Abstract

There has been compelling evidence that the GABA transporter is crucial not only for removing gamma-aminobutyric acid (GABA) from but also releasing it into extracellular space, thereby clamping ambient GABA (GABA in extracellular space) at a certain level. The ambient GABA is known to activate extrasynaptic GABA receptors and provide tonic inhibitory current into neurons. We investigated how the transporter regulates the level of ambient GABA, mediates tonic neuronal inhibition, and influences ongoing spontaneous neuronal activity. A cortical neural network model is proposed in which GABA transporters on lateral (L) and feedback (F) inhibitory (GABAergic) interneurons are functionally made. Principal (P) cell assemblies participate in expressing information about elemental sensory features. At membrane potentials below the reversal potential, there is net influx of GABA, whereas at membrane potentials above the reversal potential, there is net efflux of GABA. Through this transport mechanism, ambient GABA concentration is kept within a submicromolar range during an ongoing spontaneous neuronal activity time period. Here we show that the GABA transporter on L cells regulates the overall level of ambient GABA across cell assemblies, and that on F cells it does so within individual cell assemblies. This combinatorial regulation of ambient GABA allows P cells to oscillate near firing threshold during the ongoing time period, thereby reducing their reaction time to externally applied stimuli. We suggest that the GABA transporter, with its forward and reverse transport mechanism, could regulate the ambient GABA. This transporter-mediated ambient GABA regulation may contribute to establishing an ongoing subthreshold neuronal state by which the network can respond rapidly to subsequent sensory input.

1.  Introduction

Gamma-aminobutyric acid (GABA) is the major inhibitory neurotransmitter in the brain, and mediates phasic inhibition of neurons by activating intrasynaptic GABA receptors, that is, GABA receptors 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 the GABA receptors located on membranes outside synapses. The GABA in extracellular space and the GABA receptors on extrasynaptic membrane regions are referred to as ambient GABA and extrasynaptic GABA receptors, respectively. Extrasynaptic GABAa receptors have 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), but recent studies have identified them in the cortex as well (Drasbek & Jensen, 2006; Scimemi et al., 2006).

In the brain, intrasynaptic GABA (i.e., GABA inside synapses) rises to a millimolar level in a phasic manner triggered by a presynaptic action potential (Maconochie, Zempel, & Steinbach, 1994; Jones & Westbrook, 1995). In contrast, ambient GABA is maintained within a range of submicromolar to several micromolar levels in a tonic manner (Lerma, Herranz, Herreras, Abraira, & Martin, 1986; Tossman, Jonsson, & Ungerstedt, 1986; Scimemi, Semyanov, Sperk, Kullmann, & Walker, 2005). The lower (submicromolar) ambient GABA level is sufficient to activate extrasynaptic GABAa receptors but not intrasynaptic GABAa receptors. GABAa receptors with δ subunits found in extrasynaptic membrane regions (Somogyi et al., 1989; Nusser et al., 1995; Brickley et al., 1996; Soltesz & Nusser, 2001) are known to have high affinity for GABA (Saxena & Macdonald, 1996; Brown, Kerby, Bonnert, Whiting, & Wafford, 2002) and little desensitization to continuous activation (Bianchim, Haas, & Macdonald, 2001, 2002). This leads to the tonic inhibition of neurons even at the lower ambient GABA level.

As to the maintenance of ambient GABA, Richerson and colleagues (Wu, Wang, & Richerson, 2001; Richerson & Wu, 2003; Richerson, 2004; Wu, Wang, Diez-Sampedro, & Richerson, 2007) made an interesting suggestion. A GABA transporter such as GAT-1 is crucial not only for removing GABA from but also releasing it into the extracellular space. The transporter might clamp ambient GABA at a certain level. The transporter is near equilibrium under normal physiological conditions and would reverse with a relatively small increase in membrane potential. The researchers demonstrated that an increase in tonic inhibitory current was not prevented by blocking vesicular GABA release but decreased by GABA transporter antagonists.

Ambient GABA, even though its concentration is low (submicromolar), acts on extrasynaptic GABAa receptors, mediates to provide tonic inhibitory currents into neurons, and therefore influences the dynamic behaviors of cortices. It is speculated that such tonic inhibition has a role in restricting overall neuronal activity. However, less is known about the details of its neuronal mechanisms and how the tonic inhibition contributes to neuronal information processing in the brain. The purpose of this study is to elucidate how the ambient GABA mediates tonic inhibition of neurons and to understand its significance in neuronal information processing in the cortex. We carry out simulations of a neural network model. In the model, dynamic cell assemblies express information about elemental sensory features. Within cell assemblies, inhibitory interneurons (F cells) give a feedback inhibitory effect on principal cells (P cells). Between cell assemblies, another type of inhibitory interneurons (L cells) gives a lateral inhibitory effect on principal cells. This circuitry allows the network to respond selectively to specific sensory features as observed in early sensory cortices such as primary auditory cortex (Yost, 1994) and primary visual cortex (Ts'o & Roe, 1995) and elsewhere.

Based on a theoretical consideration (Richerson & Wu, 2003) that the reversal potential of GABA transporter is close to the resting potential of neurons, we make a simple, functional model for the GABA transporters on F and L cells. At membrane potentials below the reversal potential, there is net influx of GABA (forward transport), whereas at membrane potentials above the reversal potential, there is net efflux of GABA (reverse transport). Through this transport mechanism, ambient GABA concentration is kept within a range of submicromolar to several micromolar levels. To focus our study on the regulation of ambient GABA by transporters, we neglect here other possible GABA release into extracellular space such as spillover from synaptic clefts and nonvesicular release from neurons and glia (Somogyi et al., 1989; Nusser et al., 1995; Brickley et al., 1996; Soltesz & Nusser, 2001).

Even in the absence of sensory stimuli, there exists a submicromolar level of ambient GABA. This mediates weak but significant tonic neuronal inhibition and presumably influences ongoing (spontaneous) neuronal activity. Over the past decade, ongoing neuronal activity has attracted scientists' interest. Experimental studies have suggested that ongoing neuronal activity is not noise but rather contains important information and greatly influences subsequent cognitive information processing. For instance, Engel and colleagues (Engel, Fries, & Singer, 2001) demonstrated that self-generated ongoing neuronal activity had a distinct spatiotemporal patterning, which led to the temporal coordination of externally triggered responses and to their binding into synchronous dynamic cell assemblies. Arieli and colleagues (Arieli, Shoham, Hildesheim, & Grinvald, 1995; Arieli, Sterkin, Grinvald, & Aertsen, 1996) demonstrated that preceding ongoing neuronal activity was reflected in the activity of responding cell assemblies (i.e., ensemble activation of neurons) to subsequent sensory stimulation. Tsodyks and colleagues (Tsodyks, Kenet, Grinvald, & Arieli, 1999) suggested that in an ongoing neuronal state, where any sensory stimulus is not present, a cortical network wanders through various states expressed by the synchronous firings of different cell assemblies. When a sensory stimulus is presented, it will quickly push the network from the current state into a preferred state, in which the specific cell assembly representing the information of the applied stimulus is selectively activated.

