A simple model for the immune network.

Abstract

In this note I present a simple model for the idiotypic network among antibodies and study its relevance for the maintenance of immunological memory; in particular, the memory capacity of such a model is studied. Some of the similarities with the spin glass model and with neural networks are discussed.Comparison of the brain and the immune system has been quite fruitful in the past (1, 2). Stimulated by the analogy with the brain and by the discovery of the idiotypy (3), Jerne has proposed a network theory for the immune system. Roughly speaking, the production of a given antibody elicits (or suppresses) the production of other antibodies that elicit (or suppress) the production of other antibodies and so on. This is reminiscent of the way in which a firing neuron may induce (or inhibit) the firing of other neurons.In this note I study a specific model that demonstrates that a functional network of antibodies may be possible. I concentrate on modeling the behavior of the immune system in absence of any driving force of external antigens in order to study the maintenance of the immunologic memory. The aim is not to produce a detailed model of the system, which could be used for quantitative comparison with the experimental data, but rather to provide a simple theoretical framework in which different questions may be discussed. For this reason the construction of the model is simplified as much as possible, in the same spirit as the construction of formal neurons (4) and of a symmetric neural network (5). If the model is sufficiently simple, as the one presented here, some results may be derived analytically, without recourse to simulations, and many results obtained in statistical mechanics become available. The use of statistical techniques is inescapable, if we want to understand the behavior of a system in which >106 different kinds of molecules interact.It is well established that antiidiotypic antibodies (i.e., antibodies against antibodies) are normally generated in the process of the response to an external antigen [especially by repeated vaccination (6)]. Such antiidiotypic antibodies also exist in unprimed animals (7). Although one of the main assumptions of the network theory is satisfied, the functional role of the network is not fully understood and a spectrum of different conclusions can be found in the literature. Moreover, if we accept that the network is not a pure accident (8) and that it has a precise functional role, its properties are not clear. There are some crucial points on which there is no general agreement and various options are available.(i) It is not established whether the autoantibodies, which arise in response to a given antibody and have a functional role, are produced by a small set of high responder clones or by a large set of low responder clones.(ii) A related question concerns the effect of a new antigen on the behavior of the network: Does it modify the whole network of antibodies or does the perturbation remain localized within a given set? Does the network remain ...

A comparative analysis of artificial immune network models

“…There are also concepts that are In [21], some hypotheses and questions regarding immune network theory were outlined: (i) antigens modify the whole network or only a portion of it. (ii) the network can be seen either as a whole indivisible unit (open network) or as a set of nearly independent subnetworks (close network).…”

Topological Characterization of Complex Systems: Using Persistent Entropy

“…The important properties of this system, including memory, are then the properties of the network of cells as a whole, rather than of the individual cells [17]. The IN model has been used by Parisi [15] to derive a simplified model for describing the dynamics of a functional network of antibodies in the absence of antigens. The dynamics h i of each antibody i (i = 1, 2, .…”

“…The latter has been largely studied as a complex adaptive system [14], and several other models are available. Concerning the IN model, we consider the simplified description given by Parisi [15], and we use the agent-based simulator C-ImmSim [16] for generating the data to validate our approach. In this work, we analyzed simulated data instead of real data in order to validate the correctness of the methodology in a more controlled way.…”

The nature of immunoglobulin idiotypes and idiotype‐anti‐idiotype interactions in immunological networks

“…The introduction of a novel antigenic epitope into the network may therefore modify the entire network or the pertubation may be localized within an independent regulatory subnetwork (83).…”