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

Article (PDF Available)inPLoS Computational Biology 6(2):e1000682 · February 2010with23 Reads
DOI: 10.1371/journal.pcbi.1000682 · Source: PubMed
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.
Numerical Modelling Of The V-J Combinations Of The T
Cell Receptor TRA/TRD Locus
Florence Thuderoz
1.
, Maria-Ana Simonet
1,2.
, Olivier Hansen
1.
, Nicolas Pasqual
.
, Aure
´
lie Dariz
2,3
,
Thierry Pascal Baum
1
, Vivien Hierle
2
, Jacques Demongeot
1*"
, Patrice Noe
¨
l Marche
2,3*"
, Evelyne Jouvin-
Marche
2,3"
1 CNRS, Laboratoire TIMC-IMAG, UMR 5525, Grenoble, France, 2 INSERM, Institut Albert Bonniot, Grenoble, France, 3 Universite
´
Joseph Fourier-Grenoble I, Faculte
´
de
Me
´
decine, Grenoble, France
Abstract
T-Cell antigen Receptor (TR) repertoire is generated through rearrangements of V and J genes encoding a and b 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 Va-Ja 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 Va and Ja 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.
Citation: Thuderoz F, Simonet M-A, Hansen O, Pasqual N, Dariz A, et al. (2010) Numerical Modelling Of The V-J Combinations Of The T Cell Receptor TRA/TRD
Locus. PLoS Comput Biol 6(2): e1000682. doi:10.1371/journal.pcbi.1000682
Editor: Rob J. De Boer, Utrecht University, Netherlands
Received September 17, 2008; Accepted January 21, 2010; Published February 19, 2010
Copyright: ß 2010 Thuderoz et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was supported by the institutional Grants from Institut National de la Sante
´
et de la Recherche Me
´
dicale (INSERM), from Centre National de la
Recherche Scientifique (CNRS), and by the EC Alfa project IPECA. FT was supported by a fellowship from the Agence Nationale de la Recherche et de la
Technologie, France. M-AS was supported by a fellowship from Re
´
gion-Rhone Alpes ‘‘Cluster 10’’. NP was supported by a fellowship from the INSERM. The funders
had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: This work was supported by institutional grants from the Institut National de la Sante
´
et de la Recherche Me
´
dicale (INSERM), from the
Centre National de la Recherche Scientifique (CNRS), and from a specific grant ‘‘The
´
matiques Prioritaires de la Re
´
gion Rho
ˆ
ne-Alpes’’. M-AS was recipient of a PhD
fellowship from Cluster 10 of the Re
´
gion Rho
ˆ
ne-Alpes; NP was recipient of a fellowship from the INSERM and CEA. FT was recipient of a fellowship from the ANRT
(Agence Nationale de la Recherche et de la Technologie) and JD has been supported by the EC Alfa project IPECA. The authors have no conflicting financial
interest.
* E-mail: patrice.marche@ujf-grenoble.fr (PNM); Jacques.Demongeot@imag.fr (JD)
¤ Current address: ImmunID, Commissariat a
`
l’Energie Atomique, Grenoble, France
. These authors equally contributed to this work.
" These authors equally contributed to this work.
Introduction
Functional antigen receptors expressed by T lymphocytes (TR)
are generated during ontogeny by somatic recombination of gene
segments coding for the variable (V), the joining (J), and the
constant (C) segments [1]. The recombination mechanism is
largely dependent on both the accessibility of the loci and the
RAG enzymatic complex [2–5]. The murine TRA/TRD locus is
composite, encoding TR a and d chains and encompassed of more
than 100 functional V genes [6]. 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 59 end (proximal to the V segments) and proceeding to the
39 end [7–13]. The accessibility of the J region is controlled by the
TR a enhancer (Ea), located at the 39 end of the C gene [14] and
by two promoters: i) T early a (TEA), located at the 59 end of the
Ja region and ii) J49 located 15 Kb downstream of TEA. Both of
the promoters are activated by Ea [4,5,15]. Ea controls all the V
to J associations whereas the two promoters are required for the
rearrangements of the J genes situated at the 59 end of the Ja
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 [4,15–17].
A particularity of the TRA locus is an absence of allelic
exclusion [18] and its ability to undergo multiple cycles of
secondary rearrangements [19,20]. The process of successive
rearrangements is stopped by either positive selection, which
downregulates recombinase expression [21] or by cell death.
PLoS Computational Biology | www.ploscompbiol.org 1 February 2010 | Volume 6 | Issue 2 | e1000682
Therefore, the impact of secondary rearrangements on the TRa
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
[5,16]. 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 [9,10]. At this point in time, the mechanism
involved in the control of accessibility of V genes remains to
debate [19].
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 molec-
ular methods [22].
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 [2–5]. 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.
Results
The goal of building a model representative of the Va-Ja
associations was to reproduce the global biological features of T
lymphocyte VaJa rearrangements occurring in the TRA/TRD
locus with a software algorithm. This algorithm must be
parameterized to find the conditions that reproduce the experi-
mental data. Adequacy between biological and simulated results
tells that all the essential aspects of the studied process were
included in the model. This modelling approach led us to gather
and search for some biological data about the parameters
controlling the Va-Ja rearrangement process in the mouse
TRA/TRD locus.
Update of the parameters controlling the mouse TRA/
TRD locus utilization during rearrangements by an
experimental approach
In order to build the model, we firstly required information
about the physical position of the V and J genes in the TRA/TRD
locus. These data were provided by IMGT (ImMunoGeneTics
database; http://imgt.cines.fr/) and summarized in Table 1. In
addition, we needed to define parameters such as the opening
location (the position where the opening mechanism begins), the
opening speed for the access to V and J genes and the opening
duration. Two more parameters were added, a first maturation
step in order to eliminate the TRD genes and an opening offset as
we supposed a certain rigidity of the DNA chain, thus two genes
placed very close from each other cannot rearrange together.
Determination of the opening speeds for the V and J
regions in the thymus.
