Abstract
Recent evidence suggests that lymphocyte Ag receptor gene rearrangement does not always stop after the expression of the first productively rearranged receptor. Light chain gene rearrangement in B cells, and αchain 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 κ:λ ratio and on κ 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 κ rather than λ 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 κ allele. This order, combined with the stringency of negative selection, is shown to lead to effective allelic exclusion.
The longaccepted concept of allelic exclusion states that Ag receptor genes in B and T lymphocytes are expressed from only one of the two alleles in each cell. Combined with isotypic exclusion, allelic exclusion works to ensure that each lymphocyte expresses a single Ag receptor specificity on the cell surface. Allelic exclusion is strictly observed at both the B cell receptor (BCR)^{3} heavy chain and the TCR βchain loci. Expression of a productively rearranged heavy or βchain in the form of the preBCR or the preTCR abrogates further heavy or βchain gene rearrangement, respectively. Recent evidence suggests, however, that in the TCR αchain, 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 αchain (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 κ:λ light chain ratio, the choice of κ allele for rearrangement, and the choice of Jκ segment within this allele. The observed ratio between κ light chain and λ light chainbearing 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 κ:λ ratio can be explained solely on the basis of the higher potential for multiple rearrangements in the κ locus, combined with immature B cell death due to negative selection, without assuming preferential expansion of κ B cells over λ B cells (12, 13, 14, 15).
Previous studies attempted to calculate the κ:λ ratio based on the following observations. First, recombination signals at the κ locus are ∼100 times more efficient than those of the λ locus (16); this is called the “branching ratio.” Second, gene rearrangement at κ precedes λ 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 onethird. The presence of rearrangeable but nonfunctional V “pseudogenes,” 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 κ locus, this factor, the “crash factor,” would favor the survival of κ B cells over λ 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 κ:λ ratio of at most 2.25 (12). Even taking into account the crash factor, one cannot account for a ratio of κ:λ > 10 without assuming extremely high values for the B cell death probability. Only when considering multiple rearrangements at the κ 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 κ:λ that exceeds 10 (18). In the latter study, the κ:λ ratio was found to be related to the death probability, meaning that the fewer rearrangements the cell is allowed to try at the κ locus, the higher the resulting κ:λ ratio.
In addition to explaining the high κ:λ ratio, the ability of a B cell to make secondary rearrangements on a single κ allele explains why ∼70% of mouse splenic κ B cells have only one rearranged κ locus, the other one remaining unrearranged (19); and why, in mice that have only one functional κ locus, κ B cell production is ∼70% (rather than onehalf) of that in wildtype mice (13). Furthermore, it has been suggested (13, 20, 21) that rearrangement may proceed sequentially rather than stochastically. That is, that 5′ Jκ segments are used before 3′ Jκ 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, Jκ usage, and the κ:λ 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 negativeselection 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 κ rather than λ 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 κ allele, such that Jκ1,2 are preferentially used before Jκ4,5. 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.
A Simulation of BCR Gene Rearrangement
We have created a stochastic simulation of BCR gene rearrangement.^{4} The general structure of the simulation is given in Fig. 1⇓. Individual modules can be described as follows.
1) Cell birth: cells are “born” into the simulation having all light chain genes in the unrearranged (germline) state.
2) Light chain selection: at each rearrangement step, a preliminary selection of either κ or λ is made, according to the selection probability p_{κλ}, which is a parameter of the program.
3) BCRκ rearrangement: if κ is selected, then one or the other allele is randomly selected for rearrangement. Subsequent selections of Jκ segments for rearrangement may either rearrange the previously rearranged allele or switch to the opposite allele, depending on the probability parameter P_{switch}. For example, if P_{switch} = 0, then the cell rearranges the previously rearranged allele, provided there are Jκ segments remaining on it. Once a κ allele is selected, one of the four Jκ segments is chosen using the probability parameters p_{1}, p_{2}, p_{4}, p_{5}. Rearrangements are followed by renormalization of the allele in question, that is, a rearranged Jκ segment is deleted (as are all unrearranged Jκ segments 5′ relative to the rearranged segment), and cannot be chosen again by the program. For example, if we assume a strictly random Jκ usage, the initial values of the usage probabilities will be p_{1} = p_{2} = p_{4} = p_{5} = 1/4; after rearrangement to, say, Jκ1, these probabilities will be changed to p_{1} = 0, p_{2} = p_{4} = p_{5} = 1/3; etc.
4) BCRλ rearrangement: if λ is selected, then one of the two λ alleles is chosen at random, with equal probabilities for the two alleles. Rearrangement at λ has been simplified to two rearrangements per allele. Thus, one of two Jλ segments on the current allele is chosen at random. Failures at λ lead to deletion of only the failed segment and have no effect on any other segments, either κ or λ.
