The dlPFC portion of the model contained four, two layer cortical columns representing visuospatial working memory circuits in the dlPFC, in which each column had a preferred saccade direction of 0, 90, 180, or 270° (Figure 1A). The two layers make up the deep supragranular (layer 3) and upper infragranular (layer 5) layers. Our current understanding of the microcircuity of the dlPFC suggests that supragranular is where working memory activity occurs and the infragranular layers is where response-related activity is located (Arnsten et al., 2012). The supragranular layers of each of the four columns receive visual input from four different parietal cortex (PC 7a) layers and from lateral excitatory and inhibitory connections within the PFC as shown in Figure 1A (Goldman-Rakic, 1995). These neurons fire in response to the stimulus, hold delay related activity in working memory, and are modulated by D1, α2A, and α1 receptors (Figures 2A, 3). Each supragranular layer in a column is also involved in biasing motor outputs through projections to four motor output (MOT) areas, which accumulate evidence in order to make a saccade direction decision (Schall et al., 2011). Between areas in MOT there is lateral inhibition, promoting competition.

Figures 1A, 2A show that infragranular layers receive subcortical inputs from the superior colliculus via the mediodorsal thalamus (MD/SC layer) (Stepniewska and Kosmal, 1986; Sommer and Wurtz, 2006). The SC→ MD→ PFC pathway has been studied in detail and it has been suggested that the response in infragranular layers is from a corollary discharge that takes place after an eye movement and acts as an efference copy of the motor movement (Wang et al., 2004; Sommer and Wurtz, 2008). The corollary discharge was an external input in our model that was simulated by briefly driving MD/SC neurons with Poissonian spike trains (40 Hz) for 500 ms at the beginning of the response phase (4 s into the trial). MD/SC neurons drove infragranular (layer 5) neurons in all cortical columns as can be seen in the L5 firing rate plot in Figure 3. L5 neurons, in turn, output to the BG layer (Arnsten, 2011), which sends inhibitory projections to all cortical columns, clearing working memory in infragranular layers. The clearing of working memory mediated by BG inhibitory projections to L3 can be seen in the dip in firing rates of L3 neurons during the response phase in Figure 3. This “cortico-striatal loop,” which acts as a means for updating working memory, has been suggested by Frank and colleagues (Frank et al., 2001; Frank, 2011). In their model, however, they use the basal ganglia as a means for selectively gating information into working memory, rather than clearing information from working memory as we suggest.

To construct our model, we used a publicly available simulator, which has been shown to simulate large-scale spiking neural networks efficiently and flexibly (Richert et al., 2011). The model contained a total of 57,212 neurons and approximately 30 million synapses. The number of neurons in each area is shown in Table 1. Connection probabilities in our cortical column model, which were adapted from Wagatsuma et al. (2011), can be found in Table 2. Within each column layer, there are excitatory–excitatory, excitatory–inhibitory, inhibitory–excitatory, and inhibitory–inhibitory connections (not shown in Figure 2A). There are no connections existing between layer 3 and layer 5 neurons within a column because the model aimed to match the response profiles of the groups to empirical data (see, e.g., Arnsten et al., 2012), rather than understand their interaction. All other connections probabilities between neural groups were set equal to 0.1. The connections that exist between groups are shown in Table 3. The simulation consisted of 50 trials at 6 s per trial for each set of parameters. Thus, the total simulation time was 5 min, which took approximately 37 min to run on a Tesla M2090 GPU.

Our model incorporated simulated D1, α2A, and α1 receptors (Figure 2B). To understand the action of these receptors, it is first important to make clear the distinction between “preferred” and “non-preferred” directions and inputs. A neuron, for example, that shows persistent firing for a cue presented at 180° has a “preferred direction” of 180°. Preferred inputs to these neurons are excitatory inputs that also show persistent firing for a cue presented at 180° (i.e., recurrent excitatory connections, within a column). Non-preferred inputs are excitatory connections from neural groups that have other preferred directions, such as 0 or 90° (i.e., lateral excitatory connections, between columns). As discussed below, D1 receptors enhance non-preferred excitatory synapses onto preferred excitatory neurons (lateral excitation) and α2A receptors enhance excitatory connections for neurons encoding the same preferred direction (recurrent excitation).

