Saturation time of exposure interval for cross-neutralization response to SARS-CoV-2: Implications for vaccine dose interval

Summary Evaluating the serum cross-neutralization responses after breakthrough infection with various SARS-CoV-2 variants provides valuable insight for developing variant-proof COVID-19 booster vaccines. However, fairly comparing the impact of breakthrough infections with distinct epidemic timing on cross-neutralization responses, influenced by the exposure interval between vaccination and infection, is challenging. To compare the impact of pre-Omicron to Omicron breakthrough infection, we estimated the effects on cross-neutralizing responses by the exposure interval using Bayesian hierarchical modeling. The saturation time required to generate saturated cross-neutralization responses differed by variant, with variants more antigenically distant from the ancestral strain requiring longer intervals of 2–4 months. The breadths of saturated cross-neutralization responses to Omicron lineages were comparable in pre-Omicron and Omicron breakthrough infections. Our results highlight the importance of vaccine dosage intervals of 4 months or longer, regardless of the antigenicity of the exposed antigen, to maximize the breadth of serum cross-neutralization covering SARS-CoV-2 Omicron lineages.

The optimal booster vaccination interval is estimated to exceed 4 months INTRODUCTION by booster vaccination with first-generation vaccines or post-vaccination breakthrough infection can partially protect against Omicron variant infection. However, the surge in SARS-CoV-2 infections has not stopped, even in areas with high booster vaccine uptake, such as Japan. This situation suggests that first-generation COVID-19 vaccines have limited effectiveness at controlling the COVID-19 pandemic, and highlights the need for implementation of the second-generation booster vaccines containing Omicron antigen with improved effectiveness against Omicron variants. Second-generation booster vaccines should induce broad-spectrum protective immunity against all SARS-CoV-2 variants, including Omicron sub-lineages. However, there are many unanswered questions regarding how to induce high-quality immunity that suppresses SARS-CoV-2 variants with distinct antigenicity. A better understanding of the immune response to SARS-CoV-2 variant infection could facilitate the development of better vaccine designs. Specifically, understanding the immune response generated by breakthrough infection or reinfection, which is infection in the presence of pre-existing SARS-CoV-2 immunity due to vaccination or prior infection, respectively, might help to design better booster vaccine antigens. 2 Recently, BA.1 and BA.2 breakthrough infections in individuals vaccinated with COVID-19 mRNA vaccines were found to increase broad serum neutralizing activity against Omicron BA.1, BA.2, and prior VOCs at levels comparable to those of the ancestral strain. [3][4][5][6] In individuals vaccinated with COVID-19 mRNA vaccines, BA.1 breakthrough infection increases memory B cells primarily for conserved epitopes that are broadly shared among variants and generates robust serum cross-neutralizing activity. 6 Notably, convalescent serum samples from individuals with breakthrough infections have higher variable neutralizing activity against Omicron sub-lineages than serum samples of booster vaccination recipients. 3,4,[6][7][8][9][10][11] Furthermore, the exposure interval between vaccination and infection influences the induction of serum cross-neutralizing antibodies against BA.1, with a longer exposure interval contributing to greater induction of serum cross-neutralizing antibodies. 9,12,13 Unlike booster vaccination, in which the dosing interval between vaccinations is controlled, the exposure interval between vaccination and breakthrough infection is not controlled, resulting in individuals with breakthrough infections having a variable serum neutralizing response to SARS-CoV-2 variants. Therefore, it is difficult to compare the impact of breakthrough infections during different epidemic periods on the serum neutralizing response against the SARS-CoV-2 variants. When the ability to induce serum neutralizing responses through breakthrough infection with Omicron variants and prior VOCs is compared, individuals with breakthrough infections with prior VOCs may have had a shorter exposure interval between vaccination and infection than those with Omicron breakthrough infections, resulting in a lower ability to induce serum cross-neutralizing responses.
One approach to account for these differences is to use Bayesian hierarchical modeling. Bayesian hierarchical modeling constructs a hierarchical structure of sub-models, and by estimating probability distributions using Bayes' theorem, it enables the extension and estimation of parameters in multiple groups based on common parameters shared among these groups. 14 This approach allows for a more accurate and robust estimation of parameters while accounting for the dependencies and heterogeneity within the data hierarchy, as shown also in COVID-19 studies. 15,16 This statistical method can help adjust for the varying exposure intervals and provide a more accurate comparison of cross-neutralizing responses.
In this study, cross-neutralizing activity against SARS-CoV-2 variants, including the Omicron sub-lineages BA.1, BA.2, BA.5, BA.2.75, and BQ.1.1, was assessed using serum samples from individuals with breakthrough infections and booster vaccine recipients before or during the Omicron epidemic. Furthermore, Bayesian modeling was used to correct for the influence of different exposure intervals to enable estimation of the saturated serum cross-neutralizing responses against SARS-CoV-2 variants induced after breakthrough infection with the ideal exposure interval between vaccination and breakthrough infection.

