The ionic mechanism of gamma resonance in rat striatal fast-spiking neurons

Abstract

Striatal fast-spiking (FS) cells in slices fire in the gamma frequency range and in vivo are often phase-locked to gamma oscillations in the field potential. We studied the firing patterns of these cells in slices from rats ages 16–23 days to determine the mechanism of their gamma resonance. The resonance of striatal FS cells was manifested as a minimum frequency for repetitive firing. At rheobase, cells fired a doublet of action potentials or doublets separated by pauses, with an instantaneous firing rate averaging 44 spikes/s. The minimum rate for sustained firing was also responsible for the stuttering firing pattern. Firing rate adapted during each episode of firing, and bursts were terminated when firing was reduced to the minimum sustainable rate. Resonance and stuttering continued after blockade of Kv3 current using tetraethylammonium (0.1–1 mM). Both gamma resonance and stuttering were strongly dependent on Kv1 current. Blockade of Kv1 channels with dendrotoxin-I (100 nM) completely abolished the stuttering firing pattern, greatly lowered the minimum firing rate, abolished gamma-band subthreshold oscillations, and slowed spike frequency adaptation. The loss of resonance could be accounted for by a reduction in potassium current near spike threshold and the emergence of a fixed spike threshold. Inactivation of the Kv1 channel combined with the minimum firing rate could account for the stuttering firing pattern. The resonant properties conferred by this channel were shown to be adequate to account for their phase-locking to gamma-frequency inputs as seen in vivo.

striatal local field potentials contain gamma-frequency (35–80 Hz) oscillations that are modulated during behavior (e.g., Berke 2009; DeCoteau et al. 2007). Some of this field potential arises from synaptic responses of striatal neurons to excitatory input from gamma-locked activity in corticostriatal neurons (Cowan and Wilson 1994; Stern et al. 1997). However, even with gamma oscillating input, striatal spiny neurons do not show oscillations in their membrane potentials (Stern et al. 1997), nor do they phase-lock with the gamma component of the field potential (Sharott et al. 2009). Spiny neuron firing is likewise not phase-locked to the field potential in awake animals (Berke 2009). Neuronal firing phase-locked to the gamma field potential in both awake and anesthetized animals is confined to striatal fast-spiking (FS) interneurons (Berke 2009; Sharott et al. 2009), and they are the most likely local source of gamma-frequency field potential signals observed in the striatum.

In the cortex and hippocampus, similar FS interneurons are a key element in the generation of gamma-frequency oscillations (e.g., Cardin et al. 2009; Hausenstaub et al. 2005; Traub et al. 2004). They have an intrinsic resonance near these frequencies, which is evident in their minimum repetitive firing rate of 10–30 spikes/s (Golomb et al. 2007; Tateno et al. 2004). Feedback excitation of cortical FS cells during persistent activity engages this resonance (Hausenstaub et al. 2005; Morita et al. 2008) to produce oscillatory inhibition in the cortex. Because of these properties, cortical FS cells are easily synchronized by noisy shared synaptic excitation and gap junctions (Galaretta and Hestrin 1999; Gibson et al. 1999; Mancilla et al. 2007; Tateno and Robinson 2009).

The ionic mechanisms responsible for the resonant properties of FS cells are not fully understood. The firing patterns of cortical FS cells are shaped by two potassium currents, one triggered by action potentials and one activated when synaptic input drives the cell into the near-threshold voltage range (Erisir et al. 1999; Goldberg et al. 2008; Rudy and McBain 2001). When stimulated with constant current pulses, cortical FS cells exhibit a long delay to the first spike, followed by repetitive high-frequency firing. With current amplitudes near threshold for firing, the cells may exhibit a stuttering firing pattern, consisting of periods of repetitive firing interrupted by periods of quiescence and subthreshold oscillation (e.g., Golomb et al. 2007). The delay in onset of firing in cortical FS cells has been shown to depend on the slowly inactivating potassium channel Kv1, being abolished by treatment with a specific Kv1 blocker (Goldberg et al. 2008). In a model of the cortical FS cell, Golomb et al.(2007) showed (as expected from the previous theoretical work of Rush and Rinzel 1995) that the stuttering firing pattern seen during near-threshold constant current injection could also arise from the inactivation kinetics of inactivating potassium channels. In that model, firing is delayed by a voltage-sensitive potassium conductance that slowly inactivates. Once it inactivates sufficiently and firing begins, the spike afterhyperpolarization following each action potential during repetitive firing incrementally removes inactivation of potassium channels. Potassium channel availability accumulates spike by spike and ultimately stops repetitive firing. During the silent periods between bursts, the potassium channel gradually inactivates, and eventually the cell resumes repetitive firing. Gamma resonance probably does not depend on stuttering, because the minimum firing rate and other indications of class 2 excitability are seen in neurons whose firing is continuous (Tateno et al. 2004), as well as in those that are stuttering.

Striatal FS neurons have similar firing properties when driven by current pulses (Bracci et al. 2003; Kawaguchi 1993; Koós and Tepper 1999; Plenz and Kitai 1998; Plotkin et al. 2005), and their dendrites are also connected by gap junctions and electrical synapses (Kita et al. 1990; Koós and Tepper 1999). Although there is no excitatory feedback from the principal cells to FS neurons in the striatum as there is in the cortex, their resonant properties might be able to generate synchronous gamma oscillations in the striatum in response to the gamma component of their afferent input. Gamma-correlated input from the cortex may not be very effective at recruiting gamma-frequency firing in spiny cells, whose intrinsic properties make them more sensitive to lower frequency components in their inputs (Wilson and Kawaguchi 1996), but it might be very effective on FS interneurons whose sensitivity is matched to the gamma frequency.

In this article we report on the repetitive firing of rat striatal FS interneurons, their resonance in the gamma-frequency range, and the ionic mechanisms that are responsible for that resonance. We found that the stuttering firing pattern is more robust in striatal FS neurons than in their cortical counterparts. Striatal FS cells fire predominantly in the stuttering regime, even over a wide range of current levels. They are also highly resonant, with a minimum repetitive firing rate of about 40 spikes/s, higher than that reported for cortical FS cells. Spike frequency adaptation is also more pronounced than has been reported in cortical cells, and it contributes to the stuttering pattern. Termination of bursts occurs because spike frequency adaptation during repetitive firing causes firing rate to drop below the minimum repetitive rate. Spike frequency adaptation is largely but not completely caused by dendrotoxin-sensitive Kv1 current. We found that the resonance of the FS cells, as well as the occurrence of stuttering, requires the presence of the low-threshold slowly inactivating Kv1 current. After blockade of Kv1 current by dendrotoxin, the cells lose their gamma-frequency resonance, firing repetitively at much lower rates. Some cells acquire low-frequency autonomous activity after dendrotoxin treatment. Unlike cortical and hippocampal FS neurons, the firing patterns of striatal FS neurons are not greatly influenced by Kv3 current, although blockade of these channels does increase action potential duration.

In a model of the cell based on these findings, we show that Kv1-dependent intrinsic resonance causes preferential phase-locking of striatal FS cells to the gamma component of a broadband input signal. When the average level of depolarization is insufficient to trigger repetitive firing, this phase-locking continues to be seen despite irregular firing and an average firing rate much lower than 40 Hz. This phase-locked irregular activity is similar to that seen in vivo (Berke 2011; Sharott et al. 2009). The network of striatal FS cells is thus tuned to respond to transients with a large spectral component in the gamma range, as well as to sustained gamma-frequency input. Striatal FS cells are likely generators of gamma oscillations observed in the striatum in vivo.

