A Fractal Clonotype Distribution in the CD8+ Memory T Cell Repertoire Could Optimize Potential for Immune Responses

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Abstract
The nature of CD8+ T cell memory is still incompletely understood. We have previously reported that the response to an HLA-A2-restricted influenza-derived peptide results in a complex T cell repertoire. In this study we extend this analysis and describe the repertoire with more rigor. In one individual we defined 141 distinct T cell clonotypes on the basis of the unique DNA sequence of the third complementarity-determining region of the TCR β-chain. The frequency distribution of the clonotypes is not what is expected of a normal distribution but is characterized by a large low-frequency tail. The existence of a complex population indicates a mechanism for maintaining a large number of Ag-specific clonotypes at a low frequency in the memory pool. Ranking the clonotypes allowed us to describe the population in terms of a power law-like distribution with a parameter of decay of ∼1.6. If the repertoire is divided into subsets, such as clonotypes that use BJ2.7 or those whose third complementarity-determining region encodes the amino acid sequence IRSS, the clonotype frequencies could also be described by a power law-like distribution. This indicates a self similarity to the repertoire in which smaller pieces are slightly altered copies of the larger piece. The power law-like description is stable with time and was observed in a second individual. The distribution of clonotypes in the repertoire could be mapped onto a polygonal spiral using a recursive algorithm. Self similarity, power laws, and recursive mapping algorithms are associated with fractal systems. Thus, Ag-specific memory CD8 T cell repertoires can be considered as fractal, which could indicate optimized flexibility and robustness.