Skip to main content
SpringerLink
Log in

Mathematical Models of the Role of IL-2 in the Interactions Between Helper and Regulatory CD4+ T Cells

  • Chapter
  • First Online:
Mathematical Models and Immune Cell Biology

  • 1449 Accesses

Abstract

Mathematical models for the role of IL-2 in the dynamic interplay between CD4 +  helper and regulatory T cells are studied. These models are extensions of the crossregulation model of CD4 +  T cell dynamics including IL-2 molecules. The goal is to understand how the immune system is dynamically organized, structured by this interaction with self antigens, and how such organization might determine its overall function. We consider two model variants. In the first, regulatory T cells suppress helper T cells by competing with them for IL-2 in the lymph node. The second variant adds a direct inhibition of helper T cell activation which requires their co-localized activation on the APCs. We use the models to study the impact of treatments that either sequester or inject IL-2 in the immune system response. We show that treatment sequestering IL-2 could be used in particular conditions, both to render tolerant a preexistent immune/autoimmune system or to break a preexistent tolerant state, inducing an immune response. However, IL-2 injections will always reinforce the preexistent state, further expanding either the regulatory or helper T cells for a preexistent tolerant or immune state.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 229.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Smith K (1988) A. Interleukin-2: inception, impact, and implications. Science 240:69–76

    Google Scholar 

  2. Blattman J, Grayson J, Wherry E, Kaech S, Smith K, Ahmed R (2003) Therapeutic use of IL-2 to enhance antiviral T-cell responses in vivo. Nat Med 9:540–547

    Article  PubMed  CAS  Google Scholar 

  3. Fishman M, Hunter T, Soliman H, Thompson P, Dunn M, Smilee R, Farmelo M, Noyes D, Mahany J, Lee J, et al (2008) Phase II trial of B7-1 (CD-86) transduced, cultured autologous tumor cell vaccine plus subcutaneous interleukin-2 for treatment of stage IV renal cell carcinoma. J Immunother 31:72

    Article  PubMed  Google Scholar 

  4. Kudo-Saito C, Garnett C, Wansley E, Schlom J, Hodge J (2007) Intratumoral delivery of vector mediated IL-2 in combination with vaccine results in enhanced T cell avidity and anti-tumor activity. Cancer Immunol Immunother 56:1897–1910

    Article  PubMed  CAS  Google Scholar 

  5. Lin C, Tsai Y, He L, Yeh C, Chang T, Soong Y, Monie A, Hung C, Lai C (2007) DNA vaccines encoding IL-2 linked to HPV-16 E7 antigen generate enhanced E7-specific CTL responses and antitumor activity. Immunol Lett 114:86–93

    Article  PubMed  CAS  Google Scholar 

  6. Almeida A, Legrand N, Papiernik M, Freitas A (2002) Homeostasis of peripheral CD4 +  T cells: IL-2R {alpha} and IL-2 shape a population of regulatory cells that controls CD4 +  T cell numbers. J Immunol 169:4850

    PubMed  Google Scholar 

  7. Papiernik M, do Carmo L, Pontoux C, Joret A, Rocha B, Penit C, Dy M (1997) T cell deletion induced by chronic infection with mouse mammary tumor virus spares a CD25-positive, IL-10-producing T cell population with infectious capacity. J Immunol 158:4642

    Google Scholar 

  8. Thornton A, Shevach E (1998) CD4 + CD25 +  immunoregulatory T cells suppress polyclonal T cell activation in vitro by inhibiting interleukin 2 production. J Exp Med 188:287

    Article  PubMed  CAS  Google Scholar 

  9. Thornton A, Donovan E, Piccirillo C, Shevach E (2004) Cutting edge: IL-2 is critically required for the in vitro activation of CD4 + CD25 +  T cell suppressor function. J Immunol 172:6519

