我们使用了2023年2月13日可用的所有DMS数据5,17来评估每个SARS-COV-2变体的表型（摆脱中和抗体） 。DMS测量在酵母 - 播种测定中 ，RBD中的突变位点S会影响未在位点s突变的变体引起的抗体的结合。我们利用了836种抗体的数据分类为12个不同的表位类别17,18（见下文），并通过其平均值汇总了所有值的所有值
，从而为每个突变的位点EFS产生“逃生级分 ”，为A（值为0.99的值）
。逃逸分数表示量化抗体不结合rbd的概率的代理。因此 ，数值取决于抗体效力
，因此我们旨在将这些值转换为“折叠电阻”（抗体效力的折叠变化；另请参见扩展数据图1A – C） 。假设位点s对结合亲和力的突变作用是独立的，则可以将变体X与变体y的抗体的结合概率表示为 　　在其中 ，EFS A是相对于抗体A的突变位点S的归一化逃生部分
，并表示区分变体X和Y的RBD位点集（参考文献17）
。使用经典的药效方法，我们将结合概率建模为 　　其中frx ，y（a）表示变体y对抗体的折叠电阻性a引发x。该参数对应于针对抗体渗透变体的抗体的一半最大抑制浓度（即“效力
”）
，该抗体是从DMS数据集中提取的 。值得注意的是，CA =400μgml -1是进行DMS实验的抗体浓度4,18
。组合方程（1）和（2）的产量： 　　从扩展的数据图1A – C中已经可以明显看出 ，EFS的DMS估计值以及相应的FRX
，Y（a）可能会根据抗体浓度和抗体效能而变得不可靠，从而错误地预测过度敏感性（FRX ，Y（a））< 1). We enforce that FRx,y(a) ≥1 to avoid such artefacts. 　　On the basis of the similarity of antibody profiles in DMS data, antibodies were previously classified into 12 epitope classes (A, B, C, D1, D2, E1, E2.1, E2.2, E3, F1, F2, F3)18 (Supplementary Tables 1 and 2). As we encountered more than 30% missing values for epitope classes E2.1 and E2.2, we merged them with E1 into a new class (E12), as they bind to similar regions, including amino acid site R346 (ref. 42). Finally, we retrieved a matrix of 10 epitope classes Α = (A, B, C, D1, D2, E12, E3, F1, F2, F3) for 179 RBD sites. This classification indicates that antibodies belonging to the same class bind to overlapping epitopes, and there is little overlap between epitope classes (Fig. 2a). Consequently, we assumed that antibodies within the same epitope class would be similarly affected by RBD alterations, whereas phenotypic changes between epitope classes may vary considerably. 　　We then quantified the fold resistance associated with each epitope class as the average fold resistance of all antibodies belonging to the class 　　for all epitope classes in Α (Fig. 2a). 　　As a proof of concept, we compared DMS-derived FRx,y() using the calculations above with fold resistance values obtained from virus neutralization assays (reported in ref. 42) for antibodies targeting all epitope classes Α defined above. As can be seen in Extended Data Fig. 1d, we observed a strong and significant positive correlation between the DMS-derived FRx,y() and those obtained by neutralization assays and reasonable agreement for polyclonal sera (Extended Data Fig. 1e–g). 　　As the DMS experiments were generated only for RBD-targeting antibodies, no escape data were available to quantify the fold resistance of NTD-targeting antibodies. To overcome this limitation, we included an additional class of NTD-targeting antibodies targeting three antigenic super-sites43: spike amino acid positions 14–20, 140–158 and 245–264. Consequently, we assigned alterations in the antigenic super-sites fold resistance values of 10, which is in range with corresponding ELISA experiments43. However, the model can be updated if comprehensive DMS data for the NTD domain become available44. 　　Assuming independence between mutational effects, the total fold resistance of a variant y to binding of an NTD-targeting antibody elicited by a variant x was computed as: 　　in which |Ω(x, y)| denotes the number of mutational differences between variants x and y in the antigenic super-site of the NTD. 　　