Parameter Estimation and Model Selection

  • Gennady BocharovEmail author
  • Vitaly Volpert
  • Burkhard Ludewig
  • Andreas Meyerhans


In this chapter, we illustrate a data-driven methodology to formulation and calibration of mathematical models of immune responses. The maximum likelihood approach to parameter estimation, Tikhonov regularization method and information-theoretic criteria for model ranking and selection are presented for models formulated with ODEs, DDEs and PDEs. Experimental data on CFSE-based proliferation analysis of T cells and LCMV–CTL dynamics in a low dose experimental infection of mice are used.


  1. 1.
    Baker, C.T.H., Bocharov, G.A., Paul, C.A.H., Rihan, F.A., Computational modelling with functional differential equations: identification, selection and sensitivity, Appl. Numer. Math., 53 (2005) 107–129.Google Scholar
  2. 2.
    Baker, C.T.H., Bocharov, G.A., Ford, J.M., Lumb, P.M., Norton, S.J., Paul, C.A.H., Junt, T., Krebs, P., Ludewig, B., Computational approach to parameter estimation and model selection in immunology, J. Comput. Appl. Math., 184 (2005) 50–76.Google Scholar
  3. 3.
    Andrew, S.M., Baker, C.T.H., Bocharov, G.A. Rival approaches to mathematical modelling in immunology, J. Comput. Appl. Math., 205 (2007) 669–686.Google Scholar
  4. 4.
    Luzyanina, T., Roose, D., Bocharov, G.: Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data. J. Math. Biol. 59(5): 581–603 (2009)Google Scholar
  5. 5.
    Luzyanina, T., Mrusek, S., Edwards, J.T., Roose, D., Ehl, S., Bocharov, G.: Computational analysis of CFSE proliferation assay. J. Math. Biol. 54(1) 57–89 (2007)Google Scholar
  6. 6.
    Luzyanina, T., Roose, D., Schinkel, T., Sester, M., Ehl, S., Meyerhans, A., Bocharov, G.: Numerical modelling of label-structured cell population growth using CFSE distribution data. Theor. Biol. Math. Model. 4 1–26 (2007)Google Scholar
  7. 7.
    T. Luzyanina, J. Cupovic, B. Ludewig, G. Bocharov. (2014) Mathematical models for CFSE labelled lymphocyte dynamics: asymmetry and time-lag in division. Journal of Mathematical Biology. 69(6–7):1547–83Google Scholar
  8. 8.
    Antia, R., Ganusov, V.V., Ahmed, R., The role of models in understanding CD8+ T-cell memory, Nat. Rev. Immunol., 5 (2005) 101–111.Google Scholar
  9. 9.
    Goldstein, B., Faeder, J.R., Hlavacek, W.S., Mathematical and computational models of immune-receptor signalling. Nat Rev Immunol., 4 (2004) 445–456.Google Scholar
  10. 10.
    Mohler, R.R., Bruni, C., Gandolfi, A., A systems approach to immunology, Proc. IEEE, 68 (1980) 964–990.Google Scholar
  11. 11.
    Morel, P.A., Mathematical modeling of immunological reactions, Front Biosci., 16 (1998) d338–347.Google Scholar
  12. 12.
    Perelson A.S., Modelling viral and immune system dynamics, Nat Rev Immunol., 2 (2002) 28–36.Google Scholar
  13. 13.
    Perelson, A.S., Ribeiro, R.M., Hepatitis B virus kinetics and mathematical modeling, Semin Liver Dis., 24 (2004) Suppl 1, 11–16.Google Scholar
  14. 14.
    Perelson, A.S., Nelson, P.W., Mathematical analysis of HIV-1 dynamics in vivo, SIAM Review, 41 (1999) 3–44.Google Scholar
  15. 15.
    Petrovsky, N., Brusic, V., Computational immunology: The coming of age, Immunol. Cell Biol., 80 (2002) 248–254.Google Scholar
  16. 16.
    Ribeiro, R.M., Lo, A., Perelson, A.S., Dynamics of hepatitis B virus infection, Microbes Infect., 4 (2002) 829–835.Google Scholar
  17. 17.
    Wodarz, D., Mathematical models of HIV and the immune system, Novartis Found Symp., 254 (2003) 193–207.Google Scholar
  18. 18.
