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1Neurobiology and Behavior Program, University of Washington; and 2Departments of Otolaryngology-HNS and Pharmacology and 3the Virginia Merrill Bloedel Hearing Research Center, University of Washington, Seattle, Washington
Submitted 25 January 2005; accepted in final form 15 April 2006
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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80% with 100 nM DTX-K) or partially (50% with 1-h incubation in 3 nM DTX-K). Ikl was similar in 3 nM DTX-K–treated cells and cells from Kcna1–/– mice, allowing a comparison of these two different methods of Ikl reduction. In response to current injection, Ikl reduction increased the temporal window for AP initiation and increased jitter in response to the smallest currents that were able to drive APs. While 100 nM DTX-K caused the largest increases, latency and jitter in Kcna1–/– cells and in 3 nM DTX-K–treated cells were similar to each other but increased compared with +/+. The near-phenocopy of the Kcna1–/– cells with 3 nM DTX-K shows that acute blockade of a subset of the Kv1.1-containing channels is functionally similar to the chronic elimination of all Kv1.1 subunits. During rapid stimulation (100–500 Hz), Ikl reduction increased jitter in response to both large and small inputs. These data show that Ikl is critical for maintaining AP temporal precision at physiologically relevant firing rates. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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). The medial nucleus of the trapezoid body (MNTB) preserves the temporal pattern of inputs from the cochlear nucleus (Guinan and Li 1990; Kopp-Scheinpflug et al. 2003a,Kopp-Scheinpflug et al. 2003b; Paolini et al. 2001; Smith et al. 1998) and participates in at least two brain stem binaural processing circuits, including the medial and lateral nuclei of the superior olive (Oertel 1999). Given that not all neurons can fire with millisecond temporal precision (Reyes et al. 1994), auditory neurons must be specialized. Where measured, auditory cells that are capable of temporally precise firing express a low threshold potassium current (Ikl) (Trussell 1999), believed to be carried by Kv1.1-containing channels (Bal and Oertel 2001; Brew and Forsythe 1995; Dodson et al. 2002; Grigg et al. 2000; Wang et al. 1994).
Many studies have addressed the physiological role of Ikl with respect to auditory signal processing. For example, in auditory neurons that require multiple inputs to reach AP threshold, such as bushy cells of the cochlear nucleus, Ikl reduces temporal jitter by limiting temporal summation. In these cells, nearly coincident inputs sum to reach AP threshold, whereas staggered inputs fail to achieve sufficient depolarization (Joris et al. 1994; Manis and Marx 1991; Oertel 1983; Reyes et al. 1996; Rothman et al. 1993; Trussell 1999). In MNTB neurons, which fire to a single excitatory input, Ikl limits the output response to a single AP per input (Brew and Forsythe 1995). Also, Ikl can enhance the signal-to-noise ratio for small signals by raising threshold current, thereby limiting the number of false positive responses (Svirskis et al. 2003).
Studies using Kcna1–/– mice (the Kcna1 gene encodes the Kv1.1 protein) suggest Ikl reduction affects both AP rate and timing. During sound evoked activity in vivo, Kcna1–/– MNTB cells exhibit more first AP jitter and do not fire as fast as +/+ littermates (Kopp-Scheinpflug et al. 2003a). The reduced firing rate in vivo is surprising given in vitro measurements showing that Kcna1–/– MNTB cells have 50% less Ikl and are hyperexcitable when stimulated with current injection (Brew et al. 2003).
Using MNTB cells in a slice preparation, we examine the role of Ikl in limiting AP temporal variability in response to a wide range of input amplitudes and rates. To isolate the postsynaptic effects, we eliminate the variability of synaptic transmission (Cook et al. 2003) by evoking APs with current injection. We compare two strategies for Ikl reduction. Dendrotoxin-K (DTX-K) selectively blocks channels containing at least one Kv1.1 subunit (Hopkins 1998), so partial Ikl block with DTX-K acutely blocks a subset of Kv1.1-containing channels. Alternatively, Kcna1–/– mice constitutively lack the underlying Kcna1 gene, eliminating Kv1.1 throughout development (Brew et al. 2003; Smart et al. 1998), but preserving other subunits, likely Kv1.2 and 1.6, to carry Ikl (Brew et al. 2003; Dodson et al. 2002).
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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) were crossed into a C3HeB/FeJ background for >10 generations to establish a congenic strain, hereafter termed Kcna1–/–. Genotyping was performed on DNA isolated from tail clips from each mouse 
7 days of age as described previously (Brew et al. 2003; details available at http://depts.washington.edu/tempelab/Protocols/KCNA1.html). All chemicals for solutions were obtained from Sigma (St. Louis, MO) unless otherwise stated. Pipette internal solution consisted of (in mM) 97.5 potassium gluconate, 32.5 KCl, 5 EGTA, 10 HEPES, 1 MgCl2, 4 MgATP, and 0.4 Na2GTP, adjusted to pH 7.2. Artificial cerebrospinal fluid (ACSF) contained (in mM) 125 NaCl; 2.5 KCl; 26 NaHCO3; 1.25 NaH2PO4; 2 CaCl2; 1 MgCl2; and 10 glucose at pH 7.4, 290–310 mOsm. We used ACSF for slicing except with iso-osmotic sucrose substituted for NaCl and (in mM) 1 CaCl2 and 2 MgCl2. All external solutions were gassed with 5% O2-95% CO2 to maintain a pH of 7.4. For voltage-clamp recordings, we used 0.5 mM CaCl2 and 2.5 mM MgCl2 and applied 100 µM TTX (Sigma or Alomone Labs) to block voltage-gated Na channels. NaHCO3 and sucrose were obtained from Fisher Scientific (Pittsburgh, PA). We applied 100 nM DTX-K (Alomone Labs) to maximally block Ikl.
