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Natural variability in the abundance of signaling regulators can lead to divergence in cell fate, even within genetically identical cells that share a common differentiation state. We introduce cell-to-cell variability analysis (CCVA), an experimental and computational methodology that quantifies the correlation between variability in signaling regulator abundance and variation in the sensitivity of cells to stimuli. With CCVA, we investigated the unexpected effects of the interleukin 2 (IL-2) receptor α chain (IL-2Rα) on the sensitivity of primary mouse T lymphocytes to cytokines that signal through receptors that have the common γ chain (γc). Our work showed that increased IL-2Rα abundance decreased the concentration of IL-2 required for a half-maximal activation (EC50) of the downstream effector signal transducer and activator of transcription 5 (STAT5), but reduced the responsiveness to IL-7 or IL-15, without affecting the EC50 values of other γc cytokines. To investigate the mechanism of the effect of IL-2Rα on γc cytokine signaling, we introduced a Bayesian-inference computational framework that models the formation of receptor signaling complexes with data from previous biophysical measurements. With this framework, we found that a model in which IL-2Rα drives γc depletion through the assembly of functional IL-2R complexes was consistent with both the CCVA data and experimental measurements. The combination of CCVA and computational modeling produced quantitative understanding of the crosstalk between γc cytokine receptor signaling in T lymphocytes.