In November 2021, the SARS-CoV-2 Omicron BA.1 variant emerged and quickly rose to high frequency worldwide, in part due to its ability to escape preexisting immunity (Cao et al., 2022; Ao et al., 2022; Planas et al., 2022; Viana et al., 2022). This immune escape is mediated by mutations in the receptor binding domain (RBD) of the spike protein, which is the major target of SARS-CoV-2 neutralizing antibodies (Greaney et al., 2021b; Greaney et al., 2021c; Iketani et al., 2022; Dai and Gao, 2021). Antibodies targeting the RBD can bind different epitopes, and they have been grouped into several classes (Barnes et al., 2020b; Barnes et al., 2020a). Some previous SARS-CoV-2 variants which have a subset of the 15 mutations found in the BA.1 RBD (e.g. K417N, N501Y in Beta and T478K, N501Y in Delta) can evade some antibodies of certain epitope classes but still bind to others (Liu et al., 2021; Zhou et al., 2021; Greaney et al., 2022; Greaney et al., 2021a). In contrast, BA.1 can escape most antibodies that bind to very distinct epitopes, including antibodies elicited by previously circulating variants (Cao et al., 2022; Dejnirattisai et al., 2022; Cameroni et al., 2022).

Existing studies of SARS-CoV-2 immune escape have focused on measuring the effects of single mutations (or, in some cases, of a small subset of mutations) on antibody escape in the context of specific SARS-CoV-2 variants (Dejnirattisai et al., 2022; Starr et al., 2021b; Starr et al., 2021a). However, simultaneous escape of most antibodies is likely to require multiple mutations, and it is unclear how these mutations might interact. A large body of work has demonstrated that the specific combination of mutations in the BA.1 variant can evade various antibodies of distinct epitopes (Cao et al., 2022; Planas et al., 2022; Dejnirattisai et al., 2022; Chakraborty et al., 2022). However, the landscape on which this evolution occurred is not well understood. Do mutations involved in escape from one antibody with a certain epitope interfere with the effects of those involved in escaping others with different contact sites, or are the effects largely independent? And how are these effects mediated by epistatic interactions with other mutations in the RBD?

As we observed in previous work, several of these antibody-escape mutations also reduce affinity to ACE2, suggesting that they were positively selected because they contribute to immune escape (Starr et al., 2020; Mannar et al., 2022; McCallum et al., 2022). Importantly, epistatic interactions between these mutations dramatically impact ACE2 affinity and may also differentially impact the escape of antibodies with very different epitopes (Moulana et al., 2022; Starr et al., 2022a). For example, escape from some antibodies like S309 has been difficult to attribute to specific mutations (McCallum et al., 2022; Case et al., 2022), perhaps because measurements have so far been limited to single mutations. These observations suggest that we need to more comprehensively characterize the role of epistasis and potential trade-offs to understand the simultaneous evolution of escape from multiple antibodies of distinct epitopes and ACE2 binding affinity.

Here, to understand how immune pressure may have shaped the evolution of BA.1, we measured the equilibrium binding affinities (K_{D, app}) of the spike protein RBD to four therapeutic monoclonal antibodies (mAbs) with distinct RBD epitopes: LY-CoV016, LY-CoV555, REGN10987, and S309, for all possible evolutionary intermediates between the ancestral Wuhan Hu-1 RBD and the BA.1 variant. This set of antibodies includes the primary epitopes generally covered by therapeutic mAbs (Barnes et al., 2020a; Cameroni et al., 2022). The first three antibodies are fully escaped by Omicron BA.1, while S309 has reduced affinity. We find that for each antibody, only a few mutations significantly impact affinity, and these mutations are largely (but not entirely) orthogonal between the four antibodies. Additionally, we find that epistasis plays a limited role in determining affinity to antibodies that are fully escaped by BA.1 but contributes substantially to the reduced affinity for the partially escaped antibody, S309. Together, this work systematically characterizes how SARS-CoV-2 can evade distinct RBD-targeted antibodies while maintaining ACE2 affinity.

In previous work, we generated a combinatorically complete library comprising all possible intermediates between the ancestral SARS-CoV-2 Wuhan Hu-1 spike protein RBD and the Omicron BA.1 variant (Moulana et al., 2022). The BA.1 RBD differs from Wuhan-1 by 15 amino acid substitutions, so this library contains 2 (Dejnirattisai et al., 2022) variants containing all possible combinations of these 15 mutations. This RBD library is displayed on the surface of yeast, such that each yeast cell expresses a single variant. Here, we use Tite-seq (a high-throughput method that integrates flow cytometry and sequencing Moulana et al., 2022; Adams et al., 2016; Phillips et al., 2021; Starr et al., 2022b; see Figure 1—figure supplement 1A) to measure the equilibrium binding affinities of all 32,768 variants to four antibodies with different epitopes (LY-CoV016, LY-CoV555, REGN10987, and S309). The resulting K_{D, app} correlates between biological duplicates and with isogenic measurements made by flow cytometry (Figure 1—figure supplement 1A, Supplementary file 1).

Of the 32,768 variants in our library, we obtain K_{D, app} for at least ~30,000 variants to each of the mAbs (32,603 for LY-CoV016, 31479 for REGN10987, 27485 for LY-CoV555, and 32650 for S309) after removing variants with poor titration curves (r²<0.8 or σ>1; see Methods). These K_D,app range from 0.1 nM to 1 μM (which is our limit of detection and likely corresponds to non-specific binding), with 51% of the variants fully escaping LY-CoV016 (defined as having K_D,app above the limit of detection), 65% fully escaping LY-CoV555, 36% fully escaping REGN10897, and no variants fully escaping S309 (Figure 1A; see https://desai-lab.github.io/wuhan_to_omicron/ (Johnson and Dupic, 2022) for an interactive data browser). Escape from LY-CoV016, LY-CoV555, and REGN10897 is mediated by one or a few strong-effect mutations, with other mutations more subtly impacting affinity (Figure 1B). In general, strong-effect mutations make substantial contact with the corresponding antibody. Consistent with previous studies (Greaney et al., 2021a; Cameroni et al., 2022; Starr et al., 2021b; Windsor et al., 2022), these strong-effect mutations are largely distinct for each antibody, which presumably reflects their non-overlapping footprints on the RBD (Figure 1C) and suggests that evolution of escape from each antibody can be, to some extent, orthogonal.

Figure 1 with 2 supplements see all

Download asset Open asset

The picture is more complex for S309, where BA.1 has reduced affinity relative to Wuhan Hu-1, but ~17% of variants have lower affinity than BA.1. These differences are not attributable to one or two strong effect mutations (Figure 1A–B). In addition, although most mutations reduce affinity, three mutations have small positive effects (on average across all backgrounds at the other loci): S375F for LY-CoV016 and E484A and N501Y for REGN10987 (Figure 1B). Intriguingly, each of these mutations reduces affinity to at least one of the other antibodies, and N501Y significantly improves binding to ACE2, suggesting a potential role for trade-offs (and/or epistasis that mitigates these effects on specific backgrounds).

For each antibody, binding affinities generally decrease as the number of mutations increase (Figure 1D–G). For LY-CoV016, LY-CoV555, and REGN10897, this trend is observed amongst variants with and without the large-effect escape mutations (Figure 1D–F). For LY-CoV016, K417N is sufficient for escape (Figure 1D, green), whereas both LY-CoV555 and REGN10987 require at least two mutations for complete escape. For LY-CoV555, both E484A and Q493R decrease affinity drastically (1000- and 100-fold, respectively), but only the combination of both mutations lead to complete escape. Complete escape from REGN10987 also requires two mutations (N440K and G446S), but the individual effects of these mutations are more subtle (reducing affinity by 5- and 10-fold, respectively). For S309, affinity declines after a few mutations and in some backgrounds increases upon further mutation, suggesting that interactions between these mutations are important in determining affinity (Figure 1G).

