T cell repertoire diversity measurement; inferences from a dynamical systems model, Fourier Analysis of the T cell repertoire
T cell repertoire sequencing has unveiled a vast, complex array of T cells responsible for the human immune responses. Traditional analytic methodology fails to fully characterize and quantify the diversity of T cell receptors constituting the T cell repertoire. T cell receptor clonal frequency measured in terms of T cell receptor beta (TRB) V gene segment usage when arrayed in correspondence with the respective V gene segment positions on the TRB loci yields a periodic, undulating curve in the spatial domain of the TRB genomic locus. Using the genomic distance from the TRB-D1 segment to the TRB-V1-29 segments, Fourier analysis was performed utilizing Lomb-Scargle periodogram to obtain Spectral Power curves quantifying the TRB V clonal frequencies from 6 allogeneic stem cell transplant donors (baseline) and recipients (>/=100 days) using a variety of analytic software. Spectral Power curves revealed dominant spectral peaks at wavelengths ranging from 4-9 kb (113-252 millicycles/kb) in the six donors, with consistent frequency domain spectral patterns. This is consistent with similar use of V segments across healthy individuals. Recipients on the other hand demonstrated more dispersed spectra, with a spectral centroid shifted towards higher frequencies compared to donors (260 vs. 247 millicycles/kb). Consistent with this observation, the Low Frequency Index was lower in the recipients (0.18 vs 0.20). Power was concentrated in the <3 kb and 3-12 kb wavelengths in both groups. The analyses reported here demonstrate that the healthy SCT donors have a remarkably similar spectral signature occupying short to intermediate wavelegnths in the frequency domain, whereas recipients tend to shift towards higher frequencies. These findings are consistent with a normal organized distribution of TRB V segment usage in healthy individuals (by analogy other loci), and a more diffuse and disorderly usage in recipients, consistent with the notion of T cell responses constituting a dynamical system which evolves as a function of time. Fourier analysis of TRB (and potentially TRA) sequencing data provides a repertoire wide summary of T cell clonal distribution.