Fig 1.
Parameters governing the interaction between HIV-1 and neutralizing antibodies and study layout.
(A) Molecular parameters included in this study to define HIV-1 infectivity and nAb neutralization. (B) Parameters included in this study to define in vivo HIV-1 infection and nAb neutralization. All parameters used for modelling are highlighted in bold and are summarized in S1 Table. Parameters estimated in this study, notably the stoichiometry of trimer neutralization, N, and the probability of an infectious virion to start a host infection, ψ, are highlighted in red. (C) Shown here is the sequence of experimental and mathematical analyses in this study, starting with the experimental estimation of N and extending to the modelling of human mucosal HIV-1 transmission.
Fig 2.
Estimating the stoichiometry of HIV-1 nAb neutralization (N) with mixed trimer assays.
(A) Scheme depicting the combined experimental-mathematical approach employed here to estimate N. (B) Neutralization by nAb 2F5 of mixed trimer HIV-1 pseudovirus stocks containing the indicated ratios of JR-FL wt (2F5 sensitive) and JR-FL D664N (2F5 resistant) Envs. The relative infectivity (RI) of each stock is given by the percentage of target cell infection (i.e., the inverse of % neutralization) under saturating 2F5 nAb concentrations. (C) Theoretical model predictions of the relation between N (N = 1, 2 or 3; colored lines) and RI of virus stocks with different fractions of neutralization-sensitive to resistant Env (fR). The experimental JR-FL nAb 2F5 RI data from (B) are plotted as black dots, representing two independent experiments. Data fitting resulted in an estimate of N = 1, assuming T = 2 and trimers for each JR-FL virion (S3 Table). (D) Robustness analysis for the N = 1 estimate of HIV-1 strain JR-FL and nAb 2F5 against variation in T and
. Blue areas show combinations of T and
resulting in estimates of N = 1, green areas show combinations of T and
that would result in estimates of N = 2. The actual values of T and
for JR-FL (see above) are marked by the white dot, indicating that the N = 1 estimate is robust. (E) Since the model fit shown in (C) for JR-FL and nAb 2F5 is imperfect, we analyzed the goodness-of-fit. A slightly reduced
or slightly increased T compared to those used for the analysis (white dot, S3 Table) could improve the model fit to the experimental data.
Fig 3.
N = 1 is a general feature of broadly neutralizing antibodies and polyclonal HIV-1+ patient plasma IgG.
(A) to (E) Mixed trimer neutralization setups with the Envs and nAbs indicated in each panel, yielding estimates of N = 1 in all cases. (F) to (G) Envs with multiple nAb resistance mutations allowed parallel assessment of various nAbs on the same set of mixed trimer virus stocks. Mathematical analysis indicated N = 1 in all cases. (H) Mixed trimer setup with Envs ZA110 wt and ZA110-V1V21.7, the latter being sensitive to autologous HIV-1+ patient plasma. The model fit to the experimental data (black dots) yielded a plasma neutralization stoichiometry of N = 1. (I) Mixed trimer setup with Envs ZA110 wt and ZA110 ΔV1V2 and nAbs b6, 17B and 48D and three heterologous HIV-1+ patient plasma (Pat117, Pat118 and Pat122). The Envs in this setup are not infectivity-matched precluding mathematical analysis, but graphic comparison indicates equal N of nAbs and patient plasma. (J) Mixed trimer setup with Envs JR-FL L175P and JR-FL P369L M373R D664N and nAbs b6, 1.79, 2F5, b12 and heterologous patient plasma SP122, yielding equal estimates of N = 1. All data points depict two independent experiments. (K) N = 1 is a universal feature of all anti-HIV nAbs tested here. This defines decisive numerical requirements of HIV-1 virion neutralization by antibodies.
Fig 4.
Predicting HIV-1 antibody neutralization curves and IC50.
