A theory of regulation and self‐nonself discrimination in an immune network

Hoffmann, Geoffrey W.

doi:10.1002/eji.1830050912

Cited by 169 publications

(54 citation statements)

References 71 publications

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“…If after the response, the network settled down to a new steady-state in which these clones were more responsive to antigen, immunological memory would result. Mathematical studies of Jerne's ideas followed rapidly (Hoffmann, 1975;Richter, 1975). Both adopted the "release of suppression" idea, and both demonstrated the existence of several attractors corresponding to states of immunity or suppression.…”

Section: Introductionmentioning

confidence: 99%

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Localized memories in idiotypic networks

Weisbuch¹,

Boer

Perelson

1990

Journal of Theoretical Biology

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The present paper investigates conditions under which immunological memory can be maintained by stimulatory idiotypic network interactions. The paper was motivated by the work of (De Boer & Hogeweg, 1989b, Bull. math. Biol. 51, 381-408.) which claimed that idiotypic memory is not possible because of percolation within the network.Here we reinvestigate the issue of percolation using both the previous model and a simpler one (Weisbuch, 1990, J. theor. Biol. 143, 507-522.) that allows analytic analysis. We focus on network topologies in which each Abl is connected to several Ab2s, which in turn are connected to several Ab3s. It is demonstrated that, for a considerable range of parameters, both models account for the existence of localized memory-states in which only the Ab 1 and the Ab2 clones are activated and the clones of the Ab3 level remain virgin.The existence of localized memory-states seems to contradict the previous percolation result. This discrepancy will be shown to depend on the system dynamics. By simulation we explore the parameter regimes for which one finds percolation and those for which localized memory-states exists. We show that the conditions required for attaining the localized memory-state are considerably more stringent than those required for its existence and local stability. We conclude that both localized memory and percolation are possible in stimulatory idiotypic networks.

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Section: Introductionmentioning

confidence: 99%

“…Hoffmann et aL (Hoffmann, 1975(Hoffmann, , 1979(Hoffmann, , 1980Gunther & Hoffmann, 1982;Hoffmann et al, 1988) also developed "release of suppression" models. The basic idea of these models is to consider only the Abl and the Ab2 populations, which were called "plus" and "minus".…”

Section: Introductionmentioning

confidence: 99%

Localized memories in idiotypic networks

Weisbuch¹,

Boer

Perelson

1990

Journal of Theoretical Biology

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“…Changes with time in X| and Xi are computed using differential equations that simulate the postulated interactions thus: dT = s = s (1) where q = 1,2,3. The Cq (q = 1, 2.…”

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confidence: 99%

Co‐selection in immune network theory and in AIDS pathogenesis

Hoffmann

1994

Immunology & Cell Biology

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Summary Co-selection is a term used to denote the mutual positive selection of individual members from within two diverse populations, such that selection of members within one population is dependent on interaction with (recognition oO one or more member(s) within the other population. Coselection is a recurring theme ofthe idiotypic network model that my colleagues and I have developed. This paper discusses the role that co-seleetion plays in basic symmetrical network theory and in a network model that resolves the I-J paradox. It proposes that co-selection of helper T cells and HIV variants plays a role in the pathogenesis of AIDS. The AIDS model involves a role for the Tcell receptor in the infection of T cells. Finally, a way in which a co-selection process may potentially be used in the prevention and therapy of harmful forms of immunity is described.Key words: AIDS pathogenesis, co-selection, HIV, I-J. network theory, suppression, T cells. Idiotypic network theoryThe non-trivial task ofthe immune network theorist is to find a model that is as simple as possible and exhibits a variety of observed stimulus-response behaviours. A symmetrical network theory has been developed that provides a basis for understanding a fairly wide range of immunological phenomena in a relatively simple way.'""^ The theory includes roles for three cell types (B cells. T cells and non-specific accessory cells), antibodies, specific T cell factors and antigen non-specific 'second signal' lymphokines. The theory accounts for immune memory, low zone tolerance, an immune response, high zone tolerance, antigenic competition, the carrier effect, T independent antigens, the helper and suppressor roles of T cells. MHC restriction, the I-J phenomenon and AIDS pathogenesis. Mathematical modelling supports the existence of multiple stable steady states in the system as the basis of immunological memory.In contrast to more traditional modelling ofthe immune system, the focus ofthe theory is not on a single cell or a single clone, but on the specific interactions between each cell and the cells that recognize and are recognized by the cell. The fate of each clone depends on the size ofthe clone, the number of cells in similar clones and the number of cells in more or less complementary clones. The important dynamical variable is an /!-dimensional vector that specifies how many cells are present with each of « different specificities. Memory and learning in the system are represented by a large number of different stable states, and the possibility of antigen causing switching between these stable states. The theory includes three kinds of symmetrical interactions between X, and X, lymphocytes, namely symmetrical stimulation, symmetrical inhibition and symmetrical killing. Specific stimulation is postulated to involve the cross-linking of receptors and specific inhibition is ascribed to specific Tcell factors."'-Specific Tcell factors are believed to be soluble T cell receptors or T cell receptor-like molecules, and to have a molecular weight ...

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“…Hoffmann, 1975;Richter, 1975Richter, , 1978Segel and Perelson, 1988) studying somewhat simplified models lacking the distinction between B cells and antibody. The behavior of these simplified models is dominated by a number of stable steady states.…”

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confidence: 99%

Immune network behavior—I. From stationary states to limit cycle oscillations

DEBOER¹,

PERELSON²,

KEVREKIDIS³

1993

Bulletin of Mathematical Biology

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We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation. B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis. how each of the processes influences the model's behavior. After appropriate nondimensionalization. the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-type equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.

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A theory of regulation and self‐nonself discrimination in an immune network

Cited by 169 publications

References 71 publications

Localized memories in idiotypic networks

Localized memories in idiotypic networks

Co‐selection in immune network theory and in AIDS pathogenesis

Immune network behavior—I. From stationary states to limit cycle oscillations

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