D1 receptors have been shown to be important for blocking non-preferred excitatory inputs to cortical columns in the dlPFC (Arnsten, 2011). D1 receptors mediate the blocking of non-preferred inputs by increasing cAMP levels in spines where non-preferred inputs synapse onto preferred inputs (Vijayraghavan et al., 2007). Thus, when dopamine levels are low in PFC (weakly activating D1 receptors), non-preferred inputs to columns are enhanced. When dopamine levels are optimal, non-preferred inputs are weakened (see Figure 2B). At high levels of dopamine, which may occur during stress, it has been suggested (Arnsten, 2009) that cAMP levels in dendritic spines increase to the point that they weaken all inputs to dlPFC neurons (Figure 2C).

In contrast to D1 receptors, α2A receptors have been shown to be important for enhancing preferred excitatory inputs (i.e., inputs that code for the same saccade direction) within a cortical column in the dlPFC (Arnsten, 2011). Thus, when norepinephrine levels are low in PFC (weakly activating α2A receptors), recurrent excitatory inputs are weakened (see Figure 2B). When norepinephrine levels are optimal, on the other hand, recurrent excitatory inputs are enhanced within a column and an item can be held more robustly in working memory. This has been shown to occur by blocking cAMP in the dendrite (Wang et al., 2007). When NE levels are high, α1 receptors are activated due to a weaker affinity between NE and α1 receptors than NE and α2A receptors (Figures 2B,C). This causes a similar affect as highly stimulated D1 receptors and blocks all inputs (recurrent excitatory, lateral excitatory, and lateral inhibitory) to neurons (Mao et al., 1999).

We simulate the enhancement of non-preferred inputs when DA levels are low by increasing the strength of lateral excitatory connections (i.e., AMPA and NMDA conductances; see Equation 5) between columns encoding different preferred directions. When DA levels were low, then, μ in Equation 5 was set equal to 1.4 for AMPA and NMDA conductances on connections from non-preferred to preferred L3 excitatory connections (Table 4). When DA levels were optimal, μ was set equal to 1.0 for AMPA and NMDA conductances on connections from non-preferred to preferred L3 excitatory connections. When dopamine levels are high, it has been shown that, not only non-preferred inputs, but all inputs to dlPFC neurons are weakened as shown in Figure 2C (Vijayraghavan et al., 2007). This was simulated by setting μ equal to 0.8 in Equation 1, which decreases the overall input to a neuron. These neuromodulatory factors were chosen to match experimental data (Vijayraghavan et al., 2007), which suggest low overall activity and spatial tuning degradation in dlPFC with high DA levels and a high overall activity and spatial tuning degradation in dlPFC at low DA levels.

We simulate α2A receptor affects by decreasing the strength (i.e., NMDA conductances; see Equation 5, Table 4) of recurrent excitatory connections within a column when NE levels are low and increasing the strength of recurrent excitatory connections when NE levels are optimal and high (see Figure 2B). Thus, when NE levels were low, μ in Equation 5 was set equal to 10 for NMDA conductances on recurrent excitatory connections of L3 neurons within a column. When NE levels were optimal and high, μ was increased to 15 for NMDA conductances (see Table 4). In all of these cases, μ was set equal to 0.1 for AMPA conductances. A stronger influence of NMDA receptors on recurrent excitatory connections has been suggested previously as a means for increasing the stability of persistent states (Wang, 1999; Brunel and Wang, 2001). High NE levels, which activate α1 receptors, were simulated by multiplying the total synaptic current to a cell (see Equation 1) by a factor of 0.8. This factor was chosen to match experimental data seen in Birnbaum et al. (2004), where an α1 agonist was applied resulting in decreased firing rates and spatial tuning degradation in the dlPFC. When both NE and DA levels were high, we multiplied the total synaptic current to a cell by 0.67.

