Replaying germinal center evolution on a quantified affinity landscape

SUMMARY

Darwinian evolution of immunoglobulin genes within germinal centers (GCs) underlies the progressive increase in antibody affinity following antigen exposure. Whereas the cellular mechanics of how competition between B cells increases affinity are well established, the evolutionary dynamics of this process are less clear. We developed an experimental evolution model in which we “replay” over one hundred monoclonal GC reactions, assigning affinities to each cell using deep mutational scanning. Our data reveal how GCs achieve predictable outcomes by means of noisy but persistent selection on an affinity landscape whose exploration is heavily constrained by somatic hypermutation biases. We infer a fitness landscape that quantitatively recapitulates the affinity maturation trajectory of our clone and find that apparent features of GC selection, such as permissiveness to low-affinity lineages and rapid plateauing of affinity, are likely artifacts of survivorship biases that distort our view of how B cell affinity progresses over time.

Graphical Abstract

In brief

Antibody affinity maturation results from a somatic evolutionary process that takes place in the germinal center. A “parallel replay” experiment on germinal center B cells reveals the evolutionary forces that produce predictable increases in B cell affinity.

INTRODUCTION

The immune system generates vast repertoires of immunoglobulins (Igs) by stochastic gene recombination and subsequently improves—or matures—their affinity for antigen by rapid somatic evolution.^1,2 Affinity maturation takes place in germinal centers (GCs), clusters of rapidly dividing B cells that arise in secondary lymphoid organs upon infection or immunization.^2–4 Within GCs, B cells undergo iterative cycles of somatic hypermutation (SHM) of Ig genes followed by selective expansion of mutant lineages with improved affinity. Predicting the outcome of this evolutionary process is an important goal for vaccine design.^5,6

Although we have developed a broad cellular and molecular framework for how GC evolution operates,^2–4 the dynamical evolutionary principles at play in the GC are not completely understood. For example, “clonal bursts”—abrupt proliferations in which the descendants of a single cell take over the GC within a few days—occur in some GCs but not others, in a manner not easily predictable from the affinity of the bursting GC B cell.⁷ Likewise, empirical studies consistently show coexistence of high- and very low-affinity GC B cells within the same lymph node or even the same GC,^7–11 a degree of permissiveness that fits poorly with current mechanistic models of GC selection.²

GCs also provide a model system for studying evolutionary dynamics more broadly. Inferring the quantitative relationship between phenotype and fitness—i.e., building a “fitness landscape”¹²—is a central challenge in evolutionary biology, as genotype-to-phenotype-to-fitness mapping is confounded by complex trait spaces, pleiotropy, and the diversity of adaptive strategies that arise even in tightly controlled experimental systems.^13–19 In contrast, GC B cells evolve by rapidly mutating only two Ig genes—the heavy chain (Igh) and light chain (either Igk or Igl)—with predictable biases,^20–23 and apply selection to a single trait—the ability to bind antigen.²⁴ Multiple GCs form independently within the same animal, evolve affinity by several orders of magnitude over a few weeks, and leave behind evolutionary trajectories that can be reconstructed from Ig sequencing and phylogenetic analysis,²⁵ providing both abundant replicates and a means to track their history. GCs are therefore a tractable system for testing the predictability of evolution in a physiologically relevant setting.

We performed a “parallel replay” experiment on GC B cells, which we use as a platform for experimental evolution. Despite high variability among GC phylogenies, selection for high affinity occurred consistently across GCs. Rather than being driven by clonal bursts, affinity maturation resulted from imperfect but persistent selection of affinity-increasing mutations. By combining phylogenetic reconstructions with a fitness landscape inferred from populations sampled over time, we show that both the apparent permissiveness of GCs to low-affinity lineages and the apparent early plateau in affinity maturation are best explained by survivorship biases that distort the histories of lineages present at sampling.

RESULTS

Parallel replay of evolutionary trajectories in clonally identical GCs

A quantitative analysis of GC selection requires the ability to generate replicated GC evolutionary trajectories starting from the same pool of founder B cells. To achieve this, we established a system in which GCs are composed entirely of B cells carrying the same pre-rearranged Igh and Igk genes, ensuring identical starting specificity and affinity. We chose a B cell receptor (BCR) specific for the model antigen chicken IgY (clone 2.1).^7,26 We engineered mice carrying the rearranged, unmutated Igh and Igk genes of clone 2.1 in their respective loci, which we refer to as “chIgY” mice (Figures S1A and S1B). We then bred these mice to a ubiquitously expressed photoactivatable (PA) GFP transgene to enable isolation of B cells from individual GCs within a lymph node (LN) through in situ photoactivation.^7,24 To generate monoclonal GCs, we adoptively transferred 5 × 10⁵ purified chIgY B cells (Igh^chIgY/+.Igk^chIgY/+.PAGFP-tg) into CD23-Cre.Bcl6^flox/flox recipients that lack endogenous GC B cells.^27,28

We immunized recipients subcutaneously with IgY in alum to generate GCs consisting almost exclusively of donor cells within an otherwise polyclonal host (Figures 1A and S1C). GCs were analyzed at 15 and 20 days post-immunization (dpi)—roughly 5 and 10 days after GCs peak in cell numbers. We explanted draining LNs, photoactivated 1–4 individual GCs per node, using labeled follicular dendritic cells (FDCs) for guidance, sliced nodes into segments containing a single photoactivated GC, then sorted photoactivated B cells from each segment into 96-well plates for sequencing (Figures 1B and S1C). We obtained paired Igh and Igk sequences for 8,744 B cells from 119 replicate GCs (15 dpi: 3,758 cells from 52 GCs [18 mice], median 75 [range 30–87] cells/GC; 20 dpi: 4,986 cells from 67 GCs [6 mice], median 78 [range 25–94] cells/GC). Somatic mutations were present in most cells (10 and 1 unmutated cells at 15 and 20 dpi, respectively). Median SHM load was 5 (range 0–18) and 7 (range 0–19) nucleotide mutations per cell at 15 and 20 dpi, respectively.

Figure 1. Parallel replay of GC evolution.

(A) Experimental design. IgY-specific B cells were transferred into GC-deficient (CD23-Cre.Bcl6^flox/flox) mice, subsequently immunized with IgY. At 15 or 20 dpi, individual GCs were photoactivated, LNs were dissected into fragments containing a single photoactivated GC, and single photoactivated GC B cells were sorted for Ig sequencing.

(B) Example of GC photoactivation. Tiled multiphoton images showing GC photoactivation (left) and fluorescent stereoscope images (right) showing LN dissection. Dotted lines indicate photoactivated GCs. Scale bars, 0.5 mm.

(C and D) Example phylogenetic trees.

(E and F) NDS and REI score distributions for GCs at 15 and 20 dpi; each symbol represents one GC.

(G–J) Phylogenetic features of GCs obtained at 15 and 20 dpi. Bar is median, boxes are 25%–75%, whiskers are range. Units are GCs (G)–(I) and root-clades (J).

Data are for 52 GCs (3,758 cells; 413 root-clades) from 18 mice (2 independent experiments) for 15 dpi and 67 GCs (4,986 cells; 271 root-clades) from 6 mice (2 independent experiments) for 20 dpi. p values are for the Mann-Whitney U test.

To quantify reproducibility across replicates, we first inferred phylogenetic trees for each GC using the GCtree package.^25,29,30 This revealed a wide variety of topologies, ranging from large clonal bursts to highly branched trees with multiple lineages stemming from the unmutated ancestor (Figures 1C, 1D, and S2). We quantified this variation using two metrics, a “normalized dominance score” (NDS), denoting the size of the largest lineage in the GC, and the maximum “recent expansion index” (max REI), which measures the magnitude of the largest burst in that GC (Figures S1D and S1E). GCs displayed a wide range of NDS and REI scores at both time points (Figures 1E and 1F), which were consistent between mice and across different LNs (Figure S1F). GCs with low NDS and max REI had multiple, evenly competitive root clades (e.g., GCs #11 and #82), indicating failure of any single clade to establish dominance. At the other extreme were large clonal bursts (e.g., GCs #31 and #103), the strongest of which were able to eliminate most competing clades. Although the frequency of clonal bursts (top-right sector, e.g., GC #31) was similar between time points (7/52 at 15 dpi versus 6/67 at 20 dpi), the fraction of GCs with high NDS but low max REI (bottom-right sector; e.g., GC #118) increased significantly at 20 dpi (3/52 versus 18/67, p_Fisher = 0.0031). This was accompanied by modest decreases in max REI and number of root-clades per GC, alongside slight increases in NDS and number of descendants per root-clade, from 15 to 20 dpi (Figures 1G–1J). Thus, as established clonal bursts “age,” their descendants accumulate mutations, reducing max REI. On the other hand, root-clade diversity (equivalent to the diversity of V(D)J rearrangements in a polyclonal setting) is not restored, such that NDS remains high.

We conclude that the evolutionary trajectories of GCs are highly variable even when founder populations are identical at the Ig sequence level, with clonal bursts being observed at frequencies similar to those previously reported.^7,31 Thus, a simplified monoclonal model recapitulates the range of outcomes observed for polyclonal GCs.

Determining the effects of somatic mutation on antigen binding

To understand how features of clone 2.1 phylogenies related to changes in affinity, we used deep mutational scanning (DMS) to measure the impact of virtually all possible V(D)J single-amino-acid (aa) replacements on the naive 2.1 sequence on IgY binding and Ig surface expression (Figure S3A). We constructed a mutagenesis library containing 4,158 out of 4,161 possible single-aa replacements available to clone 2.1, cloned into a single-chain fragment variable (scFv) construct for yeast-surface display.³² We then used the Tite-Seq approach³³ to determine the impact of each replacement on IgY binding affinity (Δaffinity, defined as −Δlog₁₀(K_D)) and surface scFv expression levels (Δexpression, a proxy for folding stability^34,35) (Figures 2A and S3A–S3C).

Figure 2. Deep mutational scanning and structure of clone 2.1.

(A) Heatmaps showing effects of amino-acid replacements on 2.1 scFv binding to IgY by DMS. “X” indicates original aa, slashes indicate inaccessible replacements. Yellow, not detected. Upper bar, antigen-antibody contact residues (≤5.0 Å by cryo-EM, black boxes). Interactive version available at the following webpage: https://matsengrp.github.io/gcreplay/interactive-figures/mutation-heatmaps/naive_reversions_first.html. Data are mean of two independent experiments.

(B) Effects of all (left) and accessible (right) aa replacements on 2.1 affinity and surface expression, with counts and percentages of impairing (red), neutral (gray), and improving (blue) replacements indicated.

