Why fitness distributions might vary between germline immunoglobulin alleles, and how chance events might trump those differences

Fitness differences between B cells using different germline alleles might arise from differences in initial affinity, in the propensity to adapt during affinity maturation, or both.

1. Germline-encoded affinity. Since affinity is a property of the entire receptor, not of its individual constituent alleles, naive B cells using a particular germline allele have a distribution of possible affinities determined by stochastic recombination with other alleles and insertions and deletions at their junctions (the breadth of this distribution reflects the strength of epistasis between germline alleles). Within an individual, different germline alleles will likely have different affinity distributions. Naive B cells using a specific heavy-chain V allele might bind an antigen well across all combinations with other alleles via CDRs 1 and 2 (Fig 1, orange allele), whereas naive B cells using another V allele might bind uniformly poorly (Fig 1, purple allele) or have high affinity only in certain combinations (Fig 1, green allele). The affinity distribution of an allele may vary between individuals, since individuals vary in their germline immunoglobulin diversity and expression [34–36].
2. Germline-encoded adaptability. The potential for a B cell receptor to evolve higher affinity is also a property of the entire receptor, not of individual alleles. Receptors using different alleles might have different propensities to adapt (Fig 1), for instance, if they tend to have different rates of beneficial and deleterious mutations. Variation in the expected impact of mutations occurs not only from differences in structure that might affect mutational tolerance but also because the enzymes responsible for mutating the B cell receptor target different nucleotide motifs at different rates [37–40]. Given a mutation, the relative probabilities of beneficial and deleterious impacts fundamentally arise from epistasis: mutations are more likely to change affinity or disrupt function in some backgrounds than in others [41, 42].

The realized growth rates of B cell lineages might deviate from these germline-encoded expectations due to several sources of stochasticity:

1. Stochasticity in B cell activation and in the colonization of germinal centers. Because the number of naive B cells is finite and the probabilities of different VDJ recombinations vary by orders of magnitude [43], rare germline allele combinations with high affinity may be present in the naive repertoires of some individuals but not others. Even if present in most individuals, low-frequency, high-affinity germline-allele combinations might by chance be recruited only in some of them. Additionally, lineages that happen to arrive first in germinal centers might prevent others with higher initial affinity from establishing later, but the strength of “priority effects” in affinity maturing B cells is unclear [44, 45].
2. Stochasticity in the timing, order, and effect of mutations. Which lineages ultimately evolve the highest affinity and outcompete others depends on the timing, order, and effect of mutations in each lineage. This concept is part of clonal interference dynamics [46]. Epistasis can increase the impact of mutation order [47].
3. Demographic stochasticity and genetic drift. Demographic stochasticity and genetic drift might be especially important early in the response when population sizes are small. Some lineages might go extinct purely by chance, and genetic drift might cause new mutations to fix within a lineage even if they are neutral or deleterious. The loss of newly arisen beneficial mutations due to drift is important even in large populations [48].

Large germline-encoded advantages lead to persistent similarity between individuals, while smaller ones are overcome differently in each individual

To evaluate when germline-encoded fitness differences might be overwhelmed by chance events during recombination and affinity maturation, we used a stochastic mathematical model to simulate B cell evolution and competition in germinal centers (Methods: “Model of B cell dynamics”; Table 1). We focused on how similarity between individuals over time depends on the magnitude of germline-encoded advantages (s, defined as the increase in mean naive affinity for an allele relative to other alleles) and the rate and effect size variation of somatic mutations (with variation measured as the standard deviation β around a mean effect of zero). Different host-pathogen systems likely exist in different parts of this parameter space, since naive affinities and mutational effects are epitope-specific and depend on the host’s germline alleles, their recombination and insertion/deletion probabilities, and the frequency and targeting of somatic hypermutation. The model focuses on the subset of the B cell response derived from germinal centers without considering extrafollicular B cell populations that expand outside of germinal centers, although reports of selection and somatic hypermutation in those populations suggest they have similar dynamics [29, 49]. To simulate selection for affinity, B cells are stochastically sampled to immigrate or divide based on their affinity relative to other cells in the naive repertoire (in the case of immigration) or in the germinal center (in the case of division). Dividing B cells then undergo affinity-changing mutations with some probability. To represent variation in germline-encoded affinity, B cells using different heavy chain germline V alleles can have different naive affinity distributions. The variation within each distribution in turn represents the effects of stochasticity in VDJ recombination and the pairing of heavy and light chains. The model also allows different germline V alleles to have different mutation rates, representing one aspect of variation in adaptability. We simulated 100 individuals, varying the number of germinal centers per individual and assuming no migration occurs between germinal centers (increasing the number of individuals to 1000 produced no substantial changes; S1 Fig). For each simulated individual, we randomly sampled (with replacement) a mouse for which we empirically estimated the set of heavy chain V alleles and their frequencies in the naive repertoire. These mice typically had about 75 heavy-chain V alleles (60–70 of which were typically shared between a pair of mice), and allele frequencies in the naive repertoire were positively correlated between mice (Fig 4A-B). To simulate alleles with higher naive affinity or higher mutation rate than the others, we randomly sampled a set of 5 alleles present in all mice with average naive frequency of 1–2% (the typical median frequency in the naive repertoire) and used that same set of alleles across all mice.

