The diversity of influenza poses an ongoing public health challenge as vaccination and natural infection typically elicit immune responses that are highly strain-specific, and hence quickly lose efficacy as the virus evolves (Kubo and Miyauchi, 2020; Angeletti and Yewdell, 2018; Neher and Bedford, 2015; Dugan et al., 2020). This limited efficacy has garnered substantial interest in vaccination strategies that elicit broadly neutralizing antibodies (bnAbs) that neutralize diverse strains of influenza (Corti et al., 2017; Angeletti and Yewdell, 2018). Over the past two decades, there has been considerable effort to isolate and characterize anti-influenza bnAbs (Whittle et al., 2011; Throsby et al., 2008; Corti et al., 2011; Dreyfus et al., 2012). These bnAbs target various conserved epitopes on the hemagglutinin (HA) influenza surface glycoprotein, including the receptor binding site (RBS) (Whittle et al., 2011), the stem or stalk domain (Corti et al., 2011; Dreyfus et al., 2012; Ekiert et al., 2009), the lateral patch (Raymond et al., 2018), and the membrane-proximal anchor site (Guthmiller et al., 2022). BnAbs also vary in germline gene usage and breadth, with some binding several strains within an HA subtype and others binding nearly all characterized influenza strains (Corti et al., 2017).

Despite the immense body of work on influenza bnAbs, we still do not fully understand the evolutionary processes through which they mature (Jiang et al., 2013; Horns et al., 2019; Sangesland and Lingwood, 2021). Our strategies to elicit them therefore remain limited. It is clear, however, that distinct antibodies with diverse sequences can target the same HA epitope and evolve broad reactivity (Schmidt et al., 2013; Dreyfus et al., 2012; Ekiert et al., 2009; Schmidt et al., 2015a; Wu et al., 2020a). This redundancy suggests that there are many possible evolutionary pathways to influenza bnAbs. Still, the relatively low frequencies at which they are observed in human repertoires following vaccination suggest that there are factors constraining their maturation that we do not yet fully appreciate (Wu et al., 2017; Bajic et al., 2019; Horns et al., 2020; Abbott et al., 2018; Andrews et al., 2015).

High-throughput mutagenesis approaches are widely used as a tool to understand key properties shaping the evolution of numerous proteins (Starr et al., 2017; Miton and Tokuriki, 2016; Bank et al., 2015; Phillips et al., 2018). This work has revealed that new mutations can differentially impact distinct protein functions and often interact non-additively (i.e., epistatically), potentially constraining the order in which they can occur (Weinreich et al., 2006; Gong et al., 2013; Sailer and Harms, 2017). For antibodies, high-throughput mutagenesis studies have largely been limited to examining the effects of single mutations, either through saturating mutagenesis (e.g., deep mutational scanning) of relatively small regions (Wu et al., 2017; Adams et al., 2016; Forsyth et al., 2013) or through random mutagenesis (e.g., error-prone PCR) (Li et al., 2018; Amon et al., 2020; Bowers et al., 2018). These methods examine the local mutational landscape of a particular antibody, or in other words, how single mutations can change affinity or breadth. The advantage of these methods is that the sequences analyzed are relatively unbiased, particularly for saturating mutagenesis, and thus one can surmise why particular mutations occurred naturally. For example, this approach identified many single amino acid substitutions in the anti-influenza bnAb C05 that improve affinity to different subsets of strains but typically reduce breadth (Wu et al., 2017).

A key limitation of saturating mutagenesis approaches is that they cannot probe how epistatic interactions between mutations might constrain antibody evolutionary trajectories, which typically involve multiple mutations (Victora and Nussenzweig, 2012). Because antibodies acquire numerous mutations and experience fluctuating selection pressures on short timescales (Victora and Nussenzweig, 2012; Smith et al., 2004), they are necessarily distinct from other proteins for which epistasis has been studied. Moreover, they bind antigens through disordered loops, in contrast to the structured active sites of most enzymes, and they are relatively tolerant to mutations (Braden et al., 1998; Burks et al., 1997; Chen et al., 1999; Klein et al., 2013; Corti and Lanzavecchia, 2013). Further, the evolutionary dynamics of affinity maturation are defined by discrete rounds of mutation and selection compared to the more continuous processes most proteins are subject to, and thus mutations that occur concurrently are selected based on their collective rather than individual effects (Victora and Nussenzweig, 2012; Unniraman and Schatz, 2007). For these reasons, the evolutionary constraints on antibodies may be unique.

The few studies that have examined epistasis in antibodies indicate that it is a key determinant of affinity (Schmidt et al., 2013; Phillips et al., 2021; Pappas et al., 2014; Adams et al., 2019). For example, multiple studies have identified mutations that interact synergistically to bind an antigen (Schmidt et al., 2013; Phillips et al., 2021; Pappas et al., 2014). Still, most of this work has focused on interactions between a small subset of mutations (Schmidt et al., 2013; Xu et al., 2015). Addressing the prevalence and general importance of epistasis in shaping antibody evolution will require more comprehensive combinatorial mutagenesis strategies that sample combinations of mutations present in each somatic antibody sequence (Phillips et al., 2021). These combinatorial strategies, however, do not capture epistasis with other mutations that could have occurred in alternative evolutionary pathways, which will require integrating combinatorial mutagenesis with the saturating mutagenesis methods described above.

