Numerical modelling of the V-J combinations of the T cell receptor TRA/TRD locus

T-Cell antigen Receptor (TR) repertoire is generated through rearrangements of V and J genes encoding alpha and beta chains. The quantification and frequency for every V-J combination during ontogeny and development of the immune system remain to be precisely established. We have addressed this issue by building a model able to account for Valpha-Jalpha gene rearrangements during thymus development of mice. So we developed a numerical model on the whole TRA/TRD locus, based on experimental data, to estimate how Valpha and Jalpha genes become accessible to rearrangements. The progressive opening of the locus to V-J gene recombinations is modeled through windows of accessibility of different sizes and with different speeds of progression. Furthermore, the possibility of successive secondary V-J rearrangements was included in the modelling. The model points out some unbalanced V-J associations resulting from a preferential access to gene rearrangements and from a non-uniform partition of the accessibility of the J genes, depending on their location in the locus. The model shows that 3 to 4 successive rearrangements are sufficient to explain the use of all the V and J genes of the locus. Finally, the model provides information on both the kinetics of rearrangements and frequencies of each V-J associations. The model accounts for the essential features of the observed rearrangements on the TRA/TRD locus and may provide a reference for the repertoire of the V-J combinatorial diversity.