A mathematical model of in vitro cancer cell growth and treatment with the antimitotic agent curacin A

A mathematical model of cancer cell growth and response to treatment with the experimental antimitotic agent curacin A is presented. Rate parameters for the untreated growth of MCF-7/LY2 breast cancer and A2780 ovarian cell lines are determined from in vitro growth studies. Subsequent growth studies following treatments with 2.5, 25 and 50 nanomolar (nM), concentrations of curacin A are used to determine effects on the cell cycle and cell viability. The modelʹs system of ordinary differential equations yields an approximate analytical solution which predicts the minimum concentration necessary to prevent growth. The model shows that cell growth is arrested when the apoptotic rate is greater than the mitotic rate and that the S-phase transition rate acts to amplify this effect. Analysis of the data suggests that curacin A is rapidly absorbed into both cell lines causing an increase in the S-phase transition and a decrease in the M-phase transition. The model also indicates that the rate of apoptosis remains virtually constant for MCF-7/LY2 while that of A2780 increases 38% at 2.5 nM and 59% at 50 nM as compared to the untreated apoptotic rate.