MATERIALS AND METHODS

Animals were Sprague-Dawley rats (Charles River Laboratories, Wilmington, MA) ages 16–23 days. Animal handling and all procedures were approved by the University of Texas at San Antonio Institutional Animal Care and Use Committee and were in accordance with National Institutes of Health guidelines. All efforts to minimize both the discomfort to and the number of animals were made. Animals were anesthetized with a lethal dose of ketamine-xylazine (90 and 10 mg/kg, respectively) administered intraperitoneally and then rapidly decapitated. Brains were quickly removed and placed into artificial cerebrospinal fluid (ACSF) comprising the following (in mM): 126 NaCl, 2.5 KCl, 1.25 NaH₂PO₄, 26 NaHCO₃, 2.0 MgSO₄, 10 glucose, and 2.0 CaCl₂ continuously bubbled with 95% O₂-5% CO₂. Tissue blocks containing the striatum were prepared and sliced at 250-μm thickness in the parasagittal plane using a vibrating tissue slicer (Vibratome 3000 Plus). After the initial preparation, slices were allowed to equilibrate at room temperature for 20 min before they were used.

Electrophysiological recordings.

Slices were transferred to a recording chamber that was continuously perfused with oxygenated ACSF at a rate of 2–3 ml/min and maintained at 32–34°C. An Olympus BX51 microscope equipped with Dodt interference contrast illumination, a ×40 water-immersion lens, and digital video camera were used for visualizing the slices during recording. Patch electrodes were pulled from borosilicate glass (outer diameter 1.5 mm, inner diameter 1.17 mm) using a P-97 Flaming-Brown electrode puller (Sutter Instruments, Novato, CA). Electrodes were filled with a solution containing the following (in mM): 140.5 KMeSO₄, 7.5 NaCl, 10 HEPES, 2 Na₂ATP, and 0.2 Na₃GTP, adjusted to a pH of 7.3 with KOH. The final tip resistances ranged from 5 to 10 MΩ. Recordings were made using a MultiClamp 700b amplifier (Molecular Devices, Sunnyvale, CA). Signals were digitized at 10 or 20 kHz after being low-pass filtered with a corner frequency of 5 or 10 kHz. Digitized data were collected using a custom application written using Igor Pro 5.0 software (WaveMetrics, Lake Oswego, OR) and stored for off-line analysis. Series resistances for whole cell recordings ranged from 20 to 50 MΩ and were compensated at the amplifier. If the series resistance increased by more than 25%, the data were discarded. For whole cell recordings, we measured a −7-mV liquid junction potential, but data presented are uncorrected.

Two-photon microscopy.

Alexa Fluor 594 hydrazide sodium salt (50 μm; Molecular Probes, Eugene, OR) was added to the normal internal solution to visualize cells under two-photon excitation. Neurons were imaged at least 20 min after the establishment of the whole cell configuration using a two-photon excitation at 820 nm with 90-MHz pulse repetition frequency and 200-fs pulse duration at the sample plane. The two-photon excitation source was a Chameleon-XR tunable Ti-sapphire laser system (720–950 nm) (Coherent, Glasgow, UK). Laser average power attenuation was achieved with an electro-optic modulator (model 350-50-02; Con Optics, Danbury, CT). Images were acquired with a Prairie Technologies (Middleton, WI) Ultima 2P system and edited off-line with ImageJ software.

Data analysis and statistics.

Electrical traces were digitized using a custom program written using Igor Pro and analyzed off-line using custom-written software (http://marlin.life.utsa.edu/software.html) and routines written using Mathematica 7 (Wolfram Research, Champaign, IL). Unless otherwise stated, all numerical data are expressed as median values ± median absolute deviation, scaled by 1.4826 to be consistent with the standard deviation. Computer simulations were performed using XPPAUT (Ermentrout 2002) using the Runge-Kutta method and a time step of 0.01 ms.

RESULTS

Identification of FS neurons.

Thirty-seven neurons from 25 animals were identified as FS neurons in striatal slices prepared from rats aged 16–23 days. Candidate FS neurons were identified by somatic morphology in interference contrast images, and their identity was confirmed by intracellular staining with Alexa Fluor 594 and two-photon live imaging at the time of the experiment. FS cells had medium-size somata, highly branched recurving aspiny dendrites, and a dense axonal plexus in the vicinity of the cell body, as described from studies using [³H]GABA uptake or glutamic acid decarboxylase (GAD) immunocytochemistry and simultaneous Golgi staining (Bolam et al. 1983, 1985) and intracellular staining combined with immunocytochemistry for parvalbumin (Kawaguchi 1993). A representative example of the morphology of a live FS cell at the time of recording is shown in Fig. 1A. In addition to their common morphological features, all FS neurons shared some common physiological characteristics, which were also expected from previous studies of these cells (Bracci et al. 2003; Farries and Perkel 2002; Kawaguchi 1993; Koós and Tepper 1999; Plotkin et al. 2005). FS neurons had action potentials briefer than those of other striatal neurons, typically between 0.4 and 0.8 ms in half-width (median 0.60 ± 0.09 ms), measured from the first action potential in response to a near-rheobase current pulse. In the absence of applied current, they were silent, with uncorrected membrane potentials ranging from −82 to −59 mV (median −73.9 ± 5.7 mV). An example is shown in Fig. 1B. None of the cells had spontaneous activity while recorded either in the cell-attached configuration in preparation for rupture of the patch or in the whole cell configuration. In response to near-threshold 1-s current pulses, the cells exhibited the characteristic firing pattern of FS cells illustrated in Fig. 1, C–F, including a ramplike depolarization and delay to the first action potential, followed by a burst of action potentials. At higher current levels, an early action potential could precede the ramp, and the burst of firing was more prolonged. During the ramp that preceded the burst, a subthreshold membrane potential oscillation was evident, with a frequency close to that of firing during the bursts, and waxing in amplitude up to the point of firing (Fig. 1C), as previously reported by Bracci et al. (2003).

Fig. 1.

Identification of striatal fast-spiking (FS) neurons. A: candidate FS cells were identified by their characteristic morphology after intracellular staining with Alexa Fluor 594. B: typical appearance of the FS cell action potential. FS cells' action potentials were brief with a large but short-duration afterhyperpolarization. C: at rheobase currents, FS cells typically fired a single doublet of action potentials preceded by subthreshold oscillations. D: frequency-intensity curve for the cell shown in C, E, and F. Delay interval is the interval between the early first action potential and the beginning of the burst for current levels that produced an early spike. First and last intervals refer to the first and last interspike interval in the burst. E and F: suprathreshold firing of the same cell in C and D, showing the early spike, delay interval, and burst. Below each trace is the instantaneous firing rate calculated for each interval. The minimum firing rate, as shown in the trace in C, is approximately equal to the firing rate at which firing fails at the end of the burst.

Frequency-intensity relationship.

Because of the intermittent nature of FS cell firing, measurement of mean rate was not adequate to describe the relationship between firing rate and injected current. Figure 1D shows the frequency-intensity relationship for a representative FS neuron, defined by the first pair of action potentials in the burst after the initial delay (first interval), by the last pair of action potentials in the burst (last interval), and by the interval separating an early action potential from the burst (delay interval), for current levels sufficient to evoke the early spike. Current pulses rarely evoked single action potentials. A doublet or triplet was evoked at rheobase, and so the first and last intervals were the same and there was no delay interval. The reciprocal of the interspike interval for the doublet was considered the minimum firing rate for the neuron. With higher currents, the rate defined by the first interval increased, and the maximum instantaneous firing rate for the cell could exceed 100 spikes/s. In contrast, the last interval in the burst increased much less, or often not at all, with increases in current. Over the course of the burst, firing rate adapted continuously from a maximum for the first interval in the burst to the last interval before burst termination. The rate defined by the delay interval (when present) was much slower and was sensitive to current level, increasing severalfold over the typical range of current steps used.