Mostly orthogonal large-effect mutations

We first focused on analyzing how mutations and combinations of mutations lead to complete escape (defined as K_D,app above our limit of detection) for specific sets of antibodies. To do so, we analyze the enrichment of specific mutations among non-binders (Figure 2A). We find a largely orthogonal set of one or two mutations are enriched among variants that do not bind each antibody: almost all variants that do not bind LY-CoV016 contain K417N, almost all variants that do not bind REGN10987 contain G446S, and many also contain N440K, and E484A and Q493R are highly enriched among variants that do not bind LY-CoV555. These escape mutations were already identified on the Wuhan background (Tada et al., 2022; Starr et al., 2021c; Zhou et al., 2022). The fact that different sites are involved for each antibody suggests that the RBD can evolve to independently escape antibodies with each distinct epitope, and mutations can to some extent act independently on binding to each antibody.

Figure 2

Download asset Open asset

To analyze this further, we calculate the percentage of genetic backgrounds on which each mutation leads to complete escape from a specific antibody (i.e. that mutation converts a variant with measurable K_D,app to a K_D,app above our limit of detection). We see that for each antibody, one or two mutations abrogate binding. These sets of mutations are largely orthogonal among antibodies (Figure 2B), consistent with the enrichment analysis (Figure 2A). Specifically, K417N always abrogates binding to LY-CoV016, G446S and N440K often abrogate binding to REGN10987, and E484A and Q493R often abrogate binding to LY-CoV555.

However, we note that this orthogonality is not complete. For example, G446S is slightly enriched among LY-CoV555 binders, while mutation E484A is slightly depleted among variants that do not bind REGN10987 (Figure 2A). Consistent with this, G446S sometimes abrogates binding to LY-CoV555 (Figure 2B). In addition, some apparently smaller-effect mutations can be involved in abolishing binding to multiple antibodies. For example, S375F is weakly enriched among variants that do not bind REGN10987 and LY-CoV555 and often abrogates binding to these two antibodies, with G496S, Q498R, and N501Y also playing a role.

To summarize how these different mutations can act individually or in combination to lead to antibody escape, we inferred a decision tree to classify variants as binders or non-binders. To do so, for each antibody, we calculate the mutation that maximally partitions the variants into binders or non-binders. If this partitioning is not perfect, we then calculate the second mutation that maximally partitions the variants conditional on each possible state of the first site. We then proceed to further partition variants based on additional mutations in the same way until the variants are perfectly partitioned or no further mutations can significantly improve the partitioning (see Methods). We show the corresponding decision trees for LY-CoV016, REGN10987, and LY-CoV555 in Figure 2C, D and E, respectively. As expected, the tree associated with LY-CoV016 is very simple: the mutation K417N perfectly partitions the variants into binders and non-binders. In contrast, the trees for REGN10987 and LY-CoV555 have more complex structures, reflecting the fact that it is possible to abrogate affinity to these antibodies via multiple distinct combinations of mutations. For example, variants can escape REGN10987 by acquiring G446S and N440K (100%), or alternatively, with S375F and G446S (89%, as additional mutations may also be required). For LY-CoV555, different sets of mutations can lead to escape (e.g. Q493R and G446S or E484A and S375F). Some of these mutations partially overlap with those for REGN10987 (i.e. they are not fully orthogonal), suggesting that selection pressure from one antibody could promote subsequent escape of another.

Inference of epistatic affinity landscapes

In addition to large-effect mutations which lead to complete escape of specific antibodies, a variety of other sites contribute to more subtle but potentially important changes in binding affinities. To analyze these subtle effects as well as the large-effect mutations leading to escape, we defined a linear model for −log(K_{D, app}) as the sum of single (additive) mutational effects plus interaction terms up to a specified order (note that because −log[K_{D, app}] is proportional to the free energy of binding, we expect it to behave additively in the absence of epistatic interactions). Because non-binding variants have −log(K_{D, app}) beyond our limit of detection, we fit a Tobit model (a class of regression model capable of handling truncated measurements; see Methods for details) using maximum likelihood with an L2-norm Lasso regularization. Specifically, we partition our data into training (90%) and test (10%) sets and use the training dataset to fit epistatic coefficients to a linear model truncated at each order (e.g. truncating to first-order yields additive mutational effects, second-order includes both additive effects and pairwise terms, etc.). We then evaluate performance (as the coefficient of variation) of each model on the held-out test dataset and compare the model performance using −log(K_{D, app}) for each of the antibodies and ACE2 (Figure 3A).

Figure 3 with 1 supplement see all

Download asset Open asset

We find that adding epistatic interactions improves the predictive power of the model for all four antibodies as well as for binding to ACE2, though the optimal order varies (Figure 3A). This indicates that epistasis does play a significant role in all cases (up to second order for REGN10987, to third order for LY-CoV555, and to fourth or higher order for LY-CoV016, S309, and ACE2). The additive, pairwise, and higher-order coefficients resulting from these models are summarized in Figure 3—figure supplement 1. In general, we find many strong interactions across several positions in each antibody, involving both the sites that strongly determine escape variants for that antibody (e.g. between N440K and G446S for REGN10987) as well as others.

Notably, we find that the higher-order epistasis plays a much stronger role in determining affinity for ACE2 than for the three antibodies fully escaped by BA.1 (Figure 3B). This reflects the impact of a few strong-effect mutations in determining affinity for LY-CoV555, LY-CoV016, and REGN10987 and the role of compensatory epistasis in determining ACE2 affinity. In other words, while epistasis is relevant for all measured phenotypes, antibody escape is more simply determined by the additive effects of individual mutations, while maintaining ACE2 affinity involves more complex epistatic interactions.

High-order epistatic interactions are also important in determining affinity to S309. In Figure 3C, we highlight four neighboring mutations (G339D, S371L, S373P, and S375F) which interact non-additively to produce the reduction in affinity observed in BA.1 relative to Wuhan Hu-1. Each of these mutations weakly reduces affinity on their own, and specific combinations of these mutations can reduce affinity by up to two orders of magnitude, but the reduction in affinity resulting from all four mutations is less than some sets of three mutations. These patterns emerge from a complex set of high-order epistatic interactions among the mutations. For example, S371L reduces affinity on the Wuhan Hu-1 background but increases affinity on the background containing G339D, S373P, and S375F (and without G339D, S371L increases affinity in the presence of S373P if S375F is absent but not if it is present). Thus, some variants lacking S371L evade S309 more effectively than BA.1, and interestingly we note that this mutation is absent in BA.2 and BA.3 and replaced instead by S371F.

Tradeoffs between antibody and ACE2 affinities

In previous work, we found that antibody escape mutations (as defined in earlier studies) typically reduce ACE2 affinity, suggesting that viral evolution is constrained by a tradeoff between immune evasion and the ability to enter host cells. Consistent with this, we find here that variants that escape one or more antibodies (as defined by the data reported in this work) but have few additional mutations have reduced ACE2 affinity relative to Wuhan Hu-1. However, as additional BA.1 mutations are accumulated, the ACE2 binding affinity tends to increase until it exceeds the Wuhan Hu-1 value even in the presence of multiple antibody escape mutations (Figure 4A). This suggests that the evolution of the BA.1 variant is driven both by immune escape and the need for compensatory mutations that mitigate the negative effects of the escape mutations on ACE2 binding.

