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*
Department of Molecular Biology, Princeton University, Princeton, NJ, 08544; and
Fox Chase Cancer Center, Philadelphia, PA 19111
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Abstract |
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 Top Abstract IntroductionA Simulation of BCR...ResultsDiscussionReferences |
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-chain rearrangement in T cells can continue, which
raises the question: how is allelic exclusion maintained, if at all, in
the face of continued rearrangement? In this and the accompanying
paper, we present comprehensive models of Ag receptor gene
rearrangement and the interaction of this process with clonal
selection. Our B cell model enables us to reconcile observations on the
:
ratio and on allele usage, showing that B cell receptor
gene rearrangement must be a highly ordered, rather than a random,
process. We show that order is exhibited on three levels: a preference
for rearranging rather than light chain genes; a preference to
make secondary rearrangements on the allele that has already been
rearranged, rather than choosing the location of the next rearrangement
at random; and a sequentiality of J segment choice within each
allele. This order, combined with the stringency of negative selection,
is shown to lead to effective allelic exclusion. |
Introduction |
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TopAbstractIntroductionA Simulation of BCR...ResultsDiscussionReferences |
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-chain, and in the BCR
light chain (1, 2, 3), rearrangement may not stop after a
productive receptor gene has been formed and expressed. In the case of
the TCR -chain (see the accompanying paper), this may lead to
incomplete allelic exclusion. For the BCR light chain, there is
evidence that secondary rearrangements occur after nonproductive
rearrangements, and also after productive rearrangements that render a
B cell autoreactive ("receptor editing", reviewed in Ref.
4). Using mice transgenic for autoreactive BCRs, receptor
editing has been identified as one of the mechanisms of central
tolerance (5, 6, 7, 8). However, if the choice of allele for
secondary rearrangements is random, it is (at least theoretically)
possible that a cell will rearrange and then simultaneously express two
different light chains. How then, if at all, is allelic exclusion
maintained in the face of continued rearrangement? Using computer
simulation of light chain gene rearrangement, we show that allelic
exclusion in B cells can be maintained if rearrangement is an ordered,
rather than a random, process.
Our model relies on experimental evidence concerning three related
characteristics of light chain gene rearrangement: the : light
chain ratio, the choice of allele for rearrangement, and the choice
of J segment within this allele. The observed ratio
between light chain- and light chain-bearing B cells in the
murine serum is 
20:1, and, in immature murine bone marrow cells, it
is >10:1 (9, 10, 11). It is controversial whether the :
ratio can be explained solely on the basis of the higher potential for
multiple rearrangements in the locus, combined with immature B cell
death due to negative selection, without assuming preferential
expansion of B cells over B cells (12, 13, 14, 15).
Previous studies attempted to calculate the : ratio based on the
following observations. First, recombination signals at the locus
are 100 times more efficient than those of the locus
(16); this is called the "branching ratio." Second,
gene rearrangement at precedes gene rearrangement by 24 h
(13). Third, because there are three possible DNA reading
frames, the probability that the rearrangement will be productive is at
most one-third. The presence of rearrangeable but nonfunctional V
"pseudo-genes," may reduce this probability, called the "fusion
efficiency," even further (13). Third, evidence suggests
that a B cell is allowed to live for only a limited amount of time in
the bone marrow (17). After this time, the cell will die
if it fails to make a functional receptor. Because of the preference to
rearrange first at the locus, this factor, the "crash factor,"
would favor the survival of B cells over B cells. A model
addressing only the branching ratio and fusion efficiencies, but which
allows just one rearrangement attempt per chromosome (i.e., no receptor
editing), gives a : ratio of at most 2.25 (12). Even
taking into account the crash factor, one cannot account for a ratio of
: > 10 without assuming extremely high values for the B
cell death probability. Only when considering multiple rearrangements
at the locus, in addition to the above three factors (branching
ratio, fusion efficiency, and crash factor), can a stochastic model of
BCR gene rearrangement produce a ratio of : that exceeds 10
(18). In the latter study, the : ratio was found to
be related to the death probability, meaning that the fewer
rearrangements the cell is allowed to try at the locus, the higher
the resulting : ratio.