Antigenicity of SARS-CoV-2 Omicron sub-lineages in serum samples from individuals with breakthrough infections and booster vaccine recipients
We collected serum samples from individuals with breakthrough SARS-CoV-2 infections during the Omicron BA.1 wave and individuals who had received a booster dose of the first-generation mRNA COVID-19 vaccine containing the ancestral spike antigen alone (Table S1 and Figure S1; STAR Methods). Individuals with a history of a COVID-19 diagnosis and positive anti-nucleoprotein (N) antibodies after the second vaccination were defined as having breakthrough infections, whereas individuals who had received iScience Article three doses of vaccine and did not have a COVID-19 diagnosis or positive anti-N antibodies were defined as booster vaccine recipients in this cohort ( Figure 1A). Similarly, we used serum samples from individuals who had breakthrough infections during the pre-Omicron wave, as reported previously ( Figure S1). 9,12 Age, exposure interval between the first and second doses of vaccine, and time since the last vaccination were comparable between the three exposure groups (Table S1). Anti-spike (S) antibody titers were highest in individuals with Omicron breakthrough infections, and lowest in individuals with pre-Omicron breakthrough infections ( Figure 1A). Each square corresponds to a serum sample from one individual. Colors represent the serum source. Each grid square (1 antigenic unit) corresponds to a 2-fold dilution in the serum sample used in the neutralization assay. Antigenic distance is interpretable in any direction. The median (95% confidence interval) of the distance from the ancestral strain on the map is shown using gray dotted lines. Statistical significance: *p < 0.05, **p < 0.01, ***p < 0.001, ****p < 0.0001.  Figures 1B and 1C). The BQ.1.1 variant had the highest immuno-evasion ability among individuals in the three exposure groups, resulting in a more than 20-fold decrease in the NT relative to that against the ancestral strain ( Figure 1C).