The data given in the first column of
the Table 2 were obtained from rearrangements at the genomic
level in BALB/c mice during thymic ontogeny and resume results
presented in a previous work [9]. These data gave us the ontogeny
days where V and J genes were first seen rearranged. In
conjunction with physical gene positions, we calculated opening
speeds that describe the progression of the accessibility to
rearrangements over the Va and Ja regions. Concerning the Ja
region opening speed, in Fetal Fay 18th (F18), rearrangements of
V19 with J61 to J48 corresponded to an opening of the J locus of
14773 bp in 24 h, thus the opening speed associated to these 24 h
Table 1. TRA/TRD locus characterization.
V region J region
Length (Kb) 1300 64
Number of elements 104 60
Number of functional elements 100 49
doi:10.1371/journal.pcbi.1000682.t001
Author Summary
Lymphocytes of the immune system ensure the body
defense by the expression of receptors which are specific
of targets, termed antigens. Each lymphocyte, deriving
from the same original clone, expresses the same unique
receptor. To achieve the production of receptors covering
the wide variety of antigens, lymphocytes use a specialized
genetic mechanism consisting of gene rearrangements.
For instance, the genes encoding the receptor of the alpha
chain of the T lymphocyte receptor (TRA) spread over a
1500 Kb genetic region which includes around 100 V
genes, 60 J genes, and a single C gene. To constitute a
functional alpha chain, one of the V and one of the J genes
rearrange together to form a single exon. The precise
definition of these V-J combinations is essential to
understand the repertoire of TRA. We have developed a
numerical model simulating all of the V-J combinations of
TRA, fitting the available experimental observations
obtained from the analysis of TRA in T lymphocytes of
the thymus and the blood. Our model gives new insights
on the rules controlling the use of V and J genes
in providing a dynamic estimation of the total V-J
combinations.
Table 2. J locus accessibility: J genes seen rearranged to V19
during ontogeny.
Gestation day
1
J opening
Opening
distance
#
Maximal
opening Speed
F18 to F19 J61 to J48 14773 bp 615 bp/h
F19 to F20 J47 to J20 27618 bp 1150 bp/h
F20 to D0 J19 to J9 8998 bp 375–750 bp/h *
D0 J8 to J2 7940 bp 333 bp/h
1
Thymus from Fetal Day 18 (F18) to Day of birth (D0); data are analyzed from
Figure 5 in Pasqual et al. [9].
#
Length of the DNA sequence corresponding to the J opening.
*
For F20, the opening speed has been estimated between 375 bp/h to 750 pb/
h depending on the offset of maxima 12 hours (9000 bp/24 h or 9000 bp/
12 h).
doi:10.1371/journal.pcbi.1000682.t002
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 2 February 2010 | Volume 6 | Issue 2 | e1000682
period is estimated to 615 bp/h. The same analysis was applied on
F19, F20, and D0 (Day of birth). These data, fully presented in
Table 2, showed that during ontogeny the opening speed of the J
locus varies slightly, between 375 bp/h and 1150 bp/h,
corresponding to an average opening speed of about 713 bp/
h636396 bp/h with a 99.9% confidence interval.
For determining the Va region opening speed, there were used
single member V families at each V region extremity of the TRA/
TRD locus. For instance, V1 and V2, the most distal from the J
region, as well as V19, V20, and V21, located at the nearest
extremity to the J region, were analyzed. We found rearranged
proximal V genes from F18, while rearrangements of distal V1
and V2 genes (1300 Kb distant from the proximal V genes) were
only detected from D0. Hence, the entire V region takes about 3
days to get wide opened, allowing us to estimate the overall
‘‘opening V-speed’’ as broadly 18 Kb/h (1300 Kb/(3624 h)) with
a 99.9% confidence interval of about 186365 Kb/h.
V-J rearrangements in peripheral T lymphocytes. In
order to complete the study of thymus repertoire, we extended the
analysis of V-J rearrangements in peripheral T lymphocytes from
spleen and lymph nodes of adult mice. We reported the J use of
254 sequences extracted from peripheral T lymphocytes that
express V14 on their surfaces [10]. The V14 family is composed of
6 members spread from 1145 Kb to 492 Kb in the V region. The
Figure 1 A shows the J use by the whole V14 family. This
distribution is in accordance with the two Hot Spots reported by
Rytkonen et al. [3,23], which are indicated by two arrows over the
histogram. Indeed, according to Rytkonen et al., the J use
distribution presents a preference for the J genes located over
two regions named Hot Spots. The first Hot Spot (HSI) is located
between J59 and J48 which corresponds to the region controlled
by TEA; the second Hot Spot (HSII) is situated between J31 and
J22. In addition, the Figure 1 presents the profiles of J used by the
proximal V genes (V14-1, V14-2, and V14-3 on Fig. 1 B) and by
the distal V genes (V14D-1, V14D-2, and V14D-3 on Fig. 1 C).
These two histograms show that the proximal V to proximal J
associations appear more frequent than the distal to distal
associations and that the two Hot Spots are observed. Regarding
the J region use, HSI is well observed for proximal V genes, and
the HSII is well observed for distal V genes [10,24]. After
presenting these biological data, the results generated by the model
will be exposed.
Computational modelling approach
Values of the Parameters. Simulations were performed
using two opening speeds chosen within intervals closed to the
experimental 99.9% confidence intervals. For V speed, SV M
[0.35 Kb/h, 34 Kb/h] and for J speed, SJ M [0.4 Kb/h, 1.55 Kb/
h] with a mean opening speed of about 18 Kb/h for the V region
and 1 Kb/h for the J region. The opening location of the
simulation was fixed between the V and J genes in order to access
directly to the TRAV and TRAJ genes after the first maturation,
which was set to allow the elimination of the genes coding for
TRD genes (region encompassing TRDV1 to TRDV5). Issues
obtained from the modelling which best fit experimental data
indicated that firstly, the duration of the first maturation step has a
mean value of 5 hours, secondly, the number of successive
rearrangements is 3 or 4, and thirdly, the opening duration
before each rearrangement is 24 hours. The entire duration for
the process of successive rearrangements is then 72 h or 96 h,
which is in accordance with our data from ontogeny analyses
(Table 2). When rearrangements were simulated by pairs, in order
to account for the synchronization between the two alleles of
individual cells, identical results were obtained.
