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. Author manuscript; available in PMC: 2013 Jul 1.
Published in final edited form as: Eur J Neurosci. 2012 Jul;36(2):2146–2155. doi: 10.1111/j.1460-9568.2012.08071.x

Dopamine and Gamma Band Synchrony in Schizophrenia: Insights from Computational and Empirical Studies

Kübra Kömek 1,2, Bard G Ermentrout 2,3, Christopher P Walker 2,4, Raymond Y Cho 2,4,5
PMCID: PMC3697121  NIHMSID: NIHMS474693  PMID: 22805060

Abstract

Dopamine modulates cortical circuit activity, in part, through its actions on GABAergic interneurons, including increasing the excitability of fast-spiking interneurons. Though such effects have been demonstrated in single cells, there are no studies that examine how such mechanisms may lead to the effects of dopamine at a neural network level. With this motivation, we investigated the effects of dopamine on synchronization in a simulated neural network, composed of excitatory and fast-spiking inhibitory Wang-Buzsaki neurons. The effects of dopamine were implemented through varying leak K+ conductance of the fast-spiking interneurons and the network synchronization within gamma band (~40 Hz) was analyzed. Parametrically varying the leak K+ conductance revealed an inverted-U shaped relationship, with low gamma band power at both low and high conductance levels, and optimal synchronization at intermediate conductance levels. We also examined the effects of modulating excitability of the inhibitory neurons more generically using an idealized model with theta neurons, with similar findings. Moreover, such relationship holds both when the external input is tonic vs. periodic. Our computational results mirror our empirical study of dopamine modulation in schizophrenia and healthy controls, which showed that amphetamine administration increased gamma power in patients but decreased it in controls. Together, our computational and empirical investigations indicate that dopamine can modulate cortical gamma band synchrony in an inverted-U fashion, and that the physiologic effects of dopamine on single fast-spiking interneurons can give rise to such non-monotonic effects at the network level.

Keywords: dopamine, schizophrenia, computational modeling, gamma band synchrony, auditory steady state response

Introduction

Cortical activity operates optimally within a limited range of dopamine (DA) transmission. Accumulating behavioral and physiological studies provide convergent evidence for this relationship, usually described as an inverted-U shape (Williams & Castner, 2006; see Fig. 1a) with poorer performance at the extremes in DA levels, e.g., arising from conditions such as aging and schizophrenia (low DA; left side of the curve) and acute stress (high DA; right side). However, despite good support for this inverted-U relationship, the exact mechanisms by which DA exerts such effects on cortical activity remain unclear.

FIG. 1.

FIG. 1

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(a) The inverted-U shaped relationship between dopamine levels and cortical function. This model assumes that under normal conditions, there is a reasonable range of dopamine concentration over which cortical neurons can operate efficiently. At the center of this range is an optimum level of dopamine leading to maximal performance. The model demonstrates lower cortical function for the extreme levels of DA; schizophrenia as an example of low DA on the left side of the curve and acute stress as an example of high DA shown on the right side of the curve. (b) Schematic diagram of the network architecture used for the Wang-Buzsaki neuron simulations. An arrow means that the connection is excitatory and a filled circle means that it is inhibitory. Connectivity between all the neurons in the network is all-to-all. (c) State diagram for the theta neuron. The filled circles represent critical points achieved by the model—rest and threshold.

One possible mechanism through which DA mediates its effects may be cortical oscillations, which are found in association with various perceptual and cognitive processes. Synchronization in the gamma-frequency range (30–80 Hz) has been associated with a wide range of processes including working memory (Tallon-Baudry et al., 1999), perceptual feature binding (Singer & Gray, 1995), attentional selection (Fries et al., 2001), associative learning (Miltner et al., 1999), simple sensory stimulation (Gray et al., 1989), as well as with higher order processes such as cognitive control, which is disturbed in individuals with schizophrenia in association with gamma oscillation disturbances (Cho et al., 2006). Initial studies in animals (Ma & Leung, 2000) and humans (Demiralp et al., 2007) have provided evidence that changes in DA levels can modulate gamma oscillatory activity, suggesting that gamma oscillations can be a useful index of DA’s modulatory effects on cortical activity.

