Abstract
The role of dormant B cells and cycles is analyzed in the context of a Lotka-Volterra network. It is shown that dormant B cells stabilize a cycle and that in this way both cooperate to preserve the internal image (memory) of an antigen. The network is embedded in a hierarchical scheme which allows adaptation, learning, and innovation by biased and random mutation.
References
G. Köhler and K. Eichmann, eds.,Immunsystem (Spektrum der Wissenschaft Verlags-gesellschaft, Heidelberg, 1987).
A. S. Perelson, ed.,Theoretical Immunology, Parts 1 and 2 (Addison-Wesley, Reading, Massachusetts, 1988).
N. K. Jerne,Sci. Am. 229(1):52 (1973).
A. J. Cunningham, inThe Immune System I, C. M. Steinberg and I. Lefkovits, eds. (S. Karger, Basel, 1981).
G. W. Hoffman,J. Theor. Biol. 17:33 (1986).
G. W. Hoffman, M. W. Benson, G. M. Bree, and P. E. Kinahan,Physica 22D:233 (1986).
G. W. Hoffman, inComputer Simulation in Brain Sciences, R. Coterill, ed. (Cambridge University Press, Cambridge, 1987).
F. M. Burnet,Sci. Am. 204(1):58 (1961).
S. Tonegawa, inImmunsystem (Spektrum der Wissenschaft Verlagsgesellschaft, Heidelberg, 1987), p. 78.
G. Köhler, inImmunsystem (Spektrum der Wissenschaft Verlagsgesellschaft, Heidelberg, 1987), p. 8.
W. Ebeling and R. Feistel,Physik der Selbstorganisation und Evolution (Akademie-Verlag, Berlin, 1982).
M. Peschel and W. Mende,The Predator-Prey Model: Do We Live in a Volterra World? (Akademie-Verlag, Berlin, and Springer, Vienna, 1986).
L. N. Belykh, G. I. Marchuk, and P. V. Petrov, inMathematical Models in Immunology and Medicine, G. I. Matchuk and L. N. Belykh, eds. (Mir, Moscow, 1986) [in Russian].
Yu. M. Romanovskii, N. V. Stepanova, and D. S. Chernavskii,Mathematical Biophysics (Nauka, Moscow, 1984) [in Russian].
A. S. Perelson, Mathematical Immunology, inMathematical Models in Molecular and Cellular Biology, L. A. Segel, ed. (Cambridge University Press, Cambridge, 1980).
J. D. Farmer, N. H. Packard, and A. S. Perelson,Physica 22D:187 (1986).
J. D. Farmer, S. A. Kauffman, N. H. Packard, and A. S. Perelson, inPerspectives in Theoretical Biology and Medicine (National Institutes of Health, Bethesda, Maryland, 1986).
G. Weisbuch and H. Allan,J. Phys. A: Math. Gen. 21:L189 (1988).
I. Dayan, D. Stauffer, and S. Havlin,J. Phys. A: Math. Gen. 21:2473 (1988).
M. Kauffman, J. Urbain, and R. Thomas,J. Theor. Biol. 114:527 (1985).
K. E. Kürten,J. Stat. Phys. 52:489 (1988).
I. Anderson,A First Course in Combinatorial Mathematics (Clarendon Press, Oxford, 1974), Section 4.2.
F. R. Gantmacher,The Theory of Matrices (Chelsea, New York, 1960), Section X.2, Chapter XII;Matrizenrechnung (VEB Deutscher Verlag der Wissenschaften, Berlin, 1988), Section XIII.3, Theorem 6, and Section XIV.5.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Behn, U., van Hemmen, J.L. Network description of the immune system: Dormant B cells stabilize cycles. J Stat Phys 56, 533–545 (1989). https://doi.org/10.1007/BF01044451
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01044451