article: Cortical rhythms have been thought to play crucial roles in our cognitive abilities. Rhythmic activity in the beta frequency band, around 20 Hz, has been reported in recent studies that focused on neural correlates of attention, indicating that top-down beta rhythms, generated in higher cognitive areas and delivered to earlier sensory areas, can support attentional gain modulation. To elucidate functional roles of beta rhythms and underlying mechanisms, we built a computational model of sensory cortical areas. Our simulation results show that top-down beta rhythms can activate ascending synaptic projections from L5 to L4 and L2/3, responsible for biased competition in superficial layers. In the simulation, slow-inhibitory interneurons are shown to resonate to the 20 Hz input and modulate the activity in superficial layers in an attention-related manner. The predicted critical roles of these cells in attentional gain provide a potential mechanism by which cholinergic drive can support selective attention.
  It is widely understood that sensory processing is modulated by attention, which impacts neural responses in the sensory cortex: Elevated spiking activity [1]–[4] and enhanced synchrony in neural responses [5]–[9] were found to be associated with attended, rather than unattended stimuli. These findings suggested that endogenous signals, presumably generated at least in part in higher cognitive areas, are delivered to lower areas when attentional gain control is required. Although neural correlates of attentional gain control are not well understood, biased competition has been thought to be an underlying mechanism [10]–[17]. Recent studies indicate that beta rhythms can be associated with top-down attention [18]–[23]. In this study we used a computational model to address whether top-down beta rhythms can bias competition, and if so how they achieve this. We leave for a following paper the potential roles of top-down signals in the gamma frequency band, which have also been seen [24], [25], considering here only the induction of gamma rhythms by bottom up signals and how they interact with the top-down beta. Beta rhythms have been reported to be generated by local circuits in deep layers, particularly layer 5 (L5) [24], [26]–[28]. A recent in vitro study found that three types of deep layer cells (intrinsically bursting (IB), regular spiking (RS) pyramidal cells and a particular class of slow-inhibitory interneuron (LTS cells) ) are involved in generating deep layer beta rhythms locally in the primary auditory cortex [24], and that beta rhythms generated in higher order (parietal) cortices influence rhythm generation in auditory cortex in a highly direction-specific manner. Cortical slow-inhibitory (SI) interneurons are a diverse subclass of inhibitory cells. Their firing patterns can be regular, accommodating or low-threshold spiking, and their axonal and dendritic morphology also varies greatly from cell to cell. However, the majority of this broad class of interneuron is involved in providing inhibition between cortical layers that has slow postsynaptic kinetics relative to fast spiking interneurons. For example deep layer Martinotti cells have axons that are almost exclusively oriented radially in cortex, passing across multiple local laminae [29], [30]. In addition, Dantzker & Callaway found a class of adapting interneurons in superficial layers that received dominant inputs from deep layers [31]. These factors make SI interneurons ideal candidates for mediating interlaminar interactions, as has been shown for concatenation of deep and superficial beta and gamma rhythms [32]. Additionally, the excitability and spike output patterns in SI interneurons can be potently affected by cholinergic neuromodulation, a cortical process of fundamental importance to attention (see Reference [33] for review). Specifically, Xiang et al. [29] found that acetylcholine depolarized deep layer LTS interneurons, which can enhance interlaminar interaction. Thus, we hypothesized that primary sensory L5 cells, resonating to top-down beta frequency inputs can modulate responses of superficial neurons in sensory cortices predominantly through SI interneurons. The model given below supports this hypothesis.
  During the delay period, Fries et al. [5], [6] did not present a stimulus, but they found disparate neural responses in the attention-inside the RF condition and in the attention-outside the RF condition: LFP power in frequencies lower than 17 Hz was smaller in the attention-inside RF trials than in the attention-outside RF trials. Such differences in neural activities were attributed to top-down attention, which was induced by a cue preceding the delay period. We therefore tested whether top-down beta rhythms could reproduce these neurophysiological findings. Fries et al. [5], [6] showed that stimulus presentation generated gamma rhythms and elevated spiking activity, and attention enhanced these induced neural responses. In our model bottom-up inputs, simulated by 100 Hz asynchronous trains of EPSCs, are introduced to L4 E and FS cells of both columns. Without top-down signals, the two columns generate equivalent responses (first column of Figure 5): Even though bottom-up inputs are asynchronous, L4 E cells fire synchronously at a gamma frequency for a few gamma cycles due to interactions between L4 E and FS cells (see References [40], [41] for details). L2/3 also oscillates at the same frequency due to the ascending excitation from L4 E cells to L2/3 RS and FS cells (Figure 5A).