We took brain slices from CO2 anesthetized mice (age P14–P16). Mice were decapitated, and brains were transferred to slice solution. After placing the brain dorsal side down and separating the brain stem/cerebellum from the cortex, we glued the brain stem cut-surface (rostral side) down to a vibratome series 1000 stage (Technical Products International, St. Louis, MO) and took five to six 150-µm-thick slices from the region containing MNTB. We transferred slices to a 34°C bath of normal ACSF for 1 h and kept them for 
10 h at room temperature.
For recording, we perfused slices with ACSF at 1–2 ml/min. Under a microscope with a x60 immersion lens (Carl Zeiss, Thornwood, NY), we identified MNTB neurons visually using Nomarski optics and made patch-clamp recordings in the whole cell configuration. Current-clamp experiments were done with an Axoclamp 2A amplifier, and voltage-clamp studies were done with an Axopatch 200 (Axon Instruments). Dynamic (or conductance) clamp experiments used the Axoclamp 2A in conjunction with a custom-built analog multiplying amplifier (University of Washington, Department of Physiology and Biophysics, Seattle, WA) that received a conductance waveform command (EPSG) from the computer, the membrane potential (Vm) from the Axoclamp 2B, and a reversal potential (Vrev) set to 10 mV. Current (I) was dynamically applied according to I = EPSG x (Vm –Vrev) at 120 kHz. Voltage-clamp recording was done at room temperature (24°C) and current and dynamic clamp were done at 34°C. After achieving at least a gigaohm seal using pipettes (VWR International, West Chester, PA, or Garner Glass Co., Claremont, CA) with resistance of 3–10 M
, we established a stable recording in the whole cell configuration. To help reduce electrode capacitance in voltage-clamp recordings, VWR pipettes were coated with Silgard (DOW Chemical Co, Midland, MI). Voltage-clamp recordings were compensated at 85%. During measurements of Ikl stability, compensation was checked before and after each time-point. Recordings were accepted if cells had a rest potential between –70 and –50 mV and a series resistance of 6–19 M. Reported voltages were not adjusted for the –7-mV junction potential. Data were filtered at 2–5 kHz, digitized (20 kHz for room temperature recordings, 44 kHz for recordings at 34°C) by an ITC-16 (Instrutech Corporation, Fort Washington, NY), and acquired using Axograph software (Axon Instruments) running on a Macintosh 7100/80AV.
To determine current onsets in Fig. 2, we set current before the voltage step to zero (5-ms baseline) and fit traces from 2 to 10 ms with a single exponential function: –C x e(–t/
) + A. We compared the amplitude A and time constant between cell populations with different Ikl manipulations. Statistical analysis was done in Microsoft Excel (Microsoft, Redmond, WA) or Statview (SAS Institute, Cary, NC).
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We based the excitatory postsynaptic conductance (EPSG) waveform on rat data (Taschenberger and von Gersdorff 2000), with a 20–80% rise time of 0.114 ms, a half-width of 0.45 ms, and a double exponential decay (1 = 0.45 ms, 2 = 4.2 ms). The amplitude ratio for 1/2 was 10. As upper and lower limits, EPSG amplitudes were set at either 75 or 30 nS, based on the following: steady-state EPSG amplitude in rat brain slice was 
65 nS at 10 Hz, 40 nS at 100 Hz, and only 20 nS at 300 Hz (Taschenberger and von Gersdorff 2000); mouse MNTB cells in vivo fire spontaneously at about 40 Hz, sustain 300- to 400-Hz rates for 100 ms, fire 800 Hz for briefer periods, and follow >95% of the amplitude modulated noise cycles at 100 Hz (Kopp-Scheinpflug et al. 2003a); experimentally, we found 30 nS was close to the minimum needed to sustain 100 Hz firing for +/+ cells in ACSF at 34°C.
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RESULTS |
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To determine how Ikl affects AP timing, we first established three conditions of reduced steady-state Ikl. Figure 1A shows voltage-clamp recordings of a +/+ control (left) and a Kcna1–/– MNTB cell (right). We held cells at –60 mV, stepped for 180 ms from –90 to –30 mV in 5-mV increments, and returned to –60 mV, which is near rest potential for these neurons (+/+ cells, –60.0 ± 3 mV, n = 8; Kcna1–/– cells –60.5 ± 5 mV, n = 7). Current responses to hyperpolarizing steps revealed almost no voltage-gated conductance, except the presence of a small, slowly activating hyperpolarization-activated current in response to the –90-mV step. As shown previously (Brew and Forsythe 1995; Brew et al. 2003), small depolarizing steps opened a prominent outward current; the nonlinear current response can be seen even in the step to –55 mV.
