Genesis of the αβ T-cell receptor

Abstract

The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called α and β, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the αβ generation process. We estimate the probabilities of a rescue recombination of the β chain on the second chromosome upon failure or success on the first chromosome. Unlike β chains, α chains recombine simultaneously on both chromosomes, resulting in correlated statistics of the two genes which we predict using a mechanistic model. We find that ∼35% of cells express both α chains. Altogether, our statistical analysis gives a complete quantitative mechanistic picture that results in the observed correlations in the generative process. We learn that the probability to generate any TCRαβ is lower than 10(-12) and estimate the generation diversity and sharing properties of the αβ TCR repertoire.

Fig 1. Formation of a T-cell receptor.

The β chain is rearranged before the α chain. The recombination on the two chromosomes is sequential for β, and parallel for α. Dotted lines indicate optional events. Rescue events on the α chain correspond to successive recombinations of the same locus (see also schematic in Fig 3).

Fig 2. Mutual information (a non-parametric measure of correlations) between the recombination events of the paired chains.

V, D, and J segment choice, numbers of bases deleted from the 3’ end of the V-gene (delV), the 5′ end of the J-gene (delJ), and both ends of the D-gene for the β chain (del5′D and del3′D for the 5′ and 3′ ends, respectively); number of insertions of random nucleotides between V and J segments (insVJ) for the α chain, and between V and D (insVD) and between J and D (insDJ) segments for the β chain. Mutual information for (A) α-β pairs (on the right in green: close-up of the inter-chain mutual information); (B) α-α pairs; and (C) β-β pairs. Inter-chain correlations are highlighted by red boxes. To remove systematic biases in mutual information estimation from finite data, the mutual information of shuffled data was subtracted (see Methods). For a statistical anlaysis of the significance of the reported mutual informations, see S2 Fig.

Fig 3. Evidence of the rescue mechanism.

(A) Pearson correlation between V and J gene segment usage for TCRα. The correlation is taken between the truth values of particular V and J gene choices (a value of 1 is assigned if a given segment is observed and 0 if it is not, see Methods for details). (B) Same Pearson correlation as in (A) calculated from simulations of the rescue mechanism model depicted in (C). (C) Cartoon of the rescue mechanism. The rescue happens simultaneously on the two chromosomes. Once one of the re-arrangements results in a functional rearrangement, recombination stops. In the end, the V and J gene segments selected on both chromosomes are close to each other in the germline ordering.

Fig 4. Probability of recombination of the second chromosome.

(A) Decision tree of the recombination process for one chain (α or β). The first part shows the recombination of the first chromosome, the second part of the second chromosome. In each area a binary choice is made. Red crosses indicate decision outcomes that lead to no observed sequence. Observable outcomes (with at least one coding sequence) are indicated at the end of the tree by green ticks. C stands for coding, nC for non-coding. (B) Bounds on the allowed values of rescue probabilities for the β chain calculated from the decision tree in (A). The black part of the graph corresponds to the allowed values of $p_r^{\prime }$ (probability of a second recombination for β if the first was successful) and p_r (probability of a second recombination for β if the first was not successful). The bounds were obtained by imposing $0<p_f^{\beta }<1$ in Eq 1. (C) Bounds on the allowed values of rescue probabilities for the α chain. They are consistent with both chromosomes recombining simultaneously and independently, $p_r=p_r^{\prime }=1$.

Fig 5. Generation probability of a full αβ TCR.

(A) Distribution of the generation probabilities of αβ pairs, obtained by multiplying the generation probabilities of the α and β sequences. The graph shows the distribution for paired sequences (blue) and random associations of αβ pairs (green). The error bars represent three standard deviations, and the inset shows the same plot on a double logarithmic scale. (B) Number of CDR3 nucleotide sequences found in n among 10 individuals with a sample depth of N = 10⁶ unique αβ TCR per individual. The probability of more than two people sharing the same TCR receptor is extremely small.