Cortical DA has been shown to modulate the excitability of pyramidal cells via its actions on GABAergic fast-spiking interneurons (Zhou & Hablitz, 1999; Seamans et al., 2001; Kröner et al., 2007) through mechanisms that include suppression of a resting leak K+ current (Gorelova et al., 2002). However, it is unclear how DA’s physiologic effects at the single neuron level could give rise to non-monotonicity at the neural network level in the form of gamma band synchronization. In the current study, we hypothesized that altering the excitability of fast-spiking interneurons could be a mechanism by which DA induces its inverted-U shaped effects on gamma band synchrony in a simulated cortical network. Using a full biophysical model (Wang-Buzsaki model), we analyzed the effects of DA on network synchronization by varying the leak K+ conductance in inhibitory neurons, which revealed a non-monotonic relationship with gamma band synchrony. As this mechanism was just one way of changing interneuronal excitability, we extended this idea to a more general case using an idealized spiking neuron model (theta neuron) in which we more generically varied the excitability, replicating the finding of an inverted-U relationship. Further, in both models, the inverted-U shape held whether inputs to the network were tonic or periodic in nature, mirroring our findings in an empirical study of dopamine modulation in schizophrenia and healthy controls performing a periodic sensory stimulation task, which showed that amphetamine administration increased gamma power in schizophrenia but decreased it in healthy subjects, consistent with patients lying towards the left side of the inverted-U curve while healthy controls lie at the optimum levels of DA transmission.

Methods

Experimental Methods

To conduct an investigation of the effect of dopamine modulation on cortical gamma oscillations, 12 schizophrenia subjects and 12 healthy comparison subjects participated in a double-blind, cross-over, placebo-controlled study of single-dose amphetamine administration. Control subjects were aged 18–40 years, had no Axis I disorder diagnosis by SCID-NP (Spitzer et al., 1990b), no history of severe medical/neurological illnesses, and had no substance abuse (past 1 month) or dependence (past 6 months). For schizophrenia subjects, criteria were identical to controls except: fulfilling DSM-IV criteria for schizophrenia or schizoaffective disorder by patient SCID (Spitzer et al., 1990a) and medical records, being clinically stable (CGI less than or equal to 4 (moderately ill)), and not on benzodiazepines or mood stabilizers. All subjects provided informed consent in accordance with the Institutional Review Board at the University of Pittsburgh. To maintain clinical stability with amphetamine administration, patients were kept on their prescribed antipsychotics (aripiprazole, risperidone, clozapine, ziprasidone, olanzapine). Groups were matched for age (30.3±9.5 vs. 31.4±9.1 years, respectively), parental education (15.2±2.3 vs. 13.9±2.3 years, resp.) and gender (M:F, 7:5 vs. 7:5).

Testing on amphetamine vs. placebo occurred on separate days. Amphetamine was administered by body weight at 0.5 mg/kg, with a two-hour interval before the experimental task to allow adequate absorption (serum amphetamine levels 75±19 ng/ml at 2 hours and 76±7 ng/ml at 6 hours). Subjects performed the steady-state auditory evoked potential task, involving auditory click trains consisting of binaural presentations of 1 ms duration tones repetition frequencies of 40 Hz, 30 Hz, or 20 Hz. To ensure attention to stimuli, click trains were presented as an oddball paradigm. Subjects were asked to respond with a button press for Standard (click train consisting of 1000 Hz tones) vs. an Oddball stimulus (click train consisting of 2000 Hz tones; 10 trials/block). Each trial proceeded as follows: click train (500 ms); delay (200 ms); response interval (to indicate Standard vs. Oddball; 1000 ms); random ITI (0–800 ms). Each repetition frequency was presented in a separate block, with 120 trials/block. Electroencephalographic (EEG) data during task performance were collected on a 128 channel Geodesic Sensor Net (EGI, Eugene OR). Off-line de-noising and averaging will be performed with EEGLAB (Delorm & Makeig, 2004), and wavelet analyses with Brain Vision Analyzer (Brain Products, Munich, Germany). EEG data were acquired at 250 Hz, referenced to Cz and filtered on-line with a 0.1–100 Hz band pass hardware filter. Electrode impedances were kept below 50 kΩ. Epochs were defined as −500 to +1000 ms relative to the stimulus onset. Error trials and epochs containing artifacts were excluded (20 channels with amplitude range exceeding 200 µV within a segment and/or having 60 µV deviations between consecutive samples). Blink and ECG artifacts were removed with ICA based correction methods. Data were then filtered off-line using a 1–100 Hz IIR filter and submitted to final review using the above amplitude and gradient criteria and for 60 Hz line noise, with bad channel data being replaced by interpolation. Data were re-referenced to average reference. Time-frequency analyses were carried out using Brain Vision Analyzer (Brain Products GmbH, Munich, Germany). The data were transformed using complex Morlet wavelet transforms, defined by mo(x)=c·exp(−x2/2)·exp(iω0x), with c=7, using 40 frequency steps spanning 1–60 Hz and baseline corrected to a −350 to −150 ms pre-stimulus interval.

