Two-dose “extended priming” immunization amplifies humoral immune responses by synchronizing vaccine delivery with the germinal center response

“Extended priming” immunization regimens that prolong exposure of the immune system to vaccines during the primary immune response have shown promise in enhancing humoral immune responses to a variety of subunit vaccines in preclinical models. We previously showed that escalating-dosing immunization (EDI), where a vaccine is dosed every other day in an increasing pattern over 2 weeks dramatically amplifies humoral immune responses. But such a dosing regimen is impractical for prophylactic vaccines. We hypothesized that simpler dosing regimens might replicate key elements of the immune response triggered by EDI. Here we explored “reduced ED” immunization regimens, assessing the impact of varying the number of injections, dose levels, and dosing intervals during EDI. Using a stabilized HIV Env trimer as a model antigen combined with a potent saponin adjuvant, we found that a two-shot extended-prime regimen consisting of immunization with 20% of a given vaccine dose followed by a second shot with the remaining 80% of the dose 7 days later resulted in increased total GC B cells, 5–10-fold increased frequencies of antigen-specific GC B cells, and 10-fold increases in serum antibody titers compared to single bolus immunization. Computational modeling of the GC response suggested that this enhanced response is mediated by antigen delivered in the second dose being captured more efficiently as immune complexes in follicles, predictions we verified experimentally. Our computational and experimental results also highlight how properly designed reduced ED protocols enhance activation and antigen loading of dendritic cells and activation of T helper cells to amplify humoral responses. These results suggest that a two-shot priming approach can be used to substantially enhance responses to subunit vaccines.


Model of T cell priming
We constructed our model based on the biological observations of the mechanism of action of adjuvants (55-60).Upon administration of adjuvants, local tissue-resident cells such as neutrophils and macrophages are recruited to the site of vaccine administration and draining lymph nodes.These cells release cytokines and chemokines, which serve as chemotactic agents for dendritic cells (DCs).As a result, DCs migrate to the sites and take up antigen.The presence of adjuvant significantly enhances this process.Adjuvant facilitates the maturation of DCs, ensuring a more efficient antigen uptake (59), and aids in the delivery of antigen to the DCs (30).Following antigen uptake, the activated DCs present peptide-major histocompatibility complex (pMHC) molecules to CD4 T cells in lymph nodes.This interaction leads to the proliferation of CD4 T cells and initiates their differentiation into Tfh cells (44).
In our model, the concentrations of antigen and adjuvant rise upon administration and subsequently decay according to first-order kinetics, consistent with previous models (19,35,37).Regardless of the dosing scheme, the same total quantity of antigen is administered.Thus, we normalize the concentrations so that the total amount correspond to a concentration of 1.The same normalization is applied to the adjuvant concentration.For a dosing scheme involving n doses given times t1, … tn, the changes in concentration of the antigen from each dose are represented by f1,Ag, … fn,Ag, and of adjuvant are represented f1,Adj, … fn,Adj.These fractions satisfy the conditions respectively.Then, the differential equations that govern the antigen and adjuvant concentrations are as follows: (Equation 1) where ( −  ! ) is the Dirac delta function, whose value is zero everywhere except at  =  !, and whose integral over the domain that includes  =  ! is equal to one.
The recruitment of tissue-resident innate immune cells (TCs) and their decay are modeled as: where the first term stands for the activity of the adjuvant with  #() being the half-max adjuvant concentration.The activity increases with adjuvant concentration when  #() > [] but saturate when . Employing a saturation function to represent biological activity is widely adopted (35, 37, 61).We pick a small value for  #() based on the observation that there is not a big difference between the numbers of DCs recruited after full dose and 20 % of the dose (Fig. S3H). is the decay rate, assumed to be identical for all innate immune cells for simplicity.Its value is taken from Mayer et al. (37) The recruitment of DCs by the TCs and their activation and antigen uptake are modeled as: 4) 5) where  #$ ; represent activated antigen-loaded DCs.Here,  * is the rate of DC recruitment and its value is derived from the best fit of model prediction to experimental data in Fig. 3F.The parameter  quantifies the extent to which the adjuvant's activity expedite antigen uptake by the DCs.The adjuvant, SMNP, is a saponin/Toll-like receptor 4 agonist that can activate DCs and increase their antigen uptake (30).Given this recognized role of adjuvants, we set  to be large.
The activated antigen-primed DCs induce the proliferation of CD4 T cells, which we assume to differentiate into Tfh cells according to first-order kinetics: 6) 7) where  is the maximum proliferation of the T cells,  is the rate at which proliferating T cells differentiate into Tfh cells, and  * is the baseline number of T cells.The model of T cell proliferation and its parameter values for  and  are derived from Mayer et al. (37), which encompasses T cell proliferation and death.
In this study, rather than accounting for death, we model the process as T cells proliferating and differentiating (62).
We fit two parameters,  * and  * , based on finding the best alignment between the model prediction and experimental data of Tfh cell numbers in Fig. 3F.We utilized standard maximum likelihood estimation method.D0 controls the scale of the number of DCs and aDC Ag+ s, while T0 controls the scale of the number of T cells.Since the ratio between aDC Ag+ s and T cells affect the proliferation rate of T cells (Eq.6), appropriate scaling between D0 and T0 is required to recapitulate the fold-difference between the experimentally observed Tfh numbers after bolus and the ED schemes.If the scale of DCs is too small compared to the scale of baseline T cells, the initial doses containing small amounts of antigen and adjuvant will not generate enough aDC Ag+ s for adequate T cell proliferation.Thus, fold-difference between bolus and the ED schemes is reduced.When the scale of DCs is too large, the opposite is true.
Additionally, the absolute value of T0 affects the overall quantitative match between the experimental and simulated data.The antigen decay rate was approximated from experimental data in Fig. S1.All other epitopes on the pAg are aggregated into a single immunodominant epitope.Each B cell targets either the nAg or the pAg.In this model, the germline affinity distribution of naïve B cells displays an extended tail for the immunodominant non-native antigen.