Validation of the model by comparing simulated with
thymic experimental data.
The results of the model
simulations and its comparison with the thymic experimental
data are presented on Figure 2. Firstly, we present the global V
and J uses in the simulated population (Fig. 2, A and B). The
simulation program provides frequencies of every V to J genes
associations in a matrix form. The columns display the J genes and
the rows the V genes. Every intersection column/row indicates the
frequency of the considered V to J association. It is then possible to
sum all the V-J frequencies where a single V gene is implicated by
adding the corresponding entire row. By doing this with all of the
V genes, the global V region utilization is calculated (Fig. 2 A), and
the sums of every matrix columns result in the global J gene
utilization (Fig. 2 B). Overall, the uses of the V genes decrease
from proximal to distal V genes, and the J region uses decrease
from proximal to distal J genes. These tendencies were
experimentally observed from thymic [9] and peripheral data as
well [7,13].
Afterwards, we proceeded to quantify V1 and V21 rearrange-
ments with a set of 9 J genes scattered along the J region in the
thymus and compared these data with simulated outputs. Both
experimental and modelling data show firstly that V1, which is the
most distal V, has a low utilization rate of the proximal J genes and
rearranges essentially the middle and distal J genes (Fig. 2, C, E,
and G) and secondly that V21, which is the most proximal V, is
mainly rearranged with the proximal J genes (Fig. 2, D, F, and H),
following a Poisson distribution. The global utilization of J by V1 is
similar in both experimental and simulated data. The frequencies
from modelling are in correlation with the experimental nine J
gene use (taken as representatives of the J region) by V1 and V21.
In conclusion, the correspondence between data obtained by
experimental analyses of rearrangements and those generated by
in silico rearrangements validates the simulation program as model.
Program interface and generated graphics. The
simulation program with its user interface (Fig. 3 A) provides a
2-dimensional diagram showing a conditional V-J rearrangement
distribution for different V from proximal, central and distal
positions (Fig. 3 B). Moreover, a 3-dimensional histogram of V-J
rearrangements representing the all TRa chain combinational
repertoire can be generated (Fig. 3 C). The program offers as well
an interesting graphic representation designed to plot the J region
use by complex V families. For the V14 family, for example,
the program displays the complete J use by all the 6 V members
(Fig. 4 A).
Stimulation model for peripheral T cell repertoire. In
order to verify if the simulation model can be applied as a tool to
determine the use of the different J by given V, we further
quantified the use of 9 J by the 6 members of the V14 family in
peripheral T lymphocytes. The resulting 54 V-J combinations,
well spread along both the V and J regions, were plotted over the
global V-J association 3-D graphic given by the simulated results
(Fig. 5). For more precision, we plotted these frequencies of
experimentally determined rearrangements over a fitted by 3-
cubic spline fitting (Fig. 5 A) and a not fitted (Fig. 5 B) surfaces that
interpolate the simulated frequencies. The experimental points
over the surface appear in red, the ones under the surface appear
in green. Beyond this visual adequacy, we demonstrated the
accordance between simulated and experimental data by a
numerical approach. We distinguished proximal, central and
distal parts on the J region. For each of these parts, we compared
the percentage of V14 rearrangements from experimental versus
simulated data (Table 3). The V14 combinations with J61 to J48
represent 37% of the experimental data, and 35% of the simulated
data, those with J47 to J24 stands for 46% and 50%, and
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 3 February 2010 | Volume 6 | Issue 2 | e1000682
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 [10]. (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 59 V14 members.
doi:10.1371/journal.pcbi.1000682.g001
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 4 February 2010 | Volume 6 | Issue 2 | e1000682
combinations with J23 to J1 represent 17% and 15% of
experimental and simulated data respectively. Noticeably, when
the sums of simulated rearrangements are extended to all V, the
uses of the J localized in the proximal, central and distal parts of
the locus are in the same range than those found with V14 genes
(last column of the Table 3). Additionally, the J use by the whole
V14 family (Fig. 4 A) from our simulated repertoire presents
a distribution where two Hot Spots are clearly visible. These Hot
Spots are in accordance with our own observation from peripheral
T-lymphocytes (Fig. 1 A) and the experimental data of Rytkonen
et al [3,23].
New insights in the VJ repertoire given by the model
simulations.
Based on our modelling study, four features
concerning the V-J rearrangement process emerge. First of all,
concerning the frequencies of the associations, the main
information supplied by the model is that 96% (4704 out of
4900) of the V-J associations are probable. Hence, two areas where
V-J combinations rarely occur could be defined (Fig. 3 C): the ‘‘A’’
area as associations between proximal V and distal J and the ‘‘B’’
area as associations between distal V and proximal J. These
occasional associations are a consequence of a non-synchronized
availability for rearrangements of the concerned V and J genes, as
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 X~ x{averageðÞ
=
Std deviation: 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 [9].
doi:10.1371/journal.pcbi.1000682.g002
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 5 February 2010 | Volume 6 | Issue 2 | e1000682
already documented in experimental data [7,13,19]. Secondly, the
model gives estimation for the frequencies of each V-J
combination building the whole combinatorial repertoire shape.
In the third place, the model states the influence of the
Recombination Signal Sequence (RSS) on the V-J association
distribution, which remains until now debated [25,26]. For that
purpose, we ran simulations with and without taking into account
the RSS scores (available in IMGT). The 2D graphs of the V14
family repertoire (Fig. 4, A and B) show that introducing variations
accordingly to the RSS scores (Fig. 4 B) does not drastically affect
the shape of the global repertoire distribution but leads to a local
effect on certain J genes. The algorithm for choosing the J genes
regarding their RSS score values has been favorably tested by
using the Monte Carlo method. In the fourth place, the model
provides information on the contribution of each wave of
successive rearrangements to account for the total of V-J
associations. Therefore, we tested the occurrence of 1 to 6
successive rearrangements in simulations. With 1 or 2
rearrangements, only the proximal V to proximal J associations
are observed. With 5 or more rearrangements, the repertoire
presents a distal border effect, corresponding to numerous
rearrangements of the distal V and distal J regions, which are
incoherent with experimental data. In conclusion, the overall
repertoire generated by the simulation is in accordance with
experimental data only by allowing 3 to 4 rearrangements, with a
delay of 24 hours per rearrangement. Moreover, the contribution
of each wave of successive rearrangements appears to decrease
accordingly to their rank; 40% of the overall V-J associations is
produced by the first wave of rearrangements, 33%, 19% and 8%
come from the subsequent rearrangement waves respectively
(Table 4).