  In this study, we introduced top-down signals to L5 pyramidal cells (see Methods), as suggested in Wang [23], but we also note that top-down signals can directly target L5 interneurons [35], [46]. Even if top-down signals prominently project to L5 interneurons, L5 SI cells are dominant over FS cells [29], and deep layer beta rhythms still emerge, producing the equivalent interlaminar interaction. Thus, we did not explore the effect of top-down beta rhythms projected to L5 interneurons. Our simulation results suggested potential mechanisms for selective attention: L5 cells resonating to top-down beta rhythms can modulate superficial layer activity by generating ascending projection to upper layers. Specifically, we found exclusive roles for excitatory and inhibitory synaptic projections from L5 cells to upper layers. First, an inhibitory projection originating from L5 SI cells to L4 FS cells enhanced excitatory outputs of L4 in response to bottom-up inputs. Second, an excitatory projection from L5 IB and RS cells of the attended column generated stronger inhibition to L2/3 RS cells of the unattended column via intercolumnar connections to L2/3 interneurons of the unattended column. In our model these two types of ascending projections associated with top-down beta rhythms generated activity in superficial layers in accord with the pattern of neural response modulation induced by attention reported in Fries et al. [5], [6]: Compared with attention outside the RF, top-down beta rhythms associated with attention inside the RF can 1) enhance gamma rhythms in L2/3,2) reduce beta rhythms in L2/3 and 3) enhance spiking activity of L2/3 RS cells. Since superficial layers project to higher cognitive areas, these modulatory effects of top-down signaling may account for the enhanced Granger causality influence from V1 to V4 reported in a recent in vivo study [20]. Importantly, SI cells in both L2/3 and L5 play major roles in our model of attentional gain control. First, L5 SI cells produced ascending inhibition. Second, L2/3 SI cells enhanced synchrony in L2/3 RS cells of the attended column and induced stronger inhibition in L2/3 of the unattended column (see Figure 9 and related text), indicating that L2/3 SI cells are critical for lateral inhibition. This active role of L2/3 SI cells is consistent with findings in Kapfer et al. [47] that adaptive interneurons, which include our SI cells, are critical to lateral inhibition. During the delay period, top-down beta rhythms suppressed RS cell activity induced by background inputs only (Figure 3B). We are not aware of any evidence for or against this prediction of our simulations. In the model we have assumed that the top-down pathway have the necessary specificity. Indeed, long-distance connections are more target-specific than short-distance connections [48]. Though we do not address how specific connections are established among cortical areas (a huge question), our contribution is to show how these top-down pathways can dynamically regulate the gain of sensory signal processing. FS and SI cells of our model participate in generation of gamma and beta rhythms. What roles do these two types of interneurons play in signal processing? In a local circuit that generates gamma rhythms, inhibition from FS cells prevents RS cells from responding to synaptic inputs between cycles of gamma rhythms, a feature useful for filtering out distracting inputs [49]. Since L4 cells produce rhythmic activity in response to bottom-up inputs in our model and initiate gamma rhythms in L2/3, L2/3 FS cells can ensure L2/3 RS cells selectively respond to bottom-up inputs; this selectivity enhances signal to noise ratio of sensory signal processing significantly if the frequency of gamma rhythms in L2/3 match those from L4 [50]. This suggestion is consistent with the role of FS cells in generating gamma rhythms associated with sensory input [40], [51] and with the reduction of noise with gamma rhythms [52]. In contrast, our model suggests that SI cells, which have been thought to be critical in regulation of pyramidal cell activity [47], [53], may also be involved in modulatory control of FS cells and thus gamma rhythms. In particular, L2/3 SI cells provide additional inhibition to suppress erroneous L2/3 RS cell activity during the delay period, and L5 SI cells can enhance L4 outputs in the attended column. Surround suppression has been widely reported in visual systems, and the traditional view considers lateral inhibition as a key mechanism. However, this view has been recently challenged by studies suggesting a reduction of inhibition that is contradictory to the enhanced inhibition predicted with lateral inhibition in the cortex: Ozeki et al. [54] revealed that both inhibitory and excitatory inputs were reduced when surround suppression was in effect, leading them to conclude that surround suppression originated in the thalamus, rather than in the cortex. This issue is still under debate [55], [56]. Given the conflicting evidence, the two different mechanisms relying on different origins may coexist