Fig. 2: The single circuit model adopted to study frontostriatal neural dynamics at rest.

A Schematic of the model derived from Wong & Wang³² and Deco et al.³³, incorporating static frontostriatal (\({{{\rm{C}}}}_{21}\)) and stochastic striato-cortical (\({{{\rm{C}}}}_{12},{{{\rm{\eta }}}}_{12},{{{\rm{\sigma }}}}_{12}\)) coupling terms (Methods). B Time series of the model state variables S₁ (frontal cortex), S₂ (striatum), and \(\widetilde{{{{\rm{C}}}}_{12}}\) (striato-cortical projection, with sign determining excitation or inhibition). C State-space representation of the bistable frontal (S₁) and striatal (S₂) neural dynamics (i.e., average synaptic gating). Nullclines (\(\frac{{{\rm{d}}}{{{\rm{S}}}}_{1}}{{{\rm{dt}}}}=0\), blue; and \(\frac{{{\rm{d}}}{{{\rm{S}}}}_{2}}{{{\rm{dt}}}}=0\), green) intersections highlight stable fixed points (black circles, bottom left: low activity state; top right: high activity state) and an unstable fixed point (white circle). The trajectory (grey trace) is the resulting projection of S₁ and S₂ timeseries from panel A. D Stability analysis of the model as a function of striato-cortical coupling (C₁₂). The two variables (cortical S₁ and striatal S₂ activity) exhibit stable (solid) and unstable (dashed) equilibria separated by saddle-node bifurcations (SN1 and SN2 circles) that demarcate the ends of the bistable region. Background trajectories correspond to the projections of timeseries shown in panel A in S₁ − C₁₂ (blue) and S₂ − C₁₂ (red) spaces. E Functional connectivity (Pearson’s R) between striatum and frontal cortex as a function of drift \({{{\rm{\eta }}}}_{12}\) and volatility \({{{\rm{\sigma }}}}_{12}\) parameters. F Transition rate (number of zero-crossings in striato-cortical coupling per minute) as a function of drift \({{{\rm{\eta }}}}_{12}\) and volatility \({{{\rm{\sigma }}}}_{12}\) parameters.