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1Departments of Cell and Molecular Physiology and 2Otolaryngology/Head and Neck Surgery, University of North Carolina, Chapel Hill, North Carolina
Submitted 3 May 2006; accepted in final form 13 April 2007
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ABSTRACT |
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1–2 ms) and high reproducibility. Increasing the coefficient of variation of the noise improved the reproducibility of the spike trains, whereas increasing the firing rate of the neuron decreased the neurons' ability to respond with predictable patterns of spikes. Simulated inhibitory postsynaptic potentials superimposed on the noise stimulus enhanced spike timing for >300 ms, although the enhancement was greatest during the first 100 ms. We also found that populations of pyramidal neurons respond to the same noise stimuli with correlated spike trains, suggesting that ensembles of neurons in the DCN receiving shared input can fire with similar timing. These results support the hypothesis that spike timing can be an important aspect of information coding in the DCN. |
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INTRODUCTION |
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), precise and reproducible spike timing is also frequently observed, raising the likelihood that this firing regime is used to encode information (Abeles et al. 1993; Bair and Koch 1996; Beierholm et al. 2001; Berry et al. 1997; Buonomano 2003; Buracas et al. 1998; de Ruyter van Steveninck et al. 1997; Mainen and Sejnowski 1995; Nowak et al. 1997; Reich et al. 1997). The precision and reliability of action potential timing depends on the membrane time constant, fluctuations in both excitatory and inhibitory input, the activation of, and noise from, voltage-gated ion channels, and coincident excitation from presynaptic neurons (Azouz and Gray 2000; Diesmann et al. 1999; Dorval and White 2005; Fricker and Miles 2000; Gauck and Jaeger 2000, 2003; Grande et al. 2004; Grothe and Sanes 1994; Hausser and Clark 1997; Jaeger and Bower 1999; Schreiber et al. 2004; Sourdet et al. 2003; Svirskis et al. 2002–2004). Certain neurons in the auditory system have long been known to represent precisely timed information about the acoustic environment by phase-locking in their spike trains (Rose et al. 1967), and this depends on specific combinations of ion channels and synaptic receptors. However, many other auditory nuclei, such as the dorsal cochlear nucleus (DCN), show little high-frequency phase-locking and so have been most extensively characterized in terms of mean firing rate.
Pyramidal cells in the DCN receive auditory information via the auditory nerve, and nonauditory information that is relayed through a system of granule cells that give rise to parallel fibers, similar to the circuitry found in the cerebellum. Pyramidal cells integrate synaptic input from these excitatory inputs, as well as from at least three types of inhibitory interneurons, and pass this processed information on to the inferior colliculus (for review, see Oertel and Young 2004). Although the DCN has not previously been thought to utilize precise spike timing because it exhibits poor phase locking to high-frequency pure tones (Goldberg and Brownell 1973; Rhode and Smith 1986), recent evidence suggests that timing might play an important role in information processing. For example, parallel fiber synapses onto pyramidal cells exhibit spike-timing-dependent plasticity (Tzounopoulos et al. 2004). The excitatory postsynaptic potential (EPSP)-spike coincidence window for plasticity in the DCN is on the order of 10 ms, which is notably smaller than the window reported for other regions of the brain. Furthermore, pyramidal cells exhibit sensitivity to temporal information by encoding the envelope of amplitude modulated sounds up to a few hundred hertz (Frisina et al. 1994; Joris and Smith 1998; Kim et al. 1990; Neuert et al. 2005; Zhao and Liang 1995). Together, these observations support the hypothesis that spike timing may be an important code in this nucleus.
Because spike timing may be important in DCN information coding, we sought to characterize the ability of pyramidal cells of the DCN to respond to time-varying stimuli with reproducible spike trains in vitro and to identify features of the stimulus that affect spike timing. Using Gaussian distributed noise current pulses, to simulate fluctuations in synaptic drive, we were able to determine if time-varying input improves the reproducibility of spike times. The results indicate that pyramidal cells can fire with good precision in response to dynamic stimuli and that firing precision can be affected for several hundred milliseconds by brief hyperpolarizations.
