Abstract

Experience-dependent synaptic plasticity characterizes the adaptable brain and is believed to be the cellular substrate for perceptual learning. A chemical agent such as gamma-aminobutyric acid (GABA) is known to affect synaptic alteration, perhaps gating perceptual learning. We examined whether and how ambient (extrasynaptic) GABA affects experience-dependent synaptic alteration. A cortical neural network model was simulated. Transporters on GABAergic interneurons regulate ambient GABA levels around their axonal target neurons by removing GABA from (forward transport) or releasing it into (reverse transport) the extracellular space. The ambient GABA provides neurons with tonic inhibitory currents by activating extrasynaptic GABAa receptors. During repeated exposures to the same stimulus, we modified the synaptic connection strength between principal cells in a spike-timing-dependent manner. This modulated the activity of GABAergic interneurons, and reduced or augmented ambient GABA concentration. Reduction in ambient GABA concentration led to slight depolarization (less than several millivolts) in ongoing-spontaneous membrane potential. This was a subthreshold neuronal behavior because ongoing-spontaneous spiking activity remained almost unchanged. The ongoing-spontaneous subthreshold depolarization improved a suprathreshold neuronal response. If the stimulus was long absent for perceptual learning, augmentation of ambient GABA concentration took place and the ongoing-spontaneous subthreshold depolarization was depressed. We suggest that a perceptual memory trace could be left in neuronal circuitry as an ongoing-spontaneous subthreshold membrane depolarization, which would allow that memory to be accessed easily afterward, whereas a trace of a memory that has not recently been retrieved fades away when the ongoing-spontaneous subthreshold membrane depolarization built by previous perceptual learning is depressed. This would lead that memory to be accessed with some difficulty. In the brain, ambient GABA, whose level could be regulated by transporter may have an important role in leaving memory trace for perceptual learning.

1.  Introduction

Perceptual learning refers to our ability to improve cognitive performance as we experience the same stimulus repeatedly and has been evidenced in various sensory systems such as vision, audition, and somatosensation (Goldstone, 1998; Fahle, 2005). Experience-dependent synaptic plasticity characterizes the adaptable brain and is believed to be the cellular substrate for perceptual learning. Synaptic plasticity is evident not only at developmental (as in infants) but also at matured (as in adults) stages, between which there is a striking difference: in infants, extensive refinement in neuronal circuitry might be required as they grow, whereas in adults, the plasticity should be restricted unless severe damage caused by lesions requires drastic cellular remodeling.

It is well known that chemical agents such as gamma-aminobutyric acid (GABA), N-methyl-D-aspartate (NMDA), and acetylcholine affect synaptic alteration (Fahle, 2005). Among them, GABA has a crucial role. Dinse, Ragert, Pleger, Schwenkreis, and Tegenthoff (2003) tried to induce perceptual learning in human subjects by activating the skin of the right index finger with a pair of needles. A small distance that ranged from 0.7 to 2.5 mm separated the needles. The subject had to decide if he or she had the sensation of one or two tips of needles. Perceptual learning improved the tactile 2-point discrimination: the subject was able to detect smaller distances. The perceptual augmentation was completely eliminated if lorazepam, a GABAa receptor agonist was applied. This result indicates that GABA could modulate experience-dependent synaptic plasticity, thereby perhaps gating perceptual learning.

GABA, the major inhibitory neurotransmitter, mediates so-called phasic inhibition by activating intrasynaptic GABAa receptors (those in the synaptic cleft). Recently another type of GABA-mediated inhibition, tonic inhibition, has been recognized (Semyanov, Walker, Kullmann, & Silver, 2004; Farrant & Nusser, 2005; Ortinski et al., 2006), in which GABA in extracellular space activates GABAa receptors located on membranes outside synapses. GABA in extracellular space and GABAa receptor on extrasynaptic membrane regions are referred to as ambient GABA and extrasynaptic GABAa receptor, respectively. Extrasynaptic GABAa receptor has been found mostly in the cerebellum (Somogyi, Takagi, Richards, & Mohler, 1989; Nusser, Roberts, Baude, Richards, & Somogyi, 1995; Brickley, Cull-Candy, & Farrant, 1996; Soltesz & Nusser, 2001), and recent studies have identified it in the cortex as well (Drasbek & Jensen, 2006; Scimemi et al., 2006).

Concerning the regulation of ambient GABA levels, Richerson and colleagues (Wu, Wang, & Richerson, 2001; Richerson & Wu, 2003; Richerson, 2004; Wu, Wang, Diez-Sampedro, & Richerson, 2007) have made an interesting suggestion. A transporter such as GAT-1, located on the axon terminal of GABAergic interneuron, is crucial not only for removing GABA from but also for releasing it into the extracellular space. The transporter can clamp ambient GABA at a certain level (within a submicromolar range at rest) and is near equilibrium under normal physiological conditions and will reverse with a relatively small increase in membrane potential. The researchers demonstrated that the GABAergic transmission was prevented not by blocking vesicular GABA release but by GABA transporter antagonists.

Giovannini and colleagues (Giovannini et al., 2001; Bianchi et al., 2003) demonstrated that the level of ambient GABA in the brain varied (more than threefold) during repeated exposures to the same environment. Augmentation of ambient GABA levels in the prefrontal cortex (Giovannini et al., 2001) was greater during the second exposure than during the first exposure. Interestingly, at the second exposure trial, subjects (freely moving rats) became familiar with that environment. These studies led us to speculate that ambient GABA might have an important role in perceptual learning.

The purpose of this study is to examine whether and how ambient GABA modulates experience-dependent synaptic plasticity. We simulate a cortical neural network model. In the model, two types of GABAergic interneurons (Ia and Ib) are assumed, which project to Ib and principal cells, respectively. Transporters on the axon terminals of Ia and Ib cells regulate ambient GABA levels around their target (Ib and principal) cells. During repeated exposures to the same stimulus, the synaptic connection strength between principal cells is modified in a spike-timing-dependent manner. Statistically analyzing neuronal activities (membrane potentials and spikes), we try to elucidate how ambient GABA affects perceptual learning.

2.  Neural Network Model

2.1.  Neuronal Circuitry.

A neural network model of a primary sensory cortical area is shown in Figure 1A. The network consists of eight cell assemblies. Twenty cell units, each of which contains one principal cell (P) and two GABAergic interneurons (Ia, Ib) (see the gray circle), constitute a cell assembly. Each cell assembly has responsiveness to a specific sensory feature fn(0⩽nM). The neural network model might correspond functionally to the primary visual (V1), auditory (A1), or somatosensory (S1) cortex, which could be modified by perceptual learning (Gilbert, 1994; Buonomano & Merzenich, 1998). These cortices form cell assemblies known as feature columns (Mountcastle, 1997). V1 columns are tuned to the orientation of a bar, A1 columns to the frequency of a sound, and S1 columns to the somatosensation of a body surface. A recent study (Sale et al., 2011) clearly demonstrated that perceptual learning accompanies long-term potentiation (LTP) at processing stages as early as primary sensory cortices.