    Yates, A., Chan, C.C., Callard, R.E., George, A.J., Stark, J., An approach to modelling in immunology, Brief Bioinform., 2 (2001) 245–257.Google Scholar
  19. 19.
    Asquith B, Borghans JA, Ganusov VV, Macallan DC. Lymphocyte kinetics in health and disease. Trends Immunol. (2009); 30(4):182–9.Google Scholar
  20. 20.
    Germain RN, Meier-Schellersheim M, Nita-Lazar A, Fraser ID. Systems biology in immunology: a computational modeling perspective. Annu Rev Immunol. (2011); 29:527–85. Review.Google Scholar
  21. 21.
    Kirschner DE, Linderman JJ. Mathematical and computational approaches can complement experimental studies of host-pathogen interactions. Cell Microbiol. (2009); 11(4):531–9.Google Scholar
  22. 22.
    Klauschen F, Angermann BR, Meier-Schellersheim M. Understanding diseases by mouse click: the promise and potential of computational approaches in Systems Biology. Clin Exp Immunol. (2007); 149(3):424–9.Google Scholar
  23. 23.
    Wodarz D. Ecological and evolutionary principles in immunology. Ecol Lett. (2006); 9(6):694–705.Google Scholar
  24. 24.
    Yan Q. Immunoinformatics and systems biology methods for personalized medicine. Methods Mol Biol. (2010); 662:203–20.Google Scholar
  25. 25.
    van den Berg HA, Rand DA. Quantitative theories of T-cell responsiveness. Immunol Rev. (2007); 216:81–92.Google Scholar
  26. 26.
    Mirsky HP, Miller MJ, Linderman JJ, Kirschner DE. Systems biology approaches for understanding cellular mechanisms of immunity in lymph nodes during infection. J Theor Biol. (2011); 287:160–70.Google Scholar
  27. 27.
    Narang V, Decraene J, Wong SY, Aiswarya BS, Wasem AR, Leong SR, Gouaillard A. Systems immunology: a survey of modeling formalisms, applications and simulation tools. Immunol Res. (2012); 53(1–3):251–65.Google Scholar
  28. 28.
    Ganusov VV, Pilyugin SS, de Boer RJ, Murali-Krishna K, Ahmed R, Antia R. Quantifying cell turnover using CFSE data. J Immunol Methods. 2005; 298(1-2):183-200. Erratum in: J Immunol Methods. (2006); 317(1–2):186–7.Google Scholar
  29. 29.
    De Boer RJ, Ganusov VV, Milutinovi D, Hodgkin PD, Perelson AS. Estimating lymphocyte division and death rates from CFSE data. Bull Math Biol. (2006); 68(5):1011–31.Google Scholar
  30. 30.
    Hawkins ED, Hommel M, Turner ML, Battye FL, Markham JF, Hodgkin PD. Measuring lymphocyte proliferation, survival and differentiation using CFSE time-series data. Nat Protoc. (2007); 2(9):2057–67.Google Scholar
  31. 31.
    Len K, Faro J, Carneiro J. A general mathematical framework to model generation structure in a population of asynchronously dividing cells. J Theor Biol. (2004); 229(4):455–76.Google Scholar
  32. 32.
    Asquith B, Debacq C, Florins A, Gillet N, Sanchez-Alcaraz T, Mosley A, Willems L. Quantifying lymphocyte kinetics in vivo using carboxyfluorescein diacetate succinimidyl ester (CFSE). Proc Biol Sci. (2006); 273(1590):1165–71.Google Scholar
  33. 33.
    Yates A, Chan C, Strid J, Moon S, Callard R, George AJ, Stark J. Reconstruction of cell population dynamics using CFSE. BMC Bioinformatics. (2007); 8:196.Google Scholar
  34. 34.
    Perelson AS, Ribeiro RM. Modeling the within-host dynamics of HIV infection. BMC Biol. (2013); 11:96.Google Scholar
  35. 35.
    Canini L, Perelson AS. Viral kinetic modeling: state of the art. J Pharmacokinet Pharmacodyn. (2014); 41(5):431–43.Google Scholar
  36. 36.