(C) 4.0 Å cryo-EM reconstruction of 2.1^hi Fab complexed to IgY.

(D) Cryo-EM structure of 2.1^hi-IgY interface CDRs indicated (PDB: 9ODB).

(E) Structure of 2.1^hi V-domain with the IgY footprint (≤ 5.0 Å) outlined. Interface area, 851 Å2 (341 Å2 for V_H and 510 Å2 for V_κ).

(F) As in (E), colored by mean Δaffinity for all replacements (left), or maximum Δaffinity at each position (right). Color scale as in (A).

(G) 2.1^hi V_H (left) and V_κ (right) colored by maximum Δaffinity. Outline indicates footprint of the opposite chain (≥5 Ų buried surface area); IgY shown as gray ribbon. Color scale as in (A).

(H and I) DMS-predicted versus BLI-measured Δaffinity for recombinant Fabs. Solid line, linear fit; dotted line, x = y. LOD, limit of detection; LOQ, limit of quantitation. R² and slope exclude Fabs outside the LOD–LOQ range. (H) Recurrent 2.1 variants in prior studies of clone 2.1; (I) 8-log “affinity ladder.”(J) Example GC phylogeny from 20 dpi replay dataset (see Figure 1), colored by Δaffinity estimated by the additive DMS model.

As expected, given the relatively high-affinity of unmutated clone 2.1 (~40 nM⁷), aa changes, particularly those falling within complementarity-determining regions (CDRs), were much more likely to reduce affinity than to improve it (Figures 2A and 2B). Whereas the best available replacement improved affinity by less than one log₁₀ (N108_LR, Δaffinity = 0.91), the worst lowered affinity by 3 log₁₀ (Y38_HE, Δaffinity = −3.0; Figure 2A). Of the 4,145 aa replacements assayed for both Δaffinity and Δexpression in the DMS, 1,474 (35.6%) led to at least a 0.3 log₁₀ decrease in either binding affinity or scFv surface expression, whereas only 149 (3.6%) led to a gain in affinity of 0.3 log₁₀ or greater (Figure 2B). Similar results were obtained when only accessible replacements (those resulting from a single-nucleotide mutation, non-hatched squares in Figure 2A) were considered (400 (31.4%) deleterious and 55 (4.3%) enhancing replacements of 1,272 assayed; Figure 2B). Thus, for every enhancing replacement clone 2.1 can make, it must avoid making roughly 10 deleterious ones. No aa replacements were found that led to a substantial gain in surface expression, suggesting that the stability of clone 2.1 is near-optimal (Figures 2B and S3C).

To understand the structural basis for the DMS results, we determined negative-stain and cryo-EM structures of an affinity-matured version of the 2.1 Fab (measured K_D = 62 pM) bound to IgY. Clone 2.1 bound to the hinge-like C_H2 domain of the four-domain IgY constant region (Figures S3D and S3E). The paratope of clone 2.1 consisted of a concave pocket that contacted the outer face of IgY C_H2 (Figures 2C–2E and S3F). Mapping the DMS to the structure showed that replacements in the central groove of the paratope had strongly negative mean effects on Δaffinity, whereas affinity-enhancing replacements were found primarily at the periphery of the paratope (Figures 2E, 2F, and S3G) and along the heavy-light-chain interface (Figure 2G). Replacements that reduced scFv surface expression occurred in their expected positions (e.g., disulfide-bond cysteines and inward-facing hydrophobic residues and salt bridges³⁶; Figure S3H).

To estimate the affinities of GC B cells containing multiple mutations, we simply added the Δaffinities associated with each individual aa replacement, reasoning that, since most affinity-enhancing replacements in clone 2.1 were located along the edges of an otherwise optimal central groove (Figure 2F), epistatic interactions leading to non-additive effects would be limited. To validate this approach, we produced a series of recombinant Fabs carrying selected affinity-enhancing replacements that appear frequently in clone 2.1, either alone or in combination (Tas et al.,⁷ Jacobsen et al.,²⁶ and unpublished data), and measured their binding to IgY by biolayer interferometry (BLI; Table S2). This showed good agreement (R² = 0.89, slope = 0.69) between predicted and observed values within this series (Figure 2H). We next produced a 17-step “ladder” of Fabs derived from B cell sequences obtained from the replay experiment, spanning Δaffinities between −4.0 and +4.0. Fabs with estimated Δaffinity < −1.0 bound too weakly to the antigen to be characterized. Above this threshold, DMS-predicted and BLI-measured affinities increased linearly up to Δaffinity ≅ 2.5 (R² = 0.91, slope = 1.33; Figure 2I), after which off-rates were too long to accurately measure. Overall, the mean absolute difference in Δaffinity between BLI measurements and DMS predictions was 0.17 for antibodies with a single mutation and 0.64 for antibodies with more than one mutation. (As an estimate of the accuracy of BLI, the mean absolute difference between 9 independent BLI measurements of the unmutated Fab and the mean of these measurements was 0.20.) The predicted mean Δaffinity for all antibodies tested was 1.06, compared with a measured mean of 0.88, a difference of 0.18. We conclude that adding the DMS-determined effects of individual mutations is sufficiently accurate to predict how multiple mutations affect the affinity of clone 2.1, particularly when these affinities are averaged across many cells. Figure 2J shows an example of a 20 dpi GC phylogeny, colored using this model (for all trees, see Figure S2).

Selection of individual aa replacements across GCs

Using the DMS, we assessed how efficiently chIgY GCs identified and selected for each of the available affinity-enhancing aa replacements. Because the observed frequency of a replacement in the population depends on both its Δaffinity and on the intrinsic mutability of its codon, given SHM targeting biases,^37,38 we first measured nucleotide mutability across each of the Ig^chIgY alleles in the absence of selection using “passenger” alleles (Igh^chIgY* and Igk^chIgY*) containing frameshifts in the leader sequence upstream of each V-region (Figure S4A). These alleles are transcribed and mutated but do not produce functional proteins, and can thus be used to measure the intrinsic mutability of each nucleotide in an Ig sequence in the absence of antigen-driven selection.³⁷ Figure 3A shows relative mutation rates for each nucleotide in Igh^chIgY* and Igk^chIgY* (obtained by sequencing GC B cells induced by Plasmodium chabaudi infection; see STAR Methods). As expected, intrinsic mutability varied greatly across each sequence and was generally higher in CDRs than in frameworks (Figure 3A). Observed mutation rates correlated significantly but not perfectly with those predicted using a five-mer context model²³ (Figure S4B).

Figure 3. Accumulation of beneficial replacements in GCs is constrained by mutability.

(A) Relative mutation rate per nucleotide for passenger Igh^chIgY* and Igk^chIgY* alleles (given as the sum of rates for the three possible mutations). Data pooled from 3 mice for Igh and 2 mice for Igk.

(B) Correlation between relative mutation rate for the 1,275 codon-accessible aa replacements (based on passenger allele) and prevalence of each replacement in the replay dataset. Each symbol is one replacement, colored by Δaffinity. Black line, Poisson regression, used to calculate “replacement enrichment” in (D) and (E).

(C) Correlation between Δaffinity and prevalence of each replacement in the replay dataset. Each symbol is one replacement, colored by relative mutation rate.

(D and E) Correlation between Δaffinity (D), Δexpression (E), and replacement enrichment. Orange line, LOWESS regression with 95% CI. ρ, Spearman correlation.

(F) Affinity-enhancing replacements (Δaffinity > 0.4) found by the highest-affinity B cell in each GC at each time point. The top 15 GCs at 15 and 20 dpi, and the top 8 samples at 70 dpi, are shown. Columns are the set of affinity-enhancing replacements available at each position, grouped into accessible (left) or not (right) by a 1-nucleotide mutation. Blue squares, high-affinity replacements found by each cell, aa identity in white. Bars above indicate the sum of intrinsic mutabilities for all replacements in the column. Bars to the right are the Δaffinity of each B cell.

(G) Classification of accessible aa replacements into categories of Δaffinity (DMS) and relative mutation rate (passenger allele), defined by dashed lines.

(H) Kinetics of emergence of replacements from the 9 categories in (G) in GC B cells sequenced as detailed in Figure S4E. Lines represent the mean ± 95% CI for the normalized frequency of mutations in each category. Data pooled from 4 mice per time point.

(I) As in (G) but showing selected individual replacements.

Intrinsic nucleotide mutability was a much stronger predictor of the frequency of aa replacements in GCs in vivo than the Δaffinity associated with each replacement (Spearman ρ = 0.67 versus 0.22, respectively; Figures 3B and 3C). Nevertheless, replacements that improved affinity (blue in Figure 3B) were clearly enriched above the regression line, whereas deleterious replacements (red) were enriched below. We therefore plotted the observed frequency of a replacement against its predicted frequency based on intrinsic mutability, defining “replacement enrichment” as the log₁₀ fold change over the regression line. Replacement enrichment was better correlated with Δaffinity (Spearman’s ρ = 0.46) than observed frequency alone (Figures 3C and 3D) and also correlated well with Δexpression (Spearman ρ = 0.53; Figure 3E). Both correlations were distinctly biphasic, starting relatively flat but steepening markedly as they approached zero (Figures 3D and 3E). Presence of such “breakpoints” was confirmed using segmented regression (Figure S4C). In the range surrounding neutrality, a 10-fold change in affinity or expression led, on average, to 15- and 100-fold (1.2 and 2.0 log₁₀) changes in replacement enrichment, respectively. Thus, when replacements are analyzed in aggregate, GCs appear responsive to even small changes around neutral phenotypic values, but counterselection is near maximal already at moderate expression or affinity loss. Of note, although affinity and expression were strongly correlated for many replacements, within a given range of affinity loss, replacements that also caused loss of expression were more likely to be counter selected (Figure S4D).

To determine how efficiently GCs identified and selected for the full complement of affinity-enhancing aa replacements available to them, we collected the 15 highest-affinity B cells from each replay time point (allowing only one cell per GC) and analyzed their acquisition of the full set of 104 replacements associated with affinity gains of at least 0.4 log₁₀ (Figure 3F). GCs largely failed to find affinity-enhancing aa replacements that required more than a single-nucleotide mutation in the same codon. Only one of 64 such replacements (S109_LK, located within the highly mutable CDR_L3 region) was observed in this sample (Figure 3F), and more generally, only 156 (1.8%) of 8,744 B cells sequenced in the replay experiment carried any of these 64 replacements. Low intrinsic mutability also prevented GCs from finding several of the beneficial replacements accessible with single-nucleotide mutations. These included positions G27, R80, and W118 in IgH and Q27 and P50 in Igκ (Figure 3F). To investigate whether these replacements might be selected for if given enough time, we immunized mice as in the replay experiment but using chicken IgY in Alhydrogel adjuvant, which generates longer-lived GC responses,³⁹ then sequenced GC B cells pooled from the entire LNs 10 weeks later. These cells were heavily mutated (median 18.5 nucleotide mutations, range 11–37) and some had very high predicted affinities (Δaffinity > 4.0), indicative of prolonged GC selection. Nevertheless, no inaccessible or low-mutability aa replacements were detected in the highest-affinity B cells from each 70-dpi sample; rather, these cells achieved high affinities primarily through combinations of mutations also found at earlier time points.