In a previous study (Hoshino, 2006), we proposed a neural network model that has local excitatory and inhibitory circuitry. Simulating the model, we investigated how two distinct types of inhibitory interneurons (fast-spiking interneurons with narrow axonal arbors and slow-spiking interneurons with wide axonal arbors) have spatiotemporal influences on the ongoing activity of principal cells and subsequent neuronal information processing. In that model, dynamic cell assemblies expressed information about sensory features. Within cell assemblies, fast-spiking interneurons gave a feedback inhibitory effect on principal cells. Between cell assemblies, slow-spiking interneurons gave a lateral inhibitory effect on principal cells. These interneurons contributed to depolarizing principal cells below firing threshold during ongoing spontaneous neuronal activity time periods, by which the reaction time of principal cells to sensory stimulation was reduced.

Based on the above neural architecture, we propose a neural network model with a GABA transport mechanism. Simulating the model, we try to elucidate how the transporter regulates ambient GABA and how the ambient GABA acting on extrasynaptic GABAa receptors mediates the tonic inhibition of neurons and coordinates the ongoing subthreshold neuronal state.

2.  Neural Network Model

A schematic drawing of the neural network model is shown in Figure 1A, in which each cell assembly (k; k = 0, 1, …, n − 1, n, n + 1, …, M) has specific sensitivity to one sensory feature (fk; k = 0 − M). Each cell assembly (see the vertical brackets) consists of cell units (see the horizontal brackets). Each cell unit contains one principal cell (P), one lateral inhibitory cell (L), and one feedback inhibitory cell (F). Within cell assemblies, P cells are recurrently connected via excitatory synapses. An F cell receives an excitatory projection from its proximal P cell and sends a feedback inhibitory projection to that P cell. An L cell receives excitatory projections from P cells that belong to other cell assemblies and sends inhibitory projections to all (nearby to remote) P cells within the same cell assembly. This circuitry provides a lateral inhibitory mechanism between different cell assemblies. P cells receive intentional sensory inputs (“input”).

Figure 1:

A schematic drawing of the neural network model. (A) Each cell assembly (vertical brackets; k = 0, 1, …, n − 1, n, n + 1, …, M) has specific sensitivity to one feature (fk; k = 0 − M). The arrow indicates input to a P cell. Each cell assembly consists of cell units (horizontal brackets). P, L, and F denote, respectively, principal cell, lateral inhibitory cell, and feedback inhibitory cell. Open and filled triangles depict excitatory and inhibitory synapses, respectively. (B) A GABA transporter embedded in the extrasynaptic membrane of a GABAergic interneuron—an F or an L cell. Downward and upward arrows indicate, respectively, the forward transport (uptake) and the reverse transport (release) of GABA.

Figure 1:

A schematic drawing of the neural network model. (A) Each cell assembly (vertical brackets; k = 0, 1, …, n − 1, n, n + 1, …, M) has specific sensitivity to one feature (fk; k = 0 − M). The arrow indicates input to a P cell. Each cell assembly consists of cell units (horizontal brackets). P, L, and F denote, respectively, principal cell, lateral inhibitory cell, and feedback inhibitory cell. Open and filled triangles depict excitatory and inhibitory synapses, respectively. (B) A GABA transporter embedded in the extrasynaptic membrane of a GABAergic interneuron—an F or an L cell. Downward and upward arrows indicate, respectively, the forward transport (uptake) and the reverse transport (release) of GABA.

Figure 1B schematically shows a GABA transporter embedded in the extrasynaptic membrane of a GABAergic interneuron—on F or L cell. Based on the studies by Richerson and colleagues (Wu et al., 2001; Richerson & Wu, 2003; Richerson, 2004; Wu et al., 2007), we modeled a GABA transporter that could functionally regulate ambient GABA concentration (i.e., the level of GABA in extracellular space) in a neuronal-activity-dependent manner. The transporter has its reversal potential close to the resting potential of neurons. As long as the membrane potential is more negative than the reversal potential, the transporter operates in inward direction, removing GABA from extracellular space (see the downward arrow), which is called forward transport. In contrast, if the membrane potential is above the reversal potential, the transporter could reverse releasing GABA into extracellular space (see the upward arrow), which is called reverse transport.

Dynamic evolution of the membrane potential of the ith P cell belonging to cell assembly n is defined by
formula
2.1
where IPi,rec(n; t) is a recurrent excitatory postsynaptic current into the ith P cell from other P cells within the same cell assembly. Ii, fedP(n; t) is a feedback inhibitory postsynaptic current from its accompanying F cell, IPi,lat(n; t) a lateral inhibitory postsynaptic current from L cells, IPi,ext(n; t) an extrasynaptic GABA-mediated inhibitory current that depends on the level of ambient GABA, and Iinp(n; finp) a graded input current when the network is presented with a feature stimulus finp ∈ {f0, f1, f2, …, fM}. These currents are defined by
formula
2.2
formula
2.3
formula
2.4
formula
2.5
formula
2.6
For computational convenience, we set finp = k for feature input stimulus finp = fk.
Dynamic evolution of the membrane potential of the ith F cell belonging to cell assembly n is defined by
formula
2.7
where IFi(n; t) is an excitatory postsynaptic current and IFi,ext(n; t) is an extrasynaptic GABA-mediated inhibitory current. These currents are defined by
formula
2.8
formula
2.9
Dynamic evolution of the membrane potential of the ith L cell belonging to cell assembly n is defined by
formula
2.10
where ILi(n; t) is an excitatory postsynaptic current and ILi,ext(n; t) is an extrasynaptic GABA-mediated inhibitory current. These currents are defined by
formula
2.11
formula
2.12
formula
2.13
In these equations, cYm is the membrane capacitance of Y (Y = P, F, L) 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.

wPij,rec(n) is the recurrent excitatory synaptic strength from the jth to ith P cell within cell assembly n. wi, fedP(n) is the feedback inhibitory synaptic strength from F cell to P cell within cell unit i belonging to cell assembly n. wPij,lat(n) is the inhibitory synaptic strength from the jth L cell to the ith P cell within cell assembly n. wFi(n) is the excitatory synaptic strength from P cell to F cell within cell unit i belonging to cell assembly n. wLi(n, k) is the excitatory synaptic strength from the ith P cell that belongs to another cell assembly (k) to the ith L cell that belongs to the cell assembly n (k ≠ n), which weakens as the distance between them increases. Note that τP in equation 2.6 defines the broadness of sensory input; graded input.

