Drug resistance in cancer: principles of emergence and prevention - PubMed (original) (raw)

Drug resistance in cancer: principles of emergence and prevention

Natalia L Komarova et al. Proc Natl Acad Sci U S A. 2005.

Abstract

Although targeted therapy is yielding promising results in the treatment of specific cancers, drug resistance poses a problem. We develop a mathematical framework that can be used to study the principles underlying the emergence and prevention of resistance in cancers treated with targeted small-molecule drugs. We consider a stochastic dynamical system based on measurable parameters, such as the turnover rate of tumor cells and the rate at which resistant mutants are generated. We find that resistance arises mainly before the start of treatment and, for cancers with high turnover rates, combination therapy is less likely to yield an advantage over single-drug therapy. We apply the mathematical framework to chronic myeloid leukemia. Early-stage chronic myeloid leukemia was the first case to be treated successfully with a targeted drug, imatinib (Novartis, Basel). This drug specifically inhibits the BCR-ABL oncogene, which is required for progression. Although drug resistance prevents successful treatment at later stages of the disease, our calculations suggest that, within the model assumptions, a combination of three targeted drugs with different specificities might overcome the problem of resistance.

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Figures

Fig. 1.

Fig. 1.

Mutation diagram corresponding to three drugs. Each node corresponds to a phenotype. The binary number above each node identifies which drugs the phenotype is resistant to, e.g., 011 means this type is resistant to drugs 2 and 3 but not to drug 1. The leftmost type (000) is fully susceptible, and the rightmost one (111) is resistant to all three drugs. The mutations rates are marked above each arrow. The notation below the nodes identifies the variable used to describe each phenotype; see

supporting information

for details.

Fig. 2.

Fig. 2.

Probability of producing resistant mutants before treatment, depending on the death rate of tumor cells, D. To consider the pretreatment phase only, we artificially set the mutation rate to zero upon start of therapy. Further, to concentrate on the production of resistant mutants, we assume that the mutants do not die. We plot the tumor size, N, at which the probability of treatment failure due to preexistence equals δ. Note that all curves are scaled to be displayed on one graph. For a single drug, this dependence is linear. For a larger number of drugs, this dependence becomes increasingly stronger than linear. Parameter values were chosen as follows: L = 1, u = 10-6, δ = 0.01.

Fig. 3.

Fig. 3.

Log tumor size, N, at which treatment failure is observed, depending on the parameters of the model. (a) Dependence on the rate at which resistant mutants are generated, u. The higher the value of u, the lower the tumor size at which treatment fails. The larger the number of drugs, the stronger this dependency. (b) Dependence on the natural death rate of tumor cells, D. The higher the value of D (i.e., the higher the turnover of the cancer), the lower the tumor size at which treatment fails. The higher the number of drugs and the rate at which resistant mutants are generated, u, the more pronounced this trend. (c) Dependence on the number of drugs, n. Increasing the number of drugs increases the tumor size at which treatment fails. The higher the mutation rate, however, the lower the advantage gained from adding further drugs. Baseline parameter values were chosen as follows: L = 1, δ = 0.01.

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