Model architecture and dynamics.

<p>(A) Original architecture of the network: Rules are represented by two selective populations (R1, R2) embedded in a pool of nonselective excitatory (NS) and inhibitory (I) neurons. Decisions are implemented by the same architecture of four decision selective populations. The interplay of strong local excitation and global inhibition creates winner-take-all dynamics in both modules, leading to a stable state of globally low spiking activity and stable states corresponding to the high activity of a single selective population. (B) Schematic of the stochastic dynamics of reduced system: The rule module is reduced two a two dimensional dynamical system with three stable attracting states: A spontaneous low-activity state and two rule-selective states of high activity. The decision module is reduced to a three-dimensional nonlinear drift-diffusion process, starting at the center of a tetrahedron, where each corner represents one of the four possible choice alternatives. A drift towards one of the corners is created by a combination of direct stimulus input, which favors one of the yellow edges, and biasing input from the selective populations of the rule module, which favors either the red or the blue edge of the tetrahedron. (C) Dynamics of the rule module: The rule module is reduced to a two-dimensional system whose phase space is represented by the synaptic gating variables (S1, S2) of the two rule selective populations. The model is set up in a way in which the two rule representing states as well as the spontaneous state are stable. Trajectories (red) started at an arbitrary point explore the phase space, due to the noise, but tend to stay close to one of the attractors, due to the deterministic dynamics. (D) Slice through a potential landscape of the rule module. This cross-section following a path connecting the two rule attractors via the spontaneous state illustrates the potential barrier that has to be overcome for transitioning from one state to another. Theoretically, all two-dimensional paths are possible to transition from the rule 1 to the rule 2 state. However, due to its dynamical properties, the system stays in a valley that connects the two rule attractors via the basin of attraction of the spontaneous state. The cross-sections along those paths resemble closely the one-dimensional potential sketches often found in the literature discussing the possible effects of attractor stability on cognition [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004331#pcbi.1004331.ref018" target="_blank">18</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004331#pcbi.1004331.ref019" target="_blank">19</a>]; compare <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004331#pcbi.1004331.g001" target="_blank">Fig 1</a>. (E) Dynamics of the decision module: The figure shows the evolution of a spherical volume in the three dimensional phase space centered around the origin, which corresponds to the spontaneous state of the decision network. The trajectories rapidly converge to one of the four directions corresponding to the winner-take-all states of one of the decision selective populations. Due to the symmetry of the system, these directions form the corners of a symmetrical tetrahedron. (F) Threshold independence of decision module: Shown are the projections of a single three-dimensional decision process onto the four directions corresponding to the increase of a single selective population and the simultaneous decrease in all others. Due to the nonlinear dynamics, the trajectory rapidly converges into one of these directions and then diverges to infinity within finite time. This yields decision times that are insensitive to the exact value of the threshold, as long as it is placed far enough from the spontaneous state.