    Eftimie R, Gillard JJ, Cantrell DA. Mathematical Models for Immunology: Current State of the Art and Future Research Directions. Bull Math Biol. (2016); 78(10):2091–2134.Google Scholar
  37. 37.
    Ganusov VV. Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century. Front Microbiol. (2016); 7:1131Google Scholar
  38. 38.
    Castro M, Lythe G, Molina-Pars C, Ribeiro RM. Mathematics in modern immunology. Interface Focus. (2016); 6(2):20150093Google Scholar
  39. 39.
    Deem MW, Hejazi P. Theoretical aspects of immunity. Annu Rev Chem Biomol Eng. (2010); 1:247-76.Google Scholar
  40. 40.
    Rapin N, Lund O, Bernaschi M, Castiglione F. Computational immunology meets bioinformatics: the use of prediction tools for molecular binding in the simulation of the immune system. PLoS One. (2010); 5(4):e9862.Google Scholar
  41. 41.
    Belfiore M, Pennisi M, Aric G, Ronsisvalle S, Pappalardo F. In silico modeling of the immune system: cellular and molecular scale approaches. Biomed Res Int. (2014); 2014:371809.Google Scholar
  42. 42.
    Thakar J, Poss M, Albert R, Long GH, Zhang R. Dynamic models of immune responses: what is the ideal level of detail? Theor Biol Med Model. (2010); 7:35.Google Scholar
  43. 43.
    Lundegaard C, Lund O, Kesmir C, Brunak S, Nielsen M. Modeling the adaptive immune system: predictions and simulations. Bioinformatics. (2007); 23(24):3265–75.Google Scholar
  44. 44.
    Arazi A, Pendergraft WF 3rd, Ribeiro RM, Perelson AS, Hacohen N. Human systems immunology: hypothesis-based modeling and unbiased data-driven approaches. Semin Immunol. (2013); 25(3):193–200.Google Scholar
  45. 45.
    Kidd BA, Peters LA, Schadt EE, Dudley JT. Unifying immunology with informatics and multiscale biology. Nat Immunol. (2014); 15(2):118–27Google Scholar
  46. 46.
    Proserpio V, Mahata B. Single-cell technologies to study the immune system. Immunology. (2016); 147(2):133–40.Google Scholar
  47. 47.
    Tang J, van Panhuys N, Kastenmller W, Germain RN. The future of immunoimaging–deeper, bigger, more precise, and definitively more colorful. Eur J Immunol. (2013); 43(6):1407–12.Google Scholar
  48. 48.
    Bocharov G, Argilaguet J, Meyerhans A. Understanding Experimental LCMV Infection of Mice: The Role of Mathematical Models. J Immunol Res. (2015); 2015:739706.Google Scholar
  49. 49.
    Stephen P. Ellner, John Guckenheimer. Dynamic Models in Biology. Princeton University Press. (2006). 330 pp. ISBN: 9780691125893.Google Scholar
  50. 50.
    Bell G, Perelson AS, Pimbley G (eds): Theoretical Immunology. New York, Marcer Dekker, (1978). 646 pp.Google Scholar
  51. 51.
    Polderman, J.W., Willems, J.C., Introduction to Mathematical Systems Theory. A behavioral approach, Texts in Applied Mathematics, 26, Springer-Verlag, New York, 1998.Google Scholar
  52. 52.
    Chakraborty, A.K., Dustin, M.L., Shaw, A.S. In silico models for cellular and molecular immunology: successes, promises and challenges, Nature Immunology, 4 (2003) 933–936.Google Scholar
  53. 53.
    Baker, C.T.H., Bocharov, G.A., Paul, C.A.H., Rihan, F.A., Modelling and analysis of time-lags in some basic patterns of cell proliferation, J. Math. Biol., 37 (1998) 341–371.Google Scholar
  54. 54.
    Armitage, P., Berry G., Matthews, J.N.S., Statistical Methods in Medical Research. (Fourth Edition) Blackwell Science, Oxford (2001).Google Scholar
  55. 55.
    Gershenfeld, N.A., The Nature of Mathematical Modelling, Cambridge University Press, Cambridge, (2000).Google Scholar
  56. 56.
    Bard, Y., Nonlinear Parameter Estimation (Academic Press, 1974).Google Scholar
  57. 57.
