Development and validation of a simple antigen–antibody model

A theoretical model for investigating physical phenomena underlying immune complex formation was developed, based on the statistical mechanical theory of associating fluids that identifies each molecule as a hard sphere with a nested point charge and vector dipole. The interaction between binding molecules (epitope–paratope binding) is represented as a cone truncated by two concentric spheres in which the potential energy is a modified square well with respect to particle separation and a square well with respect to mutual molecular orientation. Equilibrium binding results predicted by the model show good agreement with results obtained experimentally for a model system containing a single antigen and a single monoclonal antibody [bovine serum albumin (BSA) – anti-BSA antibody]. Moreover, values obtained for the system isothermal compressibility and the second virial coefficient by both the model and light scattering experiments also show good agreement with one another.