Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Abstract

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. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] 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.

Personalized Therapy Design for Liquid Tumors via Optimal Control Theory

“…Despite the lower complexity, open-loop controls are still a viable option, mostly because of the applicability in a wide range of real-world scenarios for which, for instance, real-time measurements and/or therapy adjustments are unfeasible. Moreover, open-loop controls have proven to identify more effective drug concentration in therapeutic ranges than standard clinical practice [37,38,39,40,41].…”

“…Certain techniques, for instance, assume continuous -yet unrealistic -drug infusion procedures (e.g., [42]). Some methods rely on often speculative mathematical models, which cannot be evaluated due to the lack of opportune experimental data [41]. Some further methods are based on Pontryagin Maximum principle [4] and/or they assume a quadratic cost in order to ensure the optimality of the protocol, whereas such assumptions are not realistic in real-world scenarios.…”

The impact of competition between cancer cells and healthy cells on optimal drug delivery

“…On top of that, various mathematical models incorporate tumor heterogeneity and competition between distinct cell types (Bacevic et al, 2017;Lorz et al, 2013;Piretto et al, 2018;Yoon et al, 2018). Recent models using ordinary differentiation equations (ODEs) focus on competition between distinct types of cancer cells that are either resistant or sensitive to a single drug (Carrère (2017); Piretto et al (2018); Yoon et al (2018)). While ODEs can model the overall size of the population, partial differential equations can model spatial heterogeneity in either the physical space or in the phenotypic space.…”

Using selection by non-antibiotic stressors to sensitize bacteria to antibiotics

“…While the molecular mechanisms of collateral sensitivity have been identified in several specific cases-for example, modulation of proton-motor force underlies increased sensitivity to some antibiotics induced in aminoglycoside-resistant mutants (18)-they are generally difficult to uncover and may vary by species and drug, making them an ongoing focus of research. At the same time, a number of recent studies have shown that systems-level approaches based on phenotypic profiling may help identify statistical properties of these collateral effects, even when molecular mechanisms are not fully known (19,16,17,24,27,28,26).…”