    Myung, I.J. Tutorial on maximum likelihood estimation. J. Mathematical Physiology, 47 (2003) 90–100.Google Scholar
  58. 58.
    Pascual, M.A., Kareiva, P. Predicting the outcome of competition using experimental data: maximum likelihood and Bayesian approaches. Ecology, 77 (1996) 337–349.Google Scholar
  59. 59.
    Gingerich, P.D. Arithmetic or geometric normality of biological variation: an empirical test of theory. J. Theor. Biology204 (2000) 201–221.Google Scholar
  60. 60.
    Venzon, D.J., Moolgavkar, S.H.: A method for computing profile-likelihood-based confidence intervals. Appl. Statist. 37(1) 87–94 (1988)Google Scholar
  61. 61.
    B. Efron and R. Tibshirani. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Stat. Sci., 1(1):54–77, (1986).Google Scholar
  62. 62.
    B. Efron and R. Tibshirani. Introduction to the bootstrap. Chapman and Hall, New York, (1993).Google Scholar
  63. 63.
    Rubinov S.I. Cell kinetics. In: Mathematical models in molecular and cellular biology Segel L.A. (Ed) Cambridge University Press, Cambridge (1980), pp 502–522.Google Scholar
  64. 64.
    Pilyugin S.S., Ganusov V.V., Murali-Krishna K., Ahmed R. and Antia R. The rescaling method for quantifying the turnover of cell populations. J. Theor. Biol. (2003) 225: 275–283.Google Scholar
  65. 65.
    Ganusov V.V., Pilyugin S.S., de Boer R.J., Murali-Krishna K., Ahmed R. and Antia R. Quantifying cell turnover using CFSE data. J. Immunol. Methods. (2005) 298: 183–200.Google Scholar
  66. 66.
    De Boer R.J. and Perelson A.S. Estimating division and death rates from CFSE data. J. Comput. Appl. Math. (2005) 184: 140–164.Google Scholar
  67. 67.
    Hadamard, J.: Le probléme de Cauchy et les équations aux dérivées partielles linéaires hyperboliques. Paris, Hermann (1932)Google Scholar
  68. 68.
    Tikhonov, A.N., Arsenin, V.Y.: Solutions of ill-posed problems. Washington, V. H. Winston & Sons (1977)Google Scholar
  69. 69.
    Hasanov, A., DuChateau, P., Pektas, B.: An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation. J. Inv. Ill-Posed Problems 14(5) 435–463 (2006)Google Scholar
  70. 70.
    Bitterlich, S., Knabner, P.: An efficient method for solving an inverse problem for the Richards equation. J. Comput. Appl. Math. 147 153–173 (2002)Google Scholar
  71. 71.
    Tikhonov, A.N.: Solution of incorrectly formulated problems and the regularization method. Sov. Math. Dokl. 4 1035–1038 (1963)Google Scholar
  72. 72.
    Engl, H.W., Rundell, W., Scherzer, O.: A regularization scheme for an inverse problem in age-structured populations. J. Math. Anal. Appl. 182 658–679 (1994)Google Scholar
  73. 73.
    Grebennikov, A.: Local regularization algorithms of solving coefficient inverse problems for some differential equations. Inverse Probl. Eng. 11(3) 201–213 (2003)Google Scholar
  74. 74.
    Navon, I.M.: Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dynam. Atmos. Oceans 27(1) 55–79 (1997)Google Scholar
  75. 75.
    DuChateau, P., Thelwell, R., Butters, G.: Analysis of an adjoint problem approach to the identification of an unknown diffusion coefficient. Inverse Problems 20 601–625 (2004)Google Scholar
  76. 76.
    Tautenhahn, U., Jin, Q.: Tikhonov regularization and a posteriori rules for solving nonlinear ill posed problems. Inverse Problems 19 1–21 (2003)Google Scholar
  77. 77.
    Perthame, B., Zubelli, J.P.: On the inverse problem for a size-structured population model. Inverse Problems 23 1037–1052 (2007)Google Scholar
  78. 78.
    Miao, H., Jin, X., Perelson, A.S., Wu, H.: Evaluation of multitype mathematical models for CFSE-labeling experiment data. Bull. Math. Biol. 74(2) 300–326 (2012)Google Scholar
  79. 79.