    PubMed  CAS  Google Scholar 

  10. Takahashi T, Kuniyasu Y, Toda M, Sakaguchi N, Itoh M, Iwata M, Shimizu J, Sakaguchi S (1998) Immunologic self-tolerance maintained by CD25 + CD4 +  naturally anergic and suppressive T cells: induction of autoimmune disease by breaking their anergic/suppressive state. Int Immunol 10:1969

    Article  PubMed  CAS  Google Scholar 

  11. Ahmadzadeh M, Rosenberg S (2006) IL-2 administration increases CD4 + CD25hiFoxp3 +  regulatory T cells in cancer patients. Blood 107:2409

    Article  PubMed  CAS  Google Scholar 

  12. Sereti I, Imamichi H, Natarajan V, Imamichi T, Ramchandani M, Badralmaa Y, Berg S, Metcalf J, Hahn B, Shen J, Powers A, Davey R, Kovacs J, Shevach E, Lane H (2005) In vivo expansion of CD4CD45RO − CD25 +  T cells expressing foxP3 in IL-2-treated HIV-infected patients. J Clin Investig 115:1839–1847

    Article  PubMed  CAS  Google Scholar 

  13. Kamimura D, Sawa Y, Sato M, Agung E, Hirano T, Murakami M (2006) IL-2 in vivo activities and antitumor efficacy enhanced by an anti-IL-2 mAb. J Immunol 177:306

    PubMed  CAS  Google Scholar 

  14. Smith K (2006) The structure of IL-2 bound to the three chains of the IL-2 receptor and how signaling occurs. Med Immunol 5:3

    Article  PubMed  Google Scholar 

  15. Bodnár A, Nizsalóczki E, Mocsár G, Szalóki N, Waldmann T, Damjanovich S, Vámosi, G (2008) A biophysical approach to IL-2 and IL-15 receptor function: Localization, conformation and interactions. Immunol Lett

    Google Scholar 

  16. Wofsy C, Goldstein B (1992) Interpretation of Scatchard plots for aggregating receptor systems. Math Biosci 112:115

    Article  PubMed  CAS  Google Scholar 

  17. Goldstein B, Jones D, Kevrekidis I, Perelson A (1992) Evidence for p55 p75 heterodimers in the absence of IL-2 from Scatchard plot analysis. Int Immunol 4:23

    Article  PubMed  CAS  Google Scholar 

  18. Fallon E, Lauffenburger D (2000) Computational model for effects of ligand/receptor binding properties on interleukin-2 trafficking dynamics and T cell proliferation response. Biotechnol Prog 16:905–916

    Article  PubMed  CAS  Google Scholar 

  19. Fallon E, Liparoto S, Lee K, Ciardelli T, Lauffenburger D (2000) Increased endosomal sorting of ligand to recycling enhances potency of an interleukin-2 analog. J Biol Chem 275:6790

    Article  PubMed  CAS  Google Scholar 

  20. Rao B, Driver I, Lauffenburger D, Wittrup K (2004) Interleukin 2 (IL-2) Variants engineered for increased IL-2 receptor {alpha}-subunit affinity exhibit increased potency arising from a cell surface ligand reservoir effect. Mol Pharmacol 66:864

    PubMed  CAS  Google Scholar 

  21. Svirshchevskaya E, Sidorov I, Viskova N, Dozmorov I (1993) Quantitative analysis of interleukin-2-induced proliferation in the presence of inhibitors using a mathematical model. J Immunol Methods 159:17

    Article  PubMed  CAS  Google Scholar 

  22. Borisova L, Kuznetsov V (1997) A mathematical model of T lymphocyte proliferation controlled by interleukin-2 internalization. Membrane Cell Biol 11:259

    CAS  Google Scholar 

  23. Borisova L, Andreev S, Kuznetsov V Kinetics of T cell proliferation: a mathematical model and data analysis. Membrane Cell Biol 12:111

