Skip to main content
Log in

Gene therapy of T helper cells in HIV infection: Mathematical model of the criteria for clinical effect

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

The paper presents a mathematical analysis of the criteria for gene therapy of T helper cells to have a clinical effect on HIV infection. The analysis indicates that for such a therapy to be successful, it must protect the transduced cells against HIV-induced death. The transduced cells will not survive as a population if the gene therapy only blocks the spread of virus from transduced cells that become infected. The analysis also suggests that the degree of protection against disease-related cell death provided by the gene therapy is more important than the fraction of cells that is initially transduced. If only a small fraction of the cells can be transduced, transduction of T helper cells and transduction of haematopoietic progenitor cells will result in the same steady-state level of transduced T helper cells. For gene therapy to be efficient against HIV infection, our analysis suggests that a 100% protection against viral escape must be obtained. The study also suggests that a gene therapy against HIV infection should be designed to give the transduced cells a partial but not necessarily total protection against HIV-induced cell death, and to avoid the production of viral mutants insensitive to the gene therapy.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anderson, R. and R. May. 1989. Complex dynamical behavior in the interaction between HIV and the immune system. InCell to Cell Signalling, from Experiments to Theoretical Models, A. Goldbeter (Ed), pp. 335–349. New York: Academic Press.

    Google Scholar 

  • Baltimore, D. 1988. Gene therapy: intracellular immunization.Nature 335, 395–396.

    Article  Google Scholar 

  • Blaese, R. M., K. W. Culver, A. D. Miller, C. S. Carter, T. Fleisher, M. Clerici, G. Shearer, L. Chang, Y. Chiang, P. Tolstoshev, J. J. Greenblatt, S. A. Rosenberg, H. Klein, M. Berger, C. A. Mullen, W. J. Ramsey, L. Muul, R. A. Morgan and W. F. Anderson. 1995. T lymphocyte-directed gene therapy for ADA-SCID: initial trial results after 4 years.Science 270, 475–480.

    Article  Google Scholar 

  • Bogen, K. T. 1993. Reassessment of the peripheral T-lymphocyte lifespan deduced from cytogenetic and cytotoxic effects of radiation.Int. J. Rad. Biol. 64, 195–204.

    Article  Google Scholar 

  • Bordignon, C., L. D. Notarangelo, N. Nobili, G. Ferrari, G. Casorati, P. Panina, E. Mazzolari, D. Maggioni, C. Rossi, P. Servida, A. G. Ugazio and F. Mavilio. 1995. Gene therapy in peripheral blood lymphocytes and bone marrow for ADA-immunodeficient patients.Science 270, 470–475.

    Article  Google Scholar 

  • Buckton, K. E., W. M. Court Brown and P. G. Smith. 1967. Lymphocyte survival in men treated with X-rays for ankylosing spondylitis.Nature 214, 470–473.

    Article  Google Scholar 

  • Chatterjee, S., P. Johnson and K. K. Wong, Jr. 1992. Dual-target inhibition of HIV-1 in vitro by means of an adeno-associated virus antisense vector.Science 258, 1485–1488.

    Article  Google Scholar 

  • Coffin, J. M. 1995. HIV population dynamics in vivo: implications for genetic variation, pathogenesis, and therapy.Science 267, 483–489.

    Article  Google Scholar 

  • Cohli, H., B. Fan, R. Josh, A. Ramezani, X. Li and S. Josh. 1994. Inhibition of HIV-1 multiplication in a human CD4+ lymphocytic cell line expressing antisense and sense RNA molecules containing HIV-1 packaging signal and Rev response element(s).Antisense Res. Dev. 4, 19–26.

    Google Scholar 

  • Cooper, L. N. 1986. Theory of an immune system retrovirus.Proc. Natl. Acad. Sci. U.S.A. 83, 9159–9163.

    Article  Google Scholar 

  • Crystal, R. G. 1995. Transfer of genes to humans: early lessons and obstacles to success.Science 270, 404–410.

    Article  Google Scholar 

  • De Boer, R. J. and M. C. Boerlijst. 1994. Diversity and virulence thresholds in AIDS.Proc. Natl. Acad. Sci. U.S.A. 91, 544–548.

    Article  MATH  Google Scholar 

  • De Boer, R. J. and C. A. B. Boucher. 1996. Anti-CD4 therapy for AIDS suggested by mathematical models.Proc. Roy. Soc. London Ser. B 263, 899–905.

    Article  Google Scholar 

  • De Boer, R. J. and A. S. Perelson. 1994. T cell repertoires and competitive exclusion.J. Theor. Biol. 169, 375–390.

    Article  Google Scholar 

  • De Boer, R. J. and A. S. Perelson. 1995. Towards a general function describing T cell proliferation.J. Theor. Biol. 175, 567–576.

