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1The Center for Hearing Sciences and 2Departments of Biomedical Engineering and Otolaryngology-Head and Neck Surgery, The Johns Hopkins University School of Medicine, Baltimore, Maryland; and 3Departments of Otolaryngology-Head and Neck Surgery and 4Cell and Molecular Physiology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
Submitted 1 September 2004; accepted in final form 23 December 2004
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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), and the spatio-temporal code is often closely related to the features of the acoustic stimulus across several time scales (Joris et al. 2004; Trussell 2002; Ulanovsky et al. 2004). Because excitatory synaptic events are depolarizing, it is generally thought that the spike timing is largely determined by patterns of near-synchronous activity of subthreshold excitatory synapses. Inhibition, in contrast, is thought to play mostly a modulatory role, either by increasing total membrane conductance and thereby decreasing the amplitude of excitatory synaptic potentials (EPSPs) or by hyperpolarizing the membrane, decreasing the likelihood that EPSPs can reach spike threshold.
However, inhibition can play a distinct role in controlling spike timing. In the auditory system, the detection of interaural timing differences in part depends on fast inhibition in a timing circuit (Brand et al. 2002), and inhibition may be important for maintaining temporal precision in the monaural pathways that lead to the binaural comparators (Rothman and Manis 2003; Rothman and Young 1996). In many neurons that are not as specialized as those in auditory pathways, the end of strong or synchronous inhibitory input can be signaled by rebound depolarization immediately following hyperpolarization that can cause spiking (Aizenman and Linden 1999; Steriade 2001). This response can occur even without excitation and can also sharpen response timing to excitation following inhibition (Gauck and Jaeger 2000). Rebound depolarization is mediated by intrinsic conductances, including T-type Ca2+- and hyperpolarization-activated cationic channels, whose activation or deactivation following hyperpolarization causes depolarization and increased firing probability.
The timing of inhibition could also directly influence spike timing by affecting intrinsic conductances that alter spike probability. One intrinsic conductance whose availability is determined by membrane potential changes near and just hyperpolarized to rest, optimizing its potential engagement by inhibition, is the A-current, or transient K+-current. In many neurons, A-currents control the interspike interval, whereas in others, they regulate synaptic integration and spike latency. Synaptic integration in olfactory granule neurons seems to depend on differences between A-current inactivation rate and the kinetics of excitatory events, and the A-current is recruited by inhibition (Schoppa and Westbrook 1999). Similarly, computational analysis shows that spike latency regulation by A-currents depends on the balance of current density and current inactivation rate, which together determine how quickly the membrane potential rises toward spike threshold (Kanold and Manis 2001). Again, this mechanism is triggered by hyperpolarizations that are largely provided by inhibitory inputs. A-currents have also been proposed to create conditional inhibition: i.e., reduction in spike probability conditional on prior inhibition (Berman and Maler 1998).
The roles attributed to inhibition just discussed all focus on interactions of these currents with inhibition in single cells. In the dorsal cochlear nucleus, we previously observed a wide range in the operating characteristics of A-currents, even in a single population of neurons (Kanold and Manis 1999). Consequently, the voltage dependence of the discharge patterns also varied widely among cells (Kanold and Manis 1999; Manis 1990). Thus each cell can exhibit a unique sensitivity to the temporal relationship between inhibition and excitation, and in a sensory system that encodes and uses timing information on multiple time scales, this seems to be a potentially important cellular mechanism for the central representation of the sensory environment. However, in these and other previous studies, hyperpolarizations of tens of millivolts and 100 ms that are larger and longer than those produced by synaptic inhibition were used to study the involvement of A-currents in spike pattern generation. Here using electrophysiogical recordings and computational modeling, we show a role for A-currents in retaining information about the history of the membrane potential and extending the effects of brief synaptic inhibition. We also show how cells exhibiting a range of A-current inactivation and activation voltage dependence can work as a neural population to explicitly encode the temporal relationship between inhibition and subsequent excitation. Thus we propose a new role for the interaction between A-currents and inhibition: by regulating the spike latency in response to excitatory inputs, these conductances can be used to generate an explicit representation of the relative timing of inhibition and subsequent excitation in spike trains of small neuronal populations.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Brain slices (300 µm thick) were prepared from the dorsal cochlear nucleus (DCN) of Sprague-Dawley rat pups (age, P11–P17; n = 30), using procedures previously described (Kanold and Manis 1999). The bathing solution [artificial cerebrospinal fluid (ACSF)] contained (in mM) 130 NaCl, 3 KCl, 1.25 KH2PO4, 20 NaHCO3, 10 glucose, 1.3 MgSO4, 2.5 CaCl2 (pH 7.35–7.4, equilibrated with 95% O2-5% CO2). Slices were held in a recording chamber on a fixed stage microscope (Zeiss Axioskop FS) and superfused (3–5 ml/min) with ACSF at 31–33°C. All chemicals were obtained from Sigma or Aldrich (St. Louis, MO). In previous studies, we found that the discharge patterns of DCN pyramidal cells were unaffected by blocking calcium channels with 50 µM Cd2+ (Manis et al. 2003; Molitor and Manis 1999) and that the transient potassium currents were not calcium dependent (Kanold and Manis 1999). Thus it was not necessary to block calcium channels in these experiments.
