Memory but no suppression in low-dimensional symmetric idiotypic networks
type: Item
instance of: scholarly article
title: Memory but no suppression in low-dimensional symmetric idiotypic networks
zbMATH Open document ID: 0662.92006
DOI: 10.1007/BF02458444
author: Pauline Hogeweg
author: Rob J. De Boer
published in: Bulletin of Mathematical Biology
publication date: 1989-01-01T00:00:00Z
review text: 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. non-idiotypic) 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 of idiotypic interactions on normal proliferative 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 between multiple stable states. 3-D systems have, depending on the affinities, 9 qualitative 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…
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 94C99
zbMATH DE Number: 4083426
zbMATH Keywords: symmetric model
zbMATH Keywords: idiotypic immune network
zbMATH Keywords: clones of B-lymphocytes
zbMATH Keywords: Suppression
zbMATH Keywords: idiotypic interactions
zbMATH Keywords: proliferative immune responses to antigens
zbMATH Keywords: viruses
zbMATH Keywords: stable equilibria
zbMATH Keywords: virgin state
zbMATH Keywords: asymmetric immune states
zbMATH Keywords: memory by state switching
zbMATH Keywords: proliferation
zbMATH Keywords: immune regulation
zbMATH Keywords: escape from suppression model
zbMATH Keywords: absence of suppression from idiotypic interactions
Wikidata QID: Q52118136
MaRDI profile type: Publication
cites work: Q4721895
cites work: Unreasonable implications of reasonable idiotypic network assumptions
cites work: A reliable Rosenbrock integrator for stiff differential equations
full work available at URL: https://doi.org/10.1007/bf02458444
OpenAlex ID: W2103734328
description: scientific article; zbMATH DE number 4083426