In addition to explaining the high : ratio, the ability of a B
cell to make secondary rearrangements on a single allele explains
why 70% of mouse splenic B cells have only one rearranged
locus, the other one remaining unrearranged (19); and why,
in mice that have only one functional locus, B cell production
is 70% (rather than one-half) of that in wild-type mice
(13). Furthermore, it has been suggested (13, 20, 21) that rearrangement may proceed sequentially rather than
stochastically. That is, that 5' J segments are used before 3' J
segments. Recent observations on receptor editing in mice transgenic
for autoreactive Abs (6, 7, 8) have also hinted at the
possibility of order in the rearrangement process. Hence, the following
question arose: can ordered rearrangement account for the observations
on allele bias, J usage, and the : ratio?
The present study is an attempt to address this question. We identify
the degree of order in BCR gene rearrangement as a primary mechanism
ensuring allelic exclusion. Our methodology is to perform computer
simulations of receptor gene rearrangement, incorporating different
assumptions, and to compare the results to the available experimental
data. Thus, we assess the relative ability of each hypothesis in turn
to account for the experimental observations. Our model leads us to
conclude that: 1) secondary BCR gene rearrangements are
negative-selection driven, in the sense that a cell has a limited time
window in which it can edit its receptor and be rescued from deletion;
and 2) light chain rearrangement is an ordered process on three levels:
a preference for rearranging rather than light chain genes; a
preference to make secondary rearrangements on the allele that has
already been rearranged, rather than choosing the location of the next
rearrangement at random; and a sequentiality of rearrangement within
each allele, such that J1,2 are preferentially used before
J4,5. This order, combined with the stringency of negative
selection, is shown to lead, with high probability, to effective
allelic exclusion. That is, the likelihood of a cell producing two
productive rearrangements on two light chain alleles, within a limited
time window and under the constraints of ordered rearrangement, is
extremely small.
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A Simulation of BCR Gene Rearrangement |
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TopAbstractIntroductionA Simulation of BCR...ResultsDiscussionReferences |
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. Individual modules can be described as
follows.
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2) Light chain selection: at each rearrangement step, a preliminary
selection of either or is made, according to the selection
probability p, which is a
parameter of the program.
3) BCR rearrangement: if is selected, then one or the other
allele is randomly selected for rearrangement. Subsequent selections of
J segments for rearrangement may either rearrange the previously
rearranged allele or switch to the opposite allele, depending
on the probability parameter Pswitch. For
example, if Pswitch = 0, then the cell
rearranges the previously rearranged allele, provided there are J
segments remaining on it. Once a allele is selected, one of the
four J segments is chosen using the probability parameters
p1,
p2,
p4,
p5. Rearrangements are followed by
renormalization of the allele in question, that is, a rearranged J
segment is deleted (as are all unrearranged J segments 5' relative
to the rearranged segment), and cannot be chosen again by the program.
For example, if we assume a strictly random J usage, the initial
values of the usage probabilities will be
p1 =
p2 =
p4 =
p5 = 1/4; after rearrangement to, say,
J1, these probabilities will be changed to
p1 = 0,
p2 =
p4 =
p5 = 1/3; etc.
4) BCR rearrangement: if is selected, then one of the two
alleles is chosen at random, with equal probabilities for the two
alleles. Rearrangement at has been simplified to two rearrangements
per allele. Thus, one of two J segments on the current allele is
chosen at random. Failures at lead to deletion of only the failed
segment and have no effect on any other segments, either or
.
5) If a cell has run out of J segments on one allele, then it
automatically switches to the other allele. If a cell is entirely out
of J segments on both alleles, then it switches to segments
until all segments are exhausted. The cell dies if there are no more
light chain segments available for rearrangement.
