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The protein p53 functions as a tumor suppressor and can trigger either cell cycle arrest or apoptosis in response to DNA damage. We used Boolean network modeling and attractor landscape analysis to analyze the state transition dynamics of a simplified p53 network for which particular combinations of activation states of the molecules corresponded to specific cellular outcomes. Our results identified five critical interactions in the network that determined the cellular response to DNA damage, and simulations lacking any of these interactions produced states associated with sustained p53 activity, which corresponded to a cell death response. Attractor landscape analysis of the cellular response to DNA damage of the breast cancer cell line MCF7 and the effect of the Mdm2 (murine double minute 2) inhibitor nutlin-3 indicated that nutlin-3 would exhibit limited efficacy in triggering cell death, because the cell death state was not induced to a large extent by simulations with nutlin-3 and instead produced a state consistent with oscillatory p53 dynamics and cell cycle arrest. Attractor landscape analysis also suggested that combining nutlin-3 with inhibition of Wip1 would synergize to stimulate a sustained increase in p53 activity and promote p53-mediated cell death. We validated this synergistic effect in stimulating p53 activity and triggering cell death with single-cell imaging of a fluorescent p53 reporter in MCF7 cells. Thus, attractor landscape analysis of p53 network dynamics and its regulation can identify potential therapeutic strategies for treating cancer.