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Table 1. Default parameter values used in simulations.

https://doi.org/10.1371/journal.ppat.1011603.t001

We first considered the case in which all germline alleles have the same naive affinity distribution and the same mutation rate. In this “functional equivalence” scenario, individuals have similar allele frequencies early in the response, as germline alleles are initially recruited in proportion to their frequency in the naive repertoire. However, similarity between individuals decreases over time due to stochasticity, with the extent of this decline depending on the number of germinal centers per individual and the somatic hypermutation rate (Fig 2). The higher the mutation rate, the faster each germinal center tends to become dominated by a few large lineages with high affinity (Fig 2A). Without differences in initial affinity or adaptability between the germline alleles, the probability that one of these lineages uses a particular allele is equal to the allele’s frequency in the naive repertoire. The smaller the number of germinal centers, the more the set of “winner alleles” represented in the dominant lineages tends to vary between individuals, causing allele frequencies to diverge over time and experienced-to-naive ratios to remain uncorrelated (Fig 2B). In contrast, increasing the number of germinal centers per individual increasingly allows germline alleles to be represented in proportion to their frequencies in the naive repertoire, so allele frequencies remain correlated between individuals throughout the response.

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Fig 2. Simulations in the scenario with identical naive affinity distributions and mutation rates across germline alleles.

For each parameter combination, we simulated 100 individuals with varying numbers of germinal centers. A) For each germinal center, we computed the fraction of the total germinal center population occupied by the biggest lineage. Points and vertical bars represent the median and the 1st and 4th quartiles for this fraction across simulated germinal centers. B) We measured germline allele frequencies across germinal centers in each individual and computed the ratio between these frequencies and the allele frequencies in the naive repertoire. We then computed the correlation in frequencies and experienced-to-naive-ratios between all pairs of individuals. Points and vertical bars represent the median and the 1st and 4th quartiles of these correlations across all pairs (i.e., the bars represent true variation in simulated outcomes and not the uncertainty in the estimate of the median). We set β = 2 and left other parameters as shown in Table 1.

https://doi.org/10.1371/journal.ppat.1011603.g002

If some germline alleles tend to encode receptors with higher affinity than others, not only allele frequencies (S2 Fig) but also their deviations from the naive repertoire (Fig 3) are correlated between individuals early in the response. Whether this similarity between individuals persists over time depends on the rate and effect size of somatic mutations relative to the germline-encoded advantage of the high-affinity alleles. If the rate and effect size variation of mutations is small relative to that initial advantage, germinal centers are consistently dominated by B cell lineages using high-affinity alleles (S3 Fig), resulting in similar allele frequencies and experienced-to-naive ratios between individuals throughout the response. As the rate or the effect size variation of somatic hypermutation increases, so does the opportunity for B cell lineages using low-affinity alleles to overcome their initial disadvantage and reach high frequencies within germinal centers (S3 Fig). In this scenario, precisely which low-affinity alleles are used by lineages that do so is highly stochastic and varies between individuals, since all B cells are assumed to have the same probability of acquiring beneficial mutations irrespective of the germline V allele they use. As a result, the correlation in allele frequencies and the correlation in experienced-to-naive-ratios both decrease over time. We observed the same general behavior if we changed the number of high-affinity alleles to 1 or 10. (S4 Fig).

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Fig 3. Simulations in the scenario where the same 5 germline alleles have higher expected affinity than the others in all individuals.

For each parameter combination, we simulated 100 individuals with varying numbers of germinal centers. We measured germline allele frequencies across germinal centers in each individual and computed the ratio between these frequencies and the allele frequencies in the naive repertoire. We then computed the correlation in these experienced-to-naive-ratios between all pairs of individuals. Points and vertical bars represent the median and the 1st and 4th quartiles of these correlations across all pairs (i.e., the bars represent true variation in simulated outcomes and not the uncertainty in the estimate of the median). For these simulations, we assumed 15 germinal centers per individual. Other parameter values are as in Table 1.

https://doi.org/10.1371/journal.ppat.1011603.g003

Finally, when some germline alleles have a higher mutation rate than others (and the baseline rate and effect size variation of mutations are sufficiently large), the faster mutating B cell lineages eventually dominate germinal centers due to their propensity to adapt (S5 Fig), countering the tendency for allele frequencies to become less correlated over time observed in the functional equivalence scenario and leading to a positive correlation in experienced-to-naive ratios later in the response (S6 Fig).

