Dynamics of HIV infection of CD4\(^ +\) T cells. (English) Zbl 0796.92016

Perelson, Alan S.; Kirschner, Denise E.; de Boer, Rob

Math. Biosci. 114, No. 1, 81-125 (1993).

The paper examines a model for the interaction of HIV with \(\text{CD4}^ +\) T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The proposed dynamical model for T-cell depletion due to HIV infection: (a) does not account for the immune response to HIV infection or mechanisms of cell death other than direct HIV-mediating killing, (b) proves that HIV by itself can cause partial \(\text{CD4}^ +\) T-cell depletion in the face of normal T-cell replenishment, and (c) demonstrates that the loss of T cells can take place on a time scale of years, as it is characteristic of the disease process in most HIV-infected individuals.
The model exhibits two steady states, an uninfected state in which no virus is present, and an endemically infected state, in which virus and infected T cells are present. The dynamic behaviour of these steady states is examined by differential equations and numerical analysis techniques.

Reviewer: S.Curteanu (Iaşi)

MSC:

92C60	Medical epidemiology
92C50	Medical applications (general)

Keywords:

dynamics of HIV infection; T-cell depletion; immune response; T-cell replenishment; differential equations; numerical analysis

References:

[1]	Abo, T.; Kawate, T.; Itoh, K.; Kumagai, K., Studies on the bioperiodicity of the immune response. I. Circadian rhythms of human T, B, and K cell traffic in the peripheral blood, J. Immunol., 126, 1360-1363 (1981)
[2]	Albert, J.; Abrahamsson, B.; Nagy, K.; Aurelius, E.; Gaines, H.; Nyström, G.; Fenyö, E. M., Rapid development of isolate-specific neutralizing antibodies and consequent emergence of virus variants which resist neutralization by autologous sera, AIDS, 4, 107-112 (1990)
[3]	Anderson, R. M., Mathematical and statistical studies of the epidemiology of HIV, AIDS, 3, 333-346 (1989)
[4]	Anderson, R. M.; May, R. M., Complex dynamical behavior in the interaction between HIV and the immune system, (Goldbeter, A., Cell to Cell Signalling: From Experiments to Theoretical Models (1989), Academic: Academic New York), 335-349
[5]	Åsjö, B.; Morfeldt-Måanson, L.; Albert, J.; Biberfeld, G.; Karlsson, A.; Lidman, K.; Fenyö, E. M., Replicative capacity of human immunodeficiency virus from patients with varying severity of infection, Lancet, ii, 660-662 (1986)
[6]	Cheng-Mayer, C.; Seto, D.; Tateno, M.; Levy, J. A., Biologic features of HIV-1 that correlate with virulence in the host, Science, 240, 80-82 (1988)
[7]	Cooper, L. N., Theory of an immune system retrovirus, Proc. Natl. Acad. Sci. U.S.A., 83, 9159-9163 (1986)
[8]	De Boer, R. J., GRIND: Great Integrator of Differential Equations (1983), Bioinformatics Group, Univ. Utrecht: Bioinformatics Group, Univ. Utrecht The Netherlands
[9]	Doedel, E. J., AUTO: a program for the bifurcation analysis of autonomous systems, Cong. Num., 30, 265-285 (1981)
[10]	Dolez̆al, J.; Hraba, T., Application of the mathematical model of immunological tolerance to HIV infection, Folio Biol. (Praha), 34, 336-341 (1988)
[11]	Edelman, A. S.; Zolla-Pazner, S., AIDS: a syndrome of immune dysregulation, dysfunction, and deficiency, FASEB J., 3, 22-30 (1989)
[12]	Eisen, H. N., Immunology (1980), Harper and Row: Harper and Row Hagerstown, Md