Figure 1:

Neural network model. (A) Neuronal circuitry. Cell assemblies (k; k = 0, 1, …, n’, …, n, …, M) consist of cell units (see the gray circle). P, Ia, and Ib denote a principal cell and GABAergic interneurons, respectively. fn denotes a feature stimulus that is applied to the P cells belonging to cell assembly n. (B) Assay for measuring GABA transport (see the inset). A GABAergic interneuron Ib has a synaptic contact with a P cell. Ambient GABA concentration around the P cell (top trace) was measured. The GABA-mediated current into (second trace) and the membrane potential of (third trace) the P cell were recorded. The Ib was hyperpolarized to −72 mV and then depolarized to −68 and −66 mV from the resting potential (−70 mV) (bottom trace).

Figure 1:

Neural network model. (A) Neuronal circuitry. Cell assemblies (k; k = 0, 1, …, n’, …, n, …, M) consist of cell units (see the gray circle). P, Ia, and Ib denote a principal cell and GABAergic interneurons, respectively. fn denotes a feature stimulus that is applied to the P cells belonging to cell assembly n. (B) Assay for measuring GABA transport (see the inset). A GABAergic interneuron Ib has a synaptic contact with a P cell. Ambient GABA concentration around the P cell (top trace) was measured. The GABA-mediated current into (second trace) and the membrane potential of (third trace) the P cell were recorded. The Ib was hyperpolarized to −72 mV and then depolarized to −68 and −66 mV from the resting potential (−70 mV) (bottom trace).

Within cell assemblies, P cells are recurrently connected by excitatory synapses. A Ia cell receives an excitatory projection from a P cell and sends an inhibitory projection to a Ib cell. A Ib cell receives excitatory projections from P cells belonging to other cell assemblies (n′) and sends inhibitory projections to a P cell belonging to the same assembly (nn′). Each P cell belonging to cell assembly n receives a constant excitatory current as an input when the network is presented with feature fn. For these cell assemblies to work effectively as feature columns, we assumed that the Ia cell has a role in hyperpolarizing Ib cells, thereby removing GABA from the extracellular space (see section 2.2) and thus increasing the gain of P cells. The Ib cell has a role in suppressing stimulus-irrelevant P cells while stimulus-relevant P cells are being active, thereby improving the tuning performance of the network. Namely, it is a conventional lateral inhibitory cell.

It is well known that the cortex contains diverse types of GABAergic interneurons—for example, bitufted, Maritinotti, basket, small basket, and nest basket cells reported by Gupta, Wang, and Markram (2000). The researchers made multiple neuron recordings and revealed a large number of interneuron connections. It was suggested that GABAergic synapses could shape the impact of different interneurons according to their specific spatiotemporal patterns of activity and that such cortical GABAergic interneuron diversity might enable combinatorial inhibition in the cortex. In our study, we assume Ia-to-Ib GABAergic innervation. Although the proposed neuronal circuitry has been made based on some physiological evidence as addressed above, it is a hypothetical model aimed at elucidating possible roles of ambient GABA in perceptual learning.

Based on previous modeling studies (Tuckwell, 1988; Destexhe, Mainen, & Sejnowski, 1998; Hoshino, 2006, 2008), we construct a conductance-based, integrate-and-fire neuron model. Parameter values are carefully adjusted in order to achieve an ongoing-spontaneous neuronal state that allows neurons to oscillate at a subthreshold level for action potential generation. This subthreshold neuronal state is known to allow a neural network to respond rapidly and effectively to sensory input (Hoshino, 2006, 2008).

2.2.  GABA Transport System.

To regulate ambient GABA concentration, we employ a GABA transport system proposed in Hoshino (2009). As suggested by Richerson and colleagues (Richerson & Wu, 2003; Wu, Wang, & Richerson, 2003; Richerson, 2004), transporter such as GAT-1 is not simply a vacuum removing GABA from the extracellular space. Instead, it operates in an ion-coupled manner, pursuing an equilibrium point that is determined by the stoichiometry of transporter, the concentration gradients of substrates, and the membrane potential. Under normal physiological conditions, a thermodynamic reaction cycle involves coupled translocation of two Na+ ions, one Cl ion, and one uncharged GABA molecule. The cotransported molecules (2Na+, Cl, GABA) cross the membrane together. The driving force for the coupled transport is the electrochemical potential, which is the sum of the electropotential and the chemical potential.

The reversal potential of transporter is the equilibrium membrane voltage at which the value of electrochemical potential is equal to 0. Under normal conditions, the reversal potential is close to the resting potential of neurons. At membrane potentials below the reversal potential, net influx of GABA, called forward transport or GABA uptake, takes place. If membrane potentials are above the reversal potential, a net efflux of GABA, called reverse transport or GABA release, takes place.

GABA transporters, located on the axon terminals of Ia and Ib cells, regulate local ambient GABA concentrations around their target Ib and P cells, respectively. Through this transport mechanism, ambient GABA concentration is kept within a submicromolar range during an ongoing-spontaneous neuronal activity time period. Ambient GABA, acting on extrasynaptic GABAa receptors, provides P, Ia, and Ib cells with tonic inhibitory currents (Hoshino, 2009). The assumption that the reversal potential is close to the resting potential is discussed in section 4. A model definition is given in appendixes  A to  C, whose parameters and their values are listed in Table 1.

