Abstract
Mathematical immunology is the branch of mathematics dealing with the application of mathematical methods and computational algorithms to explore the structure, dynamics, organization and regulation of the immune system in health and disease. We review the conceptual and mathematical foundation of modelling in immunology formulated by Guri I. Marchuk. The current frontier studies concerning the development of multiscale multiphysics integrative models of the immune system are presented.
Acknowledgment
We thank Andreas Meyerhans for fruitful discussions of various topics of the article and for critically reading this manuscript.
Funding: The reported study was funded by the Russian Science Foundation (grant number 18-11-00171) (Sections 3.1–3.3) and by RFBR (project number 20-01-00352) (Sections 1, 2, and 3.4). G. A. Bocharov, D. S. Grebennikov, and R. S. Savinkov were partly supported by Moscow Center for Fundamental and Applied Mathematics (agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2019-1624). R. S. Savinkov was partly supported by the RUDN University Program 5-100.
References
[1] J. Ang, S. Bagh, B. P. Ingalls, and D. R. McMillen, Considerations for using integral feedback control to construct a perfectly adapting synthetic gene network. J. Theor. Biology266 (2010), No. 4, 723–738.10.1016/j.jtbi.2010.07.034Suche in Google Scholar
[2] B. R. Angermann, F. Klauschen, A. D. Garcia, T. Prustel, F. Zhang, R. N. Germain, and M. Meier-Schellersheim, Computational modeling of cellular signaling processes embedded into dynamic spatial contexts. Nature Methods9 (2012), No. 3, 283–289.10.1038/nmeth.1861Suche in Google Scholar
[3] J. Argilaguet, M. Pedragosa, A. Esteve-Codina, G. Riera, E. Vidal, C. Peligero-Cruz, V. Casella, D. Andreu, T. Kaisho, G. Bocharov, B. Ludewig, S. Heath, and A. Meyerhans, Systems analysis reveals complex biological processes during virus infection fate decisions. Genome Research29 (2019), No. 6, 907–919.10.1101/gr.241372.118Suche in Google Scholar
[4] G. I. Bell, Predator-prey equations simulating an immune response. Math. Biosci. 16 (1973), No. 3-4, 291–314.10.1016/0025-5564(73)90036-9Suche in Google Scholar
[5] G. A. Bocharov, Modelling the dynamics of LCMV infection in mice: conventional and exhaustive CTL responses. J. Theor. Biology192 (1998), No. 3, 283–308.10.1006/jtbi.1997.0612Suche in Google Scholar PubMed
[6] G. A. Bocharov and G. I. Marchuk, Applied problems of mathematical modeling in immunology. Comput. Math. Math. Phys. 40 (2000), No. 12, 1830–1844.Suche in Google Scholar
[7] G. Bocharov, A. Danilov, Yu. Vassilevski, G. I. Marchuk, V. A. Chereshnev, and B. Ludewig, Reaction–diffusion modelling of interferon distribution in secondary lymphoid organs. Mathematical Modelling of Natural Phenomena6 (2011), No. 7, 13–26.10.1051/mmnp/20116702Suche in Google Scholar
[8] G. Bocharov, J. Argilaguet, and A. Meyerhans, Understanding experimental LCMV infection of mice: The role of mathematical models. J. Immunology Research (2015), 739706.10.1155/2015/739706Suche in Google Scholar PubMed PubMed Central
[9] G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko, and D. S. Grebennikov, Maximum response perturbation-based control of virus infection model with time-delays. Russ. J. Numer. Anal. Math. Modelling32 (2017), No. 5, 275–291.10.1515/rnam-2017-0027Suche in Google Scholar
[10] G. Bocharov, V. Volpert, B. Ludewig, and A. Meyerhans, Mathematical Immunology of Virus Infections. Springer International Publishing, 2018.10.1007/978-3-319-72317-4Suche in Google Scholar
[11] G. Bocharov, V. Volpert, B. Ludewig, and A. Meyerhans, Editorial: Mathematical modeling of the immune system in homeostasis, infection, and disease. Frontiers in Immunology10 (2020), 2944.10.3389/fimmu.2019.02944Suche in Google Scholar PubMed PubMed Central
[12] A. Bouchnita, G. Bocharov, A. Meyerhans, and V. Volpert, Hybrid approach to model the spatial regulation of T cell responses. BMC Immunology18 (2017), No. 29(1), 11–22.10.1186/s12865-017-0205-0Suche in Google Scholar PubMed PubMed Central
[13] A. Bouchnita, G. Bocharov, A. Meyerhans, and V. Volpert, Towards a multiscale model of acute HIV infection. Computation5 (2017), No. 6(1), 1–22.10.3390/computation5010006Suche in Google Scholar
[14] N. A. Cilfone, D. E. Kirschner, and J. J. Linderman, Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems. Cellular Molecular Bioengrg. 8 (2015), No. 1, 119–136.10.1007/s12195-014-0363-6Suche in Google Scholar PubMed PubMed Central
