INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The diversity of inhibitory neurons (Gupta et al. 2000; Parra et al. 1998) and the complexity of their interconnections (Gibson et al. 1999; Mann-Metzer and Yarom 1999; Tamás et al. 2000) suggest that inhibitory systems play a major role in shaping the flow of information in neuronal structures and thus play a prominent role in the brain's computational processes. If precise temporal coding is involved in these computational processes, then the responses of inhibitory neurons to a given input should be temporally organized and accurately reproducible. We have therefore investigated the temporal organization of the responses of the cerebellar inhibitory neurons to synaptic-like currents.

The molecular layer of the cerebellar cortex is sprinkled with small interneurons, stellate and basket cells, collectively known as the molecular layer interneurons (MLI). Since the seminal studies of Eccles and his colleagues (1966) demonstrating the inhibitory nature of these neurons, they have been frequently used as a model for inhibitory synaptic transmission (Kondo and Marty 1998; Llano and Gerschenfeld 1993). The functional significance of MLIs activity had been studied by Häusser and Clark (1997), who showed that MLIs can delay the firing of Purkinje cells (PC), which are their main targets. In addition, a precise timing of inhibition is needed to completely abolish the Ca²⁺ response that accompanies climbing fiber input (Callaway et al. 1995). As both the MLIs and PCs receive a common excitatory input from the parallel fibers, the temporal organization of the responses of both neurons dictate their interrelated output. Exploring the mechanisms that determine the response of MLIs is therefore a fundamental step toward understanding the interactions between these neurons and the PCthe cerebellar cortex output neurons.

The use of brain slices allows investigation of the mechanisms controlling regenerative responses, but the slices are devoid of a large portion of the circuitry. Thus the parallel fiber input to the MLIs was emulated as a synaptic-like current injected into the MLI somata. As shown in Fig. 1, the responses of MLI to gradual increase in the amplitude of a synaptic-like current were almost identical to MLI responses to parallel fibers activation described by Eccles and his colleagues (compare Fig. 1, A with B). As the synaptic-like current faithfully reproduces the response to parallel fiber input, the characteristic response of the MLIs appears to reflect intrinsic, rather than network, properties. Here we have used current and voltage-clamp techniques to explore which of the intrinsic currents participate in molding this characteristic response.

View larger version (23K): [in this window] [in a new window]   Fig. 1. The in vitro response of molecular layer interneurons to synaptic-like current resembled those reported in vivo. A: reproduction from Eccles et al. (1966). In vivo extracellular recordings of responses of presumed inhibitory interneuron in cat cerebellar cortex (top trace of each of the records). Parallel fibers were stimulated at progressively increasing strength (given in arbitrary units) by a surface electrode. Bottom: the parallel fiber response recorded by a 2nd surface electrode. B: in vitro intracellular recordings of a stellate cell in a guinea pig slice preparation. The stimulating current (bottom), which decayed exponentially with a time constant of 10 ms, was delivered at progressively increasing amplitudes (given in nA).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Slice preparation

Three-hundred-micromillimeter-thick sagittal slices were prepared from the vermis of a guinea pig (80-120 g) cerebellum as previously described (Mann-Metzer and Yarom 1999). Briefly, after anesthesia, vascular perfusion, and decapitation, the cerebellum was quickly removed and sliced in cold sucrose solution [containing (in mM) 5 KCl, 1.3 MgSO₄, 1.2 KH₂PO₄, 26 NaHCO₃, 10 glucose, 2.4 CaCl₂, and 124 sucrose]. Slices were kept at room temperature in an oxygenated physiological solution [containing (in mM) 124 NaCl, 5 KCl, 1.3 MgSO₄, 1.2 KH₂PO₄, 26 NaHCO₃, 10 glucose, and 2.4 CaCl₂; pH 7.4; aerated with 95% O₂-5% CO₂] until they were transferred into the recording chamber.

