Recent developments in idiotypic network theory

A recent class of mathematical models of the immune network is reviewed. The models in this class are based upon the bell-shaped activation function that is known to be characteristic for receptor cross-linking. These network models have a large number of self-regulatory properties. This review discusses of number of these properties, i.e. immunological memory, suppression, and repertoire selection.

[1]  Jerne Nk.  Towards a network theory of the immune system. , 1974 .

[2]  A. Coutinho,et al.  Beyond Clonal Selection and Network , 1989, Immunological reviews.

[3]  P. Richter,et al.  A network theory of the immune system , 1975, European journal of immunology.

[4]  A. Perelson,et al.  Size and connectivity as emergent properties of a developing immune network. , 1991, Journal of theoretical biology.

[5]  F. Varela,et al.  Dynamics of a class of immune networks. II. Oscillatory activity of cellular and humoral components. , 1990, Journal of theoretical biology.

[6]  Gérard Weisbuch,et al.  Window automata analysis of population dynamics in the immune system. , 1992 .

[7]  F. Varela,et al.  Second generation immune networks. , 1991, Immunology today.

[8]  A S Perelson,et al.  Modeling immune reactivity in secondary lymphoid organs. , 1992, Bulletin of mathematical biology.

[9]  G. Hoffmann.  A theory of regulation and self‐nonself discrimination in an immune network , 1975, European journal of immunology.

[10]  F. Varela,et al.  Evidence for a functional idiotypic network among natural antibodies in normal mice. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[11]  D. Holmberg,et al.  Establishment and Functional Implications of B‐cell Connectivity , 1989, Immunological reviews.

[12]  F. Varela,et al.  Exploring the Meaning of Connectivity in the Immune Network , 1989, Immunological reviews.

[13]  R. J. Boer.  Symmetric idiotypic networks : connectance and switching, stability, and suppression , 1988 .

[14]  A. Perelson.  Immune Network Theory , 1989, Immunological reviews.

[15]  A S Perelson,et al.  Pattern formation in one- and two-dimensional shape-space models of the immune system. , 1992, Journal of theoretical biology.

[16]  A. Perelson.  Receptor clustering on a cell surface. I. theory of receptor cross-linking by ligands bearing two chemically identical functional groups , 1980 .

[17]  G W Hoffmann,et al.  Qualitative dynamics of a network model of regulation of the immune system: a rationale for the IgM to IgG switch. , 1982, Journal of Theoretical Biology.

[18]  Alan S. Perelson,et al.  Some mathematical models of receptor clustering by multivalent ligands , 1984 .

[19]  Pauline Hogeweg,et al.  Unreasonable implications of reasonable idiotypic network assumptions , 1989 .

[20]  Pauline Hogeweg,et al.  Memory but no suppression in low-dimensional symmetric idiotypic networks , 1989, Bulletin of mathematical biology.

[21]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[22]  Bruce J. West,et al.  Chaos and fractals in human physiology. , 1990, Scientific American.