T cells must respond differently to antigens of varying affinity presented at different doses. Previous attempts to map pMHC affinity onto T cell responses have produced inconsistent patterns of responses preventing for- mulations of canonical models of T cell signalling. Here, a systematic analysis of T cell responses to 1,000,000-fold variations in both pMHC affinity and dose produced bell-shaped dose-response curves and different optimal pMHC affinities at different pMHC doses. Using sequential model rejection/identification algorithms, we identified a unique, minimal model of cellular signalling incorporating kinetic proofreading with limited signalling coupled to an incoherent feed forward loop (KPL-IFF), that reproduces these observations. We show that the KPL-IFF model correctly predicts the T cell response to antigen co-presentation. Our work offers a general approach for studying cellular signalling that does not require full details of biochemical pathways.