Figure 4

Download asset Open asset

The strength of this tradeoff and the potential importance of compensatory evolution are distinct between the different antibodies (Figure 4B and C). For example, escape from LY-CoV016 or LY-CoV555 reduces ACE2 binding affinity in the absence of compensatory mutations (Q498R and N501Y) but not in their presence (Figure 4B). In contrast, REGN10987 escape does not strongly reduce affinity to ACE2, whether or not Q498R and N501Y are present. However, this tradeoff is likely relevant overall, as escaping all three antibodies substantially reduces ACE2 affinity in the absence of Q498R and N501Y, while the reduction in ACE2 affinity is minimal in their presence. Consistent with this general picture, the frequency of most escape mutations (G446S, E484A, and Q493R) is higher across the SARS-CoV-2 phylogeny in the presence of compensatory mutations (Figure 4D), though we note that this is not universally true (e.g. the frequency of N440K is only slightly higher in the presence of compensatory mutations, and the frequency of K417N is lower with the compensatory mutations).

Although antibody escape mutations do tend to reduce ACE2 affinity, antibody binding affinity (but not complete escape) is not strongly correlated with ACE2 affinity (Figure 4C). The details of this relationship vary by antibody. For LY-CoV016 and LY–CoV555, there is a weak overall positive correlation (i.e. lower antibody affinity also tends to correspond to reduced ACE2 affinity). However, this correlation is dominated by the variants that lack the compensatory mutations at sites 498 and 501; in the presence of Q498R and N501Y, the correlation is reduced, especially for LY-CoV016. For REGN10987 and S309, there is a similar weak overall positive correlation, which is not dependent on Q498R and N501Y. We also note that while compensatory mutations Q498R and N501Y largely drive the variance in ACE2 affinity, they minimally impact antibody binding affinities (Figure 4D).

Overall, we find that BA.1 escape from LY-CoV016, LY-CoV555, and REGN10987 is driven by a relatively small set of mutations: K417N for LY-CoV016, N440K and G446S for REGN10987, and E484A and Q493R for LY-CoV555. These mutations have largely orthogonal effects on affinity to the three antibodies, suggesting that the evolution of escape to each can occur independently, as might be expected given the distinct epitopes they target (Barnes et al., 2020b; Cameroni et al., 2022; Starr et al., 2021a).

However, despite these largely orthogonal effects of large-effect mutations on antibody escape, we do observe limited trade-offs among LY-CoV016, LY-CoV555, and REGN10987, with four mutations (S375F, T478K, E484A, and N501Y) improving affinity to one antibody and reducing affinity to another. These positive effects are modest compared to the reductions in affinity caused by other mutations. In fact, for all antibodies studied here, outside of a few large-effect mutations that abrogate or nearly abrogate binding, most mutations weakly impact binding affinity and, even collectively, are insufficient to abrogate it.

In contrast to the orthogonality of antibody escape, trade-offs between binding ACE2 and escaping antibodies are much stronger. While the mutations with a small effect on antibody escape are mostly uncorrelated to ACE2 affinity, the strong-effect mutations substantially reduce ACE2 affinity. Thus, ACE2 affinity is lower for variants that escape a larger number of antibodies unless compensatory mutations are acquired, suggesting that these compensatory mutations potentiated the establishment of the antibody escape mutations (Moulana et al., 2022; Javanmardi et al., 2022).

We also find that epistatic interactions are important in determining antibody affinity. This is particularly true for S309. Prior to this work, the reduced affinity of S309 to Omicron could not be attributed to specific mutations (Cameroni et al., 2022; Case et al., 2022). Here, we find that this ambiguity can be resolved by examining higher-order interactions between mutations, as the reduction in affinity is attributable to a fourth-order epistatic interaction. This finding suggests that the potential for future SARS-CoV-2 lineages to escape S309 and similar antibodies could depend on epistatic interactions between emerging mutations.

We note that our study focuses only on binding affinities, which may not always perfectly reflect viral escape from antibody neutralization (Steckbeck et al., 2005; Culp et al., 2007). In particular, some of the binding affinities we measure could be too weak to be physiologically relevant, and mutations may impact neutralization without impacting binding affinity significantly. However, because neutralization cannot occur in the absence of affinity, our measurements are likely to be relevant for understanding the reduced sensitivity of BA.1 to these antibodies. We also note that practical constraints limit us to studying four antibodies. This limits the generalizability of our results, particularly in light of previous structural studies which have revealed more epitopes bound by mAbs.

In spite of these limitations, our binding affinity landscapes reveal that BA.1 can escape diverse antibodies by acquiring a few large-effect mutations and can reduce affinity to others by accumulating several small-effect mutations. For the first three antibodies, one or two mutations are sufficient for total escape. However, in some cases, additional mutations can restore affinity, and in others, specific combinations of large- and small-effect mutations can abrogate affinity. Thus, despite the seemingly simple landscape of antibody escape, there are alternative, more intricate pathways that can abrogate affinity. In contrast, for the S309 antibody, four mutations drive the decline in affinity yet are also involved in higher-order epistatic interactions that counteract this decline. This epistasis results in an affinity threshold, beyond which additional mutations do not reduce affinity.

More generally, this work illustrates a broad diversity of ways in which epistasis can shape a protein landscape. While our earlier work demonstrates that the RBD ACE2 affinity landscape is defined by several epistatic interactions (Moulana et al., 2022), our results here show that escape from antibody binding can in many (but not all) cases be driven by individual mutations. It is unclear why these landscapes involve such distinct patterns of epistasis. One possibility is that the prevalence of epistasis in the ACE2 affinity landscape is a consequence of the long history of spike protein evolution to bind ACE2, which may have selected for more complex epistatic interactions among the acquired mutations over time (in contrast, evolution to escape antibodies is relatively recent). Alternatively, the relative simplicity of the antibody escape landscapes could be attributed to the fact that beneficial mutations in this case disrupt (rather than maintain or improve) an interaction (Greaney et al., 2021a; Starr et al., 2021b; Starr et al., 2020). Of course, these possibilities are not mutually exclusive (Rotem et al., 2018), and discriminating between them will require further investigation into other viral protein and antibody landscapes to determine how broadly the patterns we observe in this study generalize to other systems.

Predicting the future evolution of the Omicron lineage will also require determining how these affinity landscapes translate to immune evasion, how antibody affinity landscapes vary within a class or epitope group, and how mutations beyond this set may further enhance immune evasion. For example, neutralization assays with minimally mutated genotypes would confirm whether the strong-effect mutations are indeed sufficient for escape. Furthermore, assessing affinity landscapes for additional antibodies with similar epitopes would reveal how the landscape structure varies within such a group, and whether there are general features that we can extrapolate to unmeasured sequences. Finally, integrating these combinatorial libraries with saturating mutagenesis approaches would reveal how the evolvability of this lineage changes over time, and what additional mutations – such as those in BA.2, BA.4, or BA.5 – might confer further immune escape. Looking beyond the Omicron lineage, such approaches could provide more general insight into how mutations in SARS-CoV-2 may result in host-range expansion or antigenic evolution.

Raw sequencing reads have been deposited in the NCBI BioProject database under accession number PRJNA877045. All associated metadata are available at https://github.com/desai-lab/omicron_ab_landscape, (copy archived at swh:1:rev:9ab630decfa835b2551430ed693796ef366b1aff).

