Abstract

T cell repertoire in health and disease is complex, comprised of millions of unique T cell clones defined by hetero-dimeric T cell receptors (TCR). The a and b subunits of the TCR are products of genetic loci consisting of variable (V) and joining (J) segments in the case of TCR a (TRA), and V, J and diversity (D) segments in the case of TCR b (TRB). These gene segments are recombined to yield TCR a (VJ) or TCR b (VDJ). Recently we reported that T cell clonal frequency in normal stem cell donors, from the point of view of TCR b gene segment usage rather than being random, has a fractal ordering (Meier et al, BBMT 2013). Fractals are mathematical constructs characterized by self-similarity at different scales of measurement. Thus whether T cell repertoire is examined from the standpoint of DJ, VDJ or VDJ+nucleotide inserted TCR b clones the frequency distribution remains the same when log transformed data are examined yielding a fractal dimension (FD) of ~ 1.5.

In order to identify the origin of the observed fractal ordering of TCR b gene segment containing clones, the distribution of gene segments across the TRA and TRB loci was evaluated for self-similarity. Data describing the numeric positions of the initial and final nucleotides of the start and stop codons respectively, was obtained for each gene segment on the two loci was from the NCBI public data base. Resulting gene segment length and intervening space between successive gene segments (in base pairs) were calculated and log-transformed to assess self-similarity by calculating FD using the formula, FD = Log (magnitude)/Log (scaling factor). Length of individual gene segments was considered as scaling factor and the inter-segment space, as the magnitude of the line segment; FD was calculated for each segment. This demonstrated that the V and J gene segments for both TRA and TRB loci were arranged in a fractal, self-similar manner when the spacing between the loci was considered as a function of the size of the gene segment. Despite the apparent variability in the observed sizes of the V and J gene segments and the spacing between them, on a logarithmic scale there was marked uniformity in their size and spacing, with an average FD of 1.4±0.1 and 1.3±0.2 for TRB, V and J segments respectively (Figure). Corresponding values for TRA locus were 1.5±0.1 and 1.7±0.1, for the V and J segments.
Figure

TCR a (TRA) and b (TRB) fractal dimension calculated for each variable and joining segment (TCR d region on the TRA locus is excluded)

Figure

TCR a (TRA) and b (TRB) fractal dimension calculated for each variable and joining segment (TCR d region on the TRA locus is excluded)

During T cell receptor recombination, the J and the D segments in TRA and TRB loci respectively, are recombined with the V segments therefore the distribution of each V segment in the TRA and TRB loci was determined relative to the position of the J and the D segments in the respective loci, by the using the following formula spacing V-J or V-D = INP-D or J segment / INP nthV segment, (INP: initial nucleotide positions of gene segments). This measure demonstrated a strikingly consistent proportionality across both TRA and TRB loci, and when plotted for successive V segments on the TRB locus, the value declined logarithmically, with a slope of approximately 1.6, and similarly an average slope of 1.3 for the TRA locus, consistent with the earlier observed FD for these loci. We conclude that T cell receptor gene segments are organized in an iterating logarithmically scaled manner. This implies that aside from mechanisms such as the 12/23 rule, gene segment distribution across the T cell receptor loci may help determine the order of recombination, and thus contribute to the observed fractal ordering of the T cell repertoire.

Disclosures:

No relevant conflicts of interest to declare.

Author notes

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Asterisk with author names denotes non-ASH members.