[13]	Fauci, A. S., Current issues in developing a strategy for dealing with the acquired immunodeficiency syndrome, Proc. Natl. Acad. Sci. U.S.A., 83, 9278-9283 (1986)
[14]	Fauci, A. S., The human immunodeficiency virus: infectivity and mechanisms of pathogenesis, Science, 239, 617-622 (1988)
[15]	Fenyö, E. M.; Morfeldt-Måanson, L.; Chiodi, F.; Lind, B.; v Grerfelt, A.; Albert, J.; Olausson, E.; Åsjö, B., Distinct replicative and cytopathic characteristics of human immunodeficiency virus isolates, J. Virol., 62, 4414-4419 (1988)
[16]	Fletcher, J. E.; Shrager, R. I.; Bailey, J. J., A kinetic model of T-lymphocyte interactions with HIV (1988), Preprint
[17]	Folks, T.; Kelly, J.; Benn, S.; Kinter, A.; Justement, J.; Gold, J.; Redfield, R.; Sell, K. W.; Fauci, A. S., Susceptibility of normal human lymphocytes to infection with HTLV-III/LAV, J. Immunol., 136, 4049-4053 (1986)
[18]	Freitas, A. A.; Rocha, B.; Coutinho, A. A., Lymphocyte population kinetics in the mouse, Immunol. Rev., 91, 5-37 (1986)
[19]	Gelderblom, H. R.; Hausmann, E. H.S.; Özel, M.; Pauli, G.; Koch, M. A., Fine structure of human immunodeficiency virus (HIV) and immunolocalization of structural proteins, Virology, 156, 171-176 (1987)
[20]	Goedert, J. J.; Biggar, R. J.; Melbye, M.; Mann, D. L.; Wilson, S.; Gail, M. H.; Grossman, R. J.; DiGioia, R. A.; Sanchez, W. C.; Weiss, S. H.; Blattner, W. A., Effect of T4 count and cofactors on the incidence of AIDS in homosexual men infected with human immunodeficiency virus, JAMA, 257, 331-334 (1987)
[21]	Gowda, S. D.; Stein, B. S.; Mohagheghpour, N.; Benike, C. J.; Engleman, E. G., Evidence that T cell activation is required for HIV-1 entry in CD \(4^+\) lymphocytes, J. Immunol., 142, 773-780 (1989)
[22]	Gray, D., T cell and B cell memory are short lived in the absence of antigen, J. Cell. Biochem. (1989), Suppl. 13A: C010
[23]	Gray, D.; Leanderson, T., Expansion, selection and maintenance of memory B cell clones, Curr. Topics Microbiol. Immunol., 159, 1-17 (1990)
[24]	Harper, M. E.; Marselle, L. M.; Gallo, R. C.; Wong-Stall, F., Detection of lymphocytes expressing human T-lymphotropic virus type III in lymph nodes and peripheral blood from infected individuals by in situ hybridization, Proc. Natl. Acad. Sci. U.S.A., 83, 772-776 (1986)
[25]	Hethcote, H. W.; Yorke, J. A., Gonerrhea Transmission Dynamics and Control, (Lect. Notes Biomath., Vol. 56 (1984), Springer-Verlag: Springer-Verlag New York)
[26]	Ho, D. D.; Pomerantz, R. J.; Kaplan, J. C., Pathogenesis of infection with human immunodeficiency virus, N. Engl. J. Med., 317, 278 (1987)
[27]	Hoxie, J. A.; Alpers, J. D.; Rackowski, J. L.; Huebner, K.; Haggarty, B. S.; Cedarbaum, A. J.; Reed, J. C., Alterations in T4 (CD4) protein and mRNA synthesis in cells infected with HIV, Science, 234, 1123-1127 (1986)
[28]	Hraba, T.; Dolez̆al, J., Mathematical model of CD \(4^+\) lymphocyte depletion in HIV infection, Folio Biol. (Praha), 35, 156-163 (1989)
[29]	Hraba, T.; Dolez̆al, J.; C̆elikovsky, S., Model-based analysis of CD \(4^+\) lymphocyte dynamics in HIV infected individuals, Immunibology, 181, 108-118 (1990)
[30]	Intrator, N.; Deocampo, G. P.; Cooper, L. N., Analysis of immune system retrovirus equations, (Perelson, A. S., Theoretical Immunology (1988), Addison-Wesley: Addison-Wesley Redwood City, Calif), 85-100, Part 2
