Application of response-surface methodology to detect interactions of genotoxic agents in cultured mammalian cells

Isobolographic, Algebraic, and Search Methods in the Analysis of Multiagent Synergy

A combination of doses d1, d2, dn of n agents shows zero interaction when d1/D1 + d2/D2. + dn/Dn = 1, where D1,D2, Dn are the doses of the individual agents isoeffective with the combination. In synergy, the sum in this equation is less than 1, and in antagonism, it exceeds 1. This equation may be used to calculate the expected (zero interactive) effect of any combination, irrespective of the shapes of the dose-response curves of the agents and of whether they are linear or nonlinear, similar or dissimilar. For a given set of agents, finding the combination that has the maximum therapeutic (or toxic) effect may be logistically a huge problem because of the large number of variables (e.g., dose, dose interval, number of doses) that are generally involved. This problem may be tackled by (1) response surface methods, in which an equation (usually a low-order polynomial) is fitted to the observed effects of a number of different combinations, and the maximum on this response surface is found mathematically, or by (2) direct search methods, in which the response surface is explored one combination at a time without preconceived ideas about its form. For problems with many variables, direct search methods are more economic.

Embryotoxicity induced by alkylating agents: 10. Analysis of the combined teratogenic effects of methylnitrosourea and ethylmethanesulfonate in mice

In previous studies the direct-acting alkylating model compounds methylnitrosourea (MNU) and ethylmethanesulfonate (EMS) were investigated with regard to dose-response of teratogenicity as well as DNA adduct formation in mice. In this study the teratogenic effects induced by combined treatment with these substances were analyzed using doses which, following single treatment with either substance, were around the threshold level, i.e., no adverse effect level (NOAEL) and lowest observed adverse effect level (LAOEL). Combined treatment of LAOELs resulted in a threshold-like response, while the combination of the NOAEL of one substance with the LAOEL of the other increased the response rate dramatically to nearly 100%. This phenomenon was further evaluated using biometrical methods. The dose-response surface as well as isobolograms were calculated in order to describe the combination effect. In addition, a dose-response model was fitted to the data. In conclusion, the initially surprising high combination effect revealed to be not so extraordinary when considering the steepness of the dose-response relationships of the single substances.

Direct search methods in the optimisation of cancer chemotherapy regimens

Current cancer chemotherapy regimens may involve 20-30 or more independent variables, each affecting therapeutic response and toxicity. With standard response surface modelling methods, finding the optimum combination with as few as 10 variables entails testing over 1,000 combinations, so these methods do not provide a feasible approach to such problems. However, they may be tackled by direct search methods (DSM), i.e. stepwise searches of the response surface. Experiments were carried out in advanced L1210 leukaemia treated with combinations of adriamycin with cyclophosphamide, isophosphamide with acetylcysteine and methotrexate with leucovorin. Two established DSM (Nelder-Mead and Box) were used, and a new method was designed to find consistent search paths in spite of wide biological variation. With methotrexate and leucovorin, DSM located combinations prolonging mean survival to 40-50 days (compared with 10.4 in controls) and giving high proportions of long-term survivors. These results were achieved with single injections of drugs given 7 days after injection of 10(6) leukaemic cells, i.e. 2-3 days before deaths began in untreated mice, and appear to be unprecedented with these agents. Searching for optimal combinations of established agents may be at least as rewarding as searching for new agents, and thus DSM may prove a powerful tool for improving the results of combination cancer chemotherapy.