Decreasing similarity in the mouse response to influenza virus infection suggests affinity maturation overcomes germline-encoded differences

We compared these simulated dynamics with the B cell response of C57BL/6 mice infected with influenza virus once or twice and sacrificed at different times points (8, 16, 24, 40 and 56 days after the primary infection, with the secondary infection on day 32; Materials and methods: “Experimental infection of mice with an influenza A/H1N1 virus”). Because influenza viruses do not naturally infect mice, any germline-encoded specificities for influenza antigens are either evolutionary spandrels or the product of selection to recognize molecular patterns shared between influenza and pathogens that have historically infected mice. We used RNA sequencing of the heavy chain to estimate the frequencies of germline alleles and the relative sizes of B cell lineages in each mouse. While we did not sort cells based on the ability to bind influenza, we found that uninfected controls had very few germinal center, plasma or memory cells in the mediastinal lymph node (S7 and S8 Figs), suggesting the lymph-node B cells of infected mice were induced by influenza in agreement with previous work [50]. We therefore focused on lymph node B cells, with potentially many different specificities for influenza antigens. Early in the response, lymph node populations likely consist of extrafollicular plasma cells expanding outside of germinal centers, with germinal-center derived cells arriving later [50] and persisting for as long as six months [51].

Although C57BL/6 mice are inbred, we found differences in the set of germline V alleles between mice that could not be explained by variation in sequencing depth and that were robust to the choice of reference allele set and annotation tool (S9 Fig; Methods: “Estimating the frequencies of V alleles and B cell lineages”). To our knowledge, a systematic analysis of germline variation between mice of the same inbred strain under different reference sets and annotation tools is missing, though at least one other study suggests some variation in C57BL/6 [52]. Despite the variation we observed, mice had similar sets of germline alleles present at correlated frequencies in the naive repertoire (Fig 4). Because this correlation was nonetheless weaker than previously reported by [52], we repeated the analysis using data from that study to compute germline allele frequencies in the naive repertoire.

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Fig 4. Immunoglobulin V gene usage in the mouse B cell response to influenza infection.

(A) The number of germline immunoglobulin V alleles is shown for mice infected once or twice with a mouse-adapted H1N1 virus and sacrificed at different time points (8, 16, 24, 40 and 56 days after the primary infection, with the second infection at day 32). Uninfected control mice are shown in green. Each point represents a mouse. At the peak of the response, most alleles present in each mouse are represented in lymph-node germinal center (GC), plasma and memory cells, which were likely induced by the influenza infection. (B) Number of V alleles shared by pairs of mice in the naive repertoire (left) and the Pearson correlation in their frequencies for each pair (excluding mice with fewer than 100 reads in the naive repertoire; right). Each point represents a pair. (C) Pearson correlation within each mouse between V allele frequencies in influenza-induced populations and frequencies in the naive repertoire. Each point represents a mouse, and solid-line boxplots indicate the distribution in the observed data.

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As expected, influenza infection led to affinity maturation in mouse B cell lineages (S10 Fig). Serum antibody titers against the infecting virus measured by ELISA rose approximately 1,000-fold between days 8 and 24 and remained high. In parallel to this rise in antibody titers, germinal center and plasma cell populations became increasingly dominated by a few lineages, suggesting that lineages varied in fitness due initial differences in affinity, differences acquired during the lineages’ subsequent evolution, or both. Lineages sampled at later time points had more high-frequency amino acid mutations within them (those present in 50% or more of the reads in a lineage). Those mutations include fixed mutations and those potentially rising to fixation via selection for affinity, and they are unlikely to be deleterious or to have arisen from sequencing and amplification errors (which we estimate at 1.8 per thousand nucleotide bases; Materials and methods: “B cell receptor sequencing”). These trends were visible in the lymph nodes of infected mice but not apparent in other tissues or in control mice (S11 Fig), suggesting they were driven by the influenza infection. (Influenza-specific lineages may have been present in other tissues, but our data do not allow us to distinguish them from lineages elicited by other antigens.)