To explore these trends systematically, we generated an independent dataset consisting of a time-course of chIgY GC B cells obtained from mice immunized as in the replay experiment but sorted in bulk (i.e., B cells from multiple GCs were pooled from whole LNs of several mice per time point). Sorted cells were analyzed by droplet-based single-cell sequencing at 5, 8, 11, 14, 17, 20, 30, and 70 dpi, the last two time points using Alhydrogel as an adjuvant to extend GC lifetime (Figures S4E and S4F). We then used passenger allele and DMS data to categorize all accessible aa replacements based on mutability (low [<25%ile], medium [25%ile–75%ile], and high [>75%ile]) and Δaffinity (negative [<−0.3], neutral [−0.3–0.3], positive [>0.3]), respectively (Figure 3G). In line with our previous analysis, low-mutability replacements were largely ignored by GCs, even when leading to substantial gains in affinity (Figure 3H). By contrast, enrichment for affinity-enhancing replacements was evident in the high- and intermediate-mutability classes. High-mutability replacements accumulated progressively over time, even when neutral (but not when deleterious), again indicating strict counterselection of affinity-reducing replacements. Following selected replacements over time revealed a pattern in which neutral but high-mutability replacements (such as the S to N changes in positions S57_H, S64_H, and S109_L) accumulated early on, whereas unlikely but beneficial ones (such as D28_H to V, A, or G) caught up only much later (Figure 3I).

In summary, affinity maturation is heavily constrained by intrinsic biases in SHM and accessibility through single-nucleotide changes. These constraints limit the exploration of the full mutational landscape, even under prolonged selection.

Phylogenetic analysis identifies the drivers of affinity maturation

GCs select consistently for increases in affinity and maintenance of Ig expression

Whereas GC phylogenies varied widely in structure (Figures 1C, 1D, and S2), replay GCs were much more consistent with respect to affinity maturation. Median affinity was higher than naive in 117 of 119 GCs, whereas variance was relatively low (0.87 ± 0.38 at 15 dpi and 1.00 ± 0.34 at 20 dpi [mean ± SD]; Figures 4A and S5A). This consistency was more evident when observed trees were displayed alongside neutral drift simulations in mutational load versus Δaffinity “trajectory plots” (Figure 4B). In these simulations, replacements are introduced according to mutability alone, in the absence of affinity-based selection, while maintaining the phylogenetic structure of each GC. Neutral simulations consistently produced median affinities markedly lower than observed experimentally (Δaffinity = −0.47 ± 0.24 at 15 dpi and −0.70 ± 0.26 [mean ± SD]; Figure 4C). Thus, despite the strong downward pressure on affinity exerted by stochastic mutagenesis, GCs consistently achieved increases in affinity over time.

Figure 4. Quantifying germinal center selection for affinity and for maintenance of Ig expression.

(A) Distribution of replay GCs by median DMS-estimated affinity and Ig expression. Each symbol represents one GC. Distribution of GCs by Δaffinity (top) and Δexpression (right) is shown.

(B) Example trajectory plots. Circles represent individual nodes, colored by REI and scaled by number of identical sequences, and are plotted according to number of nucleotide mutations and Δaffinity (top) or Δexpression (bottom). Simulated trees are shown in light blue lines, which represent the median values for each node in 10 simulated trees. For all GCs, see the following repository: https://github.com/matsengrp/gcreplay/tree/main/results/notebooks/phenotype-trajectories/naive_reversions_first.

(C) As in (A) (filled symbols), with each replay GC paired to the median of 10 GCs simulated as in (B) (open symbols). p values, Wilcoxon signed-rank test.

(D) Example trajectories as in (B), with simulations constrained by affinity.

(E) Comparison of median Δexpression between experimental GCs and affinity-constrained simulations as in (D). Each symbol represents one experimental GC (“observed”) or the median of 10 simulated GCs (“simulated”).

SHM led to a noticeable decrease in Ig surface expression, consistent with previous observations.⁴⁰ Median Δexpression dropped below naive in 106 of 119 GCs (−0.13 ± 0.21 at 15 dpi and −0.17 ± 0.27 at 20 dpi [mean ± SD]), with several instances of more substantial loss (Figures 4A–4C and S5A). In the four GCs in which median Δexpression fell below −1.0 (Figures 4A and S5B), the median-expression B cell acquired replacement Y42_LN (arrowhead in Figure S4D), which causes a severe drop in expression (−1.27) while increasing antigen binding (0.26). Thus, even strongly destabilizing replacements can still undergo positive selection if they improve affinity. Δexpression was also much lower in simulated than in experimental trees (−0.48 ± 0.22 at 15 dpi and −0.73 ± 0.25 at 20 dpi [mean ± SD]; Figure 4C). Because affinity and expression are partially correlated (Figure 2B), we performed additional simulations in which we forced simulated trees to match the Δaffinity of experimental GC lineages within 0.05 log₁₀(K_D), regardless of effects on Δexpression. Median Δexpression in these simulations remained marginally higher than in vivo (medians, −0.060 versus −0.15 at 15 dpi and −0.073 versus −0.23 at 20 dpi, p < 0.0001 for both; Figures 4D and 4E), indicating some degree of selection acting specifically on Ig expression.

In conclusion, despite wide variation in tree shapes, GCs reliably select for increased antibody affinity, despite the downward pressure of random mutation. GCs also exert some independent pressure to maintain Ig expression, though large losses in expression can be tolerated if compensated by affinity gains, consistent with previous work.⁴⁰

Low-affinity B cell lineages are efficiently terminated

A recurring feature of GC trajectory plots is steep downward-trending lines leading to terminal nodes lacking detectable descendants (for example, GCs #15 and #119 in Figure 4B), appearing in affinity-colored phylogenies as red-tinted “leaves” at terminal branch ends, downstream of higher-affinity internal nodes (Figures 5A and S2). This pattern suggests that GC lineages that lose affinity are efficiently terminated, rarely leaving detectable descendants. To quantify this, we categorized nodes by Δaffinity relative to their immediate ancestor (which approximates the change in affinity incurred by a B cell in its most recent round of SHM), divided into three categories (<−1.0, −1.0 to 0.3, and >0.3), and plotted the mean mutational distance to the nearest branch tip per category. At both time points, nodes that lost affinity compared with their immediate ancestors were disproportionately enriched at leaves (i.e., more likely to be at distance zero from the closest branch tip, and thus to have been recently generated; Figure 5B). We conclude that B cells that lose affinity due to SHM rarely persist in GCs. By extension, the low-affinity B cells frequently observed in our dataset likely represent recent mutants not yet purged from the population by selection.

Figure 5. Drivers of affinity maturation as determined by phylogenetic analysis.

(A) Example phylogenies colored by Δaffinity. Arrowheads indicate cells that lost substantial affinity located at terminal nodes.

(B) Observed and inferred nodes from each replay phylogeny, classified as losing (<−1.0), maintaining (−1.0 to 0.3), or gaining (>0.3) affinity with respect to parent. For each GC, the mean distance between nodes in each category and the nearest leaf was recorded (distance = 0 when the node is itself a leaf). Plot shows the distribution of mean values for each category.

(C) Example burst phylogeny colored by Δaffinity. Arrowhead, burst point.

(D) Distribution of Δaffinities for burst nodes (REI > 0.25; blue lines, 15 dpi; orange lines, 20 dpi) compared with distribution of Δaffinities for all nodes (observed and inferred) from the same time point (gray bars).

(E) Comparison of Δaffinities predicted by additive DMS and BLI measurements of recombinant Fabs for each burst node in (D). Solid black line, linear trend; dotted red line, x = y. LOQ, limit of quantitation. R² and slope (m) calculations exclude the Fab with Δaffinity > LOQ.

(F) Distribution of NDS and max REI for 15 and 20 dpi GCs as in Figures 1E and 1F, colored by median Δaffinity; each symbol represents one GC.

(G) Definition of “sister” nodes used in (H) and Figure S5F.

(H) Distribution of replay GCs according to Δaffinity of the max REI node and mean Δaffinity of sister nodes. Statistical comparison in Figure S5F.

Clonal bursts are not the primary drivers of affinity maturation

Clonal bursts represent extreme “jackpot” events in which a single B cell proliferates enough to eliminate most competing lineages in its GC.^7,41 If burst size were reliably determined by affinity, sporadic large bursts could drive affinity maturation by increasing mean population affinity in a stepwise manner. Counter to this notion, the largest clonal bursts at 15 and 20 dpi (Figures 1E and 1F, top-right sector) originated from B cells with relatively high but far from extreme affinities (mean percentile rank 66 (range 30–94) at 15 dpi and 64 (21–97) at 20 dpi; Figures 5C and 5D). Bursts from 20 dpi were also not outliers when compared with the 15-dpi background (Figure S5D), indicating that bursting cells were also unexceptional at the time they were selected.⁴² BLI-measured affinities of recombinant Fabs derived from 13 clonal bursts (Figure 5E) were relatively well predicted by the DMS (R² = 0.53, slope = 1.05), with the exception of one Fab whose affinity fell outside the range of the instrument. There was also no correlation between max REI and BLI affinity (Figure S5E). Moreover, color-coding GCs in the NDS × max REI scatter plot (Figures 1E and 1F) by median Δaffinity revealed no marked enrichment for high-affinity cells in the upper right clonal burst sector (Figure 5F). Similarly, there was no strong correlation between affinity measures and burst size (REI) (Figure S5C). Thus, clonal bursts are not a superior strategy for affinity maturation compared with more gradual evolution. Of note, Δaffinity correlated moderately with NDS, especially at 15 dpi (Figure S5C), indicating that evolving multiple lineages simultaneously is associated with lesser affinity gains. We conclude that clonal bursts are neither primary drivers of affinity maturation nor inherently superior as a strategy to less punctuated evolution.