Recordings were obtained from pyramidal cells (n = 48) identified under infrared differential interference contrast video microscopy and Lucifer yellow fluorescence as described previously (Kanold and Manis 1999). Whole cell current-clamp recording were made with electrodes pulled from borosillicate glass (KG33, Garner Glass, Claremont, CA), fire-polished, and coated with sylgard (184, Dow Corning, Midland, MI). Electrodes had a final resistance of 3–9 M
. The recording electrodes contained (in mM) 100 K-gluconate, 4 NaCl, 20 KCl, 0.2 CaCl2, 10 HEPES (free acid), 1.1 EGTA, 2 Mg-ATP, 1 MgCl2, and 5 glutathione (pH 7.2). Lucifer yellow (K-salt, 
1 mg/ml, Molecular Probes, Eugene, OR) was added to the electrode solution for cell visualization. Recordings were made with an EPC-7 (List-Electronic, Darmstadt-Eberstadt, Germany), digitized using a 12-bit A/D converter (Digidata 1200, Axon Instruments, Foster City, CA) at 5–10 kHz, and filtered at 2–5 kHz. All voltages were adjusted for an estimated electrode-bath junction potential of –12 mV by off-line subtraction. Bridge correction was performed off-line. Digitized data were analyzed by MATLAB (version 5.2, The Mathworks, Natick, MA) on a Power Macintosh (Apple, Cupertino, CA).
A bipolar stimulating electrode was placed on the surface of the molecular layer or the ependymal surface of the DCN. Stimulus current usually ranged from 100 to 500 µA. Stimuli were applied once every 5–10 s to minimize paired pulse facilitation effects (Manis 1989). In some cases, pairs of shocks were applied to increase the hyperpolarization by paired-pulse facilitation of inhibitory postsynaptic potentials (IPSPs). The firing pattern of each cell was evaluated using intracellular current pulses of 100- to 200-ms duration. Single trials of the control condition and paired conditions were interleaved for a total of 50–100 trials per condition. Trials of an individual cell were divided into two groups for pauser and buildup trials, and the first spike latency (FSL) and first interspike interval (FISI) for trials falling in each group were compared separately. All experiments were approved by the Johns Hopkins Medical Institutions Institutional Animal Care and Use Committee and were performed in compliance with relevant laws and institutional guidelines.
