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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
J Neurosci. Author manuscript; available in PMC 2010 August 24.
Published in final edited form as:
PMCID: PMC2888157
NIHMSID: NIHMS181634

Reconciling Coherent Oscillation with Modulation of Irregular Spiking Activity in Selective Attention: Gamma-Range Synchronization between Sensory and Executive Cortical Areas

Abstract

In this computational work, we investigated gamma-band synchronization across cortical circuits associated with selective attention. The model explicitly instantiates a reciprocally connected loop of spiking neurons between a sensory-type (area MT) and an executive-type (prefrontal/parietal) cortical circuit (the source area for top-down attentional signaling). Moreover, unlike models in which neurons behave as clock-like oscillators, in our model single-cell firing is highly irregular (close to Possion) while local field potential exhibits a population rhythm. In this “sparsely synchronized oscillatory” regime, the model reproduces and clarifies multiple observations from behaving animals. Top-down attentional inputs have a profound effect on network oscillatory dynamics while only modestly affecting single-neuron spiking statistics. In addition, attentional synchrony modulations are highly selective: Inter-areal neuronal coherence occurs only when there is a close match between the preferred feature of neurons, the attended feature and the presented stimulus, a prediction that is experimentally testable. When inter-areal coherence was abolished attention-induced gain modulations of sensory neurons were slightly reduced. Therefore, our model reconciles the rate and synchronization effects, and suggests that interareal coherence contributes to large-scale neuronal computation in the brain through modest enhancement of rate modulations as well as a pronounced attention-specific enhancement of neural synchrony.

Keywords: microcircuit, attention, working memory, synchronization, extrastriate, visual motion

Introduction

During covert selective attention to locations or features of the visual scene, visual cortical neurons are modulated selectively in both their firing rate (Reynolds and Chelazzi, 2004; Desimone and Duncan, 1995) and their gamma-range synchronization (Fries et al., 2001, 2008b; Womelsdorf et al., 2006; Gregoriou et al., 2009). Several studies suggest that gamma-range synchronization facilitates attentional processing (Womelsdorf and Fries, 2007; Salinas and Sejnowski, 2001; Tiesinga et al., 2008). However, single-neuron studies indicate that spatial attention only reduces modestly the high irregularity of neuronal spiking (Mitchell et al., 2007; McAdams and Maunsell, 1999a), contrary to what would be expected from a robust enhancement of oscillatory firing. These contrasting temporal aspects of attentional modulation must be reconciled to specify the dynamics of cortical network activity, and its sensitivity to synchronization for attentional processing.

The fact that attentional enhancement of network oscillations does not impact greatly on single-neuron irregularity may constrain models that evaluate the functional role of neural synchronization in selective attention. Typically, strong synchrony-based attentional effects require that neurons enter an oscillator regime during behaviorally relevant contexts (Buehlmann and Deco, 2008; Buia and Tiesinga, 2008; Tiesinga, 2005; Zeitler et al., 2008; Börgers et al., 2005, 2008; Mishra et al., 2006; Masuda, 2009). It remains to be analyzed how attentional synchronization affects information processing in networks that consistently reside in oscillatory regimes with highly irregular neural spiking (Brunel and Wang, 2003; Geisler et al., 2005; Brunel and Hakim, 1999; Brunel and Hansel, 2006).

Attention modulates associative visual cortex responses presumably through top-down inputs from the fronto-parietal network (Corbetta and Shulman, 2002; Colby and Goldberg, 1999; Bressler et al., 2008). Indeed, attention enhances coherence between signals recorded simultaneously from visual and fronto-parietal areas (Saalmann et al., 2007; Gregoriou et al., 2009). It has been hypothesized that the source area of the top-down attentional signal is a working memory circuit of the parietal or prefrontal cortex (Desimone and Duncan, 1995; Corbetta and Shulman, 2002). Neurons in such circuits present sustained selective firing (Gnadt and Andersen, 1988; Quintana et al., 1988; Funahashi et al., 1989), possibly oscillatory (Pesaran et al., 2002; Compte et al., 2003; Joelving et al., 2007), during the delay period between sensory cue extinction and motor response, and provide input to neurons in associative sensory circuits (Moore and Armstrong, 2003). Thus, working memory circuits can maintain an internal copy of the attentional set, and modulate both firing rates and oscillations in upstream visual areas, as suggested experimentally (Gregoriou et al., 2009).

Here, we reconcile the dichotomy between modulations of local field potential synchrony and Poisson-like firing in attention using a network of two interacting cortical microcircuits in visual and working memory areas (Ardid et al., 2007). Using a manipulation that specifically abolishes inter-areal coherence, we assess the impact of synchronized sensory and executive circuits on the attentional modulations of sensory firing rates (McAdams and Maunsell, 1999b; Martinez-Trujillo and Treue, 2004; Treue and Martinez Trujillo, 1999; Reynolds et al., 1999). We find that, in a regime of irregular single-neuron spiking, inter-areal synchrony has a profound impact in gamma-range coherence across circuits, but only a limited effect on the firing rate of neurons in the sensory circuit.

Materials and Methods

The model network

Each of the two network modules represents a local circuit of the cortex. The sensory network represents a local circuit of the visual middle-temporal area (MT). We refer to the working memory module as a local circuit of the prefrontal cortex (PFC) for the sake of simplicity, although working memory and selective attention are likely to be subserved by both prefrontal and parietal cortices (Colby and Goldberg, 1999; Corbetta and Shulman, 2002; Corbetta et al., 2008). The MT and PFC circuits had exactly the same wiring structure; they only differed in the strength of the synaptic connectivity within each module. A detailed account of the local circuit model can also be found in (Compte et al., 2000). For each circuit, pyramidal cells (NE = 1024) and interneurons (NI = 256) were spatially distributed on a ring simulating the cortical columnar organization, labeled by their preferred direction of motion (θN, from 0 to 360 degrees). Their axonal collaterals differentially targeted neighboring (isodirectional) and distant (crossdirectional) neurons. This was implemented by taking the synaptic conductance between neuron i and neuron j to be gsyn,ij = Wi−θj)Gsyn, where Wi−θj) was either a constant for unstructured connections (Wi−θj) = 1), or the sum of a constant term plus a Gaussian: Wi−θj) = J + (J+J) exp(−(θi−θj)2/2σ2). This last expression depends on two parameters, J+ and σ, while J is determined from a normalization condition (Compte et al., 2000). In both networks only the excitatory-to-excitatory connectivity was structured with σEE = 14.4° and JEE+=1.62 (Compte et al., 2000). The excitatory-to-inhibitory, inhibitory-to-excitatory, and inhibitory-to-inhibitory connections were unstructured, i.e. the cross- and iso-directional components of feedback inhibitory connections were equally strong. This simplification was introduced to constrain the number of free parameters, and because inhibitory tuning can easily be obtained by additionally tuning excitatory-to-inhibitory connections without affecting much the rest of network operation (Compte et al., 2000). Following the notations in (Compte et al., 2000), the parameters defining the strengths of local connections in the two networks were: in PFC GEE,AMPA = 0.459 nS, GEE,NMDA = 0.557 nS (pyramid-to-pyramid); GEI,AMPA = 0.352 nS, GEI,NMDA = 0.430 nS (pyramid-to-interneuron); GIE = 3.20 nS (interneuron-to-pyramid); GII = 2.50 nS (interneuron-to-interneuron). In MT: GEE,AMPA = 0.801 nS, GEE,NMDA = 1.10 nS (pyramid-to-pyramid); GEI,AMPA = 0.684 nS, GEI,NMDA = 2.00 nS (pyramid-to-interneuron); GIE = 7.34 nS (interneuron-to-pyramid); GII = 7.34 nS (interneuron-to-interneuron). Thus, although recurrent synaptic conductances were very strong in both modules, recurrent inputs in MT were at least three times stronger than in PFC. On the other hand, both networks operated in an inhibition-dominated regime (Compte et al., 2000): recurrent excitatory and inhibitory inputs into excitatory neurons during stimulus response averaged 4.8467 nA and 9.4006 nA in area MT, respectively, and 1.4094 nA and 1.5515 nA in area PFC, respectively. This corresponds to an inhibition-to-excitation ratio of 1.94 in MT and 1.10 in PFC.

