Abstract

Neurons of primary auditory cortex (AI) emit spikes (action potentials) in two distinct manners, responding to sounds in an onset or a sustained manner. The former AI neurons are called phasic cells and the latter tonic cells. The phasic cells generate spikes for a brief time period (less than hundreds of milliseconds) at the onset of an auditory stimulus (e.g., a tone frequency sound), and the tonic cells continuously generate spikes throughout the stimulation period. Simulating a neural network model of AI, we investigated whether and how the onset discharges influence the sustained discharges that are believed to play a central role in encoding auditory information. Onset discharges, triggered by a phasic input, briefly excited GABAergic interneurons and transiently increased the level of ambient GABA, which was immediately recognized by extrasynaptic GABAa receptors and provided inhibitory currents into neurons. The transient alteration of ambient GABA allowed tonic cells to respond selectively to a tonic input. The timing of phasic input relative to a tonic one had a great impact on the responsiveness of tonic cells. We found optimal timing for the best selective responsiveness: phasic input preceding tonic input by several tens of milliseconds. Offset discharges induced by a secondary input to phasic cells, applied at the end of the tonic input period, suddenly terminated the sustained discharges and allowed the network to return rapidly to the ongoing-spontaneous neuronal state. We suggest that the transporter-mediated alteration of ambient GABA, triggered by onset discharges, may improve the response property of AI neurons. Offset discharges may have a role in resetting AI neurons so that they can prepare for the next auditory input.

1.  Introduction

It is well known that neurons of primary auditory cortex (AI) emit spikes (action potentials) in two distinct manners, responding to sounds in an onset or a sustained manner (Recanzone, 2000; Mickey & Middlebrooks, 2003; DeWeese, Wehr, & Zador, 2003). The former AI neurons are called phasic cells and the latter tonic cells. The phasic cells generate spikes for a brief time period (less than hundreds of milliseconds) at the onset of an auditory stimulus (e.g., a tone frequency sound), and the tonic cells continuously generate spikes throughout the stimulation period.

It is generally accepted that the sustained discharges play a central role in encoding auditory information. The moment of onset discharges provides the auditory cortex with precise timing information to mark the onset of a sound or transitions in an ongoing acoustic stream. Wang, Lu, Snider, and Liang (2005) hypothesized that onset discharges with short latency allow the auditory cortex to quickly detect the occurrence of sounds from the external environment. A computational simulation study (Hoshino, 2007) supported their notion, in which a combinatorial (feedback and lateral) inhibition of principal cells by GABAergic interneurons played a crucial role.

Cortical inhibitory interneurons (e.g., small basket cells, large basket cells, nest basket cells, chandelier cells, Martinotti cells) have a variety of anatomical and physiological characteristics (Markram et al., 2004) and are believed to have important roles in regulating the activity of cortical networks. Diverse sets of gamma-aminobutyric acid-ergic (GABAergic) processes are essential for the regulation of cortical activity (Miles, 2000; Gupta, Wang, & Markram, 2000). Receptors recognizing GABA constitute a major source of inhibitory processes (Mody & Pearce, 2004), where GABA release from interneurons into synaptic clefts, triggered by presynaptic action potentials, is the classical neurotransmission.

Recently another type of neurotransmission (known as extrasynaptic inhibition) has been attracting scientists’ attention, in which the recognition of GABA in extracellular space (i.e., ambient GABA) by GABAa receptors located on extrasynaptic membrane regions is essential. Most experiments have identified such extrasynaptic GABAa receptors in the cerebellum and hippocampus (Nusser, Sieghart, & Somogyi, 1998; Wei, Zhang, Peng, Houser, Mody, 2003; Mody & Pearce, 2004), but recent studies (Drasbek & Jensen, 2006; Scimemi et al., 2006) have identified them as well in the neocortex of humans and rats. This led us to assume extrasynaptic GABAa receptors in an AI network model, as will be proposed later.

Some experiments evidenced certain effects of ambient GABA on sensory information processing. Manunta and Edeline (1997, 1998) demonstrated that the application of GABA into the auditory cortex could improve the frequency selectivity of individual AI neurons. In vision, a similar result has been observed: the application of GABA into the primary visual cortex (V1) of macaque monkeys (26–30 years old) improved orientation selectivity of individual V1 neurons (Leventhal, Wang, Pu, Zhou, & Ma, 2003).