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METHODS |
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Sprague-Dawley rats, postnatal day 10–14, and 21–24 were deeply anesthetized with ketamine (100 mg/kg) and xylazine (10 mg/kg) and decapitated, and the brain stem was removed. The brain stem was trimmed to a block of tissue that included the dorsal cochlear nucleus. The block was mounted on agar supports, sliced in the trans-strial plane (250 µm) (Blackstad et al. 1984), and stored in an incubation chamber for 1–2 h at 34°C. All procedures were performed under protocols approved by the Institutional Animal Care and Use Committee of the University of North Carolina. Slices were transferred to the recording chamber, held in place by a net, and perfused with recording solution at 34°C at 3–5 ml/min.
Solutions
The dissection and slicing procedure was carried out in a low-Ca2+/high-Mg2+ solution, which contained the following (in mM) 122 NaCl, 3 KCl, 1.25 KH2PO4, 25 NaHCO3, 20 glucose, 2 myo-inositol, 2 sodium pyruvate, 0.4 ascorbic acid, 0.1 CaCl2, and 3.7 MgSO4. The slices were incubated and perfused with the same solution, except containing (in mM) 2.5 CaCl2 and 1.2 MgSO4. Solutions were continuously equilibrated with 95% O2-5% CO2 at 34° to maintain pH at 7.3–7.4, and the osmolarity ranged from 310–320 mOsm. Strychnine (2 µM) was added to the bath to block glycinergic inhibition in all experiments. The electrode solution contained the following (in mM), 4 NaCl, 130 potassium gluconate, 0.2 EGTA, 10 HEPES, 2 Mg2ATP, 2Mg2GTP, and 2 creatine phosphate. AlexaFluor 488 (Na+ Salt, Molecular Probes, Eugene, OR) was added to the electrode solution (0.1 mM) allowing cells to be visualized and characterized morphologically. All chemicals were obtained from Sigma-Aldrich (St. Louis, MO).
Recording
Electrodes were pulled from 1.5-mm-diam KG-33 glass (Garner Glass, Claremont, CA) to a tip diameter of 1–2 µm and a final tip resistance of 2–7 M
on a P-2000 Sutter puller. The tips were coated with silicone elastomer (Sylgard) 184 (Dow Corning, Midland, MI) to decrease pipette capacitance. The slices were transferred to the recording chamber on a fixed stage microscope and visualized with a x40, 0.75 NA or x63 0.9 NA water-immersion objectives using video-enhanced differential interference contrast illumination in infrared light. Pyramidal cells were selected based on shape and visualization of apical and basal dendrites at opposite ends of the cell body. The membrane potential was recorded using standard techniques for whole cell, tight seal recording in slices with a Multiclamp 700A amplifier (Molecular Devices, Foster City, CA). Data acquisition was carried out under computer control with custom software program written in Matlab (The Mathworks, Natick, MA) using high-speed 12- or 16-bit A-D boards (National Instruments, Austin, TX) with a sampling rate of 50 kHz. All voltages were corrected for a –12 mV electrode-bath junction potential during analysis.
Stimuli
Different types of stimuli were applied to the pyramidal cells. The first was a rectangular DC current pulse, shaped using cos2 ramps to minimize onset and offset transients. The other was a low-pass (250–1,500 Hz) filtered (8-pole Butterworth digital filter) noise current (peak-to-peak amplitude of 500 pA unless otherwise noted).
The exact amplitude and pattern of synaptic input that pyramidal cells receive is currently unknown. Although some in vivo measurements of membrane potential fluctuations have been made, these measurements probably do not accurately reflect the frequency content of the membrane potential nor the relevant amplitudes of the fluctuating and steady-state components due to the low-pass filtering effect of sharp electrodes. Therefore we chose a Gaussian noise waveform, which theoretically includes all possible combinations of current trajectories that a cell might encounter. However, only a limited range of frequency content and amplitudes are biologically plausible, so our stimulus waveform was selected so as to present an experimentally tractable part of this large parameter space.
