Bliss' and Loewe's additive and synergistic effects in Plasmodium falciparum growth inhibition by AMA1-RON2L, RH5, RIPR and CyRPA antibody combinations

Plasmodium invasion of red blood cells involves malaria proteins, such as reticulocyte-binding protein homolog 5 (RH5), RH5 interacting protein (RIPR), cysteine-rich protective antigen (CyRPA), apical membrane antigen 1 (AMA1) and rhoptry neck protein 2 (RON2), all of which are blood-stage malaria vaccine candidates. So far, vaccines containing AMA1 alone have been unsuccessful in clinical trials. However, immunization with AMA1 bound with RON2L (AMA1-RON2L) induces better protection against P. falciparum malaria in Aotus monkeys. We therefore sought to determine whether combinations of RH5, RIPR, CyRPA and AMA1-RON2L antibodies improve their biological activities and sought to develop a robust method for determination of synergy or additivity in antibody combinations. Rabbit antibodies against AMA1-RON2L, RH5, RIPR or CyRPA were tested either alone or in combinations in P. falciparum growth inhibition assay to determine Bliss' and Loewe's additivities. The AMA1-RON2L/RH5 combination consistently demonstrated an additive effect while the CyRPA/RIPR combination showed a modest synergistic effect with Hewlett’s \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=1.07 \left[95\% \mathrm{C}\mathrm{I}: 1.03, 1.19\right].$$\end{document}S=1.0795%CI:1.03,1.19. Additionally, we provide a publicly-available, online tool to aid researchers in analyzing and planning their own synergy experiments. This study supports future blood-stage vaccine development by providing a solid methodology to evaluate additive and/or synergistic (or antagonistic) effect of vaccine-induced antibodies.

RTS,S/AS01, the vaccine reduced clinical malaria cases by 39% and severe cases by 26% in children 2 . Therefore, on-going efforts are focused on the development of more effective next-generation vaccine candidates.
Clinical manifestations of the disease occur in the blood-stage infection of the parasite's lifecycle, where the parasite invades the host red blood cells (RBC), multiplies and invades other RBC to continue the asexual cycle. Invasion of the RBC by merozoites involves: (i) the initial contact by the merozoite, (ii) reorientation and deformation, (iii) binding of the merozoite to the RBC, (iv) formation of a moving junction, (v) internalization of the merozoite, and (vi) resealing the parasitophorous vacuole [3][4][5] . Various antigens such as merozoite surface proteins (MSP) 1 6 and 3 7 , erythrocyte binding antigen-175 8 , apical membrane antigen 1 (AMA1) 9 and reticulocyte-binding protein Homolog 5 (RH5) 10 are involved in these steps and have been the focus of asexual blood stage vaccine development.
AMA1 was a promising vaccine candidate since it elicited biologically active antibodies (as measured in vitro) following human vaccinations [11][12][13] . However, an AMA1 vaccination did not lead to protection in Controlled Human Malaria Infection (CHMI) model with a homologous clone 14 . In addition, AMA1 is highly polymorphic and that may be an another reason why vaccination of individuals with one or two-allelic forms of AMA1 did not protect against clinical disease in Phase IIa or IIb trials [14][15][16][17][18] . Therefore, further improvement in AMA1-based vaccines has been awaited. AMA1 binds to the rhoptry neck protein, RON2, to form a moving junction during merozoite invasion of erythrocytes. In a preclinical trial, vaccination of Aotus monkeys with the AMA1-RON2L complex completely protected 50% of the monkeys and delayed blood-stage infection in 75% of the remaining animals against homologous P. falciparum challenge, while vaccination with AMA1 alone only partially protected 13% of the monkeys 19 . Thus, AMA1 in complex with its rhoptry binding partner appears to be a more potent vaccine candidate. Another current leading blood-stage vaccine candidate is the rhoptry protein, RH5. RH5 is essential for binding to the host erythrocyte receptor basigin to facilitate invasion 20 . RH5 forms a complex with RH5-interacting protein (RIRP) 21 and cysteine-rich protective antigen (CyRPA) 22 , and recent data suggest the whole RH5/RIPR/CyRPA complex can also bind to the RBC 23 . Vaccination of Aotus monkeys with RH5 protein/ adjuvant showed complete protection against blood-stage infection in 33% of the monkeys while the rest cleared the infection with no treatment 24 . Also, in a Phase Ia clinical trial in healthy UK adults, RH5 vaccination induced significantly higher RH5 antibody responses than those observed in naturally-exposed individuals in malaria endemic regions, and the vaccine-induced antibodies showed biological activity as judged by the in vitro growth inhibition assay (GIA) 25 . Like AMA1-RON2L or RH5 antibodies, antibodies to CyRPA and RIPR (the other members of the RH5 complex) have parasite growth inhibitory activity in animal immunization studies 21,22 . RH5 antibody has been tested in combination with CyRPA, RIPR or AMA1 antibodies among others, and studies of antibody combinations of AMA1 or the RH5 complex components and with other antigens are summarized in Table 1. While an additive growth inhibitory effect was observed with RH5/AMA1 26 and RH5/RIPR antibody combinations 22 , combination with AMA1-RON2L antibodies has not been evaluated. In this report, we evaluated antibody combinations of RH5, RIPR or CyRPA with AMA1-RON2L in GIA with the aim of finding other antigens that may act additively or synergistically to improve the efficacy of the AMA1-RON2L vaccine candidate.