Modeling
The details of the single-cell model are described elsewhere (Kanold and Manis 2001). Briefly, the model represented a point soma incorporating kinetic description of the ionic currents (except the sodium channels) determined previously (Kanold and Manis 1999). The IPSP was modeled as a time varying conductance change using an alpha function (
= 0.5 ms). The maximum synaptic conductance was 10 nS, and the synaptic reversal potential was –80 mV. The model was implemented in C++ (Metrowerks Codewarrior 11) and executed as a MEX-file under MATLAB (version 5.2, The Mathworks) on a Power Macintosh G4 (Apple). Some model results were computed and/or verified with NEURON, version 5.4 (Hines 1998). The artificial neural network was implemented using the MATLAB Neural Network Toolbox (version 3.0) on a Power Macintosh G4. The network is a two-layer feedforward back-propagation network consisting of eight input neurons, each receiving as its input the relative FSL of the response of one neuron with a particular half-inactivation voltage (VhKIF) or half-activation voltage (VmKIF) for the rapidly inactivating potassium conductance. The input neurons drove 12 output neurons (1 for each pairing interval between 0 and 110 ms) and 20–50 neurons in the hidden layer (see Fig. 6A). The output of each neuron in both layers was calculated by a hyperbolic tangent transfer function y(x) = 2/[1 + exp(–2 x x)] – 1 (where x represents the value of the input, in this case, the relative FSL or the FISIs) using the TANSIG function of the Network Toolbox. All results presented were obtained with 50 neurons in the hidden layer. The exact number of neurons in the hidden layer was not found to be critical in detecting the relative first spike timing information, but only affected the sharpness of tuning. The 12 output neurons were assigned to represent the 12 different pairing intervals, in that the output neuron with the greatest response represented the reported pairing interval (see Fig. 6B). Thus the output neurons of the network represented a "labeled line," according to the inhibition-excitation interval. Each pairing interval generated a pattern of responses for each of the model neurons and thus a pattern of eight FSLs (or FISIs). The pattern of FSLs (or FISIs) was used as input for the network model, and for each input pattern of FSLs (or FISIs), an output pattern of output responses was calculated (see Fig. 6B). The detected pairing interval was determined as the output neuron with the largest response. An error was computed from the difference between the reported pairing interval and the actual pairing interval. The network was trained (using batch training where the weights are updated only once during each input vector presentation) from random starting weights on a random subset (168/252 stimuli = 66%) of the simulation data for pairing intervals of 0–110 ms (10-ms steps) and depolarizing current pulses of 50–100 pA (2.5-pA increments) using the resilient backpropagation algorithm Rprop (Riedmiller and Braun 1993) of the MATLAB Neuronal Network Toolbox (TRAINRP). This backpropagation algorithm uses only the sign of the gradient, but not its amplitude, to determine the weight update and is commonly used in multilayer networks. The remaining 33% (84 stimuli) of the data set was used to characterize the model performance. In additional simulations, the network was trained in the "pauser" regimen using larger depolarizing currents between 170 and 200 pA, and in a regimen that included both "buildup," pauser, and transitional patterns, using current pulses between 50 and 200 pA. In each case, only the relative first spike latencies across the population of cells was used as network input; the remaining spikes to the stimulus were ignored. In additional simulations we used the duration of the first spike interval as input to the network. Thus the timing of the first two spikes was considered.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Godfrey et al. 1975; Pfeiffer 1966; Rhode et al. 1983). These patterns are distinguished by different FSLs and FISIs. A buildup pattern has a long FSL (Fig. 1A), whereas a short FSL/long FISI characterizes a pauser pattern (Fig. 1E). The main difference between these two patterns is the occurrence of a short latency onset spike. Regular firing cells also have a short FSL but no long FISIs (Fig. 1C).
To characterize the discharge patterns, we compared the FSL and FISI during depolarization alone (control condition) and during pairing of an evoked IPSP followed by a depolarization (paired condition). IPSPs were evoked by stimulating the superficial DCN, which activates parallel fibers, which are excitatory, as well as interneurons that are inhibitory to pyramidal cells (Manis 1989; Zhang and Oertel 1993). The time interval between electrical stimulation and depolarization [pairing interval (PI)] was varied from 5 to 100 ms.
The pattern and level of injected current determines the specific discharge pattern generated by DCN pyramidal cells (Kanold and Manis 2001). We studied most cells under conditions that evoked only one pattern. Following hyperpolarization, cells firing in a pauser pattern show an increased FISI, whereas cells discharging in a buildup pattern show increased FSL. The underlying mechanism for FSL and FISI increases in buildup and pauser cells after preceding hyperpolarizations depend on the deinactivation of the rapidly inactivating potassium current IKIF (Kanold and Manis 1999, 2001).
In this study, few cells showed a regular pattern when depolarization was given alone. Since both the regular and pauser patterns are characterized by a short FSL and show increases in FISI after hyperpolarization, we grouped regular and pauser cells together.