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To obtain an overall picture of the antigenicity of Omicron sub-lineages in serum samples from each exposure group, we performed antigenic cartography to locate the antigens and sera in a two-dimensional map ( Figure 1D). Positions of antigens and sera on antigenic maps were calculated based on each serumneutralizing titer against each variant. 17 The antigenic distance between antigenically different variants is greater than that between antigenically similar variants in vaccinees and patients with pre-Omicron breakthrough infection. 12 Thus, calculating the distance between each variant on an antigenic map is useful for comparing the breadth of neutralizing activity for each serum. Antigenic distances from the ancestral strain to BA.5 and BQ. Notably, in serum samples from individuals in the three exposure groups, the antigenic distance between BQ.1.1 and the ancestral strain ranged from 4.5 to 6.0, indicating that BQ.1.1 is the Omicron sub-lineage that is the most antigenically distinct from the ancestral strain. Taken together with Figure 1C, the serum samples of the Omicron breakthrough infection group showed broader breadth of cross-neutralizing potency than those of the pre-Omicron breakthrough infection group.
Estimating the serum neutralization responses against SARS-CoV-2 Omicron sub-lineages corrected for the influence of different exposure intervals from the second vaccination to the third exposure A longer time between the second vaccination and third exposure, within a range of approximately 120 days, is necessary to induce broader cross-neutralizing potency in serum samples from individuals with pre-Omicron breakthrough infection, probably because memory B cell affinity maturation occurs during this period. 9,18,19 The optimal interval between the second vaccination and booster dose has not yet been determined (WHO, https://www.who.int/news/item/17-05-2022-interim-statement-on-the-use-ofadditional-booster-doses-of-emergency-use-listed-mrna-vaccines-against-covid-19). Generally, an interval of 4-6 months after the second vaccination could be considered. In Japan, a vaccination interval of at least 3 months is recommended (https://www.mhlw.go.jp/stf/covid-19/booster.html). This vaccination strategy and the periods of pre-Omicron and Omicron waves resulted in distinct exposure intervals among the three exposure groups (Figures 2A and S1, and Table S1). To complement the missing intervals in each exposure history group, we used a Bayesian hierarchical model to estimate the serum neutralizing responses against SARS-CoV-2 variants induced with different antigen exposures and intervals, and estimated the saturated neutralizing responses against SARS-CoV-2 variants with the ideal exposure interval in each exposure history group (Figures 2 and 3). The overall trend for booster vaccine recipients and individuals with breakthrough infections showed that the interval to saturate the neutralizing response was different for each variant, and that saturating the neutralizing responses against Omicron sub-lineages required a longer exposure interval than those against the ancestral strain ( Figure 2A). To evaluate differences in the exposure interval required to saturate the neutralizing response for each SARS-CoV-2 variant, the probability densities of the estimated number of days to 90% saturated NTs were calculated ( Figure 2B). The median of the density for the ancestral strain was 34 days after the third exposure. By contrast, the medians of those for Omicron BA. iScience Article shorter than the median of the estimated number of days to 90% saturated NTs to Omicron sub-lineages, and these individuals with pre-Omicron breakthrough infections experienced infection without an exposure interval sufficient to acquire cross-neutralizing antibodies. Thus, it is essential to estimate saturated cross-neutralizing potency with the ideal exposure interval to accurately assess the differences in crossneutralization responses due to varying exposure antigens in breakthrough infections, to avoid bias due to the exposure interval.
Next, we estimated the saturated neutralizing response to each SARS-CoV-2 variant in each exposure group ( Figures 3A and 3B). In the Omicron breakthrough infection group, the estimated saturated NTs against the ancestral strain, and BA. Finally, we calculated the fold decrease in the saturated NT relative to the median of the ancestral strain to evaluate the breadth of cross-neutralization potency with the ideal interval ( Figures 3B and 3C). Contrary to

