Shaping Polyclonal Responses via Antigen-Mediated Antibody Interference

Abstract

Broadly neutralizing antibodies (bnAbs) recognize conserved features of rapidly mutating pathogens and confer universal protection, but they emerge rarely in natural infection. Increasing evidence indicates that seemingly passive antibodies may interfere with natural selection of B cells. Yet, how such interference modulates polyclonal responses is unknown. Here we provide a framework for understanding the role of antibody interference-mediated by multi-epitope antigens-in shaping B cell clonal makeup and the fate of bnAb lineages. We find that, under heterogeneous interference, clones with different intrinsic fitness can collectively persist. Furthermore, antagonism among fit clones (specific for variable epitopes) promotes expansion of unfit clones (targeting conserved epitopes), at the cost of repertoire potency. This trade-off, however, can be alleviated by synergy toward the unfit. Our results provide a physical basis for antigen-mediated clonal interactions, stress system-level impacts of molecular synergy and antagonism, and offer principles to amplify naturally rare clones.

Keywords: Biological Sciences; Immunology; Mathematical Biosciences.

Graphical abstract

Figure 1

Antigen-Mediated Antibody Interference can Strongly Influence B Cell Clonal Composition (A) A sketch of the mechanism. A viral particle (pink circle) presents copies of envelope spikes on its surface, each comprising multiple epitopes. Binding of an antibody j (blue Y-shaped molecule) to its target epitope (e.g., in the head domain) can interfere with binding of B cell receptor i (green Y-shaped molecule) targeting a different epitope (e.g., in the stem region) on the same antigen, via steric inhibition or allosteric coupling. Similarly, antibodies of type i may interfere with B cells of type j. This interference, mediated by viral antigen, can be synergistic, i.e., enhancing epitope accessibility, in one direction (lower blowup, cyan acute arrow, indicating α_ij < 0), and antagonistic, i.e., reducing epitope exposure, in the reverse direction (upper blowup, orange blunt arrow, indicating α_ji > 0). Such mutual influence via the antibody product alters the effective potency of B cell clones, thus affecting their rate of expansion (looping arrows). (B–E) A specific example. (B) Interference matrix of bnAbs (PGT145, PGT121, PGT136, CH103, 35022, 3BC315) targeting six major epitopes (V1/V2 glycan, V3 glycan, OD-glycan, CD4bs, gp120-gp41, gp41) on the HIV envelope trimer (BG505 SOSIP.664), calculated from cross-competition data in Derking et al. (2015). (C) Predicted clonal dynamics with two experimental inputs: interference matrix in (B) and intrinsic reproduction rates (inversely related to 50% binding concentration, EC₅₀). With this choice of competing clones, the broad CH103 lineage targeting poorly accessible conserved epitope CD4bs will go extinct (blue curve). (D) By replacing PGT121 with PGT122, strong mutual synergy between PGT122 and CH103 lineages (white stars) allows the latter to expand to considerable abundance (blue curve, panel E).

Figure 2

Phase Diagrams for Spatially Proximal Conserved and Variable Epitopes Survival probability of unfit broad clones, ϕ₀ (color coded), as a function of the mean μ and standard deviation σ of random interactions. Left to right: γ = 1 (symmetric), γ = 0 (asymmetric), and γ = −1 (anti-symmetric). (A–C) White lines in (A) and (B) indicate the predicted transition boundary between the multiple-attractor phase (above) and the unique-fixed-point phase (below). For γ = −1 (C), this boundary lies well above the plotted range of σ. Other parameters are n = 10, r₀/r₁ = 0.5, and K = Σ = 1. See also Figure S2.

Figure 3

Numerical Examples of the Multiple-Attractor Phase Given a common interference matrix (C), starting from different initial compositions, distinct clonal makeups result (A versus B). (A) Predominant clones target epitopes 1 and 2 at t = 0; clones 2 and 4 prevail at steady state. (B) Predominant clones target epitopes 1 and 3 at t = 0; clones 3 and 6 take over at steady state. (C) Interference matrix drawn from a Gaussian distribution with mean μ = 0, width σ = 3, and symmetry γ = 0.

Figure 4

Trade-off between Repertoire Fitness (f) and Survival Probability of bnAb Lineages (ϕ₀) (A–C) Color codes for μ; the black arrow points toward larger σ. The array of black circles in (A) and (C) indicates the frontier at γ = 0, σ = 8 in (B) as a reference. Every data point is an average over 1,000 realizations of the interference matrix for given (μ, σ, γ). Same parameters as in Figure 2.

Figure 5

Clonal Composition and Repertoire Fitness for Distantly Coupled Conserved and Variable Epitopes (A) Phase diagram of surviving lineages. (B) Fitness (i.e., potency) of polyclonal responses. Blue and black lines are phase boundaries. The red symbol in (A) marks the point of no interference. The red dashed line in (B) indicates unbounded viral growth, hence vanishing repertoire fitness. Self-suppression of the fit group β = 0.17; accessibility ratio ρ = 0.5 and capacity κ = 2.4.

Figure 6

Survival of the Unfit Depends on Antigenic Complexity (n) and Relative Epitope Accessibility (r_0/r_1) The fraction of unfit cells among surviving ones shows a nonlinear dependence on (1−r₀/r₁)n. The black curve is a fit to Equation (S30) with c = 3.8 and σ = 2.6; Erf(⋅) denotes the error function.

Figure 7

Synergistic Interference can Resolve Survival-Fitness Trade-off Top: concentration of unfit clones, B₀, increases with β. Bottom: repertoire fitness f decreases with β. (A–D) Synergistic (large negative) α₁ both promotes expansion of broad clones (A) and enhances the quality of polyclonal responses (B). Varying α₀ cannot resolve the conflict (C and D). Here r₁ = 1, r₀ = 0.5, and κ = 1.

Figure 8

Structure of Antigen-Mediated Interference Strongly Impacts Composition and Potency of Polyclonal Response (A) Without interference among epitopes, only B cell clones that target highly accessible epitopes (blue) can expand. (B) Strong synergistic interaction (thick acute arrow) from fit clones (blue) to unfit ones (green) allows the latter to expand; fewer viral particles (spiky objects) indicate enhanced Ab potency compared with (A). (C) Despite moderate synergy (thin arrows) from fit clones (dark and light blue), unfit clones (green) still perish if the number of high-accessibility epitopes/clones is large. (D) If fit clones are mutually antagonistic (blunt arrows), unfit clones are more likely to expand, but at the cost of reduced repertoire potency and hence a higher viral load.

Figure 9

Survival of HIV bnAbs HIV Env glycoprotein (red star) is placed on the phase diagram using interference parameters, μ = −0.09, σ = 0.89, and γ = 0.25, estimated from HIV bnAb cross-competition data. Survival probability ϕ₀ (color coded) of most broad clones is computed the same way as those in Figure 2, with r₀ = 0.5 for two unfit clones and r₁ = 1 for four fit clones. HIV Env is located in the unique-fixed-point phase, below the theoretical phase boundary (black line) given by Equation (S21); survival probability of very broad HIV bnAbs is around 0.5%.