As to the regulation of ambient GABA levels, Richerson and colleagues (Richerson & Wu, 2003; Richerson, 2004; Wu, Wang, Diez-Sampedro, & Richerson, 2007) made an interesting suggestion. Transporter such as GAT-1 is crucial not only for removing GABA from but also releasing it into the extracellular space. The transporter clamps ambient GABA at a certain level within a submicromolar range at rest. The transporter is near equilibrium under normal physiological conditions and will reverse with a relatively small increase in membrane potential. The ambient GABA, even though its concentration is low, acts on extrasynaptic GABAa receptors and mediates to provide inhibitory currents in neurons. The researchers demonstrated that an increase in inhibitory current could be prevented not by blocking vesicular GABA release but by GABA transporter antagonists.

Inspired by these studies, we speculated that the transporter-mediated regulation of ambient GABA, continuously activating extrasynaptic GABAa receptors, might have important roles in auditory information processing. We construct a neural network model of AI, which has a nontonotopic area and a tonotopic area (Yost, 1994) comprising phasic and tonic cells, respectively. Phasic cells emit action potentials in an onset manner, responding transiently (∼100 msec) to every frequency (non-CF). Tonic cells emit action potentials in a sustained manner, responding selectively to a tone with its characteristic frequency (CF).

Transporters on GABAergic interneurons regulate the level of ambient GABA (GABA concentration) in a neuronal-activity-dependent manner. The ambient GABA is recognized by extrasynaptic GABAa receptors on tonic cells and interneurons and modulates the overall activity of the network. We investigate whether and how the transporter-mediated alteration of ambient GABA, triggered by onset discharges, influences the following sustained discharges. Some phasic cells in the AI (Chimoto, Kitama, Qin, Sakayori, & Sato, 2002) and MGB (Cetas et al., 2002) are known to respond to a tonal sound in a different manner. Namely, they discharge in an offset manner, responding to the termination of sounds. We also investigate here how the offset discharges influence the network behavior.

2.  Neural Network Model

2.1.  Model Structure.

A neural network model of a primary auditory cortical (AI) area is schematically shown in Figure 1A. Tonic (T) and phasic (P) cells constitute, respectively, multiple frequency columns (f1, f2, …, fn, …, fM) and a single nonfrequency region that has responsiveness to every tone frequency. The frequency columns and the nonfrequency region receive tonic and phasic inputs from the medial geniculate body (MGB), thereby generating sustained and onset discharges in T and P cells, respectively. The timing of paired inputs is shown in Figure 1B. Frequency columns consist of cell units (see the large gray circle), each of which contains one tonic cell (T), one lateral inhibitory cell (L), and one feedback inhibitory cell (FT). The nonfrequency region consists of cell units (see the small gray circle), each of which contains one phasic cell (P) and one feedback inhibitory cell (FP).

Figure 1:

A neural network model of a primary auditory cortical (AI) area. Tonic (T) and phasic (P) cells constitute, respectively, multiple frequency columns (f1, f2, …, fn, …, fM) and a single nonfrequency region. Frequency columns consist of cell units (see the large gray circle), each of which contains one T cell, one lateral inhibitory cell (L), and one feedback inhibitory cell (FT). The nonfrequency region consists of P and FP cells (see the small gray circle). T and P cells receive tonic and phasic inputs, respectively. (B) Timing of phasic and tonic inputs. (C) A schematic drawing of a GABA transporter embedded in the membrane of a GABAergic interneuron—an FT or an L cell. The downward and upward arrows indicate, respectively, forward transport (uptake) and reverse transport (release) of GABA, coupled with two Na+ ions and one Cl ion.

Figure 1:

A neural network model of a primary auditory cortical (AI) area. Tonic (T) and phasic (P) cells constitute, respectively, multiple frequency columns (f1, f2, …, fn, …, fM) and a single nonfrequency region. Frequency columns consist of cell units (see the large gray circle), each of which contains one T cell, one lateral inhibitory cell (L), and one feedback inhibitory cell (FT). The nonfrequency region consists of P and FP cells (see the small gray circle). T and P cells receive tonic and phasic inputs, respectively. (B) Timing of phasic and tonic inputs. (C) A schematic drawing of a GABA transporter embedded in the membrane of a GABAergic interneuron—an FT or an L cell. The downward and upward arrows indicate, respectively, forward transport (uptake) and reverse transport (release) of GABA, coupled with two Na+ ions and one Cl ion.

Within these frequency columns and the nonfrequency region, T or P cells are recurrently connected via excitatory synapses. This circuitry creates the so-called dynamic cell assemblies, which allows population activation of T or P cells when excited. An FT cell receives excitatory projections from P cells and its proximal T cell and sends a feedback inhibitory projection to that T cell. An L cell receives excitatory projections from P cells and T cells belonging to other frequency columns, and sends inhibitory projections to all (nearby to distant) T cells within the same frequency column. This circuitry provides a lateral inhibitory mechanism between different frequency columns. To focus here on what direct influences the onset discharges have on sustained discharges, we assumed feedforward projections from P to T, FT, and L cells but not their feedback projections to the P cells.

