How Diverse Should the Immune System Be?

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 $P_E$, the probability that a pathogen escapes recongnition by the immune system. Obviously, for $P_E$ to be low the diversity should be large. Our novel result is that the major factor in this relation between diversity and $P_E$ is formed by the number of self antigens. Thus our model suggests that, rather that the number of foreign antigens the systems is protecting against, the diversity relfects the number of self antigens the immune systems needs to avoid reactivity with.