A mathematical modelling tool for unravelling the antibody-mediated effects on CTLA-4 interactions

Background: Monoclonal antibodies blocking the Cytotoxic T-lymphocyte antigen 4 (CTLA-4) receptor have revolutionized the field of anti-cancer therapy for the last few years. The human T-cell-based immune responses are modulated by two contradicting signals. CTLA-4 provides a T cell inhibitory signal through its interaction with B7 ligands (B7-1 and B7-2), while CD28 provides a stimulatory signal when interacting with the same ligands. A previous theoretical model has focused on understanding the processes of costimulatory and inhibitory complex formations at the synapse. Nevertheless, the effects of monoclonal antibody (mAb)-mediation on these complexes are relatively unexplored. In this work, we expand on the previous model to develop a new mathematical framework for studying the effects of anti-CTLA-4 mAbs on the co-stimulatory (CD28/B7 ligands) and the co-inhibitory (CTLA-4/B7 ligands) complex formation at the immunological synapse. In particular, we focus on two promising anti-CTLA-4 mAbs, tremelimumab (from AstraZeneca) and ipilimumab (from Bristol-Myers Squibb), which are currently in clinical trials and the market, respectively, for targeting multiple tumors. Methods: The mathematical model in this work has been constructed based on ordinary differential equations and available experimental binding kinetics data for the anti-CTLA-4 antibodies from literature. Results: The numerical simulations from the current model are in agreement with a number of experimental data. Especially, the dose-curves for blocking the B7 ligand binding to CTLA-4 by ipilimumab are comparable with the results from a previous competitive binding assay by flow cytometry and ELISA. Our simulations predict the dose response and the relative efficacies of the two mAbs in blocking the inhibitory CTLA-4/B7 complexes. Conclusions: The results show that different factors, such as multivalent interactions, mobility of molecules and competition effects, could impact the effects of antibody-mediation. The results, in particular, describe that the competitive effects could impact the dose-dependent inhibition by the mAbs very significantly. We present this model as a useful tool that can easily be translated to study the effects of any anti-CTLA-4 antibodies on immunological synaptic complex formation, provided reliable biophysical data for mAbs are available.