As suggested by Richerson and colleagues (Richerson & Wu, 2003; Wu, Wang, & Richerson, 2003), transporter 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 the 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 co-transported molecules (2Na+, Cl, GABA) cross the membrane together (see Figure 1C). 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 calculated when electrochemical potential = 0, namely, at equilibrium. Under the normal condition, it 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 (see the downward arrow in Figure 1C), takes place. In contrast, at membrane potentials above the reversal potential, net efflux of GABA, called reverse transport or GABA-release (see the upward arrow in Figure 1C), takes place.

A conductance-based integrate-and-fire neuron model is employed (Hoshino, 2009), whose parameters and their values are listed in Table 1. GABA transporters on L cells regulate the overall level of ambient GABA across cell assemblies, and those on FT cells do so within individual cell assemblies. Through this transport mechanism, ambient GABA concentration is kept within a submicromolar range during ongoing-spontaneous neuronal activity time periods.

Table 1:
List of Parameters and Their Values.
graphic
graphic

Source: Hoshino (2009).

In the model, we assume a 1 msec pulse of intrasynaptic 1 mM glutamate or GABA (see mM in Table 1) when a neuron fires. Voltage clump recordings in excised membrane patches showed that a 1 msec pulse of 1 mM glutamate produced postsynaptic current that was quite similar to that in an intact synapse (Colquhoun, Jonas, & Sakmann, 1992; Stern, Edwards, & Sakmann, 1992). Based on these experiments, Destexhe, Mainen, & Sejnowski (1998) proposed a simplified kinetic model of postsynaptic current, in which a 1 msec pulse of 1 mM transmitter, either glutamate or GABA, is released into the synaptic cleft when an action potential invades the presynaptic terminal. The parameter values for the AMPA and GABAa receptors, (see Table 1), were obtained by fitting the kinetic model to average postsynaptic currents observed in experiments.

2.2.  Dynamics of Ambient GABA.

Depending on the level of ambient GABA (GABA concentration), extrasynaptic inhibitory currents flow in T, FT, and L cells (Hoshino, 2009). The concentration of ambient GABA within frequency column fn, [GABA]ext(fn; t), is defined by
formula
2.1
where τ and are the time constant and the concentration at rest, respectively. determines the amount of forward or reverse transport, which depends on the activities of GABAergic (FT, L) cells and is functionally described as
formula
2.2
where TF and TL correspond to the transfer coefficients of GABA and uFrev and uLrev are the reversal potentials for FT and L cells, respectively. We modeled the transporters and extrasynaptic GABA receptors only for the frequency columns (T, FT, L cells), not for the nonfrequency region (P, FP cells), in order to focus here on how the transient alteration of ambient GABA influences the tuning property of tonic (T) cells.

Concerning parameter τ (see equation 2.1), unfortunately we have found no experimentally measured values. However, we found an experiment (Wu, et al., 2007) that measured transporter-mediated current in a neuron. In that experiment, patch-clamp recordings were made from two CHO cells; one transfected with transporter GAT-1 (GAT-1 cell) and the other with GABAa receptor (Sniffer cell). The concentrations of substrates (Na+, Cl, GABA) were systematically controlled in the inside and outside of the GAT-1 cell. Hyperpolarization of the GAT-1 cell from −60 mV to −80 mV resulted in a decrease in inward current in the sniffer cell, whereas depolarization to −40 mV and to +40 mV resulted in a progressively larger inward current. The increased current was due to GABA release from GAT-1 reversal, namely, the reverse transport when crossing the reversal potential.

The timescale of the transporter-mediated current was 1 to 2 seconds, based on which we assumed τ = 2 sec for ambient GABA concentration (see Table 1). Such a long timescale for ambient GABA may determine, to a greater extent, the observed timescale of current (1–2 seconds), because the current flowing through a GABAa receptor is fast—on the order of milliseconds or so (Destexhe et al., 1998). μM (see Table 1) was assumed based on experimental studies (Lerma, Herranz, Herreras, Abraira, & Martin del Rio, 1986; Tossman, Jonsson, & Ungerstedt, 1986; Scimemi et al., 2006) that reported that ambient GABA is maintained within a range of submicromolar to several micromolar levels in the brain, including the cortex. The value 0.2 μM may correspond to that at rest. Because of the lack of relevant experimental data, we carefully set TF = 0.03 and TL = 0.07 (see Table 1). This kept ambient GABA concentration within that (submicromolar to several micromolar) range during both the ongoing-spontaneous and the stimulus-evoked neuronal activity time periods. We set and uLrev close to the resting potential: −66 mV (see Table 1).