2.3.  Synaptic Alteration.

During a sensory input period, perceptual learning takes place. The synaptic strength between P cells (see equation 4.2 in appendix  A) is modified depending on the relative timing between pre- and post-synaptic action potentials (Bi, 2002; Young et al., 2007), which is defined by
formula
2.1
formula
2.2
In these equations, Δt is a time difference between presynaptic (tpre) and postsynaptic (tpost) action potentials. αw, βw, A+, A, τ+, and τ are positive constants, and wP0 is an initial, built-in synaptic strength. Model parameters and their values are listed in Table 1.
Table 1:
List of Parameters and Their Values.
DescriptionParameterValue
Membrane capacitance of type Y (Y = P, Ia, Ib) cell cYm cPm=0.5 nF, cIam=0.2 nF, cIbm=0.6 nF 
Membrane conductance gYm gPm=25 nS, gIam=20 nS, gIbm=15 nS 
Resting potential uYrest uPrest=−65 mV, uIarest=uIbrest=−70 mV 
Maximal conductance for type Z (AMPA, GABA) receptor   
Reversal potential uZrev uAMPArev=0 mV, uGABArev=−80 mV 
Number of cell units within cell assemblies N 20 
Number of cell assemblies M 
Synaptic strength from jth to ith P cell within cell assembly n at time t wP,Pij(n; twP,Pij(n; 0)=wP0(=4.0) 
Synaptic strength from ith Ib to P cell wP,Ibi(n3.0 
Synaptic strength from ith P to Ia cell wIa,Pi(n3.0 
Synaptic strength from jth (cell assembly k) P to ith (cell assembly n) Ib cell (nkwIb,Pij(n, k1.5 
Synaptic strength from ith Ia to Ib cell wIb,Iai(n5.0 
Amount of extrasynaptic GABAa receptors on type Y (Y = P, Ia, Ib) cell δY δPIa=3×103, δIb=6×103 
Intensity of input ϵP 200 pA 
Channel opening rate for type Z (AMPA, GABA) receptor αZ αAMPA=1.1×106, αGABA=5×106 
Channel closure rate βZ βAMPA=190, βGABA=180 
Concentration of glutamate in the synaptic cleft released from P cell GlutPsyn 1 mM 
Concentration of GABA in the synaptic cleft released from type X (Ia, Ib) cell GABAXsyn GABAIasyn=GABAIbsyn=1 mM 
Steepness of sigmoid function for type Y (Y = P, Ia, Ib) cell ηY ηP=220, ηIaIb=180 
Threshold of sigmoid function ζY ζP= ζIaIb=−38 mV 
Decay constant for ambient GABA concentration γtrn 5.0 
Basal ambient GABA concentration [GABA]0ext 0.7μM 
Transfer coefficient of GABA for type X (Ia, Ib) cell TX TIa=TIb=3.5×108 
Maximal ambient GABA concentration GABAmax 5 μM 
Minimal ambient GABA concentration GABAmin 0 μM 
Reversal potential of transporter for type X (Ia, Ib) cell uXrev uIarev=uIbrev=−71 mV 
Synaptic decay rate αw 1×10−5 
Synaptic modification rate βw 0.8 
Basal, built-in synaptic strength wP0 4.0 
Potentiation scale A+ 1.0 
Depression scale A 0.42 
Potentiation time constant τ+ 10 msec 
Depression time constant τ 30 msec 
DescriptionParameterValue
Membrane capacitance of type Y (Y = P, Ia, Ib) cell cYm cPm=0.5 nF, cIam=0.2 nF, cIbm=0.6 nF 
Membrane conductance gYm gPm=25 nS, gIam=20 nS, gIbm=15 nS 
Resting potential uYrest uPrest=−65 mV, uIarest=uIbrest=−70 mV 
Maximal conductance for type Z (AMPA, GABA) receptor   
Reversal potential uZrev uAMPArev=0 mV, uGABArev=−80 mV 
Number of cell units within cell assemblies N 20 
Number of cell assemblies M 
Synaptic strength from jth to ith P cell within cell assembly n at time t wP,Pij(n; twP,Pij(n; 0)=wP0(=4.0) 
Synaptic strength from ith Ib to P cell wP,Ibi(n3.0 
Synaptic strength from ith P to Ia cell wIa,Pi(n3.0 
Synaptic strength from jth (cell assembly k) P to ith (cell assembly n) Ib cell (nkwIb,Pij(n, k1.5 
Synaptic strength from ith Ia to Ib cell wIb,Iai(n5.0 
Amount of extrasynaptic GABAa receptors on type Y (Y = P, Ia, Ib) cell δY δPIa=3×103, δIb=6×103 
Intensity of input ϵP 200 pA 
Channel opening rate for type Z (AMPA, GABA) receptor αZ αAMPA=1.1×106, αGABA=5×106 
Channel closure rate βZ βAMPA=190, βGABA=180 
Concentration of glutamate in the synaptic cleft released from P cell GlutPsyn 1 mM 
Concentration of GABA in the synaptic cleft released from type X (Ia, Ib) cell GABAXsyn GABAIasyn=GABAIbsyn=1 mM 
Steepness of sigmoid function for type Y (Y = P, Ia, Ib) cell ηY ηP=220, ηIaIb=180 
Threshold of sigmoid function ζY ζP= ζIaIb=−38 mV 
Decay constant for ambient GABA concentration γtrn 5.0 
Basal ambient GABA concentration [GABA]0ext 0.7μM 
Transfer coefficient of GABA for type X (Ia, Ib) cell TX TIa=TIb=3.5×108 
Maximal ambient GABA concentration GABAmax 5 μM 
Minimal ambient GABA concentration GABAmin 0 μM 
Reversal potential of transporter for type X (Ia, Ib) cell uXrev uIarev=uIbrev=−71 mV 
Synaptic decay rate αw 1×10−5 
Synaptic modification rate βw 0.8 
Basal, built-in synaptic strength wP0 4.0 
Potentiation scale A+ 1.0 
Depression scale A 0.42 
Potentiation time constant τ+ 10 msec 
Depression time constant τ 30 msec 

3.  Results

3.1.  Regulation of Ambient GABA Concentration by Transporter.

To understand how the transporter regulates a level of ambient GABA (concentration), we carried out a preliminary simulation of a neuronal circuit in which a GABAergic interneuron (e.g., Ib) has a synaptic contact with a principal cell (P) (see the inset of Figure 1B). The transporter on the axon terminal membrane of the Ib cell removes GABA from or releases it into the extracellular space around the P cell (see the arrows). The ambient GABA activates extrasynaptic GABAa receptor and elicits a tonic inhibitory current in the P cell. In the simulation, action potential generation was abolished. This treatment allowed us to clearly see how the transporter modulates ambient GABA concentration and how it influences the dynamic behavior of its axonal target cell.

As shown in Figure 1B, when the Ib cell is hyperpolarized (−72 mV; see the bottom trace), forward transport (i.e., GABA uptake) takes place, and thus ambient GABA concentration is reduced (see the top trace and equation B.4 in appendix  B). The reduction of ambient GABA concentration results in a decrease in tonic inhibitory current (see the second trace), and therefore the P cell depolarizes (see the third trace). If the membrane potential of the Ib cell is equal to the resting potential (−70 mV; see the bottom trace), the forward and reverse transports are balanced, that is, ambient GABA keeps an equilibrium level (see the top trace). Hence, the inhibitory current and the membrane potential are identical to those at rest (see the second and third traces). When the Ib cell is depolarized (−68 or −66 mV; see the bottom trace), reverse transport (GABA release) takes place, and thus ambient GABA concentration is augmented (see the top trace). The augmentation of ambient GABA concentration results in an increase in inhibitory current (see the second trace), thereby hyperpolarizing the P cell (see the third trace). This simulation result is basically consistent with an experimental result (Wu et al., 2007). The researchers used a CHO cell assay for detecting GABA release through GAT-1 reversal, which will be discussed in section 4.

Figure 2:

Responses to repeated stimulation with the same feature. (A) Raster plots of action potentials of P cells. Perceptual learning took place (top) or not (bottom). (B) Ongoing-spontaneous membrane potential of a P2 cell under the condition with (top) or without (bottom) learning. (C) Ongoing-spontaneous membrane potentials in an enlarged scale.

Figure 2:

Responses to repeated stimulation with the same feature. (A) Raster plots of action potentials of P cells. Perceptual learning took place (top) or not (bottom). (B) Ongoing-spontaneous membrane potential of a P2 cell under the condition with (top) or without (bottom) learning. (C) Ongoing-spontaneous membrane potentials in an enlarged scale.

Figure 3:

Subthreshold membrane depolarization by learning. (A) Ongoing-spontaneous membrane potential of a stimulus-relevant P2 cell after the first exposure to feature f2. Perceptual learning took place (top trace) or not (second trace), between which cumulative differences in membrane potential below firing threshold were calculated (bottom traces). (B) Ambient GABA concentration around the stimulus-relevant P2 cell with (top trace) or without (second trace) learning and their cumulative differences (bottom traces).