Rheobase current values varied widely among neurons, from about 200 to 2,400 pA. In FS cells of the cerebral cortex, rheobase increases during development (Goldberg et al. 2011; Okaty et al. 2009), and we likewise observed a significant correlation (r = 0.52, df = 35, P < 0.01) between rheobase and the age at which slices were prepared. There was no significant trend in membrane potential over the age range used (r = 0.004). There also was no significant age trend for action potential threshold for either the first action potential (r = 0.18, df = 35, P > 0.05) or the second action potential (r = −0.014, df = 35, P > 0.05). Thus the developmental change in rheobase was not due to the voltage change required to evoke firing but to the current required to achieve that level of depolarization. Input resistance as measured by the response to near-threshold depolarizing current pulses was negatively correlated with age (r = −0.41, df = 35, P < 0.05), averaging 75 MΩ at age 16 days and 20 MΩ at age 22 days.

Not all FS neurons fired in self-limiting bursts in response to 1-s current pulses. In 7 of 37 cells, firing in response to suprathreshold current pulses continued throughout the 1-s current pulse. Over the age range used in this experiment, burst termination in the first second of current pulses was highly correlated with age, with all 7 of the cells that fired continuously for 1 s or longer being from animals 16–18 days of age and having rheobases below 500 pA. These cells were omitted from the sample for the analysis of first and last intervals described below, because no last interval could be obtained for them.

We calculated the rates defined by the first interval and the last interval for a sample of 29 FS cells whose bursts were contained within a 1-s current pulse over a wide range of pulse amplitudes. Rheobase, minimum firing rate, and the rate associated with the first, last, and delay intervals were defined as above. The minimum firing rate, meaning the rate of the first interval at rheobase, ranged from 18 to 78 spikes/s, with a median of 44.4 ± 13.8 spikes/s. The maximum rate, meaning the first interval at the maximum current used, had a median of 74.9 ± 16.9 spikes/s. The last rate, meaning the rate determined by the last interspike interval in the burst for all levels of current, had a median value of 44.8 ± 7.6 spikes/s. We analyzed the relationship between final rate, minimum rate, and maximum firing rate averaged across all current levels for each cell. Whereas the peak firing rate during a burst was dependent on the level of injected current (signed rank test, P < 0.05), the firing rate at the end of the burst was not statistically different from the minimum firing rate measured at rheobase.

Spike frequency adaptation.

Although spike frequency adaptation was not immediately evident from visual examination of the traces, the termination of bursts in our sample was associated with adaptation sufficient to cause the firing rate to decay to the minimum rate that could be supported by the cells. It was usually impossible to measure the time constant of spike frequency adaptation, because the bursts were too short to reveal any curvature of the instantaneous firing rate vs. time curves (e.g., Fig. 1, C–F). Because the minimum rate was relatively constant, increasing the maximum rate by increasing current strength usually increased the duration of bursts. In 11 cells, high-strength current pulses produced bursts long enough to allow measurement of decay time constants for that subset of the data. Time constants of adaptation for that sample had a median value of 0.19 ± 0.025 s. Spike frequency adaptation was also age dependent. For the 7 cells in young animals whose bursts were longer than 1 s at all current levels, 1 showed no apparent adaptation and the remaining 6 had a median time constant of adaptation of 0.53 ± 0.18 s, significantly slower than that of the rest of the sample (Mann-Whitney test, P < 0.05).

Repeated bursts in response to long current pulses.

We studied the responses of 8 striatal FS cells to longer (5–30 s) current pulses, which evoked sequences of bursts. As previously reported by others (Bracci et al. 2003; Farries and Perkel 2002; Kawaguchi 1993; Koós and Tepper 1999; Plotkin et al. 2005), striatal FS cells fired repeated bursts at irregular intervals over the entire duration of depolarizing pulses. The typical profile of instantaneous firing rate during these repeated bursts is shown in Fig. 2, A and B. Before the first burst at the onset of a moderate-strength current pulse, an initial action potential at the start of the pulse was usually followed by a single long delay interval. High-frequency repetitive firing following this long interval exhibited a gradual adaptation and abruptly failed, ending the burst. If the current pulse was maintained, subsequent bursts began abruptly with no initial long interval. The peak initial firing rate at the beginning of these later bursts was less than that of the first burst, but they showed similar spike frequency adaptation. The instantaneous firing frequency at the end of bursts was nearly constant across bursts. In the period between the bursts, the membrane potential slowly depolarized and showed subthreshold oscillations in the gamma-frequency range (Fig. 2E). For the entire set of 468 bursts collected from 8 neurons, there was a weak but significant correlation between initial firing rate and burst duration (r = 0.18, df = 467, P < 0.01). As in the case of single bursts generated by shorter current pulses, the firing rate at which the bursts were terminated remained close to the minimum firing rate for repetitive firing and to the frequency of subthreshold oscillations between bursts. At the end of long current pulses, all FS cells exhibited long afterhyperpolarizations that could last more than 1 s (Fig. 2A, also see Figs. 4A and 5, C and D).

Fig. 2.

Structure of repeated bursts in response to long current pulses. A: firing of a striatal FS cell in response to a 5-s current pulse. Bursts occur at irregular intervals and are separated by periods of prolonged depolarization with subthreshold oscillations. The first action potential in each burst is of lower amplitude than the others. The termination of the current pulse is followed by a long-lasting afterhyperpolarization. B: instantaneous firing rate. Rates for intervals within a burst are connected by lines. Firing rate was elevated at the beginning of each burst and decayed to approximately the same failure point for each burst. C: action potential threshold plotted in the same way as in B. Note the elevated threshold of the first action potential in each burst. D: maximum rate of rise of the action potentials (dV/dt). Note the parallel evolution of threshold and rate of rise throughout the burst. E: frequency spectrum of subthreshold oscillations during the pauses. The peak of the spectrum corresponds to the minimum firing rate. The inset shows an example interburst membrane potential trajectory.

Fig. 4.

Repeated bursting after TEA application. A: an example showing stuttering firing of a striatal FS cell after application of TEA. Subthreshold oscillations between bursts and the long-lasting afterhyperpolarization at the end of a 5-s pulse continued to be evident. B: instantaneous firing rate during the current pulse shown in A. Inst., instantaneous. C: maximum rate of rise of action potentials. D: threshold voltage for action potential generation. None of these measures were altered by 1 mM TEA treatment, despite the change in action potential duration and single-spike afterhyperpolarization amplitude.

Fig. 5.

Effect of dendrotoxin-I (DTX; 100 nM) on firing pattern of striatal FS cells. A: control near-rheobase firing pattern in response to a 1-s current pulse. B: response of the same cell after application of DTX. Note not only the loss of the initial delay but also the loss of minimum firing rate and the stuttering firing pattern. C: the same neuron firing in response to a stronger 5-s current pulse before application of DTX. D: response to the same 5-s current pulse after application of DTX. The stuttering pattern was abolished. Note the long-lasting afterhyperpolarization at the end of the current pulse was not blocked by DTX. E: instantaneous firing rate for control (blue) and DTX traces (red) in C and D. Spike frequency adaptation was slowed but not abolished by DTX, and firing rate eventually was reduced below the control minimum firing rate.

Threshold changes during bursts.

One possible mechanism of spike frequency adaptation is a rise in threshold (e.g., Wilson et al. 2004). To determine whether the decrease in firing rates during FS cell bursting could be due to a change in threshold, we plotted action potential thresholds spike by spike during repeated bursting in 8 FS neurons tested with long (15–30 s) current pulses. An example is shown in Fig. 2, C and D. Action potential thresholds were measured as the voltage at which the rate of change of voltage exceeded 10 mV/ms. This choice of threshold was calibrated by comparison to the notch in the phase plane (dV/dt vs. V) representation of the action potential and was able to reproduce the threshold as seen in the phase plane (not shown). As in the case of firing rate, the changes in action potential threshold during a burst differed for the first burst in response to a current pulse compared with subsequent ones. As previously reported by Bracci et al. (2003), when firing begins with a single long (delay) interval, the initial short latency action potential is issued at an unusually low threshold and has a large amplitude. The first action potential in the burst (after the delay) has a much higher threshold and reduced amplitude. The second spike in the burst has a larger action potential and much lower threshold, but not as low as the initial action potential. Thresholds for subsequent action potentials in the first burst increase gradually thereafter (Fig. 2C). The action potential threshold at the end of the burst is lower than that of the first action potential in the burst. Subsequent bursts begin with a single very high-threshold action potential, followed by a lower one and subsequent moderate increases (the same sequence except without the early predelay action potential). To confirm this quantitatively, we tested the significance of threshold changes during the second burst in a sequence, as in Fig. 2, across the sample of eight neurons. We used the second burst to avoid the complications associated with the initial early spike, which was sometimes present and sometimes not. For each cell, threshold changes were averaged across all traces whose second burst contained at least 10 action potentials. We compared the thresholds of the first and third spike in the burst, and between the third and last spike, normalized by the threshold of the first spike in each trace. Both the initial decrease in threshold at the beginning of the burst and the smaller increase in threshold during the burst were statistically significant (signed rank test, P < 0.05). These changes in threshold are not consistent with threshold changes as a cause of spike frequency adaptation. In fact, the first action potential in all bursts (except the first burst) has the highest threshold but is associated with the highest firing rate. They also argue against an increase in spike threshold as a reason for the termination of bursts, because the cell can be seen to fire action potentials at much more elevated thresholds at the beginning of the burst.

