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Cells receive time-varying signals from the environment and generate functional responses by secreting their own signaling molecules. Characterizing dynamic input-output relationships in single cells is crucial for understanding and modeling cellular systems. We developed an automated microfluidic system that delivers precisely defined dynamical inputs to individual living cells and simultaneously measures key immune parameters dynamically. Our system combines nanoliter immunoassays, microfluidic input generation, and time-lapse microscopy, enabling study of previously untestable aspects of immunity by measuring time-dependent cytokine secretion and transcription factor activity from single cells stimulated with dynamic inflammatory inputs. Employing this system to analyze macrophage signal processing under pathogen inputs, we found that the dynamics of TNF secretion are highly heterogeneous and surprisingly uncorrelated with the dynamics of NF-κB, the transcription factor controlling TNF production. Computational modeling of the LPS/TLR4 pathway shows that post-transcriptional regulation by TRIF is a key determinant of noisy and uncorrelated TNF secretion dynamics in single macrophages.