We have developed a robotic platform allowing us to monitor cytokines dynamics (including IL-2, IFN-g, TNF, IL-6) of immune cells in vitro, with unprecedented resolution. To understand the complex emerging dynamics, we use interpretable machine learning techniques to build a generative model of cytokine response. We discover that, surprisingly, immune activity is encoded into one global parameter, encoding ligand antigenic properties and to a less extent ligand quantity. Based on this we build a simple interpretable model which can fully explain the broad variability of cytokines dynamics. We validate our approach using different lines of cells and different ligands. Two processes are identified, connected to timing and intensity of cytokine response, which we successfully modulate using drugs or by changing conditions such as initial T cell numbers. Our work reveals a simple "cytokine code", which can be used to better understand immune response in different contexts including immunotherapy. More generally, it reveals how robotic platforms and machine learning can be leveraged to build and validate systems biology models.