Variations in threshold are sometimes attributed to changes in sodium channel availability. We estimated sodium channel availability using the maximum rate of rise of action potentials. Changes in the maximal dV/dt during the action potential paralleled the changes in threshold throughout (e.g., Fig. 2D). Like the changes in threshold, the statistical significance of these changes was confirmed using the second burst in each cell. As expected from the threshold changes, the lowest sodium availability occurred at the end of the pause between bursts, and there was a moderate change over the course of the burst.

All cells in our sample tested with long pulses showed the pattern in Fig. 2. These results indicate that the sporadic stuttering firing pattern of striatal FS cells may be accounted for by two dynamic features, the inability to fire repetitively at low rates and spike frequency adaptation. Because repetitive firing fails if the firing rate goes below a minimum rate between 20 and 50 spikes/s, and because firing at that rate triggers spike frequency adaptation, bursts are terminated when adaptation accumulates sufficiently. During the pauses between bursts, the cell recovers sufficiently from spike frequency adaptation to allow repetitive firing to resume. Furthermore, these results argue against threshold elevation (or sodium inactivation in general) as a mechanism of spike frequency adaptation. Sodium inactivation apparently increases during the pauses, rather than being removed.

We wanted to determine whether either the spike frequency adaptation or the minimum firing frequency responsible for the stuttering firing pattern might depend on potassium channels known to be present in FS cells. Cortical FS cells have been shown to possess two voltage-dependent potassium channels, a high-threshold channel (Kv3) that contributes to fast spike repolarization (Erisir et al. 1999; Rudy and McBain 2001) and a low-threshold channel (Kv1) that controls excitability and is essential for the initial delay period (Goldberg et al. 2008, 2011; Okaty et al. 2009). We therefore examined the effects of blockade of these channels on the minimum firing rate and spike frequency adaptation in striatal FS cells.

Effects of Kv3 channel blockade with TEA.

We studied the effects of 0.1–1.0 mM tetraethylammonium (TEA), which is a potent blocker of Kv3 channels, in 11 cells from 11 animals. In the dose range used, TEA is expected to be an effective antagonist of Kv3 and large conductance calcium-dependent potassium (BK) channels (Erisir et al. 1999). As reported for cortical FS cells (Erisir et al. 1999), TEA increased the duration of striatal FS cell action potentials in a dose-dependent and reversible manner. The effects of TEA on action potential duration are shown in Fig. 3, A and B. The average action potential half-width increased from 0.77 ± 0.12 ms in controls to 1.26 ± 0.28 ms after 1 mM TEA (1-way ANOVA, F = 10.3, df = 3, 22, P < 0.01). This change in duration was not reproduced by blockade of BK channels using 50 nM iberiotoxin (n = 3, Fig. 3B), indicating that the effects of TEA were primarily mediated by blockade of Kv3, rather than BK, channels. Also as expected, TEA reduced the amplitude of the single-spike afterhyperpolarization, and especially its fastest components (Fig. 3A). The increase in action potential duration and decrease in afterhyperpolarization in striatal FS cells did not translate into a change in firing pattern or shift in action potential threshold. TEA treatment had no significant effect on the median peak firing rate calculated over all current levels (80.9 ± 24.1 spikes/s in controls, 73.3 ± 37.0 spikes/s after 1 mM TEA, Mann-Whitney test, P > 0.05), the median firing rate at the end of the first burst (44.5 ± 14.1 spikes/s in controls, 37.1 ± 12.1 spikes/s after TEA, P > 0.05), or the median burst duration (320.6 ± 164.1 ms in controls, 344.7 ± 408.3 ms after 1 mM TEA, P > 0.05). In three cells tested with long-duration current pulses, resonance and stuttering continued after TEA and were indistinguishable from that seen before the treatment (Fig. 4, A and B). The sequence of changes in action potential threshold and maximal dV/dt seen in control animals was reproduced after TEA treatment, as well (Fig. 4, C and D).

Fig. 3.

Effect of low doses of tetraethylammonium (TEA) on action potential duration and firing pattern. A: increase in action potential duration, reduction in slope of the falling phase of the action potential, and decrease in the early single spike afterhyperpolarization after 1 mM TEA. Note the lack of a change in the initial membrane potential preceding the first action potential, or in the duration of delay preceding the burst, or action potential threshold or firing pattern during the burst. B: dose-dependent effect of TEA on action potential duration, as measured by half-width. Iberiotoxin (ibTX; 50 nM) had no effect on action potential duration, suggesting the absence of a contribution from large-conductance calcium-dependent potassium (BK) channels. The number of cells tested is indicated above each data point. AP, action potential.

Effect of Kv1 channel blockade with dendrotoxin.

Application of 100 nM dendrotoxin-I (DTX) was tested on 8 cells from 8 animals. The effect of DTX on firing pattern is shown in Fig. 5, A–E. In contrast to TEA, DTX had no effect on action potential duration. DTX treatment produced a very small but statistically significant increase in membrane potential, from −76.5 ± 2.7 to −78.2 ± 1.5 mV (signed rank test, P < 0.05), and no significant change in input resistance, measured with small hyperpolarizations near the resting membrane potential using voltage clamp or current clamp (66.47 ± 40.2 MΩ for control, 72.45 ± 35.8 MΩ for DTX, signed rank test, P > 0.05). The most dramatic change after DTX treatment was a qualitative shift in firing pattern. The initial delay to first spike (for low current levels) and the long first interval (at higher levels) were abolished in all cases (Fig. 5, A and B). The stuttering firing pattern was completely abolished by DTX treatment in all cells tested. After DTX, all neurons fired continuously throughout the entire course of the current pulse (Fig. 5, C and D) for pulses as long as 30 s. Comparing the instantaneous rate for the second interval (to avoid the delay interval in control cells) revealed a small increase in firing rate at the beginning of the current pulse for the largest current strengths (signed rank test, P < 0.05). However, at near-rheobase current strengths, cells treated with DTX could maintain firing at much lower rates (e.g., Fig. 5, A and B).

Cells treated with DTX continued to show spike frequency adaptation, but firing adapted at a much slower rate (Fig. 5E). The median time constant for spike frequency adaptation in DTX-treated cells was 0.88 ± 0.75 s, which was significantly larger than that seen in controls (Mann-Whitney, P < 0.05). The loss of bursting in DTX-treated FS cells was not simply due to slowed spike frequency adaptation, however. With sufficiently long pulses, firing in DTX-treated cells eventually adapted to levels lower than the control minimum firing rate for the same FS cells, even with large currents, and the cells continued to fire repetitively (e.g., Fig. 5E). Thus DTX acted both to reduce the rate of spike frequency adaptation and to lower or abolish the minimum firing rate for FS cells. Repetitive firing at rates as low as 5 spikes/s were observed at current levels that were near rheobase before DTX application. Two of the eight neurons tested exhibited low-frequency tonic firing after DTX even in the absence of applied current (not shown).