and cooperate with each other, as discussed in [57], [58]. Although several studies support crosstalk among cortical columns, this interaction may be distance-dependent: Adesnik & Scanziani [56] found that the lateral suppression effect in vivo in anesthetized animals faded in two columns. This could be a potential concern for our model since the unattended column may be located far away from the attended column in the brain. In such a situation, lateral inhibition may be weak and attentional modulation be significantly reduced, especially in the alpha/beta frequency bands (see Figure 9 and related text). However, it should be noted that monkeys in the Fries et al. studies [5], [6] had extensive training. During the training period, long-distance connections among columns could develop to improve performance. Alternatively, lateral inhibition, assumed in our model and other computational studies, may be conveyed indirectly to distant columns via the thalamus. L5 cells project strongly to the thalamus, which projects back to superficial layers globally; they also project to LGN, which has specific projections to the cortex [59]. Indeed, a few studies suggested that interneurons could be a main target of thalamocortical (TC) projections [60], [61]; see also Reference [62]. Thus, these two pathways may allow L5 pyramidal cells to create a global and local synaptic projection from L5 pyramidal cells to L2/3 interneurons through the thalamus. Interestingly, many computational models have proposed active roles of lateral inhibition for attentional gain control [10], [16], [17], [63] (see below), different from involuntary surround suppression; top-down signals, selectively projected to a population of cells, can assist the selected population to be a winner in the competition with other populations via lateral inhibition. For instance, in the model proposed by Ardid et al. [64], excitatory to interneuron connections, uniformly implemented throughout the cortices, gave rise to biased competition; such structure is consistent with lateral connections in our model. Our model is in line with those models, in that top-down signals can bias competition. However, we add the novel proposal that interlaminar interaction, regulated by top-down beta rhythms, support selective attention. Lateral connections from L5 pyramidal cells to L2/3 interneurons in our model were adopted from the hierarchical architecture proposed by Felleman & Van Essen [34]. Indeed, most L5 pyramidal cells were also found to project into L2/3 [65], [66]; L5B projects to L2 and L3A with widely branched axons [37]. Although our study focused on functional roles of top-down beta rhythms and their underlying mechanisms, top-down gamma rhythms have also been reported in a few studies [24], [25]. Since FS cells are believed to play a critical role in gamma rhythms, top-down gamma rhythms may be associated with modulation of FS cell activity. This assumption is supported by two physiological studies. First, Mitchell et al. [4] revealed that top-down attention enhanced FS interneuron activity most strongly. Second, Roopun et al. [24] found that superficial and deep layers received top-down gamma and beta rhythms, respectively. Together, we hypothesize that top-down gamma rhythms mainly target superficial FS cells. What are the functional roles of top-down gamma rhythms? Roopun et al. [24] noted that L2/3 gamma rhythms of S2 entrained L2/3 gamma rhythms of A1. This entrainment makes A1 mirror superficial activity of S2 rather than auditory inputs from L4 of A1, and thus A1 cannot project its own auditory signals to S2 when prominent top-down gamma rhythms exist. This means that cortico-cortical projections from A1 to S2 may be disabled by top-down gamma rhythms. Thus, we further hypothesize that top-down gamma rhythms may be responsible for routing/gating feedforward processing related to bottom-up inputs, depending on attentional state. This hypothesis is explored in a forthcoming paper addressing interaction between top-down gamma and beta rhythms. We note that alpha rhythms have also been reported to be associated with suppression of neural responses induced by irrelevant stimuli when attention was demanded [67]–[69]. Spaak et al. [70] found a prominent alpha rhythmic activity in deep layers, and Buffalo et al. [28] reported a reduction of SFC in the alpha frequency band during the attention inside the RF trials. It is widely accepted that alpha rhythms are generated at least partly in the thalamus; Saalmann et al. [71] found that the pulvinar indeed regulated the alpha rhythmic activity in V1 and V4 and the coherence between them in the alpha frequency band, suggesting that attention-associated alpha rhythms may be induced by the thalamus. Since our model does not include the thalamus, we cannot explicitly test whether thalamic projections in the alpha frequency band can account for findings of Buffalo et al. [28], but our model provides a perspective on the possibility: In our model, SFC in the alpha frequency band (8–15 Hz) was significantly (t-test,) smaller