Prefrontal oscillations modulate the propagation of neuronal activity required for working memory

Cognition involves using attended information (e.g., stimuli, rules, responses), maintained in working memory (WM), to guide action. During a cognitive task, a correct response requires flexible, selective gating so that only the appropriate information flows at the proper time from WM to downstream effectors that carry out the response. Much evidence suggests that WM information is encoded in the firing rates of populations of neurons in prefrontal cortex (PFC). At the same time, many experiments have demonstrated separate, task-related modulation of oscillatory dynamics in PFC networks. In this work, we used biophysically-detailed modeling to explore the hypothesis that network oscillations, leveraging lateral inhibition, can independently gate responses to rate-coded items in working memory. Consistent with recent data, we modeled the superficial layers of PFC as a WM buffer that stores task-relevant information and the deep layers of PFC as an output gate that flexibly governs which information in the WM buffer is propagated downstream to guide action. Items in WM were stored in populations of neurons that had either asynchronous spiking or correlated spiking that was modulated at fast beta/gamma oscillation frequencies. We found that whichever WM item induced a response in the output gate with the shortest period between spike volleys would be most reliably propagated through the output gate. Furthermore, the output gate exhibited network resonance capable of selectively propagating items with resonant oscillatory modulation. We found that network resonance of the deep layer gate can be flexibly tuned by varying the excitability of deep layer principal cells. Our results demonstrate that the propagation of WM-associated neuronal activity can be modulated by tuning either the oscillatory properties of populations encoding WM items, themselves, or the resonant properties of the output gate through which item-encoding activity must propagate to reach downstream effectors. In our PFC model, these dynamics reveal how population rate-coded items embedded in superficial beta and gamma oscillations can be alternately selected by tuning network resonance in the deep layers of PFC depending on task demands. Thus, our model predicts that the experimentally-observed modulation of PFC beta and gamma oscillations could leverage network resonance and lateral inhibition to govern the flexible routing of signals in service of cognitive processes like gating outputs from working memory and the selection of rule-based actions.

gate with the shortest period between spike volleys would be most reliably propagated through the output gate. 23 Furthermore, the output gate exhibited network resonance capable of selectively propagating items with 24 resonant oscillatory modulation. We found that network resonance of the deep layer gate can be flexibly tuned 25 by varying the excitability of deep layer principal cells. Our results demonstrate that the propagation of 26 WM-associated neuronal activity can be modulated by tuning either the oscillatory properties of populations 27 encoding WM items, themselves, or the resonant properties of the output gate through which item-encoding 28 activity must propagate to reach downstream effectors. In our PFC model, these dynamics reveal how population 29 rate-coded items embedded in superficial beta and gamma oscillations can be alternately selected by tuning 30 network resonance in the deep layers of PFC depending on task demands. Thus, our model predicts that the  Ardid et al., 2018). In this work, we used biophysically-detailed modeling to 48 explore the hypothesis that network oscillations, leveraging lateral inhibition, can independently gate responses 49 to rate-coded items in working memory. The oscillatory gating mechanism we identified suggests how beta-and 50 gamma-frequency oscillations could govern the flow of information maintained in WM to govern the selection of 51 actions. 52 In the brain, WM tasks have implicated the prefrontal cortex (PFC) in all aspects of WM and cognitive control 53 (Fuster, 1973(Fuster, , 2015; Goldman-Rakic, 1995; Miller, 2000). Furthermore, the maintenance of WM item information 54 has been recently localized to the superficial layers of PFC (Bastos et al., 2018). While the maintenance mechanism 55 is debated ( (Miller et al., 2018); see Discussion), active WM items are believed to be encoded at the population- 56 level in the spike rates of PFC neurons (Mante et al., 2013). We can infer based on prefrontal anatomy (Barbas,57 2013), that WM items encoded in superficial PFC often activate deep layer projection neurons (i.e., principal cells, 58 PCs) to exert top-down influence over sensory and motor systems. Given these observations, we hypothesized 59 that the deep layers of PFC function as an output gate for rate-coded WM items represented in a superficial buffer. rate-coded WM representations are communicated through the output gate to downstream effectors. 