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. rFj(n; t) and rLj(n; t) express the fractions of intrasynaptic GABAa receptors in the open state provoked by the presynaptic action potentials of the jth F cell and L cell, respectively. rGABAext(n; t) expresses the fraction of extrasynaptic GABAa receptors in the open state prompted by ambient GABA. δP, δF, and δL denote the relative numbers of extrasynaptic GABAa receptors on P, F, and L cells, respectively.

Receptor dynamics is defined by
formula
2.14
formula
2.15
formula
2.16
where αz and βz (z = AMPA or GABA) are positive constants. [Glut]Pj(n; t) and [GABA]jY(n; t) are concentrations of glutamate and GABA in the synaptic cleft, respectively. [Glut]Pj(n; t) = GlutPmax and [GABA]jY(n; t) = GABAmaxY for 1 msec when the presynaptic jth P cell and Y cell fire, respectively. Otherwise, [Glut]Pj(n; t)= 0 and [GABA]jY(n; t) = 0. For details on the receptor dynamics, see (Destexhe, Mainen, & Sejnowski, 1998).
[GABA]ext(n; t) is the concentration of ambient GABA within cell assembly n and defined by
formula
2.17
where γ functionally determines natural GABA decay caused by the diffusion and the binding of GABA to receptors, and so forth. JGABA(n; t) determines the amount of forward or reverse transport of GABA, which depends on the activities of inhibitory (GABAergic) interneurons and is functionally described as
formula
2.18
where TF and TL correspond to the transfer coefficients of GABA for F and L cells, and uFrev and uLrev are the reversal potentials for GABA transporters.
The probability of firing the jth Y cell belonging to cell assembly n is defined by
formula
2.19
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.

Unless stated otherwise, cPm = 0.5 nF, cFm = 0.2 nF, cLm = 0.6 nF, gPm = 25 nS, gFm = 20 nS, gLm = 15 nS, uPrest = −65 mv, uFrest = uLrest = −70 mV, nS, nS, uAMPArev = 0 mV and uGABArev = −80 mV (Koch, 1999; McCormick, Connors, Lighthall, & Prince, 1985; Kawaguchi & Shindou, 1998). M = 7 and N = 20. wPij,rec(k) = 6.5, wi, fedP(k) = 50.0, wPij,lat(k) = 5.0 and wFi(k) = 70.0 for k = 0 − 7. wL = 5.0, δP = 8 × 103, δF = δL = 1 × 104, αP = 1.5 × 10−10, τP = 2.0, τlat = 3.0, αAMPA = 1.1 × 106, αGABA = 5.0 × 105, βAMPA = 190.0, βGABA = 180.0 and GlutPmax = GABAFmax = GABALmax = 1.0 mM. γ = 0.5, TF = 0.01, TL = 0.001, uFrev = uLrev = −70 mV, ηP = 200.0, ηF = ηL = 180.0 and ζP = ζF = ζL = −37 mV.

3.  Results

3.1.  Ambient GABA-Mediated Modulation of Ongoing Spontaneous Neuronal Activity.

In this section, we show how the GABA transporter regulates the level of ambient GABA in a neuronal-activity-dependent manner and how it influences the ongoing neuronal activity that emerged spontaneously in the network dynamics.

Figure 2 (top) presents the raster plots of spikes of groups of P cells (cell assemblies) that have sensitivity to specific features (fk; k = 0–7) and those of F and L cells (f4). Brief bursts of spikes emerge spontaneously during an ongoing time period, where no sensory stimulus is present. Figure 2 (bottom) presents the concentration of ambient GABA in each cell assembly. As defined by equations 2.17 and 2.18, the GABA transporters regulate the ambient GABA concentration, which depends on the membrane potentials of F and L cells (see equation 2.18). Namely, it is neuronal activity dependent.

Figure 2:

Ongoing spontaneous neuronal activity and ambient GABA concentration. (A) Raster plots of action potentials of principal (P) cells for the cell assemblies corresponding to features fk (k = 0–7) and those of F and L cells (f4). (B) Ambient (extrasynaptic) GABA concentration in each cell assembly.

Figure 2:

Ongoing spontaneous neuronal activity and ambient GABA concentration. (A) Raster plots of action potentials of principal (P) cells for the cell assemblies corresponding to features fk (k = 0–7) and those of F and L cells (f4). (B) Ambient (extrasynaptic) GABA concentration in each cell assembly.

To investigate how the activity-dependent regulation of ambient GABA influences the ongoing neuronal activity, we devised a simulation in which the level of ambient GABA was fixed at a mean value: the average GABA concentration (0.83 μM) for the ongoing time period (see Figure 2, bottom). As shown in Figure 3 (top), if the ambient GABA concentration is fixed at the mean value (bottom), the durations of the bursts of spikes tend to be prolonged compared with those in Figure 2. Note that in the both conditions, neuronal-activity-dependent (see Figure 2) and -independent (see Figure 3) ambient GABA regulatory conditions, the total amounts of ambient GABA are the same but their spatiotemporal structures are completely different.

Figure 3:

Ongoing spontaneous neuronal activity in which the ambient GABA was regulated in a neuronal-activity-independent manner. (Top) Raster plots of action potentials of principal (P) cells for cell assemblies (fk; k = 0–7) and those of F and L cells (f4). (Bottom) Ambient GABA concentration was fixed at a mean value (0.83 μM) (see Figure 2, bottom). For details, see the text.

Figure 3:

Ongoing spontaneous neuronal activity in which the ambient GABA was regulated in a neuronal-activity-independent manner. (Top) Raster plots of action potentials of principal (P) cells for cell assemblies (fk; k = 0–7) and those of F and L cells (f4). (Bottom) Ambient GABA concentration was fixed at a mean value (0.83 μM) (see Figure 2, bottom). For details, see the text.

Figure 4A presents the ongoing membrane potential of a P cell under the neuronal-activity-dependent (top) or -independent (bottom) ambient GABA regulatory condition. The traces in an enlarged scale shown in Figure 4B indicate that the ongoing membrane potential under the activity-dependent ambient GABA condition (solid line) tends to be depolarized above that under the activity-independent ambient GABA condition (dashed line). This membrane depolarization allows P cells to respond rapidly to sensory input as shown by a typical example (see the top trace of Figure 4C).

