On the organization of human T-cell receptor loci: log-periodic distribution of T-cell receptor gene segments.

The human T-cell repertoire is complex and is generated by the rearrangement of variable (V), diversity (D) and joining (J) segments on the T-cell receptor (TCR) loci. The T-cell repertoire demonstrates self-similarity in terms clonal frequencies when defined by V, D and J gene segment usage; therefore to determine whether the structural ordering of these gene segments on the TCR loci contributes to the observed clonal frequencies, the TCR loci were examined for self-similarity and periodicity in terms of gene segment organization. Logarithmic transformation of numeric sequence order demonstrated that the V and J gene segments for both T-cell receptor α (TRA) and β (TRB) loci are arranged in a self-similar manner when the spacing between the adjacent segments was considered as a function of the size of the neighbouring gene segment, with an average fractal dimension of approximately 1.5. Accounting for the gene segments occurring on helical DNA molecules with a logarithmic distribution, sine and cosine functions of the log-transformed angular coordinates of the start and stop nucleotides of successive TCR gene segments showed an ordered progression from the 5' to the 3' end of the locus, supporting a log-periodic organization. T-cell clonal frequency estimates, based on V and J segment usage, from normal stem cell donors were plotted against the V and J segment on TRB locus and demonstrated a periodic distribution. We hypothesize that this quasi-periodic variation in gene-segment representation in the T-cell clonal repertoire may be influenced by the location of the gene segments on the periodic-logarithmically scaled TCR loci. Interactions between the two strands of DNA in the double helix may influence the probability of gene segment usage by means of either constructive or destructive interference resulting from the superposition of the two helices.