Both pyramidal cells and interneurons were modeled as leaky integrate-and-fire neurons, with the same parameters as for neurons in the network model of Compte et al., (2000). Specifically, each type of cell was characterized by six intrinsic parameters: the total capacitance Cm, the total leak conductance gL, the leak reversal potential EL, the threshold potential Vth, the reset potential Vres, and the refractory time τref. The values used were Cm = 0.5 nF, gL = 25 nS, EL = −70 mV, Vth = −50 mV, Vres = −60 mV and τref = 2 ms for pyramidal cells; and Cm = 0.2 nF, gL = 20 nS, EL = −70 mV, Vth = −50 mV, Vres = −60 mV and τref = 1 ms for interneurons. All cells received random background excitatory inputs. This unspecific external input was modeled as uncorrelated Poisson spike trains to each neuron at a rate of vext = 1800 Hz per cell (or equivalently, 1000 presynaptic Poisson spike trains at 1.8 Hz), except for excitatory cells in PFC where vext = 2010 Hz. This input was exclusively mediated by AMPARs, with the maximum conductances gext,E = 2.8 nS on pyramidal cells and gext,I = 2.38 nS on interneurons, in PFC; and gext,E = 17 ns and gext,I = 9.2 nS in MT. High external conductances in MT produced the high-variance strong external input that allowed high firing rates (>60 Hz) with irregular spiking statistics (CV~1) in our integrate-and-fire neurons.

Neurons received their recurrent excitatory inputs through AMPAR and NMDAR mediated transmission and their inhibitory inputs through GABAARs. These conductance-based synaptic responses were calibrated by the experimentally measured dynamics of synaptic currents. Thus, postsynaptic currents were modeled according to Isyn = gsyns(VVsyn), where gsyn is a synaptic conductance, s a synaptic gating variable, and Vsyn the synaptic reversal potential (Vsyn = 0 for excitatory synapses, Vsyn = −70 mV for inhibitory synapses). AMPAR and GABAAR synaptic gating variables were modeled as an instantaneous jump of magnitude 1 when a spike occurred in the presynaptic neuron followed by an exponential decay with time constant 2 ms for AMPA and 10 ms for GABAA. The NMDA conductance was voltage dependent, with gsyn multiplied by 1/(1 + (Mg2+) exp(−0.062 Vm)/3.57), (Mg2+) = 1.0 mM. The channel kinetics was modeled by the following equations:

dsdt=1τss+αsx(1s)dxdt=1τxx+iδ(tti)

where s is the gating variable, x is a synaptic variable proportional to the neurotransmitter concentration in the synapse, ti are the presynaptic spike times, τs = 100 ms is the decay time of NMDA currents, τx = 2 ms controls the rise time of NMDAR channels, and αs = 0 5 kHz controls the saturation properties of NMDAR channels at high presynaptic firing frequencies. Parameters for synaptic transmission were taken from Compte et al., (2000).

The MT and PFC network modules were interconnected through bottom-up and top-down AMPAR-mediated connections (see scheme in Fig. 1B). Both bottom-up and top-down connectivities were topographic, so that for both the bottom-up and top-down pathways neurons sharing the same preference were more strongly coupled than neurons with disparate preferences. This connectivity was described by a Gaussian function: gsyn=Gsynexp((θiθj)2/2σ2)/σ2π. We used for the bottom-up connection onto PFC pyramids GEEMTPFC=0.005nS and σ = 36°, for the bottom-up connection onto PFC interneurons GEIMTPFC=0, for the top-down connection onto MT pyramids GEEPFCMT=0.146nS and σ = 72°, and for the top-down connection onto MT interneurons GEIPFCMT=0.098nS and σ = 72°. The less specific connectivity in the top-down direction is supported by recent evidence in area MT, showing that the directionality index for responses to behaviorally relevant stimuli located far from the receptive field, and presumably reflecting top-down input, was approximately half that of responses to stimuli in the receptive field (Zaksas and Pasternak, 2005). The divergence of bottom-up projections to PFC was chosen equal to bottom-up inputs from V1, which were in turn determined by fitting typical tuning curve widths for motion direction in area MT (see below).

Figure 1
Schematic description of simulated task and model architecture

The integration method used was a second-order Runge-Kutta algorithm with a time step of Δt = 0.02 ms. We confirmed that using Δt = 0.002 ms did not alter the dynamics of our control network. The custom code for the simulations was written in C++.

Monosynaptic latencies

Our code implementation considers the possibility of introducing independent latencies for each synapse in recurrent connections and also between the two networks. The values for these latencies come from two terms, an identical constant term for all the connections from a specific neuron of the same kind (recurrent vs. loop connection) plus a variable term, selected at random from an exponential distribution given its standard deviation. We have tried other types of random distributions (Gaussian truncated by discarding negative latencies; Gamma; and uniform distributions) without showing significant quantitative differences in the results. We used this technique because it allowed us to study two different issues using monosynaptic latencies. On the one hand, we could increase drastically the monosynaptic latency variability (standard deviation 100 ms) so as to break completely the synchrony between the two networks (Fig. 6). By doing that we do not pretend to consider a plausible physiological scenario, but to quantitatively analyze the role of oscillations and synchrony per se on sensory encoding in the MT network (Fig. 7Fig. 10). On the other hand, from a plausible biophysical point of view using reasonable variances [1–2 ms (Ghosh and Porter, 1988; Fanardjian and Papoyan, 1997; Sirota et al., 2005; Le Bé et al., 2007)], the technique allowed us to see to which degree the effects of synchronization persist in more realistic conditions (supplemental Fig. 6, available at www.jneurosci.org as supplemental material). In some recurrent connections fixed synaptic delays were used (< 1 ms), but these did not have a significant impact in network synchronization.

Figure 6
Random conduction latencies in the top-down signal disrupt selectively gamma band synchronization between the two networks
Figure 7
Gamma band synchronization between PFC and MT specifically enhances the firing rate effects attributed to selective visual attention, in a similar way as PFC rate increases
Figure 10
Inter-areal synchronization reduces neuronal firing variability but Fano Factors remain high, due to burstiness

Simulated feature-based attentional tasks

The chosen simulation protocol resembled other behavioral protocols used in monkey attention experiments (Martinez-Trujillo and Treue, 2004) (Fig. 1A). In attention trials, attention is focused on the direction of motion of a peripheral stimulus, whereas in non-attention trials, attention is directed elsewhere (for instance to the fixation cross luminance). Furthermore, we included a delay period, between the presentation of the stimulus to pay attention to (cue stimulus), and the presentation of the stimulus to respond to (target stimulus). Specifically, all trials consist of four periods: cue (0.5 s), delay (2.5 s), test (1.5 s), and response. In the cue period a cue stimulus appears indicating the type of trial: a random dot pattern (RDP) stimulus in coherent motion indicates attention trial and the attended feature (direction of motion), whereas a change in fixation cross luminance (not specifically modeled) indicates non-attention trial. In the delay, no visual stimulus is presented so that all task instructions have to be maintained mnemonically. During the test period, one or two transparently moving RDPs (test stimuli) are presented in the neuron’s receptive field (RF). These stimuli are behaviorally irrelevant, but in attentional trials they may be similar or dissimilar to the direction of motion of the behaviorally relevant attended stimulus (target stimulus), which is away from the neuron's RF. Using this protocol, one can gradually separate the test and the target features in attention trials. To model consistently the neural mechanism for this behavioral task and the flow of sensory information through MT to PFC, one would require the simulation of two different motion-selective MT circuits feeding into a motion-selective PFC circuit, one MT network would be selective to the RF where the cue appears and the other one would be selective to the RF where the test is presented. We noted however that the temporal separation of the cue and test period makes activity in these two periods independent for both MT circuits. This justifies reducing the model to a single MT circuit, which is responsive to motion stimuli presented in either RF. This is, however, a simplifying abstraction, and interpretation of cue activations in MT should be regarded as occurring in neurons selective for the corresponding stimulus location. In the response period, a brief and transient change in the target RDP direction of motion, or in the luminance of the fixation cross occurs, and the subject has to detect it and respond in a prescribed time window. Our model does not include these aspects of the task.

