Figure 1.
Schematics of a cortical neural circuit model of perceptual decision with different configurations of balanced synaptic input (BSI).
The basic model circuit consists of two strongly-recurrent populations of excitatory neurons (ExcL and ExcR) serving as the decision neurons and a population of inhibitory interneurons (Inh) which produces mutual inhibition between the two excitatory populations. There is an excitatory background neural population (ExcBg) that is not selective to task-relevant stimuli and maintains a baseline activity. The two decision populations receive sensory inputs and compete against each other by ramping up its activity and suppressing the other. A decision is made when the population firing rate of a decision population crosses a preset threshold first. A. In first configuration, BSIff, the balanced excitatory and inhibitory inputs to ExcL and ExcR are generated externally by two pairs of excitatory and inhibitory neuronal populations (ctr1-ctr4) in a feedforward manner. B. In the second configuration, BSIfb, the balance between excitation and inhibition is generated internally through the feedback inhibitory neurons. The circuit receives a long range excitatory projection from a top-down control module (Ctr) to all neurons in the circuit. The balance between the excitation and inhibition is determined internally by the input strength of Ctr -> Exc (pathway 1) and the increased input strength (comparing to the condition without the Ctr input) of Inh -> Exc (pathway 3) which is driven by Ctr neurons through the pathway 2.
Table 1.
The parameters for each neural population.
Figure 2.
The behavioral outcome of the decision circuit is dependent on the BSIff strength and ratio A.
Performance (top), defined as the portion of trials with correct decisions, and mean reaction time (bottom) as functions of the task difficulty (characterized by the stimulus motion strength) for different BSIff strength (black = 0, red = 0.3, green = 0.5). BSIff ratio = 1.11. B. Same as in A with ratio = 1.20 (BSIff strength: black = 0, green = 0.5, blue = 0.8). C. Same as in A with ratio = 1.25 (BSIff strength: black = 0, purple = 0.4, orange = 0.6). Depending on the ratio, the performance and mean reaction time change differently with increasing BSIff strength. With a higher ratio, stronger BSIff increases the speed of decision (shorter mean reaction time) while decreases the performance. With a lower ratio, we found an opposite trend in which a stronger BSIff increases the performance while reduces the speed of decision. The curves in the top panels in A-C are plotted only for the visualization purpose only. The curves were obtained by fitting to the data using the function where c’ is the stimulus motion strength,
and s are fitting parameters.
Figure 3.
BSIff modulates the neuronal activity and the dynamics of the decision circuit differently between different BSI ratios.
A. At a lower BSIff ratio ( = 1.11), the ramping rate of the population firing activity of the winning decision population increases with BSIff strength (top). Thick curves show trial-averaged population firing rate and thin curves are samples of population firing rate from single trials. The effect of changing ramping activity is reflected in the shape of the reaction time distribution (middle). The faster ramping rate caused by increasing BSIff strength results from the steeper energy landscape (bottom). x represents the difference between the population firing rates of ExcL and ExcR. The stimulus motion strength is 3.2% for all conditions. BSIff strength = 0 (black) and 0.5 (green) B. Same as in A with a higher BSIff ratio ( = 1.20). With more inhibition, BSIff causes an opposite effect: the ramping rate decreases with increasing BSIff strength. The slowing down in the ramping activity is due to the shallower energy landscape around the peak. When the BSIff strength is strong enough, a crater is created at the center of the peak which significantly slows down the speed of decision (falling into one of the two basins). BSIff strength = 0 (black) and 0.8 (blue) C. The trend becomes more significant with a stronger inhibitory component in BSIff (ratio = 1.25). BSIff strength = 0 (black) and 0.6 (orange).
Figure 4.
Effects of BSIff on A, task performance (portion correct) and B, mean reaction time across different values of BSIff ratio and strength for the stimulus motion strength c’ = 3.2%.
There is a critical value of the ratio ( = 1.156). Above the value, the performance and the mean reaction time increase with increasing BSIff strength. In contrast, the performance and reaction time decrease with increasing BSIff strength when the ratio is below the critical value. The gray regions indicate that under the given strength and ratio, the system could not reach a decision in more than 5% of the trials, hence we excluded them from the analysis.
