One important implementation mTOR inhibitor of Rep-Seq is in estimating the number of unique receptors, i.e. the size of the expressed repertoire in an individual at any given moment.14,17,19,20,33 Estimates of the number of non-sampled receptors

are key for an accurate quantification of the total diversity. A solution for an analogous problem was identified > 60 years ago by the legendary statistician Fisher. The problem, termed the ‘unseen species problem’, refers to the attempt to estimate the total number of species in a given large population, based on random samples of species.35–37 Fisher et al.37 developed an analytic solution, assuming a Poisson distribution, which was later extended by Efron and Thisted.35 This analytical solution is mainly a capture–recapture method, associated with statistical analysis of these repeatedly sampled collections of sequences. Various estimation attempts were made, by estimating the number of unique V(D)J combinations. Since receptor diversity is also created by nucleotide insertions and deletions (indels) and somatic hypermutations in B cells, these estimations are only lower boundaries to the actual number

of possible combinations. Most studies focused on a single chain of the immune receptor and therefore resulted in describing only a portion of the total diversity obtained Ruxolitinib by the combination of the two chains constructing the heterodimer. For example, Wang et al.20 estimated 0·47 × 106 TCR-α unique nucleotide sequences and 0·35 × 106 TCR-β sequences. Robins et al.19 suggested that CD8+ T cells express < 0·1% of the combinatorial landscape of the β chain (5 × 1011). Weinstein et al. showed a lower limit of 5000–6000 unique antibodies Rho in the zebrafish.33 Although these are only lower limits to the actual size of the repertoire, it is clear that any individual expresses only a small fraction of the potential diversity (Figs 2 and 3). In spite of substantial advances in repertoire size estimates, there remain three important issues with the capture–recapture approach that

require further attention: First, the common assumption is that the number of unique clones is distributed according to a Poisson distribution. However, recent studies show evidence of a power law distribution.33 Moreover, Fisher et al. demonstrated that several estimation approaches conflict; in terms of receptor sequences, they determined a ratio of the number of new and unique sequences discovered in a new sample divided by the total size of the data (i.e. the whole repertoire expressed in an individual). When this ratio is < 1, i.e. only a portion of the sample contains new sequences, all estimations agree. However, when the ratio is > 1, some approaches converge and stabilize while others completely diverge.