(A) Scheme depicting the virus and nAb-specific parameters necessary to predict HIV-1 neutralization by nAbs in silico. (B) to (D) Predicted HIV-1 nAb neutralization curves in dependence of (B) nAb KD, (C) HIV-1 entry stoichiometry, T, and (D) mean viron trimer number, . (E) Dependence of nAb IC50 on the number of Env trimers required for HIV-1 cell entry, T. (F) Relation between HIV-1 virion population size and the fraction of Env subunits that need to be bound by nAb to achieve virus population neutralization. (G) Comparison of experimental nAb IC50 values measured with HIV-1 strain BG505 [47, 48] (S5 Table) and IC50’s predicted by our model using BG505-specific T,
and KD [49] values (S3 and S5 Tables). For nAb PGT145 we assumed that only 1 nAb can bind per trimer; the PGT145 IC50 estimates with the 3-nAb-per-trimer model, used for all other nAbs, are shown in light grey (see also panel H). (H) For most nAbs, we assume that three nAbs can bind each trimer, while binding of one nAb is already sufficient for neutralization (N = 1). Binding of nAbs to a trimer that is already neutralized constitutes unproductive binding and may reduce antibody concentrations to a subcritical level [27]. To quantify this effect, we predicted neutralization by two nAbs with equal KD, but assuming that either three nAbs can bind each trimer, or that nAb binding is anti-cooperative as observed for PG9/PGT145-like nAbs, which are known to occupy only one of three potential epitopes per trimer. We observed a slight neutralization advantage for PG9/PGT145-like nAb binding behavior, manifested as an approximately two-fold reduction in predicted nAb IC50.
Fig 5.
Antibody neutralization and host infection in macaque passive immunization challenge studies.
(A) Scheme depicting our approach of post-hoc analysis of macaque passive nAb immunization vaginal virus challenge studies. The approach delivers both estimates of in vivo virus inoculum neutralization and the probability of each infectious virion to start a host infection. (B) Total number of SHIV-P3 virions remaining infectious in the four analysed studies, obtained by multiplying the study-specific SHIV-P3 virus inoculum sizes with the fraction of virions remaining non-neutralized by nAbs. Bars depict the lowest, mean and highest number of potentially infectious virions, based on different assumptions of nAb KD and mucosal nAb concentration (see S14 Fig). (C) Estimates for the probability that a single infectious virion starts a host infection, ψ, shown for each of the four individual macaque studies. The different symbols and bars depict the lowest, mean and highest values of ψ, based on the different estimates for the number of potentially infectious virions as shown in (B). For this analysis, only immunization and challenge regimes resulting in infection of test animals were considered. The average value of ψ (1.65x10-5) across all studies is indicated.
Fig 6.
Predicting protective antibody levels in vaginal HIV-1 transmission.
(A) Model predictions for male to female per-act HIV-1 transmission risk in absence of nAbs and in dependence of HIV-1 inoculum size. The range of typical HIV-1 inoculum sizes in semen (defined by semen viral load and semen volume) observed in chronic and acute stages of HIV-1 infection and the corresponding predicted per-act infection risks are indicated in grey shadings. (B) Model predictions for male to female per-act HIV-1 transmission risk in dependence on vaginal mucosal nAb concentrations. A relatively high HIV-1 inoculum of 100.000 virions was assumed. NAbs with four different KD are modelled, spanning the range from less potent to very potent nAbs. (C) Model predictions for male to female per-act HIV-1 transmission risk in dependence on vaginal mucosal nAb concentrations, assuming four different HIV-1 inoculum sizes and a medium-potent nAb.
Fig 7.
Modelling HIV-1 mucosal transmission and antibody neutralization.
Summary of the parameters incorporated into our model (left), allowing in silico analysis of host HIV-1 infection probabilities and the in vivo protective effects of neutralizing antibodies (right). Parameters shown in red were estimated in this study, while parameters shown in black were retrieved from the literature. The model framework can be expanded by a range of parameters to investigate additional factors involved in HIV-1 transmission and prevention (bottom), and may serve as blueprint for similar efforts in other viral disease settings or mucosal infection processes.