Figure 5.
BSIfb modulates behavior of perceptual decision in a way similar to that of BSIff.
A. Performance (left) and mean reaction time (right) are shown for three different BSIfb strengths (black: 0, red: 0.857, blue: 1.714) with the BSIfb ratio of 0.848. At this ratio, a stronger BSIfb increases the performance and mean reaction time. The curves in the left panel are plotted for visualization purpose only and were obtained by curve fittings using the same function as described in Figure 2 caption. B. A summary of the effect of BSIfb strength and ratio on the performance (left) and the mean reaction time (right) with the stimulus motion strength of 3.2%. Similar to that of BSIff, with a lower ratio (more excitation), increasing BSIfb strength speeds up the decision process whereas with a higher ratio (more inhibition), increasing BSIfb strength improves the performance. As in Figure 4, the gray regions indicate that under the given strength and ratio, the system could not reach a decision in more than 5% of the trials.
Figure 6.
BSIfb alters the dynamics of the circuit by changing its energy landscape in a way similar to BSIff.
A. (Top) Energy landscape for different BSIfb ratios. The BSI strength is set to be 0.857. If we increase the BSIfb ratio, the slope of the landscape becomes shallower while the crater on top of the hill becomes bigger and deeper. (Bottom) Energy landscape for different BSI strengths. The BSIfb ratio is set to be 0.848. A similar trend can be observed if we increased the BSI strength. B. The differences between the heights of the two walls of the crater (H) as a function of BSIfb ratio and strength. C. Performance as a function of
H plotted for several BSIfb ratios and strengths. Each color indicates data obtained from one BSIfb ratio and each dot of a given color represents a specific BSIfb strength for the corresponding BSIfb ratio. The data from different BSIfb ratios form a linear relationship with
H with overlapping distributions, which indicate that the performance is mainly determined by the size of the crater. Regardless a specific combination of BSIfb ratio and strength, as long as they give rise to the same
H, the performance of decision is the same. The stimulus motion strength c’ = 3.2% in all panels.
Figure 7.
BSIfb produces time varying inhibitory component and the energy landscape in the course of a trial.
A. The time progression of the inhibitory component (drinh) of BSIfb. With a given BSIfb ratio ( = 0.848) and strength ( = 0.857), the balance between the excitation and inhibition of BSIfb changes with time after the stimulus onset. The inhibitory component reduces gradually, indicating a trend of shifting toward excitation in BSIfb during the decision process. The black arrow indicates the mean reaction time. The motion strength c’ = 3.2%. B. The instantaneous energy landscapes are shown for four different periods: 100–200 ms, 300–500 ms, 500–600 ms and 700–800 ms. The result indicates that the center crater of the energy landscape gradually disappears during the course of a trial. This change provides an internal mechanism to speed up the decision when it takes too long.
Figure 8.
BSIfb produces a wider range of speed-accuracy tradeoff.
We plot performance versus mean reaction time with motion strength = 3.2% for the BSIfb (black curves) and BSIff (red curves) conditions. In the working range of BSIfb (preset ratio = 0.848−0.858), the system exhibits trading between speed and accuracy in wide ranges of mean reaction time and performance while for BSIff (ratio = 1.2−1.3), speed-accuracy trade-off works in a narrower range. With BSIff, when the mean reaction time exceeds 1300 ms, the performance is not improved anymore.
Figure 9.
Degree of spike synchronization between neurons significantly correlates with the reaction time, but not with the balanced synaptic input.
A. Distributions of the synchronization index between each pair of neurons in the wining decision population (ExcR or ExcL) for different trial conditions. Each distribution represents one selected trial. We selected trials with fast (reaction time ∼600 ms) and slow (reaction time ∼1300 ms) responses from both BSI conditions (BSIff strength = 0.5 and no BSI). We can find clear difference between the distributions of slow and fast trials, but not between strong BSIff and no BSI trials with similar reaction times. B. Mean synchronization index reduces significantly with reaction time for both strong BSIff and no BSI conditions. Each point represents the mean synchronization index averaged over 10 trials with similar reaction times. Error bars indicate the standard deviation and “***”s denote p<0.0005 in Student’s t test.