1. 1. Desai MM

   (2023) NCBI BioProject

   ID PRJNA877045. The landscape of antibody binding affinity in SARS-CoV-2 Omicron BA.1 evolution.

   http://www.ncbi.nlm.nih.gov/bioproject/?term=PRJNA877045

1. 1. Adams RM
   2. Mora T
   3. Walczak AM
   4. Kinney JB

   (2016) Measuring the sequence-affinity landscape of antibodies with massively parallel titration curves

   eLife 5:e23156.

   https://doi.org/10.7554/eLife.23156

   • PubMed
   • Google Scholar
2. 1. Ao D
   2. Lan T
   3. He X
   4. Liu J
   5. Chen L
   6. Baptista-Hon DT
   7. Zhang K
   8. Wei X

   (2022) SARS-cov-2 omicron variant: immune escape and vaccine development

   MedComm 3:e126.

   https://doi.org/10.1002/mco2.126

   • PubMed
   • Google Scholar
3. 1. Barnes CO
   2. Jette CA
   3. Abernathy ME
   4. Dam KMA
   5. Esswein SR
   6. Gristick HB
   7. Malyutin AG
   8. Sharaf NG
   9. Huey-Tubman KE
   10. Lee YE
   11. Robbiani DF
   12. Nussenzweig MC
   13. West AP
   14. Bjorkman PJ

   (2020a) SARS-cov-2 neutralizing antibody structures inform therapeutic strategies

   Nature 588:682–687.

   https://doi.org/10.1038/s41586-020-2852-1

   • PubMed
   • Google Scholar
4. 1. Barnes CO
   2. West AP
   3. Huey-Tubman KE
   4. Hoffmann MAG
   5. Sharaf NG
   6. Hoffman PR
   7. Koranda N
   8. Gristick HB
   9. Gaebler C
   10. Muecksch F
   11. Lorenzi JCC
   12. Finkin S
   13. Hägglöf T
   14. Hurley A
   15. Millard KG
   16. Weisblum Y
   17. Schmidt F
   18. Hatziioannou T
   19. Bieniasz PD
   20. Caskey M
   21. Robbiani DF
   22. Nussenzweig MC
   23. Bjorkman PJ

   (2020b) Structures of human antibodies bound to SARS-cov-2 spike reveal common epitopes and recurrent features of antibodies

   Cell 182:828–842.

   https://doi.org/10.1016/j.cell.2020.06.025

   • PubMed
   • Google Scholar
5. Software

   1. Borkovec M

   (2019) Ggplot” visualizations for the “partykit” package, version 1.0.0

   Ggplot.

   https://cran.r-project.org/web/packages/ggparty/ggparty.pdf
6. 1. Cameroni E
   2. Bowen JE
   3. Rosen LE
   4. Saliba C
   5. Zepeda SK
   6. Culap K
   7. Pinto D
   8. VanBlargan LA
   9. De Marco A
   10. di Iulio J
   11. Zatta F
   12. Kaiser H
   13. Noack J
   14. Farhat N
   15. Czudnochowski N
   16. Havenar-Daughton C
   17. Sprouse KR
   18. Dillen JR
   19. Powell AE
   20. Chen A
   21. Maher C
   22. Yin L
   23. Sun D
   24. Soriaga L
   25. Bassi J
   26. Silacci-Fregni C
   27. Gustafsson C
   28. Franko NM
   29. Logue J
   30. Iqbal NT
   31. Mazzitelli I
   32. Geffner J
   33. Grifantini R
   34. Chu H
   35. Gori A
   36. Riva A
   37. Giannini O
   38. Ceschi A
   39. Ferrari P
   40. Cippà PE
   41. Franzetti-Pellanda A
   42. Garzoni C
   43. Halfmann PJ
   44. Kawaoka Y
   45. Hebner C
   46. Purcell LA
   47. Piccoli L
   48. Pizzuto MS
   49. Walls AC
   50. Diamond MS
   51. Telenti A
   52. Virgin HW
   53. Lanzavecchia A
   54. Snell G
   55. Veesler D
   56. Corti D

   (2022) Broadly neutralizing antibodies overcome SARS-cov-2 omicron antigenic shift

   Nature 602:664–670.

   https://doi.org/10.1038/s41586-021-04386-2

   • PubMed
   • Google Scholar
7. 1. Cao Y
   2. Wang J
   3. Jian F
   4. Xiao T
   5. Song W
   6. Yisimayi A
   7. Huang W
   8. Li Q
   9. Wang P
   10. An R
   11. Wang J
   12. Wang Y
   13. Niu X
   14. Yang S
   15. Liang H
   16. Sun H
   17. Li T
   18. Yu Y
   19. Cui Q
   20. Liu S
   21. Yang X
   22. Du S
   23. Zhang Z
   24. Hao X
   25. Shao F
   26. Jin R
   27. Wang X
   28. Xiao J
   29. Wang Y
   30. Xie XS

   (2022) Omicron escapes the majority of existing SARS-cov-2 neutralizing antibodies

   Nature 602:657–663.

   https://doi.org/10.1038/s41586-021-04385-3

   • PubMed
   • Google Scholar
8. 1. Case JB
   2. Mackin S
   3. Errico JM
   4. Chong Z
   5. Madden EA
   6. Whitener B
   7. Guarino B
   8. Schmid MA
   9. Rosenthal K
   10. Ren K
   11. Dang HV
   12. Snell G
   13. Jung A
   14. Droit L
   15. Handley SA
   16. Halfmann PJ
   17. Kawaoka Y
   18. Crowe JE
   19. Fremont DH
   20. Virgin HW
   21. Loo YM
   22. Esser MT
   23. Purcell LA
   24. Corti D
   25. Diamond MS

   (2022) Resilience of S309 and AZD7442 monoclonal antibody treatments against infection by SARS-cov-2 omicron lineage strains

   Nature Communications 13:3824.

   https://doi.org/10.1038/s41467-022-31615-7

   • PubMed
   • Google Scholar
9. 1. Chakraborty C
   2. Sharma AR
   3. Bhattacharya M
   4. Lee SS

   (2022) A detailed overview of immune escape, antibody escape, partial vaccine escape of SARS-cov-2 and their emerging variants with escape mutations

   Frontiers in Immunology 13:801522.

   https://doi.org/10.3389/fimmu.2022.801522

   • PubMed
   • Google Scholar
10. 1. Culp TD
    2. Spatz CM
    3. Reed CA
    4. Christensen ND

    (2007) Binding and neutralization efficiencies of monoclonal antibodies, Fab fragments, and scFv specific for L1 epitopes on the capsid of infectious HPV particles

    Virology 361:435–446.

    https://doi.org/10.1016/j.virol.2006.12.002

    • PubMed
    • Google Scholar
11. 1. Dai L
    2. Gao GF

    (2021) Viral targets for vaccines against COVID-19

    Nature Reviews. Immunology 21:73–82.