73 We have previously shown through detailed modeling that a PFC deep layer with strong feedback inhibition 74 exhibits resonance (i.e., larger responses to preferred input frequencies), and that it prefers fast oscillatory inputs 75 (Sherfey et al., 2018a). Resonance in the inhibitory interneurons (INs) endowed the network with a maximum 76 output frequency (i.e., there was a lower bound on the period between spike volleys that the deep layer could 77 generate), and it depended on the synchrony and strength of the activity driving the network. 78 In this work, we sought to build on those results to explore how a PFC deep layer with strong feedback and 79 lateral inhibition can function as an output gate for rate-coded WM items. Specifically, we were interested in how 80 responses in the output gate depend on the dynamical states of encoding populations (i.e., how the gate output 81 depends on whether WM item-encoding spikes are asynchronous across a population or phase-locked to fast 82 oscillations with varying degrees of synchrony). 83 We found that, given multiple PC populations in an output gate, whichever population has the shortest period 84 between spike volleys most reliably engages local inhibition which, in turn, suppresses responses in all opposing 85 populations. Therefore, given multiple items in the WM buffer, whichever item induces an oscillatory output 86 with the shortest period between spike volleys (i.e., the highest oscillation frequency) will be the dominant signal 87 that gets through the output gate. A consequence of this is that a WM item with oscillatory modulation at the 88 maximum frequency of the output gate will be most reliably relayed through the gate for downstream readout. In 89 our PFC model, these dynamics yield a mechanism for selective gating of WM items based on shifts of resonance 90 between beta and gamma frequency modulation. 91 This paper will begin with a simulation study to investigate the mechanisms that underlie oscillatory output 92 gating, their generality, and the ability to flexibly tune the gate to select WM items in different dynamical states. 93 Gating rules and control mechanisms will be summarized in the Discussion, and the paper will close with a 94 detailed look at how oscillatory gating could serve working memory and cognitive control.

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This section begins with a review of relevant work on PFC network dynamics and an investigation of the mech-97 anisms that underlie oscillatory output gating. After that we will address how the gate can be tuned to select 98 working memory (WM) items that are asynchronous or oscillatory with different frequencies. Finally, we will 99 demonstrate the utility of our gating mechanism for winner-take-all selection of rate-coded WM items delivered 100 to the output gate along either parallel or convergent (interlaminar) projections.

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Background: inhibition-based oscillations and resonance in cortical networks 102 As was mentioned above, beta2 (20-40Hz, which we will call beta for simplicity) and gamma (40-100Hz) oscillations  Figure 1A, raster plot) and generate an input-strength dependent population frequency 113 (i.e., the inverse of the period between spike volleys). See Methods for how we compute and Table 1 for a   114 summary of all symbols used throughout the paper. The population frequency in response to a tonic drive will be 115 called the "natural frequency", , of the network; in this case, = 21 Hz. We will demonstrate the importance 116 of the natural frequency for determining responses in an output gate below. 117 Since we are interested in gating the read-out of oscillatory WM items, we will also review the impact of 118 oscillatory inputs on PC/IN networks ( Figure 1B) before examining the output gate model. A rhythmically-driven 119 PC population (Figure 1Bi) will produce spike volleys with a period matched to the input at low frequencies. At a 120 sufficiently high input frequency, the depolarizing conductances in a fraction of PCs will fail to reach threshold on 121 each cycle of the input; thus, the number of spikes per volley (i.e., the time-averaged firing rate) will decrease 122 (Figure 1Bii) The minimal output gate model consists of two PC populations connected to a common set of inhibitory INs that 133 provide feedback and lateral inhibition ( Figure 1C). Each PC population is driven by a distinct WM item; spiking in 134 a given output population represents the relaying of information from its corresponding item in the WM buffer. 135 We are interested in how the difference in spiking between the output populations depends on the oscillatory 136 state of the WM items driving them; that is, how the dynamical state of items in the WM buffer affects the relative 137 relay of information from the buffer. In some cases, all items will be relayed; in others, only a subset will be 138 relayed. To assist with exposition, when two WM items have different dynamical states, the item that induces 139 Natural oscillation frequency of asynchronously-driven output gate (Hz) Maximum oscillation frequency of rhythmically-driven output gate (Hz) -resonant frequency of output gate (Hz) (i.e., item that yields = ) more spike output in the control model (Figure 1Ci) will be called the "target" item, and the item that induces 140 less will be called the "distractor" item. To begin, in this section, items in an asynchronous state will be called 141 distractors because equal-strength oscillatory items (i.e., with correlated spiking) always induce at least as many 142 spikes (Figure 1Bii, compare solid and dashed lines). 