Recordings

The recording chamber was mounted on an upright microscope stage (Zeiss Axioskop) and maintained a constant temperature of 30°C by a temperature control unit. It was continuously perfused with aerated physiological solution containing 200 µM picrotoxin (dissolved in DMSO; Sigma). The following drugs were added individually to the physiological solution in various experiments to reach a final concentration of: 0.1 µM TTX (Molecular Probes); 5 mM CsCl; 2 mM TEA; 50 µM 6-cyano-7-nitroquinoxalene-2,3-dione (CNQX, RBI). In Ca²⁺-free solution, Ca²⁺ was replaced by CoCl₂ (5 mM) and KH₂PO₄ was omitted. Slices were perfused for 10 min with the solution containing the drug prior to the examination of its effect. The molecular layer interneurons in the slice were readily identified using infrared differential interference contrast optics, and whole cell patch recordings were easily attained. The patch pipettes were pulled on a Narishige pp-83 puller and had a DC resistance of 10-12 M. In intracellular recordings, the pipette solution contained (in mM) 140 K-gluconate, 4 NaCl, 0.5 CaCl₂, 5 EGTA, 3 Mg-ATP, and 10 HEPES (pH = 7.2). Recordings were made with an Axoclamp 2B for current-clamp experiments and with Axopatch 1D for voltage clamp (Axon Instruments). For extracellular recordings, the patch pipette, which was placed near the cell membrane, was filled with physiological solution. Data were stored on videocassette (Neurocorder DR-484) for off-line analysis. Data were sampled at 5-10 kHz, using National Instruments A/D board derived by software program written in LabVIEW. Synaptic-like current was generated by a computer using LabVIEW software. The current waveform followed the equation:

(1)

where I₀ is the maximal amplitude and  is the time constant usually set to 10 or 15 ms.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Response of molecular layer interneurons to synaptic-like current

The responses of MLIs to synaptic-like currents were recorded under current clamp. To prevent spontaneous activity, continuous hyperpolarizing current was injected to set the membrane potential at 50 to 55 mV, and picrotoxin (200 µM) was added to prevent spontaneous inhibitory postsynaptic potentials (IPSPs). Picrotoxin did not qualitatively change the responses to synaptic-like currents. As shown in Fig. 2A (top), threshold synaptic-like currents triggered a fast action potential [width 1.17 ± 0.28 (SD) ms at half-amplitude, n = 11]. This spike appeared after variable delays and was followed by a fast hyperpolarization that reset the membrane potential to just below the holding potential. Occasionally, this afterpotential was followed by a slow and prolonged depolarizing wave that lasted for more than 50 ms before returning to baseline (see high-resolution display in Fig. 3A). Increasing the current amplitude evoked a train of three to four action potentials (Fig. 2A, middle). The delay and the variability of the first action potential decreased, whereas the consecutive action potentials appeared at variable delays. The depolarizing wave, which was larger at this stimulus intensity, occasionally triggered an additional delayed action potential. Further increase in the current amplitude increased the number of action potentials and decreased the interspike intervals (Fig. 2A, bottom).

View larger version (21K): [in this window] [in a new window]   Fig. 2. The response of molecular layer interneurons (MLIs) to synaptic-like current is highly variable. A: the responses of an MLI to 3 intensities of synaptic-like currents ( = 15 ms). Three responses at each intensity are superimposed, note the variability. B: the temporal distribution of the action potentials during the response to synaptic-like currents. Raster plots of 5 repetitions were plotted for each stimulus intensity. Note the large scatter of the last spike at each stimulus intensity. C: the duration of the response (the interval between the 1st and the last spike) as a function of current intensity. D: correlation between variability of response duration and variability of the last interspike interval. Variability was measured as the mean standard deviation over all intensities of stimulations for each cell.

View larger version (21K): [in this window] [in a new window]   Fig. 3. The last spike in the train is triggered by a prolonged intrinsically generated depolarizing wave. A: 3 superimposed traces of the response to a synaptic-like current with peak current of 0.1 nA. A single action potential was evoked, followed by a depolarizing wave, which persisted after the end of the synaptic current (bottom). Its amplitude and duration are variable. B: 4 superimposed traces of the last spike in the response to synaptic-like current with peak current of 0.4 nA. The evoked train usually consisted 3 spikes. The traces were aligned by the peak of the 2nd spike.