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50% less Ikl compared with +/+ littermates) (Brew et al. 2003). We perfused +/+ slices with low concentrations of DTX-K, aiming to block a subset of the Kv1.1-containing channels. We attempted to make a dose–response curve for DTX-K, but found that low concentrations of DTX-K did not reach stable block within 20 min. Figure 1B shows the percentage of current remaining over time in response to the –40-mV step for the average of three control cells (ACSF), five cells in 100 nM DTX-K, and six individual cells in 3–30 nM DTX-K as shown. In ACSF, Ikl was stable for 30 min. After 100 nM DTX-K, Ikl was blocked maximally (80%) after 5 min and remained stable for at least the next 20 min. In three different cells, we perfused 200 nM DTX-K after 100 nM DTX-K treatment and found no additional block (data not shown). In contrast, Ikl took 10–15 min to reach stable block in two cells after the application of 30 nM DTX-K. During acute application of 3 or 10 nM DTX-K, Ikl failed to reach stable block within 20 min. These data suggest tissue penetration problems, possibly caused by the heavy myelination of MNTB.
To achieve stable, partial reduction of Ikl with DTX-K, we incubated a slice in 3 nM DTX-K for 1 h (3 nM DTX-K treatment), transferred the slice to ACSF, and established a whole cell recording within 30 min. Under these conditions, Ikl was stable for 30 min after the start of the recording (Fig. 1C). For comparison, we show the steady-state Ikl amplitude of the control and 100 nM DTX-K–treated cells from Fig. 1B. In a different set of 3 nM DTX-K–treated cells, we found 100 nM DTX-K further reduced Ikl, indicating some Kv1.1-containing channels remained unblocked (data not shown, n = 3).
In Fig. 1D, we show the steady-state Ikl in +/+ control, Kcna1–/–, 3 nM DTX-K–treated (1-h incubation), and 100 nM DTX-K–treated (acute application) cells. We found for the steps to –50, –45, and –40 mV, 100 nM DTX-K treatment reduced Ikl by 80% compared with controls, similar to rat MNTB and mouse octopus neurons (Bal and Oertel 2001; Dodson et al. 2002). This block is greater than previously observed for mouse MNTB steady-state Ikl (Brew et al. 2003), possibly because the mice in this study are slightly older (P14–P16 vs. P9–P16) and/or because our voltage-clamp protocol does not include a prolonged hyperpolarization to –100 mV. Kcna1–/– cells had 50% less Ikl compared with +/+ controls, very similar to the 3 nM DTX-K–treated cells and consistent with Brew et al. (2003).
Ikl reduction: onset current
To determine how much Ikl would be available to affect AP initiation, we compared the relative amount of Ikl at the beginning of the voltage step in the +/+ controls to the three different conditions of reduced Ikl: Kcna1–/–, 3 nM DTX-K–treated, and 100 nM DTX-K–treated cells. Measuring Ikl activation is difficult because of the capacitive current associated with voltage step responses, especially for small Ikl. We measured activation by two methods. First, we reduced the capacitive transient with the subtraction method described below to measure Ikl in all cell conditions. Second, we confirmed the result by analyzing raw traces of the –40-mV step in the +/+, Kcna1–/–, and 3 nM DTX-K–treated cells, where the currents were large enough to rise above the capacitive transient.
To reduce the capacitive current, we added the current response to a negative step and the response to a symmetrical positive step of equal amplitude using the protocol from Fig. 1A (e.g., from –60 to –80 and –40 mV; Fig. 2). This procedure subtracted leak current and largely eliminated the capacitive transient, making it possible to model Ikl activation even for very small currents.
Using this method, the measured Ikl activation could be distorted by both a hyperpolarization-activated current (Ih) and Ikl that deactivates on hyperpolarization from –60 mV. We estimated the magnitude of distortion by modeling measured Ikl as the sum of Ih, deactivating Ikl, and activating Ikl, each described by a single exponential equation: A(1 – exp–t/). In response to the –80-mV step, average Ih was <2 pA for all conditions, much smaller than Ih measured in adult rat MNTB (Banks et al. 1993), and likely distorted our Ikl measurements by <1% (see Supplemental data).1
In some cells, deactivating Ikl was large enough to substantially distort the activating Ikl measurement. To minimize the error, we eliminated cases where the Ikl amplitude at –60 mV was >15% of the Ikl activated with depolarizing steps (from Fig. 1D, 1 cell each from the +/+, Kcna1–/–, and 3 nM DTX–K-treated cells, 2 100 nM DTX-K–treated cells). We concluded the maximum error of both amplitude and would be an underestimate of <10% for each cell population (see Supplemental data for the model details and results).
Figure 2A (left) shows a typical +/+ response to –80- and –40-mV steps (top). The sum of the two responses largely eliminated the capacitive transient (middle). In the bottom trace, we overlaid the raw current from the top and the middle trace, showing that the activation rate is very similar a few milliseconds after the start of the step. When the current response is small (Fig. 2A, top right, responses to –45- and –75-mV steps in a 100 nM DTX-K–treated cell), the capacitive transient obscures Ikl activation. The sum of the responses (bottom) reveals the activation of a roughly 25-pA outward current.
To assess the amount of current available during the first 15 ms after depolarization, traces were fit with a single exponential rise from 2 to 10 ms after the voltage step (Fig. 2B, bottom). While a single exponential rise is not a complete description of channel kinetics and does not account for inactivation visible in Fig. 2B (top), it allows comparison of the relative amount of Ikl likely available to participate in AP initiation from rest.
Using the fits at the start of the voltage step, Ikl amplitude in the Kcna1–/– and 3 nM DTX-K–treated cells was 50% smaller compared with +/+ (Fig. 2C); 100 nM DTX-K treatment reduced Ikl amplitude by 85%. Although the mean time constant for Ikl activation in the 100 nM DTX-K–treated cells was not significantly different from +/+, the was smaller (faster) in both Kcna1–/– and 3 nM DTX-K–treated cells (Fig. 2D).