143 In the output gate model, the response to an asynchronous distractor item was suppressed for a finite range This can be understood most easily by considering the interaction between excitation and inhibition in the 154 output gate over time (Figure 3). Essentially, the excitatory output gate population with the shortest period 155 between spike volleys will be the dominant driver of local inhibition that suppresses spikes in all other populations 156 connected to the same interneurons. The number of spikes per PC volley (i.e., the time-averaged PC firing rate) 157 is less important than the period between volleys (i.e., the population frequency) as long as there are enough 158 spikes in an excitatory volley to engage the inhibition. 159 Figure 3A shows that when a periodic item in the WM buffer oscillated with frequency < < , its target 160 output engaged interneurons in the output gate every 1∕ seconds, which was shorter than the 1∕ seconds 161 required for the asynchronously-driven distractor output to reach threshold ( Figure 3A; compare the periods 162 marked by horizontal double arrows). We know from previous work (Sherfey et al., 2018a) that the natural 163 frequency increases with the strength of an asynchronous drive. Figure 3B shows that once an asynchronous 164 item is strong enough for to exceed , then the distractor output becomes the dominant driver of local 165 inhibition in the output gate. Consequently, the response to an oscillatory item can be suppressed by a stronger 166 Figure 2. Resonant bias supports rule-based stimulus-response mapping. Example simulation showing two pathways (i.e., alternative stimulus-response mappings) with superficial layer inputs and deep layer outputs. One pathway has a resonant input that drives its output population while the other pathway has an asynchronous input and output that is suppressed by interneuron-mediated lateral inhibition. When both inputs represent different dimensions of the same stimulus (S) and outputs map onto alternative action plans (R1, R2), context-dependent rhythmicity in a select input population can provide adequate bias for rule-based selection of stimulus-response mapping.
asynchronous item when the latter induces a faster population frequency.

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Constraints on the suppression of stronger distractors 168 The previous simulations have demonstrated that either the oscillatory or asynchronous WM item can produce a 169 larger response in the output gate depending on the relative frequencies of oscillations that they induce. Next, 170 we will explore how the output gate response depends on task-modulated properties of WM items when the 171 asynchronous item is stronger. of the target item. We found that the target output produced more spikes than the distractor output until the 184 distractor item was 50% stronger than the target item ( Figure 4B, orange curve). Similar to above, the reason 185 why the dominant output (i.e., the output producing the most spikes) switched at that point can be understood Oscillatory inputs were either sinusoidal or square wave with high synchrony (1 ms pulse width), medium synchrony (10 ms pulse width), or low synchrony (19 ms pulse width). (B) Differential output firing rates (target-distractor) for target input frequencies maximizing output population frequency (i.e., for inputs at the -resonant frequency) and distractor inputs with increasing strength (i.e., asynchronous input rate, ). Differential output is plotted against (i) the strength of distractor input and (ii) the difference in population frequencies expected in the absence of competition (i.e., in an isolated PC/IN network). The blue shaded region highlights the range of responses where target output frequency exceeds the natural frequency expected for the distractor output; the green shaded region highlights the range where distractor output oscillates faster. The star and square in Bi mark distractor strengths that produce greater target and distractor outputs, respectively, and are used to investigate the effects of recurrent excitation. In all cases, the output with higher spike rate was the output with higher population frequency (i.e., a shorter period between spike volleys). (C) Recurrent excitation amplifies output differences for winner-take-all selection. (i) Without recurrent excitation, target output is greater despite the distractor receiving a 40% stronger input. This simulation corresponds to the point marked with a star in Bi. (ii) Recurrent excitation amplifies resonant bias producing winner-take-all dynamics that select the output driven by a weaker resonant input. (iii) Without recurrent excitation, distractor output is greater when it receives an asynchronous input that is 60% stronger than an opposing resonant input. This simulation corresponds to the point marked with a square in Bi. (iv) The response to an oscillatory target is suppressed when the stronger asynchronous input elicits a faster natural frequency.