    Article  Google Scholar 

  • De Boer, R. J. and A. S. Perelson. 1996. Ecological and Immunological models of HIV-1 latency: is HIV-1 predator or prey? Unpublished manuscript.

  • Dimitrov, D. S. and M. A. Martin. 1995. HIV results in the frame. CD4+ cell turnover (Scientific correspondence).Nature 375, 194–195.

    Article  Google Scholar 

  • Dimitrov, D. S., R. L. Willey, H. Sato, L. J. Chang, R. Blumenthal and M. A. Martin. 1993. Quantitation of human immunodeficiency virus type 1 infection kinetics.J. Virol. 67, 2182–2190.

    Google Scholar 

  • Freitas, A. A., B. Rocha and A. A. Coutinho. 1986. Lymphocyte population kinetics in the mouse.Immunol. Rev. 91, 5–37.

    Article  Google Scholar 

  • Frost, S. D. and A. R. McLean. 1994. Quasispecies dynamics and the emergence of drug resistance during zidovudine therapy of HIV infection.AIDS 8, 323–332.

    Article  Google Scholar 

  • Glanz, J. 1996. Results of new AIDS drugs bring cautious optimism (News).Science 271, 755–766.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ho, D. D., A. S. Perelson and G. M. Shaw. 1995b. HIV results in the frame. Reply (Scientific correspondence).Nature 375, 198.

    Article  Google Scholar 

  • Hope, T., N. Klein, M. Elder and T. Parslow. 1992. Trans-dominant inhibition of human immunodeficiency virus type 1 Rev occurs through formation of inactive protein complexes.J. Virol. 66, 1849–1855.

    Google Scholar 

  • Hraba, T., J. Dolezal and S. Celikovsky. 1990. Model-based analysis of CD4+lymphocyte dynamics in HIV infected individuals.Immunobiol. 181, 108–118.

    Google Scholar 

  • Kohn, D. B., K. I. Weinberg, J. A. Nolta, L. N. Heiss, C. Lenarsky, G. M. Crooks, M. E. Hanley, G. Annett, J. S. Brooks, A. el Khoureiy, K. Lawrence, S. Wells, R. C. Moen, J. Bastian, D. E. Williams-Herman, M. Elder, D. Wara, T. Bowen, M. S. Hershfield, C. A. Mullen, R. M. Blase and R. Parkman. 1995. Engraftment of gene-modified umbilical cord blood cells in neonates with adenosine deaminase deficiency.Nat. Med. 1, 1017–1023.

    Article  Google Scholar 

  • Larder, B. A., G. Darby and D. D. Richman. 1989. HIV with reduced sensitivity to zidovudine (AZT) isolated during prolonged therapy.Science 243, 1731–1734.

    Article  Google Scholar 

  • Layne, S. P., J. L. Spouge and M. Dembo. 1989. Quantifying infectivity of human immunodeficiency virus.Proc. Natl. Acad. Sci., U.S.A. 86, 4644–4648.

    Article  Google Scholar 

  • Lund, O., J. Hansen, A. M. Sørensen, E. Mosekilde, J. O. Nielsen and J.-E. Hansen. 1995. Increased adhesion as a mechanism of antibody dependent and antibody independent enhancement of human immunodeficiency virus infection.J. Virol. 69, 2393–2400.

    Google Scholar 

  • Mackall, C. L., T. A. Fleisher, R. B. Margaret, M. P. Andrich, C. C. Chen, I. M. Feuerstein, M. E. Horowitch, I. T. Magrath, A. T. Shad, S. M. Steinberg, W. L. H. Steinberg and R. E. Gress. 1995. Age, thymopoesis, and CD4+ T-lymphocyte regeneration after intensive chemotherapy.New England J. Med. 332, 143–149.

    Article  Google Scholar 

  • Mackall, C. L., L. Granger, M. A. Sheard, R. Cepeda and R. E. Gress. 1993. T-cell regeneration after bone marrow transplantation: differential CD45 isoform expression on thymic-derived versus thymic-independent progeny.Blood 82, 2585–2594.

    Google Scholar 

  • Malim, M. H., S. Böhnlein, J. Hauber and B. Cullen. 1989. Functional dissection of the HIV-1 rev trans-activator—derivation of a transdominant repressor of rev function.Cell 58, 205–214.

    Article  Google Scholar 

  • McLean, A. R., V. C. Emery, A. Webster and P. D. Griffiths. 1991. Population dynamics of HIV within an individual after treatment with zidovudine.AIDS 5, 485–489.

    Article  Google Scholar 

  • McLean, A. R. and T. B. L. Kirkwood. 1990. A model of human immunodeficiency virus infection in T helper cell clones.J. Theor. Biol. 147, 177–203.