6) Selection: once a V-J rearrangement is made, the program determines whether the rearrangement is in frame, with a probability Pproduct. If it is in frame, the program determines whether the resulting light chain can pair with the existing heavy chain, with a probability PH/L. If so, the program determines whether the resulting BCR is autoreactive (anti-self), with a probability Pas. Rearrangement is repeated until a productive, H/L matched, nonautoreactive BCR is produced, or until the cell dies.
7) Cell fate after selection: Results of rearrangement are classified
into one of three categories: 1) cells containing an anti-self
rearrangement. These cells are assigned a high death probability,
denoted by Pdas. If, however, a cell does
not die after such a rearrangement, it may try another rearrangement
(receptor editing); 2) cells containing only out-of-frame V-J joins,
H/L mismatched heavy-light chain pairs, or germline . These cells
are assigned a moderate death probability,
Pd. If such cells do not die, they also
continue rearranging their light chain genes; and 3) cells containing
one in-frame, H/L matched, nonautoreactive rearrangement, are allowed
to mature.
Parameters
Table I summarizes the default
parameter values used in our simulations. The program follows each new
cell until it either matures or dies, and repeats the process for a
predetermined number of mature cells produced. We usually simulate
104 viable cells, having found that, in most
cases, 104 cells are sufficient for simulation
variability to stabilize. The program then generates as output the
distribution of genotypes among the cells that have matured. The
simulation does not include cell divisions, because developing B cells
do not divide while light chain rearrangement and selection are
going on.
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: > 2.
Pas has been independently estimated by
others (22, 23). |
Results |
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TopAbstractIntroductionA Simulation of BCR...ResultsDiscussionReferences |
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usage. To test whether a B cell’s
choice of the allele to rearrange is a random choice or biased toward
the allele previously rearranged, simulations were performed with
either Pswitch = 0.5 or
Pswitch = 0. When
Pswitch = 0.5, the choice of allele to
rearrange next is random and independent of the previous rearrangement.
When Pswitch = 0, rearrangement continues
on the same allele until that allele is exhausted.
To test the degree of order in J segment usage, we used three sets
of pi probabilities. The first set
represents the null hypothesis, that is, that J usage is completely
random, and hence the probabilities are equal for all segment choices:
p1 =
p2 =
p4 =
p5 = 0.25. The second set represents
the diametrically opposed hypothesis, strictly sequential J usage:
p1 >>
p2 >>
p4 >>
p5 (Table I
). Following Wood and
Coleclough (20), we have also tried an intermediate case,
which we call "quasi-sequential." In this scenario, we assume that
rearrangement to J1 or J2 is much more frequent than
rearrangement to J4 or J5. Hence, we set the probabilities in
this case to obey the rule p1 =
p2 >>
p4 =
p5 (Table I). The probabilities of
using each of the two alleles, and each segment within these
alleles, were always equal.
The combination of two possibilities for
Pswitch and three sequentiality cases
gives six possible basic scenarios of rearrangement, which test the
combined contribution of sequential J usage and allele preference.
The results of simulations of these six scenarios are presented in Fig. 2. A comparison of these simulation
results with the published experimental data leads to the following
conclusions.
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First, we performed simulations in which there was no allele
preference (Pswitch = 0.5). These
simulations never yielded a fraction of cells with an R/0 genotype,
that is, only one allele rearranged [R/0 = 1
- R/R = (1/0 + 2/0 + 4/0 + 5/0)], similar
to the experimentally observed (13, 19) value of 70%
(Fig. 2, A, C, and E). Rather, the
fraction of R/0 cells in simulations with
Pswitch = 0.5 is always <30%. On the
other hand, using the opposing hypothesis of strict allele preference
(Pswitch = 0) results in R/0 of at least
70%, as observed (Fig. 2, B, D, and
F), regardless of order in J segment usage (see below).