The temporal distribution of the action potentials is shown in Fig. 2B. At the lowest stimulus intensity, the single spike appeared at different delays distributed over an interval of about 10 ms. As the stimulus intensity increased, the delay and scatter of the first spikes decreased, while the scattering of the last spike remained large. As a result, the duration of the response was almost independent of the current intensity (Fig. 2C, an average slope of 33.8 ± 30 ms/nA with R² = 0.37 was calculated in 15 cells). Not only the duration, but also the variability in the duration was independent of the current intensity (not shown). We therefore averaged the standard deviation of the response duration over the different intensities as an estimate of the degree of scatter of the response. In the example in Fig. 2, the scatter was 16.2 ms, while the average scatter in 15 neurons was 8.1 ± 5.3 ms. We further confirmed the role of the last spike in determining the duration of the train by examining the correlation between the averaged standard deviations of the last interval in the train and the standard deviation of train duration (Fig. 2D). The calculated slope of 0.8 shows that, indeed, the variability of the last spike in the train to a large extent determines the variability of the duration of the train as a whole. Moreover, this plot summarizes the responses in all the different conditions tested here (see following text). While some of theses conditions increased and others decreased, the duration and variability of the response, pooling all these data did not disrupt the close to unity slope.

Figure 2A shows that a depolarizing wave follows the train. A high-resolution display of the voltage traces shows that the depolarizing wave after either a single (Fig. 3A) or a train (Fig. 3B) of action potentials had a variable amplitude and therefore cannot be attributed to a passive response of the cell. This variable depolarization occurred around the firing threshold and thus elicited spikes at variable timing. We suggest that this wave is generated by intrinsic regenerative currents, which are the source of the scatter in the duration of the response.

To test this suggestion, we prevented the activation of intrinsic currents by hyperpolarizing the membrane potential to 80 mV. As shown in Fig. 4A, the responses to synaptic-like currents resembled those obtained at 50 mV. However, the train was much shorter and there was a clear and significant decrease in scatter (from 16.2 to 2.0 ms). This change is emphasized by the plot of temporal distribution display (Fig. 4B). For example, the jitter in spike timing at just threshold stimulus was only 1 ms (Fig. 4B, bottom) as opposed to 11.6 ms obtained at 50 mV (Fig. 2B). The intensity-duration slope (Fig. 4C) declined from 8.2 to 1.95 ms/nA due both to the shortened duration in which the current is above threshold and the higher conductivity at hyperpolarization (see following text). The increase of R² from 0.002 at resting potential to 0.6, however, suggests an increased dependence of the duration of the train on the stimulus intensity. In all cells examined (n = 4), holding the membrane at 80 mV decreased the scatter by an average of 84%, thus supporting our suggestion that the duration of the trains and the variability of the last spike are largely determined by the depolarizing wave.

View larger version (22K): [in this window] [in a new window]   Fig. 4. The variability of the response to synaptic-like current is largely reduced when evoked from a membrane potential of 80 mV. Plotted as in Fig. 2, same cell. A: response to synaptic-like current. · · · , the 80 mV membrane potential. Note the decrease in the variability of the spike trains, the absence of the depolarizing wave and the prolonged after hyperpolarization. B: the temporal distribution of the action potentials during the response to synaptic-like current as in Fig. 2B. Note the decrease in duration and variability of the responses. C: the duration of the response as a function of the current intensity. Note the different scale from Fig. 2C.

Careful inspection of these data reveals two additional points. First, both the amplitude and the afterhyperpolarization (AHP) of the action potentials undergo systematic modifications (Figs. 2A and 4A). At both potential levels, the first action potentials attained the highest values, whereas the others reached lower amplitudes that were dependent on the preceding interspike interval. The changes in AHP depended on the amplitude of the action potential and on the level of the current injected. Thus a complex interplay between the stimulus and intrinsic currents creates excitability changes during the response to a synaptic-like input. Second, a slow hyperpolarizing wave followed the responses elicited at 80 mV (Fig. 4A). This hyperpolarizing wave reached maximal amplitude of 12.3 mV, which depended in a saturated fashion on the injected current. As will be shown below, this wave is due to the dynamics of an h-like current.

