This report describes the application of a new approach, the universal response surface approach, to the quantitative assessment of drug interaction, i.e., the determination of synergism, antagonism, additivity, potentiation, inhibition, and coalitive action. The specific drug combination and experimental growth system for this introductory application was that of 1-β-d-arabinofuranosylcytosine (ara-C) and cisplatin with simultaneous drug exposure (1, 3, 6, 12, or 48 h) against L1210 leukemia in vitro. To quantitate the type and degree of drug interaction, a model was fitted using nonlinear regression to the data from each separate experiment, and parameters were estimated (K. C. Syracuse and W. R. Greco, Proc. Biopharm. Sect. Am. Stat. Assoc., 127–132, 1986). The parameters included the mximum cell density over background in absence of drug, the background cell density in presence of infinite drug, the 50% inhibitory concentrations and concentration-effect slopes for each drug, and a synergism-antagonism parameter, α. A positive α indicates synergism, a negative α, antagonism, and a zero α, additivity. Maximal synergy was found with a 3-h exposure of ara-C + cisplatin, with α = 3.08 ± 0.96 (SE) and 2.44 ± 0.70 in two separate experiments. Four different graphic representations of the raw data and fitted curves provide visual indications of goodness of fit of the estimated dose-response surface to the data and visual indications of the intensity of drug interaction. The universal response surface approach is mathematically consistent with the traditional isobologram approach but is more objective, is more quantitative, and is more easily automated. Although specifically developed for in vitro cancer chemotherapy applications, the universal response surface approach should prove to be useful in the fields of pharmacology, toxicology, epidemiology, and biomedical science in general.
Supported by National Cancer Institute Grants CA18420, CA50456, and CA46732.