Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

 View ORCID ProfileNara Yoon, Robert Vander Velde, Andriy Marusyk,  View ORCID ProfileJacob Scott

doi: https://doi.org/10.1101/196824

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Abstract

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. To address this issue, researchers have proposed sequential drug therapies with which the resistance developed by a previous drug can be relieved by the next one, a concept called collateral sensitivity. The optimal times of these switches, however, remains unknown. We therefore developed a dynamical model and study the effect of sequential therapy on heterogeneous tumors comprised of resistant and sensitivity cells. A pair of drugs (DrugA, DrugB) are utilized and switched in turn within the therapy schedule. Assuming that they are collaterally sensitive to each other, we classified cancer cells into two groups, and explored their population dynamics: A_R and B_R, each of which is subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other. Based on a system of ordinary differential equations for A_R and B_R, we determined that the optimal treatment strategy consists of two stages: initial stage in which a chosen better drug is utilised until a specific time point, T, and afterward; a combination of the two drugs with relative durations (i.e. f Δt-long for DrugA and (1-f)Δt-long for DrugB with 0≤f≤1 and Δt≥0). Of note, we prove that the initial period, in which the first drug is administered, T, is shorter than the period in which it remains effective in lowing total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, ApB=A_R/B_R, and effect of each drug. We determine a specific makeup, ApB*, at which the two drugs are equally effective. While the optimal strategy is applied, ApB is changing monotonically to ApB* and then remains at ApB* thereafter. Beyond our analytic results, we explored an individual based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

https://www.biorxiv.org/content/early/2017/10/11/196824