Attractors and their basins represented in the <i>ν</i>_<i>L</i>, <i>ν</i>_<i>R</i> plane with mean dynamics.

<p>A, Top: attractors landscape for Δ<i>λ</i> = 0. Attractors (dots) and their basins (dashed lines) during stimulus condition and sure target condition. Bottom: Traces show average dynamics of correct, error and sure choices (depending on the final point reached by the trace). The color of the trace represents time. Relevant events during the trial are marked by symbols as explained in the figure. Attractors and basins as in top panels are shown for reference (dots of sure target condition replaced by crosses for clarity). B: Attractors landscape and dynamics as in A, for Δ<i>λ</i> = 7. C: Attractors landscape and dynamics as in A, for Δ<i>λ</i> = 28. Note that the traces corresponding to left and sure choices are overlapped but left trials remain near the gray decision memory attractor.</p

Probability distributions of <i>ν</i>_<i>L</i> and <i>ν</i>_<i>R</i> as in Fig 4 separated in early correct and error trials.

<p>Each panel shows the probability distribution of the state of the system at “sure” target onset for early correct (left) and early error trials (right) calculated using all stimulus durations and all values of Δ<i>λ</i> (29858 trials for early correct and 10142 trials for early error conditions).</p

Trade-off between accuracy and flexibility.

<p>A: P(C) and P(S) as a function of <i>λ</i> (color as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005250#pcbi.1005250.g006" target="_blank">Fig 6</a>). B: Mean reward amount (P(<i>correct</i>) + P(<i>suretarget</i>) ⋅ <i>w</i>_<i>S</i>) as a function of <i>λ</i>, for different values of <i>w</i>_<i>S</i>.</p

Probability distributions of firing rates and conditional probability of sure choices.

<p>We represent the state of the spiking network using the mean firing rate of pools L and R in the 50 ms before the “sure” target onset, <i>ν</i>_<i>L</i> and <i>ν</i>_<i>R</i> respectively. A: Each panel shows the probability distribution of <i>ν</i>_<i>L</i> and <i>ν</i>_<i>R</i> for a given combination of stimulus evidence (Δ<i>λ</i>) and stimulus duration (calculated using 1000 trials). B: Conditional probability of choosing the sure target given the state of the system in the <i>ν</i>_<i>L</i>,<i>ν</i>_<i>R</i> plane. Light blue indicates points with less than 30 trials. C: Cartoon showing the idealized P(<i>S</i>|<i>ν</i>_<i>L</i>, <i>ν</i>_<i>R</i>) ≈ <i>max</i>{<i>ν</i>_<i>L</i>, <i>ν</i>_<i>R</i>} predicted by the model. D: Cartoon showing the corresponding prediction of the model proposed in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005250#pcbi.1005250.ref009" target="_blank">9</a>]: P(<i>S</i>|<i>ν</i>_<i>L</i>, <i>ν</i>_<i>R</i>) ≈ <i>σ</i>(|<i>ν</i>_<i>L</i> − <i>ν</i>_<i>R</i>|).</p

Neurophysiological activity of the model.

<p>Orange/blue/green lines represent R/L/S pool firing rates. Continuous lines show average firing rates of trials when either L or R was chosen. Dashed lines are average rates of trials when the sure option was chosen (i.e. pool S won). The network shows different dynamics depending on the winning pool. When the sure target was chosen, the firing rates of the L and R pools remain similar during input presentation. This behavior closely resembles the one observed in LIP by [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005250#pcbi.1005250.ref003" target="_blank">3</a>]. A: Average firing rates for Δ<i>λ</i> = 0. B,E: magnification during stimulus period. C,F: experimental data (showing normalized firing rate), time is relative to motion input onset. D: Average firing-rates for Δ<i>λ</i> = 14 Hz (correct trials).</p

Parameters used in the simulations.

<p>Parameters used in the simulations.</p

Bifurcation diagram and psychophysics measures in different regions.

<p>A-D: P(C) for trials when the sure target was (not) shown are represented with filled (open) circles. The color of the box and the arrows indicate the value of <i>λ</i> used. E: Bifurcation diagram over parameter <i>λ</i>. The curves represent the firing rates of pools L and R in the attractor (according to the mean-field reduction of the spiking network). Four regions appear (in order of increasing <i>λ</i>): A first tiny multistable region when both decision and spontaneous attractors appear; a bistable region where only the two decision attractor are present; a multistable region, where decision attractors coexist with a “mixed” attractor (both pool have intermediate firing rate); a monostable region, where only the “mixed” attractor exists. F-I: P(S) for different values of <i>λ</i> (color convention as in A-D). Error bars indicating the standard deviation have been omitted since they are always smaller than symbols.</p

Model summary.

<p>Parameters values are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005250#pcbi.1005250.t002" target="_blank">Table 2</a>.</p

Probability of choosing the “sure target” as a function of Δ<i>λ</i> for early correct and error trials.

<p>Continuous line is the prediction from the spiking network. Dashed lines are predictions of the reduced probabilistic model (points are slightly shifted on the horizontal axis for better visibility).</p

Task description, psychophysics and model structure.

<p>(A) Experimental task procedure [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005250#pcbi.1005250.ref003" target="_blank">3</a>]. (B) Time course of input. Input to pool R, L and S is represented respectively by orange, dashed blue and green line (colors are consistent with B). A first spontaneous phase is followed by the onset of the target that elicit a strong input with temporal adaptation. At <i>t</i> = 1 s the motion input is turned on: pool L receives <i>λ</i>_<i>L</i> = <i>λ</i> − Δ<i>λ</i> and pools R receives <i>λ</i>_<i>R</i> = <i>λ</i> + Δ<i>λ</i>. After motion input, during the delay phase, the network only receives background noise. In free choice trials, pool S receives input due to the onset of the sure target 500 ms after the offset of the motion input. (C) Schematic representation of the attractor network model. Arrowhead connections represent excitatory projections, dot-head connections represent inhibitory projections. Arrows coming from outside represent external inputs. (D) Psychophysics data measured experimentally (top row) and produced by the model (bottom row). The model reproduces qualitatively the effect of both stimulus duration and coherence on the probability of correct responses in forced choice trials (open circles, right panel), as well as on the probability of choosing the “sure” option (left panel). Moreover the model correctly predicts the increased P(<i>correct</i>) in free choise trials (filled circles, right panel).</p