# Author V. Calenbuhr

Calenbuhr V., Bersini H., Stewart J. & Varela F. J. (1995) Natural tolerance in a simple immune network. Journal of Theoretical Biology 177: 199–213. https://cepa.info/1998

Calenbuhr V., Bersini H., Stewart J. & Varela F. J.
(

1995)

Natural tolerance in a simple immune network.
Journal of Theoretical Biology 177: 199–213.
Fulltext at https://cepa.info/1998
The following basic question is studied here: In the relatively stable molecular environment of a vertebrate body, can a dynamic idiotypic immune network develop a natural tolerance to endogenous components? The approach is based on stability analyses and computer simulation using a model that takes into account the dynamics of two agents of the immune system, namely B-lymphocytes and antibodies. The study investigates the behavior of simple immune networks in interaction with an antigen whose concentration is held constant as a function of the symmetry properties of the connectivity matrix of the network. Current idiotypic network models typically become unstable in the presence of this type of antigen. It is shown that idiotypic networks of a particular connectivity show tolerance towards auto-antigen without the need for ad hoc mechanisms that prevent an immune response. These tolerant network structures are characterized by aperiodic behavior in the absence of auto-antigen. When coupled to an auto-antigen, the chaotic attractor degenerates into one of several periodic ones, and at least one of them is stable. The connectivity structure needed for this behavior allows the system to adopt particular dynamic concentration patterns which do not lead to an unbounded immune response. Possible implications for the understanding of autoimmune disease and its treatment are discussed.

Calenbuhr V., Bersini H., Varela F. J. & Stewart J. (1993) The impact of the structure of the connectivity matrix on the dynamics of a simple model for the immune network. In: Mosekilde E. (ed.) Proceedings of the First Copenhagen Symposium on Computer Simulation in Biology, Ecology and Medicine. Simulation Council Inc., San Diego CA: 41–45.

Calenbuhr V., Bersini H., Varela F. J. & Stewart J.
(

1993)

The impact of the structure of the connectivity matrix on the dynamics of a simple model for the immune network.
In: Mosekilde E. (ed.) Proceedings of the First Copenhagen Symposium on Computer Simulation in Biology, Ecology and Medicine. Simulation Council Inc., San Diego CA: 41–45.
Calenbuhr V., Varela F. J. & Bersini H. (1996) Natural tolerance as a function of network connectivity. International Journal of Bifurcation and Chaos 6(9): 1691–1702. https://cepa.info/2078

Calenbuhr V., Varela F. J. & Bersini H.
(

1996)

Natural tolerance as a function of network connectivity.
International Journal of Bifurcation and Chaos 6(9): 1691–1702.
Fulltext at https://cepa.info/2078
This article investigates the following basic question: in the relatively stable molecular environment of a vertebrate body, can a dynamic idiotypic immune network develop a natural tolerance to endogenous components? Our approach is based on stability analysis and computer simulation using a model that takes into account the dynamics of two agents of the immune system, namely, B-lymphocytes and antibodies. We investigate the behavior of simple immune networks in interaction with an Ag whose concentration is being held constant as a function of the connectivity matrix of the network. The latter is characterized by the total number of clones, N, and the number of clones, C, with which each clone interacts. The idiotypic network models typically become unstable in the presence of this type of Ag. We show that idiotypic networks that can be found in particular connected regions of NC-space show tolerance towards auto-Ag without the need for ad hoc mechanisms that prevent an immune response. These tolerant network structures provide dynamical regimes in which the clone which interacts with the auto-Ag is suppressed instead of being excited such that an unbounded immune response does not occur. Possible implications for the future treatment of auto-immune disease such as IvIg-treatment are discussed in the light of these results. Moreover, we propose an experimental approach to verify the results of the present theoretical study.

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