We assumed that a virus is neutralized if at least one antibody is bound to its surface (either at the RBD or NTD of the spike protein). Here, we collectively consider all antibodies from the same epitope class as they compete for the same binding site. By assuming binding independence between epitope classes, the neutralization probability can be computed as: 　　with denoting the probability that an antibody of epitope class in Α (NTD) binds to the virus with 　　in which is the antibody’s concentration in an individual at time t, is the half-maximal inhibitory antibody concentration against the variant that elicited the antibody. FRx,y() is the fold resistance of variant y to binding of antibodies of epitope class , elicited by variant x. 　　Next, we quantified for each epitope class. As the DMS data were derived from yeast-display RBD mutant libraries, absolute antibody potencies may not directly translate to a clinical setting. However, the ranking of antibody potencies may be preserved. Consequently, we estimated the relative potency D() from the DMS data: 　　in which , and denotes the average potency of all antibodies belonging to epitope class . Epitope-class-specific clinical antibody potency was then inferred using the following relation: 　　in which denotes the averaged over all epitope classes. NTD-targeting antibodies were not included in the DMS dataset, and hence we set 　　was the only free parameter in the model, which we estimated by fitting our model to (Wuhan-Hu-1-strain) vaccine efficacy (VE) data against the Delta lineage (B.1.617.2) present between 4 July 2021 and 31 December 2021 (Fig. 2d; genomic profile in Supplementary Table 3). 　　We considered interindividual differences in antibody pharmacokinetics (see below), implemented as combinations of the parameters tmax (time of maximal antibody concentration) and thalf (antibody half-life). For parameter estimation, we first estimated optimal drug potencies (tmax, thalf) for each tmax, thalf combination in a 5 × 15 grid (ranges below) and then averaged over these 75 estimates. Parameter estimation was performed using scipy.optimize.root, applying the Levenberg–Marquardt method to solve the ordinary least-square problem. 　　in which VE(t, Wuhan-Hu-1, Delta) denotes the vaccine efficacy against the Delta strain t days after antigen exposure with the Wuhan-Hu-1 strain. Here, we assumed that VE = infection risk reduction ≈ PNeut. 　　As a proof of concept, we then tested our predictions with Wuhan-Hu-1-strain VE data against Omicron infection (Fig. 2d; genomic profile in Supplementary Table 3). Utilized VE data include those from all studies in which Wuhan-Hu-1-strain vaccines were tested and which were computed on the basis of hazard ratios or rate of confirmed infection (Supplementary Tables 4 and 5). 　　To determine the duration of sterilizing immunity against any variant y, we accounted for antibody pharmacokinetics (PK) after antigen exposure to variant x (by means of infection or vaccination). Pharmacokinetics were considered using a classical, descriptive linear model with an analytical solution 　　in which t denotes the time after antigen exposure and c(t) denotes the normalized (fraction of maximum) concentrations of the antibody. The parameters ke and ka (elimination and ‘absorption’ parameters in classical PK models) were related to known quantities through established PK relations; that is, 　　In our simulations, we considered identical PK for antibodies of the different epitope classes. Utilized parameters (tmax, thalf) were extracted from the literature: the time of maximal antibody concentrations (tmax) varied between 14 and 28 days after antigen exposure26,45,46, and the half-life (thalf) ranged between 25 and 69 days19,47,48,49,50,51,52,53. For simulation, we used different combinations of (tmax, thalf) in a 5 × 15 grid within a range of tmax within 14 to 28 days and thalf within 25 to 69 days and plotted the range of predictions (minimum, maximum). 　　We collected SARS-CoV-2 genomic data from Germany published by the Robert Koch Institute, including only genomic data from the ‘random sampling’ strategy, which denotes most of the sequence data. For other countries (Australia, Brazil, Canada, Denmark, France, Japan, Mexico, South Africa, Sweden, the UK and the USA), we downloaded data from GISAID (https://gisaid.org); however, here we could not be sure that the data are representative (randomly sampled), as anyone can upload SARS-CoV-2 data to GISAID. A dataset summary is given in Supplementary Table 6. 　　If pangolin lineage information was absent in the data, lineage information was assigned using established methods54,55. Alteration profiles for all sequences were extracted using covSonar. For each lineage, we collected all ‘characteristic’ spike amino acid changes in the RBD (amino acid position 331–541) and the NTD antigenic super-sites regions (amino acid positions 14–20, 141–158 and 245–264) for subsequent analyses. In our work, ‘characteristic’ implied that an amino acid change was present in at least 75% of all sequences from that lineage. The ‘antigenic profile’ for each lineage was then determined on the basis of the set of unique alterations within the NTD and RBD regions. Differences between lineages were defined as the set difference between alteration profiles. Clustering lineages with identical ‘antigenic profiles’ yielded spike pseudo-groups with distinct genomic profiles in the RBD and NTD region of the spike protein. On the basis of the genomic profiles and their clustering into spike pseudo-groups, we computed pseudo-group frequencies πx(t) for all x in the entire observation horizon. The frequencies were computed such that there were at least 100 sequences per time step, and daily lineage frequencies were computed by using linear interpolation between time steps. Furthermore, we filtered out spike pseudo-groups that never reached levels of >从测序误差中降低噪声的1％频率。所有国家/地区的谱系和伪群频率和更改概况的数据文件均可通过https://github.com/kleistlab/vasil获得（补充表6中给出了摘要） 。 　　不幸的是，由于SARS-COV-2的测试覆盖率和报告变得越来越不可靠
，因此无法从报告的病例中重建感染时间表
。为了克服这一数据限制，我们最近开发了基于基因组的发病率估计量Ginpipe22。该计算管道仅根据时间stamp的病毒序列重建感染时间表 。由于SARS-COV-2的短阶段（参考文献56） ，通常在传播感染之前观察到有限的患者内进化
。这意味着存在一个“进化信号” ϕ
，该ϕ与单倍型多样性以及病毒序列的时间集合中存在的变化数量与感染的数量相关联（有关详细信息，请参见参考文献22）。我们先前证实了该进化信号与时间t的实际受感染个体I（t）≈Cx（t）成正比 。 　　尽管Ginpipe在测序工作随着时间的变化而变化时非常强大 ，但极端变化可能会导致偏见22。对于美国和英国
，我们观察到可用序列数量的大量下降（2022年后约10倍），此后分别将病毒序列的数量分别降低至每天6,000和2,500 ，这对应于测序工作中下降后的最大序列数量（扩展数据5）
。 　　在管道中
，序列是根据其收集日期汇总的，因此“垃圾箱 ” b包含相同数量的序列NB或跨越相同的天数∆DB。我们选择时间跨度∆DB = 7、10和14天 ，bin尺寸为NB = 2％和所有序列的5％
