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

Abstract 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

Additional file 2: of A mathematical modelling tool for unravelling the antibody-mediated effects on CTLA-4 interactions

Table S2. Equations related to the rate of change of density for the antibody included in different complexes. The rate of change of density for the different antibody-mediated complexes are given in this file. Equations related to the rate of change of density for the antibody included in different complexes. The rate of change of density for the different antibody-mediated complexes are given in this file. (DOCX 144 kb

Additional file 4: of A mathematical modelling tool for unravelling the antibody-mediated effects on CTLA-4 interactions

Figure S1. Sensitivity of the CTLA-4/antibody (a, d) and CTLA-4/B7 (b-c, e-f) interactions towards the perturbations in the association and dissociation for the CTLA-4/B7 and the CD28/B7 complexes. This file includes various figures corresponding to the sensitivity analyses performed to study the impacts of perturbations in the association and dissociation rates for the CTLA-4/B7 and the CD28/B7 complexes. (DOCX 5236 kb

Additional file 3: of A mathematical modelling tool for unravelling the antibody-mediated effects on CTLA-4 interactions

Table S3. Different components/species included in the model and their respective abbreviation used in the text. The different components included in our mathematical model, along with their corresponding abbreviations, are provided in this file. Different components/species included in the model and their respective abbreviation used in the text. The different components included in our mathematical model, along with their corresponding abbreviations, are provided in this file. (DOCX 13 kb

Additional file 1: of A mathematical modelling tool for unravelling the antibody-mediated effects on CTLA-4 interactions

Table S1. Parameters used in the model. The parameters related to the interactions of CTLA-4 and CD28 with the B7 ligands in the current model are provided in this file. (DOCX 26 kb

Additional file 5: of A mathematical modelling tool for unravelling the antibody-mediated effects on CTLA-4 interactions

Figure S2. Sensitivity of the CD28/B7–1 and CD28/B7–2 interactions towards the perturbations in the association and dissociation for the CTLA-4/B7 and the CD28/B7 complexes. This file includes various figures corresponding to the sensitivity analyses performed to study the impacts of perturbations in the association and dissociation rates for the CTLA-4/B7 and the CD28/B7 complexes. (DOCX 181 kb