3.  Results

3.1.  Responses to Tone Frequencies.

In this section, we show the fundamental dynamic property of the network, how the level of ambient GABA (GABA concentration) is altered depending on the activity of GABAergic interneurons (FT, L cells), and how it influences neuronal responsiveness to a tone frequency sound.

Figure 2 presents the raster plots of action potentials of P (top), T (second), FT (third), L (fourth) cells and ambient GABA concentration in each frequency column f1 to f8 (bottom). Stimulation with a tone frequency f5 activates P cells in an onset manner and T cells in a sustained manner. As addressed in section 2, we assumed axonal projections from phasic cells to frequency columns: P to T, P to FT, and P to L. The transient P-to-T excitation activates T cells, by which the T cells can react rapidly to the tonic input. The transient P-to-FT and P-to-L excitation leads to releasing GABA into the extrasynaptic space, elevating ambient GABA concentration (see the dotted circles at the bottom of Figure 2). We will show in Figures 9 and 10 that the transient increase of ambient GABA is crucial for T cells to respond selectively to the tonic input.

Figure 2:

Neuronal responses and ambient GABA alterations. Raster plots of action potentials of P (top), T (second), FT (third), L (fourth) cells and ambient GABA concentration in each frequency column f1 to f8 (bottom). The short and long horizontal bars indicate the time periods of phasic and tonic inputs, respectively.

Figure 2:

Neuronal responses and ambient GABA alterations. Raster plots of action potentials of P (top), T (second), FT (third), L (fourth) cells and ambient GABA concentration in each frequency column f1 to f8 (bottom). The short and long horizontal bars indicate the time periods of phasic and tonic inputs, respectively.

Note that during the tonic input period, the ambient GABA is augmented, except for that in the stimulus-relevant column f5 (see the square at the bottom of Figure 2). is decreased soon after the termination of the phasic input. This is due largely to the suppressed activity of L cells corresponding to the tonic input f5 (see the rectangle). The lowered ambient GABA level in the stimulus-relevant column results in a decrease in GABA-mediated inhibitory current, thereby enhancing the activity of stimulus-relevant T cells (f5). In contrast, the elevated ambient GABA level in stimulus-irrelevant columns (e.g., see the oval at the bottom of Figure 2) results in an increase in GABA-mediated inhibitory current, thereby suppressing the activity of stimulus-irrelevant T cells. This leads to improving the selective responsiveness to the tonic input.

Note that ambient GABA mediates inhibitory current not only in T cells but also in FT and L cells. Hence, their balance might have a great impact on the dynamic behavior of the network. Especially the parameters relating to extrasynaptic GABAa receptors (see Table 1) are crucial. In a previous paper (Hoshino, 2009), we carefully explored the dynamic nature of a neural network model, according to which their parameter values were chosen (see Table 1).

We examined in more detail how the selective responsiveness could be assured. Figure 3 presents the membrane potential (mem. pot.), the ambient GABA concentration ()), and the GABA-mediated inhibitory current (current) for a stimulus-relevant (Figure 3A) or -irrelevant (Figure 3B) T cell. The reduced ambient GABA within the stimulus-relevant column (see the thin dashed line in Figure 3A) results in a decrease in GABA-mediated inhibitory current into stimulus-relevant T cells (see the thick dashed line in Figure 3A). Hence, their responsiveness is enhanced (see the top trace). In contrast, the augmented ambient GABA within stimulus-irrelevant columns (e.g., see the thin dashed line in Figure 3B) results in an increase in GABA-mediated inhibitory current (see the thick dashed line in Figure 3B). Hence, their activity is suppressed (see the top trace).

Figure 3:

Influences of sensory stimulation on tonic (T) cells and ambient GABA concentration. (A) Membrane potential of a stimulus-relevant (f5) T cell (top), its ambient GABA concentration (middle), and GABA-mediated inhibitory current into that T cell (bottom). (B) Those irrelevant to the stimulus, f6.

Figure 3:

Influences of sensory stimulation on tonic (T) cells and ambient GABA concentration. (A) Membrane potential of a stimulus-relevant (f5) T cell (top), its ambient GABA concentration (middle), and GABA-mediated inhibitory current into that T cell (bottom). (B) Those irrelevant to the stimulus, f6.