DISCUSSION
In this study, we showed that the ideal exposure interval between vaccination and exposure to achieve saturated neutralizing responses differed by variant in individuals with breakthrough infections, and that more antigenically distant variants from the ancestral strain required a longer exposure interval to reach to a saturated neutralizing response. In addition, we also showed that serum samples from individuals with Omicron breakthrough infections had higher saturated neutralizing responses against the ancestral strain and Omicron sub-lineages than those of individuals with booster vaccination or pre-Omicron breakthrough infection.
An exposure interval of more than 128 days was required to induce broad cross-neutralizing activity against the BQ.1.1 variant, which was antigenically distant from the ancestral strain. As stated above, WHO recommends at least 4 months (approximately 120 days) after the second vaccination before booster vaccination, which is comparable to the exposure interval needed to induce broad cross-neutralizing responses. In contrast, the US Centers for Disease Control and Prevention recommends at least 2 months (approximately 60 days) between the second and third doses (https://www.cdc.gov/coronavirus/2019-ncov/vaccines/stayup-to-date.html). Although a shorter vaccination interval during periods of transient surges in COVID-19 iScience Article cases may benefit to the level of herd immunity, it may be insufficient to induce high levels of cross-neutralizing antibodies covering antigenically distinct variants. Previous studies have shown that in vaccine recipients, higher NTs were induced with a dose interval of 16 weeks (median, 111 days) than with a dose interval of 4 weeks (median, 29 days) between the first and second doses, 20 and the NT and vaccination dose interval were positively correlated within approximately 100 days. 21 Notably, when the vaccination dose interval between the second and third dose of vaccine was between 206 and 372 days, there was no difference in the neutralizing responses between the shorter and longer interval, 22 suggesting that the effect of vaccination dose interval on inducing neutralizing responses was saturated within this period. These increases and saturation of the serum neutralization response dynamics are consistent with our model. The vaccination dose interval that affects the induction of cross-neutralizing responses can be considered equivalent to the vaccination-infection interval in breakthrough infections in terms of the time taken for the antibody affinity maturation derived from memory B cells in germinal centers after mRNA vaccination. 19,23,24 Memory B cells that recognize Omicron and other variants proliferate after the second vaccination, 18,22 and the third exposure by vaccination or breakthrough infection induces recall and proliferation of memory B cells which recognize the Omicron spike protein. 22,25 As evaluating the effect of a shorter interval between the second and third vaccine doses would be ethically challenging, our model using individuals with breakthrough infection as a surrogate provides valuable information about the optimal dose interval between the second and third doses of vaccine. In addition, our model also suggests that to induce higher levels of crossneutralizing responses, an additional booster vaccination should be considered in individuals with breakthrough infections with a vaccination-infection interval shorter than four months (120 days).
In serum samples of individuals with Omicron breakthrough infections, the saturated neutralizing responses to Omicron sub-lineages were higher than those in serum samples of individuals with pre-Omicron breakthrough infections and booster vaccine recipients vaccinated at the ideal intervals. Several studies have also found higher cross-neutralizing antibody titers to Omicron sub-lineages in individuals with BA.1 breakthrough infection than in booster vaccine recipients and individuals with Delta breakthrough infection. 4-6 Furthermore, BA.1 booster mRNA vaccination of mice and macaques inoculated with the ancestral strain mRNA vaccines also induces higher NTs than a booster dose of the ancestral strain mRNA vaccine. 26,27 Similar findings have also been reported in human studies of Omicron BA.1 and ancestral bivalent vaccine recipients, 28 suggesting that booster vaccination with the Omicron antigen induces higher levels of cross-neutralizing antibodies. However, the serum neutralizing breadth in individuals with Omicron BA.1 breakthrough infections was estimated to be similar to those of individuals with pre-Omicron breakthrough infections, regardless of the antigenicity of the infecting variant, and broader than those of booster vaccine recipients. These results suggest that breakthrough infections might contribute to the induction of broader cross-neutralizing responses, referred to as hybrid immunity. 2 Compared with three doses of vaccine, breakthrough infection with Delta or Omicron BA.1 variants induces higher levels of memory B cells recognizing ancestral spike RBDs, 4,6,29 and viral load and duration of viral antigen exposure may contribute to enhanced stimulation of memory B cells. Although the frequency of somatic hypermutations in anti-RBD + memory B cells of individuals with breakthrough infections is comparable to that of booster vaccine recipients, 4,29 antibodies isolated from memory B cells in individuals with breakthrough infections show higher cross-neutralizing activity and affinity. 29 Together, these reports and our results suggest that breakthrough infection may contribute to increased cross-neutralizing activity and affinity of memory B cells, regardless of the length of the exposure interval.