There are a number of factors that were considered in the selection of the input noise. In the present experiments, current is injected into the cell body to manipulate the membrane potential and drive the spike generator. Because this current is injected close to the spike generator, the membrane potential fluctuations should resemble those that would be seen by the spike generator when driven by both distant synaptic inputs that have been filtered by dendrites and by proximal excitatory and inhibitory conductances. Consequently, excitatory events will be low-pass-filtered by the transfer function between the dendrites and the cell body. However, this transfer function varies for each synapse, and therefore the aggregate effect of ongoing synaptic input necessarily generates synaptic potentials with a range of rise times and amplitudes. Experimental measures from other cochlear nucleus cells with membrane time constants similar to pyramidal cells suggest that during excitatory auditory drive, the spike generation site will experience both a slow sustained membrane depolarization, and superimposed rapid fluctuations that are a low-pass filtered (
20 Hz) version of the synaptic input (White et al. 1994). High-frequency barrages of both excitatory input from the auditory nerve and inhibitory input of the vertical cells can exceed 300 Hz from single inputs. Synaptic conductances from excitatory synapses onto DCN pyramidal cells have a rise time (10–90%) of 430 µs, and decay time constants averaging 1.3 ms (Gardner et al. 2001). For inhibitory inputs that occur close to the cell body, dendritic filtering is less important, and the voltage trajectory is determined instead by the time course of the synaptic conductance and by the somatic membrane time constant. IPSCs onto pyramidal cells have rise times of 2–4 ms, and decay time constants of 5–10 ms (J. G. Mancilla and P. B. Manis, unpublished observations). To estimate the spectral content produced by these synaptic inputs, we represented the conductance waveforms with an alpha function and calculated the energy spectrum of the conductance change. These calculations revealed that most of the time-averaged the energy is at 200 Hz and below for single events [tau = 2 for an alpha function for the excitatory postsynaptic currents (EPSCs)]; however, during the rising phase of the EPSCs, there is energy at frequencies approaching 1 kHz. The membrane potential may follow such rapid changes if the cell is an active state (e.g., high conductance state due to synaptic activity). We therefore expect to see frequency content in the membrane potential that includes both lower frequency components representing the time course of the EPSC and the rate of individual synaptic inputs, and components perhaps as high as 1 kHz representing rapid changes in the membrane potential during the rising phase of the EPSCs. Taken together, these considerations suggest that an appropriate stimulus to test the cell's temporal coding abilities should include a broad range of frequencies, up to 1 kHz.
The Gaussian noise was superimposed on the DC pedestal. Adjusting the amplitude of the DC pedestal controlled the average firing rate of the cell. Experiments examining spike timing used frozen noise in which the same noise token was used for 100 consecutive trials. To determine the spike triggered average of the cells, random noise was generated by changing the noise token in each trial for 50 consecutive trials. A simulated IPSP (sIPSP) or simulated EPSP (sEPSP) consisting of a short train of three alpha waves [I(t) = Imax*
*t* exp(–*t); = 0.1 ms-1], separated by a 15-ms interevent interval, was added to the stimulus with a delay of 500 ms, allowing us to compare the regularity of firing before and after the sIPSP or sEPSP. The sIPSP and sEPSP amplitudes were visually estimated from averaged traces, using a cursor. Because the sEPSPs evoked spikes, the measurements were made on the largest events that preceded spikes, or that were visible as inflections at the initiation of the spike. sIPSPs were 11.4 ± 3.4 (SD) mV for 18 cells, whereas sEPSPs were 4.8 ± 1.5 mV in the same cells. The sEPSPs are smaller than the sIPSPS even though the same current was used for each set of events. The differences arise because the cells were close to spike threshold, so the measurements are an underestimate of the true amplitude because the sEPSPs were partly obscured by the spikes and also because the cells were depolarized and had a low-input resistance at the time the sEPSPs were delivered, which reduces the amplitude of the voltage deflection. Previously published measurements of membrane hyperpolarizations were reported to be 5–9 mV (Hancock and Voigt 2002; Rhode et al. 1983)
Analysis
The digitized current and voltage traces were stored in a Matlab file and were then analyzed using custom Matlab routines. To determine the reproducibility of spike trains, we used the shuffled autocorrelogram (SAC) method first described by Joris (Joris 2003; Joris et al. 2006; Louage et al. 2004). For each cell, all nonidentical spike trains were paired with each other and the forward time intervals between all spikes of each spike train were used to calculate a cross-correlation of the delay between spike times. This histogram is referred to as the SAC. The SAC was normalized by dividing the number of coincidences in each bin (0.1 ms wide) by N(N – 1)r2
D, where N is the number of presentations (100), r is the average firing rate, is the choice of bin width, and D is the duration of the stimulus (note that the result is dimensionless). We then fit the normalized value to a Gaussian function to measure the width of the central correlation peak. The height of the Gaussian at 0 delay, the correlation index (CI) (see Joris et al. 2006) can then be used to compare the spike timing in response to different stimuli. Because this method is sensitive to changes in mean spike rate during the collection of repeated trials, we used a selection criterion to identify stable recording epochs for comparison. The slope of the firing rate as a function of time was calculated. Any cell that had a mean rate that changed by >2 spike/1-s trial was discarded. This selection criterion was specifically used for experiments that compared the CI for stimuli that included the sIPSP and the sEPSP. The SAC method does not require a priori knowledge of the correlation structure, and thus provides an objective measure of spike timing across trials.