，以及每个特定国家 /地区的平均每周序列数量 。如果垃圾箱的时间跨度小于3天，或者垃圾箱包含少于50个序列 ，则将其相关性相关性过滤掉
。我们允许最多21天（数据富含数据的设置）或尽可能多的天范围，以包括最小数量的序列（数据罚款设置）。使用内核平滑度（带宽为14）对bin的ϕB估计进行平滑 。在扩展数据中
，所有调查的国家 /地区的扩展数据中描述了杜松子酒估计的发病率相关性
。 　　为了确认杜松子酒估计的发病率的有效性，我们将我们的预测与德国的其他无偏见措施（公民科学和废水数据；扩展数据图3） ，以及来自Covid-19代表Covid-19的英国数据集
，使用了国家统计局（ONS）6，使用了第3个行为的人（在3月3日）的统计局（On）6月3日 ，这是20 3日。扩展数据图4） 。 　　然后
，使用10天的滚动总和计算出感兴趣的Ginpipe的PCR阳性个体的百分比，并根据ONS的种群规模和各个时间范围内受感染的人的比例进行了归一化
。对于报告的案件 ，英国的人口规模在10天内的滚动总和进行了归一化。 　　跨中和概率的估计使我们能够通过在考虑时间t之前将感染历史记录在给定的时间点t中估算给定时间t的预期个体对感染的预期数量 。通过应变Y免疫感染的预期个体数量由 　　其中表示在感兴趣的时间范围内存在的所有变体的集合
，而pneut（t-s，x ，y）表示菌株x感染的可能性
，发生在t-s几天前发生的t-s跨脱和中和变体y
。在上面的等式中，πx表示在第s时变体x的比例< t, derived from the molecular surveillance, and I(t) denotes the number of infected individuals at some previous time point s. The expected number of susceptible individuals to a variant y at time t can then be calculated as , in which Pop denotes the total population size. The variable I(s) is typically not available, but can be replaced by incidence correlates ϕ(s) = I(s)/c (see below). 　　To estimate whether an emerging variant may successfully out-compete existing variants, we estimated the relative growth advantage of a variant γy(t): 　　in which the denominator denotes the average growth rate across all variants existing at time t and for which αx >0表示变体的固有（抗体独立于）相对传递适应性 ，我们认为对于所有循环变体αx≈α几乎相同，这意味着变体动力学以感染史和免疫动力学为主。我们忽略了具有πx（t）的低丰度变体< 1% and renormalized accordingly. We computed the frequency-weighted average γz(t), whenever different variants were combined during analyses (as indicated in the respective graphics). 　　As infection numbers I(t) are typically unreliable, our method can utilize any incidence correlate, such as GInPipe’s ϕ(t), wastewater virus load trajectories or reliable estimates from large citizen science projects. With regard to GInPipe’s output, we showed in Extended Data Figs. 3 and 4 and in ref. 22 that I(t) ≈ cϕ(t), which allows us to use ϕ(s) instead of the number of infected individuals I(s) when computing , as performed in Figs. 3–5. To compute , we can write , for which k >0是一个缩放因素（例如
，k -1 = 2意味着每个人在感兴趣的时间范围内平均被感染了两次） 。当重建德国和英国的实际发生率时，我们发现k≈1在时间范围内（扩展数据图9）。k是一种建模选择 ，k的任何错误估计仅影响γy的缩放（t）（扩展数据图10）
。定性结果（拐点γy= 0；变体“生长
”γy> 0;变体“下降”γy< 0) remain unaffected. The interpretation of this ‘scaling’ is straightforward: if one overestimates the number of individuals that became infected, one under-predicts the number of susceptible individuals and thus infers stronger competition among variants, which is expressed in overestimation of the amplitude of γy(t) by some constant ξ >1。 　　在离散的准准物种模型57中
，理论变异频率由 　　为此，表示不同变体之间的过渡矩阵 ，我们将其设置为身份矩阵q = id
，忽略了从一个变体到另一种变体的任何突变过渡 。相对于种群平均值的任何变体的适应性值都包含在矩阵中
。因此，对于py（t）> 0 ，我们得到 　　如果健身是由人口免疫确定的。 　　由于疫苗接种时间轴包含接种疫苗的个体数量
，因此我们首先使用Ginpipe22重建了德国的实际感染数量：我们推断了时间依赖性的病例确定概率PREP（T）≤1（即，报告的感染可能性）： 　　对此 ，IREP（t）≤i（t）表示每日报告的感染（每周病例/7） 。我们以带宽为14的案例（t）平滑了案例IREP（t）
。 　　最后
，我们将案例确定概率的最大范围归一化，以估计感染的最小数量 　　然后将最小感染数量计算为 　　然后通过设置I（t）≈IMIN（T）对感染对免疫景观的影响进行建模。为了模拟德国助推器疫苗接种的影响（图7的扩展数据） ，我们将暴露于Wuhan-hu-1-variant抗原或BA.4 + BA.5-Variant抗原对应于疫苗时间线（HTTPS：////impfdashboard.de/en/）的影响 。请注意，这种对实际感染数量的重建可能会变得不稳定
，因为它已归一化为极端（最大值），因此保证了分析后检查
。此外 ，它需要使用案例报告数据
，该数据在2023年底之前大部分停止。 　　有关研究设计的更多信息可在与本文有关的自然投资组合报告摘要中获得 。