Most germline V alleles observed in a mouse (across all tissues and cell types sampled) were represented in the influenza-induced lymph node populations (Fig 4), suggesting that most mouse V alleles can produce at least some receptors capable of binding influenza antigens. We measured the correlation in germline V allele frequencies and experienced-to-naive ratios between pairs of infected mice and compared the observed patterns with a null model in which a lineage’s fitness is independent of which germline V allele it uses, mimicking the equivalent-alleles scenario in our simulations. We did so by keeping the observed distribution of lineage sizes (a proxy for lineage fitness) while randomly assigning each lineage’s germline V allele based on naive repertoire frequencies.

In plasma cells and germinal center cells, allele usage became increasingly dissimilar between mice over time despite evidence of germline-encoded advantages, suggesting those advantages were overcome by divergent B cell evolution in each mouse. In both cell types, the correlation in allele frequencies between mice was stronger than expected under the null model early in the response but close to the null expectation later on (Fig 5A, left panel). Early on in plasma cells, and throughout the response in germinal center cells, some germline V alleles were consistently overrepresented in different mice, leading to correlated experienced-to-naive ratios (Fig 5A, right panel; S12 and S13 Figs) and suggesting those alleles contributed to higher affinity or adaptability than did others. For instance, in day-8 plasma cells, IGHV14-4*01 increased in frequency relative to the naive repertoire in all 6 mice with enough data, becoming the most common V allele in 3 mice and either the second or the third most common in the other 3 (Fig 5B). Later in the plasma cell response, however, experienced-to-naive ratios became uncorrelated between mice: the most common V allele was usually different in different mice, and most germline alleles were overrepresented relative to the naive repertoire in some mice but not in others (S12 Fig). Taken together, these results suggest that some mouse V alleles are more likely than others to make good receptors against influenza, but that those germline-encoded advantages are not strong enough to drive persistently similar responses given the role of chance in B cell evolution.

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Fig 5. Correlation between mice in the V allele frequencies of influenza-induced populations and in the deviations of those frequencies from the naive repertoire.

(A) Distribution of pairwise correlations at each time point. Each colored point represents a pair of mice with at least 100 reads each in the respective B cell population. The horizontal bars indicate the observed median across mouse pairs, whereas the black circles and black vertical bars indicate the bootstrap average and 95% confidence interval for the median in a null model with V alleles randomly assigned to each B cell lineage (n = 500 randomizations). We computed correlations using Pearson’s coefficient and measured frequency deviations as the ratio between a V allele’s frequency in an influenza-induced population and its frequency in the naive repertoire. (B) Frequency of the 20 most common V alleles in the lymph node plasma cells of each mouse 8 days after primary infection. Each panel represents an individual mouse. The arrows go from each allele’s frequency in the naive repertoire to its frequency in lymph node plasma cells. Each allele was labelled as significantly over- or underrepresented in each mouse if the ratio of its experienced and naive frequencies was outside a 95% confidence interval obtained by bootstrap sampling (n = 500) of experienced frequencies from the naive repertoire (preserving the observed total number of sequences in each mouse). Mouse 40-7, which was sacrificed 8 days after the secondary infection, was considered a day-8 primary-infection mouse because it showed no signs of infection after the first inoculation and had ELISA titers similar to those of day-8 infected mice.

https://doi.org/10.1371/journal.ppat.1011603.g005

In contrast with plasma and germinal center cells, memory cells showed persistently biased V gene usage in influenza-infected mice (Fig 5A and S14 Fig). Since activated B cells with low affinity are more likely than others to exit germinal centers and differentiate into memory cells [53], dominant lineages with high affinity for influenza antigens might contribute less to the memory cell population than they do to the germinal center and plasma cell populations. Consistent with that possibility, the increasing dominance by a few large and mutated lineages seen in germinal center and plasma cells of infected mice was not evident in their memory cells (S10 Fig). Thus, memory cells at different times during the response might represent a recent sample from the naive repertoire, reflecting germline-encoded differences in initial affinity and less the divergent outcomes of affinity maturation.

We found similar results using a different germline annotation tool and different germline reference sets, using independent sequence data from [52] to estimate naive allele frequencies, and when computing allele frequencies based only on unique sequence reads (collapsing identical reads from the same mouse, tissue, cell type and isotype) (S16 Fig).

Germline V alleles consistently overrepresented early in the response have low predicted mutability in CDRs

Our simulations suggest that correlated experienced-to-naive ratios early in the response more likely reflect germline-encoded differences in affinity than in the overall mutation rate (Fig 3 and S6 Fig; we did not consider that some germline alleles may have relatively more beneficial mutations accessible to them, which might also lead to germline-encoded differences in adaptability). With sequence data alone, we cannot determine if germline V alleles overrepresented in the early mouse response generate receptors with especially high affinity for influenza antigens. We can, however, estimate potential differences in the overall mutation rate between germline alleles based on their sequences alone, using estimates of the propensity of different nucleotide motifs to undergo somatic hypermutation (although those estimates were derived from mouse light-chain rather than heavy-chain genes [54]) (Methods: “Mutability analysis of germline alleles”).

Germline alleles with higher predicted mutability in the CDRs, which might give those alleles a higher rate of affinity-enhancing mutations, did not have a clear advantage (S17 Fig). Neither did germline alleles with lower mutability in the structurally-important framework regions (FRs; where mutations are more likely to be deleterious than in CDRs). Instead, in day-8 plasma cells we found the opposite relationship: germline alleles tended to increase in frequency relative to the naive repertoire if they had high mutability in FRs and low mutability in CDRs. The consistently overrepresented and dominant allele IGHV14-4*01, for instance, is predicted to be one of the least mutable in CDRs 1 and 2, (S17 Fig). Other germline alleles consistently overrepresented in day-8 plasma cells, IGHV1-82*01, IGHV1-69*01, IGHV14-1*01 and IGHV14-2*01 (5 of 6 mice with enough data) have similarly low predicted mutability in CDR2, though not in CDR1. If those alleles do have a high propensity to bind influenza antigens, low mutability in CDRs 1 and 2 might reduce the chance that mutations disrupt this initial binding, potentially reinforcing the fitness advantage of B cells using those alleles.

B cell lineages sharing the same germline V allele rarely had mutations in common

While germinal center cells and plasma cells were increasingly dominated by large lineages with somatic mutations, the sheer number of high-frequency mutations acquired by a B cell lineage did not predict its success (S18 Fig). This observation is consistent with previous work showing that the number of mutations in the B cell receptor does not predict affinity or neutralization strength [33, 53, 55]. Thus, successful lineages might be those that acquire few substitutions with large effects on affinity, instead of many substitutions with smaller effects.

Most pairs of lineages with the same V allele had no high-frequency mutations in common (S19 Fig). For specific cell types and specific V alleles, we found some instances of high-frequency mutations shared by multiple lineages. However, they were constrained to one or two mice, suggesting they might be an artifact of the incorrect partitioning of a single large lineage into several small ones. Independent acquisition of the same mutation has been shown in lineages using the same heavy chain V allele and recognizing the same antigen or epitope [13, 56, 57]. Our analysis differs from those previous observations by investigating convergent mutations across V alleles in a population with multiple potential specificities, suggesting that convergent mutations may be rare overall when considering a whole pathogen.

Influenza antigens do not strongly select for specific CDR3 sequences

While binding can occur via the two CDRs solely encoded by the V segment, it often occurs via CDR3, which spans the junction between the segments. Thus, influenza antigens might select for receptors with specific CDR3 sequences, despite showing little selection for specific germline alleles encoding CDR1 and CDR2. To investigate this possibility, we computed the amino acid sequence and biochemical similarity of CDR3 sequences sampled from different mice and matched for the same length (Methods: “Measuring CDR3 sequence similarity”). On average, length-matched CDR3 sequences from the influenza-induced populations of different mice were no more similar than sequences sampled from their naive repertoires (S20 Fig). (We found similar results when matching sequences both for length and heavy-chain V allele, suggesting the choice of V allele does not strongly constrain the sequence of CDR3.) While individuals exposed to the same pathogen often share receptors with specific CDR3 sequences [32, 57–59], our results suggest those convergent CDR3s do not make up a large fraction of the response.

Finally, we found no evidence that the germline alleles overrepresented in the early B cell response to influenza were associated with more diverse CDR3 sequences in the naive repertoire (S21 Fig).

Ethics statement

All mouse experiments were approved by The University of Chicago Institutional Animal Care and Use Committee (IACUC protocol 71981).

Model of B cell dynamics

We modeled B cell evolution and competition in germinal centers using stochastic simulations based on a Gillespie algorithm. There are three types of independent events in the model: immigration of individual B cells into germinal centers, cell division and death. The total rate of events λ is given by (1) where the terms on the right-hand side correspond to the rate of each kind of event (mutation is associated with cell division and is therefore not an independent event). The algorithm consists of drawing the time to the next event by sampling from an exponential distribution with rate λ. Once an event has occurred, we a make a second draw to determine its type. The probability for each type of event in this second draw is proportional to the corresponding event-specific rate (e.g., the probability that the next event is a cell division is λ_division/λ). After determining the event type, we update event rates and draw the time to the next event, and so on, until a maximum time t_max is reached. For each germinal center, we record the number of cells in each B cell lineage and the V alleles used by the lineages at the end of day 1 and then every 5 days starting on day 5.