Hence, we conclude that experimental data is more consistent with a
model of gene rearrangement that exhibits a high degree of allele
preference.
Usage of J gene segments is quasi-sequential
Second, we tested the three scenarios for J usage. Simulations
implementing the hypothesis of a random J usage do not reconstruct
the observed results. However, these simulations (Fig. 2, A
and B) reveal an interesting effect. In contrast to the
intuitive expectation that, within each allele, we will get a uniform
distribution of J usage in this case, we see that the distribution
is skewed toward downstream J segments: J1 < J2 <
J4 < J5. This is a direct result of a cell’s ability to
rearrange the downstream J segments either directly (deleting
intermediate segments) or as a secondary rearrangement after first
attempting to rearrange to more upstream segments. The more downstream
the segment, the more rearrangement pathways end up with a
rearrangement to that segment. Hence, a uniform probability
distribution for choices of J segments results in a J usage
distribution skewed toward 3' Js; we call this the
"accumulation" or "pile-up" effect.
On the other hand, if we assume strictly sequential rearrangement
(p1 >>
p2 >>
p4 >>
p5), we get the opposite skew of the
results (toward upstream Js). The explanation for this is
straightforward: all cells will start by rearranging to J1. A third
will succeed in making a productive rearrangement, the rest will
proceed to rearrange to J2. A third of these (2/9 of the total) will
succeed in making a productive rearrangement, the rest will proceed to
rearrange to J3, and so on. The probability that each productive
rearrangement leads to a functional, nonautoreactive receptor is
independent of the J segment used, so that the final distribution of
J usage is determined by the order of rearrangements (Fig. 2, C and D).
Finally, simulations of quasi-sequential rearrangement give an
advantage to J1 and J2 over J4 and J5 (Fig. 2, E
and F). This scenario best reproduces the published
(20) murine J usage distribution, which was 40–45%
each of J1 or J2 vs 5–10% each of J4 or J5. Even with an
anti-self knock-in start to J1, there is still an advantage of
J2 over J4 and J5 (40% of the cells contain rearrangements
to J2; data not shown). Thus, our conclusion from this series of
simulations is that J rearrangement most likely proceeds
sequentially or quasi-sequentially, but certainly not in a random
manner.
Ordered receptor editing accounts for the : ratio
Next, we proceeded to check whether ordered rearrangements as
modeled above would reproduce not only the data on J usage and
allele preference, but also a : ratio larger than 10:1. We
noticed that estimates of the : ratio varied enormously in
simulations of 10,000 cells. As a result, we increased the number of
cells in our rearrangement model to at least 100,000 in simulations
intended to examine the : ratio. The results show that high
values of the : ratio are easily obtained once we incorporate
ordered rearrangements into our model. The : ratio is highly
sensitive to P (Fig. 3A): only values of
P > 0.95 give : > 10. Thus, our
first conclusion from this series of simulations is that rearrangement
is preferential not only within and between the alleles, but also
with respect to the choice between and . Our model reproduces
the observation (13) that a developing B cell is likely to
rearrange first. In our model, this temporal order is not
deterministic, but rather results from the higher probability of
starting with rearrangement. Cells would be much more likely to
rearrange to only upon exhausting the rearrangement possibilities
at the locus. Next, we examined the effect of negative selection on
the : ratio. We assigned the value of 0.67 to
Pas (22, 23) and varied the
values of each of the two death probabilities. Fig. 3, B and
C, contains plots of the resulting : ratio as a
function of Pdas or
Pd. As predicted above, the higher the
probability of death, the larger is the : ratio. Higher values of
Pdas and/or
Pd corresponds to allowing the cells to
perform fewer rearrangement attempts: the average number of
rearrangements in our simulations was between two and three per cell
for the parameter values given in Table I. This is in agreement with
previous results (24). In this case, cells are likely to
die before exhausting and proceeding to rearrangements.