Slow depolarizing wave

The preceding results indicate that the variability of the train duration is determined by intrinsic currents with slow kinetics. Because such currents can be carried either by Ca²⁺ or Na⁺ ions, we measured the response to synaptic-like currents in the absence of Ca²⁺ ions and in the presence of TTX. The response in the absence of Ca²⁺ (Fig. 5A) is still characterized by a prolonged train and a slow depolarizing wave (compare Fig. 5A with 2A, same cell). However, the temporal distribution of the action potentials showed that the scatter and the duration of the responses were reduced (Fig. 5B). The scatter was reduced to 5.62 ms and the duration/intensity slope increased to 61.4 ms/nA, R² = 0.2 (similar results were obtained in 3 further neurons). The fact that the scatter and duration decreased despite the presence of the slow depolarizing wave seems to contradict our hypothesis that the slow wave governs the duration and variability of the response. However, comparison of the train before and after removal of Ca²⁺ (Fig. 5, C and D) revealed that although the amplitude and the threshold of the first spike were unaffected by the removal of Ca²⁺, its afterpotential was reduced. A smaller AHP failed to reset the action potential mechanisms, resulting in a longer delay and a lower amplitude of the second action potential. The decrease in scatter and duration in the absence of Ca²⁺ is thus due to a reduction in excitability brought about by a reduction of the AHP and not by a change in the depolarizing wave (see following text).

View larger version (19K): [in this window] [in a new window]   Fig. 5. Blocking Ca2+ currents decreased the variability and duration of the response without affecting the depolarizing wave. A: 3 superimposed traces of the response to synaptic-like current in a Ca2+-free medium containing Co2+ (peak current intensity, 0.1 nA). B: the temporal distribution of the action potentials during the response to synaptic like current as in Fig. 2B. Note the reduction in variability and duration of the response. C and D: 2 superimposed traces of the response to synaptic-like current before (gray) and after (black) the blockade of Ca2+ currents, displayed at low (C) and high (D) time resolution. Note the decreased amplitude of the after hyperpolarization and the increased delay of the subsequent action potential.

Blocking the Na⁺ current by TTX not only blocked the action potentials but also blocked the prolonged depolarizing wave (compare Fig. 6A, top and middle). Under these conditions, the Ca²⁺ current is manifested as a small nonlinearity in the voltage response (arrow), which was removed by the removal of Ca²⁺ (bottom). The superposition of the three traces (Fig. 6B) reveals that response decay was unaffected by the removal of Ca²⁺. We conclude that the depolarizing wave is carried mostly by Na⁺ ions. Indeed, voltage-clamp experiments revealed a substantial, noninactivating, TTX-dependent Na⁺ current. As shown in Fig. 6C a slow voltage shift from 70 to 15 mV produced a nonlinear current response (black curve). The addition of TTX (0.1 µM) to the bath solution increased the outward currents in the depolarized levels. Subtraction of the two curves (Fig. 6D) revealed a net, TTX-sensitive, inward current with a relatively low threshold of about 45 mV. Note that a noninactivating Na⁺ current has previously been proposed as participating in the spontaneous firing of these cells (Mann-Metzer and Yarom 1999).

View larger version (18K): [in this window] [in a new window]   Fig. 6. The depolarizing wave is mediated by a TTX-sensitive current. A: the response to just threshold synaptic-like current under control conditions (top), in the presence of TTX (middle) and after blocking Na+ and Ca2+ currents (bottom). B: the 3 traces superimposed at higher gain. Note the blockade of the depolarizing wave by TTX and the Ca2+-dependent response (arrow). C: the current response (top) to a slow shift in membrane potential from 70 to 15 mV (bottom) over a period of 22 s in control (black trace) and in the presence of TTX (gray trace). D: the noninactivating, TTX sensitive, current is revealed by the subtraction of the 2 current responses in C and presented as a voltage-current curve.