Learning amplifies bias for winner-take-all output gating 209 We have seen that changing target (by varying and synchrony of the target item) or distractor = (by 210 varying in the distractor item) creates a bias in the output gate that favors one item or the other based on 211 the relative population frequencies induced in the respective outputs ( Figure 1C, Figure 4B). In the case of large 212 differences between the output population frequencies (e.g., induced by a resonant or a strong asynchronous 213 item), we have seen that this bias can produce a gated response (Figure 2, Figure 3). Next, we investigated 214 whether we could achieve winner-take-all (WTA) dynamics by incorporating a common motif in WTA networks. 215 Specifically, WTA dynamics are commonly observed in networks with both strong lateral inhibition and strong 216 recurrent excitation (Kaski and Kohonen, 1994). Our control model of the output gate already contains strong 217 lateral/feedback inhibition. When we added recurrent excitation among all cells within each output population, 218 the bias observed previously was, indeed, converted into a WTA response ( Figure 4C). In the control network, 219 the 28Hz resonant item produced more spiking in the output gate than a 40% stronger asynchronous item. 220 With recurrent excitation, the resonant item was selected in the output gate while the asynchronous item was 221 completely blocked. Conversely, when the asynchronous item was made 60% stronger, so that its natural 222 frequency exceeded 28Hz, it was selected in the output gate while the resonant item was completely blocked. 223 This suggests that learning input/output mappings (e.g., across trials of a task) can convert a rhythm-mediated 224 bias into an exclusive, WTA output gate that selects the WM item that induces the fastest output oscillation (i.e., 225 the output with the shortest period between spike volleys).  (Figure 1Biii). 248 If relative population frequencies determined which population produced more spike output, we would expect 249 the flip to occur at 28 Hz (i.e., the maximal output frequency) and the target to dominate the region marked with 250 an "x" as well (i.e., 24 Hz < < < 28 Hz). 251 Indeed, when we have the two outputs compete in the output gate (Figure 5Bi), the target most often produces 252 more output as long as < < 28 Hz (Figure 5Bii). In this range, the population labeled "target" has the highest 253 population frequency. Essentially, and in contrast to the scenario without competition, whichever population in 254 the output gate (with competition) receives an oscillatory input closer to the maximum population frequency 255 (28 Hz) in Figure 1Biii will produce more spikes here. Furthermore, plotted a different way, we can see that the 256 output with the shortest period between spike volleys usually produces more spikes (Figure 5C, lower-left and 257 upper-right quadrants). In contrast to the analogous case for rhythmic vs. asynchronous items (Figure 4Bii), 258 however, there are occasions when the lower-frequency population produces more output spikes (Figure 5C, 259 upper-left and lower-right quadrants); these exceptions will be addressed in the Discussion. (ii) Same plot as (Aii). Whichever output is closer to peak produces more spikes when the output populations are connected through shared inhibitory interneurons. (C) Relative spike outputs with competition plotted against the relative population frequencies without competition. In most cases, the population with higher population frequency produces more spikes.