Figure 1 shows the effect of IPSP depolarization pairing on the discharge patterns of three different pyramidal cells. Figure 1A shows the effect of an evoked IPSP on the discharge pattern of a cell exhibiting a buildup pattern. At a pairing interval of 50 ms, the mean FSL increased by 4.6 ms even though the IPSP has almost completely decayed to the resting potential before the onset of depolarization. Similar effects were observed in six of nine neurons firing in buildup cells (Fig. 1B; each symbol is a different cell). The increase in FSL (
FSL) was largest (
16 ms) for the shortest pairing intervals (20 ms), but was still pronounced at the longest interval tested (70 ms). The changes in FSL were accompanied by an increase in FISI of <3 ms (data not shown). Although the FSL did not change in the other three cells, a decreased depolarization was present during the period before the first spike (data not shown), indicating a weaker effect of the IPSP.
An example of a regular cell is shown in Fig. 1C. At a pairing interval of 80 ms, the mean FISI increased by 5.2 ms, reflecting conversion to a pauser pattern, although the IPSP had almost completely decayed to rest before depolarization. Note the absence of spikes immediately following the afterhyperpolarization following the onset spike (arrow). Ten of 12 cells firing in the pauser pattern (including those cells that converted from regular to pauser patterns with prior IPSPs) showed FISI increases (Fig. 1D) and slightly increased FSL (data not shown). FISI was largest for short pairing intervals, but was still substantial for longer intervals at which the IPSP had essentially decayed back to rest completely before the test depolarization.
Other cells showed dramatic shifts of their discharge patterns under pairing conditions. In 10 cells, the same depolarizing current elicited either pauser or buildup patterns on different trials. For example, the cell shown in Fig. 1E responded to 72% of the trials as a pauser and 28% of the trials as a buildup. Evoking an IPSP 50 ms before onset of the depolarization converted nearly all of the pauser response to buildup responses, with 90% of the trials generating the buildup pattern. The FISI of the remaining pauser trials was increased by 5.2 ms (data not shown). Again, note that the IPSP had almost completely decayed to rest before the depolarization.
To evaluate the extent of the transition, the percentage of pauser responses under test condition relative to control conditions is plotted for all cells showing discharge pattern transitions (Fig. 1F). The effect on firing pattern was strongest for short pairing intervals, with a complete conversion of all pauser responses to buildup responses for some cells. For longer intervals, however, the firing pattern of individual cells reverted to pauser response with different time courses. In summary, IPSPs preceding the depolarization can influence the discharge pattern in response to a fixed input, despite the fact that the IPSP had decayed to within 1 mV of rest before the onset of depolarization. These results also show that IPSPs occurring well before excitation can cause significant changes in firing patterns.
We believe that partial deinactivation of a transient K+ current (IKIF) (Kanold and Manis 1999) during the brief membrane hyperpolarization is responsible for these observations, at least under conditions where the FSL is less than 70 ms. Recovery of IKIF outlasts the hyperpolarization since the inactivation time constant of IKIF (10–25 ms) is slightly larger than the membrane time constant (<10 ms) (Kanold 2000; Manis 1990). To test the hypothesis that the IPSP voltage change alone is sufficient to shift the FSL, we must first exclude the possibility that late IPSPs or slower neurotransmitter receptor activated second messenger processes influence discharge patterns. We presented small short hyperpolarizing current steps approximating the duration and sizes of evoked IPSPs (10–15 ms, 10 mV). In contrast, previous studies used longer (100 ms) and larger (50 mV) hyperpolarizing pulses that were followed by a depolarization with no delay (Kanold and Manis 1999). Here the brief current pulses used to simulate IPSPs were separated from the depolarization by a varying time interval during which no current was injected. The effect of these brief hyperpolarizations on the discharge pattern of buildup (Fig. 2A), pauser (Fig. 2C), and pauser/buildup cells (Fig. 2E) was similar to the effect of IPSPs. Buildup cells showed increased FSL of 10 ms (n = 10, Fig. 2B) and a modest increase in FISI of 2.8 ms (data not shown). Both effects are again maximal for short pairing intervals. Pauser cells showed a large increase in FISI (n = 12, Fig. 2D) and slightly increased FSL (data not shown), both of which are maximal for short pairing intervals. The magnitudes of the shifts are comparable with the results obtained with IPSPs. Nine cells showed transitions from pauser to buildup for short pairing intervals (Fig. 2F), and these changes persisted for longer intervals. Since the hyperpolarization decays to rest after 20 ms, the changes in mean FSL and FISI for longer pairing intervals indicate that the cell retains information about the prior history of the membrane potential. The presence of discharge pattern changes with a voltage perturbation alone suggests that an intrinsic voltage-dependent mechanism such as deinactivation of IKIF is responsible for the observed effects.