Performing GIA with combinations of multiple antibodies has been done previously but, in some cases, different or contrasting results have been reported. For example, antibody combinations of RH5 with CyRPA were reported to exhibit a variation in their ability to induce synergistic or additive inhibition of parasite growth 19,24,25 . Such variability could be explained, at least in part, due to differences in the recombinant protein or adenoviral based vaccines used to induce the antibodies, antibody concentrations in the experiments, animal species where antibodies were raised, and/or by methods for analysis.
There are two common, but different, definitions of additivity and synergy used to evaluate the effect of antibody combinations: Bliss' and Loewe's 27 . Bliss' synergy may be estimated for specific doses with few concentrations tested but Bliss' synergy may in certain cases define an antibody to be synergistic with itself (discussed in detail later). Loewe's synergy avoids this "self-synergy" problem, but it is more difficult to estimate. www.nature.com/scientificreports/ In this study, we examined four combinations of antibodies (RH5/AMA1-RON2L, CyRPA/AMA1-RON2L, RIPR/AMA1-RON2L and CyRPA/RIPR) using Bliss' model first, then selected two combinations (RH5/AMA1-RON2L and CyRPA/RIPR) which were further evaluated using Loewe's model. We offer a robust statistical method to determine Loewe's synergy or additivity of antibody combinations in GIA. Furthermore, the new analysis can be performed by an online tool which we provide here.

Results and discussion
To conduct GIA with mixtures of antibodies targeting two different antigens, antibodies were made against each of the AMA1-RON2L, RIPR and CyRPA antigens in rabbits, and all the antibodies reacted with their respective antigens in ELISA as shown in Fig. 1. The antibodies had a parasite growth inhibitory effect as expected, with AMA1-RON2L antibody being the most potent in terms of total rabbit IgG, followed by RIPR and CyRPA antibodies (Fig. 2). Antibodies from each of the two rabbits immunized per group (AMA1-RON2L, CyRPA and RIPR IgG) showed identical inhibitory activity at the same total IgG concentration, therefore, purified total IgG from one rabbit per group was used in the antibody combinations. RH5 antibodies used in this study were a pool of purified total IgG from five immunized rabbits and generated in a previous study 26 where the five individual RH5 purified IgGs demonstrated the same activity at the same RH5-specific concentration. We confirmed the biological activity of the pooled RH5 IgG (Fig. 2a) before performing the antibody combination assays.
Bliss' additivity assessment of RH5/AMA1-RON2L, RIPR/AMA1-RON2L, CyRPA/AMA1-RON2L and CyRPA/RIPR antibody combinations. A fixed concentration of AMA1-RON2L antibody was mixed with various concentrations of RH5, RIPR or CyRPA antibodies to determine Bliss' additivity. The CyRPA/RIPR combination (fixed dose of RIPR antibody with various concentrations of CyRPA antibody) was also included because synergy between CyRPA and RIPR monoclonal antibodies in inhibiting parasite growth has been reported 28 . The results of the Bliss' additivity experiments are shown in Fig. 3. When an observed inhibition for the combination (purple) was significantly higher than Bliss' independent activity (blue), it was considered as synergy between the two antibodies (indicated with asterisks in Fig. 3). The RH5/AMA1-RON2L antibody combination had an additive growth inhibitory activity (Fig. 3a), while the other combinations had either additive (at lower concentrations of RIPR or CyRPA antibodies in Fig. 3c, d ) or otherwise synergistic inhibitory activity (Fig. 3b-d).
