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# Quasispecies dynamics on a network of interacting genotypes and idiotypes: Applications to autoimmunity and immunodeficiency

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### Abstract

In spite of their many facets, the phenomena of autoimmunity and immunodeficiency seem to be related to each other through the subtle links connecting retroviral mutation and action to immune response and adaptation. In a previous work, we introduced a network model of how a set of interrelated genotypes (called a quasispecies, in the stationary state) and a set of interrelated idiotypes (an idiotypic network) interact. That model, which does not cover the case of a retroviral quasispecies, was instrumental for the study of quasispecies survival when confronting the immune system and led to the conclusion that, unlike what happens when a quasispecies is left to evolve by itself, letting genotypes mutate too infrequently leads to the destruction of the quasispecies. Here we extend that genotype-idiotype interaction model by the addition of a further parameter ($$\nu$$) to account for the action of retroviruses (i.e., the destruction of idiotypes by genotypes). We give simulation results within a suitable parameter niche, highlighting the issues of quasispecies survival and of the onset of autoimmunity through the appearance of the so-called pathogenic idiotypes. Our main findings refer to how $$\nu$$ and $$\lambda$$, a parameter describing the rate at which idiotypes get stimulated, relate to each other. While for $$\nu>\lambda$$ the quasispecies survives at the expense of weakening the immune system significantly or even destroying it, for $$\nu<\lambda$$ the fittest genotypes of the quasispecies become mimicked inside the immune system as pathogenic idiotypes. The latter is in agreement with the current understanding of the HIV quasispecies.

### Author and article information

###### Journal
1512.08970

Condensed matter, Evolutionary Biology