Development of Time-Independent Method of Measuring Anti-Cancer Drug Efficacy, IC50 and Emax, Using Mathematical Modeling of Cancer Cell Proliferation

Abstract

Drug efficacy is conventionally quantified by the IC50 and emax, but these metrics are highly sensitive to the measurement time. We have proposed an alternative method of obtaining IC50 and emax from a mathematical model of the dose-dependent effect of anti-cancer drugs on cancer cells proliferation over time. These IC50 and emax, obtained from longitudinal data on cancer cell proliferation would, therefore, be independent of time. In nature and observed in experiment, cancer cell proliferation is erratic and therefore we expect there to be inherent scatter in experimental data. (1) Here, we have tested to find the error in our proposed method's ability to estimate IC50 and emax due to computer-simulated noise. We found that even with a small amount of noise at 1%, there was a large error (the standard deviation was about 200% of the mean) in our estimates of IC50 and emax. (2) We have also tested how well our modeling method fits experimental data we collected on cancer cell proliferation of MCF-7 cells, a breast cancer cell-line, with different applied doses of doxorubicin, a known anti-cancer drug. In the process, we tested the fitting of several proposed mathematical models for drug dose-dependent cancer cell proliferation and found that a modified logistic growth model had the best fit to the experimental data. Here, we have also synthesized a novel anti-cancer therapy, doxorubicin (Dox) attached to a single-walled carbon nanotube (CNT) delivery vehicle and solubilized with polyethylene glycol (PEG): Dox-PEG-CNT. (3) We loaded a greater than 1:1 ratio of doxorubicin to CNT by mass. This Dox-PEG-CNT will be used in future experiments to determine its IC50 and emax using our proposed method. We have already produced evidence that it is more effective than doxorubicin alone using traditional cell-based methods (MTT Cytotoxicity Assay). Our proposed method will, therefore, provide a complement or alternative to existing cell-based methods of discovering novel anti-cancer therapies, including but not limited to anti-cancer drug delivery with nanomaterials.