In previous work, we systematically mapped the relationship between antibody sequence and affinity (the sequence-affinity landscape) across mutational landscapes relevant for the somatic evolution of two stem-targeting bnAbs of varying breadth, CR6261 and CR9114 (Phillips et al., 2021). We found that affinity was determined by nonadditive interactions between mutations, and that such epistasis could both constrain and potentiate the acquisition of breadth. Notably, the nature of this epistasis varied considerably between the two bnAbs. For CR6261, epistatic interactions were similar for binding distinct group 1 strains, thus evolutionary pathways could simultaneously improve in affinity to divergent antigens. For CR9114, increasingly divergent antigens required additional epistatically interacting mutations such that evolutionary pathways were constrained to improve in affinity to one antigen at a time. The distinct topologies of these sequence-affinity landscapes result from differences between the various antigens and the mutations that are required for binding.

Although anti-stem bnAbs are among the broadest influenza bnAbs characterized, they are a small and biased subset of the influenza antibody response. Despite the presence of anti-stem antibodies in human sera (Yassine et al., 2018) and the ability to drive viral escape mutants in vitro (Wu et al., 2020b), the stem is minimally mutated amongst circulating viral strains and does not appear to be evolving in response to these antibodies, possibly due to the high concentration of antibody required for protection (Ellebedy, 2018; Han et al., 2021) and immune pressure. In contrast, due to the small size of the RBS pocket, RBS-directed bnAbs frequently make contacts with immunodominant epitopes surrounding the pocket that have substantial antigenic variation (Whittle et al., 2011; Schmidt et al., 2015b; Lee et al., 2014; Krause et al., 2011; Guthmiller et al., 2021). Although RBS-directed bnAbs have a relatively narrower reactivity profile compared to anti-stem bnAbs, they are potently neutralizing, do not require effector functions for potent in vivo protection as do anti-stem bnAbs (Corti et al., 2011; DiLillo et al., 2014), and have evolved broad recognition despite the accumulation of antibody escape mutations in the periphery of the RBS. Further, RBS-directed bnAbs can mature from diverse germline V_H and V_L genes (Schmidt et al., 2015b), suggesting that there are likely numerous evolutionary pathways to target this epitope. Thus, to understand more generally how epistasis constrains bnAb evolution, here we consider RBS-directed bnAbs as they target an entirely different epitope under distinct immune selection pressures.

Specifically, we examine the influence of epistasis on the evolution of a well-characterized RBS-directed bnAb, CH65, which binds and neutralizes diverse H1 strains (Whittle et al., 2011; Schmidt et al., 2013). CH65 was isolated from a donor 7 days post-vaccination. The unmutated common ancestor (UCA) and an early intermediate (I-2) have moderate affinity for a subset of H1 strains that circulated early in the donor’s lifetime (Whittle et al., 2011; Schmidt et al., 2015a). The affinity-matured CH65 has 18 mutations throughout the light (V_L) and heavy (V_H) variable regions, which improve affinity to strains that circulated early in the donor’s life and confer affinity to antigenically drifted strains (Schmidt et al., 2013; Xu et al., 2015). Thus, CH65 evolved to acquire affinity to emerging strains without compromising affinity for previously circulating strains.

The structural changes upon affinity maturation of CH65 and clonally related antibodies have been extensively characterized (Whittle et al., 2011; Schmidt et al., 2013; Schmidt et al., 2015a). This work showed that CH65 primarily matures by preconfiguring the HCDR3 loop into its binding conformation, thereby minimizing the conformational entropic cost of binding (Schmidt et al., 2013). Importantly, none of the 18 somatic mutations are in the HCDR3; rather, key mutations in HCDR1, HCDR2, and LCDR1 result in contacts that stabilize the HCDR3 loop in its binding-compatible conformation (Schmidt et al., 2013; Xu et al., 2015). This structural characterization, in addition to molecular dynamics simulations, identified specific mutations that are critical for breadth, including some that interact synergistically to stabilize the HCDR3 loop (Schmidt et al., 2013; Xu et al., 2015). In theory, such epistasis could constrain bnAb evolution by requiring multiple mutations to confer a selective advantage, or alternatively, it could compensate for the deleterious effects of other mutations and favor selection of bnAbs.