Robustness of the model. To assure that the sampling size
used in simulations was sufficient, we checked the
representativeness of the repertoire by making sets of simulations
ranging from 10
2
to 1.5610
6
rearrangements. We found that
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.
doi:10.1371/journal.pcbi.1000682.g003
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.
doi:10.1371/journal.pcbi.1000682.g004
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 6 February 2010 | Volume 6 | Issue 2 | e1000682
diversity became relevant when the population size was higher
than 5610
5
rearrangements. This showed the pertinence of a
repertoire calculation based on a 10
6
alpha chains population. A
combinatorial diversity graph is plotted in Figure 6. Variations of
about 5 to 10% in the values of the parameters (such as the
intervals of the opening speeds Sv and Sj, opening duration, and
offset) provided simulation results in concordance with the
experimental data. However, larger variations in the values of
the parameters induced major deviations (not shown) on the
modelling simulation results compared to experimental data.
Finally, the consistency between simulated data and the
frequencies observed in the thymus and the periphery validates
our model as a relevant tool accounting for the mature repertoire
of TRA/TRD.
Discussion
This article focuses on a new approach to account for the
features of the V to J rearrangement process in the TRA/TRD
locus as well as to give a first estimation of the combinational
repertoire in a 3-dimension representation. To accomplish this
purpose, we have defined a mathematical model fitting experi-
mental observations obtained from T lymphocytes rearrangements
in the thymus. Jointly, the experimental data and the mathemat-
ical model made possible the interpretation of the mouse T-cell
alpha chain repertoire characteristics. The evolution of the shapes
for the V-J rearrangement frequencies in the simulations,
presented in Figure 7, showed a transient bi-modal shape
corresponding to the Hot Spots of V-J recombinations as observed
in our experimental data and literature [3,10]. Furthermore, the
model results also fit with V-J rearrangements obtained from T
lymphocytes of the periphery. Therefore, our model provides a
major improvement to previous attempts of simulation of the TRA
combinatorial repertoire building [27].
Opening velocities and gene density. Our model is based
on the fact that V and J regions are used in a progressive and
decreasing manner from 39 to 59 for the V region and from 59 to 39
for the J region. Our quantitative approach points out that the
physical position of the genes is the main structural parameter
governing the uses of V and J genes. The J and V regions become
accessible from proximal to distal genes according to an average
‘‘opening speed’’ of approximately 1 Kb/h for the J region and
around 18 Kb/h for the V region. Interestingly, this difference
between the V and J region opening speed values can be related to
the gene density. In fact, the number of genes and the size of the V
and J regions differ significantly. As a matter of fact, the V region
length is 20 times larger than the J one (,1300 Kb versus
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.
doi:10.1371/journal.pcbi.1000682.g005
Table 3. J region use by V14: comparison between
experimental and simulation data.
Experiment Simulation
V14 * V14
#
All V
#
J61 to J48 37% 35% 33%
J47 to J24 46% 50% 51%
J23 to J1 17% 15% 16%
*
Frequencies of rearrangements of V14 genes were calculated from Figure 2 in
Aude-Garcia et al. [10], for the combinations with three J panels, corresponding
to series of J genes scattered along the J region.
#
Frequencies of rearrangements of V14 genes and of all V genes were
calculated from modelling data for the combinations with same series of J
genes.
doi:10.1371/journal.pcbi.1000682.t003
Table 4. Contribution of each rearrangement round into the
total V-J combinatorial repertoire.
Rearrangement First Second Third Fourth
Percentage 40% 33% 19% 8%
doi:10.1371/journal.pcbi.1000682.t004
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.
doi:10.1371/journal.pcbi.1000682.g006
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 7 February 2010 | Volume 6 | Issue 2 | e1000682
,60 Kb), but the density of J genes is about 10 times higher than
the density of the V genes (1 J by Kb versus 0.13 V by Kb).
Consequently, the opening speeds calculated in terms of genes per
hour is 1.4 for the V region and 0.83 for the J region (calculated as
follows: the number of genes in the locus times the speed in Kb per
hour, then divided by the length of the locus). Finally, taking into
account the gene density of each region, the opening speeds of the
V and J regions are almost identical. Our observations reinforce
two putative scenarios being previously proposed to explain the
opening of the J and V regions respectively. The first one, the J
local service scenario was proposed for the J region [28]. It consists
in a J use that follows small steps during the successive
rearrangements. This local service is controlled by promoter
activities associated to some of the other J genes. The second one,
the V region express service proposes a large window for the gene
accessibility to rearrangements controlled by enhancer activity. It
reflects the larger utilization of a V region, whose genes are more
scattered than those in the J one [9]. In addition, the speed
calculations also take into consideration the regulatory elements
controlling the gene accessibility [29]. As a remark, a parametric
study with different speed values indicates that the proposed
speeds are the only ones allowing a use of V and J regions
correlating precisely with the experimental results.
Combinatorial repertoire distribution. Given that the
totality of the V-J combination frequencies is computable in the
framework of our model, we can visualize the whole simulated TRA
combinatorial repertoire and thus estimate each V-J association
frequency. Indeed, the probability of any combination is given by
selecting a specific V-J combination on the 3D graph (Fig. 3 C).
Table 5 displays the probability of nine V-J combinations selected
along the locus. Regarding the positions of the V and J genes over
the locus, the probability of association varies between 0.01 for any
V to distal J and 0.198 for any V to proximal J, highlighting the fact
that a V to proximal J combination is about 20 times more probable
than a V to distal J association.