Figure 4:

Ongoing spontaneous membrane potential of a P cell and its reaction time to input. (A) Ongoing spontaneous membrane potentials under the neuronal-activity-dependent (top) and -independent (bottom) ambient GABA regulatory conditions. (B) Ongoing membrane potentials under the activity-dependent (solid line) and -independent (dashed line) ambient GABA conditions in an enlarged scale. (C) Reaction time of a P cell to input under the activity-dependent (top) or -independent (bottom) ambient GABA condition.

Figure 4:

Ongoing spontaneous membrane potential of a P cell and its reaction time to input. (A) Ongoing spontaneous membrane potentials under the neuronal-activity-dependent (top) and -independent (bottom) ambient GABA regulatory conditions. (B) Ongoing membrane potentials under the activity-dependent (solid line) and -independent (dashed line) ambient GABA conditions in an enlarged scale. (C) Reaction time of a P cell to input under the activity-dependent (top) or -independent (bottom) ambient GABA condition.

Figure 5A presents histograms of membrane potential (left) observed during the ongoing time period and their cumulative representations (right) for the activity-dependent (solid lines) and independent (dashed lines) ambient GABA conditions. Figure 5B presents histograms of the reaction time of a P-cell to the input (left) and their cumulative representations (right) for the activity-dependent (open rectangles and a solid line) and -independent (filled rectangles and a dashed line) ambient GABA conditions. These results indicate that the neuronal-activity-dependent ambient GABA regulation might contribute to preserving P cells near firing threshold during the ongoing time period, thereby accelerating their reaction speed to the input.

Figure 5:

Distributions of ongoing membrane potential of a P cell and its reaction time to input. (A) Histograms of membrane potential (left) observed during an ongoing time period (10 sec) and their normalized cumulative representations (right) under the activity-dependent (solid line) or -independent (dashed line) ambient GABA condition. (B) Histograms of reaction time (left) and their normalized cumulative representations (right) under the activity-dependent (open rectangles and a solid line) or -independent (filled rectangles and a dashed line) ambient GABA condition. The same input was applied repeatedly (100) at an arbitrary time.

Figure 5:

Distributions of ongoing membrane potential of a P cell and its reaction time to input. (A) Histograms of membrane potential (left) observed during an ongoing time period (10 sec) and their normalized cumulative representations (right) under the activity-dependent (solid line) or -independent (dashed line) ambient GABA condition. (B) Histograms of reaction time (left) and their normalized cumulative representations (right) under the activity-dependent (open rectangles and a solid line) or -independent (filled rectangles and a dashed line) ambient GABA condition. The same input was applied repeatedly (100) at an arbitrary time.

Figure 6A presents the dependence of ongoing-spontaneous activity (average firing rate of P cells) for each cell assembly (see the crosses) on their resting potential (uPrest) for the activity-dependent (left) or -independent (right) ambient GABA condition. Under the activity-dependent ambient GABA condition, the ongoing spontaneous activities of cell assemblies are gradually increased as the resting potential depolarizes (−68 mV → −62 mV). In contrast, under the activity-independent ambient GABA condition, the activities are similarly increased for uPrest < −65 mV, but beyond −65 mV, the activities of some cell assemblies are enormously increased while others are decreased. This distinctive difference in activity arises from their spatiotemporal dynamic nature, as shown in Figure 6B by the membrane potentials of P cells where uPrest = −64 mV. Under the activity-independent ambient GABA condition (see the bottom of Figure 6B), neuronal firings tend to continue once they are evoked, while the other cell assemblies are suppressed through lateral inhibition. Namely, they are hyperpolarized (e.g., see the dashed line in the inset).

Figure 6:

Dependence of ongoing spontaneous neuronal activity on resting potential. (A) Average firing rate of P cells for each cell assembly (see the crosses) on the resting potential (uPrest) under the activity-dependent (left) or -independent (right) ambient GABA condition. (B) Membrane potential of P cells at uPrest = −64 mV under the activity-dependent (top) or -independent (bottom) ambient GABA condition. Inset: Membrane potentials under the activity-dependent (solid line) and -independent (dashed line) ambient-GABA conditions in an enlarged scale.

Figure 6:

Dependence of ongoing spontaneous neuronal activity on resting potential. (A) Average firing rate of P cells for each cell assembly (see the crosses) on the resting potential (uPrest) under the activity-dependent (left) or -independent (right) ambient GABA condition. (B) Membrane potential of P cells at uPrest = −64 mV under the activity-dependent (top) or -independent (bottom) ambient GABA condition. Inset: Membrane potentials under the activity-dependent (solid line) and -independent (dashed line) ambient-GABA conditions in an enlarged scale.

Figure 7A presents the average membrane potential of P cells during an ongoing time period (10 sec) as a function of the resting potential under the activity-dependent (circles) or -independent (triangles) ambient GABA condition. At uPrest = −65 mV, the levels of their average membrane potentials become almost comparable (see the arrow). Note that we have shown in such a case (see Figure 5), where uPrest was −65 mV, that the ongoing depolarization was greater and the reaction speed was faster, provided that the regulation of ambient GABA took place in an activity-dependent manner.

Figure 7:

Average membrane potential and its distribution during an ongoing time period (10 sec). (A) Average membrane potential for all (20 × 7) P cells as a function of the resting potential (uPrest) under the activity-dependent (circles) or -independent (triangles) ambient GABA condition. The arrow indicates a comparable level of average membrane potential. (B) Histograms of membrane potentials (left) and their normalized cumulative representations (right). The insets are enlarged traces. For details, see the text.

Figure 7:

Average membrane potential and its distribution during an ongoing time period (10 sec). (A) Average membrane potential for all (20 × 7) P cells as a function of the resting potential (uPrest) under the activity-dependent (circles) or -independent (triangles) ambient GABA condition. The arrow indicates a comparable level of average membrane potential. (B) Histograms of membrane potentials (left) and their normalized cumulative representations (right). The insets are enlarged traces. For details, see the text.

Interestingly, as shown in Figure 7B we found an optimal resting potential, uPrest = −65 mV, at which ongoing membrane hyperpolarization could be minimized. This leads to the best ongoing subthreshold membrane oscillations and therefore to achieving the highest reaction speed. All these results imply that the average level of ongoing membrane potential could determine to some extent (uPrest < −65 mV) the reaction speed, but the level of ongoing depolarization below firing threshold might be a crucial factor for the acceleration of reaction speed.