Figure 3:

Subthreshold membrane depolarization by learning. (A) Ongoing-spontaneous membrane potential of a stimulus-relevant P2 cell after the first exposure to feature f2. Perceptual learning took place (top trace) or not (second trace), between which cumulative differences in membrane potential below firing threshold were calculated (bottom traces). (B) Ambient GABA concentration around the stimulus-relevant P2 cell with (top trace) or without (second trace) learning and their cumulative differences (bottom traces).

3.2.  Subthreshold Membrane Depolarization as Memory Trace.

As shown in Figure 2A, the network was stimulated repeatedly with the same feature (f2) under the condition with (top) or without (bottom) learning (see equations 2.1 and 2.2). The first stimulus (see the left horizontal bar) simultaneously activates, to an equal degree, the corresponding P cells (see P2) in both conditions. We found that the stimulus-evoked activity could be enhanced by learning (see the dashed oval).

We speculated that the experience-dependent synaptic alteration might affect not only stimulus-evoked (suprathreshold) but also ongoing-spontaneous (subthreshold) neuronal activity. To examine it, we recorded the membrane potential of a stimulus-relevant P cell (see Figure 2B), where the synaptic alteration took place (top trace) or not (bottom trace). At first glance, their membrane potentials oscillate in the same manner. However, as shown in Figure 2C, we found a distinct difference in subthreshold membrane oscillation, indicating that the learning slightly depolarizes the stimulus-relevant P cell (see the solid trace). For quantitative evaluations, we calculated a cumulative difference in membrane potential between these conditions (see the top and second traces of Figure 3A). We have confirmed that the stimulus-relevant P cell is depolarized below firing threshold, as indicated by its positive value (see the trace marked by P2 at the bottom of Figure 3A). In contrast, the stimulus-irrelevant P cells tend to be hyperpolarized, as indicated by their negative values (e.g., see the traces marked by P1 and P3).

Figure 4:

Modulation of subthreshold activity of Ib cells by learning. (A) Ongoing-spontaneous membrane potential of a stimulus-relevant Ib2 cell after the first exposure to feature f2 under the condition with (top trace) or without (second trace) learning. Membrane potentials in an enlarged scale (third traces) and their cumulative differences (bottom traces) are shown. (B) Ambient GABA concentration around a stimulus-relevant Ib2 cell with (top trace) or without (second trace) learning, and their cumulative differences (bottom traces).

Figure 4:

Modulation of subthreshold activity of Ib cells by learning. (A) Ongoing-spontaneous membrane potential of a stimulus-relevant Ib2 cell after the first exposure to feature f2 under the condition with (top trace) or without (second trace) learning. Membrane potentials in an enlarged scale (third traces) and their cumulative differences (bottom traces) are shown. (B) Ambient GABA concentration around a stimulus-relevant Ib2 cell with (top trace) or without (second trace) learning, and their cumulative differences (bottom traces).

These simulation results give an interesting notion that a perceptual memory trace could be left in neuronal circuitry as an ongoing-spontaneous subthreshold depolarization. Note that the learning causes only a small change in the ongoing-spontaneous firing rate (see Figure 3A; 1.49 to 1.51 spikes/sec). Nonetheless, as will be shown in Figure 5B, even a single spike is amply sufficient to depolarize an Ia cell below firing threshold and thus to drive its GABA transporter (see equation B.5 in appendix  B).

Figure 5:

Modulation of subthreshold activity of Ia cells by learning. (A) Ongoing-spontaneous membrane potential of a stimulus-relevant Ia2 cell after the first exposure to feature f2 under the condition with (top trace) or without (second trace) learning. Membrane potentials in an enlarged scale (third traces) and their cumulative differences (bottom traces) are shown. (B) Subthreshold activation of an Ia cell by a single action potential from a P cell (see the arrow).

Figure 5:

Modulation of subthreshold activity of Ia cells by learning. (A) Ongoing-spontaneous membrane potential of a stimulus-relevant Ia2 cell after the first exposure to feature f2 under the condition with (top trace) or without (second trace) learning. Membrane potentials in an enlarged scale (third traces) and their cumulative differences (bottom traces) are shown. (B) Subthreshold activation of an Ia cell by a single action potential from a P cell (see the arrow).

Reduction in ambient GABA concentration is crucial for achieving an ongoing-spontaneous subthreshold depolarization. Figure 3B presents the ambient GABA concentration around the stimulus-relevant P cell (P2) under the condition with (top trace) or without (second trace) learning. Their cumulative difference is shown at the bottom. The negative value (see P2) indicates that its ambient GABA concentration is reduced by learning, thereby slightly depolarizing the P cell (see the solid trace in Figure 2C).

Figure 4A presents the membrane potential of a stimulus-relevant Ib cell (Ib2) after the first exposure under the condition with (top trace) or without (second trace) learning, indicating that the Ib cell is hyperpolarized by learning (see the solid trace in an enlarged scale). Their cumulative difference is shown at the bottom (see the trace marked by Ib2). The hyperpolarization of the Ib cell leads to removing GABA (see the inset), thereby reducing the ambient GABA concentration around the stimulus-relevant P cell (see the trace marked by P2 in Figure 3B). Figure 4B presents the ambient GABA concentration around the stimulus-relevant Ib cell under the condition with (top trace) or without (second trace) learning. Their cumulative difference is shown at the bottom. The positive value (see the trace marked by Ib2) indicates that its ambient GABA concentration is augmented by learning, thereby hyperpolarizing the Ib cell (see the trace marked by Ib2 at the bottom of Figure 4A).

Figure 5A presents the membrane potential of a stimulus-relevant Ia cell (Ia2) after the first exposure under the condition with (top trace) or without (second trace) learning. Their cumulative (positive) difference (see the bottom trace marked by Ia2) indicates that the Ia cell tends to be slightly depolarized by learning, thereby releasing GABA (see the inset). This leads to augmenting the ambient GABA concentration around the stimulus-relevant Ib cell (see the trace marked by Ib2 at the bottom of Figure 4B). As shown in Figure 5B, even a single spike from a P cell (see the circle) is sufficient for an Ia cell to depolarize below firing threshold (see the arrow), thereby releasing GABA into the extracellular space around the Ib cell (see Ib2 at the bottom of Figure 4B).

As shown in Figure 6A, the experience of a stimulus (f2) is reflected in the following ongoing-spontaneous subthreshold depolarization (see the solid trace marked by P2 to the left). Interestingly, the experience of that stimulus remains even after the exposure to another stimulus (f5). Its memory trace is evident (see the solid trace marked by P2 to the right), though it declines to a certain level. This result indicates that a perceptual memory that has not recently been retrieved weakens when the ongoing-spontaneous subthreshold depolarization that had been built by the previous learning is depressed. This would lead that memory (f2) to be accessed with some difficulty.