    Article  Google Scholar 

  • McLean, A. R. and C. A. Michie. 1995. In vivo estimates of division and death rates of human T lymphocytes.Proc. Natl. Acad. Sci. U.S.A. 92, 3707–3711.

    Article  Google Scholar 

  • McLean, A. R. and M. A. Nowak. 1992. Competition between zidovudine-sensitive and zidovudine-resistant strains of HIV.AIDS 6, 71–79.

    Article  Google Scholar 

  • Moiser, D. E. 1995. HIV results in the frame. CD4+ cell turnover (Scientific correspondence).Nature 375, 193–194.

    Article  Google Scholar 

  • Nabel, G. J., B. A. Fox, L. Post, C. B. Thompson and C. Woffendin. 1994. A molecular genetic intervention for AIDS—effects of a transdominant negative form of Rev.Human Gene Therapy 5, 79–92.

    Article  Google Scholar 

  • Nowak, M. A. 1992. Variability of HIV infections.J. Theor. Biol. 155, 1–20.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Nowak, M. A., S. Bonhoeffer, C. Loveday, P. Balfe, M. Semple, S. Kaye, M. Tenant-Flowers and R. Tedder. 1995a. HIV results in the frame. Results confirmed (Scientific correspondence).Nature 375, 193.

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Nowak, M. and R. M. May. 1993. AIDS pathogenesis: mathematical models of HIV and SIV infections.AIDS 7, S3-S18, (Suppl. 1).

    Article  MathSciNet  Google Scholar 

  • Nowak, M. A., R. M. May and R. M. Anderson. 1990. The evolutionary dynamics of HIV-1 quasispecies and the development of immunodeficiency disease.AIDS 4, 1095–1103.

    Article  Google Scholar 

  • Nowak, M. A., R. M. May and K. Sigmund. 1995b. Immune responses against multiple epitopes.J. Theor. Biol. 175, 325–353.

    Article  Google Scholar 

  • Nowak, M. A. and A. J. McMichael. 1995. How HIV defeats the immune system.Sci. Amer. 273, 58–65.

    Article  Google Scholar 

  • Pantaleo, G., C. Graziosi, J. F. Demarest, L. Butini, M. Montorini, C. H. Fox, J. M. Orenstein, D. P. Kotle and A. S. Fauchi. 1993. HIV infection is active and progressive in lymphoid tissue during the clinically latent stage of disease.Nature 362, 355–358.

    Article  Google Scholar 

  • Pauza, C. D. and D. N. Streblow. 1995. Therapeutic approaches to HIV infection based on virus structure and the host pathogen interaction.Curr. Top. Microbiol. Immunol. 202, 117–132.

    Google Scholar 

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

    Article  Google Scholar 

  • Preston, B. D., B. J. Poisez and L. A. Loeb. 1988. Fidelity of HIV-1 reverse transcriptase.Science 242, 1168–1171.

    Article  Google Scholar 

  • Reibnegger, G., D. Fuchs, A. Hausen, E. R. Werner, M. P. Dierich and H. Wachter. 1987. 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.

    Article  Google Scholar 

  • Reibnegger, G., D. Fuchs, A. Hausen, E. R. Werner, G. Werner-Felmayer, M. P. Dierich and H. Wachter. 1989. Stability analysis of simple models for immune cells interacting with normal pathogens and immune system retroviruses.Proc. Natl. Acad. Sci. U.S.A. 86, 2026–2030.

    Article  Google Scholar 

  • Roberts, J. D., K. Bebenek and T. A. Kunkel. 1988. The accuracy of reverse transcriptase from HIV-1.Science 242, 1171–1173.

    Article  Google Scholar 

  • Roberts, M. R., L. Qin, D. Zhang, D. H. Smith, A.-C. Tran, T. Dull, J. E. Groopman, D. J. Capon, R. A. Byrn and M. H. Finer. 1994. Targeting of human immunodeficiency virus-infected cells by CD4+ T lymphocytes armed with universal T-cell receptors.Blood 84, 2878–2889.

    Google Scholar 

  • Sarver, N., E. M. Cantin, P. S. Chang, M. G. Agadjanyan K. Dang, A. I. Refaeli, Y. Sato, J. Boyer, W. V. Wiliams and D. B. Weiner. 1990. Ribozymes as potential anti-HIV-1 therapeutic agents.Science 247, 1222–1225.

    Article  Google Scholar 

  • Schenzle, D. 1994. A model for AIDS pathogenesis.Stat. Med. 13, 2067–2079.

    Article  Google Scholar 

  • Schick, P., F. Trepel, M. Eder, M. Matzner, S. Bennedek, H. Theml, K. Kaboth, H. Begemann and T. M. Fleidner. 1975a. Autotransfusion of 3H cytidine-labelled blood lymphocytes in patients with Hodgkin's thymidine. Disease and non Hodgkin patients I. Limitations of the method.Acta Haemat. 53, 193–205.