in response to a medium-synchrony rhythmic item. This causes a WM item that is modulated at a higher 40 268 Hz (gamma) frequency to induce a rhythmic response near the natural frequency, ≈ 21 Hz (Figure 1Biii). In 269 contrast, an output can match a 25 Hz (beta) rhythmic item because that is below its maximum frequency. Thus, 270 in the control case, the activity a beta-rhythmic item induces in the output gate has a shorter period between 271 spike volleys and recruits lateral inhibition to block responses to a gamma-rhythmic item ( Figure 6A). How can we 272 selectively output the less-resonant gamma-rhythmic item in WM? 273 Building on our earlier work (Sherfey et al., 2018a) to the gamma-rhythmic item then exhibited a shorter period between volleys of inhibition-recruiting spikes and, 279 consequently, suppressed the response to the beta-rhythmic item ( Figure 6B). Thus, the gamma-rhythmic item 280 was exclusively selected by making the output gate resonate to gamma frequencies. This represents a flexible 281 mechanism by which a nonspecific modulatory signal can be adjusted to tune the maximum frequency of the 282 output gate so that it selectively responds to WM items modulated at higher or lower frequencies. Oscillatory gating for rate-coded items 284 Parallel pathways 285 The WM items we have simulated so far had time-averaged firing rates that were uniform across the encoding 286 population. However, experiments have shown that PFC encodes items in the pattern of firing rates across PCs of 287 an encoding population (Mante et al., 2013). For our oscillatory gating mechanism to be used to gate outputs 288 from WM, it must be able to gate such rate-coded items. Next, we tested the ability of our oscillatory gating 289 mechanism to select rate-coded items with partial Gaussian spatial profiles (Figure 7). 290 First, we simulated two items with resonant beta-frequency modulation of the instantaneous firing rate 291 and different Gaussian spatial patterns of time-averaged firing rates. When delivered to two PC populations 292 in the output gate, the spatial pattern was largely conserved in the corresponding PC populations (Figure 7Ai). 293 This demonstrates that parallel, rate-coded items that are resonant with the output gate can be propagated 294 simultaneously. In contrast, when the fast modulation of the instantaneous firing rate occurs at a non-resonant 295 gamma-frequency, only the resonant beta-frequency item is conserved in its output population while the non-296 resonant item is blocked (Figure 7Aii) with uniform input rates (Cannon et al., 2014). 306 We repeated the previous simulations demonstrating frequency-based gating of rate-coded signals, except 307 this time we delivered both items to the same PC population in the output gate ( Figure 7B). In this case, two 308 rate-coded items with Gaussian profiles and resonant beta-frequency modulation were approximately conserved 309 in the spatial pattern of output firing rates in the single PC population (Figure 7Bi). In contrast, when one item

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We have presented a novel mechanism for gating outputs from a working memory (WM) buffer. The mechanism 315 requires strong lateral and feedback inhibition in the output gate to induce periodic responses. Essentially, the 316 output population with the shortest period between spike volleys will most reliably engage inhibitory interneurons 317 to suppress responses in competing outputs. Resonant properties that result from the feedback inhibition support 318 frequency-based output selection of items in the WM buffer. This enables the modulation frequency of WM items 319 to govern output selection, possibly in opposition to the strengths (i.e., time-averaged firing rates) of items in 320 WM. We showed that the resonant frequency can be tuned by flexible modulatory signals to select different 321 frequencies.
We also showed that with the addition of recurrent excitation (e.g., with learning), the gate can 322 exhibit exclusive, winner-take-all responses. Finally, the same oscillatory gating mechanism could be used to gate 323 flows, in general, for arbitrary, rate-coded signals along parallel and convergent pathways in any cortical region.