To shed light on a working neuronal mechanism for the ongoing membrane depolarization observed under the activity-dependent ambient GABA regulatory condition, we recorded inhibitory currents into a P cell. Figure 8 presents the feedback inhibitory current from its proximal F cell (top), the lateral inhibitory current from L cells (middle), and the ambient-GABA-mediated inhibitory current (bottom) under the activity-dependent (A) or -independent (B) ambient GABA regulatory condition. We calculated cumulative inhibitory current, which measures the amount of an inhibitory current flowing into a P cell, defined as
formula
3.1
where , lat, or ext (see equation 2.1). As shown in Figure 8C (left), the lateral (L-to-P) and the ambient-GABA-mediated (GABA) inhibitory currents are approximately comparable under the activity-dependent ambient GABA condition. In contrast, under the activity-independent ambient GABA condition (see Figure 8C, right) the lateral inhibitory current (L-to-P) far exceeds the ambient-GABA-mediated inhibitory current (GABA). These results suggest that the neuronal-activity-dependent ambient GABA regulation might contribute to minimizing the total inhibitory current flowing into P cells, by which their ongoing membrane potential could be maximally depolarized below firing threshold.
Figure 8:

Inhibitory currents into a P cell during an ongoing time period (10 sec). (A) Feedback inhibitory current from its proximal F cell (top), lateral inhibitory current from L cells (middle), and ambient-GABA-mediated inhibitory current (bottom) under the activity-dependent ambient GABA condition. (B) Inhibitory currents under the activity-independent ambient GABA condition. (C) Cumulative feedback (F-to-P), lateral (L-to-P), and ambient-GABA-mediated (GABA) inhibitory currents calculated (see equation 3.1) for those shown in A (left) and B (right). (D) Ongoing spontaneous activity (firing rate) of P cells (P) and L cells (L). Average firing rate for each cell assembly (single rectangles) under the activity-dependent (white rectangles) or -independent (gray rectangles) ambient GABA condition is shown. Each circle or triangle denotes mean activity for cell assemblies (n = 0–7).

Figure 8:

Inhibitory currents into a P cell during an ongoing time period (10 sec). (A) Feedback inhibitory current from its proximal F cell (top), lateral inhibitory current from L cells (middle), and ambient-GABA-mediated inhibitory current (bottom) under the activity-dependent ambient GABA condition. (B) Inhibitory currents under the activity-independent ambient GABA condition. (C) Cumulative feedback (F-to-P), lateral (L-to-P), and ambient-GABA-mediated (GABA) inhibitory currents calculated (see equation 3.1) for those shown in A (left) and B (right). (D) Ongoing spontaneous activity (firing rate) of P cells (P) and L cells (L). Average firing rate for each cell assembly (single rectangles) under the activity-dependent (white rectangles) or -independent (gray rectangles) ambient GABA condition is shown. Each circle or triangle denotes mean activity for cell assemblies (n = 0–7).

Note that if the ambient GABA is fixed at the mean value 0.83 μM (see Figure 8C, right), the ambient-GABA-mediated inhibitory current is slightly reduced (see the solid line marked by “GABA”). This leads to an increase in firing rate of L cells, shown in Figure 8D (right; gray rectangles), resulting in increasing L-to-P inhibition as well.

3.2.  Ambient GABA Regulation Within and Across Cell Assemblies.

We assumed here two distinct types of inhibitory (GABAergic) interneurons: F and L cells. As addressed in section 1 and described by equations 2.17 and 2.18, the concentration of ambient GABA depends on the activities of F and L cells. In this section, we show how the GABA transporters on F and L cells contribute to regulating the ambient GABA.

Figure 9A (top) presents the raster plots of spikes of P, F, and L cells, where the GABA transporter on F cells was inactivated by setting TF = 0 (see equation 2.18). Figure 9A (bottom) is the time courses of ambient GABA concentration in each cell assembly. Raster plots and ambient GABA concentrations, in which the GABA transporter on L cells was inactivated (TL = 0), are shown in Figure 9B. For the both conditions, we observed prolonged bursts of spikes (compared with those in Figure 2), which presumably arise from the depressed inhibition of P cells due to a shortage in GABA release from F or L cells into the extracellular space (i.e., due to decreased reverse transport).

Figure 9:

Influences of GABA transporter on ongoing spontaneous neuronal activity (spikes) and on the level of ambient GABA. (A) The GABA transporter on F cells was inactivated. (B) The GABA transporter on L cells was inactivated. For details, see the text.

Figure 9:

Influences of GABA transporter on ongoing spontaneous neuronal activity (spikes) and on the level of ambient GABA. (A) The GABA transporter on F cells was inactivated. (B) The GABA transporter on L cells was inactivated. For details, see the text.

This distinct difference in ambient GABA concentration indicates that the transporters on F cells and L cells contribute to regulating ambient GABA in different modes. Namely, the transporter on L cells regulates the overall level of ambient GABA across cell assemblies (or within the network; see Figure 9A, bottom). In contrast, the GABA transporter on F cells regulates the ambient GABA within individual cell assemblies (see Figure 9B, bottom).

This spatiotemporal difference in ambient GABA concentration arises from a difference in activity pattern between F and L cells. Different P cell assemblies activate the same L cells via lateral (P-to-L) projections (see Figure 1A), which leads to the broader activation of L cells that is less specific to individual cell assemblies. In contrast, since the P cells belonging to the same cell assembly behave as a whole, the activation of accompanying F cells is specific to the cell assembly that they belong to. Consequently, the L cells contribute to regulating the overall level of ambient GABA across cell assemblies (see Figure 9A), whereas the F cells regulate the individual levels of ambient GABA within cell assemblies (see Figure 9B).

To elucidate how the two modes of ambient GABA regulation achieve ongoing subthreshold membrane oscillations, we calculated cumulative membrane hyperpolarization, which measures a degree of hyperpolarization as defined by
formula
3.2
Figure 10A presents a cumulative membrane hyperpolarization index (t = 10 sec) as a function of GABA transfer coefficients TF and TL. Figure 10B presents the average ambient GABA concentration as functions of TF and TL. These results suggest that the best ongoing subthreshold membrane oscillations (see the asterisk in Figure 10A) with a minimal amount of ambient GABA (∼0.8μM; see the asterisk in Figure 10B) could be obtained, provided that the GABA transfer coefficients are properly chosen; (TF, TL) = (0.01, 0.001).
Figure 10:

Dependence of ongoing membrane hyperpolarization and ambient GABA concentration on GABA transfer coefficients, TF and TL. (A) Ongoing membrane hyperpolarization index (see equation 3.2; t = 10 sec) as functions of TF and TL. (B) Ambient GABA concentration as functions of TF and TL. The asterisk in A indicates the best ongoing subthreshold neuronal state that could be obtained with a minimal amount of ambient GABA (see the asterisk in B), determined by (TF, TL) = (0.01, 0.001). For details, see the text.