Task-related extrinsic inputs

Cells in area MT received external inputs from primary visual area V1 which were selective to the direction of motion of the visually presented stimulus (Born and Bradley, 2005) (Fig. 1B). We thus modeled motion stimuli presentation by injecting external currents to MT neurons that mimicked outputs from V1 to MT. We tried with Poisson-triggered synaptic inputs and our conclusions remained unaffected. When there was a single motion direction (θS), the current injected to a neuron labeled by θi was Ii) = I0 + I1 exp(μ(cos(θi−θS)−1)), for MT pyramidal cells we used I0E=1.65nA and I1E=0.74nA, for MT interneurons we used I0I=1.4nA and I1I=1.39nA, and for both cell types μ = 2.63 (this choice of μ gives a connectivity profile very close to a Gaussian with a constant baseline, with the same width as MT-to-PFC connections, which gives tuning widths in MT compatible with physiological data (Treue and Martínez Trujillo, 1999; Snowden et al., 1992)). When two overlapping directions of motion were visually presented, the current impinging on MT neurons was the sum of the currents corresponding to the two single stimuli, normalized so that the maximal current was still I0 + I1 (supplemental Methods and supplemental Fig. 1B, available at www.jneurosci.org as supplemental material). This normalization was derived from the observation that the maximal response of a direction-selective V1 neuron remains the same for either single motion or transparent motion stimuli (Snowden et al., 1991). When a stimulus suddenly appears or disappears from the visual scene, we simulate smooth current transitions where injected current from V1 to MT changes exponentially with a time constant of 50 ms.

Moreover, since here we want to analyze dynamical aspects of neural activity and how this dynamics is modified when feature-based attention is involved, we incorporate the experimental fact that stimulus-specific oscillations occur at gamma-range frequencies in V1 neural activity (Friedman-Hill et al., 2000). Specifically, we introduce a new oscillatory component added to the constant bottom-up input from V1, Ii) (see above). This oscillatory component is constructed as the sum of sinusoidal terms with frequencies fi = 15, 16,… 55 Hz, random phases in the range [0, 2π], and amplitudes pondered by a factor coming from a Gaussian function, A exp(−(fifc)2/2σ2), with fc = 35 Hz, σ = 10 Hz, and A = Ii)/16. Such oscillatory input adds to the oscillations that are generated internally in MT through the recurrent excitation-inhibition loop. Oscillations in the input from V1 affect the overall oscillatory character of MT neural activity in passive conditions (Fig. 4, blue lines), but not its modulations by attention or the effect of top-down conduction latencies.

Figure 4
Gamma band oscillations are detected locally in both networks

PFC model neurons received motion-specific sensory inputs only through the MT-to-PFC pathway. These inputs were weak enough so they would not drive the PFC network into a bump attractor state by themselves (see Fig. 2E). In all our simulation trials and during the attentional cue period, all PFC neurons also received a constant current injection of 0.025 nA. This current was not selective and thus it did not carry any direction of motion information. It was too weak to trigger by itself a persistent activity pattern in the PFC network (Fig. 2A, No Att.); but strong enough so that, when presented coincidentally with a visual stimulus, the PFC stored the directional information from MT (Fig. 2A, Att.). Such a “gating input” (Ardid et al., 2007) allows our model to differentiate the attentional cue from an identical visual stimulus presented during the test period (see Fig. 1A). This gating input could emanate from phasic alertness circuits in the superior temporal gyrus or in the thalamus (Sturm and Willmes, 2001; Fan et al., 2005; Thiel and Fink, 2007), or phasic neuromodulation from the locus coeruleus (Aston-Jones and Cohen, 2005).

Figure 2
Network oscillations emerge in two-area loop model

LFP signal from simulation data

LFP signals reflect a summation of synaptic potentials, subthreshold membrane oscillations and spike afterpotentials rather than spiking activity (Logothetis and Wandell, 2004; Rauch et al., 2008). In area MT, LFPs also show selectivity to direction of motion (Liu and Newsome, 2006), although the tuning properties for LFPs are usually poorer than for spiking activity (Liu and Newsome, 2006). We built the LFP signal as the sum of excitatory postsynaptic currents from 129 neurons selected uniformly among those with selectivity θi within 90° of a given central location (typically 0°). In our loop model there are three contributions to the LFP signal related to the recurrent excitatory input (we only consider the AMPAR contribution), the loop excitatory input (from the other network), and the external Poisson excitatory input. No significant differences appeared when we also considered recurrent NMDAR-mediated and GABAAR-mediated synaptic inputs in the LFP. The sampling frequency used for the LFP was 1 kHz.

SUA/MUA signal from simulation data

Our SUA (MUA) signal comes from the spike train of one (three) randomly-selected neuron(s) for each trial simulation, where the specific selection is done using a uniform probability distribution within the interval: center ± 30°, and center represents the relevant direction of motion and is typically 0° or 180°. This reflects the fact that in experimental studies, different SUA/MUA recordings are averaged together, based on an approximately similar (but not exactly equal) selectivity.

Measures of variability

To characterize the irregularity of neural spiking we measured coefficients of variation (CV) and Fano factors. To evaluate the CV we computed inter-spike intervals (ISIs) of spike trains during the test period for each neuron, lumping together ISIs from each of 20 model simulations. For each neuron, we thus obtained its CV as the ratio of s.d. to mean of its ISIs. The population average CV was then obtained as the mean of each neuron's CV. The Fano factor was calculated also individually for each neuron, following the approach that is used experimentally (Mitchell et al., 2007). For Figure 10A, we took spike trains corresponding to 101 neurons around θN = 0° in 20 simulations, each of which included cue (θA = 0°), delay, test (θS = 0°) and response periods and lasted 6 s. These spike trains were fragmented in non-overlapping pieces of duration 100 ms. For each neuron and time window, we thus had 20 spike train fragments, from which we obtained 20 spike counts. The Fano factor for each cell was computed as the variance over the mean of these spike counts. The population Fano factor for each time window was then computed as the average over the neurons' Fano factors in that time window. For Figure 10B we took spike trains corresponding to a given neuron in 128 simulations, in each of which the test-period lasted 5 s. These spike trains were fragmented in non-overlapping pieces of duration 500 ms. For each neuron we thus had 1,280 spike train fragments, from which we obtained 1,280 spike counts. The Fano factor for each cell was computed as the variance over the mean of these spike counts. The population Fano factor was then computed as the average over the neurons' Fano factors.

