Virus neutralisation: new insights from kinetic neutralisation curves

Abstract

Antibodies binding to the surface of virions can lead to virus neutralisation. Different theories have been proposed to determine the number of antibodies that must bind to a virion for neutralisation. Early models are based on chemical binding kinetics. Applying these models lead to very low estimates of the number of antibodies needed for neutralisation. In contrast, according to the more conceptual approach of stoichiometries in virology a much higher number of antibodies is required for virus neutralisation by antibodies. Here, we combine chemical binding kinetics with (virological) stoichiometries to better explain virus neutralisation by antibody binding. This framework is in agreement with published data on the neutralisation of the human immunodeficiency virus. Knowing antibody reaction constants, our model allows us to estimate stoichiometrical parameters from kinetic neutralisation curves. In addition, we can identify important parameters that will make further analysis of kinetic neutralisation curves more valuable in the context of estimating stoichiometries. Our model gives a more subtle explanation of kinetic neutralisation curves in terms of single-hit and multi-hit kinetics.

Figure 1. Illustration of the concept of stoichiometries and the parameters used in the model.

The sketch in panel (A) depicts a virion with spikes each consisting of three identical subunits. Thus, each spike has binding regions for one type of monoclonal antibodies. The virion has spikes bound to 0 antibodies, spikes bound to 1 antibody, and spikes bound to 2 and 3 antibodies, respectively. Under the assumptions that the stoichiometry of entry is and the stoichiometry of neutralisation is , the virion is still infectious because it has nine spikes with fewer than two antibodies bound. Panel (B) shows several virions that are neutralised or infectious according to the definition of stoichiometries.

Figure 2. Predictions for kinetic neutralisation curves for the elementary reaction model.

(A) All binding constants are and all dissociation constants are . The stoichiometry of entry is assumed to be . The starting concentration of antibodies is and the starting concentration of trimers is . (B) Same constants as in (A) but the starting concentration of antibodies is . (C) The binding constants are and the dissociation constants are all . The stoichiometry of entry is and the antibody starting concentration is .

Figure 3. Influence of different parameters on the kinetic neutralisation curves.

(A) Antibody starting concentration. The starting concentration of spikes is constant for all graphs, . The stoichiometry of entry is and the stoichiometry of trimer neutralisation . The binding constants are all and the dissociation constants are all . (B) Stoichiometry of entry. The parameters are the same as for (A) but the antibody starting concentration is . (C) and (D) Influence of the ratio between binding and dissociation constant in case all binding constants have the same value and all dissociation constants have the same value . In (C) the ratio between the binding and dissociation rates is kept constant at whereas in (D) the binding constant is kept constant at .

Figure 4. Influence of reaction parameters on the feasibility of estimating the stoichiometry of neutralisation,

. The concentration of spikes and antibodies is the same for all graphs, i.e. and and the stoichiometry of entry is . (A) All binding constants have the same value and all dissociation have the same value . (B) Same coloured graphs correspond to the same reaction constants. Blue curves: the -complex is built preferentially, due to the reaction constants . Red curves: the -complex is built preferentially, . Green curves: the -complexes are built preferentially, . (C) The binding constants decrease and the dissociation constants increase, i.e. . Only in this case are the kinetic neutralisation curves for different stoichiometries of neutralisation distinguishable.

Figure 5. Simultaneous fit of the reaction constants and the stoichiometric parameters.

Each panel shows the kinetic neutralisation curve (as predicted by equation 6) that best fitted kinetic neutralisation data. This data was extracted from where three monoclonal rat antibodies against HIV-1 IIIB were tested: (A) ICR39.3b (B) ICR39.13g (C) ICR41.1i. The estimated parameters for each best fit are summarised in table 2.

Figure 6. Kinetic neutralisation curves for different spike number distributions.

Binding constants are all , dissociation constants are all , the stoichiometry of entry is and the stoichiometry of trimer neutralisation is . Red curves have a spike number distribution with mean 10, where all virions in the case of the dashed line have exactly 10 spikes and in case of the dotted lines have an equal probability to have 2,3…, 18 spikes. The black curve underlies the HIV specific discretised Beta distribution with mean 14 and variance 49. The spike number distributions for the blue curves have mean 36, where the one for the dashed line has only virions expressing 36 spikes and the dotted line has 0–72 spikes.