key: cord-0281742-nctk2bs7
authors: Garg, A. K.; Mittal, S.; Padmanabhan, P.; Desikan, R.; Dixit, N. M.
title: Low dose prime and delayed boost can improve COVID-19 vaccine efficacies by increasing B cell selection stringency in germinal centres
date: 2021-09-12
journal: nan
DOI: 10.1101/2021.09.08.21263248
sha: baf6df5c09ea8025a6d7b594f0db8f443f673129
doc_id: 281742
cord_uid: nctk2bs7

The efficacy of COVID-19 vaccines appears to depend in complex ways on the vaccine dosage and the interval between the prime and boost doses. Unexpectedly, lower dose prime and longer prime-boost intervals have yielded higher efficacies in clinical trials. To elucidate the origins of these effects, we developed a stochastic simulation model of the germinal centre (GC) reaction and predicted the antibody responses elicited by different vaccination protocols. The simulations predicted that a lower dose prime could increase the selection stringency in GCs due to reduced antigen availability, resulting in the selection of GC B cells with higher affinities for the target antigen. The boost could relax this selection stringency and allow the expansion of the higher affinity GC B cells selected, improving the overall response. With a longer dosing interval, the decay in the antigen with time following the prime could further increase the selection stringency, amplifying this effect. The effect remained in our simulations even when new GCs following the boost had to be seeded by memory B cells formed following the prime. These predictions offer a plausible explanation of the observed paradoxical effects of dosage and dosing interval on vaccine efficacy. Tuning the selection stringency in the GCs using prime-boost dosages and dosing intervals as handles may help improve vaccine efficacies.

7 considered two scenarios (34, 47, 48) : the first where the boost enhanced antigen levels in pre- CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint 8 receive help from T follicular helper cells with a probability dependent on the relative amount 135 of antigen they acquired. Cells that fail to acquire antigen or receive the latter help die. Cells 136 that succeed can exit the GC to become plasma cells and secrete antibodies, become memory 137 B cells, or migrate to the dark zone, where they proliferate and mutate their antibody genes. 138 The latter cells circulate back to the light zone and become subjected to the same selection 139 process. Antibodies secreted by plasma cells can feedback into the GC and affect the selection Antigen availability and its effect on selection stringency 153 To elucidate affinity maturation in the GC reaction, we first performed simulations with 154 a constant , set here to 7. (We considered other values of  later.) The GC initially had B cells 155 with low affinity for the target antigen. As the GC reaction proceeded, B cells with increasing 156 affinity were selected in our simulations, marking affinity maturation ( Fig. 2A) . Eventually, a 9 affinity of the B cells increased and reached a plateau (Fig. 2B) . Thus, when =7, the average 162 affinity of the B cells, determined by the average match-length between the antigen and BCR 163 sequences, plateaued at ~6.7 (Fig. 2B inset) . Note that L=8 in these simulations. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101 https://doi.org/10. /2021 To examine the effect of antigen availability, we next performed simulations at different 174 values of . Increasing  resulted in a lower value of the plateau of the average affinity ( Fig.   175 2B), indicative of weaker selection. Increasing  would correspond to higher vaccine dosages.

B cells with lower affinities were selected with higher  because more opportunities were 177 available for antigen acquisition. Thus, the average affinity plateaued at ~3.4 when =15 and 178 decreased further with larger  (Fig. 2B inset) . This is consistent with the classic observations 179 of poorer affinity maturation with increasing antigen levels (26, 39) . In terms of the absolute 180 antibody titres, our simulations predicted that unless the selection stringency was so large that 181 the GC B cell population began to decline causing GC collapse (Fig. S1 ), the GC B cell 182 population was maintained, leading to a steady output of Abs from the GC (Fig. S2 ). The lower 183 affinity with increasing  thus resulted in a corresponding decrease in the affinity-weighted 184 cumulative antibody output in our simulations (Fig. 2C ). The latter output was ~417 when =7 185 and ~216 when =15 at 80 d following dosing (Fig. 2C inset) . This affinity-weighted antibody 186 output would serve as a measure of the humoral response elicited by vaccination; it accounts 187 for the effects of both the quality and the quantity of the response. At very high values of , 188 beyond ~20 in our simulations, the effect of varying  was minimal ( Fig. 2B and C), indicating 189 that at sufficiently high dosages, the effect of varying dosage on the GC reaction may not be 190 significant. At lower , between 7 and 15 in our simulations, lowering dosage resulted in a 191 substantial gain in the GC response. When  was too low, however, in our simulations, GCs 192 collapsed, as not enough antigen was available for sustaining the B cell population (Fig. S1 ).