Immigration of B cells into germinal centers is restricted to an initial period with duration t_imm. Parameter I_total controls the expected number of lineages that enter each germinal center during that time (each recruited B cell is the founder of an individual lineage). Given those parameters, we let λ_immigration be a linearly decreasing function over time reaching 0 at t_imm, with intercept and slope chosen such that I_total lineages are expected to enter each GC by that point (λ_immigration then remains at 0 until the end of the simulation).

When immigration occurs, we randomly sample a single immigrant from a newly generated recruitment pool of 1,000 naive cells whose V alleles are drawn with replacement from the naive repertoire. For each member of the recruitment pool, we sample an affinity value based on the naive affinity distribution associated with its V allele. The probability that each cell in the recruitment pool is chosen as the new immigrant is then proportional to its affinity. By default, all alleles have the same normal affinity distribution with mean a and standard deviation σ (we sample from the associated truncated distribution to avoid negative values). Depending on the scenario, naive B cells using specific V alleles may have a different distribution with mean a + sσ and the same standard deviation σ (i.e., the increment in the mean is expressed in units of the baseline standard deviation).

The rate of cell divisions depends on the total number of cells inside the germinal center, N, and on the rate of cell division for each individual cell, μ(N): (2) To represent competition for antigen, μ(N) decreases with N so that it equals a fixed per-cell death rate δ when the population is at carrying capacity (N = K): (3) Once a division event occurs, we randomly sample a B cell to divide. The probability that a B cell is chosen is proportional to its affinity. Each dividing B cell has some probability of having a mutation that changes affinity by a normally distributed amount with mean 0 and standard deviation given by βσ (i.e., in units of the baseline naive affinity standard deviation σ) (affinity is set to 0 if the mutation produces a negative value). By default, all B cells have the same baseline mutation rate regardless of their germline V allele. Depending on the scenario, naive B cells using specific V alleles may have this rate multiplied by a factor γ.

Finally, with a fixed per-cell death rate, the population-level death rate is given simply by (4)

Sensitivity of model results to truncation of naive affinity distributions

For the default values used in the analyses (a = σ = 1), the choice of a truncated normal distribution to model naive affinity distributions causes the effective variance to increase as the mean increases (since fewer values run into the truncation). To test if our results were sensitive to this effect, we repeated the simulations of the high-affinity scenario after setting σ = 0.1 (thus reducing the fraction of truncated values in the baseline distribution from 0.16 to effectively zero and causing the variance to remain approximately constant as s increases). Because the increase in mean affinity (s) and the standard deviation of mutational effects (β) are expressed as multiples of σ, we re-scaled those parameters to explore the same absolute values as in the main analysis (since σ was divided by 10, we multiplied s and β by 10).

We found the same behavior as in the main analysis, with germline-encoded specificities leading to persistent similarity if s was sufficiently large relative to β and the mutation rate, and decreasing similarity if s was relatively small (S23 Fig). Absolute increases of 0.5 and 1 in mean affinity for high-affinity alleles, which result in very low or zero correlation between individuals in the original analysis (Fig 3), now result in strong correlations. This difference is due to the fact the higher value of σ in the original simulations leads to stronger overlap between the affinity distributions of high- and low-affinity alleles.

Experimental infection of mice with an influenza A/H1N1 virus

We infected 40 8-week-old female C57BL/6 mice (Jackson Laboratories) weighing 20–22g (8 for each time point) intranasally with 0.5 LD₅₀ of a mouse-adapted pandemic H1N1 strain (A/Netherlands/602/2009) in a total of 30 μL of PBS under full anesthesia. In addition, two controls for each time point were given PBS only.

Tissue processing, cell sorting and nucleic acid extraction

We prepared single cell suspensions from the mediastinal lymph node, spleen and both femurs harvested at the indicated time points. B cells were first enriched from the splenocyte suspension by MACS (magnetic activated cell sorting) using the Pan B cell Isolation Kit (Miltenyi Biotec), followed by staining for FACS (fluorescence activated cell sorting). The lymph node and bone marrow cells were directly stained for FACS. Antibodies used for sorting were anti-B220 (clone RA3-6B2, Biolegend), IgD (clone 11-26c.2a, Biolegend), anti-CD4 (clone RM4-5, Biolegend), anti-CD8 (clone 53-6.7, Biolegend), anti-CD38 (clone 90, Biolegend), anti-CD95 (clone Jo-2; BD Biosciences), anti-CD138 (clone 281-2, Biolegend), anti-F4/80 (clone BM8, Biolegend), anti-GL7 (clone GL7, BD Biosciences), anti-Sca-1 (clone D7, Biolegend), and anti-TER-119 (clone TER-119, Biolegend). Antibody stainings were preceded by adding Fc block (anti-CD16/CD32; clone 2.4G2, BD Biosciences). For sorting, the cells were first gated on size and granularity (forward and side scatter, respectively) to exclude debris, followed by doublet exclusion. We sorted naive (IgD+B220+), plasma (IgD-Sca-1hiCD138hi), memory (IgD-B220+CD95-CD38hi) and germinal center (IgD-B220+CD95+ CD38loGL-7+) cells after excluding cells expressing CD4, CD8, TER-199 or F4/80 (to exclude T cells, erythroid cells and macrophages). After spinning down cells and removing the PBS supernatant, we extracted DNA and RNA from the cell pellets using the AllPrep DNA/RNA Mini Kit (Qiagen), according to the manufacturer’s protocol. All samples were kept frozen until sequenced.