We also calculated the reverse correlation, or spike triggered average (STA) of the current waveform that elicited an action potential. In these experiments, we presented the cell with 50 independent noise tokens and then computed the STA for spikes the preceding interspike interval (ISI) of which was >25 ms. CIs were calculated according to Bryant and Segundo (1976).
Data analysis was performed with Matlab 7.1 and Igor Pro (5.04). Statistics were calculated using both Matlab 7.1 and Prism 3.0 (GraphPad Software, San Diego, CA). All numerical data are presented as means ± SD. Statistical tests of hypotheses used one- or two-sided, paired or unpaired (as appropriate) t-test.
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RESULTS |
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We first sought to determine whether pyramidal cells of the DCN are capable of firing reliable and precise trains of action potentials. A total of 45 pyramidal cells with a mean resting membrane potential of –63.1 ± 4.9 mV and a mean input resistance of 68.2 ± 38.4 M were identified and recorded for the initial experiments. All cells showed the typical response patterns to depolarizing current pulses including regular, nonadapting trains of spikes, pauser and build-up patterns (Manis 1990). Seventeen cells were confirmed to be pyramidal cells morphologically. We do not include any cells that show bursting action potentials (likely cartwheel cells) in these results.
We tested whether cells were sensitive to the temporal structure of the membrane potential by comparing responses to a flat depolarizing current pulse with responses to stimuli with a superimposed noise. The DC current was chosen so that the cell fired at 20 ± 5 Hz. In response to the DC current (Fig. 1A), the cells typically respond with a train of action potentials with regular ISIs. The precise timing of spikes varied between trials. One can easily observe this behavior by examining a raster plot of spike times (Fig. 1B). The precision of the spike times in response to a flat current injected is high at the beginning of the spike train but decreases as the stimulus continues.
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To calculate the repeatability of the spike trains, we used the SAC analysis (see METHODS). The SAC reports both reliability (by the CI) and the precision (by the SD of the Gaussian function). The SAC uses the difference in spike times between pairs of different trials from the same cell to reveal repeatable temporal structure in the spike train. In response to the flat current pulse, the spike delays are spread out broadly and have a mean value of 1 (Fig. 2A). This flat SAC indicates that there is no repeated spike timing structure across trials. However, in response to the noisy current, the delays between spike times in different trials are frequently small, and the SAC shows a large peak around zero delay. The peak can be reasonably fit with a Gaussian function (shown by the line in Fig. 2A). Across the population of cells, noisy current pulses elicit higher central peaks than flat currents (Fig. 2B). Although our recordings were done in P10–P14 animals, the same result was seen in five cells from P20 to P24 animals where the peripheral auditory system is fully developed (P < 0.01, mean difference of CI between each pair = 12.07, mean difference of precision in each pair was 19.28 ms, P < 0.0001).
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Pyramidal cells of the DCN have been shown to phase lock to auditory input at low frequencies, and they can encode the frequency and AM of acoustic stimuli up to 500 Hz (Frisina et al. 1994; Kim et al. 1990; Rhode and Greenberg 1994; Zhao and Liang 1995). These observations led us to investigate how the frequency content of the noise current stimulus affected the ability of the pyramidal cells to fire in a repeatable manner. We varied the low-pass cutoff between 250 and 1,750 Hz. Varying the noise spectrum did not alter the ability of the cells to respond reliably to the noise (Fig. 3); although the CI values were variable across cells, there was little evidence for any frequency-dependence. Consequently, we choose to use a low-pass filter frequency of 500 Hz for our subsequent analyses.
