A mathematical model of antibody-dependent cellular cytotoxicity (ADCC)

•A time-dependent ODE model of antibody-dependent cellular cytotoxicity was developed.•Asymptotic analysis of the model reveals a natural separation of timescales.•Model analysis shows how tumour cell kill rate can be estimated from ADCC experiments. Immunotherapies exploit the immune system to target and kill cancer cells, while sparing healthy tissue. Antibody therapies, an important class of immunotherapies, involve the binding to specific antigens on the surface of the tumour cells of antibodies that activate natural killer (NK) cells to kill the tumour cells. Preclinical assessment of molecules that may cause antibody-dependent cellular cytotoxicity (ADCC) involves co-culturing cancer cells, NK cells and antibody in vitro for several hours and measuring subsequent levels of tumour cell lysis. Here we develop a mathematical model of such an in vitro ADCC assay, formulated as a system of time-dependent ordinary differential equations and in which NK cells kill cancer cells at a rate which depends on the amount of antibody bound to each cancer cell. Numerical simulations generated using experimentally-based parameter estimates reveal that the system evolves on two timescales: a fast timescale on which antibodies bind to receptors on the surface of the tumour cells, and NK cells form complexes with the cancer cells, and a longer time-scale on which the NK cells kill the cancer cells. We construct approximate model solutions on each timescale, and show that they are in good agreement with numerical simulations of the full system. Our results show how the processes involved in ADCC change as the initial concentration of antibody and NK-cancer cell ratio are varied. We use these results to explain what information about the tumour cell kill rate can be extracted from the cytotoxicity assays.