B cell receptor sequencing

We generated immunoglobulin heavy chain (IGH) DNA libraries from complementary DNA generated from 10–500 ng of total RNA using Superscript III (Invitrogen) reverse transcriptase and random hexamer primers. For PCR amplifications, we used multiplexed primers targeting the mouse framework region 1 (FR1) of IGHV in combination with isotype-specific primers targeting constant region exon 1 of IgA, IgD, IgE, IgG, or IgM (Tables 2 and 3). We performed separate PCR reactions for each isotype to avoid formation of inter-isotype chimeric products. We barcoded each sample with 8-mer primer-encoded sequences on both ends of the amplicons and performed PCR amplification in two steps. First, we generated amplicons using primers with the partial Illumina adapter, the sample-specific barcode and the locus-specific sequence. In the second step, we performed another PCR to complete the Illumina adapter sequence and to ensure final products were not amplified to saturation. We purified pooled products by agarose gel electrophoresis and extraction. We used a 600 cycle v3 kit to sequence products using an Illumina MiSeq instrument.

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Table 2. Primers for mouse heavy chain B cell receptors.

https://doi.org/10.1371/journal.ppat.1011603.t002

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Table 3. PCR conditions.

https://doi.org/10.1371/journal.ppat.1011603.t003

We estimated the rate at which errors were introduced during amplification and sequencing by comparing the sequenced reads with the reference sequence for the corresponding isotype. Because the constant region does not undergo somatic hypermutation, we counted each mismatch between the end of the J gene and the beginning of the conserved region primer as an error introduced by sequencing and amplification. Based on 187,500 errors found out of 104,092,368 bases analyzed, we estimated the error rate to be 1.80 mutations per thousand bases (95% binomial CI 1.79–1.81).

ELISA

We coated 96-well ELISA plates (Thermo Fisher Scientific) overnight at 4°C with eight hemagglutination units (HAU) of virus in carbonate buffer. We used horseradish peroxidase (HRP)-conjugated goat anti-mouse IgG antibody (Southern Biotech) to detect binding of serum antibodies, followed by development with Super Aquablue ELISA substrate (eBiosciences). We measured absorbance at 405 nm on a microplate spectrophotometer (Bio-Rad). We analyzed serum samples starting at a top dilution of 1:20 (PBS controls and day 8 animals) or 1:1000 (all other samples), followed by 2-fold dilutions in 8 (PBS controls and day 8 animals) or 16 steps. We determined the end titer as the last dilution point with an OD value of > 2x the blank average OD value for each respective plate.

Estimating the frequencies of V alleles and B cell lineages

We used partis v0.16.0 [78–80] to partition sequences into lineages and identify the germline alleles used by each lineage’s naive ancestor. Briefly, partis identifies lineages by comparing the probability that two clusters of sequences came from a single rearrangement event with the probability that they came from separate rearrangement events. Sequences in the same lineage must have the same germline V and J segments, but partis does not require a minimum degree of similarity in CDR3 for sequences to be part of the same lineage. For the main analysis, we used the reference set of C57BL/6 alleles curated by the Open Germline Receptor Database (available as an option in partis) based on sequences from [81], disabling the inference of novel alleles that partis performs by default. We also repeated the analyses of germline allele frequencies using partis with the IMGT mouse reference set (with and without inference of novel alleles) and again using IgBLAST v.1.3.0. [82]. We used the fraction of reads corresponding to each allele as a proxy for the frequency of that allele in each B cell population. To reduce the error in frequency estimates, we excluded B cell populations with fewer than 100 reads in a mouse. Since we did not barcode individual cells or RNA molecules during sequencing, the number of reads with a particular sequence reflects not only the number of B cells with that sequence but also their transcription levels. We also repeated the analyses using the number of unique sequences to estimate the abundance of each lineage or allele (i.e., counting multiple identical reads from the same mouse, tissue, cell type and isotype only once).

We measured the size of each lineage in each lymph-node B cell population as the number of reads from that lineage in that population (as opposed to the number of reads in the lineage across all cell types and tissues). B cell lineages were mostly confined to a single tissue and usually dominated by a single cell type (S22 Fig; note that the partitioning of sequences into lineages was agnostic to cell type and tissue).

While we initially considered Dump-IgD+B220+ cells as naive cells, we noticed that many sequences obtained from them were extensively mutated relative to their inferred germline genes and were also inferred to be part of large clonal expansions. To exclude reads originating from non-naive B cells sorted as IgD+B220+, we considered a read as likely coming from a naive cell if it met all of the following criteria: 1) it came from IgD+B220+ samples; 2) its isotype was IgM or IgD; 3) it belonged to a clone that had a single unique sequence across its reads (and the reads all came from IgD+B220+ samples), and 4) that sequence had at most two nucleotide mutations in the V gene region. To compute naive frequencies, we pooled sequences meeting those criteria across all tissues. When computing experienced-to-naive frequency ratios, we adjusted the frequencies of germline alleles that were sampled in an experienced B cell population but not in naive B cells, since those alleles must have been present in naive B cells even though they were not sampled. In those cases, we imputed a single sequence to the allele in the naive repertoire then recalculated naive allele frequencies accordingly. When computing frequency deviations from the naive repertoire, we excluded mice with fewer than 100 naive reads even if the corresponding experienced population had more than 100 reads.

To test if our results were robust to uncertainty in the identification of naive B cells in our data, we alternatively estimated V allele frequencies from naive B cells (CD138-CD19+IgD++IgM+CD23++ CD21+PI-) sampled by [52] from the spleen of healthy C57BL/6 mice. For these data, we processed raw paired-end reads using presto v.0.6.2. [83], then used partis to identify germline V alleles for a random sample of 20,000 sequences per mouse. V allele frequencies (measured by the fraction of total reads assigned to each gene in each mouse) were positively correlated between this independent dataset and the designated naive populations from our data (mean Pearson correlation coefficient between pairs of mice from each dataset = 0.61, interquartile range 0.52–0.76). We repeated the analysis of pairwise frequency-deviation correlations over time after replacing naive frequencies in our mice with the average frequency of each gene in the [52] dataset, preserving the number of reads in each mouse. When calculating the average allele frequencies in the alternative data set, we artificially assigned a single read to alleles present in our mice but absent from the alternative data set (since genes present in the experienced cells cannot be entirely missing from the naive repertoire) and re-normalized frequencies so they would sum to 1.

Identifying overrepresented germline alleles

To determine which germline alleles were consistently overrepresented in experienced B cell populations relative to the naive repertoire, we compared the frequency deviations for each germline allele (separately for each type of B cell) with the distribution expected if alleles were sampled based on naive frequencies alone (maintaining the observed the number of sequences in each mouse). For each germline allele, we then counted the number of mice with stronger deviations from the naive repertoire than expected under this null distribution (using a 95% bootstrap confidence interval).

Mutability analysis of germline alleles

To estimate the mutability of mouse germline V alleles, we used the RS5NF mutability scores estimated by [54] using non-functional mouse kappa light-chain sequences and implemented in R package shazam. These scores describe the relative mutability of all possible 5-nucleotide motifs. We estimated the mutability of each framework region (FR) and complementarity-determining region (CDR) as the average score across motifs in the region. We then calculated an average for all FRs weighted by the length of each FR, and similarly for CDRs. We used igblast v1.14.0 to identify the FRs and CDRs of each germline V allele sequence identified by partis.

Measuring CDR3 sequence similarity

We compared the amino acid sequence similarity and biochemical similarity of pairs of CDR3 sequences sampled from different mice and matched either for length alone or both for length and V allele. To limit the number of comparisons, we proceeded as follows. For each pair of mice, we chose one mouse and sampled 500 sequences of the same cell type. For each sequence length represented in this sample, we paired sequences from the first sample with randomly chosen sequences of the same length from the second mouse. If matching sequences both for length and V allele, we did this second sampling separately for each combination of V allele and sequence length present in the first sample. This procedure matches sequences while preserving the length distribution (or the joint distribution of length and V alleles) in the first sample.

We measured amino acid sequence similarity as the proportion of sites with the same amino acid in both sequences. Following previous work [84, 85], we measured biochemical similarity as the proportion of sites in which the amino acids of both sequences belonged to the same category in the classification by [86]: hydrophobic (F, L, I, M, V, C, W), hydrophilic (Q, R, N, K, D, E) or neutral (S, P, T, A, Y, H, G).