in deep layers of the attended column than in deep layers of the unattended column, whereas SFC in the beta frequency band (15–25 Hz) was significantly larger in the deep layer of the attended column (Figure S1). In the attended column, top-down beta rhythms entrained L5 cells, reducing the alpha rhythmic activity, which appeared in the deep layers of the unattended column as well as the control column. In other words, top-down beta rhythms to L5 cells competed with alpha rhythms and reduced the alpha rhythmic activity in deep layers, suggesting that top-down beta rhythms can reduce the impact of thalamic alpha rhythms via competition in the attended column. This raises a critical question: Why are both alpha and beta rhythms necessary for attentional modulation? We suggest that these two rhythms may play complimentary roles: Olsen et al. [72] suggested that L6, which receives thalamic inputs [73], suppresses neural activity. If the thalamus broadly projects alpha rhythms into L6 of the cortex, the cortical neural activity may be suppressed globally. For example, the pulvinar projects to superficial layers of V1 and granular layers of V2 [74], and L6 pyramidal cells can receive focused inputs from superficial and granular layers [73], suggesting that the pulvinar may be capable of inducing global inhibition via L6 cells. By contrast, our model proposes that L5 cells can enhance neural response within a specific column via ascending inhibition. Together, we propose a scenario that alpha rhythms may suppress neural responses globally, whereas beta rhythms can release a particular column/receptive field from global suppression. Acetylcholine (ACh) is a neuromodulator associated with attention (see Reference [26] for a review). Hasselmo [75] and Kimura [76] found that ACh suppresses neural transmission originating from the cortex, allowing cortical cells to be more sensitive to transmission from thalamus. However, it is still unclear how the highly diffuse projections of ACh-releasing terminals throughout cortex can support selective attention. Our model proposes a mechanism by which ACh may contribute to selective attention: Xiang et al. [29] found that ACh can depolarize L5 LTS cells via nicotinic receptors and hyperpolarize L5 FS cells via muscarinic receptors. Since FS cells inhibit LTS cells, both of these effects make the LTS cells with vertical axons, a subset of interneurons known to provide slow inhibition [77], resonate more easily to top-down beta rhythms, enhancing biased competition in superficial layers. Thus, the diffusive projection of ACh changes the network to facilitate top-down signaling in providing these selective signals. When ascending inhibition of L5 SI cells and L2/3 SI cells were removed from the model, attentional gain control disappeared; this indicates a critical role of nicotinic receptor regulation in selective attention because SI cells are depolarized by ACh via nicotinic receptors [29], [78]–[80]. Indeed, a link between nicotinic receptors and attention was supported by a few studies [81]–[83]; see Reference [84] for a review. Changes in nicotinic receptor regulation may thus be important for understanding cognitive changes in some diseases associated with attention deficit [85]–[90]. Importantly, Levin [91] found that nicotine alleviates some symptoms of Attention-Deficit/Hyperactivity Disorder (ADHD), and the procognitive effects of cigarette smoking found in patients with various psychiatric disorders are well documented (see Reference [92] for a review). Although further studies should be conducted to investigate how nicotinic receptor regulation is linked to such psychiatric disorders, our model raises the possibility that impaired nicotinic receptor function can cause imaginary sensation: the removal of L2/3 SI cells from our model produced gamma rhythmic activity in L2/3, independent of bottom-up inputs. If these gamma rhythms are misinterpreted by higher cognitive areas as resulting from stimulus presentation, they may help to account for hallucination, a symptom of some psychiatric disorders. Interestingly, Manganelli et al. [93] reported evidence suggesting that visual hallucination is caused by impaired cholinergic systems. Herrero [94] found evidence that muscarinic receptor blockers can reduce attentional focus. This phenomenon may be attributable to cholinergic switching in L5 [29]: These authors found that muscarinic receptor blockade depolarized L5 FS cells. When we simulated this effect, LFP modulation induced by top-down signals was reduced (see Results), consistent with Herrero et al. [94]. However, more complex, equivocal reports of muscarinic receptor-mediated effects on fast-spiking interneurons need to be considered as a caveat to this [80], [95]–[97]. Most spontaneous layer-specific data was collected from anesthetized animals, and its link to in vivo activity from awake animal engaging in cognitive tasks, is currently unclear. Since our model aimed to understand mechanisms underlying top-down attentional effects, we assumed our model was cholinergically