Phenomenological Modeling of Antibody Response from Vaccine Strain Composition

Abstract

The elicitation of broadly neutralizing antibodies (bnAbs) is a major goal of vaccine design for highly mutable pathogens, such as influenza, HIV, and coronavirus. Although many rational vaccine design strategies for eliciting bnAbs have been devised, their efficacies need to be evaluated in preclinical animal models and in clinical trials. To improve outcomes for such vaccines, it would be useful to develop methods that can predict vaccine efficacies against arbitrary pathogen variants. As a step in this direction, here, we describe a simple biologically motivated model of antibody reactivity elicited by nanoparticle-based vaccines using only antigen amino acid sequences, parametrized with a small sample of experimental antibody binding data from influenza or SARS-CoV-2 nanoparticle vaccinations. Results: The model is able to recapitulate the experimental data to within experimental uncertainty, is relatively insensitive to the choice of the parametrization/training set, and provides qualitative predictions about the antigenic epitopes exploited by the vaccine, which are testable by experiment. For the mosaic nanoparticle vaccines considered here, model results suggest indirectly that the sera obtained from vaccinated mice contain bnAbs, rather than simply different strain-specific Abs. Although the present model was motivated by nanoparticle vaccines, we also apply it to a mutlivalent mRNA flu vaccination study, and demonstrate good recapitulation of experimental results. This suggests that the model formalism is, in principle, sufficiently flexible to accommodate different vaccination strategies. Finally, we show how the model could be used to rank the efficacies of vaccines with different antigen compositions. Conclusions: Overall, this study suggests that simple models of vaccine efficacy parametrized with modest amounts of experimental data could be used to compare the effectiveness of designed vaccines.

Keywords: IgG; coronavirus; hemagglutinin; influenza; simulation; vaccination.

Figure 1

Illustration of the amino acid encoding procedure [31]. (A): Multiple alignment $\widehat{\mathit{S}}$ of $N_s$ sequences, each having $N_r$ residues, including gaps, with $s_{ij}\in \{A,C,D,E,F,G,H,I,K,L,M,N,$$P,Q,R,S,T,V,W,Y{,}^{\prime }{-}^{\prime }\}$. (B): Embedded alignment $\widehat{\mathit{X}}$; each residue type in $\widehat{\mathit{S}}$ shown in A is associated with a 3-dimensional real-valued vector ${\mathbf{x}}_{ij}$=$\{x_{ij}^1,x_{ij}^2,x_{ij}^3\}$, which is interpreted as Cartesian coordinates of the residue.

Figure 2

Parameter optimization ($\alpha$,$\beta$) in the strain similarity function Equation (4) applied to influenza data [20] using a diffusion constant D = 0.4. (A): A 2D scan of the ($\alpha$,$\beta$) landscape; the white line corresponds to a cubic spline curve through the minimum values of the mean squared error (MSE) over the range of $\alpha$ at each $\beta$; (B): MSE corresponding to the white line in A plotted in 1D for several values of the diffusion constant D.

Figure 3

Illustration of the nanoparticles used in the vaccinations modeled here [20,21]. The nanoparticles are drawn in black, and the antigens are in color, with different colors indicating different strains. (A): Nanoparticles corresponding to the mosaic vaccines V1, V2, V4, and V8 in Table 2. (B): Mosaic vaccine (top) vs. nanoparticle mixture vaccine (bottom). (C): Hypothetical elicitation of strain-specific Abs (blue Ab binding to blue antigens) vs. cross-reactive bnAbs (purple Ab binding to blue and red antigens) by the mosaic vaccine via different Fabs.

Figure 4

Comparison of model results with the experimental IgG titers for influenza [20]. (A,B): best fit to experiment; in (A), the colors correspond to experimental data for vaccines in Table 2 (red ■ V1, green ■ V2, orange ■ V4, blue ■ V8), and the black outer bars are model values. The black unfilled circles and squares correspond to model titers computed after setting to zero the residue weights in the HA stem and HA head, respectively (see text). (C): Comparison of 252 possible fits in which 5 strains were used for fitting (training) and 5 for testing (red ∘: $C_P$, green ▿: $C_S$). (D): Influenza hemagglutinin (PDB ID: 3LZG [39]) monomer colored by model weights using the color map blue-gray-red (corresponding to low-medium-high).

Figure 5

Comparison of Model 1 results with the experimental IgG titers for coronavirus [21]. (A,B): Best fit to experiment; in (A), the colors correspond to experimental data for vaccines in Table 3 (red ■ V1, green ■ V4A, orange ■ V4B, blue ■ V8), and the black outer bars are model values. (C): Comparison of 126 possible fits in which 5 strains were used for fitting (training) and 4 for testing (red ∘: $C_P$, green ▿: $C_S$, blue ×: $C_P$ for training sets that include SARS-2). (D): SARS-CoV-2 receptor binding domain (RBD), colored by model weights using the color map blue-gray-red (corresponding to low-medium-high); PDB ID: 6VXX [41].

Figure 6

Comparison of model results with the experimental IgG titers for mRNA influenza vaccination [44]. (A,B): Best fit to experiment; in (A), the subplot title indicates the vaccine, the titers are shown for the same 20 antigens (see Table S1). The experimental titers are shown with error bars in blue, and the model results are shown as red circles. The vertical dashed lines separate HA group 1, HA group 2, and HB antigens (going from left to right); in (B), red circles, green triangles, and blue squares correspond to 20-HA, H1, and H3 vaccinations, and to the panels in A (left to right). (C): Comparison of 1000 training/testing splits in which 10 strains were randomly chosen for fitting (training) and the remaining 10 for testing (red ∘: $C_P$, green ▿: $C_S$). (D): Influenza hemagglutinin (PDB ID: 3LZG [39]) monomer colored by model weights using the color map blue-gray-red (corresponding to low-medium-high).

Figure 7

Two–dimensional projections of influenza hemagglutinin sequences onto principal components. Colors: projections of avian, swine, and human influenza type A spike protein sequences spanning the years 1918–2019 and subtypes 1–18, which were downloaded from the NIH influenza research database [38]; the sequences were clustered to 97% identity. Principal component analysis (PCA) was performed in MATLAB [35], as described in Methods; black bullets: projections of 11 antigens with solved Xray crystal structures (labeled with PDB codes). The strains corresponding to the PDB IDs and their sequence accession numbers are listed in Table S2.

Figure 8

Comparison of predicted IgG titers for four hypothetical np vaccines using data of Cohen et al. [20]. Cocktail refers to the mixture of 11 HA antigens, as given in Table S2.