Antigenic cartography using variant-specific hamster sera reveals substantial antigenic variation among Omicron subvariants

Significance Since late 2020, severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2) variants capable of evading the immune response from previous infection or vaccination have emerged. Understanding and tracking changes in antigenicity is a crucial component of vaccine design and update. Finding human first-infection sera to measure antigenic distances between novel variants is becoming impossible, as most people have been infected or vaccinated. Therefore, an alternative (nonhuman) model is needed. We evaluated hamster sera as a surrogate to human first-infection sera to measure antigenic differences between recently circulating variants. We find a closer antigenic relationship between the pre-Omicron variants circulating in 2020 and 2021 and larger distances between Omicron variants.


Titer determination
Effects of using discrete and continuous titers Visual inspection of the neutralization curves in Dataset 11 showed that continuous titers inferred when fixing the neutralization curve at zero provide the most parsimonious fit to the data.Given the overall similarity of the fold change and antigenic maps estimated by the different methods, we therefore proceeded to use continuous titers inferred when fixing the neutralization curve at zero.However, visual inspection of the neutralization curves in Dataset 1 also indicated 28 titers (2.1 vs Alpha,2.2 vs BA.2_2,3.2 vs BA.2_12,3.3 vs Alpha,3.3 vs Beta,4.1 vs Alpha,4.2 vs Delta,4.3 vs Alpha,4.3 vs Delta,5.1 vs Alpha,5.1 vs BA.2_12,5.2 vs Alpha,5.2 vs BA.2_2,5.3 vs BA.2_2,6.1 vs BA.2_2,6.2 vs BA.2_2,7.1 vs D614G,7.1 vs Alpha,7.1 vs Delta,7.1 vs E484K,7.1 vs BA.2_12,7.1 vs Mu,7.2 vs Mu,7.3 vs Alpha,7.3 vs Mu,8.1 vs BA.2_12,9.1 vs BF.7,9.3 vs BQ.1.18)where continuous titers inferred when fixing the lower and upper ends of the neutralization curve at zero and one, respectively, provided a better fit to the data.These titers were therefore adapted as shown in Table S2.Antigenic maps with and without these adapted titers only show minimal differences (SI Appendix fig.S6, RMSD = 0.13).The final titers used for further analyses are shown in Table S3.