modulated; we depolarized L5 SI cells and hyperpolarized L5 FS cells in deep layers [29] during all simulations including the control experiments, suggesting that spontaneous activity collected from anesthetized animals cannot be used to tune our model network behaviors. Instead of capturing spontaneous in vivo activity of L4 and L5 cells, we considered L4 and L5 as simple recipient layers for bottom-up and top-down inputs, respectively, and did not introduce any external Poisson spike trains of EPSCs (external background inputs). Due to this simplification, during the delay period, L4 E cells did not have sufficient drive to overcome inhibition from L2/3 and L4 FS cells (see Figure 1) and were quiescent. We evaluated the impact of the lack of drive to L4 cells by introducing external background inputs to L4 E cells and found no significant changes: L4 E cell activity was increased with background inputs simulated by 10 Hz Poisson EPSCs with various amplitudes (Figure S2A), but attentional indices still showed significant attentional modulation during the stimulus period (Figure S2B, C and D). We also note that L5 pyramidal cells fired quite synchronously in the alpha frequency band even with external background inputs, during the control experiments, since they received inhibition from L5 SI cells. It is important to note that a few studies indeed found alpha rhythms in deep layers [28], [70], [98] while animals were awake, consistent with synchronous activity in L5 of our model. In addition, Berger et al. [99] suggested that firing of a few L5 pyramidal cells can induce feedback inhibition, and L5 Martinotti cells, a class of SI cells, were reported to provide feedback inhibition between L5 pyramidal cells [53], suggesting that synchronous activity of pyramidal cells can approximate in vivo spontaneous activity in deep layers. Our model ignored two components. First, we considered only two columns, although a lot of “inactive” columns, driven weakly by bottom-up inputs, interact with the attended and unattended columns. Second, the thalamus was missing in our model, making us unable to evaluate the effect of thalamocortical circuits on attentional modulation. Since the thalamus is known to generate alpha rhythms [71], [100], the thalamocortical interaction should be taken into the account to fully understand mechanisms underlying the prominent alpha rhythms and reduction of alpha rhythms reported in Buffalo et al. [28]. In spite of these simplifications, our model was capable of reproducing attentional modulation reported in Fries et al. [5], indicating the importance of beta-rhythmic cortico-cortical communication on attentional gain control. The importance of selective attention in cognitive abilities has attracted multiple computational model studies. Most of these studies concern competition between multiple stimuli in the same field. In particular, Reynolds et al. [10] presented both neurophysiological data supporting biased competition and a firing rate model capable of reproducing their findings. Since then, more biophysically detailed models have been proposed to study neural mechanisms underlying biased competition. These include Deco & Rolls [63], who built a model of V2 and V4; their simulation results provided a potential mechanism underlying the competition between bottom-up and top-down regulations. Similarly, resonance between MT and PFC were shown to be able to generate multiplicative gain modulation [64]. Buia & Tiesinga [16] proposed a theory that top-down signals are delivered to interneurons, instead of excitatory pyramidal cells. The effects of top-down attention on cortical columns with lamina structure were investigated in Wagatsuma et al. [17]. Tiesinga & Sejnowski [101] showed that synchrony in interneurons can regulate signal flow; also, gamma rhythms can enhance the selection of relevant stimuli [49]. By contrast, our model, which focuses on reproducing neurophysiological data reported in Fries et al. [5], involves comparing an ‘attention-inside’ condition to an ‘attention-outside’ condition. Our model is most closely related to the model proposed by Buia & Tiesinga [16], in that interneurons, activated by top-down signals, play crucial roles in attentional gain control. However, in addition to discussing a different paradigm (competing inputs), their model has no laminar structure, which is critical for the effects of our model. Our model suggests that the laminar structure can ensure that L2/3 RS cells, which project to higher cortical areas, respond to bottom-up inputs more strongly and reliably when attention is directed to the column. Wagatsuma et al. [17] used a model with laminar structure similar to ours, but without biophysical details we believe are critical to the phenomena we describe. In summary, focusing on the detailed physiology of the network receiving top-down input enabled us to suggest mechanisms for the action of those inputs in facilitating attentional gain control. The model further sheds light on how diffuse cholinergic modulation can support selective attention.