The input to our network was structured according to the oculomotor delayed response (ODR) behavioral paradigm (Goldman-Rakic, 1995). Each individual experiment can be broken down into four stages: fixation, cue, delay, and response (Figure 1B). During the fixation stage, a constant, random Poissonian input drove all four columns in the network. The cue was presented for 500 ms at the 0° location, driving PC 7a inputs, and, hence, layer 3 neurons in the dlPFC encoding this saccadic direction (see blue line in PC chart of Figure 3). This biased drive was removed during the delay period, allowing for recurrent excitatory connections in a column to reverberate and hold onto the working memory. During the response period, Poissonian spike trains drove the MD/SC layer for 500 ms, simulating a corollary discharge, driving neurons in layer 5 of all columns. Layer 5 neurons, in turn, cleared working memory in layer 3 via GABAergic projections from the BG (Figure 3). The fact that response-related activity of layer 5 neurons is driven by a corollary discharge and PFC-BG interactions are involved in working memory updating is well established (Frank et al., 2001; Wang et al., 2004; Sommer and Wurtz, 2006). The behavioral response was obtained from the MOT layer, whose activity was biased by the layer 3 excitatory neurons in the dlPFC. To get the behavioral response, we chose the MOT group that had the greatest number of spikes in the 500 ms before the response period was cued. This is reminiscent of accumulator models that have been seen in decision making and proposed to exist in the brain in the MOT (Schall et al., 2011).

We first examined the responses of neurons in the four dlPFC columns of our model as we varied the concentration of DA and NE from low to high. The peristimulus spike histograms (PSTH) in Figure 4A shows average firing rate summed over all neurons in layer 3 during a single trial as DA levels vary from low to high. Figure 4A shows the changes in working memory responses for the preferred direction (0° column) and a non-preferred direction (90° column) when keeping the NE concentration optimal and varying the DA concentration (behavioral results found in Table 5). The columns coding for 180 and 270° had similar working memory patterns to the 90° column; however, we displayed the data in this way for ease of comparison with experimental data (Figure 4B). Our results show a similar inverted-U dose-response function as was seen in experimental results (Vijayraghavan et al., 2007) and shown in Figure 4B. That is, when DA concentrations are low (Figure 4A, left), both preferred and non-preferred columns show high firing rates due to excess noise (~20 Hz preferred, ~20 Hz non-preferred; p > 0.1 using a t-test comparing the firing rates of each column). This noise is caused by the strengthening of non-preferred inputs to all columns due to a weak activation of D1 receptors. When DA concentrations are high (Figure 4A, right), input to all neurons is diminished and the firing rates for both preferred and non-preferred directions decrease and the neurons lose their spatial tuning (~10 Hz preferred, ~10 Hz non-preferred; p > 0.1, t-test). This is thought to be caused by an increase in cAMP and may occur with high levels of stress (Arnsten, 2011).

When keeping the DA concentration optimal and varying the NE concentration (Figure 5A), we also find a similar inverted-U dose-response function as was shown in Arnsten (2011). The PSTH in Figure 5A shows average firing rate summed over all neurons in layer 3 during a single trial as NE levels vary. This result matches well with the experimental result shown in Figure 5B. When NE concentrations are low (Figure 5A, left), recurrent excitatory connections within a column are weakened due to decreased activation of α2A receptors. This causes a decrease in the firing rates of both preferred and non-preferred columns and impairs delay-related firing. It has been shown that α2A activation may enhance firing by inhibiting cAMP (Wang et al., 2007). When NE concentrations are high (Figure 5A, right), inputs to all neurons are diminished (~10 Hz preferred, ~10 Hz non-preferred; p > 0.05, t-test) due to activation of α1 receptors and the firing rates for both preferred and non-preferred directions decrease (Mao et al., 1999; Birnbaum et al., 2004). These two receptors are activated at different concentrations of NE due to their different affinities for NE. That is, α2A receptors have a high affinity for NE and are activated at lower NE concentrations, while α1 receptors have a low affinity for NE and are activated at high NE concentrations.

When both NE and DA levels are optimal (Figures 4A, 5A, center), α2A and D1 receptors are optimally activated and the spatial tuning of the working memory columns are enhanced (~20 Hz preferred, 10 Hz non-preferred; p < 10⁻⁸, t-test). This is due to the fact that, in our model, when α2A receptors are optimally activated there is a strengthening of recurrent excitatory connections in layer 3 within each column. This, along with lateral inhibition, allows for the preferred column to be activated and stable at a persistently higher firing rate than non-preferred columns. When D1 is optimally active, excitatory connections between columns are weakened, decreasing the amount of noise that can activate any one column.