    https://doi.org/10.1038/s41577-020-00480-0

    • PubMed
    • Google Scholar
12. 1. Dejnirattisai W
    2. Huo J
    3. Zhou D
    4. Zahradník J
    5. Supasa P
    6. Liu C
    7. Duyvesteyn HME
    8. Ginn HM
    9. Mentzer AJ
    10. Tuekprakhon A
    11. Nutalai R
    12. Wang B
    13. Dijokaite A
    14. Khan S
    15. Avinoam O
    16. Bahar M
    17. Skelly D
    18. Adele S
    19. Johnson SA
    20. Amini A
    21. Ritter TG
    22. Mason C
    23. Dold C
    24. Pan D
    25. Assadi S
    26. Bellass A
    27. Omo-Dare N
    28. Koeckerling D
    29. Flaxman A
    30. Jenkin D
    31. Aley PK
    32. Voysey M
    33. Costa Clemens SA
    34. Naveca FG
    35. Nascimento V
    36. Nascimento F
    37. Fernandes da Costa C
    38. Resende PC
    39. Pauvolid-Correa A
    40. Siqueira MM
    41. Baillie V
    42. Serafin N
    43. Kwatra G
    44. Da Silva K
    45. Madhi SA
    46. Nunes MC
    47. Malik T
    48. Openshaw PJM
    49. Baillie JK
    50. Semple MG
    51. Townsend AR
    52. Huang K-YA
    53. Tan TK
    54. Carroll MW
    55. Klenerman P
    56. Barnes E
    57. Dunachie SJ
    58. Constantinides B
    59. Webster H
    60. Crook D
    61. Pollard AJ
    62. Lambe T
    63. OPTIC Consortium
    64. ISARIC4C Consortium
    65. Paterson NG
    66. Williams MA
    67. Hall DR
    68. Fry EE
    69. Mongkolsapaya J
    70. Ren J
    71. Schreiber G
    72. Stuart DI
    73. Screaton GR

    (2022) SARS-cov-2 omicron-B.1.1.529 leads to widespread escape from neutralizing antibody responses

    Cell 185:467–484.

    https://doi.org/10.1016/j.cell.2021.12.046

    • PubMed
    • Google Scholar
13. 1. Elbe S
    2. Buckland-Merrett G

    (2017) Data, disease and diplomacy: GISAID’s innovative contribution to global health

    Global Challenges 1:33–46.

    https://doi.org/10.1002/gch2.1018

    • PubMed
    • Google Scholar
14. 1. Gietz RD
    2. Schiestl RH

    (2007) Quick and easy yeast transformation using the liac/SS carrier DNA/PEG method

    Nature Protocols 2:35–37.

    https://doi.org/10.1038/nprot.2007.14

    • PubMed
    • Google Scholar
15. 1. Greaney AJ
    2. Loes AN
    3. Crawford KHD
    4. Starr TN
    5. Malone KD
    6. Chu HY
    7. Bloom JD

    (2021a) Comprehensive mapping of mutations in the SARS-cov-2 receptor-binding domain that affect recognition by polyclonal human plasma antibodies

    Cell Host & Microbe 29:463–476.

    https://doi.org/10.1016/j.chom.2021.02.003

    • PubMed
    • Google Scholar
16. 1. Greaney AJ
    2. Starr TN
    3. Barnes CO
    4. Weisblum Y
    5. Schmidt F
    6. Caskey M
    7. Gaebler C
    8. Cho A
    9. Agudelo M
    10. Finkin S
    11. Wang Z
    12. Poston D
    13. Muecksch F
    14. Hatziioannou T
    15. Bieniasz PD
    16. Robbiani DF
    17. Nussenzweig MC
    18. Bjorkman PJ
    19. Bloom JD

    (2021b) Mapping mutations to the SARS-cov-2 RBD that escape binding by different classes of antibodies

    Nature Communications 12:4196.

    https://doi.org/10.1038/s41467-021-24435-8

    • PubMed
    • Google Scholar
17. 1. Greaney AJ
    2. Starr TN
    3. Gilchuk P
    4. Zost SJ
    5. Binshtein E
    6. Loes AN
    7. Hilton SK
    8. Huddleston J
    9. Eguia R
    10. Crawford KHD
    11. Dingens AS
    12. Nargi RS
    13. Sutton RE
    14. Suryadevara N
    15. Rothlauf PW
    16. Liu Z
    17. Whelan SPJ
    18. Carnahan RH
    19. Crowe JE
    20. Bloom JD

    (2021c) Complete mapping of mutations to the SARS-cov-2 spike receptor-binding domain that escape antibody recognition

    Cell Host & Microbe 29:44–57.

    https://doi.org/10.1016/j.chom.2020.11.007

    • PubMed
    • Google Scholar
18. 1. Greaney AJ
    2. Eguia RT
    3. Starr TN
    4. Khan K
    5. Franko N
    6. Logue JK
    7. Lord SM
    8. Speake C
    9. Chu HY
    10. Sigal A
    11. Bloom JD

    (2022) The SARS-cov-2 delta variant induces an antibody response largely focused on class 1 and 2 antibody epitopes

    PLOS Pathogens 18:e1010592.

    https://doi.org/10.1371/journal.ppat.1010592

    • PubMed
    • Google Scholar
19. 1. Huerta-Cepas J
    2. Serra F
    3. Bork P

    (2016) Ete 3: reconstruction, analysis, and visualization of phylogenomic data

    Molecular Biology and Evolution 33:1635–1638.

    https://doi.org/10.1093/molbev/msw046

    • PubMed
    • Google Scholar
20. 1. Hunter JD

    (2007) Matplotlib: a 2D graphics environment

    Computing in Science & Engineering 9:90–95.

    https://doi.org/10.1109/MCSE.2007.55

    • Google Scholar
21. 1. Iketani S
    2. Liu L
    3. Guo Y
    4. Liu L
    5. Chan JF-W
    6. Huang Y
    7. Wang M
    8. Luo Y
    9. Yu J
    10. Chu H
    11. Chik KK-H
    12. Yuen TT-T
    13. Yin MT
    14. Sobieszczyk ME
    15. Huang Y
    16. Yuen K-Y
    17. Wang HH
    18. Sheng Z
    19. Ho DD

    (2022) Antibody evasion properties of SARS-cov-2 omicron sublineages

    Nature 604:553–556.

    https://doi.org/10.1038/s41586-022-04594-4

    • PubMed
    • Google Scholar
22. 1. Javanmardi K
    2. Segall-Shapiro TH
    3. Chou C-W
    4. Boutz DR
    5. Olsen RJ
    6. Xie X
    7. Xia H
    8. Shi P-Y
    9. Johnson CD
    10. Annapareddy A
    11. Weaver S
    12. Musser JM
    13. Ellington AD
    14. Finkelstein IJ
    15. Gollihar JD

    (2022) Antibody escape and cryptic cross-domain stabilization in the SARS-cov-2 omicron spike protein

    Cell Host & Microbe 30:1242–1254.

    https://doi.org/10.1016/j.chom.2022.07.016

    • PubMed
    • Google Scholar
23. Software

    1. Johnson M
    2. Dupic T

    (2022) Wuhan-to-omicron, version 1.0.0

    Github.

    https://desai-lab.github.io/wuhan_to_omicron/
24. 1. Khare S
    2. Gurry C
    3. Freitas L
    4. Schultz MB
    5. Bach G
    6. Diallo A
    7. Akite N
    8. Ho J
    9. Lee RT
    10. Yeo W
    11. Curation Team GC
    12. Maurer-Stroh S

    (2021) GISAID’s role in pandemic response

    China CDC Weekly 3:1049–1051.

