key: cord-1052858-ozxhc1wo authors: Padmanabhan, P.; Desikan, R.; Dixit, N. M. title: Modelling the population-level protection conferred by COVID-19 vaccination date: 2021-03-20 journal: nan DOI: 10.1101/2021.03.16.21253742 sha: 52e2acc03c3792f616f0db2f27481caf0c59541b doc_id: 1052858 cord_uid: ozxhc1wo Although severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccines work predominantly by eliciting neutralizing antibodies (NAbs), how the protection they confer depends on the NAb response to vaccination is unclear. Here, we collated and analysed in vitro dose-response curves of >70 NAbs and constructed a landscape defining the spectrum of neutralization efficiencies of NAbs elicited. We mimicked responses of individuals by sampling NAb subsets of known sizes from the landscape and found that they recapitulated responses of convalescent patients. Combining individual responses with a mathematical model of within-host SARS-CoV-2 infection post-vaccination, we predicted how the population-level protection conferred would increase with the NAb response to vaccination. Our predictions captured the outcomes of vaccination trials. Our formalism may help optimize vaccination protocols, given limited vaccine availability. Approved SARS-CoV-2 vaccines have shown remarkable but varying efficacies in 34 clinical trials, reducing the incidence of symptomatic infections by 62-96% (1-4). The 35 protection has been found to be predominantly due to NAbs elicited by the vaccines; cellular 36 immunity appeared to play a secondary role (1, 2) . The NAb response elicited by primary 37 SARS-CoV-2 infection is diverse, spanning >1000-fold variation in Ab titres and in vitro 38 neutralization efficiencies across individuals (5, 6), and appears not to correlate with disease 39 severity (7). NAb titres following vaccination were comparable to or even lower at times than 40 those from convalescent patients (1, 2, 8) . The protection accorded by the vaccines is thus 41 surprising. It is possible, based on animal studies (9), that lower NAb titres are protective at the 42 time of challenge than post infection. Knowledge of how the level of protection depends on the 43 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. NAb titres and their neutralization efficiencies is lacking. This knowledge gap hinders rational 44 optimization of vaccination protocols, which is important today given limited vaccine supplies 45 (10). Here, we developed a mathematical model that quantitatively predicts the population-46 level protection conferred by vaccines as a function of the NAb responses they elicit. 47 A major challenge to describing the effects of vaccination is the diversity of the NAb 48 responses elicited; no formalism exists to predict the diversity or its effects on protection. We 49 addressed this challenge by adapting the classic idea of shape space, which has aided 50 quantification of the immune repertoire (11), for characterizing NAbs. Accordingly, we sought 51 features, also termed shape parameters, of the NAbs that would predict their neutralization 52 efficiencies. Numerous studies have isolated individual NAbs from patients and assessed their 53 neutralization efficiencies in vitro, with the aim of developing NAbs for therapeutic 54 applications. We compiled dose-response curves (DRCs) of >70 NAbs thus isolated and fit 55 them using the standard sigmoidal function as well as the median-effect equation (12) 56 (materials and methods, fig. S1 , table S1). The equations fit the data well (Fig. 1A , and figs. 57 S2 and S3), indicating that two parameters, the 50% inhibitory concentration, IC 50 , and the 58 slope, m, of the DRC, were sufficient to characterize the neutralization efficiency of the NAbs 59 ( Fig. 1A and table S1). The best-fit IC 50 and m varied widely across NAbs (Fig. 1B) . IC 50 60 ranged from ~10 -3 µg/ml to ~140 µg/ml (Fig. 1B) , in close agreement with reported estimates, 61 giving us confidence in the fits ( fig. S4A and table S1). m, the importance of which has been 62 recognized with HIV-1 and hepatitis C (12, 13) but has not typically been reported for SARS- 63 CoV-2, spanned the range of ~0.2 to 2 ( Fig. 1 ). This variability in IC 50 and m was not restricted 64 65 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The variability was thus intrinsic to the NAbs, indicating the spectrum of NAbs elicited. 78 Furthermore, akin to HIV-1 antibodies (12), the variations in IC 50 and m of the SARS-CoV-2 79 NAbs appeared independent. For instance, the NAbs BD-361 and REGN10954 had similar IC 50 80 (both ~0.04 µg/ml), but vastly different m (~0.7 and ~1.5, respectively), whereas the NAbs 81 CC12.3 and 515-5 had vastly different IC 50 (~0.02 µg/ml and 1.6 µg/ml, respectively), but 82 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted March 20, 2021. ; https://doi.org/10.1101/2021.03.16.21253742 doi: medRxiv preprint similar m (both ~1). IC 50 and m were thus not only sufficient but also necessary for quantifying 83 the neutralization efficiencies of NAbs. We therefore employed IC 50 and m as the required 84 shape parameters. Plotting the NAbs on an IC 50 -m plot, we identified the NAb shape space 85 (Fig. 2) , which, because of its two-dimensional nature, we termed the 'landscape of SARS- (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. values, >5, and 9 had the least, <1 (D = 100 µg/mL) (Fig. 2B and table S1 ). This distribution 118 of IIP 100 values demonstrated further the wide spectrum of neutralization efficiencies of NAbs. 119 The landscape established bounds on the neutralization efficiencies of the NAbs elicited. 