Fig 1.
PKPD model schematic for optimizing combination bNAb treatment against a genetically diverse pathogen like HIV.
The model incorporates: pharmacokinetics (PK), pharmacodynamics (PD), and interactions between broadly neutralizing antibodies (bNAbs). PK quantifies bNAb concentrations over time after administration. PD quantifies potencies at a given concentration for each antibody against many viral strains with sensitivity determined by IC50ij, the level of the i-th drug needed to achieve 50% neutralization of the j-th viral strain–with some fraction ω of strains completely resistant. Titer, or the ratio of concentration to IC50 of each antibody against a certain strain, maps to neutralization proportion (0–1 scale) of viral infection events that are blocked. Interaction model includes taking either the worst (minimum) or the best (maximum) titer/neutralization between two products. Two more mechanistic interaction models combine titers (additivity) or neutralization (Bliss Hill), and generally mean combinations outperform the best single bNAb. Depending on the PKPD outcome measure of interest and when that measure is evaluated (throughout the study = AUC, at the low point = trough), we identify the optimal ratio of bNAbs.
Table 1.
Summary of equations for PD interaction models relating bNAb (i) to virus (j).
Formula for Bliss-Hill ID50 illustrated for 2-bNAb combinations only.
Table 2.
Parameter settings for global sensitivity analysis combining two bNAbs.
Fig 2.
Correlations among PKPD outcomes and between model parameters and outcomes.
A) Many metrics for PKPD outcomes are highly correlated (yellow in heatmap) and cluster into approximately 6 distinct categories: see labels. The minimum interaction was distinct across all outcomes. B) Of the 10 varied model parameters (Table 2), half-lives and resistant fractions had the largest impact on representative members of each of 6 categories from A. All categories were similarly sensitive to half-lives, whereas titer and minimum categories were less sensitive to resistance fractions. The ratio does not strongly predict any outcomes relative to variation in all other parameters, a sign that there is no general solution to optimizing the ratio and it must be adjusted on a case-by-case basis.
Fig 3.
Sensitivity of the optimal ratio to PKPD outcome choices and antibody features.
The optimal ratio was calculated for each parameter set and each outcome. A) Optimal ratios cluster by outcome similarly to the general analysis in Fig 2 with differences being that coverage and IIP can be grouped together whilst the minimum interaction model separates into 2 categories. B) Different variables drive optimization of different outcomes. Among viral pharmacodynamic inputs, the geometric mean IC50 is most influential on titer and minimum potency outcomes, while the fraction resistant is most influential for the remaining outcomes. C) A low percentage of parameter sets admitted outcomes within 95% of the optimal value.
Fig 4.
Optimizing 2 bNAb combination therapy in comparison to bi-specific therapy with the same bNAbs.
Combination antibody results for AUC (top) and trough (bottom) suggest that trough is slightly more sensitive to ratio (see curvature of outcome surface and change from optimal ratio denoted by open dot). In general, a single bi-specific bNAb will perform worse than combination therapy if it has the best neutralization potential of both parental lineages under a common interaction model but inherits the faster clearance kinetics. However, if synergetic binding occurs, enhancing the bi-specific potency by 10-fold (see Methods), it is similar or outperforms the optimal combination for all outcomes and doses. “All bNAb1” and “All bNAb2” on the x-axis correspond to 100% dosing of the second bNAb product.
Fig 5.
Additional enhancement after optimization of 3-drug therapy.
Using 3 well known anti-HIV broadly neutralizing antibodies, we performed an analysis predicting the percent of viruses covered at more than 50% and 95% protection levels using protection correlates from an NHP meta-analysis(14) and the AMP clinical trials(5). The percent viruses covered were computed over the total time course using area under the curve (auc) and at the final time point (trough). We compared coverage for the bNAbs individually, in dual combination, and in triplicate as 1:1:1, 1:1:2, 1:2:1, 2:1:1, and the optimal combination (see S2 Table). Enhancement over the best single bNAb (VRC07-523-LS) is generated through combinations when evaluating the percent of the viruses neutralized at a 95% level. However, triple drug therapy does not meaningfully enhance over optimized 2-drug therapy levels, even when completely optimized. Protection levels are more optimistically predicted using the NHP meta-analysis vs. the AMP trials (see also S3 Fig), and optimal designs can depend on the underlying protection correlate (e.g., 10-1074-T:VRC07-523LS auc). Indeed, a 1:1:1 3 drug therapy is outperformed by the optimized 2-drug therapy, highlighting the need to carefully perform case-studies for any optimization scenario.