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Fractal representation of the immune B cell repertoire

Abstract

The immune repertoire is characterized by a complex and dynamic organization. Here I suggest, based on the presence of well-defined immune reactivity patterns (RP) analyzed using a linguistic analogy, that the B cell repertoires could possess a fractal structure. A simple estimation method of the fractal dimension (D) for a given immune B repertoire was developed, and D demonstrated to be an useful tool to define what complexity is regarding the immune repertoire, and to evaluate the complexity level of the immune B repertoire among age-structured groups of mice sensitized with the hemagglutinin (HA) molecule of influenza virus. Also, since a fractal-linguistic point of view, considerations are made about the ontogeny, connectivity, chaotic regimes, and size of the immune repertoire. Fractal analysis indicates that the immune repertoire shows a Zipf-like scaling behavior, a statistical property of natural languages. This result suggests that immune repertoire is structured like a powerful language.

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