From our modeling, the maximum underestimate of is <10% (supplemental data). However, compared with +/+, in the Kcna1–/– cells is 30 and 34% smaller, and in the 3 nM DTX-K cells, is 21 and 25% smaller (responses to –45- and –40-mV step, respectively). We also compared single exponential fits to current responses to the –40-mV step with no leak subtraction in +/+, Kcna1–/–, and 3 nM DTX-K–treated cells. (The –40-mV step produced a sufficiently large Ikl to rise above the capacitive current.) The values with and without leak subtraction were similar ( in ms; for leak subtracted traces, +/+: 2.89 ± 0.18; Kcna1–/–: 1.91 ± 0.09; 3 nM DTX-K: 2.17 ± 0.11; for nonleak subtracted traces, +/+: 2.90 ± 0.19; Kcna1–/–: 1.85 ± 0.14; 3 nM DTX-K, 2.15 ± 0.12).
Another factor that might affect our measurement of Ikl activation is inactivation rate. Faster inactivation could give the appearance of faster activation when fitting the rise with a single exponential, assuming single channel activation and deactivation are somewhat coincident. We observed that the Kcna1–/– cells tended to have faster inactivation than +/+. We therefore fit +/+ and Kcna1–/– traces (–40-mV step) with the sum of two exponentials: one rising and one falling. The activation from the +/+ double exponential fits (3.08 ± 0.61 ms) was not significantly different from the +/+ single exponential fit (P = 0.4). In the Kcna1–/– cells, the double exponential fit yielded a significantly greater activation (2.39 ± 0.05 ms, P < 0.01) compared with the single exponential fit. However, the activation in the Kcna1–/– cells was still significantly smaller than the activation in the +/+ cells (P < 0.01). These data suggest more rapid inactivation in the Kcna1–/– cells can only partly explain the appearance of more rapid activation compared with +/+.
Measuring AP latency and jitter during moderate firing rates
One way Ikl may limit the variability of AP timing is by preventing long latency APs (Trussell 1999). Large inputs depolarize the membrane quickly, reaching AP threshold before Ikl can open fully. Slower depolarization results from smaller inputs; Ikl has time to open more fully, and the resulting outward current can prevent the depolarization from reaching AP threshold. If so, Ikl would create a finite temporal window for AP initiation, and Ikl reduction would increase window duration.
To measure AP latency and jitter in response to identical inputs, we injected cells with trains of 10 square current pulses (0.5-ms duration) at 50 Hz (Fig. 3). Because the amplitude of excitatory postsynaptic potentials (EPSPs) received by these cells is believed to vary widely and we were interested in the total window during which APs could initiate, pulse amplitude was increased from 0 to 3 nA in 50-pA increments. We chose 50 Hz because, in pilot studies, no temporal summation was observed in control or Kcna1–/– neurons at this stimulation rate. Although temporal summation occurred in 100 nM DTX-K–treated cells, this caused us to underestimate the effects on both jitter and the temporal window for AP initiation.
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To determine the temporal window for AP initiation, we measured the minimum and maximum latency APs for each cell. All cells fired their maximum latency APs in response to Ith (Table 1). Maximum AP latency was shortest in +/+ controls, significantly longer in 3 nM DTX-K and Kcna1–/– cells, and longest in 100 nM DTX-K–treated cells. Kcna1–/– and 3 nM DTX-K–treated cells were not different from each other. These data show that Ikl reduction limits maximum AP latency.
To measure the minimum AP latency and to see how input amplitude affected AP latency, we compared AP latency at equal current intensity (Fig. 4A). We averaged the latency at each current intensity and plotted the average latency for all cells against current intensity in 200-pA bins (minimum 5 cells in the smallest 2 bins). The 100 nM DTX-K–treated cells permitted by far the longest latency APs, but only in response to currents that were below Ith (i.e., too small to drive APs) in the other conditions (top). Kcna1–/– and 3 nM DTX-K–treated cells were not different from each other and also permitted longer latency APs compared with +/+ cells, but again only to currents that were below +/+ Ith (middle).
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Ikl-reduced cells might have shorter AP latencies compared with +/+ controls if Ikl is open at rest or opens rapidly enough after depolarization to increase AP threshold (Vth) and/or slow the AP. We found input resistance was not different between +/+ controls, Kcna1–/–, and 3 nM DTX-K–treated cells, but was significantly higher in 100 nM DTX-K–treated cells (Table 1). These data are consistent with Ikl being slightly open at rest and also opening rapidly enough to counter the Na channel driven depolarization. We also found Vth (defined as the maximum depolarization with no AP) was highest in +/+ controls, intermediate in Kcna1–/– and 3 nM DTX-K–treated cells, and lowest in 100 nM DTX-K–treated cells (Table 1). These data suggest Ikl could slow latency to AP peak by competing against Na channels before AP initiation. To see if Ikl was slowing the AP itself, we measured the maximum slope during the AP rising phase. Comparing APs of similar latency, we found the slope was smallest in +/+ controls, somewhat larger in Kcna1–/– cells, and significantly larger in 3 nM DTX-K–treated cells (Table 1). DTX-K–treated cells (100 nM) weresimilar to the Kcna1–/– and 3 nM DTX-K–treated cells, possibly because maximum slope reduction was achieved by 50% Ikl block. Alternatively, recording duration may have reduced AP slope, countering the effect of maximum Ikl block. DTX-K treatment (100 nM) always followed recordings from either +/+ or 3 nM DTX-K–treated cells. The data from 11 of 12 +/+ (untreated) and all 19 of the 3 nM DTX-K–treated cells were collected between 10 and 20 min after establishing the whole cell configuration (data from 1 untreated +/+ cell was collected 31 min after going whole cell). In comparison, all 100 nM DTX-K recordings began 20 min after establishment of the whole cell configuration, and six of eight 100 nM DTX-K–treated cells were recorded between 25 and 35 min after going whole cell. We found the AP amplitude tended to decrease over the course of long-duration recordings, so the AP waveform in the 100 nM DTX-K–treated cells may be affected by recording duration, whereas no relationship was found between recording duration and AP timing (supplemental data; Fig. 4).