Having obtained these results, it is important to note that Bliss' additivity and Loewe's additivity are two different ways of defining additivity (and hence of defining synergy and antagonism). Bliss' additivity is commonly used in this field to assess interaction effects between antibodies (Table 1) and has a clear interpretation and visualization. In addition, there is a practical benefit to perform the Bliss' additivity test. Given a minimum of three experimental conditions (antibody A alone, B alone and combination of A and B) can determine Bliss' additivity. This saves time, effort and test materials as compared to the Loewe's additivity test. These reasons are why we used the Bliss' additivity model first to screen for possible synergistic pairs of antibodies. However, determination of synergy by Bliss' additivity has a major disadvantage in that it can fail the "sham" thought experiment, depending on the shape of the dose response curve and/or test concentration of antibodies. The Figure 1. Total IgGs from rabbits immunized with AMA1-RON2L, RIPR or CyRPA binds to their specific antigens. Antibody reactivity of 1 μg/mL of AMA1-RON2L, RIPR, CyRPA or control total IgG (two rabbit IgGs per antigen) to 1 μg/mL of recombinant AMA1, RON2 peptide, RIPR or CyRPA protein was tested in ELISA. Each dot represents the average OD value of each rabbit IgGs from two independent assays. RH5 antibody was not tested by ELISA as the IgG came from a previously published study 26 .

Scientific Reports
| (2020) 10:11802 | https://doi.org/10.1038/s41598-020-67877-8 www.nature.com/scientificreports/ "sham" experiment states that if the two concentrations of the same antibody A are mixed (and we have sufficient replicates that we can ignore the GIA assay measurement variability), then the mixture should show additivity, because the same antibody A should not negatively or positively interact with itself. For example, if 1 mg/mL of A gives 25% GIA, and 2 mg/mL of A gives 50% GIA, then the Bliss model predicts 62.5% GIA at 3 mg/mL (i.e., (1 − (1 − 0.25) × (1 − 0.5) ) × 100 = 62.5). However, based on the dose-response curve of A, even when there is no GIA assay variability, it is possible that we might see either Bliss' synergy (i.e., 3 mg/mL of A shows > 62.5% GIA) or Bliss' antagonism (i.e., < 62.5% GIA at 3 mg/mL) when looking at a dose pair of A and A. As a consequence, we sought a different definition of additivity to prevent "sham" experiments from implying either synergy or antagonism. Another problem of using the Bliss' additivity model is that the conclusion could be changed depending on the antibody concentration used. As seen in Fig. 3c  Loewe's additivity assessment of RH5/AMA1-RON2L and CyRPA/RIPR antibody combinations. Loewe's additivity is defined so that the "sham" thought experiment will never allow a substance to be synergistic with itself; it will always be additive with itself. In addition, with a Loewe's additivity model, (essentially) a single parameter, Hewlett's S is calculated using all dose data and this statistic indicates whether there is Loewe's synergy, antagonism or additivity. On the other hand, however, Loewe's model has a disadvantage; it generally requires more data points to determine the effect as compared to the Bliss' additivity model. Therefore, out of the four combinations tested for Bliss' additivity, only two selected combinations were further evaluated whereby each antibody was tested at 6 different concentrations (including 0 µg/mL); i.e. a total of 36 combinations (it is called "6 × 6 grid" in this manuscript) per assay, and two independent assays, or biological www.nature.com/scientificreports/ replicates, were performed for each combination. One of the selected combinations was RH5/AMA1-RON2L, which showed additive effects at all concentrations tested in the Bliss' additivity analysis (Fig. 3a), and the other combination was CyRPA/RIPR, which showed the largest difference between observed inhibitions and Bliss' predicted additive values (Fig. 3d). We next developed a new Loewe's additivity model as shown in Eqs. (2) and (3), and determined the best-fit parameters for each combination as shown in Table 2. The expected model fit, and 95% CI are plotted in Fig. 4. Since most of the observed values were contained within the 95% CI regions, the model is considered to fit the data well. Based on the Loewe's model, there was no significant synergy effect for the pair of RH5/AMA1-RON2L with τ 1 =-0.06 (95% CI: [− 0.11, 0.01]) and Hewlett's S = 0.986 (95% CI: [0.968, 1.002]); therefore, we cannot reject the null hypothesis that the combination is additive (Tables 2 and 3). This result was similar to what was previously reported with another RH5 and AMA1 antibody combination 26 . On the other hand, the CyRPA/ RIPR combination had a significant, although modest, synergy effect with τ 1 = 0.25 (95% CI: [0.02, 0.84]) and Hewlett's S = 1.066 (95% CI: [1.025, 1.192]). The isobolograms, which show the effect of synergy for the two pairs of antibodies are seen in Fig. 5. For the RH5/AMA1-RON2L combination (Fig. 5a), the predicted ED50 curve almost completely overlapped with the dashed red line indicating additivity, while for CyRPA/RIPR (Fig. 5b), the predicted ED50 curve fell below the dashed red line, indicating synergy.
