Ues of FD-TCR were observed across the distribution of the V and J segments for both the TCR a and b loci, when the calculated FDs were plotted across the loci. Therefore, the regions of the locus bearing the V genes may be considered as a magnified version of the J segmentbearing regions for both TRA and TRB (figure 1). This indicates that despite the differences in scale of the TCR regions bearing these gene segments, when viewed on a logarithmic scale, there is uniformity in the size and distribution of gene segments both within and between the different TCR loci; a hallmark of self-similar systems. The average FD-TCR of the TRB V and J segments were 1.4 + 0.1 and 1.3 + 0.2, respectively. Corresponding values for the TRA locus were 1.5 + 0.1 and 1.7 + 0.1, for the V and J segments. The self-similarity across the TRA locus may also be seen when the spacing between successive gene segments is plotted from the 50 to 30 end in a circular area graph (figure 2). The two halves of the2.3. order Sulfatinib T-cell receptor b locus periodicityThe TCR gene segments occur periodically from the 50 to the 30 end of the loci, with V, (D in TRB and TRD), J and C segments, generally in that order. For the calculations regarding the gene segment periodicity and its influence on gene usage frequency, the helical DNA molecules were considered as a propagating spiral (or a wave). In this model, each basepair on a strand of DNA may be considered as a point x, with subsequent base pairs, x ?1 . . . x ?n being successive points on the spiral, as opposed to points on a straight number line. The spiral or helical DNA molecule, as it executes one turn goes through approximately 2p radians, in terms of angular distance spanned. One turn of the helix contains 10.4 nucleotides [21], so the space between successive nucleotides may be considered as the angular distance in radians between them (assuming a uniform unit radius of the DNA molecule). This inter-nucleotide `distance’ will be 2p/10.4 (electronic supplementary material, figure S1). The spatial position of any nucleotide x, relative to the locus origin may be then be described as the angular distance in radians ((2px/10.4) radians) and its coordinates on the DNA molecule determined. This measure may then be used to determine the relative position of the various TCR gene segments.2.4. T-cell clonal frequencySCT donor and recipient samples for determining T-cell clonal frequency were obtained as part of a clinical trial approved by the institutional review board at Virginia Commonwealth University (ClinicalTrials.gov Identifier: NCT00709592). As previously described, CD3?cells were isolated from SCT donor samples and cDNA synthesized from these cells [10]. The cDNA was then sent to Adaptive Biotechnologies (Seattle, WA) for high-throughput sequencing of the TCR b CDR3 region using the ImmunoSEQ assay. This approach comprises a multiplex PCR and sequencing assay in combination with buy ALS-008176 algorithmic methods to produce approximately 1 000 000 TCR b CDR(a)FD TRA2.5 2.0 1.5 1.0 0.5 0 990 000 1 000 000 1 010 000 1 020 000 1 030 000 1 040 000 1 050 000 1 060 000 1 070 000 1 080 000 TRA J segment positions bprsif.royalsocietypublishing.org2.5 2.0 FD TRA 1.J. R. Soc. Interface 13:1.0 0.5 0 0 200 000 400 000 600 000 TRA V and J segment positions bp 800 000 1 000 000 1 200(b)FD TRB2.5 2.0 1.5 1.0 0.5 0 638640642644 000 646 000 648 000 TRB J segment positions bp6506526542.5 2.0 FD TRB 1.5 1.0 0.5 0 0 100 000 200 000 300 000 400 000 TRB V and.Ues of FD-TCR were observed across the distribution of the V and J segments for both the TCR a and b loci, when the calculated FDs were plotted across the loci. Therefore, the regions of the locus bearing the V genes may be considered as a magnified version of the J segmentbearing regions for both TRA and TRB (figure 1). This indicates that despite the differences in scale of the TCR regions bearing these gene segments, when viewed on a logarithmic scale, there is uniformity in the size and distribution of gene segments both within and between the different TCR loci; a hallmark of self-similar systems. The average FD-TCR of the TRB V and J segments were 1.4 + 0.1 and 1.3 + 0.2, respectively. Corresponding values for the TRA locus were 1.5 + 0.1 and 1.7 + 0.1, for the V and J segments. The self-similarity across the TRA locus may also be seen when the spacing between successive gene segments is plotted from the 50 to 30 end in a circular area graph (figure 2). The two halves of the2.3. T-cell receptor b locus periodicityThe TCR gene segments occur periodically from the 50 to the 30 end of the loci, with V, (D in TRB and TRD), J and C segments, generally in that order. For the calculations regarding the gene segment periodicity and its influence on gene usage frequency, the helical DNA molecules were considered as a propagating spiral (or a wave). In this model, each basepair on a strand of DNA may be considered as a point x, with subsequent base pairs, x ?1 . . . x ?n being successive points on the spiral, as opposed to points on a straight number line. The spiral or helical DNA molecule, as it executes one turn goes through approximately 2p radians, in terms of angular distance spanned. One turn of the helix contains 10.4 nucleotides [21], so the space between successive nucleotides may be considered as the angular distance in radians between them (assuming a uniform unit radius of the DNA molecule). This inter-nucleotide `distance’ will be 2p/10.4 (electronic supplementary material, figure S1). The spatial position of any nucleotide x, relative to the locus origin may be then be described as the angular distance in radians ((2px/10.4) radians) and its coordinates on the DNA molecule determined. This measure may then be used to determine the relative position of the various TCR gene segments.2.4. T-cell clonal frequencySCT donor and recipient samples for determining T-cell clonal frequency were obtained as part of a clinical trial approved by the institutional review board at Virginia Commonwealth University (ClinicalTrials.gov Identifier: NCT00709592). As previously described, CD3?cells were isolated from SCT donor samples and cDNA synthesized from these cells [10]. The cDNA was then sent to Adaptive Biotechnologies (Seattle, WA) for high-throughput sequencing of the TCR b CDR3 region using the ImmunoSEQ assay. This approach comprises a multiplex PCR and sequencing assay in combination with algorithmic methods to produce approximately 1 000 000 TCR b CDR(a)FD TRA2.5 2.0 1.5 1.0 0.5 0 990 000 1 000 000 1 010 000 1 020 000 1 030 000 1 040 000 1 050 000 1 060 000 1 070 000 1 080 000 TRA J segment positions bprsif.royalsocietypublishing.org2.5 2.0 FD TRA 1.J. R. Soc. Interface 13:1.0 0.5 0 0 200 000 400 000 600 000 TRA V and J segment positions bp 800 000 1 000 000 1 200(b)FD TRB2.5 2.0 1.5 1.0 0.5 0 638640642644 000 646 000 648 000 TRB J segment positions bp6506526542.5 2.0 FD TRB 1.5 1.0 0.5 0 0 100 000 200 000 300 000 400 000 TRB V and.