publish with us

Policies and ethics

Search

Navigation