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Natural killer (NK) cells are currently in use as immunotherapeutic agents for cancer. Many different cytokines are used to generate NK cells including IL-2, IL-12, IL-15 and IL-18 in solution and membrane bound IL-21. These cytokines drive NK cell activation through the integration of STAT and NF-κB pathways, which overlap and synergize, making it challenging to predict optimal cytokine combinations. We integrated functional assays for NK cells cultured in a variety of cytokine combinations with feature selection and mechanistic regression models. Our regression model successfully predicts NK cell proliferation for different cytokine combinations and indicates synergy between STAT3 and NF-κB transcription factors. Use of IL-21 in solution in the priming, but not post-priming phase of NK cell culture resulted in optimal NK cell proliferation, without compromising cytotoxicity or IFN-γ secretion against hepatocellular carcinoma cell lines. Our work provides a mathematical framework for interrogating NK cell activation for cancer immunotherapy.