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). Therefore to test whether deinactivation of IKIF can account for the observed changes in discharge patterns after inhibitory stimuli, we use a previously developed computational model based on the biophysical properties of the outward currents in these cells (Kanold and Manis 1999, 2001). Without prior IPSPs, the model cell fired a regular train of spikes to a depolarizing current injection (Fig. 3A, top). When an IPSP preceded the depolarization, the FSL increased (Fig. 3A, middle). Note that the IPSP had completely decayed to rest before the onset of the depolarization. If IKIF was absent, the prior IPSP had no effect (Fig. 3A, gKIF = 0 nS). Lengthening the interval between IPSP and depolarization onset reduced the FSL increase (Fig. 3B). Nonetheless, significant FSL increases are present for intervals of 
60 ms. When more than one IPSP precedes the depolarization, the FSL increased monotonically to >30 ms as a function of the number of IPSPs in the train (Fig. 3, C, top, and D, 
). Removal of IKIF from the model was sufficient to abolish this effect (Fig. 3C, gKIF = 0 nS): the latency was constant and independent of IPSP number (Fig. 3D, triangles), indicating that prior IPSPs had no effect on the FSL. We have previously shown that another current that can be engaged by hyperpolarization, the Ih current, does not play a significant role in generating these discharge patterns (Kanold and Manis 2001).
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). At rest, h is 0.012 (i.e., just >1% of the channels are available for activation during depolarization). During a single IPSP, h increases by 75% to 0.02 (Fig. 3E, trace 1). At the onset of depolarization, h is still increased above the resting level by 35% and then slowly decays during the depolarization preceding the first spike. h subsequently remains low during the spike train. With increasing numbers of IPSPs (traces 2–5), h shows accumulated deinactivation that persists following the final IPSP, so that more IKIF is available at the beginning of a subsequent depolarization. Thus h acts as a leaky integrator of the voltage changes produced by the IPSPs. These results suggest that deinactivation of IKIF during the IPSP can account for the experimentally observed discharge pattern changes. The persistence of elevated h after the IPSP has decayed is sufficient to carry information about the history of prior hyperpolarization in these cells for 60 ms.
So far we show that a single neuron can encode the presence of an IPSP by increasing the FSL or FISI. Because the FSL is a measure relative to depolarization onset, to use the increased FSL at the next stage of processing, it is necessary to also convey information about the onset timing of the depolarization. Since properties of IKIF control the behavior of pyramidal cells (Kanold and Manis 2001), this diversity in channel properties should enable cells to respond differently to identical stimuli. A population of cells with a distribution of intrinsic properties could perform novel stimulus encoding tasks such as resolving the time reference problem by providing differential FSLs and FISIs for identical stimuli.
Experimentally, IKIF shows a range of half-inactivation voltages (VKIF) ranging from –60 to –100 mV, with a mean of –89.6 mV (Kanold and Manis 1999). Such a range of voltage sensitivity could be controlled by the phosphorylation state of the IKIF channel or by interactions with accessory subunits (Adams et al. 2000; An et al. 2000; Anderson et al. 2000). To investigate the population behavior, we chose eight values of VKIF spanning the experimentally measured range of –64.6 to –99.6 mV and generated eight model cells. The model cells were presented with identical patterns of brief hyperpolarizations and depolarization separated by a variable interval of zero current. The FSL increase at each pairing interval was larger for cells with a more positive VKIF (Fig. 4A), since hyperpolarization in these cells lead to more deinactivated IKIF, in turn leading to increased outward current during the onset of depolarization. The FISI also showed slight differences (2 ms, data not shown). To investigate the population response, we plotted the relative increase in FSL (FSL of each cell relative to the FSL of the cell that fired 1st in the population; Fig. 4B). FSL differences between neurons were present at all pairing intervals, and this difference became smaller as the pairing interval increased. Thus as the pairing interval increased more cells started firing synchronously at the onset of depolarization (e.g., within 5 ms from each other, Fig. 4C). These results suggested that the relative FSL across the population could encode the time interval between the hyperpolarization and depolarization. This time interval is represented by change in synchronization strength at the onset of the population response and the FSL distribution of the later responding units.