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It is expected that the reliability might depend on the mean firing rate of a cell. At high firing rates, spike generation is dominated by intrinsic conductances, whereas at low rates, the variability of the membrane potential due to synaptic input or noise is expected to play a larger role. We thus calculated the CI for pyramidal cells firing at low, medium, and high rates to a noisy current. The firing rate was manipulated by increasing the DC pedestal on which the noise is superimposed, without increasing the amplitude of the noise itself. In general, the faster the average firing rate, the weaker the correlation between spike times across trials with the same stimulus presented (Fig. 4, A and B). However, note that the precision of spike timing does not change (Fig. 4B).
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100 Hz, the intrinsic mechanisms do not completely govern the spike times. Because increasing the average firing rate leads to a decreased CI, we next investigated whether increasing the amplitude of the noise improved spike timing reproducibility. Frozen noise tokens with different amplitude, but the same DC pedestal, were presented to the cells for 50 trials (Fig. 5, A–C). In four of five cells, increasing the noise amplitude results in increased CI of spike times (Fig. 5, D and E). Because the CVs increases when the amplitude of the noise component is increased, the time-varying component of the stimulus drives the cell most strongly, and the cell fires in response to the stronger stimulus fluctuations.
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So far, we have shown that pyramidal cells can respond to time-varying input with reliable and precisely timed spikes. In part, the cells are responding to specific patterns of energy in the stimulus. To identify the time courses of the stimulus events driving the cells, we computed STAs by averaging the mean current injected before and after spikes, aligned on spike threshold crossings.
A comparison of STAs is shown in Fig. 6 for one cell presented with noise low-pass filtered at 250 Hz (thick line), and noise low-pass filtered at 500 Hz (thin line). The two sets of dashed lines show 95% confidence limits for the two sets of noisy current injections. STAs to flat current pulses had no significant deviations from the baseline current (not shown). However, the STA to both the 250-Hz noise and the 500-Hz low-pass filtered noise reveals a broad negative (hyperpolarizing) followed by a sharp positive (depolarizing) current. The main difference between STAs for the two different spectra is mostly in the high-frequency components, but the averages follow a similar time course (Fig. 6A). The hyperpolarizing current is small but lasts for 10 ms, whereas the depolarizing current is large and lasts for only 3 ms. There is little difference in the rising slope or shape of the action potentials that result from the different input currents (Fig. 6B). In most cases, it seems that the cells are more likely to fire an action potential if they experience a slight hyperpolarization immediately before a depolarizing current.
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Inhibition is a critical element of sensory coding in the DCN (Oertel and Young 2004). DCN pyramidal cells receive inhibitory input from at least three different types of interneurons: vertical, cartwheel, and stellate cells. We therefore asked how a sIPSP placed in the middle of the noise stimulus would affect spike timing. We hypothesized that superimposing a sIPSP might increase reliability and precision of subsequent action potentials because the STA suggests that these cells prefer to fire when a small hyperpolarizing current precedes a depolarizing current. A sIPSP, consisting of a rapid triplet of alpha waves, was superimposed on the Gaussian noise current 500 ms after the onset of the stimulus (Fig. 7, A and B). We then compare the SACs after the sIPSP.
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300 ms (Fig. 7B). Summary data for 28 cells is shown in Fig. 7, D and E. For the last 500 ms of the stimulus, the CI is higher when the stimuli contain a sIPSP. The CI of spike times that occur before the sIPSP is similar to that under control conditions indicating that the sIPSP is not affecting the CI at these times. The difference in the CI after a sIPSP is highly significant (P < 0.001; n = 31, paired t-test). To determine approximately how long the sIPSP affected the spike times, we compared the CIs of smaller time intervals using a sliding time scale of 100 ms (Fig. 7E). In the five 100-ms time intervals prior to the sIPSP, there is no difference in CI. However, the CI of the 100-ms interval that includes the spikes from the 450 ms time point to the 550 ms time point (point a in Fig. 7E) was significantly higher compared with the same time interval without an sIPSP (P = 0.0003, df = 25, mean difference = –2.088). The effect continued for the next two 100-ms intervals (see points b and c, Fig. 7E). The CIs for the 550- to 650-ms interval and 650- to 750-ms interval were both higher when an sIPSP was present in the stimulus compared with when there was no sIPSP, although the effect was not as pronounced as the 450- to 550-ms interval (b, P = 0.022, df = 32, mean difference = –0.404; c, P = 0.0104, df = 32, mean difference = –0.204). Following the sIPSP, the increase in synchrony could result from the hyperpolarization of the membrane potential, or it could result from any perturbation. We tested the second idea by presenting the frozen noise stimuli superimposed with a sEPSP (Fig. 8A). The sEPSP produced a brief increase in spike rate, followed by a small hyperpolarization and a delay to the next spike. Spike timing following the sEPSP is more reliable and precise than it would have been without the sEPSP (Fig. 8, B and C), although the increase in CI is not as pronounced with the sEPSP as with the sIPSP (P < 0.05, n = 10, paired t-test). Whereas cells fire up to three action potentials during the sEPSP, there also is a slight afterhyperpolarization might effectively recruit the same mechanisms as the sIPSP. We also used the sliding time window analysis to determine how long the effects of the sEPSP lasted. However, the there were no statistically different intervals either before or after the sEPSP (Fig. 8D). Therefore we conclude that a sEPSP is not as effective as a sIPSP in improving the spike timing. In conclusion, small perturbations of the membrane potential, such as a sIPSP, can affect the CI for several hundred milliseconds, and it is most likely that the membrane hyperpolarization engages additional mechanisms that affect subsequent spike timing.
