Modeling collaterally sensitive drug cycles: shaping heterogeneity to allow adaptive therapy

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. Particularly, there is utility in a drug sequence which completes a cycle of such relationships. With such cycles, one could, in theory, generate infinitely long drug sequences which can be used in long term therapy to mitigate the evolution of resistance in a tumor. In this work, we explored the optimal therapeutic strategy using the drugs involved in such a cycle with an arbitrary length, N (>=2). We developed a mathematical model for this research, in which tumor cells are classified as one of N subpopulations represented as { R_i|i =1,2,...,N}. Each subpopulation, R_i , is resistant to Drug i and each subpopulation, R _{ i -1} (or R_N , if i =1), is sensitive to it, so that R_i increases under Drug i as it is resistant to it, and after drug-switching, decreases under Drug i+1 as it is sensitive to that drug(s). Based on the model, we found that there is an initial period of time in which the tumor is `shaped' into a specific makeup of each subpopulation, at which time all the drugs are equally effective ( R* ). After this shaping period, all the drugs are quickly switched with duration relative to their efficacy in order to maintain each subpopulation, consistent with the ideas underlying adaptive therapy. Additionally, we have developed methodologies to administer the optimal regimen under clinical or experimental situations in which no drug parameters and limited information of trackable populations data (all the subpopulations or only total population) are known. The therapy simulation based on these methodologies showed consistency with the theoretical effect of optimal therapy.