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. On the other hand, Pd affects the
rest of the cell death cases, that is, (1 -
Pproduct) +
Pproduct(1 -
PH/L), which amount to about
three-quarters of the total number of cells.
We also examined the sensitivity of allele usage to changes in death
probabilities. Fig. 4 shows how the
percent of cells with rearrangements only on one allele, denoted by
%R/0, varies with Pd. Again, the higher
the probability of death, the stronger is the advantage of the allele
that is rearranged first. The effect of changes in
Pdas is again much smaller than the effect
of changes in Pd (data not shown).
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Discussion |
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TopAbstractIntroductionA Simulation of BCR...ResultsDiscussionReferences |
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-chain. How
allelic exclusion is maintained, if at all, in spite of secondary
rearrangements, has been a matter of debate. The molecular mechanisms
responsible for Ag receptor gene rearrangement, and those linking Ag
receptor signaling upon Ag binding to positive and negative selection,
are still largely unknown. However, understanding the dynamics of these
processes, and how mechanistic properties of the rearrangement process
account for the resulting lymphocyte repertoire, may eventually shed
light on the inner workings of rearrangement and selection. We have
chosen to address this problem using stochastic computer simulation to
examine random vs ordered models of lymphocyte Ag receptor gene
rearrangement, and the interplay between this process and repertoire
selection.
The present paper presents our results for gene rearrangement and
selection in developing B cells. We first examined the degree of order
in BCR gene rearrangement. We have found that BCR gene rearrangement is
ordered on three different levels, as follows. First, our simulations
support the hypothesis, which was recently supported also by
experimental observations (9, 10, 11, 12, 13, 14, 15), that light chain
rearrangement precedes light chain rearrangement in most, if not
all, cases. Second, our results strongly support the hypothesis of
allele preference, that is, once a rearrangement exists on one of the
alleles, the cell is more likely to perform secondary
rearrangement, if necessary and possible, on the same allele rather
than switching to the other allele. Allele preference fully
explains the high fractions of light chain B cells that contain
rearrangements on one allele only. Although the mechanism of allele
preference is not known, the possibility that it is determined by the
DNA methylation status of light chain alleles has been suggested by
Bergman and colleagues (25). Third, our results show that
experimental observations are consistent with the hypothesis of
quasi-sequential rearrangement within each allele, that is, when
J1 and/or J2 are available for rearrangement, the cell is more
likely to choose one of these segments over J4 or J5
(19).
We also studied the effect of negative selection, determined by the
death probability of cells that have not succeeded in producing a
productively rearranged, H/L matched, nonautoreactive BCR. We found
that the higher the death probability, the larger the : ratio.
Cells are allowed few rearrangement attempts (large
Pdas and Pd)
and, hence, are likely to die before exhausting and proceeding to
rearrangements. Our simulations show that, in order for the results
to be consistent with experimental observations, we must assume that
negative selection limits the number of rearrangement attempts to two
to three per cell, in agreement with previous results
(24). Therefore, we refer to BCR rearrangement as a
negative selection-limited process.
Taken together, the above results reveal our proposed answer to the question of allelic exclusion in B cells. We propose that B cell allelic exclusion results from a high degree of order in gene rearrangement and a stringent process of negative selection. A high degree of order allows a B cell to maximize the number of rearrangements attempts, first on one allele and then on the other. Then, because negative selection limits the number of rearrangement attempts to two to three per cell, ordered rearrangement means it is likely that all these attempts will be on a single allele. Thus, it is extremely unlikely for two productive rearrangements to exist simultaneously on two light chain alleles. This results in the almost complete absence of cells expressing two different BCRs from the repertoire, i.e., in effective allelic exclusion.