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The data shown so far suggest that individual cells can respond with repeatable patterns of activity in response to a frozen stimulus waveform. However, temporal coding also requires the coordinated activity of many neurons at the same time, for example. Because each neuron has different intrinsic excitability due to the differences in the voltage-dependence and density of their ion channels (for example, see Kanold and Manis 2001, 2005), such a temporal code might not be effectively retained across a population of cells receiving similar inputs. To investigate whether synchronous firing can be generated by a common stimulus to a population of cells, we computed the SAC, as a measure of synchrony, across a population of 15 cells collected in six independent experiments over a 2-mo period, where the same noise token was used for each cell. Such a calculation provides an estimate of the coherent firing that is available across the population of cells. On average, the frozen noise generated a population SAC with a similar shape to that seen in individual cells (Fig. 9A). The synchrony was good (CI = 4) and the timing of correlated spikes had a half-width of 0.84 ms. The amplitude of the central peak was smaller than for individual cells, indicating that fewer spikes were correlated between cells than within a single cell. A small secondary peak with a 2-ms half-width also appeared (arrow in Fig. 9A), suggesting that the spike timing across the population was not quite as temporally precise as in individual cells. The flat current pulse did not result in an elevated central SAC peak, in spite of the regular discharge of all cells. The SAC had the same shape and amplitude even in single trials (Fig. 9B), raising the possibility that the synchronized firing could convey information about the stimulus with good temporal precision during a single stimulus.
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2.7 times higher with the noise than with flat pulses. The correlated rate with flat pulses is probably lower than what we estimate because we chose the maximum correlation value, which is influenced by the statistical variation in the cross-correlation function due to the finite number of spikes available for the computation. Thus common features in the stimulus can lead to correlated firing among different cells, and the correlations occur in a time window 2 ms wide. |
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DISCUSSION |
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; Joris et al. 2006; Louage et al. 2004), a method that is free of assumptions regarding the timing of spikes in relationship to stimulus events, reveals that pyramidal cells can reliably report temporal events in a stimulus with millisecond precision. Precise spike timing can even be seen across a population of cells with different intrinsic properties. Characteristics of the stimulus such as amplitude and variability alter the reliability of the output spike train, whereas the degree of low-pass filtering does not affect the reliability. Longer hyperpolarizing events, such as a sIPSP embedded in the stimulus, can increase the reliability and precision of firing for 300 ms. General characteristics of DCN pyramidal cells in response to noise
Many neurons in the auditory system are known for their ability to fire action potentials that occur in a precise temporal relationship to the stimulus (Carr et al. 2001; Oertel 1999; Trussell 1999). Such cells may fire on repeated portions of the waveform with a SD on the order of 115 µs (corresponding to a phase-locking vector strength of 0.8 at 1 kHz); these cells have specialized AMPA receptor subunit and synaptic configurations and express low-voltage activated potassium conductances. Such specializations are not present in DCN pyramidal cells (Hirsch and Oertel 1988; Kanold and Manis 1999; Manis 1990; Zhang and Oertel 1994), so it expected that DCN cells respond similarly to other generic neuronal types when presented with time-varying input that resembles synaptic input (de Ruyter van Steveninck et al. 1997; Mainen and Sejnowski 1995; Nowak et al. 1997). The STA current waveform, which represents the linear contribution of current to