120 We reasoned next that the diversity of the NAb responses across individuals would arise from materials and methods, Fig. 3A) . We let the NAbs exhibit Bliss independence 134 or Loewe additivity, the former representing NAbs targeting distinct, non-occluding epitopes 135 and the latter the same or occluding epitopes (21). Our simulations recapitulated the dilution 136 curves associated with patient plasma (Fig. 3, B and C) . The values of NT 50 , the dilution at 137 which the neutralization efficiency of the plasma decreases by 50%, were in agreement with 138 experimental observations (17) (Fig. 3D ). The data was described better by Bliss independence 139 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted March 20, 2021. ; https://doi.org/10.1101/2021.03.16.21253742 doi: medRxiv preprint 8 at low NAb titres and Loewe additivity at high titres. This is expected because at low titres, the 140 NAbs are unlikely to interact with each other and would thus follow Bliss independence, 141 whereas at high titres, they may compete for binding sites on S or occlude each other and thus 142 exhibit Loewe additivity (21). At any NAb titre, there existed substantial variation in NT 50 , 143 attributed to the random combinations of NAbs sampled. The variation, however, was 144 outweighed by the overall rise of NT 50 with the NAb titre, consistent with patient data (Fig. 145 3D ). For instance, the NT 50 was 17±13 at the IgG titre of 0.1 µg/ml and 1300±1000 at 10 µg/ml. 146 Sampling from the NAb landscape thus successfully recapitulated patient responses. We were 147 able to describe the diversity of the NAb responses elicited across patients. Armed with this 148 description, we examined next the protection accorded by vaccines in clinical trials. 149 Following vaccination, NAb titres rise and are expected to remain stable (or decay 150 slowly) over weeks to months (22) , protecting individuals who might get exposed to the virus 151 during this period. Individuals were assumed to be protected if they did not report symptomatic 152 infection; loss of protection involved symptoms and a positive result on a nucleic acid 153 amplification test (1, 2) . Protection with NAbs is expected not to be sterilizing, as suggested 154 by animal studies (9); NAbs help suppress the peak in viremia, thereby reducing symptoms, 155 and facilitate more rapid clearance of the infection. If the peak is sufficiently suppressed, no 156 symptoms may result, as is the case with the ~40% of natural infections that remain 157 asymptomatic (7). Here, we assumed that an individual would be detected as symptomatically 158 infected if the viral load rose above a threshold during the infection. 159 To estimate the peak viral load, we developed a mathematical model of the early time 160 course of the infection, where the viral load typically rises, attains a peak, and declines (23), 161 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. and applied it to describe the effect of vaccination (Fig. 4A, table S2, materials and methods) . 177 The structure of the model mimics recent models that have captured patient data of viral load 178 changes following primary infection (24, 25) (see Fig. 4B, =0) . In addition, we assumed that 179 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted March 20, 2021. ; https://doi.org/10.1101/2021.03.16.21253742 doi: medRxiv preprint NAbs generated following vaccination would exist at the start of infection and neutralize free 180 viruses, effectively reducing viral infectivity. The greater the reduction in infectivity, the lower 181 the peak viral load (Fig. 4B, >0 ). Significant de novo NAb production post-infection typically 182 occurs after the peak in viremia (7). We therefore considered pre-existing NAbs as responsible 183 for protection and assumed their titres not to vary substantially during the course of the vaccination, the predicted peak viral load ranged from ~10 3 to 10 9 copies/ml, consistent with 198 the range in symptomatic individuals (26). The peaks declined as NAb titres increased. The 199 limit of detection is ~10 2 copies/ml (27), which we set as the threshold for symptomatic 200 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (table S3) . We binned the different individuals into narrow NT 50 bands and 207 calculated the mean protection in each band. We found that the mean protection was low for 208 NT 50~1 . It increased in a sigmoidal manner to 50% at NT 50~2 0 and asymptotically reached 209 100% at NT 50~2 00. Remarkably, the data for nearly all approved vaccines fell on this 210 'protection curve', explaining the protection they confer (Fig. 4D) . Thus, for instance, a single 211 dose of the vaccine BNT 162b2 elicited NAbs with NT 50 of 14 and accorded 49% protection. 212 Following two doses, the corresponding values were 361 and 94%, respectively. These values 213 as well as those for other vaccines were captured accurately by our model predictions. The only 214 exception was ChAdOx1 nCoV-19, which had a lower protection than predicted, the reasons 215 for which remain to be elucidated. 216 Our study provides the first conceptual, mechanistic and quantitative understanding of 217 the protection conferred by COVID-19 vaccines. Our findings would inform strategies for 218 optimal vaccine deployment. With limited vaccine availability, it would be useful to estimate 219 the protection realizable by a single dose of a prime-boost vaccine, especially in younger, less 220 vulnerable adults (10). Our formalism would enable this estimation: measurements of 221 corresponding NT 50 values would allow reading off the expected protection levels from our 222 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted March 20, 2021. ; https://doi.org/10.1101/2021.03.16.21253742 doi: medRxiv preprint protection curve. Similarly, using measurements of the waning of NAb titres post-vaccination, 223 how the population-level protection due to pre-existing NAbs would fade could be predicted. 224 Protection would then rely on memory B cell responses, which are yet to be fully understood 225 (28), or indicate the need for revaccination. Our study did not consider viral mutations because 226 with 5-10 NAbs active, viral escape from NAb responses is expected to be unlikely (19, 29) . 227 With the new circulating strains (30), however, the NAb landscape may have to be Efficacy and safety of the mRNA-1273 SARS-CoV-2 vaccine. 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