Given that many mutations in CH65 are important for imparting affinity to HA, including those at distant sites (Schmidt et al., 2013), we hypothesized that there are many sets of epistatic mutations in CH65 not previously identified, particularly because long-range epistatic interactions are difficult to predict from structural analyses alone. In contrast to the anti-stem bnAbs described above (Dreyfus et al., 2012; Lingwood et al., 2012), CH65 engages HA through both light and heavy chain contacts and requires mutations in both chains to bind divergent antigens (Schmidt et al., 2013; Xu et al., 2015). Thus, it is likely that mutations interact epistatically both within and between the heavy and light chains. Despite the potential importance of these interactions in shaping the evolution of CH65, and the numerous other antibodies that engage antigens using both chains (Corti et al., 2011; Schmidt et al., 2015a; Xiao et al., 2019; Ekiert and Wilson, 2012), characterizations of inter-chain epistasis have so far been limited to small sets of a few mutations (Schmidt et al., 2013; Xu et al., 2015). Although these smaller datasets have revealed some important inter-chain epistatic interactions, they measure a subset of interactions selected based on structural data, and thus we still do not know the magnitude or prevalence of this epistasis and hence how important it is in shaping antibody evolution.

Here, to elucidate the role of epistasis (both inter- and intra-chain) in shaping the evolution of an RBS antibody, we systematically characterize the CH65 sequence-affinity landscape. Specifically, we generate a combinatorially complete antibody library containing all possible evolutionary intermediates between the UCA and the mature somatic sequence (N=2¹⁶ = 65,536) and measure affinity to three antigenically distinct H1 strains to assess how epistasis can shape evolutionary pathways, leading to varying levels of breadth. We find that strong high-order epistasis constrains maturation pathways to bind antigenically distinct antigens. Although fewer epistatic mutations are needed to bind an antigen similar to that bound by the UCA, these sets of mutations overlap with those required to bind a more divergent antigen. Collectively, these landscapes provide mechanistic insight into how affinity maturation responds to an evolving epitope and how exposure history can influence future immune responses. In combination with our previous work on anti-stem bnAbs (Phillips et al., 2021), this work shows how epistasis can differentially impact the evolutionary trajectories of bnAbs of varying breadth, epitope, and variable chain gene usage.

To comprehensively examine how epistasis may have shaped the evolution of CH65, we generated a combinatorially complete antibody library comprising all possible evolutionary intermediates from the UCA to CH65. This library contains all possible combinations of mutations present in both the variable heavy and light chains of CH65, less two mutations (Q1E and S75A in V_H) distant from the paratope that do not significantly impact binding affinity (Figure 1A, Figure 1—figure supplement 1) or physically interact with other residues. Removing these mutations results in a final library size of 2¹⁶, which is within the throughput limit of our methods.

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Figure 1—source data 1

CH65 library expression and -logK_D to MA90, MA90-G189E, and SI06.

Biological duplicates, mean, and standard error are reported.

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Figure 1—source data 2

Isogenic flow cytometry measurements of -logK_D and expression for select CH65 variants.

Mean and standard error for -logK_D and expression are reported for biological duplicates, alongside the corresponding Tite-Seq -logK_D and expression measurements (as in Figure 1—source data 1).

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To profile the breadth of the corresponding antibody library, we first transform this combinatorial plasmid library into yeast for antibody surface display in a single-chain variable fragment (scFv) format (Boder and Wittrup, 1997). We then use Tite-Seq (Adams et al., 2016), a high-throughput method that couples flow cytometry with sequencing, to measure equilibrium binding affinities to three H1 strains bound by CH65. We chose these strains to sample varying levels of antigenic change (Smith et al., 2004; Bedford et al., 2014): they include a strain that circulated early in the donor’s lifetime (A/Massachusetts/1/1990, 'MA90') and a strain that circulated 16 years later (A/Solomon Islands/3/2006, 'SI06') (Schmidt et al., 2013). Additionally, because affinity maturation has been shown to confer binding to antigens that escape less mutated members of the same lineage (Muecksch et al., 2021), we drove viral escape of MA90 in vitro using the UCA and found that CH65 could bind to the resulting strain (A/Massachusetts/1/1990 G189E, 'MA90-G189E') that escapes the UCA. We use the MA90-G189E antigen to profile incremental antigenic change from MA90 (one direct escape mutation), whereas SI06 represents more substantial antigenic change during natural evolution, including loss of K133a and the mutation E156G in the RBS.

For each of these three antigens, we used Tite-Seq to measure equilibrium binding affinities for all 2¹⁶ variants in biological duplicates (Figure 1—figure supplement 2). We log-transform the binding affinities and report -logK_D, which is proportional to the free energy change of binding (and is thus expected to combine additively) (Wells, 1990; Olson et al., 2014). For each antigen, the Tite-Seq -logK_D correlate well between biological replicates (r ~ 0.98 for all antigens; Figure 1—figure supplement 3A) and accurately reflect isogenic measurements made by flow cytometry (r = 0.97; Figure 1—figure supplement 3B), as well as recombinant IgG affinity measurements made by biolayer interferometry (r = 0.86; Figure 1—figure supplement 3C).