    Banks, H.T., Thompson, W.C.: Mathematical models of dividing cell populations: Application to CFSE data. Math. Model. Nat. Phenom. 7(5) 24–52 (2012)Google Scholar
  80. 80.
    De Boer RJ, Perelson AS. Quantifying T lymphocyte turnover. J Theor Biol. (2013) 21;327:45–87.Google Scholar
  81. 81.
    Hross S, Hasenauer J. Analysis of CFSE time-series data using division-, age- and label-structured population models. Bioinformatics. (2016); 32(15):2321–9Google Scholar
  82. 82.
    Ackleh, A.S., Banks, H.T., Deng, K., Hu, S.: Parameter estimation in a coupled system of nonlinear size-structured populations. Math. Biosci. Engin. 2(2) 289–315 (2005)Google Scholar
  83. 83.
    Morozov, V.A.: On the solution of functional equations by the method of regularization. Sov. Math. Dokl. 7 414–417 (1966)Google Scholar
  84. 84.
    Morozov, V.A.: Methods for solving incorrectly posed problems. New York, Springer-Verlag (1984)Google Scholar
  85. 85.
    Schittler, D., Hasenauer, J., Allgöwer, F.: A generalized model for cell proliferation: Integrating division numbers and label dynamics. Proc. Eight International Workshop on Computational Systems Biology (WCSB 2011), Zurich, Switzerland, 165–168 (2011)Google Scholar
  86. 86.
    Hasenauer, J., Schittler, D., Allgöwer, F.: A computational model for proliferation dynamics of division- and label-structured populations. arXiv:1202.4923v1 [q-bio.PE] (2012)
  87. 87.
    Hasenauer, J., Schittler, D., Allgöwer, F.: Analysis and simulation of division- and label-structured population models: a new tool to analyze proliferation assays. Bull. Math. Biol. 74(11) 2692–2732 (2012)Google Scholar
  88. 88.
    Sabrina Hross, Jan Hasenauer; Analysis of CFSE time-series data using division-, age- and label-structured population models, Bioinformatics, Volume 32, Issue 15, 1 August 2016, Pages 23212329, Scholar
  89. 89.
    Banks, H.T., Thompson, W.C., Peligero, C., Giest, S., Argilaguet, J., Meyerhans, A.: A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assay. CRSC-TR12-03, North Carolina State University (2012)Google Scholar
  90. 90.
    De Boer, R.J., Perelson, A.S.: Estimating division and death rates from CFSE data. J Comput. Appl. Math. 184 140–164 (2005)Google Scholar
  91. 91.
    Roederer, M.: Interpretation of cellular proliferation data: avoid the panglossian. Cytometry A 79(2) 95–101 (2011)Google Scholar
  92. 92.
    Chang, J.T., Palanivel, V.R., Kinjyo, I., Schambach, F., Intlekofer, A.M., Banerjee, A., Longworth, S.A., Vinup, K.E., Mrass, P., Oliaro, J., Killeen, N., Orange, J.S., Russell, S.M., Weninger, W., Reiner, S.L.: Asymmetric T lymphocyte division in the initiation of adaptive immune responses. Science 315 (5819) 1687–1691 (2007)Google Scholar
  93. 93.
    Banks, H.T., Choi, A., Huffman, T., Nardini, J., Poag, L., Thompson, W.C.: Quantifying CFSE label decay in flow cytometry data. Appl. Math. Lett. 26(5) 571–577 (2013)Google Scholar
  94. 94.
    Banks, H.T., Sutton, K.L., Thompson, W.C., Bocharov, G., Roose, D., Schenkel, T., Meyerhans, A.: Estimation of cell proliferation dynamics using CFSE data. Bull. Math. Biol. 70 116–150 (2011)Google Scholar
  95. 95.
    Banks, H.T., Sutton, K.L., Thompson, W.C., Bocharov, G., Doumic, M., Schenkel, T., Argilaguet, J., Giest, S., Peligero, C., Meyerhans, A.: A new model for the estimation of cell proliferation dynamics using CFSE data. J. Immunol. Methods 373 143–160 (2011)Google Scholar
  96. 96.
    Schwarz, G. Estimating the dimension of a model. The Annals of Statistics, 6 (1978) 461–464.Google Scholar
  97. 97.
