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Background  Design of personalized targeted therapies involve modeling of patient sensitivity to various drugs and drug combinations. Majority of studies evaluate the sensitivity of tumor cells to targeted drugs without modeling the effect of the drugs on normal cells. In this article, we consider the individual modeling of drug responses to tumor and normal cells and utilize them to design targeted combination therapies that maximize sensitivity over tumor cells and minimize toxicity over normal cells.    Results  The problem is formulated as maximizing sensitivity over tumor cell models while maintaining sensitivity below a threshold over normal cell models. We utilize the constrained structure of tumor proliferation models to design an accelerated lexicographic search algorithm for generating the optimal solution. For comparison purposes, we also designed two suboptimal search algorithms based on evolutionary algorithms and hill-climbing based techniques. Results over synthetic models and models generated from Genomics of Drug Sensitivity in Cancer database shows the ability of the proposed algorithms to arrive at optimal or close to optimal solutions in significantly lower number of steps as compared to exhaustive search. We also present the theoretical analysis of the expected number of comparisons required for the proposed Lexicographic search that compare favorably with the observed number of computations.    Conclusions  The proposed algorithms provide a framework for design of combination therapy that tackles tumor heterogeneity while satisfying toxicity constraints.

Combination therapy design for maximizing sensitivity and minimizing toxicity