spike generation, has a relatively short time scale in DCN pyramidal cells as compared with neocortical neurons. The spike-triggered-average current waveform consisted of a small slow hyperpolarizing current followed by a rapidly rising depolarizing current as in other cells. However, in other cells, the hyperpolarizing and fast depolarizing phases of the current have been reported to last tens of milliseconds (Mainen and Sejnowski 1995). In DCN pyramidal cells, the hyperpolarizing phase lasted 10 ms, and the depolarization on average had a half-width of 3 ms. This suggests that DCN pyramidal cells should integrate synaptic conductances on a relatively short time scale. The sharp depolarization most effectively enables the cell to reach threshold, because the spike threshold is inversely proportional to the slope of the input current (Azouz and Gray 2000). Thus fast events in the stimulus not only lead to sharp membrane depolarizations but also decrease the threshold resulting in an increased probability of firing a spike. Pyramidal cells thus appear to integrate their inputs on a time scale that is between that of the specialized auditory neurons that show high-frequency phase locking, and the slower neurons of the forebrain. On the other hand, DCN pyramidal cells also have a temporally nonlinear set of membrane conductance changes that can influence spike timing well beyond the 10-ms window suggested by the STA (Fig. 7) (also see Kanold and Manis 1999, 2001; Manis et al. 2003).
When we increased the variance in the stimulus (increased CVs,), spike times became more reproducible. The higher amplitudes of the time-varying component increase the magnitude of depolarizing currents. The faster and larger membrane depolarizations permit less time for intrinsic conductances of the cell to oppose the depolarization and less time for Na+ channels to inactivate. These two features lead to a lower spike threshold and higher reliability and precision (Hunter and Milton 2003).
The variance of the synaptic input to DCN pyramidal cells in vivo has not been measured. However, even small variations in the input current can evoke reliable spike trains when the stimulus frequency resonates with the intrinsic cell membrane oscillations or with a characteristic firing frequency (Fellous et al. 2001; Haas and White 2002; Hunter et al. 1998). We also found that small increases in noise amplitude resulted in increases in the number of spikes that were tightly correlated across trials. DCN pyramidal cells exhibit subthreshold oscillations that range in frequency from 40 to 100 Hz (Manis et al. 2003). Although we did not explore small-amplitude stimuli that specifically incorporated enhanced energy within this frequency range, it is possible that these cells could increase their firing reliability when the input resonates with membrane dynamics.
We compared neurons that fired at the same average rates to determine if pyramidal cells fire more reliable trains of action potentials in response to temporally changing input. Although pyramidal cells have been reported to phase lock in vivo to low-frequency input, at higher frequencies, this phenomenon disappears (Rhode and Smith 1986). In addition, others have reported that DCN cells phase lock poorly to synchronized repetitive stimulation of the auditory nerve fibers (ANF) (Babalian et al. 2003). As the firing rate of a neuron increases, the ISI is less influenced by transient changes in membrane potential and is controlled to a greater extent by the ionic conductances that regulate the refractory period. Consistent with this, when cells were sorted according to the stimulus CVs, the precision of spike times decreased with increasing rate. However, the peak rate of the SAC, regardless of CVs and rate, is very high compared with stimuli that contain no temporal structure. The CI of the ANF SACs runs in the range 2–10, even for stimuli that produce strong phase locking (Louage et al. 2004); the temporal coding in DCN cells can easily achieve this same range though with less precision. Although reliability and precision decreases with increasing firing rate, the rates must be well above 100 Hz before the contribution of input current fluctuations ceases to be evident in the spike timing.