    Garny A, Noble D, Kohl P. Dimensionality in cardiac modelling. Prog Biophys Mol Biol. (2005); 87(1):47–66.Google Scholar
  98. 98.
    Burnham, K.P., Anderson, D.R., Model selection and inference - a practical information-theoretic approach (Springer, New York, 1998).Google Scholar
  99. 99.
    Kullback, S., Leibler, R.A. On information and sufficiency. Ann. Math. Stat., 22 (1951) 79–86.Google Scholar
  100. 100.
    Akaike H., A new look at the statistical model identification, IEEE Transactions on Automatic control, 19 (1974) 716–723.Google Scholar
  101. 101.
    Borghans, J.A., Taams, L.S., Wauben, M.H.M., De Boer, R.J., Competition for antigenic sites during T cell proliferation: a mathematical interpretation of in vitro data, Proc. Natl. Acad. Sci. USA., 96 (1999) 10782–10787.Google Scholar
  102. 102.
    Zinkernagel RM: Lymphocytic choriomeningitis virus and immunology. Curr Top Microbiol Immunol (2002), 263:1–5.Google Scholar
  103. 103.
    Burnet, F.M. The Clonal Selection Theory of Acquired Immunity (Cambridge University Press, 1959).Google Scholar
  104. 104.
    Ehl, S., Klenerman, P., Zinkernagel, R.M., Bocharov, G. The impact of variation in the number of CD8\(^+\) T-cell precursors on the outcome of virus infection. Cellular Immunology, 189 (1998) 67–73.Google Scholar
  105. 105.
    Altman, J.D., Moss, P.A.H., Goulder, P.J.R., Barouch, D.H., McHeyzer-Williams, M.G., Bell, J.I., McMichael, A.J., Davis, M.M. Phenotypic analysis of antigen-specific T lymphocytes Science, 274 (1996) 94–96.Google Scholar
  106. 106.
    Battegay, M., Cooper, S., Althage,A., Banziger, H., Hengartner, H., Zinkernagel, R.M. Quantification of lymphocytic choriomeningitis virus with an immunological focus assay in 24- or 96-well plates J. Virol. Methods, 33 (1991) 191–198.Google Scholar
  107. 107.
    Paul, C.A.H., A User Guide to Archi, MCCM Rep. 283, University of Manchester.
  108. 108.
    Paul, C.A.H., Archifortran listing. University of Manchester.
  109. 109.
    Numerical Algorithms Group The NAg fortran Library
  110. 110.
    De Boer, R.J., Oprea, M., Antia, R., Murali-Krishna, K., Ahmed, R., Perelson, A.S. Recruitment times, proliferation, and apoptosis rates during the CD8\(^{+}\) T-cell response to lymphocytic choriomeningitis virus. J. Virology, 75 (2001) 10663–10669.Google Scholar
  111. 111.
    Bocharov G, Züst R, Cervantes-Barragan L, Luzyanina T, Chiglintsev E, Chereshnev VA, Thiel V, Ludewig B. A systems immunology approach to plasmacytoid dendritic cell function in cytopathic virus infections. PLoS Pathog. (2010); 6(7):e1001017.Google Scholar
  112. 112.
    Pitt, M.A., Myung, I.J. When a good fit can be bad. Trends Cogn Sci. 2002, 6(10): 421–425.Google Scholar
  113. 113.
    Grünwald, P.D., Myung, J.I., Pitt N.A. (Editors) Advances in Minimum Description Length: Theory and Applications (MIT Press, 2007)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Gennady Bocharov
    • 1
    Email author
  • Vitaly Volpert
    • 2
    • 3
  • Burkhard Ludewig
    • 4
  • Andreas Meyerhans
    • 5
  1. 1.Marchuk Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Institut Camille Jordan, UMR 5208 CNRSCentre National de la Recherche Scientifique (CNRS)VilleurbanneFrance
  3. 3.RUDN UniversityMoscowRussia
  4. 4.Institute of ImmunobiologyKantonsspital St. GallenSt. GallenSwitzerland
  5. 5.Parc de Recerca Biomedica BarcelonaICREA and Universitat Pompeu FabraBarcelonaSpain

Personalised recommendations