  The human T cell repertoire is generated by the rearrangement of variable
(V), diversity (D) and joining (J) segments on the T cell receptor (TCR) loci.
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 alpha (TRA) and beta (TRB) loci
were arranged in a self-similar manner when the spacing between adjacent
segments was considered as a function of the size of the neighboring gene
segment. The ratio of genomic distance between either the J (in TRA) or D (in
TRB) segments and successive V segments on these loci declined logarithmically.
Accounting for the gene segments occurring on helical DNA molecules, in 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 across the locus, supporting a
log-periodic organization. T cell clonal frequencies, based on V and J segment
usage, from three normal stem cell donors plotted against the respective
segment locations on TRB locus demonstrated a periodic variation. We
hypothesize that this quasi-periodic variation in T cell clonal repertoire may
be influenced by the location of the gene segments on the 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, impacting probability of DNA recombination.