Figure 4 presents the dependence of ambient GABA levels on the activity of an L or an FT cell. Due to the hyperpolarization of L cells in the stimulus-relevant column (see the second trace of Figure 4A), the transporters on L cells remove GABA from the extracellular space (“forward”) and therefore lower ambient GABA concentration (see the top trace). In contrast, the depolarization of FT cells (see the bottom trace) contributes to releasing GABA (“reverse”). This seemed to augment ambient GABA, but it in fact reduced it (see the top trace). This is due to such a small transporter ratio (TF/TL = 0.03/0.07; see Table 1). Namely, the GABA transport by L cells prevails. Figure 4B presents those for the stimulus-irrelevant column, indicating that the depolarization of L cells (see the second trace) contributes to releasing GABA and thus to augmenting ambient GABA during the tonic stimulation period (see the top trace).

Figure 4:

Influences of phasic and tonic stimulation on ambient GABA, lateral (L) and feedback (FT) inhibitory interneurons. (A) Ambient GABA concentration in the frequency column (top), the membrane potentials of an L (middle), and an FT cell relevant to the stimulus, f5. (B) Those irrelevant to the stimulus, f6. (C) Cumulative representations of membrane potentials of L (left) and FT (right) cells shown in A and B.

Figure 4:

Influences of phasic and tonic stimulation on ambient GABA, lateral (L) and feedback (FT) inhibitory interneurons. (A) Ambient GABA concentration in the frequency column (top), the membrane potentials of an L (middle), and an FT cell relevant to the stimulus, f5. (B) Those irrelevant to the stimulus, f6. (C) Cumulative representations of membrane potentials of L (left) and FT (right) cells shown in A and B.

Figure 4C is the cumulative representations of membrane potential of an L (left) and an FT (right) cell shown in Figures 4A and 4B. The upward and downward directions of lines indicate membrane depolarization and hyperpolarization, respectively. The downward line marked by f5 (see the left of Figure 4C) during the tonic input period evidences the suppression of L cells, which leads to removing GABA. The upward line marked by f6 or f1 evidences the activation of L cells, which leads to releasing GABA. In Figure 4C (right), the upward line marked by f5 evidences that the activity of FT cells is enhanced. However, as addressed above, its contribution is less than that of L cells due to such a small transporter ratio (TF/TL = 0.03/0.07). We will show in Figure 7 that this ratio can ensure a suitable network performance.

3.2.  Significance of Transporter-Mediated Regulation of Ambient GABA.

To understand the significance of transporter-mediated regulation of ambient GABA, we devised a simulation in which the ambient GABA was fixed at a certain level. It was consistent with the average ambient GABA concentration for an ongoing-spontaneous time period (10 sec). As shown in Figure 5A (top), the selective responsiveness was deteriorated if the ambient GABA was fixed; It might remind us that the L cells, to which the stimulus-relevant T cells project laterally, could suppress the activity of stimulus-irrelevant T cells. Hence, the problem (deterioration in selective responsiveness) would be overcome when the lateral inhibitory (L-to-T) mechanism works strongly.

Figure 5:

Selective responsiveness under a fixed ambient-GABA condition. (A) Raster plots of action potentials of T cells, in which the lateral inhibitory (L-to-T) connection strength wTij,lat(fn) was increased from 0.2 (top) to 5.0 (bottom). (B) Membrane potentials of a T cell during an ongoing-spontaneous time period for wTij,lat(fn) = 0.2 (solid line) and 5.0 (dashed line). Note that the total amount of GABA for the ongoing period was the same as that under the original (transporter-mediated ambient-GABA regulatory) condition.

Figure 5:

Selective responsiveness under a fixed ambient-GABA condition. (A) Raster plots of action potentials of T cells, in which the lateral inhibitory (L-to-T) connection strength wTij,lat(fn) was increased from 0.2 (top) to 5.0 (bottom). (B) Membrane potentials of a T cell during an ongoing-spontaneous time period for wTij,lat(fn) = 0.2 (solid line) and 5.0 (dashed line). Note that the total amount of GABA for the ongoing period was the same as that under the original (transporter-mediated ambient-GABA regulatory) condition.

As expected, the selectivity was improved (see the bottom of Figure 5A), provided that the lateral inhibitory connection strength was increased to wTij,lat(fn) = 5.0. However, this causes a fatal problem for ongoing-spontaneous neuronal activity that functions as a ready network state for subsequent sensory (tonic) input. Figure 5B presents the membrane potentials of a T cell during the ongoing time period shown in Figures 5A (top; see the solid line) and 5A (bottom; see the dashed line). The enhanced lateral inhibition results in ongoing-spontaneous hyperpolarization (see the dashed line), which is known to decelerate the reaction speed of neurons to sensory input (Hoshino, 2008). These results indicate that the transporter-mediated regulation of ambient GABA is advantageous for maintaining T cells at a subthreshold level without interfering in selective responsiveness.

