Simulation and Theory of Antibody Binding to Crowded Antigen-Covered Surfaces

In this paper we introduce a fully flexible coarse-grained model of immunoglobulin G (IgG) antibodies parametrized directly on cryo-EM data and simulate the binding dynamics of many IgGs to antigens adsorbed on a surface at increasing densities. Moreover, we work out a theoretical model that allows to explain all the features observed in the simulations. Our combined computational and theoretical framework is in excellent agreement with surface-plasmon resonance data and allows us to establish a number of important results. (i) Internal flexibility is key to maximize bivalent binding, flexible IgGs being able to explore the surface with their second arm in search for an available hapten. This is made clear by the strongly reduced ability to bind with both arms displayed by artificial IgGs designed to rigidly keep a prescribed shape. (ii) The large size of IgGs is instrumental to keep neighboring molecules at a certain distance (surface repulsion), which essentially makes antigens within reach of the second Fab always unoccupied on average. (iii) One needs to account independently for the thermodynamic and geometric factors that regulate the binding equilibrium. The key geometrical parameters, besides excluded-volume repulsion, describe the screening of free haptens by neighboring bound antibodies. We prove that the thermodynamic parameters govern the low-antigen-concentration regime, while the surface screening and repulsion only affect the binding at high hapten densities. Importantly, we prove that screening effects are concealed in relative measures, such as the fraction of bivalently bound antibodies. Overall, our model provides a valuable, accurate theoretical paradigm beyond existing frameworks to interpret experimental profiles of antibodies binding to multi-valent surfaces of different sorts in many contexts.Author Summary: Antibodies are the main working horses of the human immune system. Remarkably, no matter the size or the shape of the pathological intruders, these extremely flexible three-lobe molecules are able to form a complex, thus eliciting an immune response. What makes antibodies so effective? To answer this and other questions, we have developed a simplified computational scheme to simulate the dynamics of many antibodies interacting with each other and with antigens. Coarse-grained models are a great opportunity, as they give access to a true multi-scale approach to biologically relevant problems. In this work, our innovative method allowed us to simulate the binding process of many antibodies to surface-adsorbed antigens. This led us to elucidate and quantify many important physical aspects of their biological function in agreement with experiments, such as the role of their flexibility and crowding effects at the hapten-covered surface, which were shown to finely regulate the avidity.