5) If a cell has run out of Jκ segments on one allele, then it automatically switches to the other allele. If a cell is entirely out of Jκ segments on both alleles, then it switches to λ segments until all segments are exhausted. The cell dies if there are no more light chain segments available for rearrangement.
6) Selection: once a VJ rearrangement is made, the program determines whether the rearrangement is in frame, with a probability P_{product}. If it is in frame, the program determines whether the resulting light chain can pair with the existing heavy chain, with a probability P_{H/L}. If so, the program determines whether the resulting BCR is autoreactive (antiself), with a probability P_{as}. 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 antiself rearrangement. These cells are assigned a high death probability, denoted by P_{das}. If, however, a cell does not die after such a rearrangement, it may try another rearrangement (receptor editing); 2) cells containing only outofframe VJ joins, H/L mismatched heavylight chain pairs, or germline κ. These cells are assigned a moderate death probability, P_{d}. If such cells do not die, they also continue rearranging their light chain genes; and 3) cells containing one inframe, 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 10^{4} viable cells, having found that, in most cases, 10^{4} 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.
The probability for a VJ rearrangement to be productive is onethird, because this is the probability that V will be joined to J in the correct reading frame. P_{H/L} was chosen to be 0.8 because previous studies (18) have shown that this is the minimum value required to give a ratio of κ:λ > 2. P_{as} has been independently estimated by others (22, 23).
Results
Our goal in the first series of simulations was to evaluate the hypothesis of ordered rearrangement. We tested the hypothesis of allele bias (preference to rearrange a rearranged allele) as well as the hypothesis of sequentiality in Jκ 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 P_{switch} = 0.5 or P_{switch} = 0. When P_{switch} = 0.5, the choice of allele to rearrange next is random and independent of the previous rearrangement. When P_{switch} = 0, rearrangement continues on the same allele until that allele is exhausted.
To test the degree of order in Jκ segment usage, we used three sets of p_{i} probabilities. The first set represents the null hypothesis, that is, that Jκ usage is completely random, and hence the probabilities are equal for all segment choices: p_{1} = p_{2} = p_{4} = p_{5} = 0.25. The second set represents the diametrically opposed hypothesis, strictly sequential Jκ usage: p_{1} ≫ p_{2} ≫ p_{4} ≫ p_{5} (Table I⇑). Following Wood and Coleclough (20), we have also tried an intermediate case, which we call “quasisequential.” In this scenario, we assume that rearrangement to Jκ1 or Jκ2 is much more frequent than rearrangement to Jκ4 or Jκ5. Hence, we set the probabilities in this case to obey the rule p_{1} = p_{2} ≫ p_{4} = p_{5} (Table I⇑). The probabilities of using each of the two λ alleles, and each segment within these alleles, were always equal.
The combination of two possibilities for P_{switch} and three sequentiality cases gives six possible basic scenarios of rearrangement, which test the combined contribution of sequential Jκ 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.
Rearrangement of BCR genes is biased toward the last allele rearranged
First, we performed simulations in which there was no allele preference (P_{switch} = 0.5). These simulations never yielded a fraction of cells with an R/0 genotype, that is, only one κ 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 P_{switch} = 0.5 is always <30%. On the other hand, using the opposing hypothesis of strict allele preference (P_{switch} = 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 κ gene rearrangement that exhibits a high degree of allele preference.
Usage of Jκ gene segments is quasisequential
Second, we tested the three scenarios for Jκ usage. Simulations implementing the hypothesis of a random Jκ 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 Jκ usage in this case, we see that the distribution is skewed toward downstream Jκ segments: Jκ1 < Jκ2 < Jκ4 < Jκ5. This is a direct result of a cell’s ability to rearrange the downstream Jκ 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 Jκ segments results in a Jκ usage distribution skewed toward 3′ Jκs; we call this the “accumulation” or “pileup” effect.
On the other hand, if we assume strictly sequential rearrangement (p_{1} ≫ p_{2} ≫ p_{4} ≫ p_{5}), we get the opposite skew of the results (toward upstream Jκs). The explanation for this is straightforward: all cells will start by rearranging to Jκ1. A third will succeed in making a productive rearrangement, the rest will proceed to rearrange to Jκ2. A third of these (2/9 of the total) will succeed in making a productive rearrangement, the rest will proceed to rearrange to Jκ3, and so on. The probability that each productive rearrangement leads to a functional, nonautoreactive receptor is independent of the Jκ segment used, so that the final distribution of Jκ usage is determined by the order of rearrangements (Fig. 2⇑, C and D).