Moreover, this 3D graphic points out that one central area in
the V-J association plane contains the most represented combi-
nations of the repertoire (Fig. 3 C). Furthermore, two areas (A and
B in Fig. 3 C) reveal rarely represented V-J combinations, due to
the fact that the V and J genes involved in these combinations are
not accessible to get rearranged simultaneously. Concerning the A
area, when the proximal J genes are recombining, the distal V
genes are still inaccessible, and when they become accessible, the
proximal J genes are deleted because of previous rearrangements.
Similarly, on the B area, the non-synchronized accessibility of the
proximal V genes and the distal J genes explains that their
associations are not observed in the simulation.
The J region use confirms the existence of two Hot
Spots.
The progressive opening mechanism over the TRA locus
provides V-J combinations that show a specific pattern; each given
V gene is rearranged with a contiguous set of J genes. The
distribution of these J genes presents a Poissonian distribution for
the proximal V genes or a Gaussian shape for the distal V genes.
The changes in the J use are progressive, depending on the V
position: the more distal is a V gene, the more distal and larger is
the set of J genes used, and the less represented are these V-J
associations in the whole V-J repertoire (Fig. 3 C). There are two
main probabilistic bases for the occurrence of the Hot Spots in the
J region observed in the simulation results. The successive
rearrangements are achieved by consecutive random choices of J
genes, considering the progression of their access to recombination
and optionally their RSS score values. The first J gene choice,
corresponding to the first rearrangement, follows a Poissonian law
whereas individually the two other J gene choices follow a
Gaussian law (Fig. 8). Altogether, the consecutive random choices
of J genes build a multimodal curve of occurrence, which allows
the appearance of two Hot Spots (Fig. 8, solid line). The first Hot
Spot results from the Poisson’s distribution of the first J choice and
the second one from the Gaussian distributions of the subsequent J
choices. Moreover, it is important to remark that the density of J
genes in the TRA locus is not uniform: J genes are less dense
between J58-J47, J39-J28, and J14-J4, whereas they have a higher
density between J45-J40 and J24-J15 (Fig. 9). The J gene density
reaches its maximum in the area around J21-J22, corresponding to
the place of the second Hot Spot. Interestingly, we observed the
Hot Spots when the model parameter values were in the range
where the opening dynamics allowed more frequent
rearrangements within the areas of maximal gene density.
Table 5. V-J association probabilities along the TRA locus.
V21 Proximal V4-2 Central V2 Distal
J52 Proximal 0.148 0.050 0
J31 Central 0.002 0.029 0.023
J2 distal 0 0.003 0.007
9 V-J association probabilities given by the model. These results show an unbalanced
use of the proximal and distal V and J genes. For instance, if all V-J combinations are
equiprobable, the probability of each V-J association should be about 2.10
24
.
doi:10.1371/journal.pcbi.1000682.t005
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.
doi:10.1371/journal.pcbi.1000682.g007
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 8 February 2010 | Volume 6 | Issue 2 | e1000682
Number of secondary rearrangements. Secondary V-J
rearrangements of the TRA/TRD locus are widely accepted
[20,21,28,30,31]. However, the number of plausible secondary
rearrangements remains unknown. Our model predicts that after
the first maturation step of the TRA/TRD locus, consisting in the
elimination of the TRD genes, the first V-J rearrangement of TRA
is followed by a maximum of three secondary rearrangements.
Nevertheless, each round of rearrangement contributes differently
in the building of the whole repertoire, decreasing after each wave,
and consequently, the fourth rearrangements have a weak
contribution of 8%. This estimation of 4 total rearrangements is
based on a realistic model including opening speeds from
ontogenic experiments and may be more precise than
Warmflash theoretical model’s results that proposes a higher
number of successive rearrangements [27]. It is important to
consider that the number of secondary rearrangements can be
affected by the lifespan of the rearranging T lymphocytes. For
instance, the RORc-deficient mice, presenting a shorter lifespan of
DP thymocytes, show essentially proximal J genes rearranged,
while Bcl-xL–transgenic mice, having DP with a longer lifespan,
present a higher rate of distal J genes rearranged [28].
RSS influence. Regarding the Recombination Signal
Sequence (RSS) influence, our model is able to incorporate the
RSS diversity information through scores. The simulations using
these RSS scores show a local quantitative influence but do not
change the global profile of the frequency curves (Fig. 5, A and B).
In conclusion, the RSSs may only influence local specificities
within the accessibility windows moving across the TRA/TRD
locus in a bi-directional way. This is in good accordance with
mouse TRB locus observations showing that V gene RSSs neither
correlate with any particular restriction of J genes nor with any
high V-J rearrangement frequencies [32].
The sequential windowing model: a tool to determine the
peripheral V-J association frequencies.
We previously
observed experimentally and tested statistically that the thymic
and the peripheral repertoires showed similar profiles of J uses by
the V14 family [10]. When we compared the experimental data of
the uses of J genes by the V14 family members we found that the J
use profiles fitted our model results. It is acknowledged that the
V14 is a multimember family and may be representative of the J
use by different V genes. Finally, our data suggest that the model
would be used as a tool to determine the V-J association
frequencies in the peripheral T lymphocytes.
All these remarks support the realistic character of our model,
which includes the essential features of the V-J rearrangement
process in the TRA/TRD locus. In conclusion, the combination of
experimental and mathematical approaches gives new insights on
combinatorial repertoire biases due to non-equiprobable V-J
combinations in TRA/TRD rearrangements, and allows defining
more accurately the TRA/TRD primary combinatorial reper-
toire. In the future, the model could be adapted to other loci and
other species, to propose accurate estimations of the V-J
combinatorial diversity, giving a dynamical vision of the immune
diversity generation during differentiation of T cells and B
lymphocytes.
Materials and Methods
Nomenclature. Official nomenclature for V and J genes is
chosen according to the IMGT database (http://imgt.cines.fr).
NCBI (National Center for Biotechnology Information) accession
numbers are AE008683-AE008686 for the mouse V region and
M64239 for the J region. Positions of each V and J genes were
calculated based on these data as previously described [6].
Mouse. BALB/c mice were purchased from Charles-River
(L’Abresles, France). Mice were housed and humanely killed
according to relevant national guidelines. No experimental work
was done on living animals. Fetal thymi were obtained from timed
pregnancies, where Fetal Day 1 (F1) corresponds to the day of
detection of a vaginal plug. Thymic lobes from embryonic mice
were pooled and mechanically dissociated in PBS before DNA
extraction.
