### abstract ###
T-Cell antigen Receptor repertoire is generated through rearrangements of V and J genes encoding and 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 V -J 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 V and J 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.
### introduction ###
Functional antigen receptors expressed by T lymphocytes are generated during ontogeny by somatic recombination of gene segments coding for the variable, the joining, and the constant segments CITATION.
The recombination mechanism is largely dependent on both the accessibility of the loci and the RAG enzymatic complex CITATION CITATION.
The murine TRA/TRD locus is composite, encoding TR and chains and encompassed of more than 100 functional V genes CITATION.
In theory, each of the V genes may target one of the 49 functional J genes.
The use of V and J genes during the process of recombination has been widely debated, and the studies support the consensus that V-J combinations are not random, with a use of J segments starting at the 5 end and proceeding to the 3 end CITATION CITATION.
The accessibility of the J region is controlled by the TR enhancer, located at the 3 end of the C gene CITATION and by two promoters: T early, located at the 5 end of the J region and ii J49 located 15 Kb downstream of TEA.
Both of the promoters are activated by E CITATION, CITATION, CITATION.
E controls all the V to J associations whereas the two promoters are required for the rearrangements of the J genes situated at the 5 end of the J region.
However, the analyses of TEA-deleted alleles and those of blockade of TEA transcription showed significant alterations in J use and support the hypothesis that the TEA promoter can regulate both positively the promoters located in the first 12 Kb of J genes and negatively the downstream promoters CITATION, CITATION CITATION .
A particularity of the TRA locus is an absence of allelic exclusion CITATION and its ability to undergo multiple cycles of secondary rearrangements CITATION, CITATION.
The process of successive rearrangements is stopped by either positive selection, which downregulates recombinase expression CITATION or by cell death.
Therefore, the impact of secondary rearrangements on the TR gene assembly regulation remains to be defined.
Regarding the V and J gene use, it is suggested that the first V-J association targets the secondary one into a set of J segments located near the J segment involved in the primary rearrangement CITATION, CITATION.
The rules governing the use of the V genes have not been clearly elucidated.
Nevertheless, observations converge to a consensus: the use of V segments would progress from proximal V genes, located near the J region, towards the V genes located in the distal region CITATION, CITATION.
At this point in time, the mechanism involved in the control of accessibility of V genes remains to debate CITATION .
The current state of the technology permits the analysis of some V-J combinations, essentially those at the extremities of the locus but still fails to establish a complete estimation of the V-J combinations.
The main obstacle comes from the fact that some V genes are duplicated in similar copies in the V region central part, making problematic their unambiguous identification by molecular methods CITATION .
Consequently, numerical modelling of the V-J recombination process may offer valuable support to overcome the difficulty for accessing to a global view of TRA repertoire.
For instance, if the J genes are chosen in a sequential way in the model, their use results unimodal, whereas it is known from experimental data that TRA/TRD locus displays two Hot Spots of recombination CITATION CITATION.
This discrepancy led us to build a mathematical model, parameterized from experimental data, on all V and J genes, including those in distal, proximal, and central positions.
Confrontation between the data obtained from experiments and from modelling makes possible an estimation of dynamical parameters, such as the accessibility to rearrangements and the frequencies of the V-J associations, giving a more accurate estimation of the TRA combinatorial diversity.