In Fig. 4B, we show that Ikl reduction increased the temporal window for AP initiation. We calculated the temporal window as the difference between maximum latency (the response to Ith) and the minimum latency (response to the 3-nA pulse). Compared with the window for +/+ cells [0.71 ± 0.04 (SE) ms], Kcna1–/– and 3 nM DTX-K–treated cells had longer windows but were not different from each other (0.92 ± 0.06 and 0.98 ± 0.07 ms, respectively). The 100 nM DTX-K–treated cells had by far the longest window for AP initiation (8.2 ± 2.1 ms) despite being underestimated because of the short interstimulus interval.
Ikl reduction increased jitter in response to near threshold current injection
As suggested by the cells in Fig. 3B, AP jitter (the SD of AP latencies) in response to a single current intensity was largest at Ith, and Ikl reduction increased Ith jitter (Table 1). Compared with +/+ controls, Kcna1–/– cells and 3 nM DTX-K–treated cells permitted significantly more Ith jitter but were not different from each other. DTX-K–treated cells (100 nM) permitted the most Ith jitter.
We also compared AP jitter at equal current intensity (Fig. 5A). For each cell, we measured jitter at each current intensity and plotted average jitter against current intensity for +/+ controls, Kcna1–/–, 3 nM DTX-K–, and 100 nM DTX-K–treated cells. Similar to the results for AP latency, we found Ikl reduction did increase jitter, but only at intensities below Ith for cells with more Ikl, so that Ikl reduction did not affect jitter in response to current intensities of 1.4 nA.
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1.4-fold Ith (both P < 0.05; repeated-measures ANOVA) and were not different from each other. DTX-K–treated cells (100 nM) exhibited more jitter at up to threefold Ith (P < 0.05; repeated-measures ANOVA). These data suggest that Ikl helps limit jitter at and slightly above Ith, potentially important in cells that receive inputs near Ith. Dynamic clamp simulated inputs mimic synaptic events better than current clamp
In vivo, MNTB cells can sustain up to 300- to 500-Hz firing for 100 ms with briefer firing rates of 800 Hz (Kopp-Scheinpflug et al. 2003a). First AP jitter in MNTB cells from the Kcna1–/– was greater than +/+, and unexpectedly, Kcna1–/– cells could not fire as fast (Kopp-Scheinpflug et al. 2003a). The authors suggested an up-regulation of inhibitory inputs limited the firing rate in the Kcna1–/– cells. It is also possible that reduced Ikl in Kcna1–/– cells could result in an increase in the cumulative depolarization during rapid stimulation, leading to membrane inactivation and cessation of firing (Leao and Von Gersdorff 2002). These hypotheses are not mutually exclusive.
To examine the effect of Ikl reduction on AP firing rate and jitter, we initially used square pulses as in Fig. 3 to stimulate +/+ cells with and without 100 nM DTX-K at various frequencies (data not shown). Similar to our 50-Hz experiments (Fig. 3) and unlike synaptic stimulation (Brew and Forsythe 1995), we rarely saw more than one AP per stimulus after DTX-K application, likely because square pulse–evoked APs have a very small or absent depolarizing after potential (DAP). Figure 6 compares the membrane potential (Vm) after square pulse–evoked APs to APs evoked by a simulated EPSG. Compared with square pulse–evoked APs, the EPSG-evoked APs generated significantly larger DAPs that were similar to the synaptically evoked APs in rat MNTB (Brew and Forsythe1995) and chicken n. magnocellularis (Zhang and Trussell 1994). To model synaptic events more closely, we switched to EPSG trains.
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To test the effect of Ikl on rapid firing, we held cells at –60 mV, applied trains of simulated EPSGs at various frequencies, and measured both the number of APs in response to each input [output/input ratio (O/I), used to emphasize output] and AP jitter in +/+, Kcna1–/–, and 100 nM DTX-K–treated cells (Fig. 7). Because the amplitude of EPSGs in vivo is unknown, we used 30- and 75-nS EPSGs to bracket estimated upper and lower limits (see METHODS).