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Following vaccination, antigen levels are expected to decline exponentially with time. 194 We therefore next performed simulations with  decreasing with a half-life ; i.e., = 0 exp (-195 t×ln2/), where  0 is the peak antigen level achieved soon after dosing. How antigen levels 196 quantitatively decay on follicular dendritic cells within GCs relative to that in plasma is not 197 well understood (34, 51, 52) . We therefore examined a range of values of . We found in our 198 simulations with  0 =20, that the average affinity was higher when  was lower (Fig. 2D ).

Specifically, the average affinity at day 80 from the start of the GC reaction was ~6.7 for =40 200 d and ~3.4 for =160 d (Fig. 2D inset) . The faster decay of antigen thus increased the selection 201 stringency within the GC and led to higher affinity B cells. The affinity-weighted cumulative 202 antibody output, accordingly, increased with decreasing , consistent with an improved 203 response due to increased selection stringency (Fig. 2E ).

Prime-boost vaccination: the effect of dosage 206 We now applied our simulations to mimic the prime-boost vaccination protocols 207 employed in clinical trials (5). Specifically, we considered low dose (which we set using  0 =10) 208 and standard dose ( 0 =20) combinations, administered with a dosing interval =28 d CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint 12 seen following natural infection with other viruses too (25).) If the interval  is relatively small, 215 one may expect the boost to modulate ongoing GC reactions, as has been suggested previously 216 (34, 39). However, if  is large, then the GCs formed by the prime may collapse due to antigen 217 decay before the boost, so that the seeding of new GCs by the boost is more likely. In the latter 218 scenario, the effect of the prime must come from the preferential seeding by memory B cells 219 formed following the prime (47, 48, 53) . Recruitment of memory B cells into GCs has been 220 suggested, especially those B cells that displayed cross reactivity to other circulating human 221 betacoronaviruses (24). We therefore simulated two limiting scenarios ( Fig. 1B) : First, we 222 assumed that the boost modulated existing GCs and seeded no new GCs. Second, we let the 223 boost seed GCs using the memory B cells formed from the prime and not modulate any existing 224 GCs. We also simulated a control case where the boost established new GCs de novo, without 225 using memory B cells from the prime, in which case no advantage from the prime is expected.