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Similar results were obtained in population models in which either the activation voltage of IKIF (Fig. 6K) or total conductance (gKIF, data not shown) varied among cells, showing that the availability of IKIF at the onset of the depolarization determines the FSL. These results show that a small population of DCN pyramidal cells with differences in IKIF could robustly encode the length of the interval between an inhibitory and excitatory input.
So far our simulations show that the population encodes pairing intervals of hyperpolarization and depolarization in the buildup regimen in the population FSL and that this information can be detected by the artificial network. We also paired hyperpolarizations with depolarizations in the pauser regimen depolarizations of (170–200 pA) and found that, while the variations in the population FSL are sufficient to encode the pairing interval, there is a larger error (Fig. 6D). This is not surprising, since the FSL shift for the pauser pattern is smaller than for the buildup pattern. Similar results were obtained if depolarizations over the entire amplitude range (50–200 pA) causing cell to fire in the buildup and pauser patterns were used (Fig. 6E).
Both FSL and FISI are affected by hyperpolarizations preceding the depolarization (see Figs. 1 and 2). In fact, training and testing a network with the population FISIs showed that population FISIs could encode the pairing interval for both the buildup and pauser regimens (Fig. 6, F and G), as well as for stimuli over the entire range of depolarizations (Fig. 6H). Note that the estimation error in the pauser regimen is lower than in the buildup regimen. This is due to the fact that cells fire a very precise onset spike in the pauser regimen; thus there is less variability between neurons. These results suggest that both FSL and FISI could be employed to encode pairing delays.
Background synaptic activity and channel noise both contribute to variability in the FSL in response to a depolarization. In vivo and in vitro, the FSL shows variability from trial to trial. We therefore studied how FSL variability affects the recognition of a particular pairing interval. The FSL was varied across individual trials by the addition of a normally distributed latency time shift to mimic normal variability, and the network was retrained as described above. As expected, the pairing interval detection error increased with increasing FSL variability (Fig. 6I). When depolarizations in the buildup regimen (50–100 pA) were presented, the neurons could robustly encode pairing intervals even when the SD of the FSL was 3 ms (green line). However, when using the FSL from stimuli in the pauser regimen (170–200 pA), the network was unable to report the pairing interval (red line). The larger error is expected, because the magnitude of the FSL shift is smaller for larger depolarizations in the pauser firing mode, and the FSL shift is masked by the FSL variability. If the network could use additional information, such as the FISI, the error would likely be smaller. Intermediate results were obtained with depolarizations over the entire range (50–200 pA, black line). Similar results were obtained when the population FISI instead of the FSL was used to train and test the network (Fig. 6J), with the important difference that, for low noise situations, the pauser pattern provided a better estimate of the pairing interval.
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DISCUSSION |
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Interaction between transient potassium channels and inhibition
Transient potassium channels are expressed in many neurons, but the roles that they play in neuronal information processing in a given cell depends on their voltage-dependence, their kinetic behavior, and other channels present. Some transient potassium conductances activate and inactivate over a relatively depolarized range (Chandy and Gutman 1995; Rudy 1988) and are involved principally in regulating spike discharge rates and shaping action potentials. Others, such as the IKIF current in DCN pyramidal cells (Kanold and Manis 1999), have relatively hyperpolarized activation and inactivation ranges and participate more effectively in subthreshold integration of synaptic events. A number of studies have shown that large hyperpolarizations can lead to delayed first spikes or elongated first interspike intervals, through de-inactivation of a transient potassium conductance (Berman and Maler 1998; Rusznak et al. 1997; Schoppa and Westbrook 1999; Shibata et al. 2000; Storm 1988; Turrigiano et al. 1996). However, the depths and durations of hyperpolarizations were generally longer (>100 ms) and greater (>20 mV) than are typically encountered in a neuron responding to dynamic patterns of naturally occurring synaptic input. In contrast, we have shown that normal inhibitory synaptic events can increase the availability of a transient current sufficiently that it can affect the response to a subsequent excitatory input.