VTA and LC have reciprocal connections with each other and the PFC, suggesting that the activities of these two regions are highly dependent upon one another and that DA and NE concentrations should co-vary (Sara, 2009). Experimental studies, however, only manipulate one of these neuromodulators locally, potentially leaving the other at an optimal level. To understand how working memory changes when both NE and DA are at non-optimal levels, we also ran our model when both DA and NE were low, when DA and NE were high, when DA was high and NE was low, and when DA was low and NE was high. Figure 6 depicts what happens in these four cases (4 corners of the figure), as well in the optimal cases as has been shown in Figures 4, 5. We discuss the results of each of the four cases below.

Weak and noisy delay related activity results when both NE and DA levels are low (Figure 6A). When NE is low, excitatory recurrent activity is decreased due to decreased α2A receptor activation, leading to low firing rates. When DA is low, the strength of non-preferred synapses is increased due to decreased D1 receptor activation, leading to an increase in the amount of noise and a degradation of spatial tuning. In this case, the general pattern of the firing rates looks very similar to the case in which DA is low and NE is optimal, except with lower firing rates. This low firing rate may lead to an attentional deficit in subjects in vivo due to a weaker top-down signal.

We see a similar result when DA is low and NE is high (Figure 6C). In this case, high NE decreases the overall input to the neurons due to activation of α1 receptors, which has a similar effect on the overall firing rate as decreasing recurrent activity as seen in the low NE case. Because lateral inhibition is weakened in addition to recurrent excitation (see Figure 2C), however, a further degradation in spatial tuning may result with stimulation of alpha1 receptors that wasn't seen when NE levels were low and alpha2A receptors were only weakly stimulated. This weakening of lateral inhibition can be seen in comparing the low DA/high NE plot (Figure 6C) with Figures 6B,F. In Figures 6B,F, when the stimulus is presented the firing rate of all non-preferred directions simultaneously decrease as the preferred direction increases due to lateral inhibition. In Figure 6C, however, we see that, while some firing rates decrease with stimulus presentation (red line), others are only weakly affected (teal line). This is discussed further in the Behavioral Results section. As in the low DA and low NE case above, the low firing rate in this case may lead to an attentional deficit in subjects in vivo due to a weaker top-down signal. In addition to the low firing rates, the network is noisy due to decreased activation of D1 receptors as in the low DA and low NE case.

High DA combined with low NE (Figure 6G) led to significant impairments in working memory by causing very low overall firing rates. In this case, low NE decreases the strength of recurrent excitatory connections due to inactivation of α2A receptors. High DA decreases the overall input to the working memory neurons. As can be seen in Figure 6G, the neural groups are no longer able to persistently fire during the delay period, suggesting that it will have a weak or no influence on the saccade generation process in MOT since it depends on activity in the last 500 ms before the response period. This is explained in more detail in the Behavioral Results section.

A similar result is seen when both NE and DA levels are high (Figure 6I). This happens as a result of the activation of α1 receptors and the over-activation of D1 receptors, which both cause a decrease in the overall input to all working memory neurons in the columns. There is, however, a slightly longer tail of activation in the delay period than the high DA/low NE case, suggesting that performance will not be as bad behaviorally when both DA and NE are high as compared to the high DA/low NE case described above. Compared to the optimal NE/high DA and optimal DA/high NE cases, this state could potentially cause significant behavioral and attentional deficits depending on how strongly alpha1 and D1 receptors block inputs to PFC neurons. We chose neuromodulatory parameters such that some persistent activity would remain to drive behavioral responses, however, it is possible that high DA and high NE completely block inputs to PFC neurons, which would cause more severe impairments.