Assessing antigenic map model fit
We performed several analyses to assess the dimensionality of the antigenic map (SI Appendix, fig.S10), how well the distances in the antigenic map represent the measured titers (SI Appendix, figs.S11, S12), the robustness of the map to titer noise (SI Appendix, fig.S13A-C) and missing titers (SI Appendix,, and the predictive power of the antigenic map (SI Appendix, figs.S16-S18).
In order to assess the dimensionality of the antigenic map, we investigated how well the antigenic distances in maps optimized in different dimensions fit the measured titers.To this end, we performed 1000 repeats where 10% of the titers were excluded at random, the map re-optimised using 500 optimisations in 1-5 dimensions, and calculated the root-meansquared error between the measured titers and the predicted titers in the antigenic map.The map optimized in three dimensions fit the data best (RMSE of detectable titers = 1.08), but only performed marginally better than maps optimized in two (RMSE of detectable titers = 1.13), four (RMSE of detectable titers = 1.10), and five (RMSE of detectable titers = 1.11) dimensions (SI Appendix, fig.S10C).The overall arrangement of the variants in a map optimized in three dimensions closely resembles the arrangement of variants optimized in two dimensions (SI Appendix, fig.S10A, B).For ease of representation, we show the map in two dimensions.
We next assessed how well the distances fitted in the antigenic map represent the measured distances inferred from the titers (SI Appendix, figs.S11, S12).Overall, there was a good fit between the fitted and the measured titers.The difference between the fitted and measured titers was 0.03 on the log2 scale, with a standard deviation (sd) of 0.73.When assuming a mean of 0, the standard deviation is 0.79.The standard deviation was higher than the standard deviation observed between repeated titrations (sd = 0.47) (SI Appendix, fig.S9).
However, because the repeats were not independent, the repeat variation may be underestimated, and the difference between fitted and measured titers is comparable to that observed in other studies investigating SARS-CoV-2 antigenic variation (1,2).We also found no evidence of increased differences between fitted and measured titers for specific serum groups and variant pairs (SI Appendix, fig.S12).
We next investigated the robustness of the map to measurement error, variant reactivity biases and missing data.To assess robustness to measurement error and variant reactivity biases we performed a bootstrap analysis where normally distributed noise was added to the titer and / or variant reactivity (SI Appendix, fig.S13A-C).We performed 1000 bootstrap repeats of adding random noise and summarized the positional variation of the variants and sera, such that the areas shown in SI Appendix, fig.S13 represent 68% (one standard deviation) of the positional variation of each variant or serum.Random noise added to the titers had a standard deviation of 0.33, as estimated from the standard deviation of differences between repeat titrations (SI Appendix, fig.S9).Random noise added to variant reactivity had a standard deviation of 0.4, following Wilks et al., 2022 (1).In general, positions were largely robust to the addition of random noise, in particular for the Omicron BA.1, BA.2, BA.4/BA.5,BF.7, BQ.1.18and XBB.2 variants, and larger positional uncertainty within the pre-Omicron variants and for Omicron BN. 1.3.1,EG.5.1,and JN.1. Next,we assessed the robustness of the antigenic map to the removal of each variant (SI Appendix, fig.S14A) and serum group (SI Appendix, fig.S14B) in turn.Variant positions were largely robust to the removal of individual variants, with increased variation observed for the Omicron BA.1, Omicron BA.5 and the joint removal of both Omicron BA.2 variants (SI Appendix, fig.S14A).Similarly, variant positions were stable to the removal of serum groups, albeit with slightly larger variation when removing the BA.1 and BA.5 sera (SI Appendix, fig.S14B).
Finally, we investigated how well the map is able to predict missing titrations.To this end, we performed 500 cross-validation repeats, where 10% of the titers were removed at random, the map re-optimised, and the missing titers predicted from the antigenic map.The mean difference between the predicted and measured titer was 0.52, with a standard deviation of 1.43 when assuming a mean of 0. This is higher than the difference between fitted and measured titers (SI Appendix, fig.S11, mean = 0.03, standard deviation = 0.79 when assuming a mean of 0 and only considering detectable titers).We visualized the difference between predicted and measured titers split by variant and serum group, and found that no variant is predicted to consistently have higher residuals in all serum groups.the difference in log2 titer between the first and the second repeat.Non-detectable titers were set to limit of detection -1 on the log2 scale.The mean difference between repeats was 0.02, with a standard deviation of 0.47.Assuming a mean of 0 to account for the systematic bias of titrations between repeats, the standard deviation is 0.47 on the log2 scale.

Supplementary figures
Accounting for the presence of measurement error in both the first and second titration the standard deviation of noise per measurement is !0.47 !/2 = 0.33.).Measured titers are on average 0.03 higher than the fitted titers (with a standard deviation of 0.73), with the mean indicated by the dashed black line.Assuming a mean of 0 to account for the systematic bias of titrations between repeats, the standard deviation is 0.79 on the log2 scale.This is higher than the standard deviation of the variation between repeats, however the standard deviation between repeats may be lower, since the repeats were not independent.Randomly subsample the data in panel C to include one serum per serum group.A map was constructed from each subsample and the RMSD of the variant positions in the subsampled map compared to a map made from the all-against-all titrated sera and variants was calculated.The RMSD is indicated by boxplots and colored dots, according to the number of sera in each subsampled map.Red dots indicate maps that include both the BA.1 and BA.2 serum groups, blue dots indicate maps that include either the BA.1 or BA.2 or neither of the BA.1 or BA.2 serum groups.To estimate the RMSD under a random scenario, titers in each subsampled map were randomized, a new map constructed and the RMSD from the randomized, subsampled map compared to the full map in Figure 2 was calculated, and is indicated by 'x'.Subsampled maps were constructed in two dimensions, using 100 optimisations.As the Alpha serum group only includes two sera, and the BA.2 serum groups contain six sera in total, the number of sera in panels B and C is not always a multiple of three.Table S3: Titers used to make the antigenic map.Columns correspond to the different sera, with the infecting variant given in the top row, rows correspond to the variant that was titrated.* indicate variant and serum pairs that have not been titrated.
Dataset S2 (separate file): Neutralization curves.Each sub-plot shows the neutralization curve for a variant titrated against a serum, as specified in the panel title.The y-axis shows the fraction of infectivity remaining, the x-axis shows the dilution.Blue and orange shapes show the fraction of infectivity remaining from the two runs that were done.Titer curves were fit with the neutcurve package (1).The black curve shows the titer curve inferred when constraining the lower end of the neutralization curve at zero and the upper end at one.The red curve shows the titer curve inferred when constraining the upper end of the neutralization curve at one.The blue curve shows the titer curve inferred when constraining the bottom end of the neutralization curve at 0, and the gray curve shows the titer curve inferred when not constraining the neutralization curve.