[15] J. Cohen, Combo of two HIV vaccines fails its big test. Science367 (2020), No. 6478, 611–612.10.1126/science.367.6478.611Suche in Google Scholar PubMed
[16] R. N. Germain, M. Meier-Schellersheim, A. Nita-Lazar, and I. D. Fraser, Systems biology in immunology: a computational modeling perspective. Annual Review of Immunology29 (2011), No. 1, 527–585.10.1146/annurev-immunol-030409-101317Suche in Google Scholar PubMed PubMed Central
[17] R. N. Germain, Will systems biology deliver its promise and contribute to the development of new or improved vaccines?: What really constitutes the study of systems biology and how might such an approach facilitate vaccine design. Cold Spring Harbor Perspectives in Biology10 (2018), No. 8, a033308.10.1101/cshperspect.a033308Suche in Google Scholar PubMed PubMed Central
[18] D. S. Grebennikov and G. A. Bocharov, Modelling the structural organization of lymph nodes. In: IEEE Congress on Evolutionary Computation (CEC), June 2017, 2017, pp. 2653–2655.10.1109/CEC.2017.7969628Suche in Google Scholar
[19] D. S. Grebennikov and G. A. Bocharov, Spatially resolved modelling of immune responses following a multiscale approach: from computational implementation to quantitative predictions. Russ. J. Numer. Anal. Math. Modelling34 (2019), No. 5, 253–260.10.1515/rnam-2019-0021Suche in Google Scholar
[20] D. S. Grebennikov, A. Bouchnita, V. Volpert, N. Bessonov, A. Meyerhans, and G. Bocharov, Spatial lymphocyte dynamics in lymph nodes predicts the cytotoxic T cell frequency needed for HIV infection control. Frontiers in Immunology10 (2019), No. 1213, 1–15.Suche in Google Scholar
[21] D. S. Grebennikov, D. O. Donets, O. G. Orlova, J. Argilaguet, A. Meyerhans, and G. A. Bocharov, Mathematical modeling of the intracellular regulation of immune processes. Molecular Biology53 (2019), No. 5, 718–731.10.1134/S002689331905008XSuche in Google Scholar
[22] Z. Grossman and W. E. Paul, Self-tolerance: context dependent tuning of T cell antigen recognition. Seminars in Immunology12 (2000), No. 3, 197–203.10.1006/smim.2000.0232Suche in Google Scholar PubMed
[23] Z. Grossman and W. E. Paul, Autoreactivity, dynamic tuning and selectivity. Current Opinion in Immunology13 (2001), No. 6, 687–698.10.1016/S0952-7915(01)00280-1Suche in Google Scholar
[24] Z. Grossman and W. E. Paul, Dynamic tuning of lymphocytes: physiological basis, mechanisms, and function. Annual Review of Immunology33 (2015), No. 1, 677–713.10.1146/annurev-immunol-032712-100027Suche in Google Scholar PubMed
[25] Z. Grossman, Immunological paradigms, mechanisms, and models: conceptual understanding is a prerequisite to effective modeling. Frontiers in Immunology10 (2019), 2522.10.3389/fimmu.2019.02522Suche in Google Scholar PubMed PubMed Central
[26] A. Handel, N. L. La Gruta, and P. G. Thomas, Simulation modelling for immunologists. Nature Reviews Immunology20 (2020), No. 3, 186–195.10.1038/s41577-019-0235-3Suche in Google Scholar PubMed
[27] B. F. Haynes, G. M. Shaw, B. Korber, G. Kelsoe, J. Sodroski, B. H. Hahn, P. Borrow, and A. J. McMichael, HIV-host interactions: implications for vaccine design. Cell Host & Microbe19 (2016), No. 3, 292–303.10.1016/j.chom.2016.02.002Suche in Google Scholar PubMed PubMed Central
[28] M. Jafarnejad, A. Z. Ismail, D. Duarte, C. Vyas, A. Ghahramani, D. C. Zawieja, C. Lo Celso, G. Poologasundarampillai, and J. E. Moore, Quantification of the whole lymph node vasculature based on tomography of the vessel corrosion casts. Sci. Reports9 (2019), No. 1, 13380.10.1038/s41598-019-49055-7Suche in Google Scholar PubMed PubMed Central
[29] I. D. Kelch, G. Bogle, G. B. Sands, A. R. Phillips, I. J. LeGrice, and D. P. Rod, Organ-wide 3D-imaging and topological analysis of the continuous microvascular network in a murine lymph node. Sci. Reports5 (2015), No. 1, 16534.Suche in Google Scholar
[30] D. Kirschner, E. Pienaar, S. Marino, and J. J. Linderman, A review of computational and mathematical modeling contributions to our understanding of Mycobacterium tuberculosis within-host infection and treatment. Current Opinion in Systems Biology (2017), 170–185.10.1016/j.coisb.2017.05.014Suche in Google Scholar PubMed PubMed Central
[31] A. Kislitsyn, R. Savinkov, M. Novkovic, L. Onder, and G. Bocharov, Computational approach to 3D modeling of the lymph node geometry. Computation3 (2015), No. 2, 222–234.10.3390/computation3020222Suche in Google Scholar
[32] G. I. Marchuk, Mathematical modelling of immune response in infectious diseases. Ser. Mathematics and its Applications, Vol. 395. Kluwer Academic Publishers, Dordrecht–Boston–Mass, 1997.10.1007/978-94-015-8798-3Suche in Google Scholar