Mutational effects on CH65 affinity and breadth

To understand how specific mutations shape the sequence-affinity landscape, we computed the change in affinity resulting from each of the 16 mutations on all 2¹⁵ genetic backgrounds at the other 15 sites. This analysis reveals that several mutations improve affinity to MA90 and MA90-G189E (e.g., Y35N, Y48C, D49Y (V_L) and G31D, Y33H, H35N, N52H (V_H)), and some of these distributions are multimodal, indicating that their effect on affinity depends on the presence of other mutations (Figure 2A). Consistent with this, some mutations improve affinity to MA90 and/or MA90-G189E on the UCA or I-2 backgrounds (e.g., Y35N (V_L) and Y33H, H35N (V_H)) and others on the CH65 background (Y48C, D49Y (V_L)). For SI06, N52H dramatically improves affinity and most variants lacking this mutation do not have detectable affinity. Thus, several mutations (e.g., Y35N (V_L)) improve affinity to SI06 in the I-2, but not the UCA, background (Figure 2A). In general, the effects of these mutations correlate between the different antigens, with mutations affecting affinity more substantially for MA90-G189E and SI06 compared to MA90 (Figure 2B).

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To assess which mutations confer affinity to a particular antigen, we computed the frequency of each mutation amongst binding variants in the library. Consistent with the landscapes in Figure 1B, we observe that the mutations enriched amongst binders form a hierarchical pattern between the antigens (Figure 2C). For example, a few mutations are enriched (≥55% frequency) amongst variants with nanomolar affinity for MA90 (e.g., Y35N, D49Y (V_L) and Y33H, N52H (V_H)), a few additional mutations are enriched amongst MA90-G189E binders (e.g., S29R (V_L) and G31D, H35N, R87K (V_H)), and still additional mutations are enriched amongst SI06 binders (e.g., N26D, Y48C, V98I (V_L) and M34I, R85G (V_H)) (Figure 2D). Thus, except for Y35N (V_L), which is interestingly depleted amongst SI06 binders (Figure 2—figure supplement 1), the mutations that enhance affinity to the three antigens form a hierarchical pattern.

We next characterized how epistasis between these mutations might impact affinity and result in this hierarchical pattern of breadth. To this end, we fit our measured -logK_D to a standard biochemical model of epistasis (Sailer and Harms, 2017), which is a linear model defined as the sum of single mutational effects and epistatic terms up to a specified order (see 'Materials and methods'). Using a cross-validation approach, we find that the optimal order model for affinity is fourth-order for MA90 and fifth-order for MA90-G189E and SI06, and we report coefficients at each order from these best-fitting models (Figure 3A). The magnitude and sign of these coefficients correspond to effects on -logK_D: for example, a second-order term of +1 means that two mutations occurring together improve -logK_D by 1 unit, beyond the sum of their first-order effects. For all three antigens, we find widespread epistasis between mutations in the same chain and between mutations in different chains, with many epistatic terms exceeding first-order effects in magnitude (Figure 3). In contrast to our previous work on variable heavy-chain-only antibody landscapes (Phillips et al., 2021), we find many strong epistatic interactions between mutations that are too distant to physically interact (Figure 3—figure supplements 1–4).

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Figure 3—source data 1

Interaction model coefficients for CH65.

Coefficients are reported for each antigen, with standard errors, p-values, and 95% confidence intervals.

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Structural and biophysical basis of epistasis in CH65

Because there are substantial long-range epistatic interactions, our combinatorial approach identifies numerous interactions not previously known, in addition to confirming the few interactions characterized in earlier work (e.g., Y48C and D49Y (V_L) have strong synergistic epistasis) (Schmidt et al., 2013; Xu et al., 2015). Here, we find strong epistasis between the I-2 mutations (G31D, M34I, N52H (V_H)), neighboring mutations (Y33H, H35N (V_H)), mutations known to stabilize light chain contacts (Y48C, D49Y) (Schmidt et al., 2013), as well as an uncharacterized light chain mutation (Y35N). When we examine the structural context of this epistasis, we find that mutations with strong first-order and epistatic effects often make contact with either HA or with the HCDR3 that engages the RBS (Figure 3B, Figure 3—figure supplement 5). This suggests that the effects of these mutations are either mediated through the contacts that they make with HA or through affecting the HCDR3 loop conformation. These mutations interact epistatically for each of the three antigens, though the magnitude of epistasis is higher for SI06 (explaining ~34% of the variance in K_D, relative to ~24% for MA90, and ~25% for MA90-G189E, see Figure 3—figure supplement 6).

Importantly, these epistatic interactions are essential for the acquisition of affinity to both MA90-G189E and SI06. To investigate the molecular details of this epistasis, we compared the previously determined crystal structures of the unbound UCA, I-2, CH65, and CH65 bound to SI06 (Whittle et al., 2011; Schmidt et al., 2013; Lee et al., 2015), as well as newly determined crystal structures of the unbound UCA with Y35N (V_L) and I-2 with Y35N (V_L) and H35N (V_H). Additionally, we produced several variants as recombinant IgG to assay the binding kinetics by biolayer interferometry. To mimic the Tite-Seq system, IgG was bound to biosensors and assayed for binding to full-length trimeric HA (Figure 4—figure supplements 2–4). Here, we focus on binding kinetics of minimally mutated variants that confer affinity to each antigen but binding of 12 variants was assayed to all three antigens at varying temperatures (Figure 4—figure supplement 5).