The combination of AMA1-RON2L antibody with RH5 antibody resulted in an additive effect (Figs. 3a and 5a). The step of RH5 binding to basigin on RBC during invasion process is described to precede junction formation by AMA1 binding to RON2 29 . In other words, the inhibition mechanisms for those two antibodies are likely to be independent, and the independency may explain the additive inhibition seen for the combination. On the other hand, the combination of CyRPA and RIPR antibodies demonstrated a synergistic effect (Figs. 3d www.nature.com/scientificreports/  www.nature.com/scientificreports/ and 5b), which might be due to the similar inhibition mechanisms of the two antibodies. CyRPA serves as the contact between RH5 and RIPR in the complex for efficient RH5 binding to the erythrocyte 23 , therefore, the CyRPA and RIPR antibodies may act together. Further study is required to uncover the mechanism(s) why a certain combination of antibodies shows an additive or synergistic effect. Worthy of note, an "additive" antigen is not necessarily to be excluded from a first choice of vaccine candidate. The antigen selection needs to consider multiple aspects, such as biological activity of antibodies induced by each antigen, cost of antigen production and polymorphism in the target molecules. The precise evaluation for an additive and synergistic effect will support a rational antigen selection.

Simulations and online apps for Loewe's additivity assessment.
To support future studies where researchers assess in vitro antibody combinations to evaluate additive and/or synergistic (or antagonistic) effect of antibodies, additional simulations were performed using GIA data obtained from this study. In addition, we used published GIA data of RH5/RH4 antibody combinations which were reported in a previous study 26 ; here this particular combination demonstrated a strong Loewe's synergistic effect (although to note, the GIA data were analyzed differently in the previous study). As expected from the previous report, the RH5 With respect to our new model of Loewe's synergy, simulations showed using a parametric bootstrap analysis that the percent of false positives, i.e. finding a synergy (or antagonism) when there was none, was less than or equal to the specified α-level. Also, the power to detect a significant interaction (either synergistic or antagonistic) was calculated in different test conditions using three different antibody combinations. In the simulations, the best-fit parameters were fixed based on the RH5/AMA1-RON2L, CyRPA/RIPR or RH5/RH4 combinations (the best-fit parameters are shown in Table 2 and Supplementary Material), then various test conditions in terms of  www.nature.com/scientificreports/ their grid sizes (e.g. whether each antibody was tested at two different concentrations, i.e. 2 × 2 grid, or at three concentrations, 3 × 3 grid) and number of repeat (independent) assays were evaluated. For example, Fig. 6a shows the simulation results using the best-fit parameters (β A , β B , γ A , γ B , τ 1 and τ 2 ) calculated from the RH5/ AMA1-RON2L combination data, and determined the power to detect a significant antagonistic effect if true τ 1 is equal to -0.06. When each antibody was tested at 6 different concentrations (6 × 6 grid) and the assay was repeated two times, the study design had only 35.2% power to detect a significant antagonism. The simulations with the three different antibody combinations showed the power to detect a significant effect is quite sensitive to the magnitude of τ 1 , the primary interaction effect (Fig. 6). In order to detect the small value of antagonism τ 1 = −0.06 . (Fig. 6a), at least 5 repeat experiments on an evenly spaced 10 × 10 grid of dose combinations, totaling 500 observations (100 points per assay × 5 assays) are required to have a > 80% chance of finding a significant www.nature.com/scientificreports/ antagonistic effect. However, in the case of the CyRPA/RIPR antibody combination with τ 1 = 0.25 , an evenly spaced 4 × 4 grid assay can detect a synergy about 92% of the time if the assay was repeated five times (Fig. 6b). Finally, in the case of a strong synergistic effect with τ 1 = 36 (Fig. 6c), we need only the bare minimum number of observations required to fit the model (one experiment of a 3 × 3 evenly spaced grid). These simulation results imply that preliminary screening is of great importance, because not only do we need a prior notion of which pairs may be candidates for synergy, but we also need a reasonable estimate of the magnitude of synergy in order to determine the number of observations in the grid of dose combinations as well as the number of experiments for the Loewe's additivity assessment.