Frequency domain analysis

We used the Chronux data analysis toolbox (http://chronux.org) for the spectral analysis of model data. We estimated quantitatively the amount of oscillations in our model computing the power-spectra of time-series (LFP) and/or point-process (SUA/MUA) signals. To study synchrony between two signals we used the coherence measure C(f)=S12(f)/S1(f)S2(f), where Si(f) represents the spectrum estimation for each signal, and S12(f) the cross-spectrum estimation between both of them. All spectral quantities (power spectra and coherences) were computed by using 9 orthogonal Slepian tapers and a bandwidth of 10 Hz. In Figure 3C–3F, Figure 5C and supplemental Fig. 4A,B (available at www.jneurosci.org as supplemental material) we performed time-resolved sliding window spectral analyses. These analyses consisted in the spectral evaluation of spectra/coherence in time windows of length 500 ms, which were moved along the signals in steps of 25 ms. In Figure 3CF and supplemental Fig. 4A,B (available at www.jneurosci.org as supplemental material), we plotted the average power in the range 30–50 Hz (normalized to firing rate for the case of MUA spectra) over 20 trial simulations.

Figure 3
Attentional synchrony enhancement in MT is not phase-locked to stimulus, but to response
Figure 5
Coherent neuronal activity between PFC and MT in the gamma band occurs selectively and only in attention trials

Statistical analysis

95% confidence intervals in power spectra and coherence measures in Figure 3Figure 6, and supplemental Figures 4,5 (available at www.jneurosci.org as supplemental material) were computed following a jackknife approach over simulation trials (identical simulation parameters but each one with different random number generation. Typically Nt = 20, except in Fig. 3CF, where Nt = 70). The extent of these confidence intervals is shown as shadowed areas around the mean curves. We performed unpaired t-tests (unless indicated otherwise) to establish significant differences between the means of two distributions. As the t-test relies on the assumption of normally distributed errors, we tested our data with the Kolmogorov–Smirnov normality test to establish that the data did not violate the normality assumption (p>0.05). For the cases where the assumption was violated, we applied instead the non-parametric unpaired Mann-Whitney test. All analyses were performed using the Matlab package (The MathWorks).

Parameter optimization to find a diversity of MT models

We designed an unbiased, automated optimization procedure to find the parameters of suitable MT networks. This procedure consisted in randomly initializing 13 free parameters (I0E;I1E;I0I;I1I; μ; GEE,AMPA; GEE,NMDA; GEI,AMPA; GEI,NMDA; GIE; GII; gext,E; gext,I; each within a pre-specified range of values) for each of 50 networks, henceforth called particles (Fig. 9A). Such networks were simulated to evaluate their responses to background activity, to single presented stimuli and to two stimuli presented with varying separation (30°, 60°, 90°, 120° and 180°). Evaluation was performed with predefined functions that rated the degree of accomplishment of specified target behaviors (maximal and minimal firing rates, response to two stimuli compared to single stimulus, etc., supplemental Methods, available at www.jneurosci.org as supplemental material) for each particle. Based on the overall rating of each particle, and the history of best rating for each particle and for the collection of particles (swarm), a particle swarm optimization algorithm (Kennedy and Eberhart, 1995) updated the parameters of each particle in the swarm. This procedure was repeated iteratively until the swarm converged to a network that accomplished the required functional output (typically within 50 iterations). Such swarm simulations were computationally intensive (10,000 CPU hours each) and required specialized grid computing management software (Grid SuperScalar, (Sirvent et al., 2006)). For more details, see supplemental Methods, available at www.jneurosci.org as supplemental material. We ran several swarm simulations and identified 15 different MT networks with similar functional output (supplemental Fig. 1, available at www.jneurosci.org as supplemental material) but largely divergent parameters (supplemental Fig. 2 and supplemental Table 1, available at www.jneurosci.org as supplemental material). We used this set of models to test the generality of our results (Fig. 9 and supplemental Fig. 9, available at www.jneurosci.org as supplemental material), and show that they are unlikely to emerge from a specific, singular combination of parameter values.

Figure 9
An automated optimization procedure found 14 additional MT networks, all of which showed little dependence of firing rate modulations on inter-areal synchronization

Results

The model architecture is described in a previous paper (Ardid et al., 2007). The model includes two interacting cortical networks at different stages in the processing hierarchy, one of them is a sensory area and the other one a working memory (WM) area. In order to be able to evaluate the spiking statistics of neurons in each area, single cells are described by a spiking (integrate-and-fire) neuron model. Excitatory and inhibitory neurons are interconnected through AMPA-receptor and NMDA-receptor mediated excitatory synapses and GABAA-receptor mediated inhibitory synapses, so that biologically realistic oscillations can be generated through synaptic interactions in the model networks (see Fig. 1B and Materials and Methods). To simulate the neural encoding of an analog quantity (such as direction of motion) these synaptic connections are topographically organized, so that the strength of neuronal connectivity depends parametrically on the similarity of pre- and post-synaptic neuron selectivities. Then, the two networks are interconnected through weaker, topographically organized excitatory AMPA-receptor mediated synapses that provide selective bottom-up inputs to the WM area and selective top-down inputs to the sensory area. Parameter values were calibrated based on available physiological and anatomical evidence. Some parameter values (typically synaptic strengths) were relatively unconstrained by existing data and were manipulated to find operating regimes that reproduced the neuronal responses recorded experimentally in areas MT and PFC of behaving monkeys (see (Ardid et al., 2007) for details). We focus on these two areas in order to specify our hypotheses and extract specific data from the literature. These areas have been shown to be anatomically connected (Burman et al., 2006; Roberts et al., 2007; Schall et al., 1995; Barbas, 1988), but our model might equally apply to other combination of sensory and WM-supporting associative areas, such as V4-PFC or MT-LIP. In fact, we apply a generalization principle so that in those aspects where no data are available from area MT, we extrapolate from results in area V4.

This model has been shown to integrate most attentional modulations of the firing rate in visual extrastriate neurons (Ardid et al., 2007): biased competition (Reynolds et al., 1999; Desimone and Duncan, 1995), multiplicative scaling of tuning curves (McAdams and Maunsell, 1999b; Treue and Martínez Trujillo, 1999), and selective enhancement with inhibitory surround of population activity profiles (Martinez-Trujillo and Treue, 2004; Chen et al., 2008). In addition, this biophysical computational model provides a plausible mechanistic basis for the feature-similarity gain principle proposed by Treue and Martínez-Trujillo (Treue and Martínez Trujillo, 1999; Martinez-Trujillo and Treue, 2004). According to this principle, the attentional modulation of the firing rate response of a given extrastriate neuron to arbitrary visual stimuli is given by a multiplicative factor (“modulation ratio”) that only depends on how similar the attended feature is to the neuronal preferred feature (Martinez-Trujillo and Treue, 2004). Our model network is architecturally identical to this earlier model (Ardid et al., 2007) but we operated some parameter value modifications to reproduce all the firing rate effects accounted for in (Ardid et al., 2007) plus the statistics of single neuron firing in these areas (Mitchell et al., 2007; McAdams and Maunsell, 1999a), and attentional local and long-range synchronization effects (Fries et al., 2001, 2008b; Womelsdorf et al., 2006; Saalmann et al., 2007). Using a computationally intensive search algorithm in parameter space (Fig. 9A, see Materials and Methods) we found 15 network realizations that reproduced satisfactorily the required phenomenology (supplemental Figs. 1, 2, available at www.jneurosci.org as supplemental material). We report here detailed data about one of these networks and test some of our conclusions in the rest of network models to evaluate the generality of our results.

A model simulation followed a typical protocol of selective visual attention tasks: A first cue stimulus indicates what needs to be attended, a random-duration delay forces the subject to maintain actively such attentional set in memory, and during the test period a sensory stimulus appears that is to be processed under the specific attentional condition established by the first cue (Fig. 1A and Materials and Methods). We specify this general visual attention task by assuming that stimuli are moving random dot patterns and the relevant stimulus feature is direction of motion. This type of stimulus is effective in eliciting responses in area MT (Born and Bradley, 2005) and also in PFC (Zaksas and Pasternak, 2006). Persistent working memory activity in single neurons has not yet been located in the primate brain for this type of stimulus (Zaksas and Pasternak, 2006), but there is evidence of category-based delay activity for motion stimuli in area LIP (Freedman and Assad, 2006).