We systematically assessed the dependence of selective responsiveness and ongoing membrane hyperpolarization on lateral inhibitory connection strength, wTij,lat(fn). The selectivity was measured as the ratio of evoked activity (firing rate) in a stimulus relevant (f5) to that in an irrelevant (e.g., f6) T cell. The ongoing membrane hyperpolarization was measured as the cumulative hyperpolarization below the resting potential (see uTrest = −65 mV in Table 1), which is defined by
formula
3.1
where M and NT are the numbers of frequency columns and T cells within each frequency-column, respectively (Hoshino, 2009).

Figure 6A presents the dependence of selectivity (see the diamonds) and cumulative hyperpolarization (see the circles) calculated as sec). An optimal performance is obtained at wTij,lat(fn) = 3.8 (see the arrow): the selective response property and the subthreshold ongoing property are balanced. Figure 6B (top) presents those for the original condition with ambient-GABA alteration. Its optimal performance (see the arrow) is far superior to that of Figure 6A (see the dashed line). Figure 6B (bottom) presents average ambient GABA concentrations. The decline in ambient GABA results in reducing extrasynaptic GABAa-receptor-mediated inhibition (not shown), thereby alleviating membrane hyperpolarization (compare the open circles with the filled circles in Figure 6A).

Figure 6:

Influences of ambient-GABA alteration on selective responsiveness and ongoing-spontaneous membrane potential. (A) Dependence of selectivity (see the diamonds) and cumulative hyperpolarization (see the circles) calculated as sec) (see equation 3.1) under the fixed ambient GABA condition shown in Figure 5. (B) Dependence of selectivity (see the diamonds) and cumulative hyperpolarization (see the circles) under the original condition (see Figure 2) with ambient GABA alteration. Changes in average ambient GABA concentration were shown (bottom).

Figure 6:

Influences of ambient-GABA alteration on selective responsiveness and ongoing-spontaneous membrane potential. (A) Dependence of selectivity (see the diamonds) and cumulative hyperpolarization (see the circles) calculated as sec) (see equation 3.1) under the fixed ambient GABA condition shown in Figure 5. (B) Dependence of selectivity (see the diamonds) and cumulative hyperpolarization (see the circles) under the original condition (see Figure 2) with ambient GABA alteration. Changes in average ambient GABA concentration were shown (bottom).

As addressed previously, we assumed TF/TL = 0.03/0.07 for GABA transporters on FT and L cells. Figure 7 presents how this ratio influences the activity of T cells and the level of ambient GABA. A smaller ratio (see Figure 7A; TF/TL = 0.02/0.08) results in a greater decrease in ambient GABA within the stimulus-relevant column during the tonic input period (see the small oval), thereby being able to fire even after the termination of tonic input (top; see the circle). As addressed in section 3.1, the hyperpolarization of L cells, caused by tonic stimulation, leads to removing GABA (forward transport; e.g., see Figure 4A). In contrast, the depolarization of FT cells solicits GABA release (reverse transport). Note that due to such a small ratio TF/TL = 0.02/0.08, the forward transport by L cells far prevails, thereby reducing ambient GABA and depolarizing T cells greatly. This allows generating spikes even after the termination of the tonic input (see the circle).

Figure 7:

Influences of GABA transporters on neuronal responsiveness. (A) The ratio of transfer coefficient was set as TF/TL = 0.02/0.08 (see Table 1). Top: Raster plots of action potentials. Bottom: Ambient GABA concentrations. (B, C) Those for TF/TL = 0.03/0.07 and TF/TL = 0.07/0.03, respectively. (D) Firing rates of T cells, where the time bin is 50 msec.

Figure 7:

Influences of GABA transporters on neuronal responsiveness. (A) The ratio of transfer coefficient was set as TF/TL = 0.02/0.08 (see Table 1). Top: Raster plots of action potentials. Bottom: Ambient GABA concentrations. (B, C) Those for TF/TL = 0.03/0.07 and TF/TL = 0.07/0.03, respectively. (D) Firing rates of T cells, where the time bin is 50 msec.

Figure 7B presents those obtained under the original condition (see Figure 2), indicating that the T cells cease firing soon after the termination of the tonic input. If the ratio becomes large (see Figure 7C), the reverse transport by FT cells prevails. This results in augmenting ambient GABA (see the small oval), and therefore the T cells are depressed (see the dashed line in Figure 7D).