There are several features of the rapidly inactivating transient currents in DCN pyramidal cells (and in other cells) that contribute to this result. First, the transient current is quite large in these cells: in the soma, it is the largest potassium conductance. However, despite the channel's abundance, at rest only about 1–2% of the channels are expected to be deinactivated and therefore available to open with depolarization. Consistent with this, our prior simulations suggest that only a small portion of the conductance need be recruited to be effective (Kanold and Manis 1999). This in itself is curious, because it suggests that there may be a large reserve of available channels that are never accessed during normal operation of the neuron. On the other hand, positioning the conductance in this way maximizes the nonlinear recruitment of channels by small hyperpolarizations while minimizing their impact on the integration of purely excitatory activity. Second, the transient current recovers from inactivation fairly quickly, so that even single IPSPs are of sufficient duration to produce a useful amount of deinactivation. Many transient potassium channels recover from inactivation more slowly than those in DCN pyramidal cells and cannot be significantly engaged by brief synaptic events. However, in other areas of the brain, slow IPSPs predominate and may be more effective in recruiting transient currents. Third, the conductance can be activated at voltages just above the resting potential, but below spike threshold, allowing room for it to affect subthreshold integration of synaptic inputs. Were the conductance to open only at more positive potentials, it would not be able to influence spike responses in the same manner. Taken together, these factors indicate that transient potassium conductances in DCN pyramidal cells have an optimal sensitivity for recruitment by inhibitory inputs and involvement in the subthreshold integration of synaptic events, as well as the regulation of discharge patterns. It is important to note, however, that the role of this conductance in DCN pyramidal cells may be limited to spike timing with delays of less than 70 ms relative to the onset of excitation; for longer delays, IKIF is expected to be largely inactivated, and spike timing may be influenced by additional mechanisms, such as IKIS and a persistent sodium current (Manis et al. 2003).
Enhanced recruitment of IKIF by inhibitory inputs
Our model predicts that the availability of the potassium conductance should be greatly enhanced when multiple IPSPs occur in rapid succession, because this extends the duration of the hyperpolarization and hence the time available for deinactivation of the potassium channels. Interestingly, one of the principal inhibitory inputs to the pyramidal cells is supplied by cartwheel cells (Berrebi and Mugnaini 1991; Golding and Oertel 1997), whose main discharge mode is to fire in bursts of two to four action potentials with interspike intervals of 2–6 ms (Manis et al. 1994; Zhang and Oertel 1993). Since cartwheel cells fire with a mixture of simple and complex spikes, the effectiveness of individual spikes in inhibiting pyramidal cells will be amplified by IKIF according to whether they occur singly or in a burst.
Functional role in the auditory system
One issue is how the different discharge patterns of pyramidal cells might be used. A simple circuit with feedforward inhibition and excitatory synapses showing short-term potentiation can be used to decode the temporal features of afferent activity on a time scale of tens of milliseconds (Buonomano 2000). Such a circuit could translate FSL (relative to other FSLs or another reference signal) or FISIs that are generated by pyramidal cells into a population code. The auditory midbrain possesses an appropriate neural substrate that can perform this kind of processing. The cells of the inferior colliculus (IC) receive direct excitatory projections from the pyramidal cells of the DCN (Coleman and Clerici 1987; Ryugo and Willard 1985). The DCN also projects to the GABAergic cells of the dorsal nucleus of the lateral lemniscus (Adams 1979; Adams and Warr 1976; Fernandez and Karapas 1967), which in turn project to the IC. The DNLL, as well as local inhibitory interneurons of the IC, can be sources of feedforward inhibition to cells that receive direct DCN input (Oliver and Huerta 1992). Thus all of the circuit elements necessary to decode the information present in the pyramidal cells are present at the level of the midbrain. Whether the cells of the IC actually perform this kind of computation is currently not known. One potential role for delayed excitation of the sort that could be provided by the DCN is the identification of sound duration. Neurons in the IC of both bats and mice can show tuning to the duration of the stimulus (Brand et al. 2000; Ehrlich et al. 1997), and this depends on an interaction between early inhibition and a delayed excitation in the IC (Faure et al. 2003). The delays in excitation that can be provided by the long latencies of DCN pyramidal cells could also contribute to this circuit.