Equations for the antigen dynamics
First, we describe the processes that are included in the model for antigen dynamics.We use the following abbreviations: native soluble antigen (nAg), partially degraded soluble antigen (pAg), either type of soluble antigen (Ag), soluble antibody (Ig), soluble immune complex (IC), immune complex on follicular dendritic cell (IC-FDC), plasma cell (PC).
The partial and full decay of the soluble antigen are described as: →  Decay of free native soluble antigen into partially degraded antigen

𝑝𝐴𝑔 → ∅ Decay of partially degraded antigen
The production and decay of antibodies, which apply to both the nAg and pAg-targeting antibodies are described as: →  +  Antibody production by plasma cells

𝐼𝑔 → ∅ Decay of free soluble antibody
The formation of immune complexes, deposition on FDC, and decay on FDC, which apply to both the nAg and pAg, are described as: +  ⇌  Fast equilibrium between free soluble antigen and antibody  →  −  Immune complex transport to follicular dendritic cells

Initiation of GCs
In Yang et al. ( 35), which solely focused on bolus injections, the assumption was made that 200 GCs are simultaneously initiated post each injection, with a separate pool of naïve B cells tied to each GC.This simplified model is not best suited for depicting dosing schemes with gradual administration of antigen and adjuvant.Here, we consider a single pool of naïve B cells collectively shared across all GCs.We then postulate that GCs are sequentially initiated, influenced by the increasing number of Tfh cells.The number of Tfh cells is determined by the model of T cell priming (Eqs.1-7) and is affected by the dosing scheme.
The number of active GCs at time t, NGC(t), is determined from the number of Tfh cells, NTfh(t), as follows: 15) While the total number of GCs has not reached the capacity of 200, NT0 quantifies the highest number of Tfh cells that can be attributed to any one GC.As Tfh cell numbers rise, new GCs are initiated.However, once the capacity of 200 GCs is reached, further increase in the number of Tfh cells does not lead to establishment of new GCs.Instead, these additional Tfh cells are distributed among the existing GCs, resulting in larger individual GCs.From our simulations, bolus immunization leads to an average of ~60 GCs, while 2-ED results in ~187 GCs, and 7-ED reaches the maximum capacity with 200 GCs.In terms of the average number of B cells per GC, both bolus and 2-ED present ~1400 B cells, whereas 7-ED displays significant increase to ~5900 B cells.