Figure 8 presents the derivatives of ambient GABA concentration with respect to time, d[GABA]ext(fn; t)/dt, for those shown in Figures 7A to 7C (see the bottom traces). The thick lines denote the stimulus-relevant frequency column. If the transporters on FT cells work less, the ambient GABA in the stimulus-relevant column is markedly reduced (marked by − at the top), thereby continuously firing event after the termination of the tonic input (see Figure 7A). In contrast, if the transporters on FT cells prevail, it is augmented (marked by + at the bottom), thereby depressing the stimulus-evoked activity (see Figure 7C). The ratio TF/TL = 0.03/0.07 is optimal (see the middle trace marked by −), allowing the T cells to respond effectively to the input and return rapidly to the ongoing-spontaneous neuronal state as soon as the tonic input is switched off (see Figure 7B).

Figure 8:

Derivatives of ambient GABA concentration with respect to time, , for those shown in Figures 7A (top), 7B (middle), and 7C (bottom). The thick lines denote the stimulus-relevant column. For details, see the text.

Figure 8:

Derivatives of ambient GABA concentration with respect to time, , for those shown in Figures 7A (top), 7B (middle), and 7C (bottom). The thick lines denote the stimulus-relevant column. For details, see the text.

3.3.  Significance of Onset Discharges.

To elucidate the possible roles of onset discharges in auditory information processing, we devised a simulation in which only the tonic (but not the phasic) input was applied. As shown in Figure 9, the selective responsiveness is deteriorated at the beginning of the input, letting stimulus-irrelevant T cells (see f3 and f6) respond. This unselective response arises largely from a slower increase in ambient GABA (see the bottom of Figure 9), which is shown in an enlarged scale in Figure 10A (see the top traces; “tonic”). The delayed increase in ambient GABA results in failing to suppress stimulus-irrelevant T cells and thus in responding unselectively.

Figure 9:

Neural responses to tonic input where no phasic input was applied. Raster plots of action potentials of P (top), T (second), FT (third), L (fourth) cells, and ambient GABA concentration in each frequency column f1 to f8 (bottom).

Figure 9:

Neural responses to tonic input where no phasic input was applied. Raster plots of action potentials of P (top), T (second), FT (third), L (fourth) cells, and ambient GABA concentration in each frequency column f1 to f8 (bottom).

Figure 10:

Dependence of ambient GABA concentration on the timing of phasic input. (A) Top: Tonic but not phasic input was applied (“tonic”) and vice versa (“phasic”). Phasic + tonic denotes the original condition (see Figure 2). Bottom: P-to-L connections were cut off (“phasic (P-to-L cut)”). (B) Evoked activity in stimulus-relevant (top) and -irrelevant (bottom) T cells as a function of onset time difference between phasic and tonic inputs. Onset time <0 implies that the phasic input precedes the tonic input.

Figure 10:

Dependence of ambient GABA concentration on the timing of phasic input. (A) Top: Tonic but not phasic input was applied (“tonic”) and vice versa (“phasic”). Phasic + tonic denotes the original condition (see Figure 2). Bottom: P-to-L connections were cut off (“phasic (P-to-L cut)”). (B) Evoked activity in stimulus-relevant (top) and -irrelevant (bottom) T cells as a function of onset time difference between phasic and tonic inputs. Onset time <0 implies that the phasic input precedes the tonic input.

The L cells also contribute to the transient increase of ambient GABA. The speed of GABA increase was decelerated if P-to-L connections were cut off (bottom; see the lines marked by “phasic (P-to-L cut)”). Note that the phasic input does not allow L cells to generate spikes as much as FT cells (see Figure 2). Nonetheless, even the slight depolarization of L cells is sufficient for them to release GABA when crossing the reversal potential (uLrev; see Table 1).

It has often been evidenced that onset discharges precede sustained discharges in MGB (Cetas et al., 2002) and AI (Chimoto et al., 2002). To investigate how the timing of phasic input relative to tonic input influences the sustained discharges, we applied the phasic input at different onset times. As shown in Figure 10B, we found optimal timing (i.e., phasic preceding tonic input by several tends of milliseconds), at which the maximal- (top) and minimal- (bottom) evoked activities are achieved in stimulus-relevant (top) and -irrelevant (bottom) T cells, respectively.

It is also well known that some phasic (P) cells respond to a tonal sound in a different manner. Namely, they respond to the termination of sounds (Cetas et al., 2002; Chimoto et al., 2002). To investigate whether and how such offset discharges influence the network behavior, we applied a secondary phasic input at the end of the tonic input. To suggest a possible role of offset discharges, we show a typical example (see Figure 11A), where T cells continue firing once they are excited (see f5). As shown in Figure 11B, the firing ceased as soon as the offset (secondary phasic) input was applied. A transient increase in ambient GABA within the stimulus-relevant column (see the lower oval), caused by the phasic activation of FT cells (see the upper oval), might be responsible. We suggest that the transient augmentation of ambient GABA may destabilize the active dynamic cell assembly and therefore allow the network to go back to the ongoing-spontaneous neuronal state.

