# How Diverse should the Immune System be?

Rob J. De Boer, Alan S. Perelson

## Abstract

We develop a probability-based model that suggests a novel explanation for the enormous diversity of the lymphocyte repertoire in the immune system. Taking into account the fraction of the repertoire that is expected to be rendered tolerant because of potential self reactivity, we calculate P$_{\text{E}}$, the probability that a pathogen escapes recognition by the immune system. Obviously, for P$_{\text{E}}$ to be low the diversity should be large. Our novel result is that the major factor in this relation between diversity and P$_{\text{E}}$ is formed by the number of self antigens. Thus our model suggests that, rather than the number of foreign antigens the system is protecting against, the diversity reflects the number of self antigens the immune system needs to avoid reactivity with.