In addition to the available R package, we have also developed an online app to aid researchers in evaluating their own dose-combination GIA data and in designing new, adequately powered experiments. The app is available publicly online at https:// addit ivity. niaid. nih. gov/. Features of the app include a full model description, an interface to load experimental results or look at pre-loaded data sets, a method to estimate parameters and 95% CIs of the model, three sets of graphs to visualize the model fit and synergy effect, and a "Design Experiment" tab which generates R code to use in the package loewesadditivity to find the power of the model to determine significant interactions for a given set of parameters.
There are limitations for this study. All antibodies were raised against P. falciparum 3D7 clone antigen sequences and GIA were performed with homologous 3D7 clone parasites. A previous study suggests that additive/synergistic effects could be determined not only by pairs of antibodies, but also by parasite strains 26 . Furthermore, in vitro antibody mixture GIA assessment (as conducted in this study) may not necessarily predict the anti-parasitic effect of in vivo or the results of co-immunization with pairs of antigens. For example, combinations of anti-AMA1 and anti-RON2L IgGs in in vitro GIA did not show any additive effect (anti-RON2L IgG by itself showed no GIA activity); however, an immunization with a mixture of AMA1 and RON2L induced more potent antibodies than immunization with AMA1 alone. On the other hand, even if in vitro GIA shows a strong synergy, the combination of antigens may display immune interference upon in vivo vaccination. Therefore, the definitive conclusion needs to be made based on an in vivo vaccination study with combined antigens. Also, although in vitro GIA activity has been positively correlated with in vivo protection from malaria in vaccinated non-human primates 19,24 , this is not clear in humans 30,31 . Thus, in vivo efficacy of a test vaccine (either a singleor combination-vaccines) should be evaluated in a human trial. Finally, the model we present here is just one of many that has been used to model Loewe's additivity. Our model is reasonable in the sense that τ 1 is a one number summary of synergy, our model fits the data well, and the simulation study supports our results. However, we make no claim that it is the "best" such model in the Loewe's additivity framework. Other work such as Lederer et al. 32 discusses the limitations of Loewe's additivity models in more detail. The model presented here can be extended conceptually to triples (or more) antigen combinations by adding a proper covariate interaction effect(s). However, further work is required to establish the best model for such combinations. Nonetheless, the online modelling tool and accompanying R package will strongly support future blood-stage vaccine development by allowing researchers to design their own experiments and to evaluate additive and/or synergistic (or antagonistic) effects of vaccine-induced antibodies with a solid methodology.

Methods
Production of AMA1-RON2L, RIPR, CyRPA and RH5 antibodies. Female New Zealand White rabbits (2 per group) were vaccinated three times (two sites in the scruff of the neck) with the antigens. Each of the 3 doses consisted of a mixture of 50 µg of AMA1 and 150 µg of RON2L, a synthetic cyclized peptide (AMA1-RON2L), 50 µg of RIPR or 50 µg of CyRPA emulsified in Freund's complete adjuvant (day 0) or Freund's incomplete adjuvant (days 21 and 42) to generate the antibodies. Rabbits were also vaccinated with a mixture of an equal volume of PBS and adjuvant only as controls. All rabbits were bled on day 64 and sera were collected. All antigens were generated using P. falciparum 3D7 sequences, and the details of protein production and purification were described previously 22,26,33,34 . Total IgG was purified from the rabbit sera using a Protein G sepharose column as previously described 11 .