Gamma oscillations in network dynamics

Figure 2A,B shows sample firing rate activity from two neurons, one in each network, which were selective to the direction of motion of the test and attended stimulus. Both neurons interacted synaptically, as they were mutually coupled because of their similar selectivity. Enhanced synchronization in the test period of attention trials relative to non-attention trials is reflected by the larger fluctuation amplitudes in the local field potential (LFP) signals of either network (Fig. 2A,B). Spatio-temporal patterns of network activity in attention (Fig. 2C,D) and non-attention (Fig. 2E,F) trials revealed network oscillatory activity in all high activity states in both networks (Fig. 2C,D,F). Interneurons showed similar patterns of activity (supplemental Fig. 3, available at www.jneurosci.org as supplemental material). Despite these marked population oscillations, spike trains of MT neurons were highly variable (Fig. 2D). Coefficients of variation (CVs) of inter-spike intervals of MT excitatory and inhibitory neurons, combining data from 20 test-period simulations, were 0.98 ± 0.06 and 1.11 ± 0.04, respectively (mean ± s.d., n=1024 and n=256, respectively). These high values of variability (Poisson spike trains have a CV of 1) are in qualitative agreement with experimental data (Fig. 4F, and Fig. 10A,B) (Mitchell et al., 2007; McAdams and Maunsell, 1999a; Softky and Koch, 1993) and they reflect in part the fact that spike-trains had a bursty character (Fig. 10C,D) (Constantinidis and Goldman-Rakic, 2002; Bair et al., 1994). Oscillatory firing was difficult to identify both in individual MT neuron spike trains (single unit activity, SUA) and event trains formed by collapsing spikes from several neighboring neurons (multiple unit activity, MUA) (Fig. 2D), and only became clear in the collective network activity and filtered local field potential (LFP) (Fig. 2D). The LFP was obtained from the model as the summated synaptic currents produced by a large number of neurons (see Materials and Methods). This sparse participation of neurons in the population rhythm, where oscillations are revealed in the LFP and not in the SUA, is characteristic of cortical activity during cognitive tasks (Fries et al., 2001; Pesaran et al., 2002). Theoretical work has shown that such a regime can be obtained with strong inhibitory feedback within the network (Brunel and Wang, 2003; Geisler et al., 2005), as it indeed happened in our MT network (recurrent inhibitory currents exceeded recurrent excitatory currents by a factor close to 2). However, no previous study has addressed how these regimes are modulated by oscillating top-down inputs.

Gamma-range rhythms are not phase-locked to stimulus but to response

We then investigated what specific analyses of experimentally accessible signals could reveal such weak population rhythms. It is instructive to compare SUA, MUA and/or LFP recordings from several trials (similar to typical experimental data) (Fig. 3B) with simultaneous activity of a population of neurons in a single trial (Fig. 2 and Fig. 3A). We found that raster plots and peri-stimulus time-histograms (PSTHs) of SUA spike-trains over several trials (Fig. 3B) failed to reflect the oscillatory dynamics that were readily observed for simultaneously recorded spike trains in a single trial (Fig. 3A). This can be further demonstrated by pooling together spikes from 3 different SUAs to generate a MUA spike train, and computing its average power content around the peak of the gamma oscillation (30–50 Hz) in the course of the trial (Fig. 3C,D). When the SUAs came from 3 simultaneously recorded neurons, attentional gamma-band power enhancement was observed during stimulus presentation (Fig. 3C), whereas it was absent when the MUA was formed by spike trains from a given neuron in 3 different trials (Fig. 3D). This reveals that the stimulus-triggered population rhythm was not phase-locked to the stimulus onset time on different trials. This also underlies the lack of oscillatory marks in the power spectrum of event-related potential (average LFP over trials) during stimulus presentation (Fig. 3F), which were instead present when power spectra of each individual LFP were first computed and only then averaged over trials (Fries et al., 2008a) (Fig. 3E).

Only one synchronization effect remains in the multiple-trial analyses of Figure 3D,F: a gamma-band oscillation locked to the response onset time. This effect is dependent on how the response period is simulated. Network response here consisted in the erasure of PFC persistent activity by means of general excitation of the PFC pyramidal population (Compte et al., 2000). Such sudden activity surge in PFC generated a synchronization enhancement in MT that was phase-locked to response time, and was thus detectable both from trial-averaged spectral measures and event-related potential measures (Fig. 3E,F). Such synchronization did not emerge if we reset PFC persistent activity through excitation of the PFC interneuron population. In a recent experiment, marked additional increases in gamma-band oscillations were found in area V4 right at the time of change detection in an attention task (Fries et al., 2008b). Our model would thus suggest that erasure of the maintained attentional set at the end of behavioral trials occurs through synchronizing excitation (Gutkin et al., 2001), rather than inhibition. This also shows how the degree of oscillatory synchrony in PFC can change qualitatively the temporal properties of MT responses: sudden strong oscillations in PFC reset the phase of gamma-range activity in MT, whereas this does not happen for weaker PFC oscillations as during the delay and test periods.

Local-circuit synchronization without neural oscillators

At the local circuit level, attention modulated the microcircuit oscillations. Similar to experiments in area V4 (Womelsdorf et al., 2006; Fries et al., 2008b), greater coherence was observed between MT MUA and LFP signals when the PFC maintained oscillating persistent activity in attention trials, than when it did not in non-attention trials (Fig. 4A,B). Such strong attentional enhancement of gamma-range oscillations was also clearly reflected in the LFP power spectrum (Fig. 4C) and in the MUA power spectrum, obtained by pooling several simultaneously recorded SUAs (Fig. 4D). The time course of LFP spectral enhancement in the gamma range paralleled firing-rate changes in MT through the task (supplemental Fig. 4, available at www.jneurosci.org as supplemental material), as it has also been observed experimentally (Fries et al., 2008b). However, at the level of single neuron firing the attentional enhancement of oscillatory activity was barely reflected in either the power spectrum (Fig. 4E) or the coefficient of variation (Fig. 4F). These two calculations approached the expected features of highly irregular Poisson spike trains. Therefore, strong coherence effects in the population are not a signature of neurons switching to the regime of a neural oscillator.

Selective long-range synchronization

We quantified how attention modulated the synchrony between the two areas by computing the coherence between SUAs extracted from the two networks. Gamma-range synchronization was observed between equal-selectivity neurons in the two networks, but only when they fired in response to an attended stimulus (Fig. 5A), and mostly during the cue, test and response periods (Fig. 5C). Notably, coherence between neurons in the two networks was absent if the presented stimulus was dissimilar to the stimulus being attended (Fig. 5B). This occurred because the oscillating top-down input had a limited connectivity footprint, and could only synchronize the firing of those MT neurons being targeted by the activated PFC neurons. In addition, such synchronization was only effective if these MT neurons were firing coherently in response to a preferred stimulus. Thus, neurons of distant selectivity in the two networks did not synchronize even though they were both firing at high rates (Fig. 5B, violet), and neurons of equal selectivity in the two networks did not synchronize either, if the attended feature differed from the feature being presented (Fig. 5B, green). Analogous results were obtained for the coherence between LFPs extracted from either network (Fig. 5D). Enhanced inter-areal synchronization during attention has been reported experimentally (Saalmann et al., 2007; Gregoriou et al., 2009), showing in addition that synchronization occurs only between neurons with overlapping receptive fields (Gregoriou et al., 2009). Our results predict that this selectivity projects to feature space: synchronization affects only those neurons in the two networks that are firing above baseline and only if the attended feature and the test feature coincide.