Figure 6:

Subthreshold membrane depolarization as a memory trace for perceptual learning. (A) Different stimuli were successively applied. Cumulative differences in ongoing-spontaneous membrane potential below firing threshold between two conditions (learning and nonlearning) are shown (bottom traces). P2 and P5 denote perceptual memory traces for feature stimuli f2 and f5, respectively. (B) Differences in average ongoing-spontaneous membrane potential of an f2-relevant P cell between these two conditions (learning and nonlearning) as a function of the number of trials. Perceptual learning processes were carried out repeatedly (six trials) for different sensory stimuli, where the first stimulus was f2. The time difference between the trials was 4 seconds. Ongoing-spontaneous membrane potentials were recorded after sensory stimulation during which learning took place or not. Positive and negative values indicate learning-induced membrane depolarization and hyperpolarization, respectively. τ+ denotes STDP time constant (see equation 2.2).

Figure 6:

Subthreshold membrane depolarization as a memory trace for perceptual learning. (A) Different stimuli were successively applied. Cumulative differences in ongoing-spontaneous membrane potential below firing threshold between two conditions (learning and nonlearning) are shown (bottom traces). P2 and P5 denote perceptual memory traces for feature stimuli f2 and f5, respectively. (B) Differences in average ongoing-spontaneous membrane potential of an f2-relevant P cell between these two conditions (learning and nonlearning) as a function of the number of trials. Perceptual learning processes were carried out repeatedly (six trials) for different sensory stimuli, where the first stimulus was f2. The time difference between the trials was 4 seconds. Ongoing-spontaneous membrane potentials were recorded after sensory stimulation during which learning took place or not. Positive and negative values indicate learning-induced membrane depolarization and hyperpolarization, respectively. τ+ denotes STDP time constant (see equation 2.2).

To see in more detail, we carried out perceptual learning repeatedly (six trials) for different sensory stimuli, where the first stimulus was f2. We investigated how the memory trace for the first stimulus fades away along with the trials. We recorded ongoing-spontaneous membrane potentials of f2-relevant P cells after sensory stimulation during which perceptual learning took place. Figure 6B shows differences in the average ongoing-spontaneous membrane potential between these two conditions: learning and nonlearning. A positive value indicates a subthreshold membrane depolarization, which evidences a memory trace of the first stimulus. A longer time constant of STDP (see τ+ in equation 2.2) leaves a stronger memory trace, but it quickly fades away as other memory traces accumulate (see the triangles). Note that a negative value (see the triangle at the sixth trial) indicates a membrane hyperpolarization, which evidences a kind of memory suppression. For achieving such subthreshold membrane depolarization and hyperpolarization, the interplay of the modulation of ambient GABA levels and STDP might be crucial.

3.3.  Enhancement of Suprathreshold Neuronal Activity by Learning.

In the previous section, we focused on how perceptual learning affects subthreshold (ongoing-spontaneous) neuronal activity. In this section, we show how it affects suprathreshold (stimulus-evoked) neuronal activity. Figure 7A presents stimulus-evoked activity under the condition with (solid traces) or without (dashed traces) learning. The experience of the first stimulus is clearly reflected in the enhanced (see the solid trace marked by P2) and depressed (e.g., see the solid trace marked by P3) neuronal responses to the second (same) stimulus.

Figure 7:

Influences of perceptual learning on suprathreshold neuronal activity. (A) Stimulus-evoked activity of ten P cells, where the time bin is 200 msec. Learning took place (solid traces) or not (dashed traces). (B) Concentrations of ambient GABA around P cells. (C) Membrane potentials of Ib cells. For details, see the text.

Figure 7:

Influences of perceptual learning on suprathreshold neuronal activity. (A) Stimulus-evoked activity of ten P cells, where the time bin is 200 msec. Learning took place (solid traces) or not (dashed traces). (B) Concentrations of ambient GABA around P cells. (C) Membrane potentials of Ib cells. For details, see the text.

Figure 7B shows that the ambient GABA concentration around stimulus-relevant P cells is reduced when exposed to the second stimulus (see the solid trace marked by P2). In contrast, the ambient GABA concentration around stimulus-irrelevant P cells is augmented (see the solid traces marked by P3, and P4). This improves the tuning performance of the network: the activity of stimulus-relevant P cells is enhanced, while suppressing stimulus-irrelevant P cells. Figure 7C shows that the hyperpolarization of a stimulus-relevant Ib cell (see Ib2), induced by the second stimulus (see the dashed circle), leads to removing GABA from the extracellular space around stimulus-relevant P cells (P2, see the arrows). In contrast, the frequent depolarization of stimulus-irrelevant Ib cells (see Ib3, Ib4), induced by the second stimulus (see the dashed ovals), leads to releasing GABA into the extracellular space around stimulus-irrelevant P cells (P3 and P4; see the arrows).

Figure 8:

Influences of perceptual learning on ambient GABA levels around Ib cells. (A) Concentrations of ambient GABA around Ib cells. Learning took place (solid traces) or not (dashed traces). Membrane potentials of Ia cells under the condition with (B) or without (C) learning. For details, see the text.

Figure 8:

Influences of perceptual learning on ambient GABA levels around Ib cells. (A) Concentrations of ambient GABA around Ib cells. Learning took place (solid traces) or not (dashed traces). Membrane potentials of Ia cells under the condition with (B) or without (C) learning. For details, see the text.

As shown in Figure 8A, the ambient GABA concentration around stimulus-relevant Ib cells is augmented by the second stimulus (see the solid trace marked by Ib2), for which GABA release due to the depolarization of stimulus-relevant Ia cells (Ia2; see the dashed oval at the top of Figure 8B) is responsible. In contrast, the ambient GABA concentration around stimulus-irrelevant Ib cells is reduced (e.g., see the solid trace marked by Ib3 in Figure 8A), for which GABA uptake due to the frequent hyperpolarization of stimulus-relevant Ia cells (<uIarev, see the dashed rectangle in Figure 8B) is responsible. This modulation of local ambient GABA concentrations leads to hyperpolarizing stimulus-relevant Ib cells (Ib2) and to depolarizing stimulus-irrelevant Ib cells (Ib3, Ib4), when exposed to the second stimulus (see Figure 7C).

To see whether and how the transporters on Ia and Ib cells combinatorially work, we devised a simulation in which their respective transporters were deleted. Figure 9A presents raster plots (top) and ambient GABA concentrations (bottom) under the intact condition. As shown in Figure 9B, the deletion of transporter on Ia cells leads to depressing stimulus-evoked activity (see the dashed oval), for which the insufficient reduction of ambient GABA concentration around stimulus-relevant P cells is responsible (see the bottom trace marked by P2). As shown in Figure 9C, the deletion of a transporter on Ib cells allows stimulus-irrelevant P cells to be active (see the dashed ovals), for which the insufficient augmentation of ambient GABA concentration around stimulus-irrelevant P cells is responsible (see the bottom traces marked by P1 and P3). These results indicate that the combinatorial regulation of local ambient GABA concentrations by transporters on Ia and Ib cells contributes to improving the perceptual performance of the network.