Figure S1 :
Figure S1: Fold change measured when inferring discrete titers with different sensitivity levels.Larger fold changes with wide confidence intervals result when titers are non-detectable.Fold changes are largely comparable between sensitivity levels.Dots show the estimated mean fold change, with lines showing the 95% highest posterior density interval.Ratio of titers have been log-transformed.

Figure S2 :
Figure S2: Fold change measured when inferring continuous titers with different sensitivity levels.Larger fold changes with wide confidence intervals result when titers are non-detectable.Fold changes are largely comparable between sensitivity levels.Continuous titers were inferred by constraining the neutralization curve at zero and one.Dots show the estimated mean fold change, with lines showing the 95% highest posterior density interval.Ratio of titers have been log-transformed.

Figure S3 :
Figure S3: Antigenic maps made from discrete (left) and continuous (right) titers inferred with different sensitivity levels.Antigenic maps were optimized in two dimensions, with 500 optimisation and the minimum column basis parameter set to 'none'.A-D) Maps made with discrete titers using a dilution_stepsize of 1. E-H) Maps made with continuous titers using a dilution_stepsize of 0. Arrows point to the position of the same variant and serum in the NT50 map shown in panel A for panels A-D, and panels E for panels E-H.A,E) NT50, B,F) NT75, C,G) NT90, D,H) NT99.Viruses are shown as circles, sera as squares, with sera colored by the color of their homologous variant (blue: D614G, green: Alpha, dark-yellow: Beta, orange: Delta, green-blue: Mu, cyan: B.1+E484K, red: BA.1, orchid: BA.2 (2x, on top of each other), pink: BA.4 and BA.5, ochre: BQ.1.18,maroon: BF.7, sea-green: XBB.2, light-orchid: BN.1.3.1, dark blue: EG.5.1, yellow: JN.1).The gray number at the bottom of the plot indicates the sum of the squared difference between the distance of each variant and serum in the titer table and the antigenic map.

Figure S4 :
Figure S4: Fold change measured when inferring titers using either continuous or discrete methods at NT90.Continuous titers were inferred fixing the bottom and top of the neutralization curve at zero and one, respectively (continuous_fixtop_fixbottom), only fixing the top of the neutralization curve (continuous_fixtop), only fixing the bottom of the neutralization curve (continuous_fixbottom), not fixing the neutralization curve (continuous), and using discrete titers (discrete).Fold changes are similar between different methods.Dots show the estimated fold change, with lines showing the 95% highest posterior density interval.Ratio of titers have been log-transformed.

Figure S5 :
Figure S5: Comparison of discrete and continuous NT90 maps.In each map, the arrows point to the position of the variant and serum in the antigenic map made from discrete titers, shown in panel E. A) Map made from continuous titers, fixing the bottom and top of the neutralization curve at zero and 1, respectively.B) Map made from continuous titers, fixing the top of the neutralization curve at one.C) Map made from continuous titers, fixing the bottom of the neutralization curve at one.D) Map made from continuous titers, without fixing the neutralization curve.E) Map made from discrete titers.Viruses are shown as circles, sera as squares, with sera colored by the color of their homologous variant (blue: D614G, green: Alpha, dark-yellow: Beta, orange: Delta, green-blue: Mu, cyan: B.1+E484K, red: BA.1, orchid: BA.2 (2x, on top of each other), pink: BA.4 and BA.5, ochre: BQ.1.18,maroon: BF.7, sea-green: XBB.2, light-orchid: BN.1.3.1, dark blue: EG.5.1, yellow: JN.1).The gray number at the bottom of the plot indicates the sum of the squared difference between the distance of each variant and serum in the titer table and the antigenic map.