Naïve B cell germline affinities
The model of germline-endowed binding affinities of naïve B cells follows the approach from the previous study We parametrize the distribution of the binding affinity, denoted as  = − log '* (  ( ), with a geometric distribution.The distribution takes discrete values between 6 and 8, expressed as  3 = 6 + 0.2 for  = 0 … 10.Note that a higher value of  indicates stronger binding.
We differentiate between two groups of naïve B cells: one group binding to the native antigen and the other to the partially degraded antigen.We assume that the partially degraded antigen is more immunodominant.The frequencies of naïve B cells binding to either antigen type with affinity  3 are formulated as follows: (Equation 16) (Equation 17) where  %5!67 is the number of naïve B cells and  is the fraction of B cells that target the native antigen.
The exponents  ' ,  ; determine the slope of the distribution.They are derived from the parameters  ' 2 and  '; which we directly specify.The following relationships are satisfied: 18) Given  '; > 1, this parameterization results in an extended tail of germline-endowed affinities for the naïve B cells targeting the partially degraded antigen, reflecting their immunodominance.
The above model was initially developed to represent a pool of naïve B cells associated with an individual GC.For this study, we adjust the model by amplifying the frequencies by a factor of 200, thereby consolidating a shared pool of naïve B cells across all GCs.

Activation of naïve B cells, differentiation into plasmablasts, and entry into GCs
We model the quantity of antigen captured by a B cell, denoted as , using the following equation: The probability of B cell activation at each step is determined as: Pr(B cell  is activated) = min ( !, 1) (Equation 21) The entry of activated naïve B cells to GCs is limited by competition for positive selection from helper T cells.The selection rate for an activated naive B cell , denoted as  !, is given by: Here,  5CD!65D7( stands for the total count of activated B cells, 〈〉 denotes the average quantity of antigen captured by all activated B cells, and  0 represents the limited number of helper T cells that B cells compete for.Activated naïve B cells migrate to the T-B border and interact with antigen-primed T cells before they migrate back to the B cell zone and enter GCs (62).Thus, we choose the value of  0 as the number of T cells from the model of T cell priming (Eq.6).
Upon positive selection, a naïve B cell has three potential fates: it can differentiate into a memory cell, a plasmablast, or a GC B cell (63).In our model, there is a probability p1 that a B cell differentiates into either a memory cell or a plasmablast.If it takes this path, it further has a probability p2 of becoming a plasma cell and otherwise becomes a memory cell.If the B cell becomes a plasmablast, it undergoes five division cycles (64).Conversely, there is a probability 1-p1 that the B cell enters a GC.If this path is taken, a naïve B cell is randomly allocated to one of the active GCs.

