Understanding antibody–target antigen interactions and the avidity effect using mathematical modelling

Immunotherapies are designed to exploit the immune system to target pathologies such as cancer. Monoclonal antibodies (mAbs) are an important class of immunotherapies that induce anti-tumour effects. Fundamental to the success of mAbs in cancer treatments are their interactions with target antigens. For example, binding multiple antigens, increasing binding affinity, termed the avidity effect, has been shown to impact treatment outcomes. However, there has been limited theoretical analysis addressing the impacts of antibody-antigen interactions on avidity, potency and efficacy. Hence, our aim is to use a mathematical model to develop insight on these impacts. We analyse an ordinary differential equation model of bivalent, monospecific IgG antibodies binding to membrane antigens and show that the ratio of antibody to antigen number impacts quantities that contribute to mAb potency and efficacy, such as antigen occupancy, and whether an antibody can bind both its antigen-binding arms. A global parameter sensitivity analysis shows that antigen occupancy and the ratio of bound antibody to total antigen number are sensitive to the antibody-antigen binding rates only for high antibody concentrations. We also identify parameter ranges in which the avidity effect is predicted to be large. These results could be used in the preclinical development of mAb therapies by predicting conditions that enhance mAb potency, efficacy and the avidity effect.