Figure 10:

Dependence of ongoing membrane hyperpolarization and ambient GABA concentration on GABA transfer coefficients, TF and TL. (A) Ongoing membrane hyperpolarization index (see equation 3.2; t = 10 sec) as functions of TF and TL. (B) Ambient GABA concentration as functions of TF and TL. The asterisk in A indicates the best ongoing subthreshold neuronal state that could be obtained with a minimal amount of ambient GABA (see the asterisk in B), determined by (TF, TL) = (0.01, 0.001). For details, see the text.

3.3.  Influences of Extrasynaptic GABAa Receptors on Ongoing Spontaneous Neuronal Activity.

We assumed here GABAa receptors located on the extrasynaptic membranes of P, F, and L cells. These receptors mediate tonic inhibitory currents into P, F, and L cells. In this section, we show how the extrasynaptic GABAa receptors contribute to maintaining ongoing membrane potentials to oscillate near firing threshold, namely, by establishing an ongoing subthreshold neuronal state.

Figure 11A presents the degree of ongoing membrane hyperpolarization indicated by Mc_hyp(t = 10 sec) (see equation 3.2). There exists an optimal (relative) number of GABAa receptors on P cells (δP = ∼1 × 104), at which ongoing subthreshold membrane oscillations could be achieved. Fewer GABAa receptors (e.g., δP = 4 × 103) result in prolonged bursts of spikes of P cells (see Figure 11B) and in an increase in lateral inhibitory current into P cells, as shown in Figure 11D (left, the thin line marked “L-to-P”). This leads to ongoing membrane hyperpolarization. If the GABAa receptors are greater (e.g., δP = 2.5 × 104), the durations of bursts are shortened (see Figure 11C). This is caused by an increase in ambient-GABA-mediated inhibitory current as shown in Figure 11D (left, the thick line marked by “GABA”), which leads to ongoing membrane hyperpolarization. The optimal amount of GABAa receptors (δP = 1 × 104) allows the total inhibitory current flowing into P cells to be minimized (see Figure 11D, right), and therefore the P cells can oscillate near firing threshold during the ongoing time period.

Figure 11:

Dependence of ongoing membrane hyperpolarization and neuronal activity (spikes) on the amount of extrasynaptic GABA receptors located on P cells. (A) Ongoing membrane hyperpolarization index (see equation 3.2; t = 10 sec) as a function of the number of GABAa receptors on P cells; δP. (B) Raster plots of action potentials of P cells for cell assemblies (fk; k = 0–7) and those (f4) of F and L cells, in which δP was decreased to 4 × 103. (C) Raster plots of action potentials, in which δP was increased to 2.5 × 104. (D) Left: Cumulative feedback (F-to-P), lateral (L-to-P) and ambient-GABA-mediated (GABA) inhibitory currents into a P cell calculated (see equation 3.1) for that in B (thin lines) or C (thick lines). Right: Inhibitory currents under the control (original) condition (the same traces shown in Figure 8C, left).

Figure 11:

Dependence of ongoing membrane hyperpolarization and neuronal activity (spikes) on the amount of extrasynaptic GABA receptors located on P cells. (A) Ongoing membrane hyperpolarization index (see equation 3.2; t = 10 sec) as a function of the number of GABAa receptors on P cells; δP. (B) Raster plots of action potentials of P cells for cell assemblies (fk; k = 0–7) and those (f4) of F and L cells, in which δP was decreased to 4 × 103. (C) Raster plots of action potentials, in which δP was increased to 2.5 × 104. (D) Left: Cumulative feedback (F-to-P), lateral (L-to-P) and ambient-GABA-mediated (GABA) inhibitory currents into a P cell calculated (see equation 3.1) for that in B (thin lines) or C (thick lines). Right: Inhibitory currents under the control (original) condition (the same traces shown in Figure 8C, left).

Figure 12A (left) presents the dependence of ongoing membrane hyperpolarization on the (relative) number of GABAa receptors located on F cells. Ongoing subthreshold membrane oscillations could be maintained, provided that the number of GABAa receptors is fewer than ∼1 × 104. This implies that fewer GABAa receptors on F cells are sufficient for establishing the ongoing subthreshold neuronal state. However, as shown in Figure 12A (right), the response property of P cells (stimulus-evoked activity) is greatly affected, indicating that fewer GABAa receptors result in a weaker response to sensory input. There exists an optimal number of GABAa receptors (e.g., δF = ∼1 × 104) at which a relatively higher neuronal response could be achieved (∼75 spikes/sec) while still keeping the ongoing subthreshold membrane oscillations. Note that the increase of δF (e.g., δF = 3 × 104) results in prolonged bursts of spikes (see Figure 12C), in an increase in lateral inhibitory current into P cells (see Figure 12D, thick line marked “L-to-P”), and therefore the P cells are hyperpolarized during the ongoing time period.

Figure 12:

Dependence of ongoing membrane hyperpolarization and neuronal activity (spikes) on the number of extrasynaptic GABA receptors located on F cells. (A) Ongoing membrane hyperpolarization index (left) (see equation 3.2; t = 10 sec) and stimulus-evoked activity (firing rate) of a P cell (right) as a function of the number of GABAa receptors on F cells; δF. (B) Raster plots of action potentials of P cells for cell assemblies (fk; k = 0–7) and those (f4) of F and L cells, in which δF was decreased to 0. (C) Raster plots of action potentials in which δF was increased to 3 × 104. (D) Cumulative feedback (F-to-P), lateral (L-to-P), and ambient-GABA-mediated (GABA) inhibitory currents into a P cell calculated (see equation 3.1) for that in B (thin lines) or C (thick lines).

Figure 12:

Dependence of ongoing membrane hyperpolarization and neuronal activity (spikes) on the number of extrasynaptic GABA receptors located on F cells. (A) Ongoing membrane hyperpolarization index (left) (see equation 3.2; t = 10 sec) and stimulus-evoked activity (firing rate) of a P cell (right) as a function of the number of GABAa receptors on F cells; δF. (B) Raster plots of action potentials of P cells for cell assemblies (fk; k = 0–7) and those (f4) of F and L cells, in which δF was decreased to 0. (C) Raster plots of action potentials in which δF was increased to 3 × 104. (D) Cumulative feedback (F-to-P), lateral (L-to-P), and ambient-GABA-mediated (GABA) inhibitory currents into a P cell calculated (see equation 3.1) for that in B (thin lines) or C (thick lines).

