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The metabolic network of cancer cells confers adaptive mechanisms against many chemotherapeutic agents, but also presents critical constraints that make the cells vulnerable to perturbation of the network due to drug therapy. To identify these fragilities, combination therapies based on targeting the nucleic acid synthesis metabolic network at multiple points were tested. Results showed that cancer cells overcome single hit strategies through different metabolic network adaptations, demonstrating the robustness of cancer cell metabolism. Analysis of these adaptations also identified the maintenance of pentose phosphate cycle oxidative and nonoxidative balance to be critical for cancer cell survival and vulnerable to chemotherapeutic intervention. The vulnerability of cancer cells to the imbalance on pentose phosphate cycle was demonstrated by phenotypic phase plane analysis.