Optimal performance in a countermanding saccade task

Abstract

Countermanding an action is a fundamental form of cognitive control. In a saccade-countermanding task, subjects are instructed that, if a stop signal appears shortly after a target, they are to maintain fixation rather than to make a saccade to the target. In recent years, recordings in the frontal eye fields and superior colliculus of behaving non-human primates have found correlates of such countermanding behavior in movement and fixation neurons. In this work, we extend a previous neural network model of countermanding to account for the high pre-target activity of fixation neurons. We propose that this activity reflects the functioning of control mechanisms responsible for optimizing performance. We demonstrate, using computer simulations and mathematical analysis, that pre-target fixation neuronal activity supports countermanding behavior that maximizes reward rate as a function of the stop signal delay, fraction of stop signal trials, intertrial interval, duration of timeout, and relative reward value. We propose experiments to test these predictions regarding optimal behavior.

Fig. 1

The model reproduces behavioral data. (A) Model architecture with asymmetrical mutual inhibition between movement (MN) and fixation (FN) neural units. (B) Timecourse of inputs to MN (green) and FN (red); SSD=stop signal delay. Cognitive control is assumed to vary pre-target FN input. Experimental data (C, D) and model simulations (E, F); SSDs in legends; axes for (C, D) are the same as (E, F), respectively. (C, E) Probability of noncancelled trials. (D, F) Cumulative distributions of reaction times for noncancelled and no-stop signal trials. (C, D) Adapted from Boucher et al. (2007), with permission; original data is from Hanes et al. (1998).

Fig. 2

The model’s neural activity timecourse is similar to experimental data. Time course of trial-averaged activities for movement (A, C) and fixation (B, D) neural neurons for no-stop (thin) and cancelled (bold) trials; (A, B) experimental data; (C, D) model simulations. Solid vertical lines in (A, B) denote onset of stop signal; arrows in (A, C) denote onsets of significant deviation of activities between no-stop and stop signal trials. (C, D) show SSDs of 69 ms (light grey), 117 ms (dark grey), and 169 ms (thick black). All data averaged over 200 trials. (A, B) Adapted from Boucher et al. (2007), with permission; original data is from Hanes et al. (1998).

Fig. 3

Model dynamics in phase space. (A) Orbits averaged over many trials; no-stop signal trials shown dashed, cancelled trials for two SSDs solid. (B–D) Vector fields of the noise-free system (arrows) and nullclines for fixation and movement neurons (red and green respectively); nullclines intersect at stable fixed points (black filled circles). (B) Pre-target epoch: fixation neurons stabilize at high firing rate while movement neurons have low activity. (C) Target epoch: movement neuron activities ramp up toward a new high steady state above movement threshold (dashed blue). (D) In stop-signal trials orbits turn to approach a third steady state with high fixation neuron activity.

Fig. 4

Effects of pre-target FN activity and stop-signal delay. High FN activities (red) delay ramping up of MN activities (green) in both noncancelled (A) and cancelled (B) trials; darker colors denote higher FN activity; SSD=169 ms. (C, D) Higher pre-target FN activity increases noncancelled mean reaction time (RT) (C) and probability of cancellation P(cancelled) (D); SSDs for (C, D) shown in legend on (C).

Fig. 5

Optimal countermanding with various SSDs and fractions of stop-signal trials. (A, B) Increase in only SSD (A) or fraction of stop-signal trials (B) shifts optimal FN activity to higher values (filled circles), while overall reward rate decreases. (C) Range of reward rate over a range of SSD values increases with increasing fraction of stop signal trials, allowing reward rate slope to change from negative to positive, and hence reward rate maxima to occur. Bold, dashed, dashed-dot, dotted lines denote SSDs 0, 50, 100, and 150 ms, respectively. (A–C) ITI and timeout are 500 ms. Note that vertical scales differ.

Fig. 6

Increasing ITI, timeout or reward value of cancelled trials can reveal reward rate maxima. Fraction of stop signal trials in (A–D) are fixed at 10% such that a T_ISI and a T_timeout of 500 ms does not show reward rate maxima. Increasing ITI (B), timeout (C), or reward value of a cancelled trial relative to a no-stop trial, here by FOUR times (D), can produce reward rate maxima (filled circles). Note vertical scales differ.