Given the absence of a strong link between clonal bursting and affinity gain, we sought to identify common drivers of affinity maturation present in all GCs, regardless of large-scale tree topology. To this end, we selected the highest-REI B cell in each GC as well as all of its “sister” nodes within the same branch (nodes that shared a common immediate ancestor with the node of interest), which we reasoned would be representative of the competitors of the highest-REI B cell at the time it was selected (Figure 5G). We then measured the change in affinity between each node or sister and its immediate ancestor. This showed that, although the discrimination between bursts and sisters was imperfect (i.e., the highest-REI node did not always have higher affinity than its sisters), it was, on aggregate, significantly skewed toward expanding higher-affinity B cells over their lower-affinity competitors (Figures 5H and S5F).

Taken together, our data indicate that affinity maturation in GCs, rather than being driven by sporadic clonal bursts, results from persistent selection that is relatively inaccurate but sufficiently biased toward high-affinity B cells to reliably favor their expansion over time.

A fitness landscape for the temporal evolution of GC affinity

The distribution of B cell affinities in a GC evolves over time due to three dynamical factors: Ig sequence mutations by SHM, the affinity effects of these mutations, and the fitness effects of affinity differences. This last factor—the fitness landscape¹²—is a key conceptual tool in evolutionary dynamics but is rarely directly inferred.^43,44 We sought to infer this landscape for clone 2.1 by assigning affinities to all cells in the time-course experiment (Figures S4E and S4F), which sampled pooled GC B cells from whole LNs at multiple time points (Figure 6A [gray histograms] and S6A). We formulated a minimal mathematical model^45,46,47,48 that predicts the continuous distribution of affinity $x$ ($-\mathrm{\Delta }{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\left({\mathrm{K}}_{\mathrm{D}}\right)$ from naive) among GC B cells over time $t$ (dpi). We denote this distribution $p(x,t)$ and formulate a partial differential equation for its temporal evolution, incorporating: (1) a mutation process specified by mutation targeting biases from the passenger allele experiment and the affinity effects from the DMS experiment (Figure 6B, upper panel); and (2) an affinity-fitness landscape $f(x)$ specifying fitness for each affinity $x$ (Figure 6B, lower panel). The growth (or decay) rate of a B cell population with affinity $x$ at time $t$ is $f(x)-\bar{f}(t)$, where $\bar{f}(t)$ is the mean fitness of the full population at time $t$ (Figure S6C). We used maximum likelihood to estimate $f(x)$ so that the predicted $p(x,t)$ matches our time-course data (Figure 6A).

Figure 6. Fitness landscape inferred from evolutionary dynamics.

(A) Distributions of affinity at eight time points (dpi) in the time-course experiment (gray) and corresponding dynamics under the inferred fitness landscape (red).

(B) Fitness landscape model parameters: Top, distribution of affinity mutations specified by DMS effects and mutation propensities. Bottom, fitness landscape.

(C) Solution of fitness landscape model up to day 20 (dotted lines for reference).

(D) Growth rate (intrinsic fitness minus population mean fitness) shown in a colormap over time and affinity. The affinity corresponding to population mean fitness is tracked in the dashed line (the mean-matched affinity; the difference from that line is the time-point-relative affinity).

(E) Growth rate versus time-point-relative affinity (as in [D]) at sampling times.

(F) Time-resolved tree for one GC showing nodes (birth events) and mutations (affinity jumps) in time (dpi), with all leaves positioned at the sampling time (20 dpi for this GC). 100 such trees were sampled for each GC. Red dotted line is given for reference.

(G) Heatmaps showing the temporal evolution of affinity, aggregating all candidate time-resolved trees for 15- and 20-dpi GCs (dotted lines for reference). Push-of-the-past and pull-of-the-present manifest as excess density in the upper-left and lower-right quadrants, respectively, compared with (F).

(H) The gray trendline shows median and interquartile range (IQR) affinity in the time-course experiment up to 20 dpi. Blue and orange trend lines show median ± IQR affinity derived from time-resolved trees for 15 dpi and 20 dpi GCs, respectively.

(I) Probabilities of survival until 20 dpi for cells of different affinity at various previous times, given the inferred fitness landscape model.

(J) Fitness landscape model dynamics (gray) summarized as median ± IQR affinity. Orange and blue, predicted median ± IQR affinity for ancestral population histories sampled at 15 dpi and 20 dpi, respectively, by reweighting the solution with survival probabilities as in (I).

The affinity-fitness landscape of clone 2.1 (Figure 6B, lower panel) begins linearly with a slope of 0.74—i.e., a B cell lineage with a 10-fold affinity advantage over competitors will double in size roughly once a day ($e^{0.74}=2.09\text{-fold/day}$)—before saturating at around $x=2$ (400 pM) and reaching a plateau at $x=3$ (40 pM). Inferring $f(x)$ allows us to predict how the affinity distribution would evolve under continuous sampling (Figure 6C) and how the growth potential of B cells changes with time (Figure 6D). The plateauing of $f(x)$ at higher affinities implies that the relationship between a B cell’s affinity relative to its competitors (the “time-point-relative affinity”) and its expected growth rate flattens at later time points as the mean affinity enters the pM range (Figure 6E). Thus, the selection of improved mutants becomes progressively more difficult later in the GC reaction.

Phylodynamic survivorship bias distorts tree-based signals of GC B cell fitness

The affinity-fitness landscape allows us to assess how closely time courses reconstructed from phylogenetic trees correspond to those obtained from sequential sampling. We focused on a prominent feature of the GC trajectory plots: many phylogenies appeared to show rapid early gains in affinity, followed by a plateau and eventual decline toward the leaves (Figure 4B), suggesting a slowdown in GC selection after only a few somatic mutations. To measure these trends over the ensemble of all trees, we first used Bayesian phylogenetics⁴⁹ to generate time-resolved phylogenies for each GC. These time-resolved trees (exemplified in Figure 6F) represent branch lengths as inferred time intervals, placing mutations and nodes at concrete time points in the history of the GC. Because time-resolved tree details have considerable statistical uncertainty, we used 100 posterior tree samples (each a candidate time-resolved tree) for each GC. We used these trees to reconstruct the evolution of B cell affinity over time across all GCs in the replay experiment (Figures 6G and 6H). This analysis confirmed the observations made from individual trees: affinity-increasing mutations appear to emerge rapidly and are maintained for much of the GC reaction as affinity plateaus (upper-left quadrant in Figure 6G), followed by a subpopulation of lower-affinity B cells at sampling time (lower-right quadrant). Tree-based reconstruction of GC dynamics seems to suggest a rapid change in the strength of affinity-based selection early in the reaction. However, evolution of affinity in this reconstruction differed markedly from that inferred based on the affinity-fitness model (Figure 6C), which decreased slightly in the first days after GC formation—reflecting initial acquisition of deleterious mutations by SHM—followed by a gradual increase through day 20. Likewise, we observed the late emergence of cells with negative Δaffinity in the reconstructions (Figure 6G, lower-right quadrant) that were absent from days 14–20 of the fitted time-course (Figures S6A and S6B). Thus, phylodynamic reconstruction based on an extant population fails to predict the true progression of GC B cell affinities over time.

We hypothesized that this inconsistency reflects two concepts from the macroevolution literature: the “push-of-the-past” and the “pull-of-the-present.”⁵⁰ Phylogenetic reconstruction inevitably represents a biased history of the subpopulation destined to become ancestors of the cells sampled at the endpoint—this ancestral subpopulation tends to be of higher fitness than its contemporaries because it is conditioned on leaving descendants in the present (push-of-the-past). Conversely, the apparent affinity plateau at late time points would result from the presence of low-affinity B cells that have not yet been purged from the population (pull-of-the-present). We used the fitness landscape model to predict the effects of both distortions in our replay data. Using a forward master equation approach, in which we consider the fate of a single cell’s descendants competing in the evolving population $p(x,t)$, we computed the probability of stochastic extinction of a lineage prior to sampling time at 15 or 20 dpi (Figure 6I). These calculations predicted strong survivorship effects: lineages with $x<0$ before 17 dpi are very likely to be extinct by day 20, whereas the highest-affinity lineages are most favored for survival at earlier times, when they are more distant outliers from the mean. Conversely, cells with affinities around $x=0$ at 17 dpi are much more likely to survive to day 20, indicating a lag between acquiring a deleterious mutation and being eliminated from the GC. These calculated survival probability profiles can be used to reweight the time-course prediction $p(x,t)$, giving the predicted time evolution $\tilde{p}(x,t)$ of the ancestral population (the subpopulation destined to leave descendants at the later sampling time, 15 or 20 dpi), shown in Figure 6J alongside the full population $p(x,t)$ from which they were computed. These predicted ancestral trajectories show clear distortions—early jumps of affinity followed by subsequent slowing down before the sampling time—that are consistent with our findings from inferred trees (Figure 6G).

We conclude that both sampling of current affinities and phylogenetic reconstruction of past trajectories from extant GC B cell populations are subject to survivorship biases that distort our view of selection dynamics. Modeling these effects allows us to separate true biological processes from observational artifacts, providing insight into how mutation and selection shape affinity maturation.

DISCUSSION

We present the results of an experimental evolution system in which we replay a simplified, monoclonal GC reaction over 100 times. We find that, even in this simplified setting, GC selection yields widely divergent tree topologies, ranging from clonal-burst-type structures to multi-pronged GCs where multiple lineages evolve in parallel. Thus, the diversity of GC outcomes observed in Brainbow GCs⁷ cannot be attributed exclusively to differences in founder populations in a polyclonal setting. By contrast, DMS-based affinity estimation showed that phenotypic evolution across GCs is broadly consistent: virtually all GCs gained affinity compared with the naive ancestor, despite navigating a landscape that overwhelmingly favors deleterious replacements. Thus, GCs are reproducible with respect to phenotype but not to phylogeny.

A simple additive model in which the log₁₀ DMS-measured effects of single replacements are summed, ignoring epistatic interactions, predicted the affinities of clone 2.1 variants carrying multiple replacements with a degree of accuracy sufficient to resolve large-scale features of GC selection. Similar additivity was observed in a recent study of SARS-CoV-2 antibodies, which found epistatic effects to be infrequent,⁵¹ but more substantive epistasis has been reported for broadly neutralizing antibodies (bNAbs) against influenza.^52,53 A possible reason for this discrepancy is that most affinity-enhancing replacements in clone 2.1 are distributed around an otherwise optimal paratope (Figure 2F), making them less likely to interact epistatically. Importantly, the degree of epistasis in a given antibody lineage will affect only the accuracy of DMS-based affinity predictions, not the general rules by which GCs select for high-affinity mutants. The evolutionary dynamics we describe for clone 2.1 should therefore hold even in more epistatic settings.