Role of potassium currents

As shown in the preceding text, the amplitude and duration of the AHP to a large extent determines the excitability of MLIs and, hence, the timing of action potentials within a train. To further examine this possibility, pharmacological modulation of different potassium currents was used.

TEA is a commonly used blocker of the delayed rectifier as well as other K⁺ currents. TEA (2 mM) added to the bath solution significantly increased the duration of the action potential and reduced the AHP (Fig. 7A). Despite the different mechanisms involved, the changes in the response to synaptic-like current (Fig. 7B) resembled those in Ca²⁺-free solution. The variability was reduced (Fig. 7, C and D; scatter dropped from 10.3 to 8.2 ms), and the intensity-duration slope increased by 43%. These results provide further support for AHP playing a dominant role in controlling the excitability of the neurons and thereby shaping the temporal organization of their responses to synaptic-like currents.

View larger version (21K): [in this window] [in a new window]   Fig. 7. TEA decreased the variability and the duration of the response to synaptic-like current. A: 2 superimposed traces of 1 spike before (black) and after (gray) the addition of 2 mM TEA to the medium. Note the increased duration of the action potential and decreased amplitude of the afterhyperpolarization (AHP). B: 3 superimposed traces of the response to synaptic-like current before (top) and after (bottom) the addition of TEA (peak current, 0.2 nA). C and D: the temporal distribution of the action potentials during the response to synaptic-like current before (C) and after (D) the addition of TEA (as in Fig. 2B). Note the reduction in both duration and variability.

Recent studies have demonstrated that MLIs are endowed with a variety of ionic currents that operate in a voltage range around the resting level of the neurons (Southan and Robertson 2000; Southan et al. 2000; Tan and Llano 1999). Here we tested the effect of Cs⁺ ions, which are known to block the h current. As shown in Fig. 8A, Cs⁺ induced bursting behavior. Since blocking synaptic transmission (using 200 µM picrotoxin and 50 µM CNQX) and the removal of Ca²⁺ ions from the external solution did not affect the bursting activity (not shown), we conclude that the bursting behavior is due to a direct effect of Cs⁺ ions on the intrinsic Ca²⁺-independent properties of the neurons. The mechanisms underlying these bursts were not further pursued, yet it should be mentioned that the bursts were observed only after a prolonged (more than 10 min) exposure to Cs⁺. This suggests that bursting induced by Cs⁺ is not mediated by blocking an inward current but rather by its known intracellular effect on outward currents. Indeed, the ability of Cs⁺ to enter the cell has been proposed in several studies (Trequattrini et al. 1996; Xiong and Stringer 1999).

View larger version (17K): [in this window] [in a new window]   Fig. 8. Cs+ induced bursts and blocked h-like current in MLIs. A: extracellular recordings from an MLI before (top) and after (middle) applying 5 mM Cs+ to the bath. Bottom: intracellular recording of the bursts in the presence of Cs+. B: voltage-clamp recording of membrane currents induced by stepping the membrane potential from 50 to 90 mV for 300 ms before (black) and after (gray) adding 5 mM Cs+. C: the Cs+-dependent current revealed by subtracting the trace in the presence of Cs+ from the control trace in B. D: stepping the membrane potential from 90 to 50 mV for 300 ms before (black) and after (gray) adding 5 mM Cs+. E: the time dependence of the hyperpolarization activated current. The membrane potential was stepped from 90 to 50 ms for various durations.

