Size and Connectivity of the Idiotypic Network Are Independent of the Discreteness of the Affinity Distribution

Detours, Vincent; Sulzer, Bernhard; Perelson, Alan S.

doi:10.1006/jtbi.1996.0231

Cited by 25 publications

(33 citation statements)

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“…General immune system models that include clones with receptors have been simulated with the order of 10 3 clones (DeBoer & Perelson, 1991;Celada & Seiden, 1996;Detours et al, 1996). Lattice based cellular models that use only one or two bits to represent the concentration of highly simplified clones, and measure affinity by neighborhood on the lattice, have simulated 10 4 clones (DeBoer et al, 1992a), and 10 8 clones (Stauffer & Sahimi, 1994) (the latter on a Cray-YMP).…”

Section: Discussionmentioning

confidence: 99%

“…Seiden & Celada (1992), Forrest & Perelson (1991), and Perelson et al (1996) (after Farmer et al (1986)), represented molecules as strings of 8, 32, and 64 bits respectively and measured affinity as a function of the Hamming distance 3 (or a variation on it) between them. Weisbuch & Oprea (1994) and Detours et al (1996) represented molecules as strings of digits chosen from a 4 and 16 letter alphabet respectively. Smith et al (1997b) determined that representing molecules as strings of 20 symbols, with each symbol chosen from a 4 letter alphabet, and affinity measured as a function of Hamming distance, as well as using a realistic-size repertoire of 10 7 B cell clones, gave good fits to immunological data important for a model of cross-reactive memory.…”

Section: Introductionmentioning

confidence: 99%

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Using Lazy Evaluation to Simulate Realistic-size Repertoires in Models of the Immune System

Smith

1998

Bulletin of Mathematical Biology

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We describe a method of implementing efficient computer simulations of immune systems that have a large number of unique B and/or T cell clones. The method uses an implementation technique called lazy evaluation to create the illusion that all clones are being simulated, while only actually simulating a much smaller number of clones that can respond to the antigens in the simulation. The method is effective because only 0.001% to 0.01% of clones can typically be stimulated by an antigen, and because many simulations involve only a small number of distinct antigens. A lazy simulation of a realistic number of clones and 10 distinct antigens is 1,000 times faster and 10,000 times smaller than a conventional simulation-making simulations of immune systems with realistic-size repertoires computationally tractable.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Using Lazy Evaluation to Simulate Realistic-size Repertoires in Models of the Immune System

Smith

1998

Bulletin of Mathematical Biology

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“…For the matching algorithm we used both the hamming and adjacency matches, and found similar results. The 'hamming match' between two bit strings equals the sum of all complementary bits, and the 'adjacency match' equals the longest block of adjacent complementary bits (figure 1; De Boer & Perelson 1991;Detours et al 1996). Here, we only present the results obtained with the adjacency match, because it embodies the nonlinear nature of the T-cell MHC-peptide interaction better than the hamming match does.…”

Section: Models For T-cell Tolerance Inductionmentioning

confidence: 99%

Activation–threshold tuning in an affinity model for the T–cell repertoire

Scherer

Noest

Boer

2004

Proc. R. Soc. Lond. B

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Naive T cells respond to peptides from foreign proteins and remain tolerant to self peptides from endogenous proteins. It has been suggested that self tolerance comes about by a 'tuning' mechanism, i.e. by increasing the T-cell activation threshold upon interaction with self peptides. Here, we explore how such an adaptive mechanism of T-cell tolerance would influence the reactivity of the T-cell repertoire to foreign peptides. We develop a computer simulation model in which T cells are tolerized by increasing their activation-threshold dependent on the affinity with which they see self peptides presented in the thymus. Thus, different T cells acquire different activation thresholds (i.e. different cross-reactivities). In previous mathematical models, T-cell tolerance was deletional and based on a fixed cross-reactivity parameter, which was assumed to have evolved to an optimal value. Comparing these two different toleranceinduction mechanisms, we found that the tuning model performs somewhat better than an optimized deletion model in terms of the reactivity to foreign antigens. Thus, evolutionary optimization of clonal cross-reactivity is not required. A straightforward extension of the tuning model is to delete T-cell clones that obtain a too high activation threshold, and to replace these by new clones. The reactivity of the immune repertoires of such a replacement model is enchanced compared with the basic tuning model. These results demonstrate that activation-threshold tuning is a functional mechanism for self tolerance induction.

