Large-scale biophysical circuit models provide mechanistic insights into the micro-scale and macro-scale properties of brain organization that shape complex patterns of spontaneous brain activity. We developed a spatially heterogeneous large-scale dynamical circuit model that allowed for variation in local synaptic properties across the human cortex. Here we show that parameterizing local circuit properties with both anatomical and functional gradients generates more realistic static and dynamic resting-state functional connectivity (FC). Furthermore, empirical and simulated FC dynamics demonstrates remarkably similar sharp transitions in FC patterns, suggesting the existence of multiple attractors. Time-varying regional fMRI amplitude may track multi-stability in FC dynamics. Causal manipulation of the large-scale circuit model suggests that sensory-motor regions are a driver of FC dynamics. Finally, the spatial distribution of sensory-motor drivers matches the principal gradient of gene expression that encompasses certain interneuron classes, suggesting that heterogeneity in excitation-inhibition balance might shape multi-stability in FC dynamics.