Models for antigen receptor gene rearrangement: CDR3 length.

Despite the various processing steps involved in V(D)J recombination, which could potentially introduce many biases in the length distribution of complementarity determining region 3 (CDR3) segments, the observed CDR3 length distributions for complete repertoires are very close to a normal-like distribution. This raises the question of whether this distribution is simply a result of the random steps included in the process of gene rearrangement, or has been optimized during evolution. We have addressed this issue by constructing a simulation of gene rearrangement, which takes into account the DNA modification steps included in the process, namely hairpin opening, nucleotide additions, and nucleotide deletions. We found that the near-Gaussian- shape of CDR3 length distribution can only be obtained under a relatively narrow set of parameter values, and thus our model suggests that specific biases govern the rearrangement process. In both B-cell receptor (BCR) heavy chain and T-cell receptor beta chain, we obtained a Gaussian distribution using identical parameters, despite the difference in the number and the lengths of the D segments. Hence our results suggest that these parameters most likely reflect the optimal conditions under which the rearrangement process occurs. We have subsequently used the insights gained in this study to estimate the probability of occurrence of two exactly identical BCRs over the course of a human lifetime. Whereas identical rearrangements of the heavy chain are highly unlikely to occur within one human lifetime, for the light chain we found that this probability is not negligible, and hence the light chain CDR3 alone cannot serve as an indicator of B-cell clonality.