  As can be seen in Figure 1, our model consists of nine cell populations with randomized connections among them. We ran 10 independent simulations for each condition to reduce bias from random connections and noise. To do so, we reduced the complexity of the model by limiting each population to have 20 cells, as in Kramer et al. [32]. All integrations were numerically calculated by the fourth-order Runge-Kutta methods with 0. 01 msec-time step. Noisy tonic input, injected to each neuron, generated heterogeneity in cells of the same type. This noisy current was produced using the Box-Muller algorithm [102] (see Table 1). Simulation codes were written in C. All L2/3 and L4 cells were modeled with single compartments. Pyramidal and SI cells contained a transient sodium (NaF) current, a delayed rectifier current (KDR), a leak current and a muscarinic current (M). The model FS cells did not contain a M-current, which provides frequency-adaptation [97], [103]: they contained NaF, KDR, leak currents as in Wang & Buzsaki [104]. Deep layer SI cells were modeled the same as L2/3 SI cells except the maximal conductance of M-current, which was reduced by 50%. However, L5 pyramidal cells (IB and RS) were modeled with three compartments (axon, soma and apical dendrite) to reflect the fact that L5 pyramidal cells with apical dendrites can receive top-down signals [37]. These three compartments were connected via electrical coupling as in Kramer et al. [32]. Each compartment contained NaF, KDR, and leak currents. M-current was included in both dendrite and axon, and high-threshold calcium (CaH) current was added to the dendrite. IB cells contain higher maximal conductance of CaH current than RS cells [38]. Dynamics of neurons in our model were calculated by voltage-gated conductance equations; (1) where, , , and; where the last term represents Poisson trains of EPSCs: is the Heavyside step function and are the arrival times of trains of EPSCs (see below). Membrane potentials were regulated mainly by two different sources; intrinsic ion currents and synaptic currents. Also we introduced two types of external inputs and trains of EPSCs with maximal conductance of. For all compartments (cells) except L2/3 RS cells, we used, and; we lowered by 50% for L2/3 RS cells. Table 1 shows the maximal conductances of other currents and the mean value (standard deviations) of for each type of cell. The gating variables and regulating ion currents follow Hodgkin-Huxley-type equations. (2) where and are forward and backward rate functions. With the relationships between forward and backward rate functions and steady state variables; (3) (4) Equation 2 can be described with steady-state variable; (5) We adopt steady-state variables for NaF, KDR and CaH currents from Kramer et al. [50]. Excitatory and inhibitory cells are different in dynamics of NaF and KDR currents. For excitatory cells and compartments, we set steady-state variables as; (6) (7) (8) (9) (10) For inhibitory cells, we used slightly different steady-state variables; (11) (12) (13) (14) (15) For M-current, we adopted the forward and backward rate functions from McCarthy et al. [105]; (16) (17) where. Similarly, for CaH current, we set the forward and backward rate functions following Kramer [32]; (18) (19) In each layer, all pyramidal cells and inhibitory interneurons were reciprocally connected, and recurrent excitatory and inhibitory connections were also implemented; thus cells received both excitation and inhibition from other cells belong to the same layer. 25% L2/3 FS and SI cells had NMDA receptors and thus they received excitatory inputs from L2/3 RS cells via both NMDA synapses and AMPA synapses. We did not consider NMDA-mediated excitatory connections among L4 E cells in this study since most outputs of L4 neurons in visual cortex of guinea pigs show fast kinetics, decaying within 2 msec [106]. The rise and decay time of synapses are shown in Table 2. For interlaminar connections, we used a subset reported in neurophysiological studies [37], [107]. Instead of implementing all synaptic connections reported, we focused on identifying synaptic pathways responsible for attentional gain control of sensory signal processing. Figure 1A shows the structure of the cortical column. We connected layers with excitatory and inhibitory synapses; Two columns were connected with each via ascending excitation (Figure 1B). The intercolumnar connections to L2/3 SI cells were 50% stronger than those within the column. Table 3 shows details of the connectivity of our model. We considered each synapse as a gating variable that controls the conductance of synaptic currents on a post-synaptic neuron. Each synaptic variable was simulated by the same rule: (20) where the membrane potential of pre-synaptic cell. and determine how fast synapses can close and open, respectively, and thus they were referred to as the decay time and rise time, as in Kramer et al. [32]. For a post-synaptic cell, synaptic input is the sum of excitatory and inhibitory synaptic currents: (21) where the is index for type of pre-synaptic cells (out of 9 types of cells in our model) and is the index for neurons in the population of the same type. The maximal conductance, rise time and decay time of individual synapse depends on both pre-synaptic and post-synaptic cell types, and chosen values are given in Table 2. In our model NMDA