Summary
The immune system is the natural defense of an organism. It comprises a network of cells, molecules, and organs whose primary tasks are to defend the organism from pathogens and maintain its integrity. The cooperation between the components of the immune system network realizes effectively and efficiently the processes of pattern recognition, learning, and memory. Our knowledge of the immune system is still incomplete and mathematical modelling has been shown to help better understanding of its underlying principles and organization. In this chapter we provide a brief introduction to the biology of the immune system and describe several approaches used in mathematical modelling of the immune system.
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References
Benjamini, E., Coico, R., Sunshine, G.: Immunology: A Short Course (Wiley, New York Singapore Toronto 2000)
Roitt, I., Brostoff, J., Male, D.: Immunology, 6th edn. (Harcourt, Edinburgh London New York Sydney Toronto 2001)
Bellomo, N., Preziosi, L.: Modeling and mathematical problems related to tumor evolution and its interaction with the immune system. Math. Comput. Model. 32, 413–452 (2000)
International Symposium on Computational Cell Biology (2001). http://www.nrcam.uchc.edu/conference/.
Burnet, F.: The Clonal Selection Theory of Acquired Immunity. (Vanderbilt University, Nashville, 1959)
Jerne, N.K.: The immune system. Sci. Am. 229(1), 52–60 (1973)
Jerne, N.K.: Towards a Network Theory of the Immune System. Ann. Immunol. (Inst. Pasteur) 125C, 373–389(1974)
Zorzenon Dos Santos, R.M.: Immune Responses: Getting Close to Experimental Results with Cellular Automata Models. In Stauffer, D. (ed.): Annual Reviews of Computational Physics, Vol.V (World Scientific, Singapore 1999), 159–202
Lollini, P.L.: private communication (2002)
Perelson, A.S. (ed.): Theoretical Immunology, Part One & Two, SFI Studies in the Sciences of Complexity (Addison-Wesley, Boston 1988)
Perelson, A.S., Weisbuch, G.: Immunology for physicists. Rev. Mod. Phys. 69, 1219–1267 (1997)
Celada, F., Seiden, P.E.: A computer model of cellular interactions in the immune system. Immunol. Today 13(2), 56–62 (1992)
Perelson, A.S., Oster, G.F.: Theoretical studies on clonal selection: Minimal antibody repertoire size and reliability of self-nonself discrimination. J. Theor. Biol. 81, 645–670 (1979)
Farmer, J.D., Packard, N., Perelson, A.S.: The immune system, adaptation and machine learning. Physica D 22, 187–204 (1986)
Behn, U., Leo van Hemmen, J., Sulzer, B.: Memory to Antigenic Challenge of the Immune System: Synergy of Idiotypic Interactions and Memory B-Cells. J. Theor. Biol. 165, 1–25 (1993)
Lippert, K., Behn, U.: Modeling the Immune System: Architecture and dynamics of idiotypic networks. In Stauffer, D. (ed.): Annual Reviews of Computational Physics, Vol.IV (World Scientific, Singapore 1997), 287–311
Behn, U., Celada, F., Seiden, P.E.: Computer modeling in immunology. In Lanzavecchia, A., Malissen, B., Sitia, R. (eds.): Frontiers of Life, Vol.II (Academic Press, London 2001), 611–630.
Bellomo, N., Pulvirenti, M. (eds): Modeling in Applied Sciences: A Kinetic Theory Approach (Birkhäuser, Boston 1996)
Bellomo, N., Lo Schiavo, M.: Lecture Notes on the Generalized Boltzmann Equation (World Scientific, London Singapore 2000)
Forrest, S., Hofmeyr, S.A.: Immunology as information processing. In Segel, L.A., Cohen, I. (eds.): SFI Studies in the Sciences of Complexity: Design Principles for the Immune System and Other Distributed Autonomous Systems (Oxford University Press, New York 2001)
Dasgupta, D. (ed.): Artificial Immune Systems and Their Applications (Springer, Berlin Heidelberg New York 1999)
Parisi, G.: Immunological memory in a network perspective. In Livi, R., Ruffo, S., Ciliberto, S., Buiatti, M. (eds.): Chaos and Complexity (World Scientific, Singapore 1988), 394–401
Parisi, G.: A simple model for the immune network. Proc. Natl. Acad. Sci. USA87, 429–433 (1990)
Smith, R.E., Forrest, S., Perelson, A.S.: Searching for diverse, cooperative populations with genetic algorithms. Evol. Comput. 1(2), 127–149 (1993)
Forrest, S., Javornik, B., Smith, R.E., Perelson, A.S.: Using genetic algorithms to explore pattern recognition in the immune system. Evol. Comput. 1(3), 191–211 (1993)
Kaufman, M., Urbain, J., Thomas, R.: Towards a logical analysis of the immune response. J. Theor. Biol. 114, 527 (1985)
Weisbuch, G., Atlan, H.: Control of the Immune Response. J. Phys. A 21, 189–192 (1988)
Stauffer, D.: In Pires, A., Landau, D.P., Herrmann, H.J. (eds.): Computational Physics and Cellular Automata (World Scientific, Singapore, 1989)
Cohen I.R., Atlan, H.: Network regulation of autoimmunity: an automation model. J. Autoimmun. 2(5), 613–625 (1989)
Pandey, R., Stauffer, D.: Metastability with probabilistic cellular automata in an HIV infection. J. Stat. Phys. 61, 235 (1990)