    Google Scholar 

  24. Morel B, Burke M, Kalagnanam J, McCarthy S, Tweardy D, Morel P (1996) Making sense of the combined effect of interleukin-2 and interleukin-4 on lymphocytes using a mathematical model. Bull Math Biol 58:569–594

    Article  PubMed  CAS  Google Scholar 

  25. De Boer R, Ganusov V, Milutinović D, Hodgkin P, Perelson A (2006) Estimating lymphocyte division and death rates from CFSE data. Bull Math Biol 68:1011–1031

    Article  PubMed  Google Scholar 

  26. Burroughs N, Miguel Paz Mendes de Oliveira B, Adrego Pinto A (2006) Regulatory T cell adjustment of quorum growth thresholds and the control of local immune responses. J Theor Biol 241:134–141

    Article  PubMed  CAS  Google Scholar 

  27. Carneiro J, Leon K, Caramalho Í, van den Dool C, Gardner R, Oliveira V, Bergman M, Sepúlveda N, Paixão T, Faro J, et al (2007) When three is not a crowd: a crossregulation model of the dynamics and repertoire selection of regulatory CD4 T cells. Immunol Rev 216:48–68

    PubMed  Google Scholar 

  28. Leon K, Perez R, Lage A, Carneiro J (2000) Modelling T-cell-mediated suppression dependent on interactions in multicellular conjugates. J Theor Biol 207:231–254

    Article  PubMed  CAS  Google Scholar 

  29. García-Martínez K, León K (2009) Modeling the role of IL-2 in the interplay between CD4 +  helper and regulatory T cells: assessing general dynamical properties. J Theor Biol

    Google Scholar 

  30. de la Rosa M, Rutz S, Dorninger H, Scheffold A (2004) Interleukin-2 is essential for CD4 + CD25 +  regulatory T cell function. Eur J Immunol 34:2480–2488

    Article  PubMed  Google Scholar 

  31. Scheffold A, Huhn J, Hofer T (2005) Regulation of CD4 + CD25 +  regulatory T cell activity: it takes (IL-) two to tango. Eur J Immunol 35:1336–1341

    Article  PubMed  CAS  Google Scholar 

  32. Taams L, Van Rensen A, Poelen M, Van Els C, Besseling A, Wagenaar J, van Eden W, Wauben M (1998) Anergic T cells actively suppress T cell responses via the antigen-presenting cell. Eur J Immunol 28:2902–2912

    Article  PubMed  CAS  Google Scholar 

  33. Cederbom L, Hall H, Ivars F (2000) CD4 + CD25 +  regulatory T cells down-regulate co-stimulatory molecules on antigen-presenting cells. Eur J Immunol 30:1538–1543

    Article  PubMed  CAS  Google Scholar 

  34. Tang Q, Adams J, Tooley A, Bi M, Fife B, Serra P, Santamaria P, Locksley R, Krummel M, Bluestone J (2006) Visualizing regulatory T cell control of autoimmune responses in nonobese diabetic mice. Nat Immunol 7:83–92

    Article  PubMed  CAS  Google Scholar 

  35. Smith K (2005) Determining to divide: how do cells decide? J Biol Phys 31:261–272

    Article  Google Scholar 

  36. Barthlott T, Moncrieffe H, Veldhoen M, Atkins C, Christensen J, O’Garra A, Stockinger B (2005) CD25 + CD4 +  T cells compete with naive CD4 +  T cells for IL-2 and exploit it for the induction of IL-10 production. Int Immunol 17:279

    Article  PubMed  CAS  Google Scholar 

  37. Almeida A, Zaragoza B, Freitas A (2006) Indexation as a novel mechanism of lymphocyte homeostasis: the number of CD4 + CD25 +  regulatory T cells is indexed to the number of IL-2-producing cells. J Immunol 177:192