The DCN may contribute to sound localization by analyzing spectral cues arising from the pinna’s acoustic transfer function (Oertel and Young 2004). A functionally significant input to the granule cell system of the DCN is somatosensory afferents originating from the pinna muscles (Kanold 2000). Activation of peripheral nerves or ascending nuclei of the somatosensory pathway drives neurons of the DCN (Davis et al. 1996; Kanold 2000; Young et al. 1995) and ultimately affects the responses of pyramidal cells to acoustic stimuli (Kanold 2000). Cartwheel cells are part of the pathway that relays nonauditory information from a variety of sources, including the pinna muscles (Davis et al. 1996; Kanold and Young 2001; Young et al. 1995), to DCN pyramidal cells. Activity in these pathways could effectively recruit IKIF according to the activity in nonauditory afferents and can alter subsequent sound evoked responses. Our data suggest that the output patterns of DCN neurons can contain information about both auditory and nonauditory information even when those two events are not synchronous. Consequently, one can hypothesize a coding scheme in which the mean discharge rate of the neuron carries information about the spectral content of the acoustic stimulus (Spirou and Young 1991; Young et al. 1992), whereas the relative FSL or FISI provides information regarding pinna position (or recent changes in pinna position). Such integration makes sense since knowledge of pinna position and the pinna-dependent acoustic transfer function would be necessary both for identification (potentially predictive) of a sound by its spectrum and for localization using spectral cues. Preliminary in vivo data suggest that activation of pinna inputs to the DCN shortly before acoustic stimulation can affect the latency of the response to sound, consistent with this proposed mechanism (Kanold 2000; Kanold et al. 2001).
Potential plasticity of the timing encoding mechanism
The inhibition-dependent recruitment of IKIF may be plastic, allowing neurons to adjust their relative sensitivity to different input patterns of excitation and inhibition. Such a mechanism could be of use since the sensory inputs (both auditory and somatosensory) can change during the lifetime of the animal due to growth or injury. There is evidence that modifications of the relevant conductances can and do occur in other systems. The biophysical properties of IKIF are similar to the voltage gated K+ channel encoded by Kv4.2 (Kanold and Manis 1999). The voltage dependence and kinetics of Kv4.2 in individual cells can be modified by phosphorylation via extracellular-regulated kinases and protein kinase A (PKA) (Adams et al. 2000; Anderson et al. 2000) or calcium-dependent interactions with accessory subunits such as potassium channel interacting proteins (An et al. 2000). Because ERK and PKA activity can be regulated by paradigms that generate synaptic plasticity, it is possible that plasticity mechanisms, including those showing sensitivity to spike timing (Bell et al. 1997; Feldman 2000; Magee and Johnston 1997; Markram et al. 1997; Zhang et al. 1998), alter not only synaptic strength, but via actions on specific ion channels also change the relationship between synaptic inputs and spike generation. Such a mechanism could operate in addition to the recently shown synaptic plasticity at the parallel fiber synapses (Fujino and Oertel 2003; Tzounopoulos et al. 2004).
Although our model focused on an array of cells with varying activation and inactivation voltages, the time scale over which these mechanisms can be influential will depend also on the inactivation and deinactivation kinetics of the transient currents (Kanold and Manis 2001), which also may be modulated. The relatively short time scales used by DCN pyramidal cells may be related to their role as first-order central sensory processing cells, which must operate on rapidly changing events in the acoustic environment. We predict that cells expressing A-currents with longer inactivation time constants could potentially encode longer time intervals (up to seconds).
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Present address and address for reprint requests and other correspondence: P. O. Kanold, Dept. of Neurobiology, Harvard Medical School, 405 Goldenson Bldg., 220 Longwood Ave., Boston, MA 02115 (E-mail: patrick_kanold{at}hms.harvard.edu)
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