Dynamic excitatory and inhibitory gain modulation can produce flexible, robust and optimal decision-making

Abstract

Behavioural and neurophysiological studies in primates have increasingly shown the involvement of urgency signals during the temporal integration of sensory evidence in perceptual decision-making. Neuronal correlates of such signals have been found in the parietal cortex, and in separate studies, demonstrated attention-induced gain modulation of both excitatory and inhibitory neurons. Although previous computational models of decision-making have incorporated gain modulation, their abstract forms do not permit an understanding of the contribution of inhibitory gain modulation. Thus, the effects of co-modulating both excitatory and inhibitory neuronal gains on decision-making dynamics and behavioural performance remain unclear. In this work, we incorporate time-dependent co-modulation of the gains of both excitatory and inhibitory neurons into our previous biologically based decision circuit model. We base our computational study in the context of two classic motion-discrimination tasks performed in animals. Our model shows that by simultaneously increasing the gains of both excitatory and inhibitory neurons, a variety of the observed dynamic neuronal firing activities can be replicated. In particular, the model can exhibit winner-take-all decision-making behaviour with higher firing rates and within a significantly more robust model parameter range. It also exhibits short-tailed reaction time distributions even when operating near a dynamical bifurcation point. The model further shows that neuronal gain modulation can compensate for weaker recurrent excitation in a decision neural circuit, and support decision formation and storage. Higher neuronal gain is also suggested in the more cognitively demanding reaction time than in the fixed delay version of the task. Using the exact temporal delays from the animal experiments, fast recruitment of gain co-modulation is shown to maximize reward rate, with a timescale that is surprisingly near the experimentally fitted value. Our work provides insights into the simultaneous and rapid modulation of excitatory and inhibitory neuronal gains, which enables flexible, robust, and optimal decision-making.

Figure 1. Dot-motion discrimination task and neural recording data.

(A,B) Sequence of time epochs within a trial in the reaction time (RT) task (A) and the fixed duration (FD) task (B). The trial begins with the appearance of a fixation point followed by two choice targets, and then a motion stimulus in the form of computer-generated random dots. The motion stimulus has a fraction of the dots moving towards either the left or the right choice target, constituting the motion coherence of the stimulus. The subject is trained to discriminate this motion coherence and make a motor choice (saccade) in the same direction as this motion coherent direction towards the corresponding choice target (right in the above figure). In the RT task, the subject makes a saccade once it has accumulated sufficient evidence in support of its decision, and the motion stimulus is removed once a saccade is made. In the FD task, the motion stimulus is presented for a fixed duration of time (e.g. 1 second) before it is removed during a delay period. The subject has to remember the motion coherent direction to guide its saccadic choice. (C,D) LIP neural firing rate timecourse from the RT task (C) and the FD task (D). Dashed (bold) lines are neural activities with eventual saccade moving away from (towards) their response fields, T2 (T1). Reproduced with permission from .

Figure 2. A decision-making model.

(A) Network model architecture. The network is fully connected, with recurrent inhibition provided by an implicit population of inhibitory interneurons (dashed lines). Inputs to the left- or right-motion selective population of LIP neurons include that from upstream MT/V5 neurons ( or ) and the choice targets (). (B) Sample gain modulation on a single-cell input-output relation. Dotted to solid curves show effect of increasing gain. Inset: Temporal evolution of gain, light to dark colours show decreasing time constant of gain modulation. (C) Timecourse of input currents. (D) Firing rate of an upstream MT neuron encoding motion stimulus, when motion is into or out of its response field (RF).

Figure 3. Network model reproduces neural and behavioural data in the RT task.

(A) Activity timecourse of model, averaged over multiple trials, with different motion coherences, locked to motion onset (left) or saccadic response (right). Response threshold at Hz, compare with Figure 1. (B,C) Accuracy (B) and mean RT (C) generated by model and in the experiment of . Psychometric functions fitted with a Weibull function, :, where is the discrimination threshold at which performance is at correct, and yields the slope of the psychometric function. and of the model (experiment): and ( and ), respectively. Error bars denote standard errors. (D,E) RT distributions generated by model and in the experiment for correct (D) and error (E) trials. Upper, middle, lower panels: , , coherence, respectively.

Figure 4. Phase-planes at different epochs of a trial in the RT task.

(A) Fixation (pre-target onset): , , . Orange and green curves represent nullclines: where and , respectively. (B) Fixation with targets: , , . Grey regions show the basin of attraction for the symmetric (on-diagonal) attractor (see text for definition). (C) Fixation, with targets and gain onset: . Solid (dashed) nullclines: , (, ). Solid nullclines: with inhibitory gain onset prior to excitatory gain onset; dashed nullclines: with both inhibitory and early stage of excitatory gain increase. (D) Fixation, with targets, gain modulation, and motion stimulus (zero coherence): , , . Closed and open circles represent stable (attractors) and unstable steady states, respectively. Diagonal line (stable manifold) and the curve to which off-diagonal trajectories near an unstable steady state are repelled to (unstable manifold), are shown in black and denoted by arrows moving towards or away from the unstable steady state, respectively. Blue: a sample trial with the corresponding epochs in a trial in bold and labeled in inset, grey lines denote the unobserved part of the simulation trial after saccade initiation. Red: denotes the time when the phase plane was viewed. Note the different scales between the top and bottom panels.

