We implement a Coulomb rate-and-state approach to explore the nonlinear relation between stressing rate and seismicity rate in the Groningen gas field. Coulomb stress rates are calculated, taking into account the 3-D structural complexity of the field and including the poroelastic effect of the differential compaction due to fault offsets. The spatiotemporal evolution of the Groningen seismicity must be attributed to a combination of both (i) spatial variability in the induced stressing rate history and (ii) spatial heterogeneities in the rate-and-state model parameters. Focusing on two subareas of the Groningen field where the observed event rates are very contrasted even though the modeled seismicity rates are of similar magnitudes, we show that the rate-and-state model parameters are spatially heterogeneous. For these two subareas, the very low background seismicity rate of the Groningen gas field can explain the long delay in the seismicity response relative to the onset of reservoir depletion. The characteristic periods of stress perturbations, due to gas production fluctuations, are much shorter than the inferred intrinsic time delay of the earthquake nucleation process. In this regime the modeled seismicity rate is in phase with the stress changes. However, since the start of production and for two subareas of our analysis, the Groningen fault system is unsteady and it is gradually becoming more sensitive to the stressing rate.