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Consistent with rat MNTB (Brew and Forsythe 1995), Ikl reduction increased O/I, but the increase was typically <100%, even after 100 nM DTX-K treatment (Fig. 7C). The O/I increase depended on degree of Ikl reduction, input amplitude, and stimulation frequency. In response to 30-nS EPSGs (Fig. 7C, left), every +/+ control had an O/I of exactly 1 500 Hz. O/I decreased to 0.37 at 800 Hz, indicating failures caused in part by a relative refractory period, because O/I increased when the same cells where stimulated with 75-nS trains (Fig. 7C, right). During stimulation at 100–500 Hz, Kcna1–/– cells occasionally fired extra APs, but typically had an O/I of 1. At 800 Hz, the Kcna1–/– O/I decreased to 0.72, significantly greater than +/+. After 100 nM DTX-K treatment of +/+ cells, O/I always increased 500 Hz; the average O/I was between 1 and 2, indicating that cells did not always fire more than one AP per EPSG. This may have been partly because the next EPSG occurred before the cell could fire a second AP, at least at 333 and 500 Hz. Interestingly, the O/I was nearly 1 (0.83) at 800 Hz in 100 nM DTX-K–treated cells. Ikl-reduced cells followed 800-Hz stimulation better than +/+ controls.
In response to 75-nS inputs (Fig. 7C, right), +/+ cells had an O/I of 1.1 during 100-Hz stimulation and 1 at 333 and 500 Hz. At 800 Hz, only one +/+ cell had an O/I = 1 and O/I < 1 in three other cells. The O/I for Kcna1–/– cells was >1 during stimulation 500 Hz, but dropped below 1 at 800 Hz. DTX-K–treated cells (100 nM) had an average O/I > 2 at 100 Hz and 1.1 at 800 Hz. Ikl helps limit O/I to 1, but Ikl reduction increased the maximum firing rate, enabling cells to fire more reliably during 800-Hz stimulation. These data are consistent with previous slice experiments showing that Ikl reduction by pharmacology or genetics increases excitability (Brew et al. 2003) but do not support our previously stated hypothesis that Ikl reduction may decrease maximum firing rate during rapid stimulation.
Ikl reduction increased jitter during high firing rates
Figure 7D (left) shows AP jitter in response to 30-nS EPSG trains for +/+, Kcna1–/–, and 100 nM DTX-K–treated cells at 100- to 800-Hz stimulation. +/+ cells permitted very little jitter 500 Hz stimulation, but jitter increased when the cells were driven at 800 Hz, possibly because the interstimulus interval was so short and Vm was so depolarized that Na channel recovery was incomplete; AP timing may have been a function of Na channel recovery as well as input timing. After 100 nM DTX-K treatment, jitter increased significantly at all frequencies compared with +/+ controls, except at 800 Hz. The increase was frequency dependent, with the maximum increase occurring at 333 Hz, presumably because of the duration of the DAP and typical interspike interval for the extra APs. The Kcna1–/– cells permitted slightly more jitter than +/+ cells at 100 and 500 Hz, but the increase was only significant at 333 Hz.
Figure 7D (right) shows jitter in response to 75-nS trains. Both Kcna1–/– and 100 nM DTX-K–treated cells permitted significantly more jitter compared with +/+ at all frequencies except at 800 Hz. Similar to the 30-nS trains, +/+ jitter during 800-Hz stimulation was also significantly greater compared with +/+ jitter at lower frequencies. These data show Ikl reduction increases jitter during rapid stimulation and also suggest the jitter increase is frequency dependent (P < 0.01; repeated-measures ANOVA).
Ikl stabilizes the membrane potential after each AP
Because the O/I was typically <2 even in 100 nM DTX-K, we wanted to know if Ikl reduction increased AP jitter when there were no extra APs. We therefore measured jitter after an EPSG when there was only one AP in response to the previous EPSG (Fig. 8). To control for position in the train, we analyzed responses to the same EPSG no. from repeated trains. Figure 8A shows 20 overlaid responses from repeated 333-Hz, 30-nS trains to EPSG 6, 12, 14, and 20 when the previous EPSG (5, 11, 13, and 19) evoked only one AP. There was little jitter in ACSF, despite 30 nS being close to the minimum conductance able to drive APs (Gth). In contrast, 100 nM DTX-K treatment resulted in considerable jitter, even though Gth had (presumably) decreased compared with ACSF (Figs. 3–5). Looking more quantitatively at EPSG 14, Vm amplitude measured 0.2 ms before the EPSG pulse correlated with the AP latency (Fig. 8B; P < 0.01, linear regression); latency decreased with increasing depolarization. Similar results were found for EPSG 12 and also using 100-Hz data (data not shown).
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Is Ikl activation rate faster in Kcna1–/– cells?
We found that Ikl in Kcna1–/– and 3 nM DTX-K–treated cells reached peak values significantly faster than in +/+ cells. Only part of the difference in the Kcna1–/– cells could be explained by faster inactivation compared with +/+, suggesting a difference in activation. One possibility is that the Kv1.1 subunit affects channel behavior in the +/+, but Kv1.6 has a more prominent effect on channels in the partially Ikl-reduced cells. In cell expression systems, channels with heteromeric 
-subunit composition exhibit behavior that is intermediate with respect to homomeric channels composed of the constituent subunits (Akhtar et al. 2002; Kerr et al. 2001). For example, in one study using Xenopus oocytes, the half activation voltage (V1/2) of Kv1.1 homomers was –31 mV, the V1/2 of Kv1.2 homomers was –15 mV, and the V1/2 of channels composed of Kv1.1–1.2 tandem dimers was –26.5 mV (Akhtar et al. 2002). Bertoli et al. (1994) found that the activation time constant for Kv1.1 homomers was 4 ms, whereas for Kv1.6 homomers, it was 2.1 ms. In Kcna1–/– cells, channels could contain relatively more Kv1.6 compared with +/+ channels that are richer in Kv1.1, resulting in faster Ikl activation in the Kcna1–/– cells. In the case of 3 nM DTX-K–treated cells, DTX-K may preferentially bind channels with relatively more Kv1.1 (Akhtar et al. 2002), leaving the channels with relatively more Kv1.6 unblocked.