    https://doi.org/10.46234/ccdcw2021.255

    • PubMed
    • Google Scholar
25. 1. Liu C
    2. Ginn HM
    3. Dejnirattisai W
    4. Supasa P
    5. Wang B
    6. Tuekprakhon A
    7. Nutalai R
    8. Zhou D
    9. Mentzer AJ
    10. Zhao Y
    11. Duyvesteyn HME
    12. López-Camacho C
    13. Slon-Campos J
    14. Walter TS
    15. Skelly D
    16. Johnson SA
    17. Ritter TG
    18. Mason C
    19. Costa Clemens SA
    20. Gomes Naveca F
    21. Nascimento V
    22. Nascimento F
    23. Fernandes da Costa C
    24. Resende PC
    25. Pauvolid-Correa A
    26. Siqueira MM
    27. Dold C
    28. Temperton N
    29. Dong T
    30. Pollard AJ
    31. Knight JC
    32. Crook D
    33. Lambe T
    34. Clutterbuck E
    35. Bibi S
    36. Flaxman A
    37. Bittaye M
    38. Belij-Rammerstorfer S
    39. Gilbert SC
    40. Malik T
    41. Carroll MW
    42. Klenerman P
    43. Barnes E
    44. Dunachie SJ
    45. Baillie V
    46. Serafin N
    47. Ditse Z
    48. Da Silva K
    49. Paterson NG
    50. Williams MA
    51. Hall DR
    52. Madhi S
    53. Nunes MC
    54. Goulder P
    55. Fry EE
    56. Mongkolsapaya J
    57. Ren J
    58. Stuart DI
    59. Screaton GR

    (2021) Reduced neutralization of SARS-cov-2 B.1.617 by vaccine and convalescent serum

    Cell 184:4220–4236.

    https://doi.org/10.1016/j.cell.2021.06.020

    • PubMed
    • Google Scholar
26. 1. Mannar D
    2. Saville JW
    3. Zhu X
    4. Srivastava SS
    5. Berezuk AM
    6. Tuttle KS
    7. Marquez AC
    8. Sekirov I
    9. Subramaniam S

    (2022) SARS-cov-2 omicron variant: antibody evasion and cryo-EM structure of spike protein-ACE2 complex

    Science 375:760–764.

    https://doi.org/10.1126/science.abn7760

    • PubMed
    • Google Scholar
27. 1. McCallum M
    2. Czudnochowski N
    3. Rosen LE
    4. Zepeda SK
    5. Bowen JE
    6. Walls AC
    7. Hauser K
    8. Joshi A
    9. Stewart C
    10. Dillen JR
    11. Powell AE
    12. Croll TI
    13. Nix J
    14. Virgin HW
    15. Corti D
    16. Snell G
    17. Veesler D

    (2022) Structural basis of SARS-cov-2 omicron immune evasion and receptor engagement

    Science 375:864–868.

    https://doi.org/10.1126/science.abn8652

    • PubMed
    • Google Scholar
28. Software

    1. Moulana A

    (2022) Omicron_ab_landscape, version swh:1:rev:9ab630decfa835b2551430ed693796ef366b1aff

    Software Heritage.

    https://archive.softwareheritage.org/swh:1:dir:0599e6e6640e13cd79e4d3fb6b501a2cffef990c;origin=https://github.com/desai-lab/omicron_ab_landscape;visit=swh:1:snp:f18aa333a6ab0e00e7bcd705b96aa5a37096749b;anchor=swh:1:rev:9ab630decfa835b2551430ed693796ef366b1aff
29. 1. Moulana A
    2. Dupic T
    3. Phillips AM
    4. Chang J
    5. Nieves S
    6. Roffler AA
    7. Greaney AJ
    8. Starr TN
    9. Bloom JD
    10. Desai MM

    (2022) Compensatory epistasis maintains ACE2 affinity in SARS-cov-2 omicron BA.1

    Nature Communications 13:7011.

    https://doi.org/10.1038/s41467-022-34506-z

    • PubMed
    • Google Scholar
30. 1. Nguyen Ba AN
    2. Cvijović I
    3. Rojas Echenique JI
    4. Lawrence KR
    5. Rego-Costa A
    6. Liu X
    7. Levy SF
    8. Desai MM

    (2019) High-Resolution lineage tracking reveals travelling wave of adaptation in laboratory yeast

    Nature 575:494–499.

    https://doi.org/10.1038/s41586-019-1749-3

    • PubMed
    • Google Scholar
31. 1. Olson CA
    2. Wu NC
    3. Sun R

    (2014) A comprehensive biophysical description of pairwise epistasis throughout an entire protein domain

    Current Biology 24:2643–2651.

    https://doi.org/10.1016/j.cub.2014.09.072

    • PubMed
    • Google Scholar
32. 1. Otwinowski J
    2. McCandlish DM
    3. Plotkin JB

    (2018) Inferring the shape of global epistasis

    PNAS 115:E7550–E7558.

    https://doi.org/10.1073/pnas.1804015115

    • PubMed
    • Google Scholar
33. 1. Pettersen EF
    2. Goddard TD
    3. Huang CC
    4. Meng EC
    5. Couch GS
    6. Croll TI
    7. Morris JH
    8. Ferrin TE

    (2021) UCSF chimerax: structure visualization for researchers, educators, and developers

    Protein Science 30:70–82.

    https://doi.org/10.1002/pro.3943

    • PubMed
    • Google Scholar
34. 1. Phillips AM
    2. Lawrence KR
    3. Moulana A
    4. Dupic T
    5. Chang J
    6. Johnson MS
    7. Cvijovic I
    8. Mora T
    9. Walczak AM
    10. Desai MM

    (2021) Binding affinity landscapes constrain the evolution of broadly neutralizing anti-influenza antibodies

    eLife 10:e71393.

    https://doi.org/10.7554/eLife.71393

    • PubMed
    • Google Scholar
35. 1. Planas D
    2. Saunders N
    3. Maes P
    4. Guivel-Benhassine F
    5. Planchais C
    6. Buchrieser J
    7. Bolland W-H
    8. Porrot F
    9. Staropoli I
    10. Lemoine F
    11. Péré H
    12. Veyer D
    13. Puech J
    14. Rodary J
    15. Baele G
    16. Dellicour S
    17. Raymenants J
    18. Gorissen S
    19. Geenen C
    20. Vanmechelen B
    21. Wawina-Bokalanga T
    22. Martí-Carreras J
    23. Cuypers L
    24. Sève A
    25. Hocqueloux L
    26. Prazuck T
    27. Rey FA
    28. Simon-Loriere E
    29. Bruel T
    30. Mouquet H
    31. André E
    32. Schwartz O

    (2022) Considerable escape of SARS-cov-2 omicron to antibody neutralization

    Nature 602:671–675.

    https://doi.org/10.1038/s41586-021-04389-z

    • PubMed
    • Google Scholar
36. Software

    1. R Development Core Team

    (2017) R: A language and environment for statistical computing

    R Foundation for Statistical Computing, Vienna, Austria.

    https://www.r-project.org/index.html
37. 1. Rotem A
    2. Serohijos AWR
    3. Chang CB
    4. Wolfe JT
    5. Fischer AE
    6. Mehoke TS
    7. Zhang H
    8. Tao Y
    9. Lloyd Ung W
    10. Choi J-M
    11. Rodrigues JV
    12. Kolawole AO
    13. Koehler SA
    14. Wu S
    15. Thielen PM
    16. Cui N
    17. Demirev PA
    18. Giacobbi NS
    19. Julian TR
    20. Schwab K
    21. Lin JS
    22. Smith TJ
    23. Pipas JM
    24. Wobus CE
    25. Feldman AB
    26. Weitz DA
    27. Shakhnovich EI

    (2018) Evolution on the biophysical fitness landscape of an RNA virus

    Molecular Biology and Evolution 35:2390–2400.

    https://doi.org/10.1093/molbev/msy131

    • PubMed
    • Google Scholar
38. 1. Sailer ZR
    2. Harms MJ

    (2017) High-Order epistasis shapes evolutionary trajectories

    PLOS Computational Biology 13:e1005541.

    https://doi.org/10.1371/journal.pcbi.1005541

    • PubMed
    • Google Scholar
39. Software

    1. Schrodinger LLC

    (2015) The pymol molecular graphics system, version 2.5

    Pymol.