Computational Methods

Wang-Buzsaki model of an excitatory-inhibitory network

We simulated a network composed of 50 excitatory and 20 inhibitory Wang-Buzsaki (Wang & Buzsaki, 1996) cells, a ratio within the range used in the literature in line with physiological data (Fellous et al., 2001; Börgers & Kopell, 2003; Vierling-Claassen et al., 2008), coupled through synapses with an all-to-all connectivity (Fig. 1b). The membrane potentials of each excitatory and inhibitory neuron satisfy the following dynamics:

CdVjedt=−IKLe−INae−IKe−ICa−IAHP−Ijee−Ijei+Iappj(t)ξewje,j=1,..,50 (1)
CdVjidt=−IKLi−INaLi−INai−IKi−Ijii−Ijie+ξiwji,j=1,..,20 (2)

wje and wji are independent white noise processes with magnitudes ξe=1.2, and ξi=1.2.

The synaptic currents are governed by the following:

Ieej=∑k=1Ngeesek(Vej−Vsyne), (3)
Ieij=∑k=1Mgeisik(Vij−Vsyni), (4)
Iiej=∑k=1Ngiesek(Vej−Vsyne), (5)
Iiij=∑k=1Mgiisik(Vij−Vsyni), (6)

with gee=0.05, gei=0.7, gii=0.10, gie=0.6, Vsyne=0mV, and Vsyni=−75mV, where the synaptic gating variables are given by:

dsjedt=αeK(Vje)(1−sje)−βesje, (7)
dsjidt=αiK(Vji)(1−sji)−βisji, (8)

with parameters αe = 1.1, αi = 5, βe = 0.19, βi = 0.1, where K(V)=Tmax/(1+exp(−V−VtVs)) with parameters Vt = 2, Vs = and Tmax = 1 ms.

All the neurons in the system have the same initial conditions for the simulations as follows: V(0) = −64mV, h(0) = 0.78, and n(0) = 0.09.

There is heterogeneous external constant input current given to each excitatory neuron, denoted by Iappj, with a random distribution between 2.0 and 2.5 µA/cm2 in the tonic input model and 1.0 and 1.5 µA/cm2 in the periodic input model. Moreover, in the periodic forcing model both the excitatory and inhibitory cells receive additional periodic currents governed by Ie(t) = Aez(t) and Ii(t) = Aiz(t) with Ae=90 and Ai=50 representing the amplitude of the periodic drive given to the excitatory and inhibitory neurons, respectively. Also, z(t) is a filter function defined by dz/dt = (−z + P(t))/τ, where P(t) is a periodic square pulse of duration of 1 ms and period of 25 ms, with decay time constant τ=20. The fast sodium, INA and delayed rectifier IK currents are the same as in Wang and Buzsaki (1996). INaL = gNaL (V − ENa) with gNaL =0.017 mS/cm2 and IKL = gKL (V − EK) with gKL =0.083 mS/cm2, specifically gKLe=0.12mS/cm2 for the excitatory neurons and gKLi was parametrically varied in the simulations.

In order to account for the observed slower firing rates of the excitatory cells (McCormick et al., 1985), there is spike frequency adaptation added to the excitatory neurons in the simulated network. This is produced mainly by a voltage-independent, Ca2+ -dependent K+ current and is associated with the slow after hyperpolarization after a burst of spikes (Hotson & Prince, 1980; Wang, 1998; Ermentrout & Terman, 2010), instead of using M-type currents mediated by voltage-dependent, high-threshold K+ channels (Brown & Adams, 1980), that could cause complications by converting type 1 cell to type 2. Currents associated with the spike frequency adaptation included in the membrane potentials of the excitatory neurons are ICa and IAHP. The high-threshold calcium current ICa = gCam∞ (V − ECa) with gCa=1 mS/cm2 and ECa=120 mV, where m is replaced by its steady-state m∞(V) = 1/(1+exp(−(V − Vlth) / Vshp)), with Vlth = −25 mV, and Vshp = 5 mV. The voltage-independent calcium-activated potassium current is IAHP = gAHP ([Ca+2]/([Ca+2]+ KD))(V − EK) with gAHP=5 mS/cm2 and KD=30 µM. The intracellular Ca+2 concentration is governed by d[Ca2+]dt=−αICa−[Ca2+]/τCa, where α=0.002 [in µM (msµA)−1cm2] and ιCa=80 ms.

