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A fit of CD4+ T cell immune response to an infection by lymphocytic choriomeningitis virus

1 Departamento de Matemática, Faculdade de Ciências da Universidade do Porto and LIAAD-INESC. Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
2 Faculdade de Ciências da Nutrição e Alimentação da Universidade do Porto, and LIAAD-INESC. Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

Special Issues: Mathematical Methods in the Biosciences

We fit an immune response model to data reporting the CD4+ T cell numbers from the 28 days following the infection of mice with lymphocytic choriomeningitis virus LCMV. We used an ODE model that was previously used to describe qualitatively the behaviour of CD4+ T cells, regulatory T cells (Tregs) and interleukine-2 (IL-2) density. The model considered two clonotypes of T cells in order to fit simultaneously the two time series for the gp61 and NP309 epitopes. We observed the proliferation of T cells and, to a lower extent, Tregs during the immune activation phase following infection and subsequently, during the contraction phase, a smooth transition from faster to slower death rates. The six parameters that were optimized were: the beginning and ending times of the immune response, the growth rate of T cells, their capacity, and the two related with the homeostatic numbers of T cells that respond to each epitope. We showed that the ODE model was able to be calibrated thus providing a quantitative description of the data.
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Keywords T cells; Regulatory T cells (Tregs); Lymphocytic choriomeningitis virus (LCMV); epitope gp61; epitope NP309; antigenic stimulation; fit

Citation: Atefeh Afsar, Filipe Martins, Bruno M. P. M. Oliveira, Alberto A. Pinto. A fit of CD4+ T cell immune response to an infection by lymphocytic choriomeningitis virus. Mathematical Biosciences and Engineering, 2019, 16(6): 7009-7021. doi: 10.3934/mbe.2019352