Multiplex PCR assay analysis. multiplex PCR assays and
quantification analysis were done as described in [9,33,34].
Quantitative PCR. Real time PCR were performed on a
Light CyclerTM (Roche diagnostics, Meylan, France). The
specificity of the unique amplification product was determined by
melting curve analysis and using migrations on agarose gels followed
by southern blotting with the corresponding internal V probes [9].
Description of the computational model
Our sequential windowing model is a specific model of
successive windows, each step corresponding to a differential
motion of the window extremities, with opening velocity faster on
the V side than on the J one. The simulation of the V-J
rearrangements in the TRA/TRD locus is based on a computa-
tional occurrence discrete model using parameters determined
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.
doi:10.1371/journal.pcbi.1000682.g009
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.
doi:10.1371/journal.pcbi.1000682.g008
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 9 February 2010 | Volume 6 | Issue 2 | e1000682
Figure 10. Flow diagram for the sequential windowing model algorithm.
doi:10.1371/journal.pcbi.1000682.g010
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 10 February 2010 | Volume 6 | Issue 2 | e1000682
from experimental data (Fig. 10). The model consists in dynamical
rules depending on constant (structural) and experimental
parameters. The constant parameters are the physical positions
of the 100 V and 49 J functional genes and the first TRA/TRD
locus opening points. The varying parameters (whose sensitivity
will be studied by simulation) are the opening speed intervals of the
V and J regions, the opening duration before each rearrangement,
and the opening offset.
We define variables and dynamical rules of the model as follows:
1) The physical positions of V and J genes in the TRA/
TRD locus are calculated by measuring the genomic
distance from the TRAC chain.
2) The first maturation step is fixed before the first
rearrangement allowing the deletion of the region encom-
passing TRDV1 to TRDV5 including the TRD locus. Its
duration value is a constant parameter, which was determined
by simulation varying values between 0 hours and 10 hours.
3) The opening locatio n describes the site where the
opening mechanism begins. This site is fixed at the TEA
location [35].
4) The opening speeds of the V and J genes calculated above
are denoted respectively by S
V
and S
J
. They are random
variables between a minimum and a maximum. Each TCRA
locus is simulated independently to be consistent with the
absence of allelic exclusion. Furthermore, rearrangements
were also simulated by pairs using the same V and J opening
speeds, in order to account for the synchronization between
the two alleles of individual cells.
5) The Opening duration before each rearrangement is
a constant parameter whose value was determined through
simulations, by varying values between 2 hours and 50 hours.
6) N denotes the number of authorized secondary rear-
rangements during the simulation. It is a varying
parameter as well, values between N = 0 to N = 6 were
studied by simulations.
7) The probability to perform an in-frame rearrange-
ment at any step k (1#k#N) is fixed to 1/3 that is the
maximal possibl e value. If the rearrangement is randomly
determined in-frame, the procedure is stopped for this
locus and the V-J association generated is s tored. If the
simulation gives an out-of frame rearrangement at the step
k, a new secondary rearrangement is randomly executed at
the s te p k+1 on the available part of the locus. The new
window of accessibility is calculated in base of the
‘‘opening speeds’’ and the ‘‘opening duration
before each rearrangement’’ parameters. This suc-
cessive rearrangement procedure remains until either an
in-frame rearrangement occurs or k equals the maximum
number of rearrangements N.
8) We refer to the length of the window of accessible DNA over
the V region at a step k as LV
k
(and LJ
k
for the J window
length), These windows progress from the proximal to distal
extremities of the TRA/TRD locus V and J regions. The
LVs and LJs verify the equations:
LV
1
~S
V
t
0
zt
1
ðÞ, ..., LV
k
~LV
k{1
zS
V
t
k
ðÞ, fork§2,
LJ
1
~S
J
t
0
zt
1
ðÞ, ..., LJ
k
~LJ
k{1
zS
J
t
k
ðÞ, fork§2
where the opening offset time t
0
denotes a minimal time
of opening and t
k
(k$1) are random variables uniformly
distributed between t
0
and the end of the opening process.
9) For every rearrangement occurrence, we define for each
gene V
i
(J
j
respectively) a Boolean variable BV
ik
(resp. BJ
jk
)
equal at the k
th
rearrangement to 1 if the gene is open
(‘‘accessible’’), and to 0 if it is closed (‘‘non-accessible’’) or if
it has been deleted during a previous rearrangement of order
i(i,k).
10) TheRSSscoreKV
i
(resp. KJ
j
) represents for each gene V
i
(J
j
respectively) t he homology percentage compared to a
consensus sequence. This score b asically takes value p,
0#p#1 , if there is p % of identity bet ween the R SS and
the consensus proposed by Glusman et al. [25], allo wing us
to estimate a RSS identity score ranging from 0.3 t o 1,
where 1 corresponds to a fully consensus RSS (see
additional data). Our RSS score is in agreeme nt with
the status of functional v ersus pseudo V or J gen e (0.3,
pseudo rearrangement score ,0.65; 0.65, functional
score ,1). Accordin g to its no n-functional status, a J-
pseudo recombination is never found rearranged and
consequently the corresponding J-RSS score is
assimilated to zero in simulations. RSS score is equal to
1 when simulation is done without taking account
the RSS. We call FV
k
(resp. FJ
k
) the distribution
function (i.e., the relative length) obtained after the
k
th
rearrangement by adding the BV (resp. BJ)
variables:
FV
k
iðÞ~
X
m~1,...,i
KV
m
BV
mk
!,
X
m~1,...,104
KV
m
BV
mk
!
FJ
k
jðÞ~
X
m~1,...,j
KJ
m
BJ
mk
!
X
m~1,...,60
KJ
m
BJ
mk
!,
11) At step k, we choose the distribution functions FV
k
and FJ
k
corres ponding to the random variables RV
k
(resp. RJ
k
)
uniform on [0,1] and we calculate a number NVk
(resp.NJk) equal to inf(FV
k
21
(RV
k
)) (resp. inf(FJ
k
21
(RJ
k
))).