Figure S7 :
Figure S7: Pairwise comparison of titers of two variants expected to be antigenically similar.A) Comparison of the titers from the two different BA.2 isolates.The mean fold difference between the two variants is 1 (95% highest posterior density interval: -1.14, 1.13).B) Comparison of the titers from the BA.4 and BA.5 variants.The mean fold difference between the two variants is -1 (95% highest posterior density interval: -1.16, 1.15).Dots are colored by serum group.The intercept of the colored line shows the mean fold difference between the titers from the two variants, the slope is equal to 1.The shaded area shows the 95% posterior density interval of the fold difference.

Figure S8 :
Figure S8: Fold change compared to the homologous variant.Circles show the point estimate for the mean fold change, while the intervals show the 95% highest posterior density interval of the fold change estimate.Variants are ordered by decreasing fold change within each serum group.Ratio of titers have been log-transformed.

Figure S9 :
Figure S9: Repeat variation.Each titer was measured in duplicate wells.The figure shows

Figure S10 :
Figure S10: Testing map dimensionality.A and B) The map optimized in three dimensions, shown from the top (A) and from the side (B).The black lines point to the position of the variants in the two-dimensional map shown in Figure 2. Viruses are shown as spheres, sera as cubes, with sera colored by the color of their homologous variant (blue: D614G, green: Alpha, dark-yellow: Beta, orange: Delta, green-blue: Mu, cyan: B.1+E484K, red: BA.1, orchid: BA.2 (2x, on top of each other), pink: BA.4 and BA.5, ochre: BQ.1.18,maroon: BF.7, sea-green: XBB.2, light-orchid: BN.1.3.1, dark blue: EG.5.1, yellow: JN.1).C) Dimensionality test, where 1000 repeats were performed with 10% of titers excluded at random and the map optimized in one to five dimensions.The plot shows the root mean squared error and standard error of the excluded titers between the titers estimated from the map and the known titers.

Figure S11 :
Figure S11: Comparison of measured log2 titers and fitted log2 titers as inferred from the antigenic map.Detectable measured titers are shown in red, non-detectable measured titers in blue.A) Scatter plot of measured and fitted log2 titers.Fitted log2 titers were inferred from the distances in the antigenic map.B) Histogram of the difference between the measured and the fitted log2 titers.When measured titers were non-detectable, the residuals were inferred as described in (1).The histogram of detectable titers is shown in red, nondetectable titers in blue.Variant and serum group pairs where all titers were non-detectable were excluded (BA.2 sera vs D614G and B.1+E484K, BA.1 sera vs D614G, BA.2-12 sera vs D614G).Measured titers are on average 0.03 higher than the fitted titers (with a standard

Figure S12 :
Figure S12: The difference between the measured log2 titer and the fitted log2 titer as inferred from the antigenic map, split by serum group and variant.Residuals for detectable titers are shown in black, residuals for non-detectable titers in blue.Variant and serum group pairs where all titers were non-detectable were excluded (BA.2 sera vs D614G and B.1+E484K, BA.1 sera vs D614G, BA.2-12 sera vs D614G).The boxplot indicates the median and 25 th and 75 th percentile.

Figure S13 :
Figure S13: Assessing sensitivity of the antigenic map to measurement error (A-C) and missing titers (D-F).A-C) Sensitivity of antigenic map to measurement error.1000 bootstrap repeats were performed where normally distributed noise was added to each titer and / or to the titers of each variant.A) Noise added to titers and variant reactivity.B) Noise added to titers only.C) Noise added to variants only.Normally distributed noise added to the titers had a standard deviation of 0.33, following the standard deviation of the measurement error estimated in SI Appendix, fig.S9.Normally distributed noise added on a per-variant basis had a standard deviation of 0.4.D-F) Robustness of the antigenic map to missing titers.1000 bootstrap repeats were performed, where a random subset of titers was sampled with replacement, and the map re-optimised.A) Sera and variants were re-sampled.B) Variants were resampled.C) Sera were resampled.The colored regions indicate the area where 68% (1 standard deviation) of the positional variation of each variant (filled blobs) and serum (empty blobs) is captured.Circles are colored by variant (blue: D614G, green: Alpha, dark-yellow: Beta, orange: Delta, green-blue: Mu, cyan: B.1+E484K, red: BA.1, orchid: BA.2 (2x, on top of each other), pink: BA.4 and BA.5, ochre: BQ.1.18,maroon: BF.7, sea-green: XBB.2, light-orchid: BN.1.3.1, dark blue: EG.5.1, yellow: JN.1).