Figure 13A (left) presents the dependence of ongoing membrane hyperpolarization on the (relative) number of GABAa receptors located on L cells. An increase in the number results in oscillating near firing threshold. However, care must be taken, as shown in Figure 13A (right), indicating that the selective responsiveness (SR) of P cells gradually deteriorates as the number increases.

Figure 13:

Dependence of ongoing membrane hyperpolarization and neuronal activity (spikes) on the number of extrasynaptic GABA receptors located on L cells. (A) Ongoing membrane hyperpolarization index (left) (see equation 3.2; t= 10 sec) and selective responsiveness (SR; see equation 3.3) of a P cell (right) as a function of the number of GABAa receptors on L cells; δL. (B) Raster plots of action potentials of P cells for cell assemblies (fk; k = 0–7) and those (f4) of F and L cells, in which δL was decreased to 1 × 103. (C) Raster plots of action potentials in which δL was increased to 3 × 104. (D) Cumulative feedback (F-to-P), lateral (L-to-P) and ambient-GABA-mediated (GABA) inhibitory currents into a P cell calculated (see equation 3.1) for that in B (thin lines) or C (thick lines).

Figure 13:

Dependence of ongoing membrane hyperpolarization and neuronal activity (spikes) on the number of extrasynaptic GABA receptors located on L cells. (A) Ongoing membrane hyperpolarization index (left) (see equation 3.2; t= 10 sec) and selective responsiveness (SR; see equation 3.3) of a P cell (right) as a function of the number of GABAa receptors on L cells; δL. (B) Raster plots of action potentials of P cells for cell assemblies (fk; k = 0–7) and those (f4) of F and L cells, in which δL was decreased to 1 × 103. (C) Raster plots of action potentials in which δL was increased to 3 × 104. (D) Cumulative feedback (F-to-P), lateral (L-to-P) and ambient-GABA-mediated (GABA) inhibitory currents into a P cell calculated (see equation 3.1) for that in B (thin lines) or C (thick lines).

SR is a measure similar to orientation bias (OB) that is frequently employed for the lateral geniculate nucleus (LGN) (Xu, Ichida, Shostak, Bonds, & Casagrande, 2002) and the primary visual cortex (Leventhal, Thompson, Liu, Zhou, & Ault, 1995). We briefly explain how to calculate OB. Responses of a cell to different orientations (angles) of a bar stimulus {e.g., 0, π/8, 2π/8, 3π/8, 4π/8, 5π/8, 6π/8, 7π/8} are stored as a series of vectors. The vectors are added and divided by the sum of the absolute values of the vectors. The angle and the length of the resultant vector provide, respectively, the preferred direction and the degree of orientation preference of that cell. The degree of orientation preference is termed orientation bias (OB). Note that since the periodicity of orientation is π, the angles of the bar stimulus are multiplied by a factor of two. As a result, OB ranges from 0 to 1.0, with 0 being completely insensitive to any orientation and 1.0 responding to only one orientation.

Similarly SR is defined as
formula
3.3
where R(fk) is the firing rate of a P cell provoked by feature stimulus fk (k = 0 − 7).

The results shown in Figure 13A imply that there exist an optimal number of GABAa receptors on L cells, δL = ∼1 × 104, at which ongoing subthreshold membrane oscillations could be achieved while still keeping a comparatively higher selective responsiveness to sensory input. Note that the increase of δL (e.g., δF = 3 × 104) results in prolonged bursts of spikes (see Figure 13C). However, the lateral inhibitory current into a P cell (see Figure 13D, the thick line marked “L-to-P”) is not likely to be increased. This is because too many GABAa receptors on L cells lead to an increase in ambient-GABA-mediated inhibitory current into L cells, which depresses the activity of L cells and therefore decreases the lateral inhibitory current into P cells.

3.4.  Robustness to Model Parameters.

In this section, we show the robustness of the network to model parameters by systematically varying their values. We employed two typical parameters, steepness and threshold of sigmoid function (see equation 2.19; ηP and ζP), that determine action potential generation. Neuronal behavior was explored in term of ongoing spontaneous neuronal activity on which this study focused.

Figure 14A presents how robust the model is to these parameters. Ongoing spontaneous activity (firing rate) is plotted as a function of the resting potential (uPrest; see equation 2.1). The firing rate is gradually elevated as the steepness decreases (top) or the threshold lowers (bottom), where it is robustly maintained within a certain range (subhertz to tens of hertz). This covers (or stays within) a range that has been observed in the cortex (Paisley & Summerlee, 1984; Arieli et al., 1995; Gur, Kagan, & Snodderly, 2005).

Figure 14:

Robustness of the network to model parameters. (A) Dependence of neuronal activity on the steepness (ηP, top) or the threshold (ζP, bottom) of the sigmoid function (see equation 2.19). Ongoing spontaneous activity (firing rate) is plotted as a function of the resting potential (uPrest). A certain range (subhertz to tens of hertz) could be covered. (B) Relationship between ongoing spontaneous neuronal activity and ambient GABA concentration. Top: Dependence of ongoing spontaneous activity (firing rate) and average ambient GABA concentration ([GABA]ext_avg) on the GABA transfer coefficient; TL. Bottom: Dependence of ongoing spontaneous neuronal activity on average ambient GABA concentration. For details, see the text.

Figure 14:

Robustness of the network to model parameters. (A) Dependence of neuronal activity on the steepness (ηP, top) or the threshold (ζP, bottom) of the sigmoid function (see equation 2.19). Ongoing spontaneous activity (firing rate) is plotted as a function of the resting potential (uPrest). A certain range (subhertz to tens of hertz) could be covered. (B) Relationship between ongoing spontaneous neuronal activity and ambient GABA concentration. Top: Dependence of ongoing spontaneous activity (firing rate) and average ambient GABA concentration ([GABA]ext_avg) on the GABA transfer coefficient; TL. Bottom: Dependence of ongoing spontaneous neuronal activity on average ambient GABA concentration. For details, see the text.

Leventhal and colleagues (2003) demonstrated that ongoing spontaneous neuronal activity (∼4 Hz) in the primary visual cortex was reduced by about 10% when applied with GABA or muscimol (a GABAa receptor agonist). The relationship between ongoing spontaneous activity and muscimol concentration has been investigated in rat brainstem (Yuan et al., 2004). Ongoing spontaneous activity was decreased in a concentration-related fashion: 30 μM produced on approximate 40% decrease in firing rate compared with that (∼1 Hz) under a control condition (2 μM).