Figure 9:

Combinatorial effects of transporters on suprathreshold neuronal activity. (A) Raster plots of (top) and ambient GABA concentrations around (bottom) P cells under the intact (original) condition. Transporters on Ia (B) or Ib (C) cells were deleted. For details, see the text.

Figure 9:

Combinatorial effects of transporters on suprathreshold neuronal activity. (A) Raster plots of (top) and ambient GABA concentrations around (bottom) P cells under the intact (original) condition. Transporters on Ia (B) or Ib (C) cells were deleted. For details, see the text.

Figure 10 presents stimulus-evoked activity after learning as a function of input intensity (input current) for the learning, where GABA transporter worked (see the circles) or not (see the triangles). These results indicate that perceptual learning is possible without transporter, if a stronger input (>240 pA) is used for the learing. Concerning the intensity of sensory input, it is well known that perceptual learning can take place for a weak or even subliminal input (see Hirst, 1997, for a review). For instance, a brief exposure to an item will increase a subject's preference for that item. Interestingly, even though the sensory input is too brief, weak, or degraded for subjects to perceive, its memory is maintained for minutes or more: it can become a long-term memory. Given this simulation result, the modulation of ambient GABA concentration would not be the sole underlying mechanism of perceptual learning but a possible means of leaving its memory trace in the brain. The transporter-mediated regulation of ambient GABA concentration may contribute effectively to perceptual learning, especially when salient sensory information is unavailable.

Figure 10:

Stimulus-evoked activity after learning. A constant excitatory current, ranging from 100 to 300 pA, was provided to each (stimulus-relevant) P cell as an input, during which the synaptic strength between principal cells was modified. After each learning process, the same constant excitatory current (200 pA) as a stimulus was provided, and its evoked activity (firing rate) was measured. The circles and triangles denote learning with and without GABA transporter, respectively.

Figure 10:

Stimulus-evoked activity after learning. A constant excitatory current, ranging from 100 to 300 pA, was provided to each (stimulus-relevant) P cell as an input, during which the synaptic strength between principal cells was modified. After each learning process, the same constant excitatory current (200 pA) as a stimulus was provided, and its evoked activity (firing rate) was measured. The circles and triangles denote learning with and without GABA transporter, respectively.

4.  Discussion

We examined whether and how ambient (extrasynaptic) GABA affects experience-dependent synaptic alteration. A cortical neural network model was simulated. Transporters on two types of GABAergic interneurons regulated ambient GABA levels around their axonal target neurons in a combinatorial manner. The ambient GABA provided neurons with tonic inhibitory currents by activating extrasynaptic GABAa receptors. During repeated exposures to the same stimulus, we modified the synaptic strength between principal cells in a spike-timing-dependent manner. This modulated the activity of GABAergic interneurons and reduced or augmented local ambient GABA concentrations.

Reduction in ambient GABA concentration led to slight depolarization (less than several millivolts) in ongoing-spontaneous membrane potential. This was a subthreshold neuronal behavior, because ongoing-spontaneous spiking activity remained almost unchanged. The ongoing-spontaneous subthreshold depolarization improved suprathreshold neuronal responses. If the stimulus was long absent for perceptual learning, augmentation of ambient GABA concentration occurred, and the ongoing-spontaneous subthreshold depolarization was depressed. We suggest that a perceptual memory trace could be left in neuronal circuitry as an ongoing-spontaneous subthreshold depolarization (see the solid trace marked by P5 in Figure 6A), which would allow that memory to be accessed easily afterward. A trace of a memory that has not recently been retrieved tends to fade away when the ongoing-spontaneous subthreshold depolarization built by previous perceptual learning (see the solid trace marked by P2 to the left in Figure 6A) is depressed (see the solid trace marked by P2 to the right in Figure 6A). This would lead that memory to be accessed somewhat with difficulty. In the brain, ambient GABA, whose levels could be regulated by transporter, may have an important role in leaving a memory trace for perceptual learning.

A recent experiment (Vajda et al., 2008) has demonstrated that electrical stimulation can induce alteration in ongoing-spontaneous neuronal activity in the cortex. Another experiment (Wagenaar, Pine, & Potter, 2006) has found no such alteration. Our study showed a small change in firing rate, less than subHerz (see Figure 3A). We also found a small change in membrane potential (less than several millivolts) below firing threshold (see Figure 2C). These learning-induced changes in ongoing-spontaneous neuronal activities are very slight and thus may be difficult to detect in experiments. Nonetheless, we hope the results derived from our simulations will be confirmed experimentally in the future.

We showed that perceptual learning reduced the ambient GABA concentration around stimulus-relevant principal cells, while those around stimulus-irrelevant principal cells were augmented (see Figure 3B). This result indicates that synaptic modification by perceptual learning entails the alteration of ambient GABA levels. An experiment by Massie and colleagues (2003) may support this notion in part. When cortical reorganization took place following visual deprivation in cat visual cortex, the researchers observed the augmentation of ambient GABA concentration in nondeprived areas. The stimulus-irrelevant cell assemblies in which ambient GABA concentrations were augmented may correspond to the nondeprived area. Contrary to their expectation (Arckens et al., 2000), they failed to detect the reduction of ambient GABA concentration in the sensory-deprived area, which may correspond to the reduction of ambient GABA concentration in the stimulus-relevant cell assembly. Changes in local ambient GABA concentrations induced by learning shown here were very slight and thus might be difficult to detect in experiments. Nonetheless, we hope future experiments will confirm that perceptual learning entails the alteration of ambient GABA levels in the cortex.

The assumption that the reversal potential for GABA transporter (GAT-1) is close to the resting potential of neurons is based on experimental and theoretical studies by Wu and colleagues (2003, 2007). The researches made patch-clamp recordings from a pair of CHO cells, one transfected with subunits of GABAa receptor (called a sniffer cell) and the other with GAT-1 (called a GAT-1 cell). Concentrations of Na+, Cl, and GABA were systematically controlled in the inside (Na+= 15 mM, Cl= 10 mM, GABA = 2 mM) and on the outside (Na+= 151 mM, Cl= 135 mM, GABA = 100 nM) of the GAT-1 cell. These concentrations were within ranges reported for some adult mammalian neurons.

A slow ramp depolarization was applied to the GAT-1 cell, and the current induced in the sniffer cell was recorded. The voltage in the GAT-1 cell at which an increase in inward current was first detected in the sniffer cell (when ambient GABA first began to rise) was estimated to be the reversal potential for GAT-1. The reversal potential determined by this method was −69.5 mV. The proposed method using the CHO cell assay has several advantages: it is highly sensitive for detecting the reversal of GABA transport, there is good control of membrane potential and substrate concentrations in the inside and on the outside of the membrane, and the CHO cells do not have synaptic vesicles, by which GAT-1-mediated GABA release can be detected in isolation. We hope the reversal potential will be determined for cortical neurons in the near future.