We tested the role of local-circuit AMPA receptors in generating the attentional enhancement of synchronization (supplemental Fig. 5, available at www.jneurosci.org as supplemental material). We found that when AMPA receptors were replaced by NMDA receptors in MT recurrent connections, both oscillations in MT and synchronization across MT and PFC were reduced significantly. Removing AMPA receptors from PFC totally abolished inter-areal synchronization and reduced the attentional effects on local-circuit oscillations in MT. Therefore, fast recurrent dynamics in both networks were necessary to implement synchronization enhancement by attention but had little effect on the irregular firing statistics of MT neurons.

Random top-down latencies disrupt inter-areal synchronization

What are the functional consequences of this temporal coordination of spiking activity in the two network areas? One way to address this question is to selectively abolish inter-areal coherence in the network and assess the computational consequences. To this end, we introduced long (non-physiological) random conduction latencies in the top-down signal from PFC excitatory neurons to MT neurons. These latencies were taken randomly from an exponential distribution of standard deviation 100 ms, and chosen independently for each pair of pre- and post-synaptic neurons (see Materials and Methods). This non-physiological manipulation (the s.d. in conduction latencies between cortical areas is typically < 2 ms (Ghosh and Porter, 1988; Fanardjian and Papoyan, 1997; Sirota et al., 2005; Le Bé et al., 2007)) produced the temporal shuffling of all top-down synaptic events onto MT, but no significant change in the total number of top-down events received (Fig. 7C, orange and green lines). Thus, we expected rate effects due to the top-down signal to remain, while specific effects of the temporal organization of top-down spikes should be removed. Indeed, the temporal fluctuations of the LFP signals extracted from the MT network were significantly diminished by this manipulation (s.d. of MT LFP 0.74 ± 0.04 nA before, and 0.70 ± 0.05 nA after introducing random latencies; mean ± s.d., n=20 trials, t-test p<0.001. A single trial is illustrated in Fig. 6A), while there was no such effect in PFC (s.d. of PFC LFP was 0.23 ± 0.01 nA before, and 0.22 ± 0.01 nA after introducing random latencies; mean ± s.d., n=20 trials, t-test p>0.05. Fig. 6A). When we repeated the coherence analyses of Figure 4 and Figure 5 on the data from the long-latency top-down input, we confirmed that the attentional synchronization enhancement was significantly reduced at the local level (Fig. 6B) and practically vanished at the inter-areal level (Fig. 6C,D).

Inter-areal synchronization affects attentional rate modulations weakly

The firing-rate effects of feature-based attention (Martinez-Trujillo and Treue, 2004; Ardid et al., 2007) were diminished by the introduction of random top-down latencies, albeit by a small amount (Fig. 7). In particular, the selectivity enhancement of population activity induced by attention was reduced (Fig. 7A,B). Thus, attentional modulation of MT activity can be considered as composed of two different contributions: a main term, proportional to the mean PFC input, and another weaker contribution, that depends on the inter-areal synchronization.

We confirmed that a physiologically realistic dispersion of synaptic latencies in long-range connections (ca. 1.2 ms (Ghosh and Porter, 1988)) was insufficient to eliminate the effect of inter-areal synchronization in the attentional modulations of firing rate responses in area MT (supplemental Fig. 6, available at www.jneurosci.org as supplemental material). Because attentional selectivity enhancement is thought to underlie the behavioral advantage of selective attention (Lee et al., 1999), our finding identifies a specific way through which inter-areal synchronization may contribute to distributed cortical network processing.

We wondered whether it would be possible to dissociate these two effects of the attentional signal. We ran simulations in the attended condition with random top-down latencies, now with the addition of an oscillating (at 35 Hz) external input (with zero mean) to MT that restored the intra-MT coherence to the control values of Figure 4. Because top-down input from PFC retained long, random top-down latencies, there was no coherence between MT and PFC in these simulations and we could specifically test how the sole change in intra-MT coherence during attention trials with an asynchronous top-down input from PFC affected rate modulations in area MT. Our simulations revealed that the same rate effect was achieved whether MT synchrony was enhanced by virtue of a synchronizing top-down input from our PFC network, or via synchronization by a separate input pathway (supplemental Fig. 7, available at www.jneurosci.org supplemental material). It is important to note that, in these simulations, the additional oscillatory input was attention-specific, and spatially tuned the same way as the top-down asynchronous input. The result shows that the overall attentional effect observed in the control condition can be decomposed into two additive components.

On the other hand, inter-areal synchronization during attention acts similarly as modest rate increases in the area from which the attentional signal originates. We demonstrated this by injecting additional current into active neurons (ca. 0.04 nA) of the PFC network, when random top-down latencies disrupted inter-areal synchronization. We calibrated this injected current so that the modulation ratio in MT recovered the modulation ratio of the original network with intact inter-areal synchrony (Fig. 7B, red and orange curves). The average firing rate in the PFC population increased by 25% (from 10.6 Hz to 13.3 Hz), while peak rates increased by 12% (from 42.2 Hz to 47.5 Hz) (Fig. 7C). Thus, synchrony between the sensory and WM network achieved a given attentional effect on MT population rate coding with lower PFC firing. This metabolic efficiency represents an advantage of inter-areal synchronization. In addition, the same correspondence between inter-areal synchronization and rate increases suggests that MT populations with enhanced oscillations (orange in Fig. 7B) will have greater impact on their downstream targets by virtue of their enhanced synchronization (Salinas and Sejnowski, 2001), much as if they were firing at a higher rate.

We also tested the multiplicative scaling of tuning curves in our network by running simulations with the test stimulus at different directions of motion θS (n=36) while attention was maintained at a fixed direction θA = 0° (Martinez-Trujillo and Treue, 2004; Ardid et al., 2007). Firing rates and input currents were recorded for an MT neuron located within the focus of attention, both in simulations with and without top-down random latencies. Inter-areal synchronization steepened the power-law relating current input and firing rate in MT neurons (Fig. 7D). Earlier studies have shown that input fluctuations underlie the power-law relationship between firing rate and input currents in neurons, and that the higher the exponent in this power-law, the more multiplicative the responses to additive currents are (Murphy and Miller, 2003). Consistent with this, input current fluctuations in our network were reduced by 10% when the desynchronizing top-down latencies were introduced (s.d. of total current into an active MT neuron went from 2.67 ± 0.05 nA to 2.39 ± 0.03 nA; mean ± s.d., n=20 trials, t-test, p<0.001), and this manipulation also compromised slightly the multiplicative character of neural response modulations to additive top-down biases (supplemental Fig. 8, available at www.jneurosci.org as supplemental material).

We then studied how inter-areal synchronization affected the attentional processing of competing stimuli in area MT. The modulation of competitive interactions between simultaneously presented stimulus representations is a fundamental component of attentional processing (Reynolds et al., 1999; Desimone and Duncan, 1995). Similar biased competition effects as those observed in V4 (Reynolds et al., 1999) have been found in MT neural activity driven by transparent motion stimuli (Wannig et al., 2007; Patzwahl and Treue, 2009), as our model predicted (Fig. 8 and (Ardid et al., 2007)). In our model, desynchronizing random top-down synaptic latencies reduced slightly the attentional bias of responses to either competing stimulus (Fig. 8A,B). Therefore, inter-areal synchronization might constitute an incremental mechanism behind biased competition in the cortex.