We confirmed the presence of a Cs⁺-sensitive h-like current by a series of voltage-clamp experiments. When the membrane potential was stepped from 50 to 90 mV (Fig. 8B), a prominent slow hyperpolarization activated inward current (black trace) was found. This current was reversibly blocked by 5 mM Cs⁺ (gray trace). Subtracting the two traces (Fig. 8C) revealed that under this experimental paradigm, the inward current activation followed an exponential time course with a time constant of 100 ms. As expected, stepping the membrane potential from 90 to 50 mV revealed a slow and delayed increase in outward current and a prolonged outward tail current (Fig. 8D). The latter depended on the duration of the step (Fig. 8E). Adding Cs⁺ to the external solution abolished both components (Fig. 8D, gray trace) and significantly reduced the holding current. Stepping the membrane potential from 90 mV correspond to the condition where the synaptic-like current was elicited from a hyperpolarized level. Activation of I_h in this state explains the high conductivity and the slow hyperpolarizing wave at the end of the train.

Examining the effect of Cs⁺ ions on the response to synaptic-like currents (Fig. 9, A and B), was possible only during the short time before the bursting activity emerged. This revealed a significant increase in the duration of the response, and the temporal distribution plot (Fig. 9, C and D) shows that the increase in duration was accompanied by increased scatter from 4.4 to 11.6 ms. The slow hyperpolarizing wave that followed the response to synaptic-like current, when the membrane was held at 80 mV (see Fig. 4A), was completely abolished in the presence of Cs⁺ (not shown).

View larger version (22K): [in this window] [in a new window]   Fig. 9. Cs+ increased the duration and variability of the response to synaptic-like current. A and B: 3 superimposed traces of the response to synaptic-like current before (A) and after (B) the addition of Cs+ (peak current, 0.1 nA). C and D: the temporal distribution of the action potentials during the response to synaptic-like current before (C) and after (D) the addition of Cs+ (as in Fig. 2B). Note the increase in both duration and variability.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The ability to simulate stellate cell responses to parallel fiber input in a slice preparation enables us to study the mechanisms governing the characteristic train response. A first question is, to what extent we accurately mimicked the parallel fiber input. The current used here had a time constant of 10-15 ms, whereas a single synaptic current lasts 1-2 ms (Barbour et al. 1994; Llano and Gerschenfeld 1993). The longer time constant was used for two reasons. First, the parallel fiber volley described by Eccles et al. (1966) (Fig. 1A) lasted about 10 ms, suggesting a long duration for the overall input. Second, it is well known that parallel fibers have different conduction velocities (Ito 1984); stimulating a group of parallel fibers would thus necessarily induce a prolonged presence of the neurotransmitter and hence a prolonged synaptic potential. The remarkable similarity between our results and those described by Eccles strongly suggests that indeed we have captured the essence of the transmission between parallel fibers and MLIs. However, one should bear in mind that simulating synaptic conductance with current injection have its limitation particularly when large currents are used. In these conditions, synaptic currents will tend to saturate, whereas current injection will not. In our case, it might affect only the responses to high intensities.

Under natural conditions, the input to the cerebellar cortex is conveyed by groups of mossy fibers, giving rise to the well-known patchy somatotopic organization of the granular layer (Bower and Woolstone 1983). Thus it is reasonable that the natural excitatory input to the MLIs is composed of a synchronized volley propagating along a beam of parallel fibers. Whether or not this volley activates a beam of postsynaptic Purkinje cells is still in dispute; however, there is no doubt that the action potentials do propagate in a synchronized beam. The degree of synchronization will determine the duration of the input to the MLIs. Therefore the time constant used here, although nicely reproduces the response to surface stimulation, might not be an actual representation of the time course of a natural input.

The most striking property of the MLI response here is that the averaged duration and its variability, or jitter, are almost independent of the stimulus intensity (Fig. 2, B and C). This peculiar observation is due to the long and variable delay of the last spike in the train (Fig. 2D), which is triggered by an intrinsic noninactivating Na⁺ current (Fig. 6). Preventing the persistent Na⁺ current by hyperpolarizing the membrane potential resulted in a significant reduction of the scatter (Fig. 4). Increasing the membrane resistance by blocking the I_h, amplified the voltage expression of the Na⁺ current and increased the scatter (Fig. 9). The significant properties of this persistent Na⁺ current are its rather low threshold and its graded activation levels (Figs. 3A and 6, C and D). These features ensure that the last spike arises almost from resting potential after a prolonged and variable delay after the end of the synaptic current (Figs. 2A and 7B). This persistent Na⁺ is also active during the synaptic current itself but is masked by the dominant action potentials. It is reset by the AHP of the last spike evoked directly by the synaptic current. The amplitude of the remaining synaptic current at that time determines whether, and to what extent, the persistent Na⁺ current is activated and generates the last spike far beyond the end of the synaptic current. Hence, the large jitter results from the variable timing of the spike before last and is greatly amplified by the stochastic nature of the persistent Na⁺ current. As the activation of the sodium current is independent of the stimulus duration, the jitter and elongation of the response due to the last spike will prevail under different input duration.