The animal work was approved by the Animal Care and Use Committee at the National Institutes of Health on animal study proposal LMIV 1E and carried out under Division of Intramural Research Animal Care and Use Committee guidelines at the National Institute of Allergy and Infectious Disease.
The RH5 antibody (rabbit) was a pool of five purified total IgG obtained from a previous study 26 . Briefly, the rabbits were vaccinated with 7 × 10 7 to 4 0.5 × 10 8 infectious units of replication-deficient adenovirus human serotype 5 (AdHu5) on day 0 and 5 × 10 7 to 1 × 10 8 plaque-forming units of attenuated poxvirus modified vaccinia virus Ankara (MVA) on day 56. Both AdHu5 and MVA contained RH5 sequence from the 3D7 clone. The animal work in the previously published study was approved by the University of Oxford Animal Care and Ethical Review Committee.

ELISA.
The purified total IgG were tested for an antigen specific antibody responses by ELISA using a previously described standard protocol 35  Growth inhibitory activity (GIA). P. falciparum 3D7 parasites were cultured in RPMI 1640 supplemented with 10% human serum. The assay was done using the lactate dehydrogenase assay, as previously described 11  GIA to determine synergy by Bliss' additivity. While two rabbits were immunized for each antigen, as the two IgGs showed almost identical activity in the GIA (Fig. 1) Statistical analyses. Both the Bliss' and Loewe's additivity models' details are described fully in the Supplementary Material. To estimate Bliss' additivity, we used a mixed effects model where the fixed effect was the antibody combination and the two random effects, well-to-well (replicate-to-replicate) and assay-to-assay (experiment to experiment), were included in the model. For dose i , experiment j , and replicate k , we estimate the log % GIA as a sum of the fixed and random effects, From Eq. (1), we were then able to estimate the threshold parameter for the Bliss' additivity model. For each dose combination, the Bliss method uses a different standard threshold parameter φ AB such that if φ AB > 1 then there is antagonism, if φ AB = 1 there is additivity (Bliss independence), and if φ AB < 1 there is synergy between the pair of antibodies A and B.
The Loewe's additivity model used to predict GIA for two combination of antibodies was based on the logit model seen in Harbron 36 and Zhao et al. 37 with added parameters to induce more flexibility to model heterogeneous data. Briefly, the Loewe's additivity model is described below. We assumed that the GIA value was (usually) between 0 and 100% plus some random noise ǫ i , In Eq. (1), ǫ i ∼ N 0, σ 2 i is the random noise from a Normal distribution with mean zero and standard deviation σ i possibly dependent on the dose combination i. The model in Eq. (2) allows for negative values of % GIA, which is by design as negative measurements may be recorded.
The value of ψ i is a function of concentrations of combinations of antibodies A and B and parameter θ . The doses of the respective antibodies are A i and B i . The model parameter is θ = (β A , β B , γ A , γ B , τ 1 , τ 2 ) , where β A and β B are the respective ED50 doses of A and B; γ A and γ B are respective shape parameters; and τ 1 , τ 2 are interaction terms between concentrations A and B. Specifically, is the proportion of the doses due to A, with respect to the ED50s of A and B. The interaction parameters are both τ 1 and τ 2 , but τ 1 is of primary interest. The parameter τ 2 exists to allow for flexibility in the slope of the response curve. We are primarily concerned with τ 1 = 0 , and in that case the contribution from τ 2 does not matter. A value of τ 1 = 0 corresponds to additivity, τ 1 > 0 to synergy and τ 1 < 0 to antagonism, except in very special circumstances (described in Supplementary Material).
We estimated the parameters θ by minimizing the sum of squares between the observed and estimated values. Practically, this was done using the R package we developed, loewesadditivity, which is available publicly online from the R CRAN repository (https:// cran.r-proje ct. org).
All parameter confidence intervals shown here were estimated using a parametric bootstrap. The details of parametric bootstrap and power simulations are shown in Supplementary Material.