Access to the full universe of affinity-enhancing replacements available to clone 2.1 revealed that GCs “miss” the large majority of replacements with affinity-enhancing potential, primarily due to codon constraints and the low intrinsic mutability of many Ig positions due to activation-induced citidine deaminase (AID) and SHM targeting biases.^37,38 Inaccessibility along these lines has previously been shown to limit the evolution of certain bnAbs to HIV.^54,55 Our data allow us to quantify the full extent of these biases. These findings also suggest that DMS-guided mutagenesis could increase monoclonal antibody affinities well beyond what is obtainable by affinity maturation in vivo.

Previous studies have reported high frequencies of low-affinity B cells within GCs, suggesting that GCs may be permissive to low-affinity clones and variants, which would both help lineages traverse local low-affinity “valleys” as well as maintain broader clonal diversity.^{7–10,56–58} Our trajectory plots show instead that most low-affinity GC B cells are evolutionary dead ends, likely representing recent mutants not yet purged by selection. The presence of low-affinity lineages in GCs in previous work may be explained by specificity for cryptic “dark” epitopes^8,59 generated by antigen degradation or by the blocking of immunodominant epitopes by circulating antibody,^60–63 either of which would decouple a B cell’s in vitro measured affinity from its capacity to retrieve antigen in vivo.

Clonal bursts originated from B cells spanning the full spectrum of affinities present in the GC, and phylogenies containing large bursts did not have higher median affinities than those lacking them. A scenario in which affinity maturation results from sporadic large-scale expansion of very high-affinity clones is therefore inconsistent with our observations. Notwithstanding, these findings do not negate the importance of clonal bursts to GC biology, as they lead to important losses in clonal diversity in polyclonal settings^7,31 and may also serve as critical sources of GC-derived plasma cells.⁵⁶ By contrast, comparing the most successful node of each GC to its sisters revealed a distinct, if imperfect, association between affinity and number of progeny. Thus, while selection at the level of individual B cell fate decisions may appear noisy,^7,41 this same process reliably drives long-term affinity maturation when repeated across thousands of individual decisions. The multi-step process by which competition for T cell help drives GC selection^24,64—including the stochastic nature of B cell access to antigen and T cell help in a highly dynamic environment^65–68—offers ample opportunity for stochasticity to influence the outcomes of competition while preserving the overall selective bias. Thus, the GC operates as an “imperfect cell sorter,” in which individually error-prone fate decisions, when repeated across thousands of B cells, produce reliable long-term affinity gains.

From the standpoint of evolutionary biology, we established an experimental platform capable of quantitatively mapping genotype-to-phenotype-to-fitness. This landscape shows, for example, that a 10-fold affinity advantage translates to approximately a doubling of the size of a population each day, with fitness saturating in the high-to-mid-pM range—broadly matching a previously reported affinity ceiling.^69,70 Whether this reflects true saturation or a decline in affinity discrimination over time, as antigen availability declines and T cell help wanes,⁷¹ remains to be resolved. Finally, combining fitness-based modeling with time-resolved reconstruction of ancestral phylogenies revealed systematic survivorship biases, initially described in the context of macroevolution,⁵⁰ which obscure the true dynamics of selection. Modeling these biases explicitly allows us to correct for such distortions and better understand how mutation and selection interact to produce reliable affinity maturation.

Limitations of the study

We trace the outcomes of GC selection acting on one particular B cell clone. The affinity of clone 2.1 for IgY is relatively high (40 nM) but representative of the naive affinities of clones that dominate secondary responses in mice.⁷² The 2.1 affinity-fitness landscape plateaus at a level compatible with prior estimates, suggesting some degree of generalizability of our results to other systems. Nevertheless, it is possible that particular features of GC evolution, such as the association between affinity and clonal bursting and the strictness of counterselection against affinity-losing mutants, differ in settings in which mean affinity is lower. Moreover, to ensure strict reproducibility at the clonal level, our GCs are engineered to lack polyclonal competitors. Thus, our setup assays intraclonal, but not interclonal, GC competition, ignoring potential factors such as antibody-mediated feedback.^60,61 Further experimentation with different antigen-antibody pairs and using more clonally complex systems will help clarify each of these points.

RESOURCE AVAILABILITY

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Gabriel D. Victora (victora@rockefeller.edu).

Materials availability

All unique/stable reagents generated in this study are available from the lead contact upon reasonable request.

STAR★METHODS

Detailed methods are provided in the online version of this paper and include the following:

METHOD DETAILS

Mice

Igh^2.1 and Igk^2.1 mice were generated by CRISPR-Cas9 gene-editing in fertilized mouse oocytes. For Igh^2.1, we inserted the pre-rearranged unmutated V_H sequence of clone 2.1, preceded by the 443 bp proximal promoter of Ighv9–4⁷³ in place of the 4 endogenous Igh J segments, using two flanking sgRNAs and a single-stranded DNA (ssDNA) megamer (IDT) as described in the easi-CRISPR method.⁷⁴ Igk^2.1 mice were generated by inserting the pre-rearranged unmutated V_κ sequence of clone 2.1, preceded by the 188 bp proximal promoter of Igkv3.12,⁷³ in place of the 5 endogenous Igk J segments, using two sgRNAs and an ssDNA template generated by PCR amplification of a cloned template plasmid followed by opposite-strand digestion using the Guide-it Long ssDNA production system v2 (Takara Bio). Passenger allele mice (Igh^2.1* and Igk^2.1*) were generated using single sgRNAs to introduce indels into the leader sequence of fertilized Igh^2.1/+ and Igk^2.1/+ oocytes, respectively. Sequences of the sgRNA protospacers and ssDNA donor templates used for mouse generation are provided in Table S3). CD23-Cre (Fcer2a-Cre) BAC transgenic mice²⁷ (Jax strain #028197) were provided by M. Busslinger (IMP Vienna). Bcl6^f/f mice²⁸ (Jax strain #023727) were provided by A. Dent (U. Indiana). PAGFP-transgenic mice²⁴ (Jax strain #022486) were generated and maintained in our laboratory. All animal experiments were approved by the Rockefeller University's Institutional Animal Care and Use Committee (IACUC). Mice of both sexes were used for all in vivo studies without distinction, with the exception that male B cells were never transferred into female recipients to avoid immune-mediated rejection.

Cell transfers, immunizations, and Plasmodium infection

Resting splenic B cells were purified by filtering splenocytes through a 70 μm mesh into PBS supplemented with 0.5% BSA and 1mM EDTA (PBE). CD43 MACS beads were used to purify resting B cells from single-cell suspensions according to the manufacturer’s protocol (Miltenyi Biotec). The percentage of Igh^2.1/+/Igk^2.1/+ resting B cells was determined prior to transfer by staining with chicken IgY-BV421 (conjugated in-house) followed by flow cytometry. For all experiments, 5 × 10⁵ Igh^2.1/+/Igk^2.1/+ resting B cells were transferred into each recipient mouse intravenously. 24 hours following cell transfer, mice were immunized subcutaneously in the hind footpads, inner thighs, and/or forearms with 5, 10, and 20 μg, respectively, of chicken IgY (Exalpha Biologicals) precipitated in 1/3 volume of Imject Alum (ThermoFisher Scientific Cat# 77161) to generate similar-sized GCs in popliteal, inguinal, brachial, and axillary nodes. The immunization schemes were the same for the day-70 experiments, except that Imject Alum was replaced with Alhydrogel (InvivoGen) used according to the manufacturer’s protocol. For analysis of SHM in passenger alleles, either Igh^2.1*^/+.Igk^+/+ or Igh^+/+.Igh^2.1*^/+ mice were injected intraperitoneally with 10⁵ Plasmodium chabaudi-infected red blood cells (BEI Resources Cat# MRA-741).

Imaging and Photoactivation

Multiphoton imaging and photoactivation were performed as described previously,^7,24 using an Olympus FV1000 upright microscope fitted with a 25X 1.05NA Plan water-immersion objective and a Mai-Tai DeepSee Ti-Sapphire laser (Spectraphysics). One day prior to photoactivation, PAGFP-transgenic mice were injected intravenously with 10 μg of a non-blocking antibody to CD35 (clone 8C12, produced in house) conjugated to Cy3 to label networks of follicular dendritic cells (FDCs).⁷⁵ A Leica M165FC fluorescence stereomicroscope with a dsRed filter was used to register the location of FDCs. Clusters of CD35-expressing cells were then identified using multiphoton imaging at λ = 950 nm, at which photoactivation does not take place, and three-dimensional regions of interest were photoactivated by higher-power scanning at λ = 830 nm. Lymph nodes were then sliced manually under a Leica M165FC fluorescence stereomicroscope using double-edged safety razor blades (Astra Superior Platinum) for subsequent flow cytometry and sorting.

Flow cytometry and cell sorting

For replay time points, sliced LN fragments (15 and 20 dpi) or whole LNs (70 dpi) were placed into microcentrifuge tubes containing 100 μl PBE, macerated using disposable micropestles, and dissociated into single-cell suspensions by gentle vortexing. We then added 100 μl of 2× antibody stain (B220-BV785, TCRβ-APC Cy7, CD38-APC, Fas-PE-Cy7, biotinylated chicken IgY, Streptavidin-BV421, mouse Igκ-PE, supplemented with Fc block) to the cell suspension, which was incubated on ice for 30 min. Photoactivated transferred GC B cells were index-sorted into 96-well plates containing 5 μl TCL buffer (Qiagen) supplemented with 1% β-mercaptoethanol. For passenger allele sequencing, spleens from P. chabaudi-infected mice were harvested at 20–21 days post-infection. Single-splenocyte suspensions were obtained by forcing spleens through a 70 μm mesh followed by hypotonic lysis of red blood cells using ACK buffer. CD19 magnetic (MACS) beads (Miltenyi Biotec) were used according to the manufacturer’s protocol to enrich for B cells prior to sorting for splenic GC B cells as described above. For 10X Genomics single-cell Ig sequencing, LN cell suspensions were stained with individual hashtag oligonucleotide (HTO)-labeled antibodies to CD45 and MHC-I for sample barcoding prior to GC B cell sorting as above. A combination of two HTO’s per sample was used to accommodate for the number of samples in the experiment. Cells were sorted into microfuge tubes with PBS supplemented with 0.4% BSA and were counted for viability by trypan blue staining prior to loading onto a 10X Genomics Chromium Controller.