References

  • 1. J. Banchereau, F. Briere, C. Caux, et al., Immunobiology of dendritic cells, Annu. Rev. Immunol., 18 (2000), 767–811.
  • 2. J. Zhu and W. E. Paul, CD4 T cells: fates, functions, and faults, Blood, 112 (2008), 1557–1569.
  • 3. N. J. Burroughs, B. M. P. M. Oliveira and A. A. Pinto, Regulatory T cell adjustment of quorum growth thresholds and the control of local immune responses, J. Theor. Biol., 241 (2006), 134–141.
  • 4. A. L. Cava, Tregs are regulated by cytokines: Implications for autoimmunity, Autoimmun. Rev., 8 (2008), 83–87.
  • 5. B.-I. Moon, T. H. Kim and J.-Y. Seoh, Functional modulation of regulatory T cells by IL-2, PLoS One, 10 (2015), 1–13.
  • 6. E. M. Shevach, R. S. McHugh, C. A. Piccirillo, et al., Control of T-cell activation by CD4+ CD25+ suppressor T cells, Immunol. Rev., 182 (2001), 58–67.
  • 7. A. M. Thornton and E. M. Shevach, CD4+ CD25+ immunoregulatory T cells suppress polyclonal T cell activation in vitro by inhibiting interleukine 2 production, The Journal of Experimental Medicine, 188 (1998), 287–296.
  • 8. L. A. Turka and P. T. Walsh, IL-2 signaling and CD4+ CD25+ Foxp3+ regulatory T cells, Front. Biosci., 13 (2008), 1440–1446.
  • 9. S. Sakaguchi, Naturally arising CD4+ regulatory T cells for immunological self-tolerance and negative control of immune responses, Annu. Rev. Immunol., 22 (2004), 531–562.
  • 10. J. Zhu, H. Yamane and W. E. Paul, Differentiation of Effector CD4 T Cell Populations, Annu. Rev. Immunol., 28 (2010), 445–489.
  • 11. D. Homann, L. Teyton and M. B. Oldstone, Differential regulation of antiviral T-cell immunity results in stable CD8+ but declining CD4+ T-cell memory, Nat. Med., 7 (2001), 913–919.
  • 12. R. E. Callard and A. J. Yates, Immunology and mathematics: crossing the divide, Immunology, 115 (2005), 21–33.
  • 13. G. Lythe and C. Molina-París, Some deterministic and stochastic mathematical models of naïve T-cell homeostasis, Immunol. Rev., 285 (2018), 206–217.
  • 14. R. J. de Boer and P. Hogeweg, Immunological discrimination between self and non-self by precur-sor depletion and memory accumulation, J. Theor. Biol., 124 (1987), 343–369.
  • 15. A. Pinto, N. Burroughs, F. Ferreira, et al., Dynamics of immunological models, Acta Biotheor., 58 (2010), 391–404.
  • 16. K. Blyuss and L. Nicholson, The role of tunable activation thresholds in the dynamics of autoim-munity, J. Theor. Biol., 308 (2012), 45–55.
  • 17. S. Khailaie, F. Bahrami, M. Janahmadi, et al., A mathematical model of immune activation with a unified self-nonself concept, Front. Immunol., 4 (2013), 474.
  • 18. K. León, A. Lage, and J. Carneiro, Tolerance and immunity in a mathematical model of T-cell mediated suppression, J. Theor. Biol., 225 (2003), 107–126.
  • 19. C. Bianca and L. Brézin, Modeling the antigen recognition by B-cell and T-cell receptors through thermostatted kinetic theory methods, Int. J. Biomath., 10 (2017), 1750072.
  • 20. R. F. Alvarez, J. A. Barbuto and R. Venegeroles, A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity, J. Theor. Biol., 471 (2019), 42–50.
  • 21. N. Burroughs, M. Ferreira, B. Oliveira, et al., Autoimmunity arising from bystander proliferation of T cells in an immune response model, Math. Comput. Modell., 53 (2011), 1389–1393.
  • 22. B. M. P. M. Oliveira, R. Trinchet, M. V. Otero-Espinar, et al., Modelling the suppression of au-toimmunity after pathogen infection, Math. Methods Appl. Sci., 41 (2018), 8565–8570.
  • 23. B. M. P. M. Oliveira, I. P. Figueiredo, N. J. Burroughs, et al., Approximate equilibria for a T cell and Treg model, Appl. Math. Inform. Sci., 9 (2015), 2221–2231.
  • 24. N. Burroughs, B. Oliveira, A. Pinto, et al., Immune response dynamics, Math. Comput. Modell., 53 (2011), 1410–1419.
  • 25. N. Burroughs, B. Oliveira, A. Pinto, et al., Sensibility of the quorum growth thresholds controlling local immune responses, Math. Comput. Modell., 47 (2008), 714–725.
  • 26. N. Burroughs, M. Ferreira, B. Oliveira, et al., A transcritical bifurcation in an immune response model, J. Differ. Eq. Appl., 17 (2011), 1101–1106.
  • 27. B. M. P. M. Oliveira, A. Yusuf, I. P. Figueiredo, et al., The effect of a linear tuning between the antigenic stimulations of T cells and Tregs. In Preparation.
  • 28. N. J. Burroughs, M. Ferreira, J. Martins, et al., Dynamics and biological thresholds, in Dynam-ics, Games and Science I, DYNA 2008, in Honor of Maur´ ıcio Peixoto and David Rand (editors A. A. Pinto, D. A. Rand, and M. M. Peixoto), volume 1 of Springer Proceedings in Mathematics, Springer-Verlag Berlin Heidelberg (2011), pp. 183–191.
  • 29. R. J. de Boer, D. Homann and A. S. Perelson, Different Dynamics of CD4+ and CD8+ T Cell Responses During and After Acute Lymphocytic Choriomeningitis Virus Infection, J. Immunol., 171 (2003), 3928–3935.
  • 30. R. J. de Boer and A. S. Perelson, Quantifying T lymphocyte turnover, J. Theor. Biol., 327 (2013), 45–87.
  • 31. R. E. Callard, J. Stark and A. J. Yates, Fratricide: a mechanism for T memory-cell homeostasis, Trends Immunol., 24 (2003), 370–375.
  • 32. S. Nagata, Fas ligand-induced apoptosis, Annu. Rev. Genet., 33 (1999), 29–55.
  • 33. P. M. Anderson and M. A. Sorenson, Effects of route and formulation on clinical pharmacokinetics of interleukine-2, Clin. Pharmacokinet., 27 (1994), 19–31.
  • 34. A. R. Mclean and C. A. Michie, In vivo estimates of division and death rates of human t lympho-cytes., Proceedings of the National Academy of Sciences, 92 (1995), 3707–3711.
  • 35. C. Michie, A. McLean, C. Alcock, et al., Life-span of human lymphocyte subsets defined by CD45 isoforms, Nature, 360 (1992), 264–265.
  • 36. D. Moskophidis, M. Battegay, M. Vandenbroek, et al., Role of virus and host variables in virus persistence or immunopathological disease caused by a non-cytolytic virus, J. Gen. Virol., 76 (1995), 381–391.
  • 37. H. Veiga-Fernandes, U. Walter, C. Bourgeois, et al., Response of naïve and memory CD8+ T cells to antigen stimulation in vivo, Nat. Immunol., 1 (2000), 47–53. 38. G. A. Seber and C. J. Wild, Nonlinear Regression, Wiley and Sons (2003).

 

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