This study shows that the persistent Na⁺ current determines the duration of the suprathreshold response rather than the amplitude of subthreshold excitatory postsynaptic potentials (EPSPs) as was suggested previously (Schwindt and Crill 1995; Stuart and Sakmann 1995). Fricker and Miles (2000) have recently reported that persistent Na⁺ current prolonged the EPSP and generated delayed firing. However, in their experiments, the inhibitory interneurons responded with a single and accurately timed action potential while the principal neurons responded with variable spiking.

Although the duration of the MLI responses is determined by the persistent Na⁺ current, their pattern results from a complex interaction between the synaptic current, the spike amplitude, and its AHP. This pattern is characterized by a gradual increase in both interspike interval and spike amplitude (except for the 1st spike, which always has the highest amplitude). At any given time, the probability of initiating an action potential is determined by the threshold and the current at that time. The threshold is a function of Na⁺ inactivation level and thus depends on the history of the neuron's activity. The first action potential is triggered after a quiescent period and therefore attains the highest amplitude. The second action potential, which is triggered by relatively large synaptic current, occurs after a short delay during the relative refractory period and therefore has a low amplitude and as a result a small AHP. The interspike interval increases as the synaptic current decreases, resulting in an increase in the amplitude of the action potentials and the AHPs. This course of events implies that the amplitude of the AHP, whose function is to reset the membrane potential after the spike, will play a prominent role in shaping the pattern of activity. Indeed, treatments that reduced the AHP, decreased the excitability and weakened the responses (Figs. 5 and 7). The central role of the potassium currents in shaping the pattern of the response has been demonstrated in the fast nonadapting firing of cortical inhibitory interneurons (Erisir et al. 1999), in hippocampal fast spiking interneurons (Martina et al. 1998), and in layer V pyramidal cells (Kang et al. 2000).

Thus in summary, our results show that in cerebellar MLIs, the duration and jitter of the response is governed by a persistent Na⁺ current, whereas the pattern is shaped by the synaptic current and the spiking mechanism.

Possible functional significance

The almost constant duration of the response and its lack of precise timing may be of functional significance. In evaluating the importance of these properties, we need to examine the resultant effect on the target cells of MLIs, the Purkinje cells. An invariant duration of inhibition could have two functions: either to block another invariant event, such as the complex spike, or to create a refractory period and, hence, rhythmicity. In the latter case, the efficiency of the relative refractory period would depend on the intensity of the inhibitory response, while its duration will remain invariant. It should be remembered that the intensity of inhibition seen by one PC is the summation of inputs from several MLIs, which receive a similar parallel fiber input and are interconnected by electrotonic coupling (Mann-Metzer and Yarom 1999). Because of this, our observations of the responses of single MLI indicate the qualitative features of the response. The response amplitude, resulting from many such MLIs inputs, would be much greater.

The jitter of the response is of particular interest. It has been suggested that the inhibition from MLIs determines the pattern of PC firing (Häusser and Clark 1997; Jaeger and Bower 1999). Our results, which emphasize the jittery nature of this inhibition, question the ability of the system to generate precise timing and thus also question its use of temporal coding in information processing. Either precise timing is not essential for the operation of MLIs or else the interconnections between the MLIs can reduce response jitter. Although electrical coupling combined with chemical inhibitory synapses can greatly synchronize the firing of a group of neurons (Tamás et al. 2000), we need to carefully explore whether this could also be the case in the MLI system.