[31]	Kiernan, R.; Marshall, J.; Bowers, R.; Doherty, R.; McPhee, D., Kinetics of HIV-1 replication and intracellular accumulation of particles in HTLV-1 transformed cells, AIDS Res. Hum. Retrovirus, 6, 743-752 (1990)
[32]	Lajmanovich, A.; Yorke, J. A., A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci., 28, 221-236 (1976) · Zbl 0344.92016
[33]	Lane, H. C.; Fauci, A. S., Immunologic abnormalities in the acquired immunodeficiency syndrome, Ann. Rev. Immunol., 3, 477-500 (1985)
[34]	Lane, H. C.; Fauci, A. S., Infectious complications of AIDS, (Broder, S., AIDS: Modern Concepts and Therapeutic Challenges (1987), Marcel Dekker: Marcel Dekker New York), 185-203
[35]	Larder, B. A.; Darby, G.; Richman, D. D., HIV with reduced sensitivity to zidovudine (AZT) isolated during prolonged therapy, Science, 243, 1731-1734 (1989)
[36]	Layne, S. P.; Spouge, J. L.; Dembo, M., Quantifying the infectivity of HIV, Proc. Natl. Acad. Sci. U.S.A., 86, 4644-4648 (1989)
[37]	Leonard, R.; Zagury, D.; Desportes, I.; Bernard, J.; Zagury, J.-F.; Gallo, R. C., Cytopathic effect of human immunodeficiency virus in T4 cells is linked to the last stage of virus infection, Proc. Natl. Acad. Sci. U.S.A., 85, 3570-3574 (1988)
[38]	McLean, A., HIV infection from an ecological viewpoint, (Perelson, A. S., Theoretical Immunology (1988), Addison-Wesley: Addison-Wesley Redwood City, Calif), 77-84, Part 2
[39]	McLean, A. R.; Kirkwood, T. B.L., A model of human immunodeficiency virus infection in T helper cell clones, J. Theor. Biol., 147, 177-203 (1990)
[40]	Malone, J. L.; Simms, T. E.; Gray, G. C.; Wagner, K. F.; Burge, J. R.; Burke, D. S., Sources of variability in repeated T-helper lymphocyte counts from human immunodeficiency virus type 1-infected patients: total lymphocyte count fluctuations and diurnal cycle are important, J. AIDS, 3, 144-151 (1990)
[41]	Margolick, J. B.; Volkman, D. J.; Folks, T. M.; Fauci, A. S., Amplification of HTLV-III/LAV infection by antigen-induced activation of T cells and direct suppression by virus of lymphocyte blastogenic responses, J. Immunol., 138, 1719-1723 (1987)
[42]	Merrill, S., AIDS: background and the dynamics of the decline of immunocompetence, (Perelson, A. S., Theoretical Immunology (1987), Addison-Wesley: Addison-Wesley Redwood City, Calif), 59-75, Part 2
[43]	Merrill, S., Modeling the interaction of HIV with cells of the immune response, (Castillo-Chavez, C., Mathematical and Statistical Approaches to AIDS Epidemiology (1989), Springer-Verlag: Springer-Verlag New York), 371-385, (Lect. Notes Biomath., Vol. 83)
[44]	Murray, J. D., Mathematical Biology (1989), Springer-Verlag: Springer-Verlag New York · Zbl 0682.92001
[45]	Nara, P. L.; Smit, L.; Dunlop, N.; Hatch, W.; Merges, M.; Waters, D.; Kelliher, J.; Gallo, R. C.; Fischinger, P. J.; Goudsmit, J., Emergence of viruses resistant to neutralization by V3-specific antibodies in experimental human immunodeficiency virus type 1 IIIB infection of chimpanzees, J. Virol., 64, 3779-3791 (1990)
[46]	Nelson, G. W.; Perelson, A. S., A mechanism of immune escape by slow-replicating HIV strains, J. AIDS, 5, 82-93 (1992)
[47]	Nowak, M. A.; May, R. M., Mathematical biology of HIV infections: antigenic variation and diversity threshold, Math. Biosci., 106, 1-21 (1991) · Zbl 0738.92008
[48]	Nowak, M. A.; May, R. M.; Anderson, R. M., The evolutionary dynamics of HIV-1 quasispecies and the development of immunodeficiency disease, AIDS, 4, 1095-1103 (1990)
