Memory but no suppression in low-dimensional symmetric idiotypic networks

Abstract

We present a new symmetric model of the idiotypic immune network. The model specifies clones of B-lymphocytes and incorporates: (1) influx and decay of cells; (2) symmetric stimulatory and inhibitory idiotypic interactions; (3) an explicit affinity parameter (matrix); (4) external (i.e. nonidiotypic) antigens. Suppression is the dominant interaction, i.e. strong idiotypic interactions are always suppressive. This precludes reciprocal stimulation of large clones and thus infinite proliferation. Idiotypic interactions first evoke proliferation, this enlarges the clones, and may in turn evoke suppression. We investigate the effect ofidiotypic interactions on normal proliferaJtive immune responses to antigens (e.g. viruses).A 2-D, i.e. two clone, network has a maximum of three stable equilibria: the virgin state and two asymmetric immune states. The immune states only exist if the affinity of the idiotypic interaction is high enough. Stimulation with antigen leads to a switch from the virgin state to the corresponding immune state. The network therefore remembers antigens, i.e. it accounts for immunity/memory by switching beteen multiple stable states. 3-D systems have, depending on the affinities, 9 qualitatively different states. Most of these also account for memory by state switching.Our idiotypic network however fails to account for the control of proliferation, e.g. suppression of excessive proliferation. In symmetric networks, the proliferating clones suppress their anti-idiotypic suppressors long before the latter can suppress the former. The absence of proliferation control violates the general assumption that idiotypic interactions play an important role in immune regulation. We therefore test the robustness of these results by abandoning our assumption that proliferation occurs before suppression. We thus define an "escape from suppression" model, i.e. in the "virgin" state idiotypic interactions are now suppressive. This system erratically accounts for memory and never for suppression. We conclude that our "absence of suppression from idiotypic interactions" does not hinge upon our "proliferation before suppression" assumption.

Localized memories in idiotypic networks

“…A new class of network models has been developed by De Boer (1988), Perelson (1988Perelson ( , 1989a, Varela et al (1988), De Boer & Hogeweg (1989a, De Boer et aL (1990), and Weisbuch (1990). These models rely only upon stimulatory network interactions; a decrease in the amplitude of stimulation plays the role of suppression.…”

“…The problem of immunity and the chain reaction in networks with only stimulatory interactions was analyzed by De Boer (1988) and De Boer & Hogeweg (1989a. These authors first showed that a stimulatory idiotypic interaction between an Abl and an Ab2 clone accounts for a stable immune-state in which an elevated Ab2 clone maintains the stimulation of an even larger Abl clone (De Boer, 1988;De Boer & Hogeweg, 1989a ).…”

“…These authors first showed that a stimulatory idiotypic interaction between an Abl and an Ab2 clone accounts for a stable immune-state in which an elevated Ab2 clone maintains the stimulation of an even larger Abl clone (De Boer, 1988;De Boer & Hogeweg, 1989a ). Then they went on to show that if the Ab2 clone is to maintain the proliferation of the Ab 1 clones, it is also expected to stimulate clones on the Ab3 level (De Boer, 1989;De Boer & Hogeweg, 19896).…”

Contributions of memory B cells to secondary immune response

“…de, Perelson and Delisi, 1980;used in De Boer, 1988;De Boer et al, 1989a,b, 1991Weisbuch et al, 1990;Perelson and Weisbuch, 1992) and its value gives the proportion of normal B cells or memory B cells which can be activated to differentiate into plasma cells depending on the field H. 8, and 8, are the threshold parameters at which the function approximately reaches its half-maximum, i.e. 0.5 (see Fig.…”

A new bell-shaped function for idiotypic interactions based on cross-linking

“…Jerne's (1974) hypothesis that the immune system functions by means of a network of idiotypic interactions has been investigated extensively by theoretical biologists. Theoretical models that can account for memory, tolerance and repertoire selection (Hoffmann, 1980;De Boer and Hogeweg, 1989a;Weisbuch et al, 1990;De Boer and Perelson, 1991) have been developed and they have interesting self-organizing properties (De Boer and Perelson, 1991;De Boer et al, 1992aStewart and Varela, 1991).…”