While the above explanation is plausible, the story is likely more complicated. First, the cell expression system used affects channel behavior. Reported V1/2 values for Kv1.2 homomers range from –30 mV in Xenopus oocytes to nearly +30 mV in mouse fibroblasts (Grissmer et al. 1994; Stuhmer et al. 1989). Other factors must also contribute; the studies using Xenopus oocytes report a V1/2 range for Kv1.2 homomers from 0 to –34 mV (Accili et al. 1997; Akhtar et al. 2002; Stuhmer et al. 1989). Second, 
-subunits, which are well known to increase the rate of inactivation (Martens et al. 1999), were shown to increase the activation rate of Kv1.4 homomers (McIntosh et al. 1997). Third, phosphorylation by protein kinase-A (PKA) shifts the V1/2 of rat Kv1.1 homomers expressed in HEK293 cells, but does not alter V1/2 in mouse Kv1.1 homomers expressed in Chinese hamster ovary cells (Bosma et al. 1993; Winklhofer et al. 2003). Unlike our results, activation of Kv1.1 homomers slowed by a factor of two after partial block with DTX-K (Robertson et al. 1996). Taken together, measurements of Kv1channels expressed in cultured cells may not be perfectly predictive of channel behavior in slice. Our measurements are only suggestive of a difference in Ikl activation; a more thorough study is needed.
Ikl limits the temporal window for AP initiation
Ikl limits temporal summation, which can improve temporal precision in cells requiring coincident inputs to fire (Oertel 1983; Rothman et al. 1993; Svirskis et al. 2003). In response to 0.5-ms-duration inputs, we showed that Ikl reduction widened the temporal window for AP initiation, permitting longer latency APs. We also found that Ikl reduction decreased the minimum AP latency in response to large, suprathreshold inputs. This suggests that Ikl activates rapidly enough to compete against Na channels before AP onset, further narrowing the temporal window for AP initiation by preventing very short latency APs. By narrowing the temporal window on both sides, Ikl would limit jitter in neurons that receive a wide range of input amplitudes. For example, in cells that have multiple afferents, such as bushy neurons of the cochlear nucleus, input amplitude would vary depending on the number of synapses contributing to the EPSP. In MNTB cells, input amplitude would depend on the recent firing history; slice experiments show the calyceal EPSCs depressed on average 85% during 300-Hz stimulation (Taschenberger and von Gersdorff 2000), well within the maximum in vivo firing rate (Kopp-Scheinpflug et al. 2003a,Kopp-Scheinpflug et al. 2003b), potentially creating large variability in EPSC amplitude.
Ikl limits near-threshold jitter
We also found that Ikl limits AP jitter in response to near-Ith inputs. The earliest electrophysiological recordings in axons reported that AP latencies were remarkably consistent except in response to the minimum stimulus strength to generate an AP, when jitter, although still small, increased (Pecher 1939). Subsequent studies concluded that the stochastic behavior of subthreshold Nav channels increased jitter (Conti et al. 1976; Lecar and Nossal 1971; Mann-Metzer and Yarom 2002; Schneidman et al. 1998; Steinmetz et al. 2000). Compared with other cell types, temporally precise auditory neurons are "axon-like" in that they exhibit relatively little jitter in response to near-Ith inputs (Reyes et al. 1994). Finding that Ikl reduction increased near-Ith jitter suggests a critical role in temporally precise auditory neurons, many of which strongly express Kcna1 (Brew et al. 2003; Trussell 1999; Wang et al. 1994). Cells such as those in the mammalian medial and lateral superior olive, octopus and bushy cells in the cochlear nucleus, and avian nuclei laminaris and magnocellularis are believed to require multiple inputs to fire, and therefore likely receive near-Ith stimulation (Goldberg and Brown 1969; Golding et al. 1995, 1999; Joris et al. 1994; Oertel 1983; Paolini et al. 1997). While MNTB cells normally fire in response to a single, large excitatory input (the calyx of Held), in vivo evidence suggests that the calyceal input can fail to evoke a postsynaptic AP under some conditions (Guinan and Li 1990; Kopp-Scheinpflug et al. 2003b), and measurements of synaptic depression in slice show EPSCs can drop below the Ith during moderate stimulation rates (von Gersdorff et al. 1997). Therefore MNTB cells may also receive near-Ith inputs and benefit from Ikl jitter limitation.
Increased jitter and O/I under dynamic clamp
During stimulation with high-frequency trains of simulated EPSGs, we found Ikl reduction increased jitter and increased O/I. The jitter increase was largely independent of EPSG amplitude, unlike the response to current pulses at 50 Hz. Previously, Brew and Forsythe (1995) showed that rat MNTB cells fire extra APs in response to synaptic stimulation and suggested that this would reduce temporal fidelity. We confirmed this hypothesis in the mouse, and found that jitter increase was greatest during 333-Hz stimulation, well within the sustained firing capabilities of these cells (Kopp-Scheinpflug et al. 2003a). We also found increased jitter even when no extra APs were fired, but the increase was small in comparison (see Figs. 7D vs 8, C and D).
