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The Integrated Stress Response (ISR) is a conserved signaling network that detects cellular damage and computes adaptive or terminal outcomes. Understanding the mechanisms that underly these computations has been difficult because natural stress inputs activate multiple parallel signaling pathways and classical ISR inducers have pleiotropic effects. To overcome this challenge, we engineered photo-switchable control over the ISR stress sensor kinase PKR (opto-PKR), which allows virtual control of the ISR. Using controlled light inputs to activate opto-PKR we traced information flow in the ISR both globally, in the transcriptome, and for key ISR effectors. Our analyses revealed a biphasic, input-proportional transcriptional response with two dynamic modes, transient and gradual, that correspond to adaptive and terminal ISR outcomes. Using this data, we constructed an ordinary differential equation (ODE) model of the ISR which predicted system hysteresis dependent on prior stress durations and that stress memory encoding may lead to resilience. Our results demonstrate that the input dynamics of the ISR encode information in stress levels, durations, and the timing between stress encounters.