NVk and NJk corresponding to the V and J genes to
rearrange.
The number of simulated TRAD loci gives the size of the
simulated population. In the figures shown in this paper, 1 million
of V-J rearrangements have been simulated.
The simulation Output is presented in a matrix form
incremented by the successive V-J in-frame rearrangements. Final
results show the total number of V-J combinations available at the
end of the whole simulation. These results can be plotted in
different 3D representations using the interface. It is also possible
to display the results for multi member V famillies corresponding
to the real time PCR’s.
Author Contributions
Conceived and designed the experiments: JD PNM EJM. Performed
the experiments: FT MAS NP AD TPB. Analyzed the da ta: FT MAS
OH NP TPB VH JD EJM. Contributed reagents/materials/analysis
tools: OH AD TPB VH. Wrote the paper: FT MAS OH NP JD PNM
EJM.
5)
6)
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 11 February 2010 | Volume 6 | Issue 2 | e1000682
References
1. Cobb RM, Oestreich KJ, Osipovich OA, Oltz EM (2006) Accessibility control of
V(D)J recombination. Adv Immunol 91: 45–109.
2. Jouvin-Marche E, Aude-Garcia C, Candeias S, Borel E, Hachemi-Rachedi S,
et al. (1998) Differential chronology of TCRADV2 gene use by alpha and delta
chains of the mouse TCR. Eur J Immunol 28: 818–827.
3. Rytkonen M, Hurwitz JL, Tolonen K, Pelkonen J (1994) Evidence for
recombinatorial hot spots at the T cell receptor J alpha locus. Eur J Immunol
24: 107–115.
4. Abarrategui I, Krangel MS (2007) Noncoding transcription controls downstream
promoters to regulate T-cell receptor alpha recombination. Embo J 26:
4380–4390.
5. Villey I, Caillol D, Selz F, Ferrier P, de Villartay JP (1996) Defect in
rearrangement of the most 59 TCR-J alpha following targeted deletion of T early
alpha (TEA): implications for TCR alpha locus accessibility. Immunity 5:
331–342.
6. Baum TP, Pasqual N, Thuderoz F, Hierle V, Chaume D, et al. (2004) IMGT/
GeneInfo: enhancing V(D)J recombination database accessibility. Nucleic Acids
Res 32: D51–54.
7. Thompson SD, Pelkonen J, Rytkonen M, Samaridis J, Hurwitz JL (1990)
Nonrandom rearrangement of T cell receptor J alpha genes in bone marrow T
cell differentiation cultures. J Immunol 144: 2829–2834.
8. Thompson SD, Pelkonen J, Hurwitz JL (1990) First T cell receptor alpha gene
rearrangements during T cell ontogeny skew to the 5 9 region of the J alpha locus.
J Immunol 145: 2347–2352.
9. Pasqual N, Gallagher M, Aude-Garcia C, Loiodice M, Thuderoz F, et al. (2002)
Quantitative and qualitative changes in V-J alpha rearrangements during mouse
thymocytes differentiation: implication for a limited T cell receptor alpha chain
repertoire. J Exp Med 196: 1163–1173.
10. Aude-Garcia C, Gallagher M, Marche PN, Jouvin-Marche E (2001) Prefe rential
ADV-AJ association during recombination in the mouse T-cell receptor alpha/
delta locus. Immunogenetics 52: 224–230.
11. Krangel MS (2003) Gene segment selection in V(D)J recombinati on: accessibility
and beyond. Nat Immunol 4: 624–630.
12. Oltz EM (2001) Regulation of antigen receptor gene assembly in lymphocytes.
Immunol Res 23: 121–133.
13. Davodeau F, Difilippantonio M, Roldan E, Malissen M, Casanova JL, et al.
(2001) The tight interallelic positional coincidence that distinguishes T-cell
receptor Jalpha usage does not result from homologous chromosomal pairing
during ValphaJalpha rearrangement. Embo J 20: 4717–4729.
14. Sleckman BP, Bardon CG, Ferrini R, Davidson L, Alt FW (1997) Function of
the TCR alpha enhancer in alphabeta and gammadelta T cells. Immunity 7:
505–515.
15. Hawwari A, Bock C, Krangel MS (2005) Regulation of T cell receptor alpha
gene assembly by a complex hierarchy of germline Jalpha promoters. Nat
Immunol 6: 481–489.
16. Hawwari A, Krangel MS (2007) Role for rearranged variable gene segments in
directing secondary T cell receptor {alpha} recombination. Proc Natl Acad
Sci U S A 104: 903–907.
17. Mauvieux L, Villey I, de Villartay JP (2003) TEA regulates local TCR-Jalpha
accessibility through histone acetylation. Eur J Immunol 33: 2216–2222.
18. Marche PN , Kindt TJ (1986) Two distinct T-ce ll receptor alpha-chain
transcripts in a rabbit T-cell line: implications for allelic exclusion in T cells.
Proc Natl Acad Sci U S A 83: 2190–2194.
19. Krangel MS (2009) Mechanics of T cell receptor gene rearrangement. Curr
Opin Immunol 21: 133–139.
20. Petrie HT, Livak F, Schatz DG, Strasser A, Crispe IN, et al. (1993) Multiple
rearrangements in T cell receptor alpha chain genes maximize the production of
useful thymocytes. J Exp Med 178: 615–622.
21. Wang F, Huang CY, Kanagawa O (1998) Rapid deletion of rearranged T cell
antigen receptor (TCR) Valpha-Jalpha segment by secondary rearrangement in
the thymus: role of continuous rearrangement of TCR alpha chain gene and
positive selection in the T cell repertoire formation. Proc Natl Acad Sci U S A
95: 11834–11839.
22. Lefranc MP (2001) IMGT, the international ImMunoGeneTics database.
Nucleic Acids Res 29: 207–209.
23. Rytkonen MA, Hurwitz JL, Thompson SD, Pelkonen J (1996) Restricted onset
of T cell receptor alpha gene rearrangement in fetal and neonatal thymocytes.
Eur J Immunol 26: 1892–1896.