Proliferation, mutation, and death of GC B cells
GC B cells must be activated by antigen and then receive help from Tfh cells to proliferate.The activation step for GC B cells is identical to that of naïve B cells.The rate of positive selection,  !, of a GC B cell, , is modeled based on competition for limited number of Tfh cells: where  E5F is the maximum rate of positive selection, and the number of Tfh cells in each active GC is calculated as  012 / /. .Upon positive selection, a B cell exits the GC with a probability of p1 and proliferates inside the GC with a probability of 1-p1.When it exits the GC, it becomes a plasma cell with a probability of p2 or a memory cell with a probability of 1-p2.When it proliferates, one offspring undergoes mutation.This mutation can result in apoptosis (probability 0.3), no affinity change (probability 0.5), or a change in the mutation state of a randomly selected residue (probability 0.2).
The affinities of GC B cells change with mutations.Each B cell is represented as a string of 0's and 1's with a total length of  97G .The residues are all 0's for a naïve B cell.Each time an affinity-affecting mutation occurs, one of the residues is randomly chosen and its value is flipped.The affinity of a B cell is determined by the sum of its germline-endowed affinity and the contributions of the mutations, as follows: (Equation 24) where  !,) ∈ {0,1} is the mutational state of residue , and  !,) is the effect of the mutation at residue  on the binding affinity.The values of  !,) ( = 1 …  97G ) are independent and identically distributed as follows: !,) ~  I(J,K) −  (Equation 25) This shifted log-normal distribution with , ,  chosen to fit experimentally determined distribution leads to ~5 % of affinity-affecting mutations increasing the binding affinity.

Expansion and differentiation of B cells in Extra Germinal Center
In schemes involving multiple injections, we model the expansion of memory cells and their differentiation into plasma cells outside of germinal centers, termed extra germinal centers (EGCs).Any injection beyond the first dose initiates an EGC, unless there is already an ongoing one.EGC proliferation is rapid and short-lived (65).An EGC terminates after a 6-day period without a new injection.The process of affinity-based positive selection, which results in either differentiation or proliferation, is identical to that in the GCs.However, no mutations are introduced to B cells in EGCs, and proliferating cells in EGC differentiates into plasma cells with higher probability,  ; :/.(65, 66).Moreover, to reflect the fast kinetics in the EGC, the number of Tfh cells is maintained at its peak value,  0* .

Modifications from the original model
In our study, we have introduced several changes from the original model proposed by Yang et al. (35), which are described in detail in the relevant sections.We summarize these changes here to aid readers interested in understanding the modifications.
(1) T cell priming: We developed a detailed T cell priming model that is suitable for gradual dosing schemes.
(2) Antigen decay and targeting: We introduced partial decay of antigen and B cells targeting the partially degraded antigen.
(3) Initiation of GCs: We introduced asynchronous initiation of GCs, which is suitable for gradual dosing schemes.
figure S5: Additional data on Alum-pSer immunizations.(A-C) C57Bl/6J mice (n=5 animals/group) were immunized with 10 µg MD39 trimer anchored onto 50 ug Alum combined with 5 µg SMNP adjuvant (20% vaccine on day 0, 80% on day 7, red) or with alum anchoring only used for the second dose (green).Shown are experimentally measured responses on day 14 for GC B cells (A), Tfh cells (B), and trimerspecific GC B cells (C).(D-E) In silico predictions modeling the same experiment as in (A-C), showing numbers of native antigen-binding GC B cells (D), and total GC B cells (E) over time.Shown are data from one independent experiment for each immunization series.****, p < 0.0001; ***, p < 0.001; **, p < 0.01; *, p < 0.05; ns, not significant; by one-way ANOVA with Dunnett's multiple comparison post test compared to bolus immunization.
signifies antigen availability,  * = 6 serves as the reference affinity, and  represents the selection stringency.The min function accounts for the effect of affinity ceiling.The term  = 0.01([] + []) + [ − ] represents the effective antigen concentration, accounting for the predominant influence of surface-presented immune complexes. * is the reference concentration.For B cells targeting the native or partially degraded antigen, the appropriate antigen concentration is applied respectively.

Table S1 . Antigen decay kinetics data.
Measured antigen trimer mass per lymph node after immunization.Maximum likelihood estimate of the antigen decay rate assuming first-order kinetics is ~2.7 / day, corresponding to half-life of ~6.2 hrs.

Table S2 . Simulation parameters for the model of T cell priming Descriptions
and values of the parameters used in the simulation of T cell priming.

Table S3 . Simulation parameters for the model of B cell responses Descriptions
and values of the parameters used in the simulation of B cell responses.Highlighted parameters have values changed from the model in ref. (35).