Appendix A:  The Neural Network Model

Dynamic evolution of the membrane potential of the ith P cell belonging to cell assembly n is defined by
formula
A.1
where IP,Pi(n; t) is a postsynaptic excitatory current from other P cells, IP,Ibi(n; t) a postsynaptic inhibitory current from an Ib cell, IPi,ext(n; t) a GABA-mediated extrasynaptic (nonsynaptic) inhibitory current, and Iinp(n) an input current when the network is presented with a sensory feature finp: 0⩽inpM. These currents are defined by
formula
A.2
formula
A.3
formula
A.4
formula
A.5
Dynamic evolution of the membrane potential of Ia cells is defined by
formula
A.6
where IIa,Pi(n; t) is a postsynaptic excitatory current from P cells and IIai,ext(n; t) is a GABA-mediated extrasynaptic inhibitory current. These currents are defined by
formula
A.7
formula
A.8
Dynamic evolution of the membrane potential of Ib cells is defined by
formula
A.9
where IIb,Pi(n; t) and IIb,Iai(n; t) are postsynaptic excitatory and inhibitory currents from P cells and an Ia cell, respectively. IIbi,ext(n; t) is a GABA-mediated extrasynaptic inhibitory current. These currents are defined by
formula
A.10
formula
A.11
formula
A.12
In these equations, cYm is the membrane capacitance of Y (Y = P, Ia, Ib) cell, uYi(n; t) the membrane potential of the ith Y cell at time t, gYm the membrane conductance of Y cell, and uYrest the resting potential. and uZrev (Z = AMPA or GABA) are, respectively, the maximal conductance and the reversal potential for the current mediated by a Z-type receptor. N and M denote the number of cell units constituting each cell assembly and the number of cell assemblies, respectively.

wP,Pij(n; t) is the excitatory synaptic strength from the jth to ith P cell within cell assembly n. wP,Ibi(n) is the inhibitory synaptic strength from the ith Ib to P cell. wIa,Pi(n) is the excitatory synaptic strength from the ith P to Ia cell. wIb,Pij(n, k) is the excitatory synaptic strength from the jth P cell belonging to another cell assembly (k) to the ith Ib cell belonging to cell assembly n (n≠k). wIb,Iai(n) is the inhibitory synaptic strength from the ith Ia to Ib cell. εP denotes the intensity of input: constant excitatory current.

rPj(n; t) expresses the fraction of AMPA receptors in the open state provoked by the presynaptic action potentials of the jth P cell belonging to cell assembly n at time t. rIbi(n; t) and rIai(n; t) express the fractions of intrasynaptic GABAa receptors in the open state provoked by the presynaptic action potentials of the ith Ib and Ia cell, respectively. rYi,ext(n; t), where Y=P, Ia, or Ib, expresses the fraction of extrasynaptic GABAa receptors in the open state prompted by ambient GABA around the ith Y cell. δY denotes the relative number of extrasynaptic GABAa receptors on Y cell. For parameter values, see Table 1.

Appendix B:  Receptor and Transporter Descriptions

Receptor dynamics is defined by
formula
B.1
formula
B.2
formula
B.3
where αZ and βZ (z = AMPA or GABA) are positive constants. [Glut]Pj(n; t) and [GABA]Xj(n; t) are concentrations of glutamate and GABA in the synaptic cleft, respectively. [Glut]Pj(n; t) = GlutPsyn, and [GABA]Xj(n; t) = GABAXsyn for 1 msec when the presynaptic jth P cell and X cell fire, respectively. Otherwise, [Glut]Pj(n; t) = 0 and [GABA]Xj(n; t) = 0.
Concentrations of ambient GABA around P and Ib cells, to which GABAergic interneurons Ib and Ia project (see Figure 1A), are defined by
formula
B.4
formula
B.5
where γtrn and [GABA]0ext are a positive constant and a concentration at rest, respectively. The second term on the right-hand side of each equation determines the amount of forward or reverse transport of GABA. TIb and TIa correspond to the transfer coefficients. GABAmax and GABAmin are the maximal and minimal concentrations, respectively. uIbrev and uIarev are the reversal potentials. Concentration of ambient GABA around Ia cells is simply set to [GABA]0ext, because Ia cells do not receive GABAergic innervations. For parameter values, see Table 1.

Appendix C:  Action Potential Generation

The probability of firing of the jth Y cell belonging to cell assembly n is defined by
formula
C.1
where ηY and ζY are, respectively, the steepness and the threshold of the sigmoid function. When a cell fires, its membrane potential is depolarized toward −10 mV, which is kept for 1 msec, and then reset to the resting potential. For parameter values, see Table 1.

Acknowledgments

I am grateful to Hiromi Ohta for her encouragement throughout this study and to the reviewers for giving me valuable comments and suggestions on the earlier drafts.