We were able to capture how changes in neuromodulatory levels would affect behavior by having neurons in layer 3 project to MOT groups, which acted as a motor output layer. The responses of MOT neurons are shown in Figure 7 for low, optimal and high neuromodulatory level combinations. To get the behavioral response, we chose the MOT group that had the greatest number of spikes during the 500 ms prior to the response cue. This is reminiscent of accumulator models that have been seen in decision making and proposed to exist in the brain in the MOT (Schall et al., 2011). Table 5 shows the percentage of correct, incorrect, and null responses by the model. A null response occurs when no neuron fires during 500 ms before the response period.

Notice in comparing Figures 6, 7 that even when working memory is noisy due to low DA or high NE, behavioral performance may not significantly decline due to the architecture of the MOT. Specifically, because there is lateral inhibition in MOT, initially strong excitation of the preferred direction from L3 of the dlPFC will make it more likely it to “win out” over the other directions and choose the correct saccade direction. This is illustrated in comparing Figures 6, 7. Notice the low DA (Figures 7A–C), optimal DA + high NE (Figure 7F), and optimal NE + high DA (Figure 7H) conditions and compare them with the working memory plots in Figure 6. Working memory is extremely noisy during the last 3 s of the trial, however, since the earliest input to the MOT layer is most significant, lateral inhibition in the MOT will filter out the noise later in the delay period and the correct saccade direction will have a higher probability of being chosen. This suggests that lateral inhibition in the MOT may be another means for filtering out noise and optimizing behavioral performance.

Behavior was the worst when NE was low and DA was high as a result of extremely low firing rates in all layers (Figure 6G). This was due to weakened recurrent excitatory activity as a result of weakly activated α2A receptors and the overall input to the network was diminished due to overactive D1 receptors. As a result, the percentage of non-decision trials (meaning no neurons fired during last 500 ms before the response phase) was 96%. The only other case that had non-decision trials (32%) was when both NE and DA were high. Behavioral deficits were also quite high when NE was high and DA was low. This is due to activation of α1 receptors and inactivation of D1 receptors. Inactive D1 receptors strengthened non-preferred inputs and led to a large amount of noise leaking into each cortical column, whereas activation of α1 receptors decreased firing rates to all neurons. Low firing rates due to activation of α1 receptors (i.e., high NE) seems to hinder behavioral performance more than deactivation of α2A receptors (low NE), which also decrease firing rates. This behavioral deficit was explicitly due to noise as opposed to non-decision trials as discussed above in the low NE + high DA case.

Another interesting result found in our model is that behavior is significantly worse under optimal DA + high NE conditions compared to optimal DA + low NE conditions. In low NE conditions, α2A receptors are only weakly stimulated, which decreases recurrent activity, whereas, at high NE conditions, α1 receptors are activated and decrease all inputs to the neurons. Physiologically these changes have the same end result: a decrease in overall activity and a degradation of spatial tuning. Our behavioral results, however, further suggest that α1 activation may be more detrimental to behavior than α2A inactivation. Decreasing the overall input to a neuron (via α1 receptor activation) introduces more noise into working memory than decreasing recurrent excitatory activity (via α2A receptor deactivation). This is likely due to the fact that α1 receptor activation decreases recurrent activity and lateral inhibition between columns in dlPFC (see Figure 2C). Decreasing lateral inhibition degrades spatial tuning more so than decreasing recurrent excitation alone, leading to a greater amount of noise in the network. Thus, the strength of the signal, which depends on recurrent excitation, seems less important in terms of behavioral performance than the ability to block out noise with lateral inhibition. This highlights the importance of GABAergic neurons in working memory and behavioral performance.

Our behavioral results also match quite well with monkey behavioral results. Systemic injection of cirazoline, an α1 agonist, showed a 20% reduction in the number of correct responses (Birnbaum et al., 2004), whereas local application of yohimbine, an α2 antagonist, showed a 10% reduction in the number of correct responses (Li and Mei, 1994). These results match well with the above result suggesting that the optimal DA, high NE condition, which activates α1 receptors, is more detrimental to behavioral performance than the optimal DA, low NE condition, which weakens α2A receptor activation. Likewise, local application of a D1 antagonist caused an approximately 30% reduction in the number of correct responses (relate to our optimal NE, low DA case) and local application of a D1 agonist caused an approximately 20% reduction in the number of correct responses (relate to our optimal NE, high DA case).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.