With the boost modulating existing GCs, our simulations predicted an advantage of the 227 low dose prime over the standard dose prime (blue and red lines in Fig. 3A , B). The average 228 affinity increased with time more steeply with the low dose until day 28, when the boost was 229 administered (Fig. 3A) . Just prior to boost administration, the average affinity was ~4.9 for the 230 low dose versus ~2.8 for the standard dose prime. Correspondingly, the affinity-weighted 231 cumulative antibody output was higher for the low dose than the standard dose (Fig. 3B) . The 232 administration of the boost caused an increase in antigen availability ( Fig. 3A inset) , relieving 233 the selection stringency. The average affinity thus saw a temporary dip (Fig. 3A) . However, as 234 affinity maturation continued, the higher affinity B cells selected with the low dose prime 235 expanded substantially, yielding a much higher affinity-weighted antibody output than with the 236 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint 13 standard dose prime (Fig. 3B ). The average affinity and the affinity-weighted cumulative 237 antibody output was higher with the low dose prime than the standard dose prime throughout 238 our simulations. When we let the boost seed GCs using memory B cells from the prime, the difference 249 between low dose and standard dose prime was smaller in our simulations following the boost 250 (green and orange curves in Fig. 3A , B). This is because we assumed that only B cells above a 251 certain affinity for the antigen (here, match length ≥ 3; see Methods) could differentiate into CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint 14 regardless and thus seeding GCs with low affinity memory B cells may be no different from 257 seeding GCs de novo. Yet, even within the memory pool, the low dose prime yielded higher 258 affinity B cells than the standard dose prime, explaining the advantage of the low dose prime To assess the influence of the dosing interval, we compared next the antibody responses 266 elicited by two dosing intervals, =28 d and =56 d. We let =80 d here to avoid GC collapse 267 following low dose prime with shorter antigen half-lives (Fig. S4 ). The average GC B cell 268 affinity was significantly higher with =56 d than =28 d when the GCs were allowed to persist 269 until the boost (Fig. 4A , B). For instance, the average affinity was ~6.6 and ~4.4, respectively, 270 in the two cases, just before the administration of the boost following low dose prime, because 271 affinity maturation continued longer with the longer dosing interval. Besides, the declining 272 antigen levels further increased selection stringency in the latter case. This qualitative trend 273 remained with the standard dose prime. The affinity-weighted cumulative antibody output was 274 also significantly higher with the =56 d than =28 d (Fig. 4C, D) . For instance, 28 d after the 275 boost, the output was ~380 and ~174, respectively, in the two cases, when low dose prime was 276 used and the boost modulated existing GCs. With standard dose prime too, the difference was 277 nearly 2-fold. This effect remained whether the boost seeded new GCs or modulated surviving 278 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. any , increasing  increased the peak affinity, regardless of the use of low dose or standard 287 dose prime or whether the boost seeded new GCs or affected existing GCs (Fig. 4E ). Thus, a 288 longer duration yielded a GC response of better quality. Further, the lower was , the higher 289 was the peak affinity at any , consistent with stronger selection stringency associated with 290 lower antigen availability (Fig. 4E) .

This latter effect influenced the overall response, combining quality with quantity, which we 292 assessed using the affinity-weighted cumulative antibody output 28 d post the boost (Fig. 4F ).

While the overall trend of improved output with longer  remained, the trend was more 294 nuanced. The nuances were due to the complex dynamics of the GC responses following 295 multiple dosing. We examined first the effect of low dose prime. When  was large, the GC 296 reaction was sustained longer, allowing greater affinity maturation (Fig. S4) . Thus, delayed 297 dosing interval would lead to better responses. Indeed, with =56 d and =84 d, our simulations 298 predicted that the cumulative output improved with  (Fig. 4F) . With =28 d, the GCs may not 299 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

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The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint Figure S4C . GCs tended to collapse after the boost (Fig. S4) . With large , the selection stringency was 313 weaker and it therefore took longer for affinities to rise. Consequently, intermediate  yielded 314 the best response (Fig. 4F) .

With standard dose prime, too, the effects were similar. The GCs were sustained longer 316 as  increased, but weaker selection due to greater antigen availability led to poorer affinity 317 maturation (Fig. S4) . The trade-off tended to yield the best response at intermediate . In our 318 simulations, when the boost contributed to existing GCs, it was not efficient in rescuing GCs 319 that were beginning to collapse. Thus, with low and intermediate , GCs tended to collapse 320 (Fig. S4) . When the boost was assumed to seed new GCs using memory cells from the prime, 321 because the latter had higher affinities for the antigen, the GCs not only survived, but also 322 expanded. The benefit was amplified with delayed dosing as better memory cells became 323 available for seeding the GCs. Thus, as long as  was not too small, the cumulative output 324 tended to improve with increasing  (see =40 d and 80 d in Fig. 4F ). (With very small , the 325 increased GC collapse compromised the response at high ; see =20 d in Fig. 4F ). These 326 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint trends were maintained when the output was considered 56 d post boost (Fig. S4) . That GCs 

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The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint Experimental evidence supports the above reasons. Antibody titres targeting the SARS-348 CoV-2 spike were measured in individuals administered the boost 8-12 weeks, 15-25 weeks, 349 and 44-45 weeks after the prime (9). The titres were consistently higher in the individuals with 350 the longer dosing intervals. However, interestingly, the titres just before the boost, were lower 351 in the individuals with the longer intervals. This was consistent with lower antibody output due 352 to declining antigen availability with time in the GC and the associated GC shrinkage. 