Single-cell PCR amplification and sequencing of Igh^2.1 and Igk^2.1 alleles

Sorted single cells were processed and analyzed essentially as described previously,⁷ except that specific forward primers were used to amplify chIgY BCR, and both chains were amplified simultaneously for all wells. Primers were limited to the leader sequences of each Ig^chIgY allele to enable full sequencing of framework (FR)1 regions. Specific primers used were 5’-AGCGACGGGAGTTCACAGACTGCAACCGGTGTACATTCC-3’ (Igh^2.1 V_H leader forward recoded) and 5’-AGCGACGGGAGTTCACAGGTATACATGTTGCTGTGGTTGTCTG-3’ (Igk^2.1 Vκ leader forward). The first 18 nucleotides of the Igh^2.1 V_H leader forward sequence were prepended to the Vκ primer so that same barcoding primers could be used for both chains in the next step. After PCR reactions as described previously,⁷ pooled PCR products were purified using SPRI beads (0.7× volume ratio), gel-purified, and sequenced with a 500-cycle Reagent Nano kit v2 for single-cell libraries on the Illumina Miseq platform.

Bulk PCR amplification and sequencing of Igh^2.1* and Igk^2.1* passenger alleles

To sequence passenger alleles from a large enough population of GC B cells, we first generated GCs in Igh^chIgY*^/WT and Igk^chIgY*^/WT mice by infection with Plasmodium chabaudi, which generates large numbers of GC B cells in the spleen.⁷⁶ We then bulk-sequenced the Igh and Igk genes of sorted pools of 7.5 × 10⁵ GC B cells at days 20–21 post-infection, when B cells carried on average 2.2 and 2.6 nucleotide mutations per chain, respectively. 750,000 GC B cells were sorted directly into 750 μl of TRIzol LS (Thermofisher #10296010), bulk RNA was extracted using the manufacturer’s protocol. Quality of RNA was checked using TapeStation D1000, and only samples with RIN > 8 were used for generating BCR libraries. The NEBNext Immune Sequencing kit mouse (#E6330S) was used according to the manufacturer’s instructions, with IgM, IgGa, and IgGb primers used to sequence BCR heavy chains and Igκ primers for light chains. Each chain was amplified in separately to ensure even amplification. BCR libraries were sequenced using Illumina NextSeq 2000 flow cell P1, to generate 100 million reads.

10X Genomics single-cell Ig sequencing

GC B cells sorted as above were sequenced for gene expression and BCR using the 10x Chromium Next GEM Single Cell 5’ Reagent kit v3 with Feature Barcode technology for Cell surface Protein, according to the manufacturer’s protocol. The resulting library was sequenced on a NovaSeq SP (Illumina) flow cell with a minimum sequencing depth of 30,000 reads per cell. De-multiplexing of the samples based on their unique molecular identifier (UMI) and HTO counts were generated with Cell Ranger v6.0.1, v7.0.1 or v8.0.1 with mm11 reference. BCR libraries were also processed with CellRanger “vdj” with default parameters.

Recombinant Fab fragment production and affinity measurements

Fabs were produced in one of two ways. For Figure 2H, Igh^chIgY and Igk^chIgY variable regions were synthesized by Twist Bioscience and directly cloned into a custom human IgG1 Fab expression vector, as described previously.⁷ Plasmids were transfected into Freestyle Expi-293 suspension cells (Life Technologies), and monoclonal Fab fragments were purified using Ni-NTA beads (GE Healthcare), according to the manufacturer’s protocol. Protein purity was assessed by SDS-PAGE and functional protein concentrations were calibrated using biolayer interferometry on an Octet Red96 instrument using anti-Fab coated sensors (FortéBio). For Figures 2I and 5E, Fabs were cloned and produced by GenScript based on Igh^chIgY and Igk^chIgY variable region sequences and were purified using Capture Select CH1-XL Magnetic Agarose Beads (ThermoScientific). Purity and functional concentrations were measured as mentioned above. BLI affinity measurements were performed as described previously using Octet SAX biosensors.⁷ K_D values were calculated using a kinetic 1:1 model. Only Fabs with good global fits (R² > 0.98) over multiple concentrations were used for K_d calculations. For Fabs that could not fit globally due to their low affinity (n = 3), partial fits were averaged over multiple concentrations and used instead.

Yeast-surface display deep mutational scanning

The clone 2.1 scFv was ordered as a yeast codon-optimized gene and cloned into the pETcon yeast surface-display expression vector containing a previously described barcode sequencing landing pad.⁷⁷ A site-saturation mutagenesis library was synthesized by Twist Bioscience, precisely encoding every possible aa substitution at each of the sites in the heavy- and light-chain variable domains. In duplicate, N16 barcodes were appended to mutagenesis products and cloned into the vector as previously described.^77,78 The duplicate libraries were electroporated into E. coli (NEB C3020K) and plated into a bottlenecked target of 88,000 cfu per library, aiming for an average of 20 redundant barcodes representing each of the possible aa substitutions in the library. PacBio sequencing was used to link N16 barcode to scFv genotype as previously described.^77,78

Mutation effects on CGG-binding affinity and scFv surface expression were determined by FACS and sequencing as previously described.^77,78 Briefly, libraries were cloned into yeast (Saccharomyces cerevisiae strain AWY101⁷⁹), induced for surface expression and labeled with a FITC-conjugated anti c-Myc antibody (Immunology Consultants Lab, CYMC-45F) to label for scFv surface expression, or anti-c-Myc antibody and biotinylated CGG (Exalpha IgY-B) followed by PE-conjugated streptavidin (Thermo Fisher S866) to label for CGG-binding. CGG incubations were set up across 10-fold ligand concentrations from 10⁻⁶ to 10⁻¹³ M, plus a 0 M baseline sample. Library cells were sorted into four bins of Myc-FITC (for expression) or SA-PE (for CGG binding) as described,^77,78 plasmid extracted from outgrown cells from each sort bin, and barcode counts in each FACS bin were determined via 50 bp single end sequencing on an Illumina NextSeq. Illumina sequencing counts were processed into mutant effects on surface expression and CGG-binding affinity as detailed in https://github.com/jbloomlab/Ab-CGGnaive_DMS/blob/main/Titeseq-modeling.ipynb. An interactive version of the DMS and Fab structure is available at https://matsen.group/gcreplay-viz/.

Negative-stain electron microscopy (EM)

IgY, either alone or in complex with clone 2.1 Fab, was diluted to ~0.02 mg/ml in Tris-buffered saline and applied to plasma-cleaned, carbon-coated 400 mesh grids. Grids were stained with 2% (w/v) uranyl formate for 30–60 s and blotted. Imaging was performed on an FEI Tecnai Spirit operating at 120-keV, and micrographs recorded with an FEI Eagle 4k CCD camera. Data were processed using Relion 3.0⁸⁰ or cryoSPARC v3.2.⁸¹

Cryo-EM

IgY was incubated with a threefold molar excess of a Fab fragment of a high-affinity variant of clone 2.1 (2.1^hi, which includes replacements D28_HA, K49_HR, S64_HG, A40_LG, Y42_LF, A52_LS, Q105_LH, and N108_LY) at room temperature for 5 hours. The final concentration of the complex was diluted to 0.06 – 1.0 mg/ml for vitrification. To aid with sample dispersal on the grid, the complex was mixed with lauryl maltose neopentyl glycol (final concentration of 0.005 mM; Anatrace) and deposited on plasma-cleaned Quantifoil 1.2/1.3 300 mesh grids. A Thermo Fisher Vitrobot Mark IV set to 4°C, 100% humidity, 10 s wait time, and a 3-s blot time was used for the sample vitrification process.

Data were collected using Leginon⁸² over 3 separate imaging sessions on a Thermo Fisher Talos Arctica operating at 200 keV and equipped with a Gatan K2 Summit direct electron detector. Combined movies were aligned and dose weighted using MotionCor2.⁸² Aligned frames were imported into cryoSPARC v3.2 and the contrast transfer function (CTF) was estimated using GCTF.⁸³ Particle picking was done by automated picking using templates created from an initial round of 2D classification, then extracted and subjected to multiple rounds of 2D classification for cleaning. An ab initio volume was generated, followed by 3D classification and the best classes were further refined. To further improve the resolution, the maps were subjected to global and local CTF refinements. A mask was created using UCSF Chimera⁸⁴ and cryoSPARC Volume Tools to cover both clone 2.1 Fabs and the central C_H2 portion of IgY, and used during local refinement without symmetry. A summary of data collection and processing statistics can be found in Table S1.

Initial models were generated by fitting coordinates from sAbPred⁸⁵ for the Fab and ColabFold⁸⁶ for the C_H2 dimer into the cryo-EM map. Several rounds of iterative manual and automated model building and relaxed refinement were performed using Coot 0.9.4,⁸⁷ Rosetta Relax⁸⁸ and Phenix real_space_refine.⁸⁹ Models were validated using EMRinger⁹⁰ and MolProbity⁹¹ as part of Phenix software suite. IMGT numbering was applied to the antibody Fab variable light and heavy chains. Final refinement statistics and PDB/EMDB deposition codes can be found in Table S1. Buried surface area was calculated as the mean for the two monomers in the asymmetrical structure, calculated using PISA interface list (https://www.ebi.ac.uk/pdbe/pisa/).

Western blotting

Truncated IgY-GFP fusion constructs were generated by cloning each Ig domain of the IgY heavy chain into the XhoI and EcoRI sites of pEGFP-C1-PRKAA1 (Addgene plasmid #30305). 2 μg of each construct was transfected into HEK293T cells using standard calcium phosphate transfection protocols. 24 hours, cells were harvested and 20 μg of protein extracts were loaded onto SDS-PAGE gels and transferred to nitrocellulose membranes using standard wet transfer protocols. All membrane incubations were performed on an orbital shaker. 5% BSA in Tris buffered saline-Tween 20 (TBST) was used to block the membrane for 1 h at 4°C. Both 0.5 μg/ml of recombinant clone 2.1 (A40G) and a 1:5000 dilution of anti-GFP antibody (Biolegend, cat# 902605) were diluted in TBST with 5% BSA for primary staining overnight at 4°C on an orbital shaker. A 1:2,000 dilution of HRP anti-human IgG or a 1:10,000 dilution of HRP anti-mouse IgG antibodies were diluted in TBST with 5% milk for secondary staining against clone 2.1 and anti-GFP antibody, respectively. After 1 h incubation at room temperature on an orbital shaker, membranes were washed, ECL substrate (Pierce) was added, and membranes were exposed for 300 s for signal detection on an Azure c300 imaging system (Azure Biosystems).

COMPUTATIONAL AND QUANTITATIVE METHODS

Most plots were generated in Jupyter notebooks, and an index of which plots appear in what notebooks can be found in https://matsen.group/gcreplay/key-files/#manuscript-figures. This pipeline hosted at https://github.com/matsengrp/gcreplay/ and these notebooks form a reproducible artifact describing the analysis.

