Localized memories in idiotypic networks

Weisbuch, Gérand; Boer, Rob J. de; Perelson, Alan S.

doi:10.1016/s0022-5193(05)80374-1

“…The equilibrium fields of the idiotypic network models are typically located in the rising and the falling part of the bell-shaped function (Weisbuch et al, 1990;De Boer et al, 1992a, 1993a. Here we develop a rule of thumb for understanding the equilibria.…”

Section: Idiotypic Networkmentioning

confidence: 99%

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

Boer

¹

,

Boerlijst

²

,

Sulzer

³

et al. 1996

Bltn Mathcal Biology

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and asp@tlO.lanl.goc) Most recent models of the immune network are based upon a phenomenological log bell-shaped interaction function. This function depends on a single parameter, the "field," which is the sum of all ligand concentrations weighted by their respective affinities. The typical behavior of these models is dominated by percolation, a phenomenon in which a local stimulus spreads globally throughout the network.The usual reason for employing a log bell-shaped interaction function is that B cells are activated by cross-linking of their surface immunoglobulin receptors. Here we formally derive a new phenomenological log bell-shaped function from the chemistry of receptor cross-linking by bivalent ligand. Specifying how this new function depends on the ligand concentrations requires two fields: a binding field and a cross-linking field.When we compare the activation functions for ligand-receptor pairs with different affinities, the one-field and the two-field functions differ markedly. In the case of the one-field activation function, its graph is shifted to increasingly higher concentration as the affinity decreases but keeps its width and height. In the case of the two-field activation function, the graph of a low-affinity interaction is nested within the graphs of all higheraffinity interactions.We show that this difference in the relations among activation functions for different affinities radically changes the network behavior. In models that described B cell proliferation using the one-field activation function, network behavior was dominated by low-affinity interactions. Conversely, in our new model, the high-affinity interactions are the most significant. As a consequence, percolation is no longer the only typical network behavior.

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“…The new model has the same five steady states as we previously described (De Boer, 1988;De Boer and Nogeweg, 1989a;Weisbuch et al, 1990;De Boer et al, 1993a). Three of the steady states are stable and we called them virgin, immune and suppressed.…”

Section: Idiotypic Networkmentioning

confidence: 99%

“…We have shown that in a network with a Cayley tree topology memory can remain localized, i.e. need not percolate (Weisbuch et al, 1990;Anderson et al, 1993) This result, however, is not robust because percolation is prevalent in Cayley trees with different affinities assigned to different branches and in trees whose topology is slightly modified by the addition of short odd loops (Neumann and Weisbuch, 1992a, b;Boutet de Monvel and Martin, 1995).…”

mentioning

confidence: 99%

“…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).…”

mentioning

confidence: 99%

“…Many recent idiotypic network models are based upon a phenomenological log bell-shaped function determining B cell activation as a function of the total concentration of ligand, or more precisely of the "field" (De Boer, 1988;De Boer and Hogeweg, 1989a, b;Weisbuch et al, 1990;De Boer and Perelson, 1991;De Boer et al, 1992a, b;De Boer et al, 1993a-c;Anderson et al, 1993). This log bell-shaped function is frequently interpreted as a phenomenological description of the fraction of B cell receptors crosslinked by ligand (Perelson, 1984).…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Boer

¹

1996

Bulletin of Mathematical Biology

4

0

View full text Add to dashboard Cite

and asp@tlO.lanl.goc) Most recent models of the immune network are based upon a phenomenological log bell-shaped interaction function. This function depends on a single parameter, the "field," which is the sum of all ligand concentrations weighted by their respective affinities. The typical behavior of these models is dominated by percolation, a phenomenon in which a local stimulus spreads globally throughout the network.The usual reason for employing a log bell-shaped interaction function is that B cells are activated by cross-linking of their surface immunoglobulin receptors. Here we formally derive a new phenomenological log bell-shaped function from the chemistry of receptor cross-linking by bivalent ligand. Specifying how this new function depends on the ligand concentrations requires two fields: a binding field and a cross-linking field.When we compare the activation functions for ligand-receptor pairs with different affinities, the one-field and the two-field functions differ markedly. In the case of the one-field activation function, its graph is shifted to increasingly higher concentration as the affinity decreases but keeps its width and height. In the case of the two-field activation function, the graph of a low-affinity interaction is nested within the graphs of all higheraffinity interactions.We show that this difference in the relations among activation functions for different affinities radically changes the network behavior. In models that described B cell proliferation using the one-field activation function, network behavior was dominated by low-affinity interactions. Conversely, in our new model, the high-affinity interactions are the most significant. As a consequence, percolation is no longer the only typical network behavior.

show abstract