    PubMed  CAS  Google Scholar 

  38. Horak I (1995) Immunodeficiency in IL-2-knockout mice. Clin Immunol Immunopathol 76:172–173

    Article  Google Scholar 

  39. Sadlack B, Merz H, Schorle H, Schimpl A, Feller A, Horak I (1993) Ulcerative colitis-like disease in mice with a disrupted interleukin-2 gene. Cell 75:253–261

    Article  PubMed  CAS  Google Scholar 

  40. Peschon J, Morrissey P, Grabstein K, Ramsdell F, Maraskovsky E, Gliniak B, Park L, Ziegler S, Williams D, Ware C (1994) Early lymphocyte expansion is severely impaired in interleukin 7 receptor-deficient mice. J Exp Med 180:1955

    Article  PubMed  CAS  Google Scholar 

  41. von Freeden-Jeffry U, Vieira P, Lucian L, McNeil T, Burdach S, Murray R (1995) Lymphopenia in interleukin (IL)-7 gene-deleted mice identifies IL-7 as a nonredundant cytokine. J Exp Med 181:1519

    Article  Google Scholar 

  42. Purton J, Tan J, Rubinstein M, Kim D, Sprent J, Surh C (2007) Antiviral CD4 +  memory T cells are IL-15 dependent. J Exp Med

    Google Scholar 

  43. Lodolce J, Boone D, Chai S, Swain R, Dassopoulos T, Trettin S, Ma A (1998) IL-15 receptor maintains lymphoid homeostasis by supporting lymphocyte homing and proliferation. Immunity 9:669–676

    Article  PubMed  CAS  Google Scholar 

  44. King C, Ilic A, Koelsch K, Sarvetnick N (2004) Homeostatic expansion of T cells during immune insufficiency generates autoimmunity. Cell 117:265–277

    Article  PubMed  CAS  Google Scholar 

  45. Read S, Mauze S, Asseman C, Bean A, Coffman R, Powrie F (1998) CD38 CD45RB low CD4 T cells: a population of T cells with immune regulatory activities in vitro. Eur J Immunol 28:3435–3447

    Article  PubMed  CAS  Google Scholar 

  46. Lombardi G, Sidhu S, Batchelor R, Lechler R (1994) Anergic T cells as suppressor cells in vitro. Science 264:1587

    Article  PubMed  CAS  Google Scholar 

  47. Malek T, Yu A, Vincek V, Scibelli P, Kong L (2002) CD4 Regulatory T cells prevent lethal autoimmunity in IL-2Rβ-deficient mice implications for the nonredundant function of IL-2. Immunity 17:167–178

    Article  PubMed  CAS  Google Scholar 

  48. Wolf M, Schimpl A, Hunig T (2001) Control of T cell hyperactivation in IL-2-deficient mice by CD4 CD25 and CD4 CD25 T cells: evidence for two distinct regulatory mechanisms. Eur J Immunol 31:1637–1645

    Article  PubMed  CAS  Google Scholar 

  49. Frasca L, Carmichael P, Lechler R, Lombardi G (1997) Anergic T cells effect linked suppression. Eur J Immunol 27:3191–3197

    Article  PubMed  CAS  Google Scholar 

  50. León K, Peréz R, Lage A, Carneiro J (2001) Three-cell interactions in T cell-mediated suppression? A mathematical analysis of its quantitative implications. J Immunol 166:5356

    PubMed  Google Scholar 

  51. Smith K (2004) The quantal theory of how the immune system discriminates between “self and non-self”. Med Immunol 3:3

    Article  PubMed  Google Scholar 

  52. Hemar A, Subtil A, Lieb M, Morelon E, Hellio R, Dautry-Varsat A (1995) Endocytosis of interleukin 2 receptors in human T lymphocytes: distinct intracellular localization and fate of the receptor alpha, beta, and gamma chains. J Cell Biol 129:55

    Article  PubMed  CAS  Google Scholar 

  53. Duprez V, Dautry-Varsat A (1986) Receptor-mediated endocytosis of interleukin 2 in a human tumor T cell line. Degradation of interleukin 2 and evidence for the absence of recycling of interleukin receptors. J Biol Chem 261:15450

    Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  55. Murali-Krishna K, Altman J, Suresh M, Sourdive D, Zajac A, Ahmed R (1998) In vivo dynamics of anti-viral CD8 T cell responses to different epitopes. An evaluation of bystander activation in primary and secondary responses to viral infection. Adv Exp Med Biol 452: 123

    Google Scholar 

  56. León K, Faro J, Carneiro J (2004) A general mathematical framework to model generation structure in a population of asynchronously dividing cells. J Theor Biol 229:455–476

    Article  PubMed  Google Scholar 

  57. Jelley-Gibbs D, Lepak N, Yen M, Swain S (2000) Two distinct stages in the transition from naive CD4 T cells to effectors, early antigen-dependent and late cytokine-driven expansion and differentiation. J Immunol 165:5017

    PubMed  CAS  Google Scholar 

  58. Usherwood E, Crowther G, Woodland D (1999) Apoptotic cells are generated at every division of in vitro cultured T cell lines. Cell Immunol 196:131–137

    Article  PubMed  CAS  Google Scholar 

  59. Borghans J, de Boer R, Segel L (1996) Extending the quasi-steady state approximation by changing variables. Bull Math Biol 58:43–63

    Article  PubMed  CAS  Google Scholar 

  60. Leon K, Garcia K, Carneiro J, Lage A (2007) How regulatory CD25 + CD4 +  T cells impinge on tumor immunobiology? On the existence of two alternative dynamical classes of tumors. J Theor Biol 247:122–137

    Article  PubMed  CAS  Google Scholar 

  61. Sakaguchi S, Ono M, Setoguchi R, Yagi H, Hori S, Fehervari Z, Shimizu J, Takahashi T, Nomura T (2006) Foxp3 + CD25 + CD4 +  natural regulatory T cells in dominant self-tolerance and autoimmune disease. Immunol Rev 212:8–27

    Article  PubMed  CAS  Google Scholar 

  62. Kuniyasu Y, Takahashi T, Itoh M, Shimizu J, Toda G, Sakaguchi S (2000) Naturally anergic and suppressive CD25 + CD4 +  T cells as a functionally and phenotypically distinct immunoregulatory T cell subpopulation. Int Immunol 12:1145

    Article  PubMed  CAS  Google Scholar 

  63. Pandiyan P, Zheng L, Ishihara S, Reed J, Lenardo M (2007) CD4 + CD25 + Foxp3 +  regulatory T cells induce cytokine deprivation-mediated apoptosis of effector CD4 +  T cells. Nat Immunol 8:1353–1362

    Article  PubMed  CAS  Google Scholar 

  64. Willerford D, Chen J, Ferry J, Davidson L, Ma A, Alt F (1995) Interleukin-2 receptor alpha chain regulates the size and content of the peripheral lymphoid compartment. Immunity 3:521

    Article  PubMed  CAS  Google Scholar 

  65. Suzuki H, Kundig T, Furlonger C, Wakeham A, Timms E Matsuyama T, Schmits R, Simard J, Ohashi P, Griesser H, et al (1995) Deregulated T cell activation and autoimmunity in mice lacking interleukin-2 receptor beta. Science 268:1472

    Article  PubMed  CAS  Google Scholar 

  66. Schorle H, Holtschke T, Hünig T, Schimpl A, Horak I (1991) Development and function of T cells in mice rendered interleukin-2 deficient by gene targeting. Nature 352:621–624

    Article  PubMed  CAS  Google Scholar 

  67. Razi-Wolf Z, Höllander G, Reiser H (1996) Activation of CD4 +  T lymphocytes form interleukin 2-deficient mice by costimulatory B7 molecules. Proc Natl Acad Sci USA 93:2903