Figure 5. Robust decision-making regime with excitatory-inhibitory gain increase.

Stability diagram of a single selective excitatory population as a function of the net stimulus input with zero motion coherence. Black: without gain modulation, . Grey: gains increase to . Solid and dashed lines are the stable and unstable steady-states, respectively. Double horizontal arrows show the range where a symmetric unstable steady state (dashed symmetric curves) co-exists with asymmetric stable steady states (upper and lower stable branches). These are the dynamic ranges of decision-making under these two conditions. Circle, triangle and square represent the fitted firing rate for the net stimulus input during fixation, target and motion periods, respectively. Vertical dashed double arrows show the winner-take-all effect (from the square) during motion stimulus and gain increase, either transiting to the upper winning branch or lower losing branch. Note that with gain modulation, the upper branch is mostly higher than the Hz response threshold, enabling saccade initiation to the winning direction.

Figure 6. Excitatory or inhibitory gain modulation alone results in restrictive neural dynamics.

(A,B) Stability diagrams of a single selective excitatory population as a function of excitatory gain (A) and inhibitory gain (B). Arrows in (A) and (B) show direction of change as or varies, respectively. Vertical dashed lines partition regimes of in (A) and in (B), respectively. A regime can have a single symmetric stable steady state, which is either low (LSS) or high (HSS), or multiple stable steady states: one symmetric and two asymmetric, with two asymmetric unstable steady states. The symmetric steady state can be low (LMS) or high (HMS). Or it may have a symmetric unstable steady state with asymmetric stable and unstable steady states. This constitutes the decision-making (DM) regime. (C,D) Sample activity timecourses showing either no winner-take-all behaviour (C) or divergence at low firing rates, when the excitatory (inhibitory) gain is increased (decreased) in isolation (C), or when the excitatory (inhibitory) gain is decreased (increased) in isolation (D), respectively.

Figure 7. Dynamical regimes for excitatory and inhibitory gains.

Distinct regimes of the network's operation as a function of excitatory and inhibitory gains and , respectively. A regime can have (i) a symmetric low single stable steady state (LSS), (ii) a symmetric high single stable state (HSS), (iii) multiple stable steady states: one low symmetric and two asymmetric (LMS) with two asymmetric unstable steady states, (iv) multiple stable steady states: one high symmetric and two asymmetric (HMS) with two asymmetric unstable steady states and (v) a symmetric unstable steady state with asymmetric stable and unstable steady states, which constitutes the decision-making (DM) regime. Compare with Figure 6 A,B. The regimes of are analysed for different net-stimulus inputs (), i.e. during (A) fixation, (B) target, and (C) target and motion. Black dots show our fitted parameters during these epochs, with black and open dots showing the fitted parameters during the RT and FD tasks, respectively.

Figure 8. Network model reproduces neural and behavioural data in the FD task.

(A) Sample activity timecourse for zero motion coherence of model with weaker gains ( and ). motion stimulus duration: 1 second. Delay period: 1 second. (B) Activity timecourse of model averaged across trials. Inset: Accuracy from model simulations, compared with that in RT task. Coherence threshold and slope of model (experiment): and ( and ), respectively. The ratio is similar to that in the experiment.

Figure 9. Weak recurrent excitation in the FD task.

(A) Stability diagram for a single selective excitatory population as a function of net stimulus input current , with weak recurrent excitation () in the absence of gain modulation (), with low gains (, ) and large gains (, ). Solid and dashed lines show stable and unstable steady states, respectively. (B) Without any gain modulation, the network cannot perform decision-making nor store decisions. (C) With sufficient gain modulation, network can form a decision and store it below a motor threshold (dotted horizontal line at 70 Hz). Upon cue to respond, higher set of gains allow threshold to be crossed and saccade to be made.

Figure 10. Optimal timescale of gain modulation for maximizing mean reward rate.

Network model performance as a function of the time constant of gain modulation . (A) mean reward rate (RR); (B) accuracy; (C) mean trial duration (TD). Dashed horizontal lines show our model's fit to the data, with ms. Inset: zoomed in around the optimal timescale, showing the optimal timescale is .

Figure 11. Optimal timescale of gain modulation for maximizing reward rate for individual coherences.

(A) Network's accuracy (upper panel) and RT (lower panel) with the optimal timescale of ms (dashed), compared with experimental data (open circles), and our previous model's fit to it with ms (black bold). Dash-dotted: model with an optimal gain time constant for each motion coherence. Lighter colours in the lower panel are for error RTs. Error bars denote standard errors of the mean. (B) Comparing optimal for each individual motion coherence (triangles, dash-dotted curve) with model fit ( ms, (black bold line)), and single optimal ( ms, (dashed line)). (C) Comparing RR for optimal for each individual coherence with that of model fit ( ms), and single optimal ( ms). Dotted: average of the RR with over all motion coherences.