Zipf-scaling behavior in the immune system

Abstract

The Zipf law, an approach to analyzing linguistic texts, was applied to study the Cytotoxic T Lymphocytes (CTL) repertoire, one of the major components of the immune system. A Zipf-scaling behavior was observed in those CTL repertoires obtained in normal or conventional mice. In contrast, CTL repertoires from irradiated chimeric animals, showed a non-scaling statistical behavior when tested by the Zipf analysis,suggesting that normal repertoires work like a structured biological language. The fractal dimension ( D) was derived from the Zipf plots, and correlates well with the nature of the repertoires: high, D > 0.8, in conventional mice. Non-fractal, D > 1, in chimeric animals, and low, D < 0.3, in athymic mice. Then, D seems to be an useful tool to characterize the current status of the immune system.