An Asymptotic Analysis of Bivalent Monoclonal Antibody-Antigen Binding

Ligand-receptor interactions are fundamental to many biological processes. For example in antibody-based immunotherapies, the dynamics of an antibody binding with its target antigen directly influence the potency and efficacy of monoclonal antibody (mAb) therapies. In this paper, we present an asymptotic analysis of an ordinary differential equation (ODE) model of bivalent antibody-antigen binding in the context of mAb cancer therapies, highlighting the complexity associated with bivalency of the antibody. To understand what drives the complex temporal dynamics of bivalent antibody-antigen binding, we construct approximate solutions to the model equations at different timescales that are in good agreement with numerical simulations of the full model. We focus on two scenarios: one for which unbound antigens are abundant, and one for which they are scarce. We show how the dominant balance within the model equations changes between the two scenarios. Of particular importance to the potency and efficacy of mAb treatments are quantities such as antigen occupancy and bound antibody number. We use the results of our asymptotic analysis to estimate the long-time values of these quantities that could be combined with experimental data to facilitate parameter estimation.