All simulations were performed using XPPAUT 6.10 using the Euler integration method with a time step of 0.01 ms. The network was simulated for 20 seconds and the mean voltage across the excitatory neurons in the network was calculated. These data were divided into 1 second time bins and Fast Fourier Transform (FFT) Analysis was run on the mean voltage in each time bin using MATLAB. In each time bin, FFT analysis was run to search for the frequency corresponding to the peak amplitude in the power spectrum in the tonic input case. Furthermore, in order to account for noise and to smooth the results, an average of the amplitude was calculated corresponding to ±1 Hz of the peak frequency. In the periodic forcing case, mean power corresponding to ±3 Hz of 40 Hz was calculated to specifically analyze the entrainment to the forcing frequency. The same process was repeated for each time bin and an average across the 20 different 1 second time bins was calculated.

Theta Neuron Model

For some of our analysis, we used an idealized spiking neuron model, theta neuron, to examine the dynamics and synchronization in a network of inhibitory and adapting excitatory neurons (Ermentrout & Kopell, 1986). The Wang-Buzsaki neuron model exhibits a saddle-node on an invariant circle (SNIC) bifurcation (Izhikevich, 2007). Therefore, if the system is close to the bifurcation, we can reduce this model to a theta neuron model with adaptation. The theta neuron is a simple, one-dimensional model for the spiking of a neuron that reduces the dimensionality from the Wang-Buzsaki biophysical model while still retaining type 1 dynamics and is able to reproduce behavior such as spiking and refractory period as depicted in Fig. 1c (Gutkin et al., 2003). Although fast-spiking neurons have been shown to be of type 2 excitability (Tateno et al., 2004), our simulations involved type 1 neurons since we used Wang-Buzsaki neurons for the full biophysical model which can be studied as a reduced model using theta neurons of type 1 excitability (c.f. Börgers et al., 2005). Using the reduced model, it is easier to understand the dynamics of the network and much more efficient in simulating larger networks.

We preserve the overall network architecture as in the Wang-Buzsaki model (50 excitatory and 20 inhibitory cells, full connectivity):

θ̇je=1−cosθje+(1+cosθje)(Ie−gzzj−giesi+geese+ξewje) (9)
τzżj=bexp(−bcos(θje−zj−2.5))−zj (10)
θ̇ki=1−cosθki+(1+cosθki)(Ii−giisi+geise+ξiwki) (11)

with parameters Ie=1, gz=0.2, gie=2, gee=0.1, ξe=0.5, τz=50, b=100, gii=0.15, gei=0.4, and ξi=0.02. The synaptic gating variables are given by:

ṡe=−seτe+1N∑j=1Nbexp(−b(1−cos(θje−2.5)),N=50 (12)
ṡi=−siτi+1M∑k=1Mbexp(−b(1−cos(θki−2.5)),M=20 (13)

with parameters τe=1 and τi=3.

Equation (9) describes the evolution of each excitatory neuron with external input Ie in the presence of spike frequency adaptation with strength gz. Each excitatory neuron receives the same external input, Ie, and a noisy component with strength ξe where wje is a white noise process and j=1,..,50. The adaptation current associated with each excitatory neuron j is discretely incremented with each spike and decays with a time constant τz with dynamics following equation (10). The evolution of each inhibitory neuron is shown in equation (11) with external drive Ii, and a white noise component, wki, with strength ξi. Equations (12) and (13) describe the excitatory and inhibitory synapses, respectively with parameter b defining how sharp the curve is when it crosses the synapse, equivalent to Vs in the Wang-Buzsaki model. For simulations with periodic input, we used the same stimuli as in the Wang-Buzsaki model, but altered the following parameters: Ie=0.4, gz=0.5, gie=3, gee=2, ξe=0.5, ξi=0.01 and Ae=70 and Ai=10. Simulation and analysis of the theta model was identical to that of the Wang-Buzsaki model; gamma power was measured by looking at the summed excitatory synaptic conductances.

Results

Experimental observations

The average evoked gamma power was derived for the 40 Hz stimuli over the interval 225–525 ms after stimulus onset. Repeated measures ANOVA with Diagnosis (schizophrenia vs. healthy control) as a between-subject factor and Drug Status (amphetamine vs. PBO) as a within-subject factor revealed a Drug Status X Diagnosis interaction (F=10.2, p<0.005). Post-hoc comparisons revealed that for the PBO condition, schizophrenia patients showed lower gamma power compared to controls (t=2.6, p<.05), consistent with many previous studies (Kwon et al., 1999; Spencer et al., 2008; Vierling-Claassen et al., 2008; Krishnan et al., 2009). However, schizophrenia patients showed increases in gamma power with amphetamine compared to PBO (t=2.3, p<.05), while controls showed decreases in gamma power with amphetamine (t=−2.3, p<.05). This pattern of findings (see Fig. 2) was specific to the 40 Hz stimuli as none of the main effects or interactions were significant for the 20 Hz and 30 Hz stimuli (data not shown) and all post-hoc comparisons were also not significant (all p’s > 0.25).