[33] G. I. Marchuk, Mathematical modeling in immunology and medicine. Selected works, Vol. 4. Russian Academy of Sciences, Institute of Numerical Mathematics, Moscow, 2018 (in Russian).Suche in Google Scholar
[34] I. Mondor, A. Jorquera, C. Sene, S. Adriouch, R. H. Adams, B. Zhou, S. Wienert, F. Klauschen, and M. Bajénoff, Clonal proliferation and stochastic pruning orchestrate lymph node vasculature remodeling. Immunity45 (2016), No. 4, 877–888.10.1016/j.immuni.2016.09.017Suche in Google Scholar PubMed
[35] C. A. Mims, Mims’ pathogenesis of infectious disease. Academic Press, London, 1995.Suche in Google Scholar
[36] Yu. M. Nechepurenko, M. Yu. Khristichenko, D. S. Grebennikov, and G. A. Bocharov, Bistability analysis of virus infection models with time delays. Discrete Continuous Dynamical Systems–S (2018), 10.3934/dcdss.2020166.Suche in Google Scholar
[37] M. Novkovic, L. Onder, J, Cupovic, J. Abe, D. Bomze, V. Cremasco, E. Scandella, J. V. Stein, G. Bocharov, S. J. Turley, and B. Ludewig, Topological small-world organization of the fibroblastic reticular cell network determines lymph node functionality (Ed. T. Schroeder). PLOS Biology14 (2016), No. 7, e1002515.10.1371/journal.pbio.1002515Suche in Google Scholar PubMed PubMed Central
[38] M. Novkovic, L. Onder, H. Cheng, G. Bocharov, and B. Ludewig, Integrative computational modeling of the lymph node stromal cell landscape. Frontiers in Immunology9 (2018), 2428.10.3389/fimmu.2018.02428Suche in Google Scholar PubMed PubMed Central
[39] M. Novkovic, L. Onder, G. Bocharov, and B. Ludewig, Topological structure and robustness of the lymph node conduit system. Cell Reports30 (2020), No. 3, 893–904.e6.10.1016/j.celrep.2019.12.070Suche in Google Scholar PubMed
[40] M. Rinas, Data-driven modeling of the dynamic competition between virus infection and the antiviral interferon response. PhD Thesis, University of Heidelberg, 2015.Suche in Google Scholar
[41] R. Savinkov, A. Kislitsyn, D. J. Watson, R. van Loon, I. Sazonov, M. Novkovic, L. Onder, and G. Bocharov, Data-driven modelling of the FRC network for studying the fluid flow in the conduit system. Engrg. Appl. Artificial Intelligence62 (2017), 341–349.10.1016/j.engappai.2016.10.007Suche in Google Scholar
[42] O. Shcherbatova, D. Grebennikov, I. Sazonov, A. Meyerhans, and G. Bocharov, Modeling of the HIV-1 life cycle in productively infected cells to predict novel therapeutic targets. Pathogens9 (2020), No. 4.10.3390/pathogens9040255Suche in Google Scholar PubMed PubMed Central
[43] R. Tretyakova, R. Savinkov, G. Lobov, and G. Bocharov, Developing computational geometry and network graph models of human lymphatic system. Computation6 (2017), No. 1, 1.10.3390/computation6010001Suche in Google Scholar
[44] N. Wiener, Cybernetics: or Control and Communication in the Animal and the Machine. The MIT Press, Cambridge, MA, 2019.10.7551/mitpress/11810.001.0001Suche in Google Scholar
[45] V. Zheltkova, J. Argilaguet, C. Peligero, G. Bocharov, and A. Meyerhans, Prediction of PD-L1 inhibition effects for HIV-infected individuals. PLOS Computational Biology15 (2019), No. 11, e1007401.10.1371/journal.pcbi.1007401Suche in Google Scholar PubMed PubMed Central
[46] R. M. Zinkernagel, H. Hengartner, and L. Stitz, On the role of viruses in the evolution of immune responces. British Medical Bulletin41 (1985), No. 1, 92–97.10.1093/oxfordjournals.bmb.a072033Suche in Google Scholar PubMed
[47] R. M. Zinkernagel, On immunity against infections and vaccines. Scandinavian J. Immunology60 (2004), No. 1-2, 9–13.10.1111/j.0300-9475.2004.01460.xSuche in Google Scholar PubMed
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Preface
- Methods of variational data assimilation with application to problems of hydrothermodynamics of marine water areas
- Mathematical immunology: from phenomenological to multiphysics modelling
- Iterative solution methods for elliptic boundary value problems
- Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform
- Tensor decompositions and rank increment conjecture
- Global optimization based on TT-decomposition
Artikel in diesem Heft
- Frontmatter
- Preface
- Methods of variational data assimilation with application to problems of hydrothermodynamics of marine water areas
- Mathematical immunology: from phenomenological to multiphysics modelling
- Iterative solution methods for elliptic boundary value problems
- Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform
- Tensor decompositions and rank increment conjecture
- Global optimization based on TT-decomposition