Figure 8
Gamma-range synchronization strengthens the attentional bias of network responses to multiple stimuli (transparent motion)

Testing generality in a population of network models

Our analysis showed that inter-areal synchronization had effects on all major attentional rate modulations in area MT. However, these effects were small and did not attribute a major computational role to synchronization-based rate enhancements in selective attention. We were concerned about the generality of our results: was the weak role of synchronization in our network a particular result of our specific parameter selection? In order to address this in our simulations, we designed an unbiased optimization procedure on 13 of our network parameters (Materials and Methods, and supplemental Methods, available at www.jneurosci.org as supplemental material). In brief, we let these parameters take values within a pre-specified region of a 13-dimensional hyperspace (Fig. 9A), and we evaluated the neural responses of the corresponding MT network models upon the presentation of one and two motion stimuli. An optimization procedure based on the particle swarm optimization algorithm (Kennedy and Eberhart, 1995) was guided by the known properties of passive responses to random dot patterns in area MT (Albright, 1984; Britten et al., 1992; Snowden et al., 1991, 1992; Maunsell and Van Essen, 1983; Mikami et al., 1986) (supplemental Methods and supplemental Fig. 1, available at www.jneurosci.org as supplemental material). Repeated optimization runs starting from different random initial conditions allowed us to obtain 14 additional MT networks consistent with these data. These networks were highly diverse in terms of the varied parameters (coefficients of variation of the various parameters were in the range 0.26–0.93, with a mean at 0.47 and standard deviation 0.19. See supplemental Fig. 2 and supplemental Table 1, available at www.jneurosci.org as supplemental material). By construction, these different MT networks had similar activity upon stimulus presentation (supplemental Fig. 1, available at www.jneurosci.org as supplemental material) and for each of them we manually tuned top-down connections from our PFC network to generate also similar attentional firing rate enhancements (supplemental Fig. 9, orange traces, available at www.jneurosci.org as supplemental material), compatible with experiments (Treue and Maunsell, 1996; Treue and Martínez Trujillo, 1999; Martinez-Trujillo and Treue, 2004; Zaksas and Pasternak, 2005). We studied the synchronization properties of the resulting MT-PFC networks and found that in all the available 15 networks: 1) the PFC and MT circuits synchronized at gamma frequencies in attention trials (Fig. 9B, mean peak PFC-MT coherence in the attended condition was 0.30±0.10 at a frequency of 40±2 Hz, and in the non-attended condition 0.08±0.02 at 41±16 Hz; n=15, mean±s.d.; coherence values were different, paired t-test, p<0.001); 2) randomization of top-down latencies disrupted this inter-areal synchronization (Fig. 9B, mean peak PFC-MT coherence in attention was reduced by random latencies to 0.09±0.04; mean±s.d.; n=15, p<0.001; not significantly different from non-attention coherence, p>0.1). For most of the 15 networks the attentional top-down input from PFC enhanced existing gamma-range oscillatory dynamics in area MT (Fig. 9C, mean peak MUA-MUA coherence in MT was 0.25±0.17 at 40±8 Hz for attended, and 0.13±0.07 at 39±14 Hz for non-attended trials; n=15, mean±s.d.; coherence values were different, paired t-test, p<0.001); and random top-down latencies abolished attentional synchrony effects in MT (Fig. 9C, random latencies brought mean peak MT MUA-MUA coherence down to 0.12±0.09; mean±s.d.; n=15, p<0.001; not significantly different from non-attention levels, p>0.1). This confirms that our results of Fig. 4Fig. 6 are generally valid for many MT networks that are functionally constrained by the experimental data detailed above. We then tested what impact inter-areal synchronization had on MT firing rate enhancements by attention in the population of 15 models. Despite the large variance in parameter values, all the networks responded similarly at the level of the peak firing rate to the abolishment of inter-areal synchronization through the introduction of random top-down synaptic latencies: The attentional enhancement at the peak of population rate responses was unaffected or only slightly modified by inter-areal synchronization removal (Fig. 9D; and supplemental Fig. 9, available at www.jneurosci.org as supplemental material). From all the tested networks, the control network that we illustrate in Figure 2Figure 8,Figure 10 is the one that showed the most pronounced effects on MT firing rates by inter-areal synchronization (Fig. 9D, gray dot).

Inter-areal synchronization reduces slightly the high variability of neuronal firing

Neural spiking was highly irregular in our MT network, with CVs and Fano Factors (FFs) close to unity, the expected value for Poisson spike trains (Fig. 4F and Fig. 10A,B). Fano Factors were higher for interneurons than for pyramidal neurons (1.24 ± 0.05 and 0.97 ± 0.10, respectively; mean ± s.d., n=256, 1024 neurons, Mann-Whitney test, p<0.001; see Fig. 10B). Despite the pronounced effect of attentional modulatory inputs on the coherence of neuronal firing (Fig. 5), the attentional effects on irregularity were much less pronounced (Fig. 10A,B) and were only sizable if PFC presented very strong oscillations (response period in Fig. 10A). We designed a test to show how much of this modest attentional modulation was specifically due to inter-areal synchronization and not to changes in the firing rate of MT neurons. We computed the Fano Factor of stimulus-activated pyramidal neuron spike trains in the attentional condition in the three different cases shown in Figure 7B,C: control case with intact inter-areal synchronization, case with largely dispersed top-down random latencies, and case with top-down random latencies and PFC boost to recover the firing rate modulations of the intact case. Fano Factors increased significantly by a small amount when random synaptic latencies were included in top-down connections, irrespective of whether MT neurons responded with a higher or lower firing rate to the presented test stimulus (Fig. 10A). This proves that the attentional modulation of Fano Factor was primarily due to inter-areal synchronization, and not to changes in the firing rate of MT neurons (Mitchell et al., 2007). Taken together, our results are consistent with available data on spike count variability in neurons of area V4 (Mitchell et al., 2007; McAdams and Maunsell, 1999a), and suggest that a portion of the reduction in Fano Factor during attention observed experimentally (Mitchell et al., 2007) might be due to an oscillating top-down signal, which regularizes V4 neuronal firing slightly.

Importantly, the Fano Factor of MT neurons remains generally very high in our model, even in the coherent oscillating dynamics regime that characterizes the attentional state in our network (FF ~ 0.8). We found that this fact was explained by the bursty character of MT neurons spike trains, also detected experimentally (Bair et al., 1994). Indeed, the distribution of inter-spike intervals (ISI) presented an over-representation of short ISIs (Fig. 10C,D) and inter-areal synchrony enhanced only slightly ISI probability in E-cells within the 20–30 ms range, corresponding to gamma-range synchronization (Fig. 10C).

Discussion

In this study, we investigated network synchronization induced by attention in a computational model of two interacting, sensory and executive, cortical areas. Apart from attentional rate effects (Ardid et al., 2007), the model matched both the synchronization and the irregular statistics of neuronal firing in these areas (Fries et al., 2001; Womelsdorf et al., 2006; Mitchell et al., 2007; McAdams and Maunsell, 1999a; Gregoriou et al., 2009). These measures offer conflicting views on the impact of temporal dynamics modulations in attentional processing, and our model integrates these results in a single coherent framework. We show that significant attentional modulation of local and long-range coherence is compatible with little attentional modulation of highly irregular statistics in single-neuron firing. We then evaluated the impact that such weak inter-areal synchronization had on attentional processing in our network. The impact of synchrony was assessed by comparing rate-based attentional modulations in MT with or without coherence with PFC. Random latencies in PFC-to-MT connections removed totally the attentional MT synchrony enhancement, taking it to non-attention levels, while only marginally affecting MT neuron Fano Factors. Furthermore, we show that the temporal organization of top-down incoming spikes into MT is responsible of not more than 10–15% of the various attentional modulations of firing rate identified experimentally. The modest effects of synchronization on MT firing rates are in contrast with the marked and highly selective effects of inter-areal synchronization on the coherence of neural activity across areas. This suggests that selective attention might encode in activity coherence across areas the results of selection and detection, adding this information to the rate code of sensory areas.