To see whether our model could reproduce this relationship, we altered the level of ambient GABA (concentration) by systematically varying the GABA-transfer coefficient; TL (see equation 2.18). As shown in Figure 14B (top), we could have obtained a certain range (see the triangles) of submicromolar to several micromolar levels. This covers a range of GABA concentrations that have been observed in the brain (Lerma et al., 1986; Tossman et al., 1986; Scimemi et al., 2005). Figure 14B (bottom) shows that the ongoing spontaneous activity of P cells tends to be decreased in a concentration-related fashion: approximately 3 μM produced on approximate 60% decrease in firing rate compared with that (about 7 Hz) under the control (original) condition (about 0.7 μM).

4.  Discussion

In this study, we investigated how the neuronal-activity-dependent regulation of ambient GABA (i.e., GABA in extracellular space), mediated by transporters on feedback (F) and lateral (L) inhibitory (GABAergic) interneurons, contributes to maintaining principal (P) cells to oscillate near firing threshold during ongoing spontaneous neuronal activity time periods. We found that the transporters could regulate the level of ambient GABA in two distinct modes. The transporter on F cells was responsible for regulating the GABA level within cell assemblies (see Figure 9B), and the transporter on L cells was responsible for across-cell assemblies or within the network (see Figure 9A). This combinatorial regulation of ambient GABA allowed the ongoing membrane potential to oscillate near firing threshold with a minimal amount of ambient GABA (see Figure 10).

We also investigated how the ambient GABA acts on the extrasynaptic GABAa receptors located on P, F, and L cells and modulates the ongoing neuronal activity. These receptors moderately controlled the excitability of dynamic cell assemblies, allowing P cells to fire with brief bursts. This minimized the total inhibitory current into P cells, leading them to oscillating near firing threshold during the ongoing time period.

We found a lesser influence of the extrasynaptic GABAa receptors located on F cells on achieving the ongoing subthreshold membrane oscillations. However, this GABAa receptor contributed to enhancing the responsiveness of P cells to sensory input (see Figure 12A, right). We also found that the extrasynaptic GABAa receptors located on L cells contribute to achieving the ongoing subthreshold membrane oscillations. However, too many GABAa receptors on L cells resulted in a deterioration of the selective responsiveness of P cells to the input (see Figure 13A, right). We suggest that an optimal number of extrasynaptic GABAa receptors on F and L cells may exist, at which maximal neuronal and selective responsiveness could be achieved while still keeping the ongoing subthreshold membrane oscillations.

The key issue for the model proposed here might be that the reversal potential of GABAergic interneurons determines the direction of GABA transport—forward (uptake) and reverse (release) transport. Concerning this, neurophysiological recordings have been made for GABA transporter (such as GAT-1) currents (Richerson & Wu, 2003). The direction of current was the same as the direction of Na+ and GABA flux. At membrane potentials below the reversal potential, there was a net influx of GABA (forward transport), whereas at membrane potentials above the reversal potential, there was a net efflux of GABA (reverse transport). The stoichiometry of the transporter has been well defined. A thermodynamic reaction cycle involves coupled translocation of 2 Na+ ions, one Cl− ion, and 1 GABA molecule (for details, see Richerson & Wu, 2003).

The model examined here was based not strictly but functionally on the findings. Namely, the direction of GABA was simply determined by the reversal potential and membrane potential (see equation 2.18), and therefore we were not able to record transporter currents. The recorded ambient GABA concentration was also hypothetical and would be adjusted by some experimental studies. Nevertheless, this study showed that the GABA transporter could regulate the level of ambient GABA and contribute to achieving ongoing subthreshold membrane oscillations.

We assumed the two distinct types of GABAergic interneurons: feedback inhibitory interneurons (F cells) and lateral inhibitory interneurons (L cells). A variety of GABAergic interneurons has been found in the cortex, such as horizontal cells and large, medium, and small-sized multipolar cells (for a survey, see Prieto, Peterson, & Winer, 1994). The large multipolar cells with their wide axonal arbors can send signals even to distant principal cells, while the small multipolar cells, with their narrow axonal arbors, are limited to proximal principal cells. Based on these observations, we let each L cell project to all (nearby to distant) P cells within cell assemblies, and the F cell only to its proximal P cell. Fundamental properties of ongoing spontaneous neuronal activity emerged in the network dynamics without ambient GABA have been investigated in detail (Hoshino, 2006, 2008a).

GABA spillover from synaptic cleft or nonvesicular GABA release from neurons and glia into extracellular space (Somogyi et al., 1989; Nusser et al., 1995; Brickley et al., 1996; Soltesz, & Nusser, 2001) are other likely major sources of ambient GABA. In a previous study (Hoshino, 2008b), we proposed a neural network model in which GABA spills over from presynaptic interneurons into extracellular space and intracortical tonic inhibition takes place. The amount of GABA spillover depends on the activity (firing rate) of inhibitory interneurons. We made a simulation for that case—that GABA spillover, instead of GABA transport, took place. Figure 15 (top) presents ambient GABA concentration in each cell assembly. The levels of ambient GABA are roughly comparable among cell assemblies, compared with those regulated by the GABA transporter (bottom; the same traces shown in Figure 2). The almost identical GABA levels (top) resulted in similar neuronal activities (not shown) as shown in Figure 3, in which the level of ambient GABA was kept constant. We suggest that the GABA transporter, with its forward and reverse transport mechanism, could not only compensate GABA spillover into extracellular space but also well regulate ambient GABA so that principal cells can oscillate near firing threshold during ongoing spontaneous neuronal activity time periods.

Figure 15:

Influences of GABA spillover on the regulation of ambient GABA. (Top) Ambient GABA concentrations, where GABA spillover instead of GABA transport took place. (Bottom) Ambient GABA concentrations, where the GABA transport mechanism worked (the same traces shown in Figure 2). For details, see the text.

Figure 15:

Influences of GABA spillover on the regulation of ambient GABA. (Top) Ambient GABA concentrations, where GABA spillover instead of GABA transport took place. (Bottom) Ambient GABA concentrations, where the GABA transport mechanism worked (the same traces shown in Figure 2). For details, see the text.

Acknowledgments

Discussions with Takami Matsuo are gratefully acknowledged. I express my gratitude to Hiromi Ohta for her encouragement throughout this study and to anonymous reviewers for giving me valuable comments and suggestions on the earlier drafts.

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