Figure S15 :
Figure S15: Antigenic map made with different combinations of Omicron sera.The left column always shows the antigenic map inferred without a subset of Omicron sera, with the arrows pointing to the positions of the variants in the full map (as in Figure2).The middle column shows the antigenic map inferred without a subset of Omicron sera with triangulation blobs.The blobs show the area that each variant (filled blob) or serum (empty blob) could take up without increasing the stress of the map by more than 1.The right column shows the antigenic map inferred without a subset of Omicron sera with resampling bootstrap blobs.An antigenic map was inferred 500 times, and each time titers were sampled with replacement.

Figure S16 :
Figure S16: Uncertainty of the position of variants and sera.A) Antigenic map with error lines.For each variant/serum pair a blue or red line is plotted showing the target distance between the variant and serum.A blue line indicates a target distance smaller, a red line a distance larger than the one shown in the map.B) Antigenic map with triangulation blobs.The blobs show the area that each variant (filled blob) or serum (empty blob) could take up without increasing the stress of the map by 1. Circles are colored by variant (blue: D614G, green: Alpha, dark-yellow: Beta, orange: Delta, green-blue: Mu, cyan: B.1+E484K, red: BA.1, orchid: BA.2 (2x, on top of each other), pink: BA.4 and BA.5, ochre: BQ.1.18,maroon: BF.7, sea-green: XBB.2, light-orchid: BN.1.3.1, dark blue: EG.5.1, yellow: JN.1).

Figure S17 :
Figure S17: Assessing predictive power of the antigenic map.500 repeats were performed where the map was re-optimized leaving out 10% of the data at random.The histogram shows the difference between the measured log2 titer and the predicted log2 titer as inferred from the map with 10% of the data removed.Only detectable titers were considered.The mean difference between measured and predicted detectable titers on the log2 scale was 0.52, with a standard deviation of 1.34.Assuming a mean of 0, the standard deviation is 1.43.

Figure S18 :
Figure S18: Assessing predictive power of the antigenic map, split by serum group and variant.The difference between measured and predicted log2 titers was inferred as described in the legend of SI Appendix, fig.S14.Only detectable titers are considered.The boxplot shows the median and 25 th and 75 th percentile.

Figure S19 :
Figure S19: Subsampling pre-Omicron serum groups.Each map was made from the BA.1 and BA.2 sera, and one (first row), two (second and third row), three (fourth and fifth row), or four (bottom row) pre-Omicron serum groups.The arrows point to the position of the variants in a map made from the all-against-all titrated sera and variants (without the Omicron BF.7, BQ.1.18,XBB.2, BN.1.3.1,EG.5.1 and JN.1 variants, and the BA.5 and XBB.2 sera).The number in the bottom right corner shows the total root mean squared deviation of the positions of the variants between the full map and the subsampled map.The text in the top-left indicates the included pre-Omicron serum groups, in addition to the BA.1 and BA.2 serum groups.Each map was made with 100 optimisations.Viruses are shown as circles, sera as squares, with sera colored by the color of their homologous variant (blue: D614G, green: Alpha, dark-yellow: Beta, orange: Delta, green-blue: Mu, cyan: B.1+E484K, red: BA.1, orchid: BA.2 (2x, on top of each other), pink: BA.4 and BA.5).The black number at the bottom right of the plot indicates the sum of the squared difference between the distance of each variant and serum in the titer table and the antigenic map.

Figure S20 :
Figure S20: Root mean squared deviation (RMSD) of variant positions of subsampled maps compared to complete map.In order to investigate map stability when reducing the number of sera used, we subsampled a map made from the all-against-all titrated sera and variants (without the Omicron BF.7, BQ.1.18,XBB.2, BN.1.3.1,EG.5.1 and JN.1 variants, and the BA.5 and XBB.2 sera) in different ways: A) Randomly subsample from all sera.B) Randomly sample which serum groups are included.C) Randomly sample which serum groups are included, but always include the BA.1 and BA.2 serum groups.D) Randomly subsample the data in panel C to include two sera per serum group.E)

Table S1 :
Description of isolates.*Re-sequencing of the stock used for hamster infection showed a non-synonymous substitution in S (S:L179F) for this isolate.

Table S2 : Adaptations made to the PRNT90 titers inferred when constraining the neutralization curve at zero.
In the titrations above, visual inspection of the titer curve revealed that the neutralization curve fixed at zero did not give an ideal fit.Therefore, the adaptations listed above were made to those titers.