The I-2 intermediate (which contains G31D, M34I, N52H (V_H)) is amongst the least-mutated variants that binds MA90-G189E (Figure 1B). The N52H mutation, which substantially improves affinity to MA90-G189E (Figure 4A), would potentially clash with one of the binding-incompatible HCDR3 conformations observed in crystal structures of the UCA and I-2; thus, this mutation may increase the occupancy of the binding-compatible HCDR3 conformation (Figure 4—figure supplement 1A). In the bound state, N52H π-stacks with Y33H and hydrogen bonds with G31D (Figure 4B and C, Figure 4—figure supplement 1B). Consequently, N52H and G31D, which together provide high affinity for MA90-G189E (Figure 4A), form a network of interactions between HCDR1, HCDR2, and the 150-loop of HA to stabilize the binding interaction (Figure 4C). Thus, while N52H alone confers affinity to MA90-G189E, G31D and M34I (I-2) reduce the dissociation rate by ~3.5–5-fold to improve affinity (Figure 4C, Figure 4—figure supplement 5). Notably, these interactions are distant (~15–20 Å) from the residue conferring viral escape, precluding any direct interaction (Figure 4C). Though these mutations are also important for affinity to the antigenically drifted SI06, they are insufficient to confer appreciable affinity in the absence of other epistatic mutations (Figure 4D, top).

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Figure 4—source data 1

Binding kinetics for selected antibody variants determined by biolayer interferometry.

Association rates, dissociation rates, and dissociation constants are reported for 12 antibody variants at multiple temperatures against MA90, MA90-G189E, and SI06. Standard errors for each parameter, χ², and R² values are reported from global curve fitting using the bivalent analyte model.

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Figure 4—source data 2

X-ray data collection and refinement statistics for unbound Fabs.

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In examining the minimally mutated variants that can bind SI06, we find that Y35N in the light chain and H35N in the heavy chain interact synergistically with the I-2 mutations (G31D, M34I, N52H) to confer affinity to SI06 (Figure 4D, bottom). Thus, the hierarchical sets of mutations that confer broad reactivity to these antigens (Figure 2D) do so through epistasis. In particular, the germline residue Y35 in the light chain framework (FWR) 2 is part of a cluster of aromatic residues at the V_H-V_L interface and makes π-stacking, methionine–aromatic, and hydrogen bonding interactions between LFWR2 and LCDR3, HCDR3, and HFWR4 (Figure 4E). The somatic mutation Y35N effectively removes these interactions with the HCDR3. Although the loss of the aromatic moiety from tyrosine to asparagine likely has a destabilizing effect, we attribute the observed changes in affinity to the loss of hydrogen bonding between LFWR2 and HCDR3; this is in part because the lineage member CH67, which has similarly broad reactivity, acquires a Y35F mutation upon affinity maturation that is only a removal of a hydroxyl group, preventing the ability to form hydrogen bonding interactions through the side chain (Schmidt et al., 2013). Similarly, H35N removes a methionine–aromatic interaction, known to have a stabilizing effect in proteins (Valley et al., 2012), between the HFWR2 and HCDR3 (Figure 4E). Addition of Y35N and H35N into the UCA background did not confer affinity to SI06 (Figure 4D and E). However, the addition of H35N into the I-2 background produced weak but detectable affinity with an association rate that was improved upon addition of Y35N (Figure 4D and E, Figure 4—figure supplement 6). Notably, while Y35N confers affinity to SI06 for variants with few somatic mutations, the magnitude of this effect diminishes as the number of mutations increases. Indeed, Y35N is depleted amongst the highest affinity variants (Figure 2C, Figure 2—figure supplement 1) and in the context of a mutated background decreased the association rate and overall affinity (Figure 4E), suggesting that Y35N, which removes inter-chain contacts, is likely only beneficial during early rounds of affinity maturation.

Previous studies on this lineage (Schmidt et al., 2013; Xu et al., 2015) showed that HCDR3 rigidification contributed to high-affinity binding to SI06: crystal structures of the unbound, affinity-matured Fabs had the same HCDR3 configurations as those in the antigen-bound state; the UCA and I-2, however, were either disordered or constrained, due to crystal packing, in a binding-incompatible state. To determine whether the mutations Y35N and H35N could stabilize a binding-compatible HCDR3 conformation, we determined X-ray crystal structures of unbound Fabs containing Y35N in the UCA background or Y35N and H35N in the I-2 background and compared them to previously determined structures (Figure 4—figure supplement 1C). These variants were insufficient to rigidify the HCDR3 as observed by the HCDR3 conformation and high B factors or the lack of density corresponding to the HCDR3 (Figure 4—figure supplement 1C). These data show that the I-2 mutations conferred affinity towards MA90-G189E by stabilizing the HCDR1 and HCDR2 with HA and were required for the addition of Y35N and H35N, which remove contacts with HCDR3, to confer affinity against SI06 without complete HCDR3 rigidification, revealing a biophysical mechanism through which inter-chain epistasis can determine broad affinity in a hierarchical manner.