Finally, simulations of quasisequential rearrangement give an advantage to Jκ1 and Jκ2 over Jκ4 and Jκ5 (Fig. 2⇑, E and F). This scenario best reproduces the published (20) murine Jκ usage distribution, which was 40–45% each of Jκ1 or Jκ2 vs 5–10% each of Jκ4 or Jκ5. Even with an antiself knockin start to Jκ1, there is still an advantage of Jκ2 over Jκ4 and Jκ5 (∼40% of the cells contain rearrangements to Jκ2; data not shown). Thus, our conclusion from this series of simulations is that Jκ rearrangement most likely proceeds sequentially or quasisequentially, but certainly not in a random manner.
Ordered receptor editing accounts for the κ:λ ratio
Next, we proceeded to check whether ordered rearrangements as modeled above would reproduce not only the data on Jκ usage and allele preference, but also a κ:λ ratio larger than 10:1. We noticed that estimates of the κ:λ 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 κ:λ ratio. The results show that high values of the κ:λ ratio are easily obtained once we incorporate ordered rearrangements into our model. The κ:λ ratio is highly sensitive to Pκλ (Fig. 3⇓A): only values of Pκλ > 0.95 give κ:λ > 10. Thus, our first conclusion from this series of simulations is that rearrangement is preferential not only within and between the κ alleles, but also with respect to the choice between κ and λ. Our model reproduces the observation (13) that a developing B cell is likely to rearrange κ first. In our model, this temporal order is not deterministic, but rather results from the higher probability of starting with κ rearrangement. Cells would be much more likely to rearrange to λ only upon exhausting the rearrangement possibilities at the κ locus. Next, we examined the effect of negative selection on the κ:λ ratio. We assigned the value of 0.67 to P_{as} (22, 23) and varied the values of each of the two death probabilities. Fig. 3⇓, B and C, contains plots of the resulting κ:λ ratio as a function of P_{das} or P_{d}. As predicted above, the higher the probability of death, the larger is the κ:λ ratio. Higher values of P_{das} and/or P_{d} 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 κ and proceeding to λ rearrangements.
Note that the effect of changing P_{das} is much smaller than the effect of changing P_{d}, because P_{das} affects a much smaller fraction of the cells. P_{das} affects only those cells with productive, but selfreactive, rearrangements, that is, P_{product} × P_{H/L} × P_{as}, which is about onefifth of the cells for the probabilities given in Table I⇑. On the other hand, P_{d} affects the rest of the cell death cases, that is, (1 − P_{product}) + P_{product}(1 − P_{H/L}), which amount to about threequarters 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 P_{d}. Again, the higher the probability of death, the stronger is the advantage of the allele that is rearranged first. The effect of changes in P_{das} is again much smaller than the effect of changes in P_{d} (data not shown).
Discussion
The widely accepted concept of allelic exclusion has been challenged in recent years by multiple observations of continued rearrangement of both the BCR light chain and the TCR αchain. 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 κ light chain rearrangement precedes λ 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 κ alleles, the cell is more likely to perform secondary rearrangement, if necessary and possible, on the same allele rather than switching to the other κ allele. Allele preference fully explains the high fractions of κ light chain B cells that contain κ 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 quasisequential rearrangement within each κ allele, that is, when Jκ1 and/or Jκ2 are available for rearrangement, the cell is more likely to choose one of these segments over Jκ4 or Jκ5 (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 κ:λ ratio. Cells are allowed few rearrangement attempts (large P_{das} and P_{d}) and, hence, are likely to die before exhausting κ and proceeding to λ 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 selectionlimited 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 Jκ 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 Jαs first is not essential. This difference may be explained by the fact that, while B cells have only 4 functional Jκ segments per allele (and two Jλs) and thus need to use them efficiently, T cells have ∼50 Jα 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 TCRα 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 TCRα 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 αchains. 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.
Acknowledgments
We thank Drs. Martin Weigert and Philip Seiden for useful discussions, and Dr. Lee Segel for reviewing the manuscript.
Footnotes

↵1 The study was supported by National Institutes of Health Grants GM2096425 for the study of genetics and regulation of autoimmunity, R01 AI34882 (to S.L.), and AI1022701 (to R.M.), and an American Heart Association Grant 9704047A (to M.S.).

↵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. Email address: s_litwin{at}fccc.edu

↵3 Abbreviation used in this paper: BCR, B cell receptor.

↵4 The program is available from the authors upon request.
 Received December 17, 1998.
 Accepted June 1, 1999.
 Copyright © 1999 by The American Association of Immunologists