Understanding Antibody-Target Antigen Interactions and the Avidity Effect Using Mathematical Modelling

Abstract

AbstractBackground and PurposeImmunotherapies are designed to exploit the immune system to target pathologies, for instance, but not exclusively, cancer. Monoclonal antibodies (mAbs) are an important class of immunotherapies that induce anti-tumour effects in numerous ways. Fundamental to the success of mAbs in cancer treatments are their interactions with target antigens. For example, binding multiple antigens, which increases 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 develop a mathematical model to develop insight on these impacts.Experimental ApproachWe analyse an ordinary differential equation model of bivalent, monospecific IgG antibodies binding to membrane bound antigens. We obtain equilibrium solutions of the model and conduct a global parameter sensitivity analysis to identify which antibody-antigen interactions impact quantities, such as antigen occupancy, that contribute to mAb potency and efficacy.Key ResultsWe show that the ratio of antibody to antigen number impacts antigen occupancy, bound antibody number and whether an antibody can bind both its antigen-binding arms. A sensitivity analysis reveals 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 identify parameter ranges in which the avidity effect is predicted to be large for antigen occupancy and bound antibody numbers.Conclusion and ImplicationsThese results could be used in the preclinical development of mAb therapies by predicting conditions which enhance mAb potency, efficacy, and the avidity effect.