This model integrates and helps to clarify multiple, hitherto disconnected, experimental results on attentional modulations of neural dynamics. Oscillations in the local cortical circuit in extrastriate cortex are enhanced by a synchronizing top-down input (Fries et al., 2001, 2008b; Womelsdorf et al., 2006; Gregoriou et al., 2009), with a time-course that parallels that of rate modulations (Fries et al., 2008b). This local network synchrony is concomitant with enhanced synchronization between neurons in the sensory and associative networks (Saalmann et al., 2007; Gregoriou et al., 2009). However, such increase in oscillatory dynamics does not affect greatly the high variability of extrastriate neuron firing (Mitchell et al., 2007; McAdams and Maunsell, 1999a). An element that contributes to firing variability is the incidence of bursty firing in a significant proportion of neurons (Constantinidis and Goldman-Rakic, 2002; Bair et al., 1994). All these results are integrated in our network model, where population oscillations and synchrony are compatible with neuronal irregular firing: rhythmic activity emerges as a population phenomenon, without entraining individual neurons into a clock-like oscillatory regime (Brunel and Wang, 2003; Geisler et al., 2005). Then, top-down inputs modulate local and long-range synchronization significantly, without affecting much single neuron firing statistics. However, we found that inter-areal synchronization induces a small but significant decrease in Fano factor at high rates (Fig. 10A and 10B). This suggests that synchronization might underlie an analogous attentional effect observed in neurons of area V4 (Mitchell et al., 2007). However, the attentional reduction of Fano Factor observed experimentally is larger than suggested by our model, and affects more significantly inhibitory neurons (Mitchell et al., 2007). Recent evidence suggests that a portion of these attentional effects comes from the attentional suppression of low frequency (< 5 Hz) fluctuating dynamics in the cortex (Mitchell et al., 2009). The presence of such slow cortical dynamics especially during the non-attention condition has not been contemplated in our model and we therefore expect the model Fano Factor in this condition to underestimate the experimental value, possibly in a cell-type specific manner. Finally, our model also replicates the finding of additional gamma-range synchronization at the time of detection and response (Fries et al., 2008b). This might reflect the sudden increase of synchronizing top-down inputs, due to the removal of the attended item from the WM buffer in the PFC network.

In addition, our model produces specific experimentally testable predictions. On the one hand, the increase in gamma oscillations in extrastriate areas right at the time of change detection and response (Fries et al., 2008b) should be phase-locked to stimulus change (Fig. 3D,F) if we assume the model of working memory erasure through synchrony (Gutkin et al., 2001). This is in contrast to attentional oscillatory enhancement in the test period prior to stimulus change, whose phase is not reset by test stimulus presentation (Fries et al., 2008a). In our model, this qualitative difference is due to the different dynamics of the PFC network at each of these time points. At the time of test stimulus presentation, neurons in PFC are sustaining an attentional set, which is mostly unaffected by stimulus presentation. On the contrary, detection and response is triggered through a sudden increase in PFC oscillatory activity, which resets synchronization dynamics in area MT. Secondly, gamma-range attentional coherence between neural firing in the sensory and executive areas occurs between neurons of similar selectivity, and only if the attended and test feature coincide with the neuronal preference. Underlying this high specificity of inter-areal coherent firing is the footprint of top-down synaptic projections. We propose that this experiment would help estimate the synaptic footprint of top-down attentional connections in feature space. Previous experiments have already shown such selectivity of inter-areal synchronization for the case of spatial attention, where attention enhanced the coherence only between neurons with shared receptive field (Gregoriou et al., 2009).

Our model has some quantitative biases in the evaluation of coherence measures, which could explain the difference with experimentally measured coherence values, typically lower (Saalmann et al., 2007; Fries et al., 2008b; Gregoriou et al., 2009). On the one hand, we are using all-to-all connectivity for simplicity. However, multiple recordings in vitro have typically reported a rate of connectivity in the order of 10% for pyramidal neurons in the neocortex (Markram et al., 1997; Song et al., 2005). Introducing a diluted random connectivity architecture in our model would make the direct connectivity between units in the MUAs unlikely, and reduce peak coherence values, especially for MUA-MUA and SUA-SUA analyses. On the other hand, based on the results by (Liu and Newsome, 2006) we took a weaker motion selectivity for LFPs (input currents from neurons within ± 90° were averaged together) than for MUA (neurons were gathered from a window of selectivity of ± 30°). The peak values of coherence measures based on LFPs and MUAs will also depend quantitatively on their precise selectivity.

By incorporating for the first time a spiking model for the source of the top-down signal, our model represents the first quantitative evaluation of the computational role of inter-areal synchronization for selective visual attention, recently demonstrated experimentally (Saalmann et al., 2007; Gregoriou et al., 2009). Previous models have instead focused on other synchronizing mechanisms, such as inhibitory interneurons (Tiesinga et al., 2004; Buia and Tiesinga, 2008; Börgers et al., 2008; Mishra et al., 2006), feedforward processing (Buehlmann and Deco, 2008), or neuromodulation (Börgers et al., 2005, 2008), and have assumed a rate-based top-down signal. These modeling studies have found that oscillations may have more impact in sensory activity than the 10% modulation reported here. However, our study is the first in finding explicitly a network regime that reconciles strong attentional modulations in LFP oscillations with weak attentional modulations of irregular neuronal spiking. Such constraint might be important in evaluating the functional impact of attentional synchronization on cortical processing.

Modulations of both synchrony and firing rate characterize attentional selection. It is not clear how these two types of attentional modulations are related. On the one hand, they can represent independent mechanisms by which information processing is enhanced by attention. For instance, irrespective of rate modulations gamma-range synchronization could facilitate information transmission between neuronal groups selectively (Womelsdorf and Fries, 2007; Fries, 2009), it could enhance the impact of neural activity on downstream targets (Salinas and Sejnowski, 2001) (see also supplemental Fig. 7, available at www.jneurosci.org as supplemental material), or it could reduce the latencies of neural and behavioral responses (Womelsdorf et al., 2006; Buehlmann and Deco, 2008) (but see supplemental Fig. 4, available at www.jneurosci.org as supplemental material). Alternatively, rhythmic activity and rate modulations could be causally-related concomitant effects of attention. Thus, rate increases might entail concomitant synchronization enhancement, or the enhancement of rhythmic firing might cause biased competition rate modulations (Börgers et al., 2005, 2008; Tiesinga et al., 2004; Mishra et al., 2006). Along this line, we find that inter-areal synchronization contributes at most a small fraction of firing rate modulations in extrastriate cortex. From this point of view, synchronization is just an energy-efficient substitute of rate increases in top-down afferent neurons (Fig. 7B,C). Because inter-areal synchronization not only modulates modestly firing rates, but it makes those rates more able to drive downstream neurons, our model shows that inter-areal synchronization incrementally helps in routing communication along behaviorally relevant neural populations (Womelsdorf and Fries, 2007), through the incremental added effects of modest rate increases and enhanced downstream impact. Such a role of synchronization is however only secondary to the primary role of afferent rate changes. However, we also found that the coherence between activity in distant areas encoded selectively and robustly the detection of the attended item (Fig. 5). Thus, an appropriate mechanism for the read-out of inter-areal gamma-range coherence would extract a robust detection signal that is masked in the weak attentional rate effects of area MT. Further research should address whether such read-out mechanism exists and whether this may be the primary functional role of inter-areal synchronization in selective attention.

Supplementary Material

Supp1

Acknowledgements

We are thankful to Stefan Treue for fruitful discussions and to Jorge Ejarque for technical support in efficiently implementing the search optimization procedure in a grid cluster computing system. Also, we thankfully acknowledge the computer resources and assistance from the Barcelona Supercomputing Center-Centro Nacional de Supercomputación, Spain. This work was funded by the Volkswagen Foundation, the Spanish Ministry of Science and Innovation and the European Regional Development Fund. A.C. is supported by the Researcher Stabilization Program of the Health Department of the Generalitat de Catalunya. X.-J.W. is supported by the NIH grant 2R01MH062349 and the Kavli Foundation.

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