synapses were simulated with slow rise and decaying time constants (Table 2). To understand the modulatory effect of top-down signals on bottom-up sensory signal processing, we introduced top-down and bottom-up signals to our model. In this study, we did not explicitly implement higher cognitive areas or the thalamus, the sources of top-down and bottom-up signals. Instead, we assumed that top-down signals were synchronous synaptic inputs and bottom-up inputs were asynchronous ones. Specifically, both top-down signals and bottom-up inputs were simulated as trains of excitatory post synaptic currents (EPSCs), which caused instantaneous increase of AMPA current up to a maximal conductance and exponential decay with a 2 msec time-constant: Top-down signals were synchronized and oscillating at 20 Hz, and thus all L5 pyramidal cells of the attended column received the same EPSC trains; we did not introduce top-down signals to deep layer interneurons. In contrast, L4 E and FS cells of both columns received asynchronous 100 Hz EPSC trains generated from Poisson processes. We also introduced additional 50 Hz Poisson trains of EPSCs to L2/3 RS cells to simulate inputs from other parts of cortex [44], [109] and non-selective thalamic inputs such as matrix projections [110]; these inputs are referred to as background inputs in Results. Table 1 shows the maximal conductance values of external inputs. We ran the network for 1 sec each during the delay and stimulus periods. To simulate the delay period (after the cue and before the presentation of a stimulus), we introduced top-down signals into the attended column with no bottom-up input. In contrast, during the stimulus period, bottom-up inputs were introduced to both columns, with the attended column continuing to receive top-down signals. As control experiments for both periods, we considered simulations without top-down inputs; only background inputs were introduced to our model in a control experiment for the delay period. In order to uncover functional roles of SI cells and lateral inhibition, we also ran simulations removing such components from our model. For each set of simulations, we created 10 realizations of networks with randomly chosen connections among cells (Table 3) and ran each of them with independently generated EPSC trains to minimize any bias from random connections and stochastic EPSC trains. The firing rate of cells is the average number of action potentials produced per second by 20 cells of each type, and we reported mean and standard errors of those values from 10 simulations. LFPs were simulated by summing up synaptic currents projecting onto L2/3 RS cells from all neurons in our model [111], and spike-triggered average (STA) of LFPs were calculated. In order to calculate STA of LFPs, we collected segments of LFPs surrounding each spikes of L2/3 RS cells from 10 independent simulations; thus, the simulated STA is averaged over spikes from 200 L2/3 RS cells. Specifically, we took 600 msec-long LFP segments; 300 msec before and 300 msec after each spike. All spectral analysis is done with Chronux, a matlab toolbox [112]. For each simulation run, we also calculated the spike-field coherence (SFC), a ratio of the power spectrum of STA of LFPs over the average of spike-triggered spectral spectra: This measure allows us to evaluate the synchrony of cell activity independently from the firing rate and spectral power of raw LFPs [5]. We reported mean values and standard errors of attentional indices from 10 simulations to show the modulatory effect of top-down beta rhythms [31]; three attentional indices are given as: where is the spike-field coherence in the high frequency band, 25–70 Hz, calculated from each simulation run; is the spike-field coherence in the low frequency band, 8–25 Hz; is the average firing rate of L2/3 RS cells from each simulation run. We also measured synchrony of L2/3 RS cell activity with Equation (22) [104] (22) where and are the spike trains of two RS cells with 1-msec resolution.
summary: Top-down signals originate from higher cognitive areas such as parietal and prefrontal cortex and propagate to earlier stages of the brain. They have been thought to be associated with selective attention, and recent physiological studies suggest that top-down signals in the beta frequency band can support selective attention. In this study, we employ a computational model to investigate potential mechanisms by which top-down beta rhythms can influence neural responses induced by presentation of stimuli. The model includes several cell types, reportedly crucial for generating cortical rhythmic activity in the gamma and beta frequency bands, and the simulation results show that top-down beta rhythms are capable of reproducing experimentally observed attentional effects on neural responses to visual stimuli. These modulatory effects of top-down beta rhythms are mainly induced via activation of ascending inhibition originating from deep layer slow inhibitory interneurons. Since the excitability of slow interneurons can be increased by cholinergic neuromodulators, these interneurons may mediate the effects of cholinergic tone on attention.
keywords: circuit models
  biophysic al simulations
  computational neuroscience
  sensory systems
  biology
  computational biology
title: Top-Down Beta Rhythms Support Selective Attention via Interlaminar Interaction: A Model