Sequencing data pipeline

BCR sequencing data were processed using a custom Nextflow v24.04.3.5916 pipeline to reconstruct clonal relationships within germinal centers. The pipeline takes, as input, raw MiSeq paired-end sequencing reads, which were first trimmed to remove the first three bases using fastx_trimmer,⁹² and subsequently combined using pandaseq.⁹³ The resulting sequences were demultiplexed based on plate and well barcodes using the fastx_toolkit,⁷⁸ producing individual files for each 96-well plate. Heavy and light chain sequences were then separated by identifying conserved motifs using cutadapt⁹⁴ with a 20% error allowance. To reduce noise and focus on biologically relevant sequences, each well's heavy and light chain sequences were collapsed to unique sequences, and low-abundance BCRs (fewer than 5 reads by default) were pruned to generate ranked files.

The filtered BCR light and heavy chain sequences were then merged across all wells, maintaining identifiers of their origins, and subsequently annotated using partis,⁹⁵ primarily to identify V(D)J gene segments, and somatic mutations compared to the naive sequence. The annotated BCR's were then processed to generate comprehensive datasets containing paired heavy and light chain information for each germinal center. With this, the workflow then performs downstream phylogenetic inference with GCtree (described next), and all other downstream analysis on the resulting GC trees.

Phylogenetic inference and tree-based analysis

We inferred phylogenies on clonal families using GCtree v4.3.0. GCtree uses PHYLIP's dnapars utility to infer a collection of maximum parsimony (MP) phylogenetic trees on observed sequences. GCtree then uses a data structure called a history sDAG to expand the collection of MP trees found by dnapars, by swapping parsimony-optimal substructures between them.³⁰ Next, GCtree ranks the resulting collection of maximally parsimonious trees. For our analysis we configured the ranking to first minimize the number of mutations reverting to the naïve ancestral state, then optimize a branching process likelihood, then a context-based Poisson likelihood, and finally minimize the number of unique sequences in the trees to arbitrarily break any remaining ties. The branching process likelihood uses observed abundances of genotypes to implement the intuition that sequences observed with higher abundance should have more mutant offspring. Trees which follow this intuition have greater branching process likelihood.²⁵ The context-based Poisson likelihood measures how inferred mutations in the tree agree with context-dependent mutation rates and targeting probabilities of an S5F model.^23,30 Dnapars infers ancestral states, marking sites for which multiple ancestral states are possible under maximum parsimony. GCtree attempts to enumerate all possible maximally parsimonious ancestral states for ranking. If this is not possible for a topology found by dnapars, a single maximally parsimonious ancestral reconstruction is chosen.

GC selection metrics

NDS was calculated by splitting each GC into root-clades (branches that stem directly from the unmutated ancestor) then dividing the number of cells in the largest lineage by the total sequenced cells in that GC. REI is calculated as follows: For each node X in a phylogeny, the REI represents the sum of the number of descendants of node X weighted according to their mutational distance from node X using a decay factor τ = 0.5, such that cells at 0, 1, 2, … nucleotide distance from node X are weighted 1, 0.5, 0.25, …; the sum of weighted descendants is then divided by the total number of cells in the GC. A phylogeny in which all cells have the same sequence therefore has an REI of 1.0. This metric relies on the assumption is that GC B cells cease SHM when undergoing rapid clonal burst-type expansion.^42,96 The NDS and REI scores are computed on these trees using utilities that are part of our computational pipeline stored on GitHub (https://github.com/matsengrp/gcreplay/blob/main/analysis/NDS-LB.ipynb).

Calculation of intrinsic mutability

BCR libraries were processed utilizing the pRESTO suite tools.⁹⁷ We adhered to the Illumina MiSeq 2×250 BCR mRNA pipeline. Initially, low-quality reads were filtered out, followed by primer masking and unique molecular identifier (UMI) quantification to correct sequencing errors and PCR amplification biases. Sequences were paired, and consensus sequences were constructed for R1 and R2 reads. These consensus sequences were further paired and assembled into contiguous sequences. Finally, identical sequences were collapsed and quantified. Sequences represented by at least two reads were used for downstream analysis.

BLAST was used to identify sequences with full-length matches for the regions around the CRISPR/Cas9-induced indels that defined the passenger alleles using a 90% identity threshold. The corresponding reads were then subject to a series of filters: the identifying sequence could only be found once in the read, the read could only have one additional indel, and the read could have at most 9 mutations and at most 9 N positions. As is typical in the field^23,98 the SHM model was described in terms of a “substitution probability,” namely the probability of the new base conditioned on there being a substitution, and a per-site mutability estimate of having a mutation at each position.

In order to combine information across multiple runs for each of the heavy and light chains, we used a Poisson modeling strategy that allowed for the read depth and the overall mutation load to differ between experiments, as well as the mutation rate to differ between sites (further details are provided in https://github.com/matsengrp/gcreplay/blob/main/passenger/igh_passenger_aggregate.ipynb). The per-site rates are parameterized using softmax, resulting in a collection of rates across the sites that sum to 1. A small number of Igk positions that had > 0.001% Ns (Igk nucleotides 295, 306, 307, 319, 321), indicative of potential sequencing errors, were excluded and replaced by the value obtained using from the five-mer model.²³

Affinity fitness landscape modelling

The minimal mathematical model for the distribution of affinities over time was developed as follows: we denote the log₁₀ affinity change with respect to naive as $x$ and specify an evolution equation for the probability density of affinities $p(x,t)$ at each time $t$. There are two key parameter functions that influence the time evolution of $p(x,t)$ in our model. First, a function $q(x,y)$ represents the mutational flux (mutation rate per unit $x$ and $y$) from affinity state $x$ to affinity state $y$, and can be specified (up to a multiplicative scale) by weighting the distribution of log₁₀-affinity effects measured in DMS by the mutabilities of each mutation measured from the passenger mouse experiment. Second, an affinity fitness landscape $f(x)$ specifies the intrinsic fitness for a cell with affinity $x$, and is an unknown function of key interest, as it can be used to predict GC competition between cells of different affinities. The interpretation of this fitness is competitive, so that the Malthusian growth rate of a cell with affinity $x$ at time $t$ is given by $f(x)-\bar{f}(t)$, where $\bar{f}(t)$ is the mean fitness in the population at time $t$. Because the affinity distribution evolves through time, $\bar{f}(t)$ is expected to increase with time, so that a cell with a given affinity becomes less competitive as its competitors tend to improve in affinity. Assuming a large population, the deterministic evolution equation is

$$\frac{\partial }{\partial \mathrm{t}}\mathrm{p}(x,t)=(f(x)-\bar{f}(t))\mathrm{p}(x,t)+{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}(q(y,x)p(y,t)-q(x,y)p(x,t))\mathrm{d}\mathrm{y},$$ (1)

where the first term models birth and death, and the second term models mutation into and out of affinity state $x$.⁴⁵ Because the replay mouse has monoclonal naïve cells starting GCs, we have the initial condition $p\left(x,t_0\right)=\delta (x)$, i.e. a Dirac mass at initial time $t_0$. Note that this equation is nonlinear due to the dependence of the mean fitness $\bar{f}$ on $p$, via $\bar{f}(t)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}f(x)p(x,t)\mathrm{d}x$. Also note that this is an equilibrium population size model, which can be seen by integrating both sides of the evolution equation (1) over $x$, which shows the time derivative of the normalization of $p$ vanishes identically.

We now detail how we solve the evolution equation, fitting it to the time-course experiment data at time points 5, 8, 11, 14, 17, 20, and 70 dpi. We implement a custom Crank-Nicholson numerical PDE solver as a differentiable program⁹⁹ and use maximum likelihood estimation (MLE) to infer the parameters of the evolution equation that best fit the time-course data, chiefly the fitness landscape $f(x)$ which we represent nonparametrically as a smooth monotonic function. The time-course data $𝒟$ consists of a set of sampling times $t$ and a set of real-valued affinities $𝒳$ at each such time. The sample size of a sample $(t,𝒳)\in 𝒟$ is $\left|𝒳\right|$. The log-likelihood of $f(x)$ given the time-course data is

$$I(f)=\sum _{(t,𝒳)\in D\mathrm{X}\in 𝒳}\sum \mathrm{l}\mathrm{o}\mathrm{g}p(x,t).$$ (2)

This likelihood represents the likelihood of observing the time course data given a density of affinities through time $p(x,t)$. This $p(x,t)$, in turn, is derived deterministically by solving the PDE (1): although $f$ does not appear explicitly on the right-hand side of (2), $p$ is a functional of $f$. We perform MLE by backpropagating through the PDE solver to maximize the log-likelihood, using an entropic penalty to encourage the fitted mutational flux profile $q$ to match the empirical data from passenger mouse and DMS, and a spline penalty on $f$ to suppress high-frequency artifacts that aren’t supported by the data fit. More details are available in https://github.com/matsengrp/gcreplay/blob/main/analysis/affinity-fitness-response.ipynb.

Stochastic extinction calculation for survivorship bias effects

We now derive a master equation approach for the stochastic extinction probability $r_T(x,t)$ of a lineage with affinity state $x$ at time $t$ before sampling time $T$. This lineage undergoes a continuous-state birth-death-mutation process¹⁰⁰ according to birth rate $\lambda (x)=\mathrm{f}(x)-{\mathrm{f}}_0$, death rate $\mu (t)=\overline{\mathrm{f}}(t)-{\mathrm{f}}_0$, and mutation flux $\mathrm{q}(x,y)$ to affinity state $y$. We define reference fitness $f_0$ corresponding to millimolar affinity. Note that the expected growth rate is $\mathrm{f}(x)-\overline{\mathrm{f}}(t)$, matching the previous deterministic model. Whence the forward master equation is

$$\frac{\partial r_T(x,t)}{\partial t}=-(\lambda (x)+\mu (t)+Q(x))r_T(x,t)+\lambda (x)r_T(x,t{)}^2+\mu (t)+{\int }_{\mathrm{\infty }}^{\mathrm{\infty }}q(x,y)r_T(y,t)\mathrm{d}\mathrm{y},$$ (3)

where $Q(x)={\int }_{\mathrm{\infty }}^{\mathrm{\infty }}q(x,y)\mathrm{d}y$ is the total mutation intensity. Such a master equation can be derived by considering the probability of events (birth, death, mutation, or nothing) that can happen in a small time interval $\mathrm{\Delta }t$ (such that at most one event occurs), then evaluating ${\mathrm{r}}_{\mathrm{T}}(\mathrm{x},\mathrm{t}+\mathrm{\Delta }\mathrm{t})$ and taking $\mathrm{\Delta }t$ to be infinitesimal, yielding a partial differential equation. The first term corresponds to nothing happening; it is linear in the extinction probability because the lineage remains non-extinct after the infinitesimal time interval. The second term corresponds to a birth event in the infinitesimal time interval; it is quadratic in the extinction probability because both daughter lineages must independently go extinct for the parent lineage to go extinct. The third term corresponds to a death event, given simply as the instantaneous Poisson death rate because the lineage is then extinct. The integral in the last term describes a mutation event to any possible other affinity state; it is linear in the extinction probability at the alternative affinity state because the mutated lineage would then have to go extinct. A full derivation for a related problem can be found in Kuhnert et al. (2016)¹⁰¹ and a briefer derivation for a birth-death process can be found in Barido-Sottani et al. (2020).¹⁰² We solve the equation backward in time from final condition $r_T(x,T)=0$, again using our custom Crank-Nicholson solver.