DTX treatment also produced a substantial shift in the apparent voltage threshold for action potential generation (Fig. 6, A–C) for all action potentials during the burst, including the first action potential in the series (signed rank test, P < 0.05) but especially for later action potentials. The profile of changes in threshold that occurred during the first burst of firing in response to a current pulse were not changed but were only shifted in the hyperpolarized direction (Fig. 6B). The median shift in threshold for second action potentials in a burst was 14 mV (Fig. 6D). Unlike changes in action potential threshold that occurred over the course of bursting in control cells, this decrease in threshold was not accompanied by an increase in the rate of rise of the action potential. For the first action potential, there was a small but significant decrease in maximal dV/dt (Fig. 6C, signed rank test, P < 0.05), and there was no significant difference for subsequent action potentials. Thus the shift in action potential threshold produced by DTX was probably not accompanied by a corresponding change in sodium current availability. There was no effect of DTX on the sequence of changes in dV/dt over the course of firing in response to long current pulses, aside from those caused by the change in firing pattern. The rapid decrease in dV/dt over the course of the first burst occurred at the same rate after DTX (e.g., Fig. 6B) and paralleled the change in threshold, but not in spike frequency adaptation, which was much slower. The large changes in threshold and maximum dV/dt at the start of bursts were absent after DTX.

Fig. 6.

Changes in threshold but not action potential rate of rise after DTX. A: initial firing (top trace) and onset of the last burst (bottom trace) from the same data shown in Fig. 5. Action potential threshold is indicated by red dots. Note the large negative shift in threshold in DTX trace (black). The elevated threshold for the first action potential in the control burst is in addition to this shift. B: action potential threshold (top) and maximum action potential rate of rise (bottom) for every action potential in both long traces shown in Fig. 5. C: threshold shifts and maximum action potential rate of rise for the first action potential in a sample of 8 cells treated with DTX. Lines represent individual cells, averaged over traces at all current levels. Red horizontal lines are medians. D: threshold and maximum rate of rise of the action potential for the second action potentials. Note the consistent difference in threshold but not in maximum rate of rise of action potentials. V_m, membrane potential.

Ionic origin of the minimum firing rate.

Although the theoretical work of Golomb et al. (2007) had suggested that stuttering might depend on Kv1 channels, an effect of DTX on the minimum firing rate was not expected from previous experimental or theoretical studies. To understand the role of Kv1 on minimum firing rate, we reexamined the dynamics produced by the model of Golomb et al. (2007). In that model, the existence of a minimum firing rate was described as class 2 excitability caused by a Hopf bifurcation (e.g., Rinzel and Ermentrout 1989) that controls the transition to firing in response to injected current. This means that persistent currents, whose inactivation is slow compared with the interspike interval, are always net outward in the subthreshold range. Thus the steady-state current-voltage (I-V) curve in the model neuron is monotonic and has no negative-slope region in the subthreshold range. Firing in class 2 excitability arises from voltage-dependent differences in the rate of change of voltage and of state variables controlling inward and outward currents, rather than from voltage-dependent differences in their steady-state values. Class 1 excitability, characterized by repetitive firing that can be slowed arbitrarily, is associated with a negative-slope region in the steady-state I-V curve. Golomb et al. (2007) noted that if the persistent sodium current in their model was increased, the model was transformed from a resonant class 2 cell to an integrative class 1 cell, in which repetitive firing could be sustained at low firing rates. In the resonant version of the model, steady-state inward currents, such as the persistent component of the sodium current, are more than balanced by outward currents, which in that model included a leak conductance and the Kv1 current. Their model included a sufficient leak current to offset inward currents over the entire subthreshold voltage range, even in the absence of Kv1. We reduced the leak current and increased the contribution of Kv1 to the current balance at subthreshold membrane potentials. We also altered the slope factor for activation to 10 mV to better match experimental data on DTX-sensitive currents recorded in neurons (e.g., Guan et al. 2006). The model cell had a minimum firing frequency of 35 spikes/s. With this model, blockade of Kv1 channels reproduced the loss of the minimum repetitive firing rate as seen in our DTX experiments. This result is shown in Fig. 7, A–C. In this simple model, the transformation of the cell from class 2 to class 1 excitability arises not from an increase in persistent voltage-dependent inward currents near threshold for firing but from the loss of a counterbalancing voltage-dependent persistent outward current (Kv1 window current) that overwhelms persistent inward currents at membrane potentials near threshold.

Fig. 7.

Origin of the minimum rate. A single-compartment model is shown for the FS cell. Parameters are as listed in Table 1. A: steady state current-voltage (I-V) curve as measured using a 1-s voltage ramp from −80 to −40 mV. When Kv1 conductance (ḡ_Kv1) is intact (3 mS/cm²), the curve is monotonic. For interspike intervals comparable to the duration of the ramp, outward currents exceed inward ones and firing at this rate is impossible. Firing in this case (class 2 excitability) only occurs when the voltage changes more quickly so that kinetic differences between inward and outward currents can favor regenerative depolarization. Blockade of Kv1 removes an outward current in the −60- to −45-mV range of membrane potentials and creates a negative conductance region. Addition of a small constant current (red line, i_app = 0.85) causes loss of the subthreshold equilibrium potential, and firing can occur. Firing will slow asymptotically as the I-V curve nears the 0 current line, allowing firing at arbitrarily low rates. B: response of the model to a 2.5 μA/cm² current with Kv1 current at 3 mS/cm². C: response to a near-rheobase current (0.85 μA/cm²) in the absence of Kv1 current.

A model of Kv1 effects on threshold.

In cortical FS neurons, Kv1 channels are localized on the axon initial segment, between the soma and the spike trigger zone (Goldberg et al. 2008). We reasoned that if striatal FS neurons had the same distribution, it might explain the effects of DTX on apparent action potential threshold as measured from the soma. We constructed a 10-compartment cable model representing the soma and axon initial segment of the FS neuron, with one end of the axon representing the action potential trigger zone. Studies in a variety of cell types have indicated that the threshold at the action potential trigger zone is shifted negative to that of the soma, and persistent sodium current is greatly enhanced in the axonal trigger zone because of both an increased density of sodium channels and a negative shift in their activation curves (Fleidervish et al. 2010). To represent the axon, we used compartments possessing ion channels as used in Fig. 7, except that the sodium channel activation and inactivation curves were shifted slightly positive to the single-compartment model in every compartment except the trigger zone, and shifted slightly negative in the trigger zone. We also tripled the sodium channel density in the compartment representing the trigger zone. This gave the trigger zone a voltage threshold about 10 mV more negative than that in the other compartments when measured using a local current pulse. The axon contained Kv1 channels, but the soma compartment did not. The equations and parameters for the model are presented in the Appendix. The results of these simulations are shown in Fig. 8, A–C. Injection of square current pulses at the somatic end of the cable produced a slow ramp to spiking and a bursting pattern. At the onset of the current pulse, there was a large voltage attenuation between the soma and spike trigger zone that increased during Kv1 activation. During the rest of the delay period, the attenuation along the cable gradually decreased as the membrane conductance was reduced by inactivation of Kv1. Action potentials were all triggered in the spike trigger zone and antidromically conducted to the soma. Sodium channels were more inactivated in the soma because of its greater depolarization during the delay period, causing its excitability to decrease further, but the axonal action potential propagated actively into the soma. The apparent threshold at the soma at the time of firing was 10–15 mV more depolarized than the threshold in the spike trigger zone. Of course, the apparent somatic threshold was not the true action potential threshold of the soma at the time of the spike, because an antidromically conducted action potential preempted local generation of an action potential at the somatic location. Reduction of Kv1 availability to zero produced a firing pattern similar to that seen after DTX (Fig. 8C). Apparent action potential threshold as observed at the soma was shifted greatly in the hyperpolarized direction because of the reduced electrotonic decay on the axon between soma and trigger zone, and the apparent somatic threshold was close to that of the axon trigger zone, which continued to be the source of action potentials. Rheobase current was greatly reduced because of the increased input resistance and reduced voltage decay between the current injection site and the site of action potential initiation. Thus this model reproduces both the change in apparent voltage threshold and the change in rheobase seen after DTX.