[49]	Perelson, A. S., Modeling the interaction of the immune system with HIV, (Castillo-Chavez, C., Mathematical and Statistical Approaches to AIDS Epidemiology (1989), Springer-Verlag: Springer-Verlag New York), 350-370, (Lect. Notes Biomath. Vol. 83)
[50]	Phillips, A.; Lee, C. A.; Elford, J.; Janossy, G.; Bofill, M.; Timms, A.; Kernoff, P. B.A., Prediction of progression to AIDS by analysis of CD4 lymphocyte counts in a haemophilic cohort, AIDS, 3, 737-741 (1989)
[51]	Psallidopoulos, M. C.; Schnittman, S. M.; Thompson, L. M.; Baseler, M.; Fauci, A. S.; Lane, H. C.; Salzman, N. P., Integrated proviral human immunodeficiency virus type 1 is present in CD \(4^+\) peripheral blood lymphocytes in healthy seropositive individuals, J. Virol., 63, 4626-4631 (1989)
[52]	Purcell, E. M., Life at low Reynolds number, Am. J. Phys., 45, 3-11 (1977)
[53]	Redfield, R. R.; Wright, D. C.; Tramont, E. C., The Walter Reed staging classification for HTLV-III/LAV infection, N. Engl. J. Med., 314, 131-132 (1986)
[54]	Reibnegger, G.; Fuchs, D.; Hausen, A.; Werner, E. R.; Dierich, M. P.; Wachter, H., Theoretical implications of cellular immune reactions against helper lymphocytes infected by an immune system retrovirus, Proc. Natl. Acad. Sci. U.S.A., 84, 7270-7274 (1987)
[55]	Schnittman, S. M.; Psallidopoulos, M. C.; Lane, H. C.; Thompson, L.; Baseler, M.; Massari, F.; Fox, C. H.; Salzman, N. P.; Fauci, A. S., The reservoir for HIV-1 in human peripheral blood is a T cell that maintains expression of CD4, Science, 245, 305-308 (1989)
[56]	Schnittman, S. M.; Greenhouse, J. J.; Psallidopoulos, M. C.; Baseler, M.; Salzman, N. P.; Fauci, A. S., Increasing viral burden in CD \(4^+\) T cells from patients with human immunodeficiency virus (HIV) infection reflects rapidly progressive immunosuppression and clinical disease, Ann. Int. Med., 113, 438-443 (1990)
[57]	Somasundaran, M.; Robinson, H. L., Unexpectedly high levels of HIV-1 RNA and protein synthesis in a cytocidal infection, Science, 242, 1554-1557 (1988)
[58]	Taylor, J. M.G.; Fahey, J. L.; Detels, R.; Giorgi, J. V., CD4 percentage, CD4 number and CD4:CD8 ratio in HIV infection: which to choose and how to use, J. AIDS, 2, 114-124 (1989)
[59]	Tersmette, M.; Gruters, R. A.; de Wolf, F.; de Goede, R. E.Y.; Lange, J. M.A.; Schellekens, P. T.A.; Goudsmit, J.; Huisman, H. G.; Miedema, F., Evidence for a role of virulent human immunodeficiency virus (HIV) variants in the pathogenesis of acquired immunodeficiency syndrome: studies on sequential HIV isolates, J. Virol., 63, 2118-2125 (1989)
[60]	Tindall, G.; Cooper, D. A., Primary HIV infection, AIDS, 5, 1-14 (1991)
[61]	Weiss, L., The Cells and Tissues of the Immune System (1972), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J
[62]	Wiggins, S., Introduction to Applied Nonlinear Dynamic Systems and Chaos (1990), Springer-Verlag: Springer-Verlag New York
[63]	Willems, J. L., Stability Theory of Dynamical Systems (1970), Wiley: Wiley New York · Zbl 0222.93010
[64]	Wu, L.; Scollay, R.; Egerton, M.; Pearse, M.; Spangrude, G. J.; Shortman, K., CD4 expressed on earliest T-lineage precursor cells in adult murine thymus, Nature, 349, 71-74 (1991)
[65]	Zack, J. A.; Arrigo, S. J.; Weitsman, S. R.; Go, A. S.; Haislip, A.; Chen, I. S.Y., HIV-1 entry into quiescent primary lymphocytes: molecular analysis reveals a labile, latent viral structure, Cell, 61, 213-222 (1990)