Advertisement

A Mathematical Model of the Effects of Aging on Naive T Cell Populations and Diversity

  • Stephanie Lewkiewicz
  • Yao-li Chuang
  • Tom ChouEmail author
Article
  • 11 Downloads

Abstract

The human adaptive immune response is known to weaken in advanced age, resulting in increased severity of pathogen-born illness, poor vaccine efficacy, and a higher prevalence of cancer in the elderly. Age-related erosion of the T cell compartment has been implicated as a likely cause, but the underlying mechanisms driving this immunosenescence have not been quantitatively modeled and systematically analyzed. T cell receptor diversity, or the extent of pathogen-derived antigen responsiveness of the T cell pool, is known to diminish with age, but inherent experimental difficulties preclude accurate analysis on the full organismal level. In this paper, we formulate a mechanistic mathematical model of T cell population dynamics on the immunoclonal subpopulation level, which provides quantitative estimates of diversity. We define different estimates for diversity that depend on the individual number of cells in a specific immunoclone. We show that diversity decreases with age primarily due to diminished thymic output of new T cells and the resulting overall loss of small immunoclones.

Keywords

Immunosenescence T cell Aging Diversity Thymus 

Notes

Acknowledgements

This work was supported by the NIH via Grants R56HL126544 (SL) and R01HL146552 (TC), the NSF via Grants R56HL126544 (TC), and the Army Research Office (YLC, W1911NF14-1-0472).