Fig. 8.

Computer simulation of the Kv1-dependent voltage attenuation in the axon and its affect on the apparent threshold seen at the soma. A: action potentials are triggered at the axon because of its greater excitability. Kv1 is localized to the initial segment of the axon, between the somatic recording and current injection site and the spike trigger zone. B: simulated response to a somatic current pulse, showing large voltage attenuation between the soma (red) and the spike trigger zone (black). The voltage difference is reduced as Kv1 current inactivates during the prolonged depolarization. Action potentials triggered in the axon propagate antidromically to the soma, which is depolarized because of current injection. The threshold measured at the soma has a large error that increases with increased Kv1 conductance. C: after removal of Kv1 current, the voltage attenuation along the axon is greatly reduced. Action potentials are still triggered in the axon, but the apparent threshold seen at the somatic end of the axon is nearly the same as at the trigger zone.

Resonance and gamma phase-locking.

To determine whether the gamma resonance seen in FS cells in slices could account for phase-locking of these cells' firing during irregular firing in vivo, we applied noisy simulated synaptic currents to the FS cell model used in Fig. 7. We used excitatory postsynaptic currents (EPSCs) with an instantaneous onset and a 2.5-ms decay time constant. The stimulus noise was calculated using a time step of 0.01 ms. The amplitude and average frequency of EPSCs were selected to evoke an irregular firing pattern with an average firing rate near 10 Hz, to approximately match the pattern shown in vivo (Berke 2011). An example generated using an average EPSC rate of 2,000 EPSCs/s and an EPSC peak amplitude of 0.37 μA/cm² is shown in Fig. 9, A–F. An excerpt of the resulting current noise is shown in Fig. 9A, and its amplitude spectrum is shown in Fig. 9B. As expected (e.g., Anderson and Stevens 1973), the spectrum of the noise is flat between 0 Hz and the cutoff frequency of about 63 Hz [1/(2πτ_decay)]. We used this flat spectrum noise, instead of a pattern containing a peak in the gamma range, to test whether the model FS cell would respond preferentially to gamma-frequency components of the input even in the presence of other components. We collected 160 s of simulated activity from the single-compartment model FS cell in the presence of noise, which triggered about 1,600 action potentials. We also used this stimulus to approximate the local field potential produced by synaptically generated currents in the vicinity of the cell and filtered it to obtain a filtered local field potential that could be compared with the pattern of action potentials. Our use of synaptic current as a proxy for the field potential is based on the assumption that the field potential, or at least the components of it that matter, is generated by synaptic current. In Fig. 9, depolarizing currents are shown as positive, and so our estimate of field potentials should be viewed as negative-up. Filtered local field potentials were calculated by performing the Fourier transform of the stimulus waveform and multiplying the complex components by a Tukey window filter function (α = 0.25) that was zero everywhere except in the frequency range of interest. Frequency bands 5 Hz wide were calculated every 5 Hz between 5 and 110 Hz. The filtered local field potential was generated by inverse transformation of the filtered frequency components. An example showing a segment of the field potential filtered 35 ± 2.5 Hz is shown in Fig. 9C and compared with spike timing in the model neuron during the same period. The strength of the 35-Hz component waxed and waned randomly, and firing was not directly related to its amplitude. However, the model neuron did exhibit a strong tendency to fire in a narrow range of phases of the 35-Hz-filtered local field potential, slightly after the depolarizing peaks in the filtered current. This can be seen in the phase distribution histogram in Fig. 9D. The average phase was 0.85 of the period (with 0 and 1 being the nearest zero-crossings of the filtered input, and peak depolarizing current occurring on average at 0.75). We measured the frequency specificity of this effect by calculating the Kolmogorov-Smirnov distance between the obtained spike phase distribution and the uniform distribution for each frequency band. This statistic varies between 0 and 1, with 0 indicating that the distribution is effectively uniform and larger numbers indicating a deviation from a uniform distribution. The result of this analysis is shown in Fig. 9E. The model cell showed strong phase-locking to frequency components between 0 and 50 Hz, with a peak near 35 Hz, corresponding to the minimum firing frequency of the model. The contribution of Kv1 current to the preferred frequency of phase-locking during irregular firing was examined by zeroing the Kv1 current and repeating the simulation. This produced an increase in the excitability of our model cell. We wanted to keep the firing rate and pattern similar to that in the presence of Kv1 current. To keep firing rate at about 10 Hz and to maintain irregular firing, we reduced the frequency of the EPSCs to 1,500/s and reduced EPSC size to 0.22 μA/cm². Because the time constant of the EPSC was not altered, this stimulus had the same normalized amplitude spectrum as the one in Fig. 9B. We then repeated the simulation and analyzed phase-locking over a range of filtered local field potentials. The result is shown as a dotted line in Fig. 9E. Removing the resonance responsible for the minimum repetitive firing rate of 35 Hz also removed the tendency of cells to phase-lock to the gamma-frequency component of noisy stimulus currents. The cell without Kv1 showed a preferred phase-locking at about 15 Hz, and phase-locking dropped off rapidly at higher frequencies.

Fig. 9.

Phase-locking of the model FS cell to gamma-frequency components of a broadband signal. The model cell had a minimum firing rate of 35 spikes/s. A: sample of the noisy current waveform composed of randomly timed exponential excitatory postsynaptic currents used for the simulation. B: magnitude spectrum of the synaptic barrage. C: sample of the noisy current, bandpass filtered at 32.5–37.5 Hz to show a gamma-frequency component, and the resulting model cell membrane potential waveform. Action potentials occur irregularly but preferentially occur near zero-crossings in the noise waveform. D: histogram showing average phase of firing for 160 s of simulated firing at ∼10 spikes/s as in C. E: deviation of histograms like that in D from a uniform distribution, as measured by Kolmogorov-Smirnov (K-S) distance, for 5-Hz frequency bands from 5 to 110 Hz. Solid line represents an intact cell; dotted line represents a cell without Kv1 conductance. Note the prominent peak in phase-locking in the gamma range, which is lost with blockade of Kv1. F: spike-triggered average of the current waveform showing 35-Hz (29 ms) resonance.

The resonance of the model FS cell was also evident in the spike triggered average of the stimulus current, shown in Fig. 9F. Irregularly firing striatal FS cells show a strong gamma-frequency component in the spike triggered average of the local field potential in vivo (Berke 2009). The spike-triggered average of the input noise in the model striatal FS cell showed similar periodicity, except that the strength of the correlation dropped off much more rapidly, presumably because of the absence of any long-range autocorrelations in the gamma-frequency component of the noise stimulus used, in contrast to the local field potential in vivo. For both phase-locking of action potentials and the spike-triggered average current, the action potential occurred at a time slightly later than the peak synaptic current. This was due to a capacitive phase lag in the membrane potential relative to the current, which was also present when the cells were driven with sinusoidal currents (not shown).

DISCUSSION

Gamma resonance.

The mechanisms of gamma resonance and stuttering in FS cells are related but not the same. FS cells for which spike frequency adaptation is weak may fire continuously and never stutter but may still show a minimum firing frequency and resonance (e.g., Tateno et al. 2004). Resonance cannot be attributed to single ion channels but arises from an interaction between them, and so it has most often been approached from a theoretical rather than an experimental perspective (Golomb et al. 2007; Rush and Rinzel 1995; Tateno et al. 2004). The resonance seen in striatal FS cells is associated with the nature of their firing threshold and is most evident by the existence of their high minimum rate for repetitive firing. They have no fixed action potential threshold voltage, but rather the threshold is determined by the rate at which the cell is depolarized. This is indicated by the presence of a single stable equilibrium (zero-crossing with positive slope) in the steady-state I-V curve regardless of injected current, as shown in Fig. 7A. Repetitive firing in FS neurons depends on the rate at which the membrane potential depolarizes after a previous action potential. The afterhyperpolarization following a single action potential produces enough recovery from sodium inactivation and deactivation of Kv1 current to shift the balance in favor of a subsequent action potential, but only for a brief time window. This permits repetitive firing, but only at rates equal to or exceeding a minimum rate, set by the time course of depolarization and the kinetics of the sodium and potassium currents. If the firing rate slows and the voltage changes more gradually during the interspike interval, restorative processes (sodium inactivation and Kv1 activation) will keep pace with the regenerative effect of sodium activation, and repetitive firing will fail. This explains why there is a minimum rate and why it depends on both sodium and potassium channels. If the noninactivating component of the sodium current is increased (as in the model by Golomb et al. 2007), or if potassium currents are sufficiently reduced (as in the results of the current study), the cell acquires a negative conductance region in its steady-state I-V curve (as in Fig. 7B) and can fire arbitrarily slowly with rheobase current injection. In the present study, specific blockade of Kv1 current with DTX abolished gamma resonance, and the cells were able to fire repetitively at much lower frequency. In some cases, DTX shifted the balance of currents sufficiently that the cells fired continuously at low rates in the absence of injected current.

Stuttering.

Although resonance does not depend on inactivation of the Kv1 channel, both resonance and potassium channel inactivation are essential for stuttering. Our results confirm the predictions of theoretical studies of the stuttering firing pattern (Golomb et al. 2007; Rush and Rinzel 1995). In those models, bursting arises because of the slow inactivation of potassium current at subthreshold voltages. If the cell remains depolarized without firing for a sufficient time, potassium channels will partly inactivate and the cell will slowly depolarize and eventually fire. The onset of firing is accompanied by subthreshold oscillations. These oscillations represent the alternation of regenerative and restorative influences on membrane potential described above and are critical for the onset of firing because of the absence of a fixed voltage threshold in the resonant cell. Subthreshold oscillations of increasing amplitude increase the rate of change of voltage to the critical level for firing, and firing always starts on the rising phase of the subthreshold oscillation. The afterhyperpolarization following each action potential removes some potassium channel inactivation so that the available outward current increases with each action potential during the burst, slowing the rate of firing and the rate of membrane depolarization during the interspike interval. After a sufficient number of action potentials, the net potassium current is increased enough that firing slows below the minimum sustainable rate, and repetitive firing fails. Thus the modest amount of spike frequency adaptation seen in FS cells is crucial to the stuttering pattern. In some cortical FS cells, and in immature striatal FS cells, there may not be enough spike frequency adaptation to support stuttering at high levels of injected current, and continuous firing results.

An earlier study of cortical FS cells (Goldberg et al. 2008) showed that blockade of Kv1 channels with DTX abolished the initial delay, which according to the model is generated by the same mechanism that causes stuttering, but the cells in that study fired continuously. Our results provide a direct test of the model's predictions for stuttering and confirm that Kv1 is the inactivating potassium current responsible. We also confirmed that spike frequency adaptation was slowed by blockade of Kv1 channels with DTX, as expected from the model. However, some spike frequency adaptation, albeit slower, was seen after DTX. This was not associated with a shift in sodium current availability, and so there is apparently another DTX-insensitive accumulating adaptation current in striatal FS cells. Kv1 channels also explain the presence of the early action potential at the onset of large current pulses. Activation and deactivation of Kv1 are fast (Grissmer et al. 1994), but not as fast as for the sodium current. Sufficiently large depolarizations can trigger a first action potential before the onset of the Kv1-dependent delay period (Meng et al. 2011).

Development of stuttering.

As expected given their common embryological origin and morphology (e.g., Marin et al. 2000), striatal FS cells are similar to cortical FS cells, but they are not identical. Most studies report less spike frequency adaptation and less stuttering in the cortex than we have seen in the striatum (e.g., Goldberg et al. 2008). The expression of Kv1 currents, stuttering, and spike frequency adaptation of FS cells are developmentally regulated in the cortex (Goldberg et al. 2011; Okaty et al. 2009). Our results and those of Plotkin et al. (2005) suggest a similar developmental sequence in striatal FS cells. Between days 16 and 23, there was a substantial increase in the rheobase of FS cells and a transition from sustained firing to stuttering. Another difference between striatal and cortical and hippocampal FS cells is the dependence of the firing pattern on Kv3 current (e.g., Erisir et al. 1999; Lien and Jonas 2003). Although the duration of action potentials of striatal FS cells is strongly dependent on Kv3 currents, the firing pattern is not much affected by their blockade with TEA. This is apparently because spike frequency adaptation in striatal FS cells prevents the cells from firing at high rates for long periods of time, which is the condition in which Kv3 has its greatest effect on firing of cortical FS cells (e.g., Lau et al. 2000).

Location of Kv1 currents and effect on apparent threshold.

In cortical FS interneurons, Kv1 channels are specifically located on the axon initial segment (Goldberg et al. 2008). Our results are consistent with a similar location for Kv1 in striatal FS cells. This is required to explain the large change in apparent action potential threshold seen after DTX treatment, without any corresponding change in sodium channel availability. An error in the measurement of the action potential threshold is expected when spikes are evoked by somatic depolarization but action potentials originate remotely on the axonal membrane (Yu et al. 2008). The error is dependent on the electrotonic distance between the recording site and the site of action potential generation, and thus on the membrane conductance of the axon initial segment. Near threshold, Kv1 channels are activated and so contribute to that conductance and increase the electrotonic length of the axon. By decreasing the axonal membrane conductance between the somatic recording electrode and the remote trigger site, DTX should decrease the error in threshold measurement. This should not have as great an effect on the maximal dV/dt achieved during the action potential if action potentials are actively propagated into the soma, and so dV/dt at each place on the axon is determined by local sodium currents. Our results imply that when the soma is depolarized with suprathreshold constant current, there is at least a 10-mV voltage gradient between the soma and the trigger zone in the axon. Although large, this difference in apparent threshold is comparable to that observed by Goldberg et al. (2008) after application of DTX to cortical FS cells. It is also comparable to that shown by Yu et al. (2008) to occur over the first 100 μm of the axon of cortical pyramidal neurons.

The voltage gradient between the somatodendritic membrane and the axonal trigger zone may contribute to synaptic integration in FS cells. The access of somatodendritic synaptic inputs to the spike initiation zone may depend critically on the level of activation (or inactivation) of Kv1 currents. With prolonged depolarization, Kv1 currents are substantially inactivated, and somatic voltage membrane potential changes are more faithfully conducted to the spike trigger zone. On the other hand, excessive inactivation of Kv1 would abolish resonance to gamma-frequency inputs, and cells would become much less sensitive to the timing of fast synaptic inputs. In the depolarization range that produced firing similar to that seen in vivo, a substantial amount of Kv1 availability was maintained, there was large voltage attenuation in the initial segment of the axon, and the cells were highly resonant.

Resonance implies phase-locking in vivo.

Striatal FS cells excited by constant current pulses in slices manifest gamma resonance as a 40-Hz minimum repetitive firing rate. In awake animals, striatal FS cells do not usually fire repetitively, but rather irregularly at rates well below 40 Hz (Berke 2008, 2011). Under these circumstances, the cells exhibit phase-locking to the gamma-frequency component of the local field potential. Striatal FS cells in slices are far from firing threshold, have relatively low input resistances, and receive a high density of excitatory afferent synaptic inputs (Tepper et al. 2010). A substantial excitatory synaptic barrage is required to maintain even a low irregular firing rate in these cells. The structure of corticostriatal afferents ensures that striatal neurons receive synaptic excitation from a large number of different axons, and there is little input sharing among cells (Zheng and Wilson 2002). Thus the in vivo background synaptic input to striatal FS cells, like that of the spiny neurons, is a noisy composite of many inputs. Our results show that although striatal FS cells may not fire rhythmically in response to this input, their resonance is manifest in their ability to isolate the gamma-frequency component of this signal and to respond selectively to it, a property not shared by other striatal neurons.

