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Modeling of the Time-Dependency of in Vitro Drug Cytotoxicity and Resistance¹

Departments of Biomathematics [L. M. L., W. R. G.] and Experimental Therapeutics [L. M. L., H. K. S., Y. M. R., W. R. G.], Roswell Park Cancer Institute, Buffalo, New York, 14263

For potential clinical extrapolation of in vitro findings, it is of interest to relate the measured effect of an anticancer agent to concentration and exposure time. The Hill model (A. V. Hill, J. Physiol., 40: iv–vii, 1910) is commonly used to describe pharmacodynamic (PD) effects, including drug-induced growth inhibition of cancer cells in vitro. The IC_Xⁿ x T = k relationship, in which IC_X is the concentration of agent required to reduce cell growth by X%, T is the exposure time, and n and k are estimable parameters, was first applied to bacterial disinfectant action and then was successfully used to model anticancer drug potency as a function of exposure time (D. J. Adams, Cancer Res., 49: 6615–6620, 1989). Our goal was to create a new global PD modeling paradigm to facilitate the quantitative assessment of the growth-inhibitory effect of anticancer agents as a function of concentration and exposure time. Wild-type human ovarian A2780 and ileocecal HCT-8 carcinoma cells and sublines that were resistant to cisplatin (A2780/CP3), doxorubicin (A2780/DX5B), and raltitrexed (RTX) (HCT-8/DW2) were exposed to various anticancer agents, cisplatin, doxorubicin, paclitaxel, trimetrexate, RTX, methotrexate, and AG2034, for periods ranging from 1 to 96 h. Cell growth inhibition was measured with the sulforhodamine B protein dy assay. Patterns of time-dependency of drug potency, slope of the concentration-effect curves, and relative degree of resistance were characterized. Empirical mathematical expressions were built into a global concentration-time-effect model. The global PD model was then fit to the concentration-time-effect data with iteratively reweighted nonlinear regression. Under specific treatment conditions, the examination of the slope and the shape of the concentration-effect curves revealed a large heterogeneity in drug response, e.g., shallow concentration-effect curve or double or triple Hill "roller coaster" concentration-effect curve. These patterns, which were observed at intermediate exposure times in parental and resistant cells for paclitaxel and trimetrexate or only in resistant HCT-8/DW2 cells for RTX, methotrexate, and AG2034, revealed mechanistic insights for the former cases but possible methodological artifacts for the latter cases. The comprehensive PD modeling of the cytotoxic effect of anticancer agents showed that it was possible to modulate drug effect, response heterogeneity, and drug resistance by altering the time of exposure to the agents. This approach will be useful for: (a) describing complex concentration-time-effect surfaces; (b) refining biological interpretations of data; (c) providing insights on mechanisms of drug action and resistance; and (d) generating leads for clinical use of anticancer drugs.

¹ This work was supported by NIH Grants RR10742, CA65761, and CA16056.

² To whom requests for reprints should be addressed. Phone: (716) 845-8641; Fax: (716) 845-8467; E-mail: rosgreco@acsu.buffalo.edu.

Received 3/20/98. Accepted 10/15/98.

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