Neumann, A.U.: Control of the immune response by a threshold automata model on a lattice. Physica A 162, 1–19 (1989)
Dayan, I., Havlin, S., Stauffer, D.: Cellular automata generalization of the Weisbuch-Atlan model for immune response. J. Phys. A 21(3), 2473–2476 (1988)
Atlan, H., Cohen, I.R. (eds.): Theories of Immune Networks (Springer, Berlin Heidelberg New York 1989)
Stewart, J., Varela, F.J.: Morphogenesis in shape-space. Elementary metadynamics in a model of the immune network. J. Theor. Biol. 153, 477–498 (1991)
De Boer, R.J., Segel, L.A., Perelson, A.S.: Pattern formation in one-and twodimensional shape-space models of the immune system. J. Theor. Biol. 155(3), 295–333 (1992)
Segel, L.A., Perelson, A.S.: A paradoxical instability caused by relatively short range inhibition. J. Appl. Math. 50, 91–107 (1990)
Weisbuch, G., De Boer, R.J., Perelson, A.S.: Localized memories in idiotypic networks. J. Theor. Biol. 146(4), 483–99 (1990)
Stauffer, D., Weisbuch, G.: High dimensional simulation of shape space model for immune system. Physica A 180, 42–52 (1992)
Stauffer, D.: Monte-Carlo simulation of Ising-like immunological shape space. Int. J. Mod. Phys. C 5(3), 513–518 (1994)
Dasgupta, S.: Monte Carlo simulation of the shape space model of immunology. Physica A 189, 403–419 (1992)
Bernardes, A.T., Zorzenon dos Santos, R.M.: Immune network at the edge of chaos. J. Theor. Biol. 186(2), 173–187 (1997)
Zorzenon dos Santos, R.M., Bernardes, A.T.: Immunization and Aging: A Learning Process in the Immune Network. Phys. Rev. Lett. 81, 3034–3037 (1998)
Pandey, R., Stauffer, D.: Immune response via interacting three dimensional network of cellular automata. J. de Physique 50, 1 (1989)
Chowdhury, D., Stauffer, D., Choudary, P.V.: A unified discrete model of immune response. J. Theor. Biol. 145(2), 207–215 (1990)
Chowdhury, D.: Immune Network: An Example of Complex Adaptive Systems. In Dasgupta, D. (ed.): Artificial Immune Systems and Their Applications (Springer, Berlin Heidelberg New York 1999)
Chowdhury, D., Stauffer, D.: Statistical Physics of Immune Networks. Physica A 186, 61–81 (1992)
Zorzenon dos Santos, R.M., Coutinho, S.C.: The dynamics of the HIV infection: a cellular automata approach. Phys. Rev. Lett. 87, 168102–168114 (2001)
Bernaschi, M., Castiglione, F.: Selection of escape mutants from immune recognition during HIV infection. Immunol. Cell Biol. 80, 307–313 (2002)
Seiden, P.E., Celada, F.: A model for simulating cognate recognition and response in the immune system. J. Theor. Biol. 158, 329–357 (1992)
Castiglione, F., Bernaschi, M., Succi, S.: Simulating the immune response on a distributed parallel computer. Int. J. Mod. Phys. C 8, 527–545 (1997)
Castiglione, F., Mannella, G., Motta, S., Nicosia, G.: A network of cellular automata for the simulation of the immune system. Int. J. Mod. Phys. C 10, 677–686 (1999)
Motta, S., Nicosia, G.: A plain cellular automata for the simulation of the immune system. In Heemink, A.W., Dekker, L., Arons, H.d.S., Smit, I., v. Stijn, T.L. (eds.): EUROSIM 2001: Shaping Future with Simulation, TU Delft, The Netherlands, 2001
Morpurgo, D., Serenthá, R., Seiden, P.E., Celada, F.: Modeling thymic functions in a cellular automaton. Int. Immunol. 7, 505–516 (1995)
Celada, F., Seiden, P.E.: Affinity maturation and hypermutation in a simulation of the humoral immune response. Eur. J. Immunol. 26(6), 1350–1358 (1996)
Kohler, B., Puzone, R., Seiden, P.E., Celada, F.: A systematic approach to vaccine complexity using an automaton model of the cellular and humoral immune system. Vaccine 19, 862–876 (1999)
Castiglione, F., Motta, F., Nicosia, G.: Pattern Recognition by Primary and Secondary Response of an Artificial Immune System. Theory Biosci. 120(2), 93–106 (2001)
Castiglione, F., Motta, S., Nicosia, G., Zammataro, L.: The effects of an apoptosis mechanism on the immune response. In Heemink, A.W., Dekker, L., Arons, H.d.S., Smit, I., v. Stijn, T.L. (eds.): EUROSIM 2001: Shaping Future with Simulation, TU Delft, The Netherlands, 2001
Jamin, C., Le Corre, R., Lydyard, P.M., Youinou, P.: Anti-CD5 extends the proliferative response of humane CD5+ B cells activated with anti-IgM and interleukine-2. Eur. J. Immunol. 26, 57–62 (1996)
Castiglione, F., Agur, Z.: The Effect of Dose and Inter-Dosing Interval on the Patient’s Hypersensitivity to the Drug: Analyzing a Cellular Automata Model of the Immune System. In Preziosi, L. (ed.): Cancer Modeling and Simulation (Chapman & Hall/CRC Press 2003)
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Motta, S., Brusic, V. (2004). Mathematical Modelling of the Immune System. In: Ciobanu, G., Rozenberg, G. (eds) Modelling in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18734-6_10
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DOI: https://doi.org/10.1007/978-3-642-18734-6_10
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