    https://pymol.org/2/
40. 1. Shu Y
    2. McCauley J

    (2017) GISAID: global initiative on sharing all influenza data-from vision to reality

    Euro Surveillance 22:30494.

    https://doi.org/10.2807/1560-7917.ES.2017.22.13.30494

    • PubMed
    • Google Scholar
41. 1. Starr TN
    2. Greaney AJ
    3. Hilton SK
    4. Ellis D
    5. Crawford KHD
    6. Dingens AS
    7. Navarro MJ
    8. Bowen JE
    9. Tortorici MA
    10. Walls AC
    11. King NP
    12. Veesler D
    13. Bloom JD

    (2020) Deep mutational scanning of SARS-cov-2 receptor binding domain reveals constraints on folding and ACE2 binding

    Cell 182:1295–1310.

    https://doi.org/10.1016/j.cell.2020.08.012

    • PubMed
    • Google Scholar
42. 1. Starr TN
    2. Czudnochowski N
    3. Liu Z
    4. Zatta F
    5. Park YJ
    6. Addetia A
    7. Pinto D
    8. Beltramello M
    9. Hernandez P
    10. Greaney AJ
    11. Marzi R
    12. Glass WG
    13. Zhang I
    14. Dingens AS
    15. Bowen JE
    16. Tortorici MA
    17. Walls AC
    18. Wojcechowskyj JA
    19. De Marco A
    20. Rosen LE
    21. Zhou J
    22. Montiel-Ruiz M
    23. Kaiser H
    24. Dillen JR
    25. Tucker H
    26. Bassi J
    27. Silacci-Fregni C
    28. Housley MP
    29. di Iulio J
    30. Lombardo G
    31. Agostini M
    32. Sprugasci N
    33. Culap K
    34. Jaconi S
    35. Meury M
    36. Dellota E
    37. Abdelnabi R
    38. Foo SYC
    39. Cameroni E
    40. Stumpf S
    41. Croll TI
    42. Nix JC
    43. Havenar-Daughton C
    44. Piccoli L
    45. Benigni F
    46. Neyts J
    47. Telenti A
    48. Lempp FA
    49. Pizzuto MS
    50. Chodera JD
    51. Hebner CM
    52. Virgin HW
    53. Whelan SPJ
    54. Veesler D
    55. Corti D
    56. Bloom JD
    57. Snell G

    (2021a) SARS-cov-2 RBD antibodies that maximize breadth and resistance to escape

    Nature 597:97–102.

    https://doi.org/10.1038/s41586-021-03807-6

    • PubMed
    • Google Scholar
43. 1. Starr TN
    2. Greaney AJ
    3. Addetia A
    4. Hannon WW
    5. Choudhary MC
    6. Dingens AS
    7. Li JZ
    8. Bloom JD

    (2021b) Prospective mapping of viral mutations that escape antibodies used to treat COVID-19

    Science 371:850–854.

    https://doi.org/10.1126/science.abf9302

    • PubMed
    • Google Scholar
44. 1. Starr TN
    2. Greaney AJ
    3. Dingens AS
    4. Bloom JD

    (2021c) Complete map of SARS-cov-2 RBD mutations that escape the monoclonal antibody LY-cov555 and its cocktail with LY-cov016

    Cell Reports. Medicine 2:100255.

    https://doi.org/10.1016/j.xcrm.2021.100255

    • PubMed
    • Google Scholar
45. 1. Starr TN
    2. Greaney AJ
    3. Hannon WW
    4. Loes AN
    5. Hauser K
    6. Dillen JR
    7. Ferri E
    8. Farrell AG
    9. Dadonaite B
    10. McCallum M
    11. Matreyek KA
    12. Corti D
    13. Veesler D
    14. Snell G
    15. Bloom JD

    (2022a) Shifting mutational constraints in the SARS-cov-2 receptor-binding domain during viral evolution

    Science 377:420–424.

    https://doi.org/10.1126/science.abo7896

    • PubMed
    • Google Scholar
46. 1. Starr TN
    2. Zepeda SK
    3. Walls AC
    4. Greaney AJ
    5. Alkhovsky S
    6. Veesler D
    7. Bloom JD

    (2022b) Ace2 binding is an ancestral and evolvable trait of sarbecoviruses

    Nature 603:913–918.

    https://doi.org/10.1038/s41586-022-04464-z

    • PubMed
    • Google Scholar
47. 1. Steckbeck JD
    2. Orlov I
    3. Chow A
    4. Grieser H
    5. Miller K
    6. Bruno J
    7. Robinson JE
    8. Montelaro RC
    9. Cole KS

    (2005) Kinetic rates of antibody binding correlate with neutralization sensitivity of variant simian immunodeficiency virus strains

    Journal of Virology 79:12311–12320.

    https://doi.org/10.1128/JVI.79.19.12311-12320.2005

    • PubMed
    • Google Scholar
48. 1. Tada T
    2. Zhou H
    3. Dcosta BM
    4. Samanovic MI
    5. Chivukula V
    6. Herati RS
    7. Hubbard SR
    8. Mulligan MJ
    9. Landau NR

    (2022) Increased resistance of SARS-cov-2 omicron variant to neutralization by vaccine-elicited and therapeutic antibodies

    EBioMedicine 78:103944.

    https://doi.org/10.1016/j.ebiom.2022.103944

    • PubMed
    • Google Scholar
49. Software

    1. Therneau T
    2. Atkinson B
    3. Ripley B

    (2013) Rpart: recursive partitioning, version 4.1-3

    R Package.

    http://CRAN.R-project.org/package=rpart
50. 1. Tobin J

    (1958) Estimation of relationships for limited dependent variables

    Econometrica 26:24.

    https://doi.org/10.2307/1907382

    • Google Scholar
51. Software

    1. Van Rossum G
    2. Drake FL

    (2009) Python 3 reference manual.3 reference manual, version 0.1

    Createspace.

    https://dl.acm.org/doi/book/10.5555/1593511
52. 1. Viana R
    2. Moyo S
    3. Amoako DG
    4. Tegally H
    5. Scheepers C
    6. Althaus CL
    7. Anyaneji UJ
    8. Bester PA
    9. Boni MF
    10. Chand M
    11. Choga WT
    12. Colquhoun R
    13. Davids M
    14. Deforche K
    15. Doolabh D
    16. du Plessis L
    17. Engelbrecht S
    18. Everatt J
    19. Giandhari J
    20. Giovanetti M
    21. Hardie D
    22. Hill V
    23. Hsiao N-Y
    24. Iranzadeh A
    25. Ismail A
    26. Joseph C
    27. Joseph R
    28. Koopile L
    29. Kosakovsky Pond SL
    30. Kraemer MUG
    31. Kuate-Lere L
    32. Laguda-Akingba O
    33. Lesetedi-Mafoko O
    34. Lessells RJ
    35. Lockman S
    36. Lucaci AG
    37. Maharaj A
    38. Mahlangu B
    39. Maponga T
    40. Mahlakwane K
    41. Makatini Z
    42. Marais G
    43. Maruapula D
    44. Masupu K
    45. Matshaba M
    46. Mayaphi S
    47. Mbhele N
    48. Mbulawa MB
    49. Mendes A
    50. Mlisana K
    51. Mnguni A
    52. Mohale T
    53. Moir M
    54. Moruisi K
    55. Mosepele M
    56. Motsatsi G
    57. Motswaledi MS
    58. Mphoyakgosi T
    59. Msomi N
    60. Mwangi PN
    61. Naidoo Y
    62. Ntuli N
    63. Nyaga M
    64. Olubayo L
    65. Pillay S
    66. Radibe B
    67. Ramphal Y
    68. Ramphal U
    69. San JE
    70. Scott L
    71. Shapiro R
    72. Singh L
    73. Smith-Lawrence P
    74. Stevens W
    75. Strydom A
    76. Subramoney K
    77. Tebeila N
    78. Tshiabuila D
    79. Tsui J
    80. van Wyk S
    81. Weaver S
    82. Wibmer CK
    83. Wilkinson E
    84. Wolter N
    85. Zarebski AE
    86. Zuze B
    87. Goedhals D
    88. Preiser W
    89. Treurnicht F
    90. Venter M
    91. Williamson C
    92. Pybus OG
    93. Bhiman J
    94. Glass A
    95. Martin DP
    96. Rambaut A
    97. Gaseitsiwe S
    98. von Gottberg A
    99. de Oliveira T