References

Arckens
,
L.
,
Schweigart
,
G.
,
Qu
,
Y.
,
Wouters
,
G.
,
Pow
,
D. V.
,
Vandesande
,
F.
, et al
(
2000
).
Cooperative changes in GABA, glutamate and activity levels: The missing link in cortical plasticity
.
Eur. J. Neurosci.
,
12
,
4222
4232
.
Bi
,
G. Q.
(
2002
).
Spatiotemporal specificity of synaptic plasticity: Cellular rules and mechanisms
.
Biol. Cybern.
,
87
,
319
332
.
Bianchi
,
L.
,
Ballini
,
C.
,
Colivicchi
,
M. A.
,
Della Corte
,
L.
,
Giovannini
,
M. G.
, &
Pepeu
,
G.
(
2003
).
Investigation on acetylcholine, aspartate, glutamate and GABA extracellular levels from ventral hippocampus during repeated exploratory activity in the rat
.
Neurochem. Res.
,
28
,
565
573
.
Brickley
,
S. G.
,
Cull-Candy
,
S. G.
, &
Farrant
,
M.
(
1996
).
Development of a tonic form of synaptic inhibition in rat cerebellar granule cells resulting from persistent activation of GABAA receptors
.
J. Physiol.
,
497
,
753
759
.
Buonomano
,
D. V.
, &
Merzenich
,
M. M.
(
1998
).
Cortical plasticity from synapses to maps
.
Annu. Rev. Neurosci.
,
21
,
149
186
.
Destexhe
,
A.
,
Mainen
,
Z. F.
, &
Sejnowski
,
T. J.
(
1998
).
Kinetic models of synaptic transmission
. In
C. Koch & I. Segev
(Eds.),
Methods in neuronal modeling
(pp.
1
25
).
Cambridge, MA
:
MIT Press
.
Dinse
,
H. R.
,
Ragert
,
P.
,
Pleger
,
B.
,
Schwenkreis
,
P.
, &
Tegenthoff
,
M.
(
2003
).
GABAergic mechanisms gate tactile discrimination learning
.
Neuroreport
,
14
,
1747
1751
.
Drasbek
,
K. R.
, &
Jensen
,
K.
(
2006
).
THIP, a hypnotic and antinociceptive drug, enhances an extrasynaptic GABAA receptor-mediated conductance in mouse neocortex
.
Cereb. Cortex
,
16
,
1134
1141
.
Fahle
,
M.
(
2005
).
Perceptual learning: Specificity versus generalization
.
Curr. Opin. Neurobiol.
,
15
,
154
160
.
Farrant
,
M.
, &
Nusser
,
Z.
(
2005
).
Variations on an inhibitory theme: Phasic and tonic activation of GABA(A) receptors
.
Nat. Rev. Neurosci.
,
6
,
215
229
.
Gilbert
,
C. D.
(
1994
).
Neural dynamics and perceptual learning
.
Curr. Biol.
,
4
,
627
629
.
Giovannini
,
M. G.
,
Rakovska
,
A.
,
Benton
,
R. S.
,
Pazzagli
,
M.
,
Bianchi
,
L.
, &
Pepeu
,
G.
(
2001
).
Effects of novelty and habituation on acetylcholine, GABA, and glutamate release from the frontal cortex and hippocampus of freely moving rats
.
Neurosci.
,
106
,
43
53
.
Goldstone
,
R. L.
(
1998
).
Perceptual learning
.
Annu. Rev. Psychol.
,
49
,
585
612
.
Gupta
,
A.
,
Wang
,
Y.
, &
Markram
,
H.
(
2000
).
Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex
.
Science
,
287
,
273
278
.
Hirst
,
W.
(
1997
).
Cognitive aspects of consciousness
. In
M. S. Gazzaniga
(Ed.),
The cognitive neurosciences
(pp.
1307
1319
).
Cambridge, MA
:
MIT Press
.
Hoshino
,
O.
(
2006
).
Coherent ongoing subthreshold state of a cortical neural network regulated by slow- and fast-spiking interneurons
.
Network: Comput. Neural Syst.
,
17
,
351
371
.
Hoshino
,
O.
(
2008
).
An ongoing subthreshold neuronal state established through dynamic coassembling of cortical cells
.
Neural Comput.
,
20
,
3055
3086
.
Hoshino
,
O.
(
2009
).
GABA transporter preserving ongoing spontaneous neuronal activity at firing subthreshold
.
Neural Comput.
,
21
,
1683
1713
.
Massie
,
A.
,
Cnops
,
L.
,
Smolders
,
I.
,
Van Damme
,
K.
,
Vandenbussche
,
E.
,
Vandesande
,
F.
, et al
(
2003
).
Extracellular GABA concentrations in area 17 of cat visual cortex during topographic map reorganization following binocular central retinal lesioning
.
Brain Res.
,
976
,
100
108
.
Mountcastle
,
V. B.
(
1997
).
The columnar organization of the neocortex
.
Brain
,
120
,
701
722
.
Nusser
,
Z.
,
Roberts
,
J. D.
,
Baude
,
A.
,
Richards
,
J. G.
, &
Somogyi
,
P.
(
1995
).
Relative densities of synaptic and extrasynaptic GABAA receptors on cerebellar granule cells as determined by a quantitative immunogold method
.
J. Neurosci.
,
5
,
2948
2960
.
Ortinski
,
P. I.
,
Turner
,
J. R.
,
Barberis
,
A.
,
Motamedi
,
G.
,
Yasuda
,
R. P.
,
Wolfe
,
B. B.
, et al
(
2006
).
Deletion of the GABA(A) receptor alpha1 subunit increases tonic GABA(A) receptor current: A role for GABA uptake transporters
.
J. Neurosci.
,
26
,
9323
9331
.
Richerson
,
G. B.
(
2004
).
Looking for GABA in all the wrong places: The relevance of extrasynaptic GABA(A) receptors to epilepsy
.
Epilepsy Curr.
,
4
,
239
242
.
Richerson
,
G. B.
, &
Wu
,
Y.
(
2003
).
Dynamic equilibrium of neurotransmitter transporters: not just for reuptake anymore
.
J. Neurophysiol.
,
90
,
1363
1374
.
Sale
,
A.
,
De Pasquale
,
R.
,
Bonaccorsi
,
J.
,
Pietra
,
G.
,
Olivieri
,
D.
,
Berardi
,
N.
, et al
(
2011
).
Visual perceptual learning induces long-term potentiation in the visual cortex
.
Neurosci.
172
,
219
225
.
Scimemi
,
A.
,
Andersson
,
A.
,
Heeroma
,
J. H.
,
Strandberg
,
J.
,
Rydenhag
,
B.
,
McEvoy
,
A. W.
, et al
(
2006
).
Tonic GABA(A) receptor-mediated currents in human brain
.
Eur. J. Neurosci.
,
24
,
1157
1160
.
Semyanov
,
A.
,
Walker
,
M. C.
,
Kullmann
,
D. M.
, &
Silver
,
R. A.
(
2004
).
Tonically active GABA A receptors: Modulating gain and maintaining the tone
.
Trends Neurosci.
,
27
,
262
269
.
Soltesz
,
I.
, &
Nusser
,
Z.
(
2001
).
Neurobiology: Background inhibition to the fore
.
Nature
,
409
,
24
25
.
Somogyi
,
P.
,
Takagi
,
H.
,
Richards
,
J. G.
, &
Mohler
,
H.
(
1989
).
Subcellular localization of benzodiazepine/GABAA receptors in the cerebellum of rat, cat, and monkey using monoclonal antibodies
.
J. Neurosci.
,
9
,
2197
2209
.
Tuckwell
,
H. C.
(
1988
).
Introduction to theoretical neurobiology. Vol. 2, Nonlinear and stochastic theories
.
Cambridge
:
Cambridge University Press
.
Vajda
,
I.
,
van Pelt
,
J.
,
Wolters
,
P.
,
Chiappalone
,
M.
,
Martinoia
,
S.
,
van Someren
,
E.
, et al
(
2008
).
Low-frequency stimulation induces stable transitions in stereotypical activity in cortical networks
.
Biophys. J.
,
94
,
5028
5039
.
Wagenaar
,
D. A.
,
Pine
,
J.
, &
Potter
,
S. M.
(
2006
).
Searching for plasticity in dissociated cortical cultures on multi-electrode arrays
.
J. Negat. Results Biomed.
,
5
,
16
.
Wu
,
Y
,
Wang
,
W.
,
Diez-Sampedro
,
A.
, &
Richerson
,
G. B.
(
2007
).
Nonvesicular inhibitory neurotransmission via reversal of the GABA transporter GAT-1
.
Neuron
,
56
,
851
865
.
Wu
,
Y.
,
Wang
,
W.
, &
Richerson
,
G. B.
(
2001
).
GABA transaminase inhibition induces spontaneous and enhances depolarization-evoked GABA efflux via reversal of the GABA transporter
.
J. Neurosci.
,
21
,
2630
2639
.
Wu
,
Y.
,
Wang
,
W.
, &
Richerson
,
G. B.
(
2003
).
Vigabatrin induces tonic inhibition via GABA transporter reversal without increasing vesicular GABA release
.
J. Neurophysiol.
,
89
,
2021
2034
.
Young
,
J. M.
,
Waleszczyk
,
W. J.
,
Wang
,
C.
,
Calford
,
M. B.
,
Dreher
,
B.
, &
Obermayer
,
K.
(
2007
).
Cortical reorganization consistent with spike timing—but not correlation-dependent plasticity
.
Nat. Neurosci.
,
10
,
887
895
.