Supplementary material

References

  1. Appay V, Sauce D (2014) Naive T cells: The crux of cellular immune aging? Expe Gerontol 54:90–93Google Scholar
  2. Bains I, Antia R, Callard R, Yates AJ (2009a) Quantifying the development of the peripheral naive CD4+ T-cell pool in humans. Immunobiology 113(22):5480–5487Google Scholar
  3. Bains I, Thiébaut R, Yates AJ, Callard R (2009b) Quantifying thymic export: Combining models of naive T cell proliferation and TCR excision circle dynamics gives an explicit measure of thymic output. J Immunol 183(7):4329–4336Google Scholar
  4. Berzins SP, Boyd R, Miller JF (1998) The role of the thymus and recent thymic migrants in the maintenance of the adult peripheral lymphocyte pool. J Exp Med 187(11):1839–1848Google Scholar
  5. Bradley LM, Haynes L, Swain SL (2005) IL-7: maintaining T-cell memory and achieving homeostasis. Trends Immunol 26(3):172–176Google Scholar
  6. Brass D, McKay P, Scott F (2014) Investigating an incidental finding of lymphopenia. Br Med J 348:1–3Google Scholar
  7. Britanova OV, Putintseva EV, Shugay M, Merzlyak EM, Turchaninova MA, Staroverov DB, Bolotin DA, Lukyanov S, Bogdanova EA, Mamedov IZ, Lebedev YB, Chudakov DM (2014) Age-related decrease in TCR repertoire diversity measured with deep and normalized sequence profiling. J Immunol 192(6):2689–2698Google Scholar
  8. Chao A (1984) Nonparametric estimation of the number of classes in a population. Scand J Stat 11(4):265–270MathSciNetGoogle Scholar
  9. Chao A, Lee SM (1992) Estimating the number of classes via sample coverage. J Am Stat Assoc 87(417):210–217MathSciNetzbMATHGoogle Scholar
  10. Colwell RK, Coddington JA (1994) Estimating terrestrial biodiversity through extrapolation. Philos Trans R Soc B 345(1311):101–118Google Scholar
  11. de Boer RJ, Perelson AS (2013) Quantifying T lymphocyte turnover. J Theor Biol 327:45–87MathSciNetzbMATHGoogle Scholar
  12. den Braber I, Mugwagwa T, Vrisekoop N, Westera L, Mögling R, de Boer AB, Willems N, Schrijver EHR, Spierenburg G, Gaiser K, Mul E, Otto SA, Ruiter AF, Ackermans MT, Miedema F, Borghans JAM, de Boer RJ, Tesselaar K (2012) Maintenance of peripheral naive T cells is sustained by thymus output in mice but not humans. Immunity 36:288–297Google Scholar
  13. Desponds J, Mora T, Walczak A (2015) Fluctuating fitness shapes the clone-size distribution of immune repertoires. Proc Natl Acad Sci 113(2):274–279Google Scholar
  14. Desponds J, Mayer A, Mora T, Walczak AM (2017) Population dynamics of immune repertoires. arXiv e-prints arXiv:1703.00226
  15. Ewens W (1972) The sampling theory of selectively neutral alleles. Theor Popul Biol 3(1):87–112MathSciNetzbMATHGoogle Scholar
  16. Fagnoni FF, Vescovini R, Passeri G, Bologna G, Pedrazzoni M, Lavagetto G, Casti A, Franceschi C, Passeri M, Sansoni P (2000) Shortage of circulating naive CD8+ T cells provides new insights on immunodeficiency in aging. Blood 95(9):2860–2868Google Scholar
  17. Fleming DM, Elliot AJ (2008) The impact of influenza on health and health care utilisation of elderly people. Vaccine 32(1):S1–S9Google Scholar
  18. Fry TJ, Mackall CL (2005) The many faces of IL-7: from lymphopoesis to peripheral T cell maintenance. J Immunol 174(11):6571–6576Google Scholar
  19. Gergely P (1999) Drug-induced lymphopenia. Drug Saf 21(2):91–100Google Scholar
  20. Ginaldi L, Loreto MF, Corsi MP, Modesti M, de Martinis M (2001) Immunosenescence and infectious diseases. Microbes Infect 3(10):851–857Google Scholar
  21. Globerson A, Effros RB (2000) Aging of lymphocytes and lymphocytes in the aged. Immunol Today 21(10):515–521Google Scholar
  22. Goronzy JJ, Lee WW, Weyland CM (2007) Aging and T-cell diversity. Exp Gerontol 42(5):400–406Google Scholar
  23. Goronzy JJ, Fang F, Cavanagh MM, Qi Q, Weyand CM (2015a) Naïve T cell maintenance and function in human aging. J Immunol 194(9):4073–4080Google Scholar
  24. Goronzy JJ, Qi Q, Olshen RA, Weyland CM (2015b) High-throughput sequencing insights into T-cell receptor diversity in aging. Genome Med 7:1–3Google Scholar
  25. Goyal S, Kim S, Chen ISY, Chou T (2015) Mechanisms of blood homeostasis: lineage tracking and a neutral model of cell populations in rhesus macaques. BMC Biol 13(85):1–14Google Scholar
  26. Grossman SA, Ellsworth S, Campian J, Wild AT, Herman JM, Laheru D, Brock M, Balmanoukian A, Ye X (2015) Survival in patients with severe lymphopenia following treatment with radiation and chemotherapy for newly diagnosed solid tumors. J Natl Compr Cancer Netw 13(10):1225–1231Google Scholar