Likelihood of mutational pathways to CH65

The extent of epistasis we observe suggests that the evolution of CH65 is contingent on mutations occurring in a particular order. Further, the hierarchical pattern of mutations that confer affinity to the different antigens indicates that the likelihood a mutation fixes depends on the selecting antigen. Because we measured affinities for a combinatorially complete library, we can infer the likelihood of all possible evolutionary trajectories from the UCA to CH65 (with and without the constraint of passing through the I-2 intermediate) in the context of various possible antigen selection scenarios (e.g., maturation to MA90 alone, or to SI06 alone, etc.). To this end, we implement a framework in which the probability of any mutational step is higher if -logK_D increases and lower if -logK_D decreases (see 'Materials and methods'; Phillips et al., 2021). We use -logK_D to each antigen to compute the likelihood of all possible mutational trajectories in the context of each of the antigens, as well as in the context of all possible sequential selection scenarios, where the selecting antigen can change. We focus on scenarios involving the two antigens that the donor was likely exposed to (Figure 5) – MA90 early in their life and SI06 later in their life – but we also perform this analysis with the MA90-G189E data (Figure 5—figure supplement 1). Additionally, we consider selection resulting from a mixture of antigens, which we approximate by randomly selecting an antigen for each mutational step (Wang et al., 2015) and average this pathway likelihood over 1000 random draws.

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This pathway likelihood inference reveals that mutational trajectories leading to CH65 are most favorable in sequential selection scenarios that begin with MA90 and end with SI06, consistent with the donor’s likely exposure history (Schmidt et al., 2013; Schmidt et al., 2015a). This order is preferred regardless of whether paths are constrained to pass through I-2 (Figure 5A). Further, the MA90-SI06 sequential scenarios are considerably more likely than either antigen alone, a mixture of antigens, or SI06-MA90 sequential scenarios.

These drastic differences in scenario likelihood result from the effects of specific mutations on various genetic backgrounds. Mutations on the UCA background can improve affinity to MA90 but not to SI06, so MA90 is favored as the selecting antigen initially. After a few mutations, however, MA90 reaches maximal affinity and cannot improve further, at which point mutations begin to improve SI06 affinity. Thus, SI06 is favored later in mutational trajectories (Figure 5B). These constraints reflect the structure of the sequence-affinity landscape: selection with MA90 favors mutations that enable the acquisition of SI06 affinity and would be unlikely to occur under selection with SI06 alone. Similarly, when we consider all three antigens, we find that scenarios that begin with MA90 or MA90-G189E and end with SI06 are most likely, again reflecting the hierarchical nature of the sequence-affinity landscape (Figure 5—figure supplement 1).

We also leverage our combinatorial data to infer the probability of each mutation occurring at a given step along the evolutionary pathway from UCA to CH65 (Figure 5C). Even when we do not constrain pathways to pass through I-2, we find that two of the I-2 mutations (G31D and N52H) and the epistatic mutations that interact with the HCDR3 (e.g., Y33H, H35N, and the previously uncharacterized Y35N) are most likely to occur early in mutational trajectories, especially in scenarios that begin with MA90 selection. Additionally, the highly synergistic HCDR3-stabilizing mutations Y48C and D49Y are most likely to occur late, and consecutively, with D49Y preceding the otherwise-deleterious Y48C. These general trends are robust to constraining paths to pass through the I-2 intermediate. Consistent with our structural analyses, we find that when pathways are constrained to pass through I-2, Y35N is the most probable subsequent mutation, and this likelihood rapidly decreases with additional mutations. However, when we consider all possible pathways in the optimal antigen selection scenario, I-2 is not the most likely 3-mutation intermediate, suggesting that the evolution of CH65 was not contingent on passing through I-2 (Figure 5—figure supplement 2). Still, the likelihood of passing through the I-2 intermediate is ~55% higher than that expected by chance – it is a minimally mutated antibody with improved affinity to MA90 and MA90-G189E, and it contains the N52H mutation that is essential for SI06 affinity. Thus, while there are many accessible paths to CH65, the three mutations in I-2 result in rapid improvements in affinity and breadth and favor subsequent selection for epistatic mutations that ultimately provide the breadth of CH65.