    Article  PubMed  CAS  Google Scholar 

  68. Van Parijs L, Biuckians A, Ibragimov A, Alt F, Willerford D, Abbas A (1997) Functional responses and apoptosis of CD25 (IL-2Rα)-deficient T cells expressing a transgenic antigen receptor. J Immunol 158:3738

    PubMed  Google Scholar 

  69. Malek T, Yu A, Scibelli P, Lichtenheld M, Codias E (2001) Broad programming by IL-2 receptor signaling for extended growth to multiple cytokines and functional maturation of antigen-activated T cells. J Immunol 166:1675

    PubMed  CAS  Google Scholar 

  70. Malek T, Bayer A (2004) Tolerance, not immunity, crucially depends on IL-2. Nat Rev Immunol 4:665–674

    Article  PubMed  CAS  Google Scholar 

  71. León K, Faro J, Lage A, Carneiro J (2004) Inverse correlation between the incidences of autoimmune disease and infection predicted by a model of T cell mediated tolerance. J Autoimmunity 22:31–42

    Article  Google Scholar 

  72. Miyara M, Sakaguchi S (2007) Natural regulatory T cells: mechanisms of suppression. Trends Mol Med 13:108–116

    Article  PubMed  CAS  Google Scholar 

  73. Setoguchi R, Hori S, Takahashi T, Sakaguchi S (2005) Homeostatic maintenance of natural Foxp3 + CD25 + CD4 +  regulatory T cells by interleukin (IL)-2 and induction of autoimmune disease by IL-2 neutralization. J Exp Med 201:723

    Article  PubMed  CAS  Google Scholar 

  74. Schippling D, Martin R (2008) Spotlight on anti-CD25: daclizumab in MS. In: International MS journal/MS Forum. vol 15:94

    Google Scholar 

  75. Waldmann T (2007) Anti-Tac (daclizumab, Zenapax) in the treatment of leukemia, autoimmune diseases, and in the prevention of allograft rejection: a 25-year personal odyssey. J Clin Immunol 27:1–18

    Article  PubMed  CAS  Google Scholar 

  76. Cesana G, DeRaffele G, Cohen S, Moroziewicz D, Mitcham J, Stoutenburg J, Cheung K, Hesdorffer C, Kim-Schulze S, Kaufman H (2006) Characterization of CD4 + CD25 +  regulatory T cells in patients treated with high-dose interleukin-2 for metastatic melanoma or renal cell carcinoma. J Clin Oncol 24:1169

    Article  PubMed  CAS  Google Scholar 

  77. Montero E, Alonso L, Perez R, Lage A (2007) Interleukin-2 mastering regulation in cancer and autoimmunity. Clin Immunol 123:125–125

    Article  Google Scholar 

  78. Boyman O, Surh C, Sprent J (2006) Potential use of IL-2/anti-IL-2 antibody immune complexes for the treatment of cancer and autoimmune disease. Expert Opin Biol Therapy 6:1323–1331

    Article  CAS  Google Scholar 

  79. Wilson M, Pesce J, Ramalingam T, Thompson R, Cheever A, Wynn T (2008) Suppression of murine allergic airway disease by IL-2: anti-IL-2 monoclonal antibody-induced regulatory T cells. J Immunol 181:6942

    PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center of Molecular Immunology, Havana, Cuba

    Kalet León

Authors
  1. Kalet León
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karina García-Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kalet León .

Editor information

Editors and Affiliations

  1. School of Mathematics, Dept. Applied Mathematics, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom

    Carmen Molina-París

  2. School of Mathematics, Dept. Applied Mathematics, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom

    Grant Lythe

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

León, K., García-Martínez, K. (2011). Mathematical Models of the Role of IL-2 in the Interactions Between Helper and Regulatory CD4+ T Cells. In: Molina-París, C., Lythe, G. (eds) Mathematical Models and Immune Cell Biology. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7725-0_15

Download citation

Publish with us

Policies and ethics

Search

Navigation