Ordered secondary rearrangements thus maximize the cell’s ability to
make a productive, nonautoreactive rearrangement before exhausting all
J segments. In an accompanying paper, we show that, in contrast to B
cells, the process of secondary rearrangement in T cells does not have
to be as stringently ordered; rearrangement goes on simultaneously on
both alleles, and the observed bias toward rearranging upstream
Js first is not essential. This difference may be
explained by the fact that, while B cells have only 4 functional J
segments per allele (and two Js) and thus need to use them
efficiently, T cells have 50 J segments at their disposal.
A more important difference between BCR and TCR rearrangement is that
the latter is limited by positive, rather than negative selection;
i.e., rearrangement may continue even after the expression of a
productively rearranged TCR gene, and stops only after positive
selection has been completed. Using a computer simulation similar to
our B cell simulation, we show in the second paper that these two
features of TCR gene rearrangement, simultaneity and persistence
until positive selection, combine to account for the appearance of T
cells that have two productively rearranged and expressed TCR
-chains. Thus, allelic exclusion in B cells and allelic inclusion in
T cells can be brought about by similar rearrangement processes,
operating however on different gene structures and under different
rules of selection.
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Acknowledgments |
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Footnotes |
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2 Address correspondence and reprint requests to Dr. Samuel Litwin, Fox Chase Cancer Center, Institute for Cancer Research, Biostatistics Department, 7701 Burholme Avenue, Philadelphia, PA 19111. E-mail address:
3 Abbreviation used in this paper: BCR, B cell receptor.
4 The program is available from the authors upon request.
Received for publication December 17, 1998. Accepted for publication June 1, 1999.
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TopAbstractIntroductionA Simulation of BCR...ResultsDiscussionReferences |
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-deficient animals: a potential mechanism of B cell tolerance. J. Exp. Med. 180:1805./ ratio expressed by antigen-unselected B cells be explained?. Res. Immunol. 143:804.[Medline]
locus: efficient generation of chain-expressing B cells, independent of gene rearrangements in Ig. EMBO J. 12:811.[Medline]
and light chains changes following antigenic selection. Immunol. Today 16:141.[Medline]
and loci. Int. Immunol. 8:91./ ratio of immature B cells (letter). Immunol. Today 17:200.[Medline]
/ ratio of immature B cells". Immunol. Today 17:200.
light-chain recombination signal sequences mediate recombination more frequently than do those of a light chain. Proc. Natl. Acad. Sci. USA 88:10721./ ratio. Res. Immunol. 143:838.
immunoglobulin light chain locus are used at markedly different frequencies. Proc. Natl. Acad. Sci. USA 81:4756. gene repertoire of IgM+ B cells. J. Clin. Invest. 99:1614.[Medline]
chain monoallelic demethylation and the establishment of allelic exclusion. Genes Dev. 12:1801.This article has been cited by other articles:
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L. Delpy, C. Sirac, C. Le Morvan, and M. Cogne Transcription-Dependent Somatic Hypermutation Occurs at Similar Levels on Functional and Nonfunctional Rearranged IgH Alleles J. Immunol., August 1, 2004; 173(3): 1842 - 1848. [Abstract] [Full Text] [PDF]
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G. Kalmanovich and R. Mehr Models for Antigen Receptor Gene Rearrangement. III. Heavy and Light Chain Allelic Exclusion J. Immunol., January 1, 2003; 170(1): 182 - 193. [Abstract] [Full Text] [PDF]
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M. van der Burg, B. H. Barendregt, E. J. van Gastel-Mol, T. Tumkaya, A. W. Langerak, and J. J. M. van Dongen Unraveling of the Polymorphic C{lambda}2-C{lambda}3 Amplification and the Ke+Oz- Polymorphism in the Human Ig{lambda} Locus J. Immunol., July 1, 2002; 169(1): 271 - 276. [Abstract] [Full Text] [PDF]
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) or random (
). All
other parameters were assigned the default values; in particular,
Pswitch = 0. Each point represents a
simulation of 100,000 cells.