Limitations of the study
This study has several limitations. First, the number of samples evaluated was relatively small. Second, the exposure intervals varied among the various exposure groups in this study, with a significant difference between the pre-Omicron breakthrough infection and booster vaccination groups, which could potentially bias the cross-neutralizing activity. This study's Bayesian hierarchical modeling with the three groups, including the Omicron breakthrough infection group, enabled more optimal estimations based on the various time intervals. Third, the possibility that reduced neutralizing activity at the time of breakthrough infection results in efficient viral replication in the upper respiratory tract may contribute to a better antibody response 12 was not evaluated because of the lack of respiratory specimens. Fourth, our study does not support the idea that breakthrough infection can act as a substitute for booster vaccination because natural infection can cause long-term complications and is particularly dangerous for vulnerable individuals. Fifth, this study did not include any individuals with a second booster dose of vaccine or breakthrough infection after the first booster dose of vaccine. Finally, our investigation did not evaluate the actual risk of iScience Article reinfection by SARS-CoV-2 in individuals with a history of breakthrough infection, although there is evidence that NTs are correlated with protection against ancestral strains and different variants. [30][31][32] Conclusion In conclusion, estimating serum cross-neutralizing responses in individuals with breakthrough infection using Bayesian modeling to compensate for the effect of varying exposure intervals revealed the ideal dose interval and fairly compared the impact of breakthrough infection on breadth of cross-neutralizing responses by variants with distinct antigenicity and epidemic timing. Our results highlight that optimizing the dose interval is critical for maximizing the breadth of cross-neutralizing activity elicited by booster vaccines, with or without Omicron antigens. Understanding how breakthrough infection increases the neutralization breadth would significantly contribute to the development of next-generation COVID-19 booster vaccines covering emerging variants of SARS-CoV-2.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following:

ACKNOWLEDGMENTS
We thank Akiko Sataka, Asato Kojima, Izumi Kobayashi, Yuki Iwamoto, Yuko Sato, Milagros Virhuez Mendoza, Noriko Nakajima, Kenta Takahashi, and Emi Taeda at NIID for their technical support; Jumpei Ito at the University of Tokyo for technical advice on Bayesian modeling; and the healthcare facilities, local health centers, and public health institutes for their contribution in providing us with patient information and samples on pre-Omicron breakthrough cases as listed previously. 9 We also thank the Miyagi, Tokyo, Aichi, Osaka, and Fukuoka prefecture governments for their support in implementing the study; staff members at the Survey Research Center and Mitsubishi Research Institute for their administrative and technical assistance; and GISAID for the platform to share and compare our data with data submitted globally.

Participants and sampling
The characteristics of the participants are listed in Table S3 and summarized in Table S1. Serum samples collected 7 to 30 days after the last vaccination were used in the study. The serum samples of booster vaccine recipients and patients with Omicron breakthrough infections were obtained from residual samples of a national seroprevalence survey conducted in Japan from February to March 2022 (peak of the Omicrondominant period) ( Figure S1). 33 In Japan, the BNT162b2, mRNA-1273, and AZD1222 vaccines have been approved for use since February 2021. Participants received the primary series (doses 1 and 2) at the intervals recommended by the manufacturers. The rollout of the mRNA booster (third) dose was initiated in December 2021, and individuals became eligible 6 to 7 months after the second dose, depending on local availability. Booster vaccine recipients had received three doses of BNT162b2 mRNA vaccine, had no history of SARS-CoV-2 infection, and had no anti-nucleoprotein (N) antibody detected.
Sera from individuals diagnosed with SARS-CoV-2 infection and positive for anti-N antibodies during the Omicron-dominant period following two doses of BNT162b2 or mRNA-1273 mRNA vaccine were used as Omicron-breakthrough infection sera. Based on the date of infection, the majority of the cases of breakthrough infection was probably caused by the Omicron BA.1 and BA.2 lineages, with BA.1, accounting for more than 90% of the cases ( Figure S1). The Omicron-breakthrough infection sera (n = 30) in this study were collected 7 to 30 days after diagnosis of SARS-CoV-2 infection. An equal number of booster vaccine recipients were selected using optimal pair matching based on propensity scores calculated according to age and days since the last exposure using the MatchIt R functions (Table S1 and Figure S1).
Serum samples from patients with pre-Omicron breakthrough infections were obtained as described previously. 9,12 Briefly, pre-Omicron breakthrough infection was defined according to a positive SARS-CoV-2 RNA or antigen test result on a respiratory specimen collected R14 days after the second vaccine dose. Demographic information, vaccination status, and respiratory samples for determining the infecting variant were collected as part of the public health activity led by the Japan National Institute of Infectious Diseases (NIID) under the Infectious Diseases Control Law, and the data were published on the NIID website in order to meet statutory reporting requirements. Serum samples obtained from individuals with breakthrough infections were collected concurrently for clinical testing provided by the NIID (with patient consent), and neutralization assays were performed using residual samples as a research activity with ethics approval from the Medical Research Ethics Committee of NIID and informed consent.
To examine neutralization, the serum samples were heat-inactivated at 56 C for 30 min before use. The median dose interval between the first and second vaccine doses for individuals with breakthrough infections and booster vaccine recipients was 21 days (Table S1).