The correlation between Vm variability and jitter in the absence of extra APs may be important in light of in vivo experiments using Kcna1–/– mice. Kopp-Scheinpflug et al. (2003a) suggested the increased variability in first AP latency observed in Kcna1–/– cells resulted from increased variability in axons of the subthreshold Vm. This subthreshold Vm variability likely results from Na channel fluctuations and is correlated with variability in AP propagation rate (Conti et al. 1976; Hales et al. 2004; Lecar and Nossal 1971; Stys and Waxman 1994). Thus in axons, Kv1.1-containing channels may limit Vm variability at rest and/or in the recovery cycle after each AP, possibly by curtailing subthreshold Na channel activity.
Our results show that Ikl reduction increased firing rate, consistent with other in vitro studies showing Ikl reduction increases excitability (Brew and Forsythe 1995; Brew et al. 2003; Smart et al. 1998; Zhou et al. 1998). In contrast, experiments in vivo show Kcna1–/– MNTB cells do not fire as fast as +/+ littermates (Kopp-Scheinpflug et al. 2003a). Kopp-Scheinpflug et al. (2003a) suggested that the lower maximum firing rate could result from an up-regulation of inhibition in the Kcna1–/– (van Brederode et al. 2001). As an alternate (or additional) hypothesis, we propose here that, during rapid stimulation, Vm in Ikl-reduced cells would depolarize sufficiently to inactivate Na channels, reducing AP number (Leao and Von Gersdorff 2002). Our experiments using simulated EPSGs do not show reduced firing rates after Ikl reduction. However, our EPSG simulation may underestimate the EPSC tail, because it is modeled on EPSCs recorded while holding cells at –80 mV and doesn't account for the voltage sensitivity of N-methyl-D-aspartate (NMDA) receptors (Mayer et al. 1984). More importantly, we only test somatic inactivation; inactivation may take place in the axon instead.
Just as the jitter increase observed in the Kcna1–/– cells in vivo may take place in the axon (Kopp-Scheinpflug et al. 2003a), the mechanism reducing in vivo firing rates may be axonal. Axonal APs have a prominent DAP, thought to result from the internode charging as an AP passes and discharging into the node afterward (Barrett and Barrett 1982). Kv1.1-containing channels lining the juxtaparanodes of myelinated axons (Wang et al. 1993) are perfectly positioned to shunt the DAP and limit nodal depolarization. In a Kcna1–/– axon where the juxtaparanodal channels are compromised (Zhou et al. 1998), rapid firing may lead to accumulated internodal depolarization large enough to inactivate Na channels, ultimately reducing firing rates. This hypothesis can be tested directly.
3 nM DTX-K treatment is a near phenocopy of Kcna1–/– cells
We compared two different methods of Ikl reduction: genetic and pharmacological. Deletion of the Kcna1–/– gene eliminates Kv1.1 (Smart et al. 1998). The Ikl present in Kcna1–/– MNTB cells is sensitive to DTX-I, indicating the presence of Kv1.2 and/or 1.6 in the underlying channels (Brew et al. 2003). In contrast, Kv1.1-containing channels carry 50% of Ikl in 3 nM DTX-K–treated cells, because application of 100 nM DTX-K to these cells blocked 50% of the remaining current. Although the channels underlying Ikl were of different subunit composition, these two manipulations produce very similar results in nearly all of our physiological measurements, even though Ikl reduction was determined at ambient temperature, whereas excitability and AP timing were characterized at 34°C. An exception was that the minimum AP latency was longer in the Kcna1–/– compared with the 3 nM DTX-K–treated cells, suggesting Ikl in Kcna1–/– cells was more effective at limiting Na channel activity. There may be a compensatory change in the Kcna1–/–, such as altered Na channels or K channel location.
For example, the channels underlying Ikl could be preferentially localized near the spike initiation zone (SIZ) in the Kcna1–/–. Here, they might better compete against Na channels and partially compensate functionally for reduced Ikl. Sufficient DTX-K to reduce total +/+ Ikl to levels measured in the Kcna1–/– would mean less Ikl near the SIZ compared with Kcna1–/– cells, assuming a somewhat evenly distributed block. Ikl near the SIZ might more effectively curtail Na channel activity, delaying the time to reach AP threshold.
Another possibility is that chronically reduced Ikl in the Kcna1–/– may lead to fewer Na channels available at voltages between rest and Vth, either by a reduction in the total number of Na channels or a positive shift in voltage sensitivity. Fewer Na channels could mean an increase in Vth and/or a decrease in the AP maximum slope. Although the difference was not significant, we found the AP maximum slope was smaller in Kcna1–/– cells compared with 3 nM DTX-K–treated cells (Table 1), consistent with fewer Na channels in the nulls.
Our slice experiments show that Ikl can limit AP jitter under several conditions, most importantly during 100- to 500-Hz firing, which is well within the physiological range for auditory neurons. These results suggest a critical role for Ikl in fast firing neurons in addition to coincidence detection and preventing extra APs. We show very similar alterations in excitability and AP timing in cells with partial Ikl reduction by acute DTX-K application or by chronic deletion of the Kcna1 gene, suggesting partial pharmacological block of Kv1.1-containing channels can duplicate (phenocopy) most changes in Ikl function observed in the Kcna1–/–.
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1 The online version of this article contains supplemental data). 
Address for reprint requests and other correspondence: B. L Tempel, V. M. Bloedel Hearing Research Ctr. and Dept. of Otolaryngology, Univ. of Washington, Box 357923, Seattle, WA 98195 (E-mail: bltempel{at}u.washington.edu)
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