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

In previous work, we focused on the optimal therapeutic strategy with a pair of drugs which are collaterally sensitive to each other, that is, a situation in which evolution of resistance to one drug induces sensitivity to the other, and vice versa. Here, we have extended this exploration to the optimal strategy with a collaterally sensitive drug sequence of an arbitrary length, N(≥2). To explore this, we have developed a dynamical model of sequential drug therapies with N drugs. In this model, tumor cells are classified as one of N subpopulations represented as {Ri|i=1,2,...,N}. Each subpopulation, Ri, is resistant to Drug i and each subpopulation, Ri−1 (or RN, if i=1), is sensitive to it, so that Ri 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). Similar to our previous work examining optimal therapy with two drugs, we found that there is an initial period of time in which the tumor is 9shaped9 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.