Ethical statement approval
All samples, protocols, and procedures were approved by the Medical Research Ethics Committee of NIID (approval numbers 1178, 1275, and 1312).

Live virus neutralization assay
Live virus neutralization assays were performed as described previously. 9,19 Briefly, serum samples were serially diluted (in two-fold dilutions starting from 1:5) in high-glucose DMEM supplemented with 2% FBS and 100 U/mL penicillin/streptomycin and mixed with 100 median tissue culture infectious dose (TCID 50 ) SARS-CoV-2 viruses, followed by incubation at 37 C for 1 hour. Before adding of the virus-serum mixtures, 1.0 x 10 4 VeroE6/TMPRSS2 cells were seeded in each well of the 96-well plates to ensure a consistent cell number across all wells. The virus-serum mixtures were then placed on the cells and cultured at 37 C with 5% CO 2 for 5 days. The cells were then fixed with 20% formalin and stained with crystal violet solution. NTs were defined as the geometric mean of the reciprocal of the highest sample dilution that protected at least 50% of the cells from a cytopathic effect, using two to four multiplicate series. Because of the limited volume of serum samples from individuals with breakthrough infections, this assay was performed only once. All experiments using authentic viruses were performed in a biosafety level 3 laboratory at NIID.

Antigenic cartography
Antigenic maps based on NTs against SARS-CoV-2 viruses were created using the Racmacs R function with 2,000 optimizations, with the minimum column basis parameter set to ''80''. 17,34 Each grid square (1 antigenic unit) corresponded to a two-fold dilution in the neutralization assay. The median the antigenic distances from the ancestral strain and 95% confidence intervals of were calculated according to the Pythagorean theorem using the coordinates of the antigenic maps in the optimization steps as described previously. 12

Statistical analysis of measured antibody titers
Data analysis and visualization were performed using GraphPad Prism 9.3.1 (San Diego, CA, USA) and R 4.1.2 (https://www.r-project.org/). Measurements below the detection limit were recorded as half the detection limit. One-way analysis of variance with Dunnett's test or Tukey's test were used to compare the antibody titers. Statistical significance was set at p < 0.05.

Estimating saturated cross-neutralizing titers against SARS-CoV-2 variants
For each exposure group, we estimated the NT and time of vaccination using a Bayesian hierarchical model. The log10 NT after breakthrough infection or booster vaccination was described using a threeparameter logistic model for each exposure interval between the second vaccination and the third exposure (vaccination or breakthrough infection). We inferred population means (m v ) separately for NTs against the ancestral strain, and BA.1, BA.2, BA.2.75, BA.5, and BQ.1.1 variants. We used a hierarchical structure to describe the distribution of m hv for each exposure group. Arrays in the model index over one or more indices: H=3 exposure history h; N=108 participants n; V=6 target viruses v. The model was as follows: