Optimizing combination therapies with existing and future CML drugs

Abstract

Small-molecule inhibitors imatinib, dasatinib and nilotinib have been developed to treat Chromic Myeloid Leukemia (CML). The existence of a triple-cross-resistant mutation, T315I, has been a challenging problem, which can be overcome by finding new inhibitors. Many new compounds active against T315I mutants are now at different stages of development. In this paper we develop an algorithm which can weigh different combination treatment protocols according to their cross-resistance properties, and find the protocols with the highest probability of treatment success. This algorithm also takes into account drug toxicity by minimizing the number of drugs used, and their concentration. Although our methodology is based on a stochastic model of CML microevolution, the algorithm itself does not require measurements of any parameters (such as mutation rates, or division/death rates of cells), and can be used by medical professionals without a mathematical background. For illustration, we apply this algorithm to the mutation data obtained in [1], [2].

Figure 1. A mutation network for a three-drug treatment.

The nodes correspond to different resistance phenotypes, and the arrows to mutation processes; mutation rates are marked next to the arrows. Singly-resistant mutations are denoted my solid lines, doubly-resistant mutations – by dashed lines and italic font, and the triply-resistant mutation by a thick line and bold font.

Figure 2. The probability of treatment success as a function of the numbers and .

Different markers correspond to different treatment parameters: circles (division rate L = 10, death rate d = 9, drug-induced death rate h_i = 10, mutation rate u = 10⁻⁷, cancerous population size at the start of treatment N = 10¹⁰), squares (), diamonds ( ), triangles (). Empty markers denote three-drug treatments, and solid ones – two-drug treatments. The data are presented in tables 5 and 6.

Figure 3. The ordered set of the best treatment protocols resulting from a application of Algorithm A2.

The probability of treatment success is plotted as a function of treatment protocols, see also table 7. The parameters are as in figure 2.