Improved antibody responses following delayed boost dosing has now been observed with 357 multiple vaccines (9-12).

With dosing intervals smaller than 8-12 weeks or with the low dose prime, the 359 differences in antibody titres have been less apparent (5, 8, 21) . Yet, the improvement in 360 vaccine efficacy is substantial (5). While we have argued that this improvement may be due to CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint 20 efficiencies tend to be much higher than corresponding in vivo efficiencies (58). Nonetheless, 370 greater affinity maturation with lower antigen availability has been long recognized as a 371 hallmark of the GC reaction (26, 34, 35, 39) . In independent studies on HIV vaccination, for 372 instance, protocols that allowed antigen levels to rise with time, akin to low dose prime as has been the case with other modeling studies of the GC reaction (34-36, 39, 40, 42, 45) .

This is because a number of key biological processes associated with the GC reaction remain 391 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint 21 to be elucidated, including the link between dosage and the number of GCs seeded, and between 392 measurable antigen levels in circulation and those within individual GCs (22, 23, 34, 35, 39) .

Only recently have these links begun to be evaluated (37). As a simplification, our simulations 394 have assumed that increased dosage leads to increased antigen availability within GCs while 395 keeping the number of GCs seeded fixed. It is possible that the number of GCs seeded may 396 also increase with dosage but with a commensurately smaller rise in the antigen levels per GC.

Future studies that elucidate the links above may help define these quantities better.

Nonetheless, the poorer quality of the antibody response with increasing dosage is a widely 399 observed and accepted phenomenon (26, 34, 39) , giving us confidence in our findings. 400 We recognize that other arms of the immune system that could be triggered by the 401 vaccines, particularly T cells, may affect the vaccine efficacies realized (5-9, 13, 14) . The 402 strength and timing of the T cell response has been argued to be important in determining the 403 severity of the infection (59), which in turn may affect the estimated vaccine efficacy (60). We 404 have focused here on the antibody response, to which the efficacies have been found to be 405 strongly correlated (18, 19, 60) , and which in our simulations qualitatively explained the effects 406 of the different dosing protocols on vaccine efficacies. 407 Other hypotheses have been proposed to explain the effects of low dose prime and 408 delayed dosing intervals, the predominant of which has been the undesirable response to the 409 adenoviral vector in the case of the Oxford/AstraZeneca vaccine that could blunt the response 410 to the boost (61). While these hypotheses remain to be tested, that the effects are now evident 411 with more than one vaccine, including lipid nanoparticle mRNA vaccines that do not use the 412 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.08.21263248 doi: medRxiv preprint adenoviral vectors (10-13), suggests that the effects are intrinsic to the responses elicited by 413 the SARS-CoV-2 antigens in the vaccines, supporting our hypothesis.

In summary, our study offers an explanation of the confounding effects of different 415 dosages and dosing protocols on COVID-19 vaccine efficacies. The resulting insights would 416 inform studies aimed at designing optimal vaccine deployment strategies. If the antibody production rate of plasma cells was β per generation (64), the instantaneous 509 affinity-weighted antibody output would be βP(g), which given the clearance rate,  A , of 510 circulating antibodies yielded the affinity-weighted cumulative antibody output as

We performed the simulations and analysed the results using programs written in MATLAB.

The authors declare that no conflicts of interests exist. 516 517 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101 https://doi.org/10. /2021 affordability, allocation, and deployment. Lancet 397, 1023-1034 (2021 

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