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“…e-mail: asp@lanl.gov. (66). Affinity, K, is the sum of interaction strengths of contacting digits in aligned strings.…”

Section: Modelmentioning

confidence: 99%

Explaining high alloreactivity as a quantitative consequence of affinity-driven thymocyte selection

Detours

Perelson

1999

Proc. Natl. Acad. Sci. U.S.A.

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Interactions between T cell receptors and peptides bound to molecules encoded by the MHC genes underly T cell activation. More than 1% of T cells are activated by foreign (allogenic) MHC molecules, a phenomenon called alloreactivity. Reconciling the high frequency of alloreactivity with the fact that only 1 T cell in 10 4 -10 6 responds to a given foreign antigen presented on self MHC has been a longstanding puzzle. We show, by using a quantitative model, that this difference follows from the affinity model of T cell selection. Further, we demonstrate that highly alloreactive pre-and post-selection repertoires can be obtained without assuming germline bias of T cell receptors toward recognition of allelespecific MHC residues. It has been proposed that alloreactivity occurs because self and foreign MHCs bind different subsets of self peptides or alter their conformation differently. We find that such effects decrease rather than increase alloreactivity. Overall, our results show that the affinity model of T cell selection can quantitatively explain both self MHC restriction and high alloreactivity.Maturation of T cells in the thymus involves a two-step selection process driven by the affinity of their T cell receptors (TCR) for self peptides presented on proteins encoded by MHC genes. The first step, positive selection (1, 2), disgards thymocytes bearing TCRs with low affinity for MHC-peptide complexes expressed in the thymus. This eliminates T cells that cannot recognize MHC molecules. The second step, negative selection (3, 4), deletes cells with high affinity receptors for thymic MHC-peptide complexes. Thus, removing many self reactive cells. Overall, only 3% of the T cells produced in the thymus have TCRs with the intermediate affinity required to reach the periphery (5).Because MHC genes are extremely polymorphic, two individuals are very unlikely to express the same set of MHC molecules. As a result of positive selection, T cells are self MHC restricted: they recognize pathogens presented by self MHC molecules but ignore them if presented by foreign MHC molecules (6-14). MHC polymorphism is also the main obstacle to tissue transplantation (15). Typically, 1-24% of T cells are alloreactive (16, 17), i.e., they respond to foreign (allogenic) MHC molecules. Reconciling this high alloresponse frequency with the fact that among naive T cells only 1 in 10 4 -10 6 recognizes a given pathogen (18, 19) is a long-standing immunological puzzle. In this paper, we examine quantitatively three hypotheses proposed to explain the high frequency of alloreactivity.The first hypothesis, due to Matzinger and Bevan (20), suggests that the 2-4 orders of magnitude difference between antigen and MHC response frequencies results from the difference in the diversity of these two types of molecule on the surface of antigen presenting cells (APCs). Because each individual expresses only a few distinct MHC molecules and eachThe publication costs of this article were defrayed in part by page charge payment. This article must the...

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Size and Connectivity of the Idiotypic Network Are Independent of the Discreteness of the Affinity Distribution

Cited by 25 publications

References 0 publications

Using Lazy Evaluation to Simulate Realistic-size Repertoires in Models of the Immune System

Using Lazy Evaluation to Simulate Realistic-size Repertoires in Models of the Immune System

Activation–threshold tuning in an affinity model for the T–cell repertoire

Explaining high alloreactivity as a quantitative consequence of affinity-driven thymocyte selection

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