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Summary of oscillatory gating rules 325 The results from this study can be organized into a set of rules that depend on dynamical states and determine 326 which WM item(s) will dominate the output gate. 327 Asynchronous vs. asynchronous items 328 The strongest item in WM (i.e., the item with the highest time-averaged spike rate) will produce the strongest 329 response in the output gate. This occurs in an output gate with strong feedback inhibition because the strongest 330 asynchronous item will induce the highest natural frequency (i.e., the shortest period between spike volleys) (see 331 Figure 1A for the natural response to asynchronous items and Figure 3, lower plots, for dependence of natural 332 frequency on item strength). 333 Beta/gamma rhythmic item vs. asynchronous items 334 A (possibly weaker) rhythmic WM item will produce the strongest response in the output gate if its modulation 335 frequency is within some bounds that yield a population response with the shortest period between spike volleys 336 (Figure 2, Figure 3A). That occurs when the modulation frequency of the WM item is between the strength-337 dependent natural frequency induced by the asynchronous items and the maximal frequency of the output gate 338 as determined by the strength and synchrony of oscillatory items (Figure 4B, Ci-ii). Otherwise, the asynchronous 339 item can produce an equally-strong or stronger response depending on how much the natural frequency that it 340 induces exceeds the frequency induced by the rhythmic item ( Figure 3B, Figure 4Ciii-iv). 341 Rhythmic vs. rhythmic items 342 The item with modulation frequency that is most resonant (Figure 5) with the tunable output gate (Figure 6) will 343 produce the strongest response.

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Control mechanisms 345 According to the gating rules, responses in the output gate depend on the resonant frequency of the gate (i.e., its 346 maximum frequency) as well as the synchrony and modulation frequency of rhythmic items in the WM buffer. 347 Each of these properties can be dynamically regulated to guide the flow of information from working memory 348 without requiring changes in the relative strengths of WM items (i.e., changes in the time-averaged firing rates). 349 Controlling the resonant frequency of the output gate 350 We have shown that the resonant frequency can be flexibly tuned by changing the level of background excitation 351 present in the output gate using an asynchronous modulatory signal (Figure 6) (Sherfey et al., 2018a). By having two competing interneuron populations that can alternately 362 pace rhythms in the same PC population, differential drives to the interneuron populations could switch the same 363 PC population between different degrees of synchrony. For instance, this could be achieved in cortical layers 364 containing both parvalbumin-positive (PV+) and calbindin-positive (CB+) interneurons (e.g., L2/3 in DLPFC) which 365 are known to be driven by distinct inputs (Medalla and Barbas, 2009). This mechanism supports rapid switching 366 between dynamical states (e.g., oscillatory vs. asynchronous) and could be used to gate population signals. Precise 367 control over which cells participate in the resonant oscillation may be achievable using this mechanism with PV+ 368 and somatostatin-positive interneurons (Khan et al., 2018) or, more likely, experience-dependent plasticity. items stored in asynchronous rate-codes with 70% higher mean firing rates) (Figure 4). The selected items would 394 then be available in an oscillatory state for read-out in subcortical structures and participation in downstream 395 processing. 396 Consistent with this hypothesized mechanism for dynamic routing of WM representations, beta-synchrony 397 has been observed between PFC and higher-order thalamus during a WM task, and it was correlated with 398 performance (Parnaudeau et al., 2013). Our results suggest that beta-rhythmic synchrony may serve thalamo-  (DeFelipe, 1997). The output gating mechanism presented here does not require that the input items are 443 maintained in a working memory buffer. It can gate stimulus-driven flows equally well. In that context, it can be 444 seen as a general-purpose mechanism for shaping functional connectivity between upstream source regions and 445 downstream receivers. 446 In the present model, the mechanism holds only in the beta/gamma frequency range because below beta 447 the oscillation period is too long compared to the duration of inhibition. The mechanism may work at lower 448 frequencies in the presence of INs with longer-lasting inhibition. This mechanism works for sine wave rhythms as 449 well; however it is most effective when the rhythmic spikes are synchronized in periodic volleys (see Figure 4Bi).  (Durstewitz et al., 2000). Membrane potential 513 (mV) was governed by: where is time (ms), = 1 µF/cm 2 is the membrane capacitance, denotes the intrinsic membrane currents 515 (µA/cm 2 ) listed above, ( , ) is an excitatory current (µA/cm 2 ) reflecting inputs from external sources described 516 below, and denotes synaptic currents (µA/cm 2 ) driven by PC and IN cells in the network. We chose to explore 517 the prefrontal model as part of a larger project on prefrontal oscillations. We confirmed the generality of our 518 qualitative results using a leaky integrate-and-fire model; see Appendix 1 for details. 519 The output layer had either one or two populations of PC cells with each output population receiving inputs 520 from one or two working memory (WM) items (defined below). Input frequency-dependent response profiles 521 were characterized using a network with one input item and one output population ( Figure 8A). Competition 522 between outputs was investigated using a network with two homogeneous PC populations driven by one input 523 item each while interacting through a shared population of inhibitory cells (Figure 8B).
