Fig 1.
Boosting of antibodies to the head and stem epitopes of HA following vaccination with inactivated H5N1.
Panel A shows IgG titers against HA head (red) and stem (blue) epitopes measured prevaccination and 30 days post-vaccination. Panel B shows the fold-increase in IgG antibody titers against HA head (red) and stem (blue) epitopes calculated from the data in panel A. Panel C shows the relationship between the pre- and post-vaccination antibody titers. In the absence of boosting, we expect the data to fall on the dashed line (slope = 1). If the degree of boosting is independent of the initial titer, boosting would result in the data falling on a line parallel to (and above) the dashed line. The solid line, representing the best fit line, has slope less than one (least squares; slope = 0.28; 95% CI = [0.090;0.476]), indicating that there is less boosting when initial antibody titers are high. Data are from [20].
Fig 2.
Dynamics of the immune response during primary and booster immunizations in the one-epitope model.
Panel A shows a schematic and the equations for the basic one-epitope model with addition of enhanced antibody-bound antigen clearance (in green), FcγR-mediated inhibition (in blue), or epitope masking (in orange). Panels B-E show the dynamics of antigen and immune responses following primary and secondary immunization in these models. Panel B shows that in the basic model primary and secondary immunizations result in identical boosts (fold increases in antibody). Panels C, D and E show that in the ACM, FIM and EMM, respectively, the antibody generated during the primary response reduces the boosting of antibody following the second immunization. Parameters are shown in Table 1, db = 3 for the ACM, α = 0 for basic, ACM, EMM and α = 0.01 for FIM.
Table 1.
Model parameters and initial values for variables.
Fig 3.
Panel A: A schematic for the two-epitope EMM. The HA antigen has two epitopes: X on the head and S on the stem. Binding of antibodies specific for these epitopes masks them and masked epitope is indicated by O. Panel B-D: We plot for the two-epitope model how pre-existing antibody to the stem of HA, AS, affects boosting (fold increase) in the antibody to both the head (AX) and the stem (AS) of HA following immunization. In the basic model (Panel B) boosting is independent of the level of pre-existing antibody. In the ACM (Panel C) prevaccination antibody to the stem clears the antigen and causes an equal reduction in boosting of antibodies to both the head and stem of HA. In the FIM (in the absence of epitope masking) (Panel D), prevaccination antibody rapidly binds antigen and these antigen-antibody complexes downregulate B cell proliferation to both epitopes. In the EMM (Panel E) pre-existing antibody to the stem masks only the stem epitope, thus reducing only the boosting of antibody to the stem of HA (and boosting of antibody to the head remains unaffected). Corresponding models equations are shown in Methods section. Parameters are in the Table 1. For ACM parameter db is equal 3, for FIM parameter α = 0.01 and α = 0 for other models.
Fig 4.
Illustration of steric interference between antibodies to the epitopes on the head of HA in the multi-epitope model.
We describe antigenic drift by changing only epitope Y on the head of HA between the two virus strains. Antibody to X generated in response to a previously experienced strain sterically hinders efficient stimulation of B cells specific for the new epitope Y.
Fig 5.
Predictions of the different models when different individuals vary in the level of pre-existing antibody to both head (red circles) and stem (blue triangles) epitopes.
The basic, antigen clearance (ACM), Fc-mediated inhibition (FIM) and epitope-masking (EMM) models generate different predictions. Using a three-epitope framework we calculate how different amounts of pre-existing immunity to the head and stem of HA affect boosting of the antibody responses to these epitopes. We consider individuals with different amounts of antibody to the head and stem of HA prior to immunization. The ten different initial conditions are shown. Antibody boosting to a pair of epitopes (head epitope X in red and stem epitope S in blue) in a given individual is connected by a line. In the basic model (Panel A) boosting is independent of the level of pre-existing antibody. In the ACM (Panel B), pre-existing antibody to either epitope clears the entire antigen and thus causes an equal reduction in the boosting of responses to both head and stem epitopes (the lines for each individual are horizontal). In the FIM (Panel C), antibodies bound to antigens (antigen-antibody complexes) equally inhibit the activation of B cells specific for both head and stem epitopes. In the EMM (Panel D), pre-existing antibody binding to either the head or stem epitopes only reduces the boosting of the response to that epitope and not the other one. Other parameters as in Table 1. For ACM parameter db is equal 3, for FIM parameter α = 0.01 and α = 0 for other models.
Fig 6.
Analysis for how the fold increase in antibodies to the head and stem of HA depend on their pre-immune levels in individuals.
We plot lines obtained by joining the data for head and stem for individuals vaccinated with H5N1 (Panel A) and H1N1 (Panel B) (see Tables C and D in S1 Text). We find the slope of these lines is not significantly different from an average line using all the data (thick line). This result consistent with the EMM model, but inconsistent with the ACM and FIM models which predict the slopes of the individual lines should be zero. Also see corresponding Table 2.
Table 2.
Statistical analysis of data shown in Fig 6.