FIG. 2.

FIG. 2

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Time frequency plots of gamma power for healthy control and schizophrenia subjects for 40 Hz stimuli. Ordinate is frequency (0–60 Hz) and abscissa is time (−500 to 1000 ms with respect to stimulus onset. Controls have lower response with AMPH (amphetamine) vs. Placebo while patients show enhancement with AMPH vs. Placebo.

Tonic Input Models

Effects of leak K+ current in the biophysical model

To examine the effects of leak K+ conductance of the inhibitory neurons (gKLi) on the network synchronization, we simulated a biophysical model composed of Wang-Buzsaki neurons and looked at how gamma power varied with respect to varying gKLi levels. Fig. 3 shows the results for the peak power and corresponding frequency obtained from simulations with two parameter variations, gie and gKLi. Although the effects of gKLi were the focus of this work, initially we parametrically varied gie also as another important determinant of inhibitory neuron activation to provide additional insights regarding the dynamic range for network activity. For instance, the network activity remained very low in terms of gamma power at low values of gie (e.g., gie = 0.1, 0.2, and 0.3). Conversely, very high gie values lead to consistently high network gamma power regardless of variations in gKLi values (gie =0.9, 1.0). Midrange values of gie better reveal the effects of gKLi on network synchronization, where it can be seen that there is a non-monotonic relationship between gKLi and network gamma power (Fig. 3a). Such a relationship, usually described as an inverted-U shape, is most clearly visible for gie values such as 0.6 and 0.7. Although gamma power increases with increasing gKLi levels initially, after a peak power value, it decreases with further increases in gKLi. As depicted in the Figure 3b, there is also good stability in the peak network frequency, which remains within the gamma band range with slight fluctuations.

FIG. 3.

FIG. 3

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Effects of varying the synaptic coupling strength from excitatory to inhibitory cells (gie) and the leak K+ conductance of inhibitory cells (gKLi) on the Wang-Buzsaki network synchronization. (a) The dependence of peak power on the parameters. (b) Peak frequency (in Hz) corresponding to the power values shown in (a).

Also of note is that network gamma power appears to also display a non-monotonic relationship with gie. For values of gKLi such as 0.13 or 0.17, there is an optimum gie that gives rise to a peak in gamma power, with changes in gie in either direction leading to decreases in power. This highlights the fact that modulating other determinants of interneuron excitability may also give rise to non-monotonic relationships in network level gamma synchrony.

Changes in gamma band synchrony in the idealized model

The key role leak K+ conductance plays in the detailed biophysical model is to modulate the excitability of the inhibitory neurons. High values of gKL increase the amount of K+ efflux, repolarizing the neuron, hence decreasing the excitability of the inhibitory neurons, whereas low values of gKL lead to increased excitability through the reverse mechanism. Therefore, the frequency output of a single Wang-Buzsaki neuron with respect to a fixed external drive increases as gKL decreases (Fig. 4). With this motivation in mind, an idealized model based on theta neuron was formulated to generalize the effects of varying gKL to a broader concept. With the network formulation, this model had varying levels of external drive to the inhibitory neurons in order to replicate the effects of varying gKLi in the full biophysical model by modulating the excitability of the inhibitory neurons in the network. However, the drive to the excitatory neurons was kept constant (Ie=1). The power spectrum obtained from FFT analysis for the peak power and corresponding frequency is shown in Fig. 5. Similar to the full biophysical model, here is also another non-monotonic relationship in the form of an inverted-U shape between the power and the drive to the inhibitory cells (Fig. 5a) corresponding to gamma band frequency range (Fig. 5b). Raster plots corresponding to three different Ii values on the curve depict how excitability and resulting firing patterns vary depending on the levels of external input (Fig. 5c–e). Low levels of drive (Ii=−0.13) fail to provide enough drive to excite the inhibitory cells and resulting low activity in the inhibitory cells cannot provide the necessary inhibition for the excitatory cells to synchronize, hence leading to low gamma power (Fig. 5c). However, increasing the external drive leads to optimum excitability of the inhibitory cells (Ii=0), thus providing the necessary inhibition for the excitatory cells to synchronize perfectly (Fig. 5d). Further increased drive (Ii=0.14) leads to inhibitory cells that are too excitable and fire spontaneously at high rates and, suppress the excitatory cells. The suppressed excitatory activity leads to low gamma power in the pool of excitatory neurons (Fig. 5e). These results suggest that any type 1 neuron model can be used to replicate the same findings as in the full biophysical model (Ermentrout, 1996). Such reduced neuron models provide computation efficiency and allow for further mathematical analysis that we plan on doing following this study.