Collectively, we find that the breadth of an RBS influenza bnAb, CH65, is determined by high-order epistatic interactions that differ between divergent antigens (Figure 5—figure supplement 3). This epistasis is widespread within and between both the heavy and light chains. To our knowledge, this is the first comprehensive study of inter-chain epistasis and illustrates the extent to which mutations can differentially impact affinity depending on the presence of other mutations, even those too far apart to physically interact. This suggests that the maturation of antibodies that engage antigen with both chains may be distinct compared to those that do not. There are more opportunities for epistatic interactions across two chains compared to just one, and the degree of both intra- and inter-chain epistasis is likely contingent on the chain pairing. Given the importance of both light and heavy chain mutations across diverse bnAbs (Corti et al., 2011; Schmidt et al., 2015a; Xiao et al., 2019; Ekiert and Wilson, 2012), understanding the nature of this epistasis may be useful for designing therapeutic antibodies and eliciting broadly protective immune responses.

Further, our structural analysis shows that the epistasis that confers broad reactivity in this antibody is mediated through sets of mutations that both interact with HA and those that do not interact with HA. These epistatic mutations add or remove interactions between CDRs, FWRs, and chains that act by different mechanisms of stabilizing the binding conformation (e.g., G31D and N52H) or removing constraints on the HCDR3 (e.g., Y35N and H35N). The Y35N mutation effectively removes interactions between the LFWR2 and the HCDR3 at the V_H-V_L interface and mediates affinity improvement to a more antigenically advanced influenza strain by increasing the association rate. An analogous observation was noted for the anti-HIV bnAb CH103 that co-evolved during a natural infection within in a single individual (Liao et al., 2013). Structural studies of CH103 identified mutations at the V_H-V_L interface (which is the region containing residue 35 in CH65) that were associated with reconfiguration of the HCDR3 to enable broad reactivity against a viral escape variant (Fera et al., 2014). Although additional work will be needed to address the generality of this finding, it appears that antibodies can evolve to bind viral escape variants by modulating the V_H-V_L interface and the HCDR3 configuration, in response to both chronic (HIV) and punctuated (influenza) exposures. While Y35N is advantageous early in affinity maturation, it becomes detrimental in highly mutated backgrounds that have undergone HCDR3 rigidification. Consequently, Y35N may function to initially increase flexibility, enabling acquisition of affinity to SI06 after acquiring mutations in the heavy chain, and subsequent maturation rigidified the HCDR3. This increased flexibility followed by rigidification is reminiscent of molecular dynamics studies of anti-HIV bnAbs that suggest initial increases in flexibility may provide a means to sample additional conformational space prior to rigidification (Ovchinnikov et al., 2018).

In comparing CH65 mutations that improve affinity to diverse H1 antigens, we find that increasingly divergent antigens require additional epistatically interacting mutations, resulting in a hierarchical pattern of mutations that improve affinity to distinct antigens. The I-2 mutations (e.g., G31D, M34I, N52H) may compensate for the G189E mutation by stabilizing interactions with HA opposite this site, potentially allowing the antibody to shift to relieve the clash; a similar observation was made for another RBS-directed antibody (McCarthy et al., 2019). These same mutations help to stabilize binding in the antigenically distant SI06 but do not sufficiently compensate for the loss of potential contacts between the HCDR3 and the RBS (e.g., ∆K133a and E156G) within the antigen combining site; further mutations Y35N and H35N that likely influence HCDR3 conformations are needed. These structural observations and the data generated here suggest that mutations confer broad reactivity in the CH65 lineage in a hierarchical manner. Although the hierarchical landscape of CH65 is not as striking as that of CR9114 (Phillips et al., 2021), where larger sets of mutations are required to bind substantially more divergent antigens, it is intriguing that the landscape for a considerably narrower bnAb can also have this structure. This suggests that hierarchical sequence-affinity landscapes may be quite common, as they are not unique to CR9114, to anti-stem bnAbs, or to bnAbs that engage distinct HA subtypes.

If hierarchical sequence-affinity landscapes are common amongst bnAbs, they may contribute to the low frequencies of bnAbs in human repertoires. For bnAbs with such landscapes, epistatically interacting mutations are required to bind a given antigen, additional epistatic mutations (that interact favorably with those acquired previously) are required to bind a distinct antigen, and so on. Determining how this might constrain bnAb evolution will require assessing how rare these sets of synergistic mutations are. Importantly, the landscapes measured here and in our previous work focus exclusively on mutations present in the affinity-matured antibodies, which are biased by the selection pressures those bnAbs experienced. Thus, while these landscapes show that diverse bnAbs can mature by acquiring hierarchical sets of epistatic mutations that are favored in sequential exposure regimens, there may be alternative mutational pathways to breadth that are not hierarchical and are favored in other exposure regimes.

