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

Abstract

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.

Figure 1. Quantification of the J region use by the V14 family.

254 V14 rearrangements were cloned from T lymphocytes, the V14 members and J genes were determined by sequencing . (A) Profile of the J use by the six members of the V14 family. The two arrows indicate the localization of the two Hot Spots. (B) Profile of the three members the nearest from J genes and (C) J use by the most 5′ V14 members.

Figure 2. Validation of the modelling approach: analysis of the V and J region uses.

(A) V region utilization: the X axis represents the V region in Kb. The Y axis shows the V gene percentage utilization in simulation. The simulated data sets have been normalized in order to be compared according to the following formula The fixed parameters of the simulation were as follow, one million of alpha chains, ongoing 1 to 4 rearrangements with opening speeds of 18 Kb/h and 1.03 Kb/h for the V and the J region respectively; (B) J region utilization: the X axis represents the J region in Kb; (C) and (D) Amplitude of J region utilization by opposite V genes, V1 (distal) and V21 (proximal). The X axis represents experimental quantification on 9 J genes. The Y axis shows the experimental utilization frequency of 9 J genes by the V1 and V21 genes. (E) and (F) Amplitude of J region utilization in the model. The X axis represents the J genes. The Y axis shows the model frequency utilization by each J genes. (G) and (H) Superposition of experimental and simulated data for the 9 J genes. The X axis represents experimental quantification on 9 J genes. V and J regions utilization from simulated data are similar to experimental data obtained from .

Figure 3. Model interface and results.

(A) The main user interface window of the simulation program, (B) 2D representation of the rearrangement frequencies, (C) 3D representation of the rearrangement frequencies over all V and J gene associations.

Figure 4. Representation of the V14 family rearrangement frequencies.

Y axis represents the cumulated frequencies of all V14 genes with the J genes presented on the X axis, (A) without correction for RSS scores, (B) with correction accordingly to RSS scores. The two red ellipses show the localization of the two Hot Spots of recombination.

Figure 5. 3-D superposition of V14 family rearrangements.

(A) The fitted simulated data and (B) non fitted simulated data are shown in grey shapes. The experimental points above the simulation shape are represented in red. The experimental points under the simulation shape are represented in green.

Figure 6. Combinational diversity of V-J combinations and population size.

X axis represents the number of TR tested in the simulation, and Y axis indicates the percentage of the number of the different V-J combinations obtained by the simulation over the total number of possible V-J combinations.

Figure 7. Schematic representation of the TRA/TRD locus use.

The scheme shows the rearrangement distribution of 4 V genes with all J genes. The dashed red arrow indicates the decreasing frequency of rearrangements which correlates with the associations of distal V and J genes. A distal V gene is very rarely rearranged with proximal J genes because of the high recombination frequency between proximal V and J genes, leading to the proximal J genes deletion. 1) the first step governing the TRA/TRD locus utilization is defined by the opening of the most proximal V-J region, 2) According that T cells can undergo 1 to 3 secondary rearrangements, the second step giving the V and J accessible windows, is defined by the opening speeds of V and J regions. V speed is about 18 Kb/h whereas J speed is about 1 Kb/h, 3) J region has two Hot Spots of rearrangement. HSI is centred on J48 and HSII is centred on J30.

Figure 8. Successive rearrangements and building of the combinatorial repertoire shape.

Three successive draws of random integers were done successively, the first one giving an integer x1 between 0 and 10 following a Poissonian law. The second and the third ones follow a Gaussian law, the second giving an integer x2 between x1 and x1+10, and the third giving an integer x3 between x2 and x2+10, and that 300 000 times. The first, second and third curves were added to build the sum curve.

Figure 9. Density and RSS scores of the J genes.

Values for the density (open squares) and RSS scores (dark circles) were calculated, as described in methods, for each J gene from the four previous and next genes. X axis represents the J genes, the Y axis the density or the RSS score for all J genes.

Figure 10. Flow diagram for the sequential windowing model algorithm.