FIG. 4.

FIG. 4

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Firing rate – current (f-I) dependence on the leak K+ conductance (gKL) of a single Wang-Buzsaki neuron. The effects of varying gKL of a single Wang-Buzsaki neuron were analyzed and depicted here with colored plots representing the f-I curves associated with various values of gKL.

FIG. 5.

FIG. 5

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The effects of varying drives to the inhibitory cells (Ii) in the theta neuron model with tonic input. (a) Peak power obtained for varying drives to the inhibitory cells and (b) the corresponding frequencies. The raster plots for points on the curve corresponding to (c) left side of the curve where Ii=−0.13, (d) optimum level with a peak in gamma power Ii=0, and (e) right side of the curve with Ii=0.14.

Effects of DA modulation of cortical entrainment to a periodic auditory stimulus

The entrainment of both networks to periodic stimuli and how such entrainment varied with respect to varying levels of excitability of the inhibitory cells was addressed by adding periodic forcing at 40 Hz to both networks. Results from Wang-Buzsaki model are represented in Fig. 6a and continue to preserve the non-monotonicity in the form of an inverted-U shape, with the associated raster plots corresponding to three different gKLi values on the curve. Network activity prior to the onset of the periodic stimuli are also demonstrated in the raster plots (t=0–150 ms), where it can be seen that the network maintains a low activity state at the baseline. High gKLi levels (gKLi=0.30), corresponding to low DA levels, lead to poor excitability of the inhibitory cells and low 40-Hz power due to lack of sufficient temporal organization in the excitatory network (Fig. 6b). On the other hand, low gKLi levels—high DA— (gKLi=0.11), lead to too much activity in the inhibitory pool, leading to too much suppression in the excitatory pool and low 40-Hz power due to low activity levels (Fig. 6d). In between those two extremes lies an optimum range for gKLi,(gKLi=0.19), where excitatory cells fire in perfect synchrony, leading to high 40-Hz power (Fig. 6c).

FIG. 6.

FIG. 6

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The network activity in the Wang-Buzsaki model with periodic forcing at gamma frequency (40 Hz). (a) Gamma power plotted as a function of the leak K+ conductance of the inhibitory cells (gKLi) in the Wang-Buzsaki network. The raster plots depict the network behavior at baseline (t=0–150 ms) and periodic stimulus comes on at t=150 ms The raster plots for points on the curve corresponding to (b) left side of the curve where gKLi=0.30, (c) optimum level with a peak in gamma power gKLi=0.19, and (d) right side of the curve with gKLi=0.11.

Results from the theta neuron network with periodic forcing and varying Ii levels are shown in Fig. 7, where the same non-monotonicity with 40-Hz power holds. Increases in the parameter Ii are associated with increases in DA levels and similar to the full biophysical model, low Ii (DA) levels (Ii=−1.32) lead to low 40-Hz power due to lack of enough inhibition necessary for synchrony in the excitatory pool (Fig. 7b) and high Ii (DA) levels (Ii=0) lead to low 40-Hz power due to too much suppression in the excitatory pool (Fig. 7d). Optimum levels (Ii=−0.45) lead to perfect synchrony in entrainment to the periodic stimuli (Fig. 7c).

FIG. 7.

FIG. 7

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The network activity in the theta neuron model with periodic forcing at gamma frequency (40 Hz). (a) Gamma power plotted as a function of the drive to the inhibitory cells (Ii). The raster plots depict the network behavior at baseline (t=0–150 ms) and periodic stimulus comes on at t=150 ms The raster plots for points on the curve corresponding to (b) left side of the curve where Ii=−1.32, (c) optimum level with a peak in gamma power Ii=−0.45, and (d) right side of the curve with Ii=0.