Still, the observation that antibodies can evolve breadth through hierarchical mutational landscapes lends support for vaccination with sequential doses of distinct antigens. These findings are consistent with a recent study that demonstrates memory B cell recruitment to secondary germinal centers upon vaccination in humans, allowing for additional rounds of antibody maturation to antigenically drifted strains (Turner et al., 2020). Here, we find that sequential exposures with antigenically drifted strains may help elicit within-subtype potent bnAbs like CH65, in addition to the cross-subtype bnAbs described in our previous work. Several theoretical and computational models of bnAb affinity maturation also favor sequential immunization strategies as they allow antibodies to acquire the mutations necessary to bind one antigen before experiencing selection pressure to bind another, ultimately producing bnAbs that have ‘focused’ on conserved epitopes (Wang et al., 2015; Sachdeva et al., 2020; Wang, 2017; Molari et al., 2020; Sprenger et al., 2020). Our work indicates that this focusing process may occur by favoring selection on hierarchical sets of epistatically interacting mutations. We note that while the hierarchical epistasis we observe favors the acquisition of breadth to a set of specific antigens, antagonistic epistasis between these mutations and new mutations could prevent the acquisition of breadth to other antigens. Further, both CH65 and CR9114 have higher affinity to the strain most like the inferred original immunogenic stimulus, and weaker affinity to more divergent strains (Dreyfus et al., 2012; Schmidt et al., 2015a). This is consistent with the concept of immunological imprinting or original antigenic sin, where antibodies boosted upon vaccination or infection typically have high affinity for the eliciting strain (Guthmiller and Wilson, 2018). Although we show that the CH65 antibody lineage can evolve breadth that compensates for viral escape mutations, the affinities are lower for more antigenically distant strains, suggesting that there is likely a trade-off between antibody breadth and affinity. Further work will be needed to assess whether RBS-targeting bnAbs like CH65, which target highly variable epitopes compared to stem-targeting bnAbs (Schmidt et al., 2013; Schmidt et al., 2015a), can mature to bind substantially divergent strains (e.g., post-pandemic H1N1 strains that CH65 does not effectively neutralize), or whether historical contingency prevents them from doing so.

Finally, although epistasis can make evolution more difficult to predict (de Visser et al., 2018; Park et al., 2022), the general patterns of epistasis emerging from these combinatorial landscapes suggest that there are indeed broadly applicable insights. For example, these hierarchical synergistic interactions reveal how epistasis constrains the evolution of antibody affinity, breadth, and trade-offs between the two. Moving forward, additional combinatorial antibody libraries will advance our understanding of how pervasive these features are – for example, for antibodies that target distinct viruses. Ultimately, though, to understand why we observe these particular bnAbs and not others, we need to explore the unobserved regions of sequence space. We also need to assess the numerous other properties that likely impact selection on antibodies (e.g., stability, folding, polyreactivity). Thus, integrating approaches like this combinatorial approach with methods for assessing local mutational landscapes (e.g., deep mutational scanning) and methods to measure other antibody properties in high throughput will provide a more comprehensive view of the factors that constrain and potentiate antibody evolution.

For all methods, ‘biological replicates’ refer to independent experiments performed on different days, and ‘technical replicates’ refer to multiple measurements of the same biological sample.

Data and code used for this study are available at https://github.com/amphilli/CH65-comblib, (copy archived at swh:1:rev:cea336dfd05fa31d675f79038428bf7f0d177e78). Antibody affinity and expression data are also available in an interactive data browser at https://ch65-ma90-browser.netlify.app/. FASTQ files from high-throughput sequencing are deposited in the NCBI BioProject database under PRJNA886089. X-ray crystal structures of the Fabs reported here are available at the Protein Data Bank (8EK6 and 8EKH).

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Author details

1. Angela M Phillips

   1. Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, United States
   2. Department of Microbiology and Immunology, University of California, San Francisco, San Francisco, United States

   Contribution

   Conceptualization, Formal analysis, Supervision, Validation, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   Contributed equally with

   Daniel P Maurer

   For correspondence

   angela.phillips@ucsf.edu

   Competing interests

   has recently consulted for Leyden Labs

   "This ORCID iD identifies the author of this article:" 0000-0002-9806-7574

2. Daniel P Maurer

   1. Ragon Institute of MGH, MIT, and Harvard, Cambridge, United States
   2. Department of Microbiology, Harvard Medical School, Boston, United States

   Contribution

   Conceptualization, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   Contributed equally with

   Angela M Phillips

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-2074-5416

3. Caelan Brooks

   Department of Physics, Harvard University, Cambridge, United States

   Contribution

   Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

4. Thomas Dupic

   Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, United States

   Contribution

   Formal analysis, Visualization, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

5. Aaron G Schmidt

   1. Ragon Institute of MGH, MIT, and Harvard, Cambridge, United States
   2. Department of Microbiology, Harvard Medical School, Boston, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing – review and editing

   Competing interests

   No competing interests declared

6. Michael M Desai

   1. Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, United States
   2. Department of Physics, Harvard University, Cambridge, United States
   3. NSF-Simons Center for Mathematical and Statistical Analysis of Biology, Harvard University, Cambridge, United States
   4. Quantitative Biology Initiative, Harvard University, Cambridge, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing – review and editing

   For correspondence

   mdesai@oeb.harvard.edu

   Competing interests

   recently consulted for Leyden Labs

   "This ORCID iD identifies the author of this article:" 0000-0002-9581-1150

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