  27. Gruver A, Hudson L, Sempowski J (2007) Immunosenescence of aging. J Pathol 211(2):144–156Google Scholar
  28. Hapuarachchi T, Lewis J, Callard RE (2013) A mechanistic mathematical model for naive CD4 T cell homeostasis in healthy adults and children. Front Immunol 4(366):1–6Google Scholar
  29. Hodes RJ, Hathcock KS, Np Weng (2002) Telomeres in T and B cells. Nat Rev Immunol 2:699–706Google Scholar
  30. Jenkins MK, Chu HH, McLachlan JB, Moon JJ (2009) On the composition of the preimmune repertoire of T cells specific for peptide-major histocompatibility ligands. Annu Rev Immunol 28:275–294Google Scholar
  31. Johnson PLF, Yates AJ, Goronzy JJ, Antia R (2012) Peripheral selection rather than thymic involution explains sudden contraction in naive CD4 T-cell diversity with age. PNAS 109(52):21432–21437Google Scholar
  32. Johnson PLF, Goronzy JJ, Atia R (2014) A population biological approach to understanding the maintenance and loss of the T-cell repertoire during aging. Immunology 142(2):167–175Google Scholar
  33. Laydon DJ, Bangham CRM, Asquith B (2015) Estimating T-cell repertoire diversity: limitations of classical estimators and a new approach. Philos Trans R Soc B 370(1675):1–11Google Scholar
  34. Lythe G, Callard RE, Hoare RL, Molina-Par’ıs C (2016) How many TCR clonotypes does a body maintain? J Theor Biol 389:214–224zbMATHGoogle Scholar
  35. Marcou Q, Mora T, Walczak AM (2018) High-throughput immune repertoire analysis with IGoR. Nat Commun 9(1):561Google Scholar
  36. Mason D (1998) A very high level of crossreactivity is an essential feature of the T-cell receptor. Trends Immunol 19(9):395–404Google Scholar
  37. McElhaney JA, Dutz JP (2008) Better influenza vaccines for older people: What will it take? J Infect Dis 198(5):632–634Google Scholar
  38. Mehr R, Perelson AS, Fridkis-Hareli M, Globerson A (1996) Feedback regulation of T cell development: manifestations in aging. Mech Ageing Dev 91(3):195–210Google Scholar
  39. Mehr R, Perelson AS, Fridkis-Harelic M, Globersond A (1997) Regulatory feedback pathways in the thymus. Immunol Today 18(12):581–585Google Scholar
  40. Metcalf D (1963) The autonomous behavior of normal thymus grafts. Aust J Exp Biol Med Sci 41:437–444Google Scholar
  41. Mora T, Walczak A (2016) Quantifying lymphocyte receptor diversity. arXiv e-prints arXiv:1604.00487
  42. Moro-García MA, Arias RA, López-Arrea C (2013) When aging reaches CD4+ T-cells: phenotypic and functional changes. Front Immunol 4(107):1–12Google Scholar
  43. Morris EK, Caruso T, Buscot F, Fischer M, Hancock C, Maier TS, Meiners T, Müller C, Obermaier E, Prati D, Socher SA, Sonnemann I, Wäschke N, Wubet T, Wurst S, Rillig MC (2014) Choosing and using diversity indices: insights for biological applications from the German biodiversity exploratories. Ecol Evol 4:3514–3524Google Scholar
  44. Murphy K (2012) Immunobiology. Garland Science, Taylor and Francis Group LLC, RoutledgeGoogle Scholar
  45. Murray JM, Kaufmann GR, Hodgkin PD, Lewin SR, Kelleher AD, Davenport MP, Zaunders JJ (2003) Naive T-cells are maintained by thymic output in early ages but by proliferation without phenotypic change after age 20. Immunol Cell Biol 81(6):487–495Google Scholar
  46. Naylor K, Li G, Vallejo AN, Lee WW, Koetz K, Bryl E, Witkowski J, Fulbright J, Weyand CM, Goronzy JJ (2005) The influence of age on T cell generation and TCR diversity. J Immunol 174(11):7446–7452Google Scholar
  47. Np Weng, Levine BL, June CH, Hodes RJ (1995) Human naive and memory T lymphocytes differ in telomeric length and replicative potential. PNAS 92(24):11091–11094Google Scholar
  48. Oakes T, Heather JM, Best K, Byng-Maddick R, Husovsky C, Ismail M, Joshi K, Maxwell G, Noursadeghi M, Riddell N, Ruehl T, Turner CT, Uddin I, Chain B (2017) Quantitative characterization of the T cell receptor repertoire of Naïve and memory subsets using an integrated experimental and computational pipeline which is robust, economical, and versatile. Front Immunol.  https://doi.org/10.3389/fimmu.2017.01267 Google Scholar
  49. Poland GA, Langley J, Michel J, Van Damme P, Wicker S (2010) A global prescription for adult immunization: time is catching up with us. Vaccine 28(44):7137–7139Google Scholar
  50. Pulko V, Davies JS, Martinez C, Lanteri MC, Busch MP, Diamond MS, Knox K, Busch ES, Sims PA, Sinari S, Billheimer D, Haddad EK, Murray KO, Wertheimer AM, Nikolich-Žugich J (2016) Human memory T cells with a naive phenotype accumulate with aging and respond to persistent viruses. Nat Immunol 17(8):966–975Google Scholar
