Mechanism-based model for tumor drug resistance.

The development of tumor resistance to cytotoxic agents has important implications in the treatment of cancer. If supported by experimental data, mathematical models of resistance can provide useful information on the underlying mechanisms and aid in the design of therapeutic regimens. We report on the development of a model of tumor-growth kinetics based on the assumption that the rates of cell growth in a tumor are normally distributed. We further assumed that the growth rate of each cell is proportional to its rate of total pyrimidine synthesis (de novo plus salvage). Using an ovarian carcinoma cell line (2008) and resistant variants selected for chronic exposure to a pyrimidine antimetabolite, N-phosphonacetyl-L-aspartate (PALA), we derived a simple and specific analytical form describing the growth curves generated in 72 h growth assays. The model assumes that the rate of de novo pyrimidine synthesis, denoted alpha, is shifted down by an amount proportional to the log10 PALA concentration and that cells whose rate of pyrimidine synthesis falls below a critical level, denoted alpha 0, can no longer grow. This is described by the equation: Probability (growth) = probability (alpha 0 less than alpha-constant x log10 [PALA]). This model predicts that when growth curves are plotted on probit paper, they will produce straight lines. This prediction is in agreement with the data we obtained for the 2008 cells. Another prediction of this model is that the same probit plots for the resistant variants should shift to the right in a parallel fashion. Probit plots of the dose-response data obtained for each resistant 2008 line following chronic exposure to PALA again confirmed this prediction. Correlation of the rightward shift of dose responses to uridine transport (r = 0.99) also suggests that salvage metabolism plays a key role in tumor-cell resistance to PALA. Furthermore, the slope of the regression lines enables the detection of synergy such as that observed between dipyridamole and PALA. Although the rate-normal model was used to study the rate of salvage metabolism in PALA resistance in the present study, it may be widely applicable to modeling of other resistance mechanisms such as gene amplification of target enzymes.