Figure 11:

Influences of offset discharges on network behavior. (A) An example in which T cells continue firing once they are excited (see f5). (B) Neuronal responses where a secondary phasic input was applied as an offset input. Raster plots of action potentials of P (top), T (second), FT (third), L (fourth), cells and ambient GABA concentration in each frequency column f1 to f8 (bottom) are shown.

Figure 11:

Influences of offset discharges on network behavior. (A) An example in which T cells continue firing once they are excited (see f5). (B) Neuronal responses where a secondary phasic input was applied as an offset input. Raster plots of action potentials of P (top), T (second), FT (third), L (fourth), cells and ambient GABA concentration in each frequency column f1 to f8 (bottom) are shown.

4.  Discussion

In this study, we proposed a neural network model of a primary auditory cortical (AI) area. Tonic (T) principal cells emitted spikes (action potentials) in a sustained manner, responding selectively to a tone sound with its characteristic frequency (CF). Phasic (P) principal cells emitted spikes in an onset manner, responding to every frequency (non-CF). The onset discharges briefly excited GABAergic interneurons, by which the level of ambient GABA (GABA concentration) was transiently altered. The ambient GABA was recognized by extrasynaptic GABAa receptors and modulated the dynamic behavior of the network.

The transient augmentation of ambient GABA, triggered by onset discharges, allowed T cells to respond selectively to a tone frequency sound. To achieve a selective response, the transient alteration of ambient GABA was not necessary, provided that the lateral inhibition between frequency columns was enhanced (see Figure 5A, bottom). However, the enhanced lateral inhibition had an undesirable effect. Namely, T cells were hyperpolarized during ongoing-spontaneous time periods (see Figure 5B, dashed line), which is known to decelerate the response speed of neurons to sensory input (Hoshino, 2008). We suggest that the transient alteration of ambient GABA, induced by onset discharges, may improve selective responsiveness while keeping an ongoing subthreshold neuronal state that prepares for subsequent auditory input.

We investigated how the timing of phasic input relative to tonic input influences the response property and found optimal timing, with the phasic input preceding the tonic input by several tens of milliseconds (see Figure 10B). In fact, phasic discharges that precede tonic ones by tens of milliseconds have been observed in the AI (Chimoto et al., 2002) and MGB (Cetas et al., 2002). The optimal time difference, several tens of milliseconds derived from our simulations, is a rough estimate and would be regarded as a plausible indication.

It is well known that some phasic (P) cells in the AI (Chimoto et al., 2002) and MGB (Cetas et al., 2002) respond to a tonal sound in a different manner: they discharge in an offset manner, responding to the termination of sounds. To investigate whether the offset discharges influence the network behavior, we applied a secondary phasic input as an offset input at the end of the tonic input period. The offset input ceased the sustained discharges (see Figure 11). The transient augmentation of ambient GABA, triggered by the offset discharges, destabilized the cell assembly that was currently appearing as a stable attractor in the network dynamics. This let the network go back into an ongoing-spontaneous neuronal regime as soon as the input was switched off. We suggest that the offset discharges may have a role in resetting the network, thereby preparing for auditory inputs that come one after another, involved in an acoustic stream.

Concerning ongoing-spontaneous neuronal activity, we studied in a previous paper (Hoshino, 2006) its fundamental dynamic property in relation to the anatomy and neurophysiology of inhibitory interneurons. The study demonstrated that two distinct types of inhibitory interneurons, fast-spiking interneurons with narrow axonal arbors and slow-spiking interneurons with wide axonal arbors, had a spatiotemporal influence on the ongoing activity of principal cells and their responsiveness to sensory input. In that model, dynamic cell assemblies, or population activation of principal cells, expressed information about specific sensory features. Within cell assemblies, the fast-spiking interneurons gave a feedback inhibitory effect on principal cells. Between cell assemblies, the slow-spiking interneurons gave a lateral inhibitory effect on principal cells. These interneurons contributed to depolarizing principal cells below firing threshold during ongoing-spontaneous time periods, by which the reaction speed of principal cells to sensory stimulation was accelerated.

We assumed here two distinct GABAergic interneurons: feedback inhibitory interneurons (F) and lateral inhibitory interneurons (L). A variety of types of GABAergic interneurons have been found in the primary auditory cortex (AI), including 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 send signals limited to proximal principal cells. Based on these observations, we let each L cell project to all (nearby to distant) T cells within the same frequency column and let each F cell project only to its proximal P cell or T cell.

Acknowledgments

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

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