Quantitative model for multiple levels of drug resistance in clinical tumors.

A mathematical model to examine the effect of cellular differentiation on phenotypic drug resistance in neoplasms is proposed. Attention is restricted to the maintenance of stem cell proliferative capacity. For fixed mutation rates, tumors in which loss of stem cell capacity occurs with high frequency will have a higher proportion of resistant stem cells than those in which such loss is infrequent. The acquisition of multiple levels of drug resistance will proceed at a disproportionately accelerated pace, which leads to greater degrees of incurability for tumors with a stem cell compartment of a given size. This model directly predicts that the phenotypic heterogeneity of slow-growing advanced clinical tumors will be very great. However, as this heterogeneity depends on both the size and the age of the tumor, there will be a period early in the development of the tumor when it should be susceptible to drug-induced cure. This potential for curability at an early stage may not be reflected in the pattern of drug responsiveness of the advanced tumor.