    (2022) Rapid epidemic expansion of the SARS-cov-2 omicron variant in southern Africa

    Nature 603:679–686.

    https://doi.org/10.1038/s41586-022-04411-y

    • PubMed
    • Google Scholar
53. 1. Wells JA

    (1990) Additivity of mutational effects in proteins

    Biochemistry 29:8509–8517.

    https://doi.org/10.1021/bi00489a001

    • PubMed
    • Google Scholar
54. 1. Wentz AE
    2. Shusta EV

    (2007) A novel high-throughput screen reveals yeast genes that increase secretion of heterologous proteins

    Applied and Environmental Microbiology 73:1189–1198.

    https://doi.org/10.1128/AEM.02427-06

    • PubMed
    • Google Scholar
55. Book

    1. Wickham H

    (2016) Ggplot2

    Springer International Publishing.

    https://doi.org/10.1007/978-3-319-24277-4

    • Google Scholar
56. 1. Windsor IW
    2. Tong P
    3. Lavidor O
    4. Moghaddam AS
    5. McKay LGA
    6. Gautam A
    7. Chen Y
    8. MacDonald EA
    9. Yoo DK
    10. Griffths A
    11. Wesemann DR
    12. Harrison SC

    (2022) Antibodies induced by an ancestral SARS-cov-2 strain that cross-neutralize variants from alpha to omicron BA.1

    Science Immunology 7:eabo3425.

    https://doi.org/10.1126/sciimmunol.abo3425

    • PubMed
    • Google Scholar
57. 1. Zhou D
    2. Dejnirattisai W
    3. Supasa P
    4. Liu C
    5. Mentzer AJ
    6. Ginn HM
    7. Zhao Y
    8. Duyvesteyn HME
    9. Tuekprakhon A
    10. Nutalai R
    11. Wang B
    12. Paesen GC
    13. Lopez-Camacho C
    14. Slon-Campos J
    15. Hallis B
    16. Coombes N
    17. Bewley K
    18. Charlton S
    19. Walter TS
    20. Skelly D
    21. Lumley SF
    22. Dold C
    23. Levin R
    24. Dong T
    25. Pollard AJ
    26. Knight JC
    27. Crook D
    28. Lambe T
    29. Clutterbuck E
    30. Bibi S
    31. Flaxman A
    32. Bittaye M
    33. Belij-Rammerstorfer S
    34. Gilbert S
    35. James W
    36. Carroll MW
    37. Klenerman P
    38. Barnes E
    39. Dunachie SJ
    40. Fry EE
    41. Mongkolsapaya J
    42. Ren J
    43. Stuart DI
    44. Screaton GR

    (2021) Evidence of escape of SARS-cov-2 variant B.1.351 from natural and vaccine-induced sera

    Cell 184:2348–2361.

    https://doi.org/10.1016/j.cell.2021.02.037

    • PubMed
    • Google Scholar
58. 1. Zhou T
    2. Wang L
    3. Misasi J
    4. Pegu A
    5. Zhang Y
    6. Harris DR
    7. Olia AS
    8. Talana CA
    9. Yang ES
    10. Chen M
    11. Choe M
    12. Shi W
    13. Teng I-T
    14. Creanga A
    15. Jenkins C
    16. Leung K
    17. Liu T
    18. Stancofski E-SD
    19. Stephens T
    20. Zhang B
    21. Tsybovsky Y
    22. Graham BS
    23. Mascola JR
    24. Sullivan NJ
    25. Kwong PD

    (2022) Structural basis for potent antibody neutralization of SARS-cov-2 variants including B.1.1.529

    Science 376:eabn8897.

    https://doi.org/10.1126/science.abn8897

    • PubMed
    • Google Scholar

Author details

1. Alief Moulana

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

   Contribution

   Conceptualization, Resources, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   Contributed equally with

   Thomas Dupic and Jeffrey Chang

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-0389-7082

2. Thomas Dupic

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

   Contribution

   Conceptualization, Resources, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   Contributed equally with

   Alief Moulana and Jeffrey Chang

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1803-1617

3. Angela M Phillips

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

   Contribution

   Conceptualization, Resources, Data curation, Software, Formal analysis, Supervision, Validation, Investigation, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   angela.phillips@ucsf.edu

   Competing interests

   has or has recently consulted for Leyden Labs

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

4. Jeffrey Chang

   1. Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, United States
   2. Department of Physics, Harvard University, Cambridge, United States

   Contribution

   Conceptualization, Resources, Data curation, Software, Formal analysis, Supervision, Validation, Investigation, Visualization, Methodology, Project administration, Writing – review and editing

   Contributed equally with

   Alief Moulana and Thomas Dupic

   Competing interests

   No competing interests declared

5. Anne A Roffler

   Biological and Biomedical Sciences, Harvard Medical School, Boston, United States

   Contribution

   Investigation, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8412-0322

6. Allison J Greaney

   1. Basic Sciences Division and Computational Biology Program, Fred Hutchinson Cancer Research Center, Seattle, United States
   2. Department of Genome Sciences, University of Washington, Seattle, United States
   3. Medical Scientist Training Program, University of Washington, Seattle, United States

   Contribution

   Conceptualization, Resources, Writing – review and editing

   Competing interests

   is an inventor on Fred Hutch licensed patents related to viral deep mutational scanning (patent numbers WO2022146484, WO2020006494 and application number US20210147832)

7. Tyler N Starr

   Basic Sciences Division and Computational Biology Program, Fred Hutchinson Cancer Research Center, Seattle, United States

   Contribution

   Conceptualization, Resources, Writing – review and editing

   Competing interests

   is an inventor on Fred Hutch licensed patents related to viral deep mutational scanning (patent numbers WO2022146484, WO2020006494 and application number US20210147832)

   "This ORCID iD identifies the author of this article:" 0000-0001-6713-6904

8. Jesse D Bloom

   1. Basic Sciences Division and Computational Biology Program, Fred Hutchinson Cancer Research Center, Seattle, United States
   2. Department of Genome Sciences, University of Washington, Seattle, United States
   3. Howard Hughes Medical Institute, Seattle, United States

   Contribution

   Conceptualization, Resources, Supervision, Writing – review and editing

   Competing interests

   is an inventor on Fred Hutch licensed patents related to viral deep mutational scanning (patent numbers WO2022146484, WO2020006494 and application number US20210147832). JDB has or has recently consulted for Apriori Bio, Oncorus, Moderna, and Merck

   "This ORCID iD identifies the author of this article:" 0000-0003-1267-3408

9. 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, Resources, Funding acquisition, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   mdesai@oeb.harvard.edu

   Competing interests

   has or has recently consulted for Leyden Labs

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

• 1,818

  views

• 286

  downloads

• 37

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.