  51. Qi Q, Liu Y, Cheng Y, Glanville J, Zhang D, Lee JY, Olshen RA, Weyand CM, Boyd SD, Goronzy JJ (2014) Diversity and clonal selection in the human T-cell repertoire. Proc Natl Acad Sci 111(36):13139–13144Google Scholar
  52. Reynolds J, Coles M, Lythe G, Molina-París C (2013) Mathematical model of naive T cell division and IL-7 survival thresholds. Front Immunol 4(434):1–13Google Scholar
  53. Ribeiro RM, Perelson AS (2007) Determining thymic output quantitatively: using models to interpret experimental T-cell receptor excision circle (TREC) data. Immunol Rev 216(1):21–34Google Scholar
  54. Rubinstein MP, Lind NA, Purton JF, Filippou P, Best JA, McGhee PA, Surh CD, Goldrath AW (2008) IL-7 and IL-15 differentially regulate CD8+ T-cell subsets during contraction of the immune response. Blood 112(9):3704–3712Google Scholar
  55. Salam N, Rane S, Das R, Faulkner M, Gund R, Kandpal U, Lewis V, Prabhu HMS, Ranganathan V, Durdik J, George A, Rath S, Bal V (2013) T cell ageing: effects of age on development, survival, and function. Indian J Med Res 138(5):595–608Google Scholar
  56. Saule P, Trauet J, Dutriez V, Lekeux V, Dessaint JP, Labalette M (2005) Accumulation of memory T cells from childhood to old age: central and effector memory cells in CD4+ versus effector memory and terminally differentiated memory cells in CD8+ compartment. Mech Ageing Dev 127(3):274–281Google Scholar
  57. Shugay M, Bagaev DV, Turchaninova MA, Bolotin DA, Britanova OV, Putintseva EV, Pogorelyy MV, Nazarov VI, Zvyagin IV, Kirgizova VI, Kirgizov KI, Skorobogatova EV, Chudakov DM (2015) VDJtools: unifying post-analysis of T cell receptor repertoires. PLOS Comput Biol 11(11):1–16Google Scholar
  58. Steinmann GG (1986) The human thymus, current topics in pathology, vol 75. Chap changes in the human thymus during aging. Springer, Berlin, Heidelberg, pp 43–88Google Scholar
  59. Steinmann G, Klaus B, Müller-Hermelink H (1985) The involution of the ageing human thymic epithelium is independent of puberty. Scand J Immunol 22(5):563–575Google Scholar
  60. Strauss A, Yorke JA (1967) Perturbation theorems for ordinary differential equations. J Differ Equ 3(1):15–30MathSciNetzbMATHGoogle Scholar
  61. Surh CD, Sprent J (2008) Homeostasis of naive and memory T cells. Immunity 29(6):848–862Google Scholar
  62. Tan JT, Dudl E, LeRoy E, Murray R, Sprent J, Weinberg KI, Surh CD (2001) IL-7 is critical for homeostatic proliferation and survival of naive T cells. Proc Natl Acad Sci 98(15):8732–8737Google Scholar
  63. Thomas-Crussels J, McElhaney JE, Aguado MT (2012) Report of the ad-hoc consultation on aging and immunization for a future who research agenda on life-course immunization. Vaccine 40(32):6007–6012Google Scholar
  64. Trepel F (1974) Number and distribution of lymphocytes in man. Klinische Wochenschr 52(11):511–515Google Scholar
  65. Vivien L, Benoist C, Mathis D (2001) T lymphocytes need IL-7 but not IL-4 or IL-6 to survive in vivo. Int Immunol 13(6):763–768Google Scholar
  66. Vrisekoop N, den Braber I, de Boer AB, Ruiter AFC, Ackermans MT, van der Crabben SN, Schrijver EHR, Spierenburg G, Sauerwein HP, Hazenberg MD, de Boer RJ, Miedema F, Borghans JAM, Tesselaar K (2008) Sparse production but preferential incorporation of recently produced naive T-cells in the human peripheral pool. Proc Natl Acad Sci 105(16):6115–6120Google Scholar
  67. Westera L, van Hoeven V, Drylewicz J, Spierenburg G, van Velzen JF, de Boer RJ, Tesselaar K, Borghans JAM (2015) Lymphocyte maintenance during healthy aging requires no substantial alterations in cellular turnover. Aging Cell 14(2):219–227Google Scholar
  68. Westermann J, Pabst R (1990) Lymphocyte subsets in the blood: A diagnostic window on the lymphoid system? Immunol Today 11(11):406–410Google Scholar
  69. Wick G, Dürr PJ, Berger P, Blasko I, Grubeck-Loebenstein B (2000) Diseases of aging. Vaccine 18(16):1567–1583Google Scholar
  70. Xu S, Chou T (2018) Immigration-induced phase transition in a regulated multispecies birth-death process. J Phys A 51:425602zbMATHGoogle Scholar
  71. Yagger EJ, Ahmed M, Lanzer K, Randall TD, Woodland DL, Blackman MA (2008) Age-associated decline in T cell repertoire diversity leads to holes in the repertoire and impaired immunity to the influenza virus. J Exp Med 205(3):711–723Google Scholar
  72. Yates AJ (2014) Theories and quantification of thymic selection. Front Immunol 5(13):1–15Google Scholar

Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Department of MathematicsCalState-NorthridgeNorthridgeUSA
  3. 3.Department of BiomathematicsUCLALos AngelesUSA

Personalised recommendations