24. Gahery-Segard H, Jouvin-Marche E, Six A, Gris-Liebe C, Malissen M, et al.
(1996) Germline genomic structure of the B10.A mouse Tcra-V2 gene subfamily.
Immunogenetics 44: 298–305.
25. Glusman G, Rowen L, Lee I, Boysen C, Roach JC, et al. (2001) Comparative
genomics of the human and mouse T cell receptor loci. Immunity 15: 337–349.
26. Livak F, Burtrum DB, Rowen L, Schatz DG, Petrie HT (2000) Genetic
modulation of T cell receptor gene segment usage during somatic recombina-
tion. J Exp Med 192: 1191–1196.
27. Warmflash A, Dinner AR (2006) A model for TCR gene segment use. J Immunol
177: 3857–3864.
28. Guo J, Hawwari A, Li H, Sun Z, Mahanta SK, et al. (2002) Regulation of the
TCRalpha repertoire by the survival window of CD4(+)CD8(+) thymocytes. Nat
Immunol 3: 469–476.
29. Osipovich O, Milley R, Meade A, Tachibana M, Shinkai Y, et al. (2004)
Targeted inhibition of V(D)J recombination by a histone methyltransferase. Nat
Immunol 5: 309–316.
30. Huang J, Muegge K (2001) Control of chromatin accessibility for V(D)J
recombination by interleukin-7. J Leukoc Biol 69: 907–911.
31. Rytkonen-Nissinen M, Hurwitz JL, Pelkonen S, Levelt C, Pelkonen J (1999)
Early activation of TCR alpha gene rearrangement in fetal thymocytes.
Eur J Immunol 29: 2288–2296.
32. Wilson A, MacDonald HR, Radtke F (2001) Notch 1-deficient common
lymphoid precursors adopt a B cell fate in the thymus. J Exp Med 194:
1003–1012.
33. Fuschiotti P, Pasqual N, Hierle V, Borel E, London J, et al. (2007) Analysis of the
TCR alpha-chain rearrangement profile in human T lymphocytes. Mol
Immunol 44: 3380–3388.
34. Mancini SJ, Candeias SM, Di Santo JP, Ferrier P, Marche PN, et al. (2001)
TCRA gene rearrangement in immature thymocytes in absence of CD3, pre-
TCR, and TCR signaling. J Immunol 167: 4485–4493.
35. de Chasseval R, de Villartay JP (1993) Functional characterization of the
promoter for the human germ-line T cell receptor J alpha (TEA) transcript.
Eur J Immunol 23: 1294–1298.
Estimation of V-J TCRa Repertoire
PLoS Computational Biology | www.ploscompbiol.org 12 February 2010 | Volume 6 | Issue 2 | e1000682
    • "This suggests that these segments may be more efficiently rearranged resulting in their over representation in the repertoire and vice versa. The effect of spatial organization of TCR gene segments on recombination frequency is also evident when modelling the rearrangement likelihood in the murine TRA taking into account the relative positioning of V and J segments [37] . Assuming sequential availability of V and J segments to recombine with each other in a time-dependent process, it was demonstrated that the proximal, central and distal J segments had a greater likelihood of recombining with the correspondingly positioned V segments. "
    [Show abstract] [Hide abstract] ABSTRACT: The human T-cell repertoire is complex and is generated by the rearrangement of variable (V), diversity (D) and joining (J) segments on the T-cell receptor (TCR) loci. The T-cell repertoire demonstrates self-similarity in terms clonal frequencies when defined by V, D and J gene segment usage; therefore to determine whether the structural ordering of these gene segments on the TCR loci contributes to the observed clonal frequencies, the TCR loci were examined for self-similarity and periodicity in terms of gene segment organization. Logarithmic transformation of numeric sequence order demonstrated that the V and J gene segments for both T-cell receptor a (TRA) and b (TRB) loci are arranged in a self-similar manner when the spacing between the adjacent segments was considered as a function of the size of the neighbouring gene segment, with an average fractal dimension of approximately 1.5. Accounting for the gene segments occurring on helical DNA molecules with a logarithmic distribution, sine and cosine functions of the log-transformed angular coordinates of the start and stop nucleotides of successive TCR gene segments showed an ordered progression from the 50 to the 30 end of the locus, supporting a log-periodic organization. T-cell clonal frequency estimates, based on V and J segment usage, from normal stem cell donors were plotted against the Vand J segment on TRB locus and demonstrated a periodic distribution. We hypothesize that this quasi-periodic variation in genesegment representation in the T-cell clonal repertoire may be influenced by the location of the gene segments on the periodic-logarithmically scaled TCR loci. Interactions between the two strands of DNA in the double helix may influence the probability of gene segment usage by means of either constructive or destructive interference resulting from the superposition of the two helices. © 2016 The Author(s) Published by the Royal Society. All rights reserved.
    Full-text · Article · Jan 2016
  • [Show abstract] [Hide abstract] ABSTRACT: The classical models of epidemics dynamics by Ross and McKendrick have to be revisited in order to incorporate elements coming from the demography (fecundity, mortality and migration) both of host and vector populations and from the diffusion and mutation of infectious agents. The classical approach is indeed dealing with populations supposed to be constant during the epidemic wave, but the presently observed pandemics show duration of their spread during years imposing to take into account the host and vector population changes as well as the transient or permanent migration and diffusion of hosts (susceptible or infected), as well as vectors and infectious agents. Two examples are presented, one concerning the malaria in Mali and the other the plague at the middle-age.
    Article · Sep 2010
    J GaudartJ GaudartM GhassaniM GhassaniJ MintsaJ Mintsa+1more author...[...]
  • [Show abstract] [Hide abstract] ABSTRACT: Classical models of epidemics by Ross and McKendrick have to be revisited in order to take into account the demography (fecundity, mortality and migration) both of host and vector populations and also the diffusion and mutation of infectious agents. The classical models are supposing the populations involved in the infectious disease to be constant during the epidemic wave, but the presently observed pandemics show that the duration of their spread during months or years imposes to take into account the host and vector population changes, and also the transient or permanent migration and diffusion of hosts (susceptible or infected), as well as those of vectors and infectious agents. One example is presented concerning the malaria in Mali.
    Article · Jan 2012
Show more