Discussion

In the current study, we found that increasing the excitability of fast-spiking interneurons could give rise to an inverted-U shaped relationship with synchrony, consistent with that between DA and cortical activity. Implementing DA’s effects on single neurons as a suppression of the leak K+ current, simulations using a full biophysical model composed of Wang-Buzsaki neurons with a tonic drive revealed an inverted-U shaped relationship with network gamma power as an index of cortical activity. Similarly, we replicated these findings in an idealized model composed of theta neurons with varying degrees of drive to the inhibitory neurons, showing the generalizability of the excitability of the inhibitory neurons as a potential mechanism for modulation of network synchrony. In a computational paper, van Vreeswisk et al. (1994) showed that inhibition often rather than excitation synchronizes firing, emphasizing the importance of interneurons in synchronization, and our results provide further evidence for the importance of interneuron activity for synchronization. Furthermore, simulations using identical network architectures but with periodic forcing showed a similar inverted-U shaped relationship of network gamma power as interneuron excitability was varied. These computational investigations provide a possible mechanistic account of the findings of our empirical study of dopamine modulation neural synchrony, which showed that amphetamine administration increased gamma synchrony in schizophrenia patients but decreased it in controls, consistent with patients residing on the left-hand side of the inverted-U curve with controls lying at more optimal, mid-range levels of DA transmission.

The direct link between DA and working memory was illustrated first by Brozoski and colleagues (1979), who showed that following lesions of the dorsolateral prefrontal cortex (DLPFC) of nonhuman primates via 6-hydroxdopamine administration, delay-dependent impairments in working memory were observed. Following this seminal work, other studies have shown that dopamine’s effects on working memory are mediated specifically by D1 receptors in the DLPFC (Sawaguchi & Goldman-Rakic, 1991, 1994). In schizophrenia, disturbances in dopamine projections (Akil et al., 1999) and D1 receptor physiology (Okubo et al., 1997; Abi-Dargham et al., 2002) and amelioration of cognitive deficits by amphetamine administration (Daniel et al., 1991; Goldberg et al., 1991; Goldman-Rakic et al., 2004; Barch & Carter, 2005) are consistent with reduced DA transmission contributing to working memory deficits in the illness. On the other hand, acute stress, which has been shown to increase prefrontal DA levels beyond the optimum range, in part through D1 receptor mechanisms (Arnsten & Goldman-Rakic, 1998; Hutson et al., 2004), also leads to poor cognitive performance as observed in working memory tests. Together, these findings imply an inverted-U shaped relationship between the strength of DA transmission and working memory function (Fig. 1; Williams & Castner, 2006).

Studies of the role of gamma band synchrony in working memory suggest a mechanism by which DA could affect cortical function. Gamma oscillations increase parametrically with working memory load (Howard et al., 2003) and impaired working memory in schizophrenia is associated with impaired gamma oscillatory activity (Haenschel et al., 2009). DA could have a direct role in such network oscillations through its effects on fast-spiking interneurons, cells which are critical to the dynamics of gamma oscillations in terms of generating them both in hippocampus and neocortex (Bartos et al., 2007). Gorelova and colleagues (2002) found that DA suppressed a voltage-independent leak K+ current via D1/D5 receptors in fast-spiking interneurons thus providing a potential mechanism by which network level synchrony could be modulated. In our simulations we manipulated the leak K+ conductance levels of the inhibitory neurons, with low leak K+ conductance representing high DA levels and vice versa, and both of those extremes lead to low gamma power. However, another important finding from Gorelova et al. (2002) was the suppression of a Cs+-sensitive inward rectifier K+ current by DA. While these two currents differ considerably in terms of their contributions to the membrane potential due to their different voltage-dependence properties (North, 2000), they both modulate the excitability of the fast-spiking interneurons. This motivated our extension to the broader framework of the theta neuron model, which more generically implemented interneuron excitability through varying external drive levels and reproduced qualitatively similar findings to the biophysical model. In both model simulations, increasing inhibitory neuron excitability improved network gamma synchrony, but only to a point, after which inhibition from interneurons played less of a role in regulating the timing of excitatory neuron firing, and increasingly suppressed excitatory cell firing altogether thereby decreasing network gamma oscillations. Thus, our computational simulation findings show that DA’s apparently simple modulation of interneuron excitability at the single cell level can have qualitatively different effects at the network level depending on the specific degree of induced excitability, helping to detail a plausible mechanism by which DA leads to the inverted-U shaped relationship with cortical activity.