Equipped with a numerical solution to this master equation, we compute the ancestral affinity distribution (the distribution conditioned to leave descendants at the sample time $T$) by weighting $p(x,t)$ by the probability of survival to time $T$ and renormalizing

$$\widetilde{p_T}(x,t)=\frac{\left(1-r_T(x,t)\right)p(x,t)}{{\int }_{\mathrm{\infty }}^{\mathrm{\infty }}\left(1-r_T(y,t)\right)p(y,t)}\mathrm{d}y.$$ (4)

We used this forward master equation approach to compute the probability $r_T(x,t)$ of stochastic extinction before sampling time $T=15\text{dpi}$ or $T=20\text{dpi}$.

Bayesian phylogenetic analysis

We performed Bayesian phylogenetic analysis using BEAST v1.10.4. Nucleotide sequences were analyzed under an HKY substitution model with a strict molecular clock and a constant coalescent demographic model. Markov chain Monte Carlo (MCMC) sampling was conducted for 25 million iterations, with trees sampled every 10,000 steps. After discarding the first 96% of samples as burn-in, the remaining 100 trees were used for the push-of-the-past analysis. The XML template file for the BEAST analysis can be found at https://github.com/matsengrp/gcreplay/blob/main/data/beast/beast_templates/constantsize_histlog.template.patch.

Other software

Flow cytometry data were analyzed using FlowJo v. 10. Plots and statistical analyses not included in Jupyter notebooks were generated using Graphpad Prism v. 10. Figures were edited for appearance using Adobe Illustrator.

Additional resources

Silver et al.¹⁰³ and Zuo et al.¹⁰⁴ are cited in the Figure S6 legend.

Supplementary Material

SUPPLEMENTAL INFORMATION

Supplemental information can be found online at https://doi.org/10.1016/j.cell.2026.05.013.

KEY RESOURCES TABLE.

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
Anti-CD16/32 (Fc block) (clone 2.4G2)	BD Biosciences	RRID: AB_394656
Anti-B220 BV785 (clone RA3-6B2)	Biolegend	RRID: AB_11218795
Anti-CD38 APC (clone 90)	Invitrogen	RRID: AB_469382
Anti-CD95 (Fas) Pe-Cy7 (clone Jo2)	BD Biosciences	RRID: AB_396768
Streptavidin BV421	Biolegend	Cat# 405226
Anti-Igκ PE (clone 187.1)	BD Biosciences	Cat# 559940; RRID:AB_397384
Streptavidin PE	Thermo Fisher Scientific	Cat# S866
Anti-TCRβ APC-eFluor780 (clone H57–597)	eBioscience	RRID: AB_1272173
Anti-c-Myc FITC (CYMC-45F)	Immunology Consultants Lab	Cat# CYMC-45F
Anti-CD35 Cy3 (clone 8C12)	In house	N/A
Anti-GFP	BioLegend	Cat# 902605; RRID: AB_2734671
TotalSeq™-C0307 anti-mouse Hashtag Antibody (1–16)	BioLegend	Various
Bacterial and virus strains
E. Coli	New England Biolabs	Cat# C3020K
Biological samples
Plasmodium Chabaudi	BEI Resources	Cat# MRA-741
Chemicals, peptides, and recombinant proteins
Imject Alum	Thermo Fisher Scientific	Cat# 77161
Alhydrogel adjuvant 2%	InvivoGen	Cat# vac-alu-250
Normal Chicken IgY (egg-derived)	Exalpha Biologicals	Cat# IgY-100
ACK lysing buffer	Thermo Fisher Scientific	Cat# A10492-01
Tween20	Sigma-Aldrich	Cat# P9416-50ML
Bovine Serum Albumin (BSA)	Sigma-Aldrich	Cat# A9647-500G
Fetal bovine serum (FBS)	Thermo Fisher Scientific	Cat# A3160401
Buffer TCL	Qiagen	Cat# 1031576
EDTA	Spectrum Laboratories	Cat# 40520000-3
Trizol LS	Thermo Fisher Scientific	Cat# 10296010
Beta mercaptoethanol	Thermo Fisher Scientific	Cat #21985023
ECL substrate	Pierce	N/A
Critical commercial assays
Zeba desalting column purification	Thermo Fisher Scientific	Cat# 89883
Protein-G Sepharose	Fisher Scientific	Cat# 45-000-116
Ni-INDIGO Agarose Beads	PureCube	Cat# 75105
MACS Cell Separation Column LS	Miltenyi Biotec	Cat# 130-042-401
CD43 (Ly-48) microbeads, mouse	Miltenyi Biotec	Cat# 130-049-801
EZ-Link Sulfo-NHS-LC-LC-Biotin	Thermo Fisher Scientific	Cat# 21338
CD19 microbeads, mouse	Miltenyi Biotec	Cat# 130-121-301
RNAClean XP	Beckman Coulter	Cat# A63987
CaptureSelect CH1-XL Affinity Matrix	Thermo Fisher Scientific	Cat# 1943462005
High Precision Streptavidin (SAX) Biosensors	Sartorius	Cat# 18-5117
Biosensor/Anti-Human Fab-CH1 2nd Generation (FAB2G)	ForteBio	Cat# 18-5125
10x Chromium Next Gem Single Cell 5′ Reagent kit v3	10× Genomics	Cat# CG000734
NEBNext Immune Sequencing Kit (Mouse)	New England Biolabs	Cat# E6330S
Experimental models: Cell lines
Expi293F Cells	ThermoFisher Scientific	Cat# A14527
Experimental models: Organisms/strains
Mouse: C57BL6/J	The Jackson Laboratory	JAX: 000664
Mouse: Cd23-Cre	M. Busslinger (IMP Vienna)	N/A
Mouse: Bcl6fl/fl	A Dent (Indiana U.) (Hollister et al.105)	N/A
Mouse: UBC-PA-GFP-transgenic	Victora et al.24	JAX: 022486
Mouse: Igh2.1	This paper	N/A
Mouse: Igk2.1	This paper	N/A
Mouse: Igh2.1*	This paper	N/A
Mouse: Igk2.1*	This paper	N/A
Saccharomyces cerevisiae strain AWY101	Wentz and Shusta79	Cat# AWY101
Oligonucleotides
CRISPR guide-RNA targeting the Igh ^2.1 allele #1: CAGGGGCAGCCTGAGCTATG	Integrated DNA technologies	N/A
CRISPR guide-RNA targeting the Igh ^2.1 allele #2: GGAGCCGGCTGAGAGAAGTT	Integrated DNA technologies	N/A
CRISPR guide-RNA targeting the Igk ^2.1 allele #1: CTGTGGTGGACGTTCGGTGG	Integrated DNA technologies	N/A
CRISPR guide-RNA targeting the Igk ^2.1 allele #2: AAGACACAGGTTTTCATGTT	Integrated DNA technologies	N/A
CRISPR guide-RNA targeting the Igk ^2.1* allele: TCTTTGTATACATGTTGCTG	Integrated DNA technologies	N/A
CRISPR guide-RNA targeting the Igh ^2.1* allele: TGCAACCGGTGTACATTCCG	Integrated DNA technologies	N/A
Igh ^2.1 leader forward primer: AGCGACGGGAGTTCACAGACTGCAACCGGTGTACATTCC	Integrated DNA technologies	N/A
Igk ^2.1 leader forward primer: AGCGACGGGA GTTCACAGGTATACATGTTGCTGTGGTTGTCTG	Integrated DNA technologies	N/A
Recombinant DNA
pETcon yeast display expression vector	Starr et al.77	N/A
pEGFP-C1-PRKAA1	Addgene	#30305
Software and algorithms
Prism	Graphpad	RRID: SCR_002798
FlowJo	FlowJo LLC	RRID: SCR_008520
Excel	Microsoft	RRID: SCR_016137
Illustrator	Adobe	RRID: SCR_010279
sAbPred	Dunbar et al.85	N/A
Claude	Anthropic	N/A
ChatGPT	OpenAI	N/A
ColabFold	Mirdita et al.86	N/A
Coot 0.9.4	Casahal et al.87	N/A
Rosetta Relax	Frenz et al.88	N/A
Phenix real_space_refine	Afonine et al.89	N/A
EMRinger	Barad et al.90	N/A
MolProbity	Williams et al.91	N/A
UCSF Chimera	Pettersen et al.84	N/A
pRESTO suite tools	Vander et al.97	N/A
Plots and analysis	Github	https://matsen.group/gcreplay/key-files/#manuscript-figures
Custom Code and BCR Data	Github	https://github.com/matsengrp/gcreplay/
DMS TiteSeq CGG Binding Affinity	Github	https://github.com/jbloomlab/Ab-CGGnaive_DMS/blob/main/Titeseq-modeling.ipynb
GCtree	DeWitt et al.25	N/A
BEAST v1.10.4 – Bayesian Phylogenetic Analysis	Github	https://github.com/matsengrp/gcreplay/blob/main/data/beast/beast_templates/constantsize_histlog.template.patch
Other
96-Well Half Area Microplates	Greiner Bio-One	Cat# 675061
Prepared Microtubes, Z-Gel	Sarstedt	Cat# 41.1378.005
96-Well PCR plates	USA Scientific	Cat# 1402-9596

Highlights.

• GCs yield predictable phenotypic outcomes despite variable phylogenetic trajectories

• Presence of low-affinity B cells in GCs is not evidence of permissive selection

• Imperfect but persistent selection of higher-affinity B cells drives affinity maturation

• We infer a full genotype-phenotype-fitness landscape for GC evolution

Data and code availability

All data and code, including a reproducible analysis pipeline, are openly available at the following repository: https://github.com/matsengrp/gcreplay. Jupyter notebooks for the figures can be found at the following repository: https://matsen.group/gcreplay/key-files/#manuscript-figures. Cryo-EM maps and atomic coordinates of Fab 2.1 in complex with IgY are deposited at the Electron Microscopy Data Bank (EMDB) and the Protein Data Bank (PDB) under accession codes EMD-70353 and 9ODB, respectively.