    Article  Google Scholar 

  • Schick, P., F. Trepel, M. Eder, M. Matzner, S. Bennedek, H. Theml, K. Kaboth, H. Begemann and T. M. Fleidner. 1975b. Autotransfusion of 3H cytidine-labelled blood lymphocytes in patients with Hodgkin's thymidine. Disease and non Hodgkin patients II. Exhangeable lymphocyte pools.Acta Haemat. 53, 206–218.

    Article  Google Scholar 

  • Sczakiel, G. and M. Pawlita. 1991. Inhibition of human immunodeficiency virus type 1 replication in human T cells stably expressing antisense RNA.J. Virol. 65, 468–472.

    Google Scholar 

  • Sidorov, I. A. and A. A. Romanyukha. 1993. Mathematical modeling of T-cell proliferation.Math. Biosci. 115, 187–232.

    Article  MATH  Google Scholar 

  • Smith, M. E. and W. L. Ford. 1983. The recirculating lymphocyte pool of the rat: a systematic description of the migatory behaviour of recirculating lymphocytes.Immunol. 49, 83–94.

    Google Scholar 

  • Sprent, J. and A. Basten. 1973. Circulating T and B lymphocytes of the mouse. II. Lifespan.Cell. Immunol. 7, 40–59.

    Article  Google Scholar 

  • Sprent, J. and D. Tough. 1995. HIV results in the frame. CD4+ cell turnover (discussion).Nature 375, 194.

    Article  Google Scholar 

  • Sprent, J. and D. F. Tough. 1994. Lymphocyte life-span and memory.Science,265, 1395–1400.

    Article  Google Scholar 

  • Stutman, O. 1986. Postthymic T-cell development.Immunol. Rev. 91, 159–194.

    Article  Google Scholar 

  • Tough, D. F. and J. Sprent. 1994. Turnover of naive- and memory-phenotype T cells.J. Exp. Med. 179, 1127–1135.

    Article  Google Scholar 

  • Trepel, F. 1974. Number and distribution of lymphocytes in man. A critical analysis.Klin. Wschr. 52, 511–515.

    Article  Google Scholar 

  • Trono, D., M. Feinberg and D. Baltimore. 1989. HIV-1 Gag mutants can dominantly interfere with the replication of the wild type virus.Cell 59, 113–120.

    Article  Google Scholar 

  • Walker, R., R. M. Blaese, C. S. Carter, L. Chang, H. Klein, H. C. Lane, S. F. Leitman, C. A. Mullen and M. Larson. 1993. A study of the safety and survival of the adoptive transfer of genetically marked syngeneic lymphocytes in HIV-infected identical twins.Human Gene Therapy 4, 659–680.

    Article  Google Scholar 

  • Walker, R., R. M. Blaese, R. T. Davey, J. Fallon, C. A. Mullen and M. A. Polis. 1996. A phase I/II pilot study of the safety of the adoptive transfer of syngeneic gene-modified cytotoxic T lymphocytes in HIV-infected identical twins.Human Gene Therapy 7, 367–400.

    Article  Google Scholar 

  • Wang, B., D. Ugen, V. Srikatan, J. A. Zaia, P. A. Ladne, D. A. Stephens and J. J. Rossi. 1993. Gene inoculation generates immune responses against HIV-1.Proc. Natl. Acad. Sci. U.S.A. 90, 4156–4160.

    Article  Google Scholar 

  • Wei, X., S. K. Ghosh, M. E. Taylor, V. A. Johnson, E. A. Emini, P. Deutsch, J. D. Lifson, S. Bonhoeffer, M. A. Nowak, M. S. Hahn, B. H. Saag and G. M. Shaw. 1995. Viral dynamics in human immunodeficiency virus type 1 infection.Nature 117–122.

  • Woffendin, C., U. Ranga, Z.-Y. Yang, L. Xu and G. J. Nabel. 1996. Expression of a protective gene prolongs survival of T cells in human immunodeficiency virus-infected patients.Proc. Natl. Acad. Sci. U.S.A. 93, 2889–2894.

    Article  Google Scholar 

  • Yamada, O., M. Yu, J. K. Yee, G. Kraus, D. Looney and F. Wong-Staal. 1994. Intracellular immunization of human T cells with a hairpin ribozyme against human immunodeficiency virus type 1.Gene Therapy 1, 38–45.

    Google Scholar 

  • Yu, M., E. Poeschla and F. Wong-Staal. 1994. Progress towards gene therapy for HIV infection.Gene Therapy 1, 13–26.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lund, O., Lund, O.S., Gram, G. et al. Gene therapy of T helper cells in HIV infection: Mathematical model of the criteria for clinical effect. Bltn Mathcal Biology 59, 725–745 (1997). https://doi.org/10.1007/BF02458427

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458427

Keywords

Navigation