As an empirical test of the putative role of DA in cortical gamma oscillations, we studied amphetamine’s effects on auditory cortical oscillations with findings that were broadly consistent with the inverted-U relationship. Perceptual deficits in the auditory domain have been shown in schizophrenia across various behavioral measures involving tone matching (Strous et al., 1995), temporal discrimination (Todd et al., 2003), and pitch discrimination (Leitman et al., 2010). One useful approach for characterizing the neurophysiological basis of auditory cortical deficits has been the utilization of steady state responses of the EEG in response to external stimuli, allowing testing of the functional state of the networks subserving neuronal synchrony (Lins & Picton, 1995). Individuals with schizophrenia show deficits in entraining to external auditory stimuli in the gamma frequency range, particularly at 40 Hz (Kwon et al., 1999; Brenner et al., 2003; Spencer et al., 2008; Krishnan et al., 2009;). Employing the auditory steady state paradigm in the current study, we hypothesized that administration of amphetamine, which increases DA levels by facilitating release and inhibiting reuptake, would improve gamma range auditory entrainment in schizophrenia patients and produce minimal change or decrease it for healthy controls. Our experimental findings were consistent with this hypothesis, with increases in gamma oscillations in patients interpretable as having a low baseline cortical dopamine state that was increased by amphetamine. In contrast, decreases in gamma oscillations for controls could be understood in terms of having already optimal dopamine levels at baseline, with amphetamine inducing an excess of dopamine that decreased gamma power.

Our empirical findings from a task paradigm that involved cortical steady state responses to periodic auditory stimuli motivated extensions of our simulation work with tonic inputs to the case of periodic forcing. We found that a similar inverted-U shaped relationship could be obtained by varying inhibitory neuron leak K+ conductance in the Wang-Buzsaki model and by varying the external drive applied to the inhibitory neurons in the theta model, indicating that DA’s modulation of interneuron excitability could give rise to the observed effects on network level synchrony for different types of cortical inputs that vary in their temporal structure.

Our mechanistic account of the non-monotonic relationship between DA and cortical function could have important implications for understanding the pathophysiology of various clinical disorders such as schizophrenia and inform novel therapeutic development. In our experimental study, we employed amphetamine in order to increase DA but as it does so in a nonspecific manner, it would be inappropriate for clinical use due to its propensity to induce psychosis through D2 receptor stimulation. However, since DA’s increasing of fast-spiking neuron excitability is D1 receptor mediated (Gorelova et al., 2002), a specific D1 agonist could help to ameliorate disturbances in cortical gamma oscillations without precipitating psychotic symptoms of the illness. Further, in addition to helping to correct any hypodopaminergic states, a D1 agonist could have beneficial effects on other types of neurotransmission disturbances thought to be important to the pathophysiology of schizophrenia such as in GABA (Gonzalez-Burgos & Lewis, 2008) and NMDA (Kantrowitz & Javitt, 2010) transmission. Since D1 agonists increase the excitability of fast-spiking interneurons, disturbances in GABA transmission could possibly be addressed through D1 stimulation even if the primary deficit was not in DA itself. Vierling-Claassen and colleagues (2008) conducted a computational study of gamma oscillatory disturbances in schizophrenia, modeling reductions in GAT-1 (GABA reuptake transporter) in schizophrenia as an increase in the time constant for the decay of inhibition. While it is not clear that acute DA increases could ameliorate such disturbances, increases in interneuron excitability could improve GABA neurotransmission, which, over time, may correct the reductions in GAT-1, which presumably first arose as a compensatory mechanism for reductions in GABA. Other computational studies have shown that NMDA glutamatergic transmission is important for sustaining gamma oscillations over a delay period (Compte et al., 2000) and can be positively modulated by D1 stimulation (Brunel & Wang, 2001), thus providing a potential alternate pathway by which DA agonists could help to correct impaired cortical oscillations in schizophrenia. Future computational studies will investigate more systematically the potential for dopamine-based mechanisms to correct disturbances in cortical oscillations due to other neurotransmitter systems in schizophrenia. We also plan to study the specificity of the computational mechanisms investigated here to oscillatory disturbances in the gamma band vs. those reported for other frequency bands in the illness. Finally, in a follow-up paper to their prior work, Vierling-Claassen and Kopell (2009) developed methods for analyzing locking patterns in a simple forced theta neuron network. Using our reduced theta model, future work will apply similar methods with a focus on the effects of varying the excitability of the inhibitory neurons.

Acknowledgements

We would like to thank Nicola Riccardo Polizzotto for insightful discussions regarding the manuscript. K.K. is supported by R.K. Mellon Foundation; G.B.E. is supported by NSF DMS 0817131; C.P.W. is supported by K08 MH080329 and P50 MH084053; R.Y.C. is supported by K08 MH080329, P50 MH084053 and NARSAD.

Abbreviations

DA

dopamine

EEG

electroencephalogram

DLPFC

dorsolateral prefrontal cortex

FFT

fast Fourier transform

GABA

gamma amino acid butyric acid

PFC

prefrontal cortex

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