Inhibition and spike timing in the DCN
Inhibition's effect on spike timing has received immense attention in recent years. In both the cerebellum and the medial superior olive, inhibition masks integrated, subthreshold input, which results in the cell failing to fire when the input is weak; instead the cell only responds to stronger, coincident synaptic events that elicit more reliable spikes (Gauck and Jaeger 2000; Grothe and Sanes 1994). Inhibition also leads to a delay in spike times in the cerebellum and DCN (Hausser and Clark 1997; Kanold and Manis 2005), whereas it shortens the membrane time constant and increases the membrane conductance. Consequently, nonsynchronous EPSPs become smaller and briefer, allowing the neuron to act as a more precise coincidence detector (Grande et al. 2004; Jaeger and Bower 1999). The DCN contains at least three types of inhibitory interneurons that share excitatory input with pyramidal cells (Golding and Oertel 1997; Hackney et al. 1990; Oertel and Young 2004). These interneurons can strongly inhibit pyramidal cells in conjunction with activity in ANFs and parallel fibers. Because inhibition is prominent in this nucleus, we imposed a sIPSP to mimic the inhibitory input from the bursting cartwheel cells. This perturbation transiently silenced the cell firing but resulted in an increased precision of spike timing when the cell resumed activity. The hyperpolarization from the sIPSP most likely perturbs the state of the cell's intrinsic conductances, such as sodium channels and transient potassium currents, and puts the cell membrane into a regime where it is can reliably fire at the next sharp depolarization. Cartwheel cells and stellate cells, both of which receive input from parallel fibers, could provide synchronized inhibitory input to pyramidal cells after they are excited by the parallel fibers. This inhibition might prevent pyramidal cells from firing imprecisely timed spikes to small depolarizing events after the initial excitation from the parallel fibers. This inhibition could also deinactivate membrane conductances so that the cells would be prepared to fire at the next sharp depolarization.
Population coding
A surprising result was that correlated spike times could be measured in a population of cells from different animals and slices in response to the same stimulus. This suggests that a population of pyramidal cells could use a timing-based, population-coding scheme to represent auditory information (Kanold and Manis 2005). This hypothesis depends on two principal assumptions. First it is assumed that the firing of individual auditory nerve fibers that connect to a group of pyramidal cells shows stimulus-dependent correlations in their firing. Indirect evidence suggests that this is the case, even for high-CF auditory nerve fibers. Responses to repeated stimuli in individual fibers show a significant central peak in their SAC (Louage et al. 2004). In addition, these correlations need to be detected by the pyramidal cells, and the presence of stimulus-dependent central mounds in the cross-correlations of pyramidal cells suggests that this may occur (Voigt and Young 1988). Second, this hypothesis assumes that the pyramidal cells receiving common inputs converge onto individual neurons in the inferior colliculus in a way that allows the collicular neurons to respond to the correlations in the input; this assumption is necessary for correlated synaptic events across the cell population to be detected. The convergence patterns between pyramidal cells and their collicular targets are presently not well understood.
Recent studies have demonstrated the existence of long-term synaptic plasticity between parallel fibers and two target neurons in the DCN, the pyramidal and the cartwheel cells (Fujino and Oertel 2003; Tzounopoulos et al. 2004). The timing dependence of this plasticity is relatively precise: in the pyramidal cells the window is <20 ms wide and in cartwheel cells it is <5 ms wide. Such a narrow window demands that the firing of the postsynaptic cells to fluctuating synaptic inputs also be temporally precise and implies that precise spike timing is an integral part of information processing in the DCN, at least as it relates to long-term synaptic plasticity. Our results also demonstrate that precise spike timing can occur in response to dynamic stimulation and that interactions among inhibition, potassium conductances, and other conductances regulating intrinsic cell excitability can modulate the precision of spike timing over hundreds of milliseconds.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Address for reprint requests and other correspondence: P. B. Manis, Dept. of Otolaryngology/Head and Neck Surgery, 1123 Bioinformatics Bldg., CB#7070, 130 Mason Farm Rd., Univ. of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7070 (E-mail: pmanis{at}med.unc.edu)
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ABSTRACT
INTRODUCTION
, delay times for flat currents; 
, times for the noisy currents. —, Gaussian fits. The abcissa is on a log scale to emphasize the correlation for delays <1 ms. A value of 1 is expected for a random process, or spike timing that is uncorrelated across trials. B: pooled data comparing correlation index, (CI) for 45 cells. The noisy CI is significantly larger than the flat CI (P < 0.001, paired t-test; mean difference = 13.0).
, medium rate; 
, high rate. The SACs are fitted by a Gaussian function. C: scatterplot of CI with the stimulus variance, CVs, for 26 cells driven at different rates. The CI and CVs are positively correlated. D: scatterplot of CI and spike rate, grouped by CVs. Low (
); intermediate (
). The correlation between CI and spike rate was significant for cells where the CVs was at high or intermediate ranges (R = 0.2513, P < 0.05 for high; R = 0.1838, P < 0.05 for intermediate).
near the origin in D is expanded to show increases with small amounts of noise. - - -, CI = 1.