GRANTS

This work was supported by National Institute of Neurological Disorders and Stroke Grants NS37760 and NS072197 (to C. J. Wilson) and an International Brain Research Organization student fellowship (to G. Sciamanna).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

G.S. and C.J.W. conception and design of research; G.S. performed experiments; G.S. and C.J.W. analyzed data; G.S. and C.J.W. interpreted results of experiments; G.S. and C.J.W. drafted manuscript; G.S. and C.J.W. edited and revised manuscript; G.S. and C.J.W. approved final version of manuscript; C.J.W. prepared figures.

APPENDIX: EQUATIONS AND PARAMETERS FOR THE COMPUTER SIMULATIONS

The model for each compartment was from Golomb et al. (2007). Each compartment possessed a fast sodium conductance, a high-threshold rapidly inactivating spike repolarization conductance (delayed rectifier), a constant leak conductance, and a Kv1-like conductance with rapid activation and slow inactivation. Activation of the sodium conductance was treated as instantaneous. Activation and inactivation voltage sensitivities were represented by sigmoid curves, as was the voltage sensitivity of the inactivation time constant. The delayed rectifier had sigmoid activation and activation time constant voltage sensitivities. The Kv1 current had sigmoid activation and inactivation voltage sensitivities, but the time constants of activation and inactivation were fixed. Activation and inactivation state variables were defined by a differential equation of the form

$$\frac{\text{d}k}{\text{d}t}=\left(k_{\infty }-k\right)/{\tau }_k,k=\left(h,n,a,b\right),$$

where k is one of the state variables h, n, a, or b, representing inactivation of the sodium conductance, activation of the delayed rectifier, activation of Kv1, and inactivation of Kv1, respectively. The steady-state value of each activation variable was determined by an equation of the form

$$k_{\infty }=1/\left(1+e^{-\left(v-V{H}_k\right)/{\sigma }_k}\right),k=\left(m,h,n,a,b\right),$$

where VH_k is the half-activation (or inactivation) voltage and σ_k is the slope factor. The time constant for sodium inactivation (τ_Na) was calculated as

$${\tau }_{\text{Na}}=0.5+14.5/\left(1+e^{-\left(v+60\right)/12}\right),$$

and the time constant for the delayed rectifier (τ_K) was calculated as

$${\tau }_{\text{K}}=\left[0.087+11.4/\left(1+e^{\left(v+14.6\right)/8.6}\right)\right]\times \left[0.087+11.4/\left(1+e^{-\left(v-1.3\right)/18.7}\right)\right].$$

For the single-compartment model, the differential equation for voltage was

$$C\frac{\text{d}v}{\text{d}t}=-{\overline{g}}_{\text{Na}}{m}_{\infty }^{3}h\left(v-E_{\text{Na}}\right)-{\overline{g}}_{\text{DR}}{n}^4\left(v-E_{\text{K}}\right)-{\overline{g}}_{\text{Kv}1}{a}^{3}b\left(v-E_{\text{K}}\right)-g_{\text{L}}\left(v-E_{\text{L}}\right)+i_{\text{app}},$$

where i_app could be a constant applied current or a random barrage of synaptic currents.

For the cable model of the FS cell axon, the axon was represented by nine compartments and the soma by one compartment. The trigger zone was the most distal compartment. The axonal compartments were identical, except that the sodium current activation and inactivation voltage sensitivities were shifted 6 mV in the negative direction on the trigger zone. The somatic compartment was the same as the rest of the axonal compartments, except that it did not have any Kv1 current. The difference in surface area between the soma and axon was represented by a value 100 times larger for leak conductance and capacitance. This gave the soma a surface area 11 times larger than the combined surface area of the axonal compartments. This approach obviated the need for specifying diameters, and the coupling conductances between compartments were given as densities normalized by surface area, the same as for the membrane conductance. The differential equation for voltage for each of the 10 compartments (numbered 0, …, 9, with the soma being compartment 0) was

$$C_{\text{S}}\frac{\text{d}v\left[0\right]}{\text{d}t}=-{\overline{g}}_{\text{Na}}m{\left[0\right]}_{\infty }^{3}h\left[0\right]\left(v\left[0\right]-E_{\text{Na}}\right)-{\overline{g}}_{\text{DR}}{n}^4\left[0\right]\left(v\left[0\right]-E_{\text{K}}\right)-g_{\text{LS}}\left(v\left[0\right]-E_{\text{L}}\right)+g_c\left(v\left[1\right]-v\left[0\right]\right)+i_{\text{app}}$$

$$C\frac{\text{d}v\left[i\right]}{\text{d}t}=-{\overline{g}}_{\text{Na}}m{\left[i\right]}_{\infty }^{3}h\left[i\right]\left(v\left[i\right]-E_{\text{Na}}\right)-{\overline{g}}_{\text{DR}}{n}^4\left[i\right]\left(v\left[i\right]-E_{\text{K}}\right)-g_{\text{Kv}1}a{\left[i\right]}^{3}b\left[i\right]\left(v\left[i\right]-E_{\text{K}}\right)-g_{\text{L}}\left(v\left[i\right]-E_{\text{L}}\right)+g_{\text{c}}\left(v\left[i-1\right]+v\left[i+1\right]-2v\left[i\right]\right)$$

$$C\frac{\text{d}v\left[9\right]}{\text{d}t}=-{\overline{g}}_{\text{Na}}m{\left[9\right]}_{\infty }^{3}h\left[9\right]\left(v\left[9\right]-E_{\text{Na}}\right)-{\overline{g}}_{\text{DR}}{n}^4\left[9\right]\left(v\left[9\right]-E_{\text{K}}\right)-g_{\text{Kv}1}a{\left[9\right]}^{3}b\left[9\right]\left(v\left[9\right]-E_{\text{K}}\right)-g_{\text{L}}\left(v\left[9\right]-E_{\text{L}}\right)+g_{\text{c}}\left(v\left[8\right]-v\left[9\right]\right)$$

for i = 1, …, 8, and with all parameters as listed in Table 1, but C_S = 100C and g_LS = 100g_L.

Table 1.

Model parameters

Parameter	Value
Na+conductance single-compartment model
ḡNa	112 mS/cm2
VHm	−24 mV
VHh	−57 mV
σm	11.5 mV
σh	−6.7 mV
Na+changes in axon, trigger zone
ḡNa	140, 420 mS/cm2
VHm	−21, −27 mV
VHh	−54, −60 mV
Delayed rectifier conductance
ḡDR	225 mS/cm2
VHn	−12.4 mV
σn	6.8 mV
Kv1 conductance
ḡKv1	3 mS/cm2
VHa	−50 mV
σa	10 mV
τa	4 ms
VHb	−65 mV
σb	6 mV
τb	150 ms
Leak conductance
gL	0.13 mS/cm2
Reversal potentials
EL	−70 mV
ENa	50 mV
EK	−90 mV
General
iapp	Varied
gc	4.0 mS/cm2
C	1.0 μF/cm2

Parameters for Na⁺ conductance: ḡ_Na, maximum conductance; VH_m, half-activation voltage; VH_h, half-inactivation voltage; σ_m, activation slope; σ_h, inactivation slope. Parameters for delayed rectifier conductance: ḡ_DR, maximum conductance; VH_n, half-activation voltage; σ_n, activation slope. Parameters for Kv1 conductance: ḡ_Kv1, maximum conductance; VH_a, half-activation voltage; σ_a, activation slope; τ_a, activation time constant; VH_b, half-inactivation voltage; σ_b, inactivation slope; τ_b, inactivation time constant. Other parameters: g_L, leak conductance; E_L, E_Na, and E_K, leak, Na⁺, and K⁺ reversal potentials; i_app, applied current; g_c, coupling conductance; C, capacitance.