Large-scale biophysical circuit models can provide mechanistic insights into the fundamental micro-scale and macro-scale properties of brain organization that shape complex patterns of spontaneous brain activity. By allowing local synaptic properties to vary across brain regions, recent large-scale circuit models have demonstrated better fit to empirical observations, such as inter-regional synchrony averaged over several minutes, i.e. static functional connectivity (FC). However, most previous models do not capture how inter-regional synchrony patterns vary over timescales of seconds, i.e., time-varying FC dynamics. Here we developed a spatially-heterogeneous large-scale dynamical circuit model that allowed for variation in local circuit properties across the human cortex. We showed that parameterizing local circuit properties with both anatomical and functional gradients was necessary for generating realistic static and dynamical properties of resting-state fMRI activity. Furthermore, empirical and simulated FC dynamics demonstrated remarkably similar sharp transitions in FC patterns, suggesting the existence of multiple attractors. We found that time-varying regional fMRI amplitude tracked multi-stability in FC dynamics. Causal manipulation of the large-scale circuit model suggested that sensory-motor regions were a driver of FC dynamics. Finally, the spatial distribution of sensory-motor drivers matched the principal gradient of gene expression that encompassed certain interneuron classes, suggesting that heterogeneity in excitation-inhibition balance might shape multi-stability in FC dynamics.

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