where is the postsynaptic membrane voltage, is the maximal synaptic conductance, is a synaptic gating 531 variable, and = 0 mV is the synaptic reversal potential. Synaptic gating was modeled using a first-order 532 kinetics scheme: For the square wave input, we chose to hold constant so that across frequencies the only significant change 561 is in the patterning of spikes and not the total number of spikes; this results in larger pulses being delivered to 562 postsynaptic PCs at lower frequencies as would be expected if lower frequencies are produced by larger networks 563 (Nunez et al., 2006). Throughout the paper, WM item parameters , , and are assigned superscripts or 564 indicating whether they represent "target" or "distractor" items, respectively (see Table 1 for notation details). 565 All principal cells in the output gate received additional asynchronous inputs representing uncorrelated 566 background activity from 100 cells in other brain areas spiking at 1 sp/s. Notably feedforward inhibition was 567 excluded from the present work so that asynchronous items were maximally effective at driving PC cells in the 568 output gate. Control values for WM item parameters were = 1000 sp/s (corresponding to an item-encoding 569 population with 1000 projection neurons spiking at 1 sp/s); = 1 ms (high synchrony), 10 ms (medium synchrony), 570 or 19 ms (low synchrony), and = .0015 mS/cm 2 . High synchrony inputs are similar to strong, periodic spikes 571 while medium and low synchrony inputs distribute spikes uniformly over intervals comparable to sine waves at 572 100 Hz and 53 Hz, respectively. 573 In simulations probing resonant properties of the output gate, the item modulation frequency was varied 574 from 1 Hz to 50 Hz (in 1 Hz steps) across simulations. In simulations exploring output gating among parallel 575 pathways, input items had the same mean strength (i.e., ); this ensures that any difference between the ability 576 of WM items to drive their corresponding outputs resulted from differences in the dynamical states of the 577 item-encoding populations and not differences in their activity levels.

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For each simulation, instantaneous output firing rates, iFR, were computed with Gaussian kernel regression 580 on population spike times using a kernel with 6 ms width for visualization and 2 ms for calculating the power 581 spectrum. Mean population firing rates,̄ and̄ , were computed by averaging iFR over time for PC and IN 582 populations, respectively; they index overall activity levels by the average firing rate of the average cell in the 583 population (Figure 9Ci-ii). The frequency of an output population oscillation, , is the dominant frequency of 584 the iFR oscillation and was identified as the spectral frequency with peak power in Welch's spectrum of the iFR 585 (Figure 9Ciii). In the beta/gamma range, this is equivalent to the inverse of the period between output spike 586 volleys. The natural frequency of the output network was identified as the population frequency produced 587 in response to an asynchronous input. 588 Across simulations varying input frequencies, statistics were plotted as the mean ± standard deviation calcu-589 lated across 10 realizations. Input frequency-dependent plots of mean firing rates and population frequencies