Abstract
The capacity of a model immune network in terms of the number of different antigens that can be vaccinated against without any memory lost is computed and tested by numerical simulations. We also investigate memory loss and failure to vaccinate due to overcrowding the network with too many antigens. The computations are done for two different strategies for proliferation, one implying all the antigen specific clones and the second one being more thrifty.
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Literature
Cohen, I. R. 1989. Natural Id-anti-Id networks and the immunological homonculus, 6–12. In:Theories of Immune Networks, H. Atlan and I. R. Cohen (Eds). Springer: Berlin, F.R.G.
De Boer, R. J. 1983. GRIND: Great Integrator Differential Equations. Bioinformatics Group, University of Utrecht, The Netherlands.
De Boer, R. J. and P. Hogeweg. 1989. Unreasonable implications of reasonable idiotypic network assumptions.Bull. Math. Biol. 51, 381–408.
De Boer, R. J. and A. S. Perelson. 1991. Size and connectivity as emerging properties of a developing immune network.J. Theoret. Biol. 149, 381–424.
Farmer, J. D., N. H. Packard and A. S. Perelson. 1986. The immune system, adaptation, and machine learning.Physica D 22, 187–204.
Gergely, J. 1988.Multifunctional IgG and IgG Binding Receptors. Akademia Kiado, Budapest.
Gollub, E. S. 1992.Immunology: A Synthesis. Sinauer, Sunderland, MS, U.S.A.
Hertz, J., A. Krogh and R. G. Palmer. 1990.Introduction to the Theory of Neural Computation. Addison-Wesley, Redwood, CA, U.S.A.
Hindmarsh, A. C. 1983. Odepack, a systematized collection of ode solvers. In:Scientific Computing, R. S. Stepleman (Ed.), pp. 55–64. North-Holland, Amsterdam.
Hoffmann, G. W. 1979. A mathematical model of the stable states of a network theory of self-regulation.Lect. Notes Biomath. 32, 239–257.
Jerne, N. K. 1974.Ann. Immunol. (Inst. Pasteur) 125C, 373–389.
Kaufman, M. 1988. Role of multistability in an immune response model: a combined discrete and continuous approach. In:Theoretical Immunology, Part One, A. S. Perelson (Ed.), pp. 199–222. Addison-Wesley, Redwood, CA, U.S.A.
Mézard, M., G. Parisi and M. A. Virasoro. 1988.Spin Glass Theory and Beyond. World Scientific, Singapore.
Nadal, J. P. 1983. Thesis,Etude de Systèmes Dirigés en Physique Statistique. Paris.
Nadal, J. P., G. Toulouse, J. P. Changeux and S. Dehaene. 1986. Networks of formal neurones and memory palimpsests.Europhysics Lett. 1, 535–542.
Neumann, A. U. and G. Weisbuch. 1992a. Window automata analysis of population dynamics in the immune system.Bull. Math. Biol. 54, 21–44.
Neumann, A. U. and G. Weisbuch. 1992b. Dynamics and topology of immune networks.Bull. Math. Biol. 54, 699–726.
Nossal, G. J. V. 1983. Cellular mechanisms of immunological tolerance.Ann. Rev. Immunol. 1, 33–62.
Perelson, A. S. 1984. Some mathematical models of receptor clustering by multivalent ligands. In:Cell Surface Dynamics: Concepts and Models, A. S. Perelson, C. DeLisi and F. W. Wiegel (Eds), pp. 223–276. Marcel Dekker, NY, U.S.A.
Perelson, A. S. and G. Weisbuch. 1994. Immunology for physicists,Rev. Modern Physics, in press.
Segel, L. A. and A. S. Perelson. 1990a. Some reflections on memory in shape space. In:Theories of Immune Networks, H. Atlan and I. R. Cohen (Eds), pp. 63–70. Springer-Verlag, Berlin.
Vakil, M. and J. F. Kearney. 1988. Regulatory influences of neonatal multispecific antibodies on the developing B cell repertoire.Int. Rev. Immunol. 3, 117–131.
Weisbuch, G., R. De Boer and A. S. Perelson. 1990. Localized memories in idiotypic networks.J. Theoret. Biol. 146, 483–499.
Weisbuch, G. 1990.Complex Systems Dynamics. Addison-Wesley, Redwood, CA, U.S.A.
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Weisbuch, G., Oprea, M. Capacity of a model immune network. Bltn Mathcal Biology 56, 899–921 (1994). https://doi.org/10.1007/BF02458273
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DOI: https://doi.org/10.1007/BF02458273