Cerebellar On-Beam and Lateral Inhibition: Two Functionally Distinct Circuits

Dana Cohen and Yosef Yarom

Department of Neurobiology, Life Science Institute and Center for Neural Computation, The Hebrew University, Jerusalem 91904, Israel


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Cohen, Dana and Yosef Yarom. Cerebellar On-Beam and Lateral Inhibition: Two Functionally Distinct Circuits. J. Neurophysiol. 83: 1932-1940, 2000. Optical imaging of voltage-sensitive dyes in an isolated cerebellum preparation was used to study the spatiotemporal functional organization of the inhibitory systems in the cerebellar cortex. Responses to surface stimulation of the cortex reveal two physiologically distinct inhibitory systems, which we refer to as lateral and on-beam inhibition following classical terminology. Lateral inhibition occurs throughout the area responding to a stimulus, whereas on-beam inhibition is confined to the area directly excited by parallel fibers. The time course of the lateral inhibition is twice as long as that of the on-beam inhibition. Both inhibitory responses increase with stimulus intensity, but the lateral inhibition has a lower threshold, and it saturates at lower stimulus intensity. The amplitude of the on-beam inhibition is linearly related to the excitation at the same location, whereas that of the lateral inhibition is linearly related to the excitation at the center of the beam. Repetitive stimulation is required to activate on-beam inhibition, whereas the same stimulus paradigm reveals prolonged depression of the lateral inhibition. We conclude that lateral inhibition reflects the activation of molecular layer interneurons, and its major role is to increase the excitability of the activated area by disinhibition. The on-beam inhibition most likely reflects Golgi cell inhibition of granule cells. However, Purkinje cell collateral inhibition of Golgi cells cannot be excluded. Both possibilities suggest that the role of the on-beam inhibition is to efficiently modulate, in time and space, the mossy fiber input to the cerebellar cortex.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The cerebellum is built up of basically similar units: the cerebellar modules. Each module receives inputs from the mossy fibers and the climbing fibers, whereas a Purkinje cell axon, the only output from the cortical modules, transmits the processed information to the deep cerebellar nuclei. The climbing fibers activate the Purkinje cells directly, whereas the mossy fibers excite them indirectly via the granule cells (Ito 1984; Llinas 1981; Palay and Chan-Palay 1974). This excitatory circuit is modulated by a comprehensive inhibitory system, composed of the molecular layer interneurons, the Purkinje cell collaterals, and the Golgi cells. A thorough exploration of the inhibitory system is essential to elucidate the computational process that is performed in each module. Here we have used optical imaging of voltage-sensitive dyes in an isolated preparation to study the functional spatiotemporal organization of the inhibitory system of the cerebellar cortex.

The molecular layer interneurons, which are classically divided into basket and stellate cells, operate within the molecular layer (Palay and Chan-Palay 1974; Sultan and Bower 1998). They are activated by the parallel fibers and inhibited both by Purkinje cell collaterals (Llinas and Precht 1969) and by other molecular layer interneurons (Hausser and Clarck 1997; Llano and Gerschenfeld 1993). Their axons either remain in the immediate vicinity of their cell body or run up to 500 µm perpendicular to the parallel fibers (Ito 1984). The short axons of stellate cells may inhibit each Purkinje cell proportional to its excitation (De Schutter and Bower 1994; Marr 1969). The long-range axons of the stellate and basket cells are thought to induce lateral inhibition that sharpens the borders of the area activated by the parallel fibers (Eccles et al. 1967). However, in view of our recent demonstration that beams of Purkinje cells activity are unlikely to be generated by mossy fiber activation (Cohen and Yarom 1998), the role of the long-range axons of the molecular layer interneurons remains to be elucidated.

The Golgi cells are the largest inhibitory interneuron in the cerebellar cortex. Their cell bodies are located in the upper part of the granular layer, and their dendrites ascend to the molecular layer, where they receive excitatory input from the parallel fibers. Their axons ramify within the granular layer in a limited space underneath their cell bodies, preventing the activation of granule cells by mossy fiber input. The spatial distribution of the inhibitory output of Golgi cells is therefore limited to the area activated by the parallel fibers. The Golgi cells provide the only feedback inhibition to the cerebellar modules, serving as a gain control of their mossy fiber input (Marr 1969). Recent theoretical work has demonstrated that Golgi cells may induce synchronized rhythmic activity in granule cells, thereby increasing the parallel fiber input to the Purkinje cells (Maex and De Schutter 1998).

Although the extensive collaterals of Purkinje cell axons were described by Cajal at the beginning of the century (Cajal 1955), knowledge about the target neurons of these collaterals and the effects of their activity is rather limited. Recently, Bishop and colleagues (Bishop 1982, 1988; Bishop and O'donoghue 1986; O'donoghue and Bishop 1990) showed that each Purkinje cell axon gives rise to one to three collaterals that form a plexus of varicose axonal branches. With few exceptions, this plexus is formed in the immediate vicinity of the parent cell, extending 300-400 µm in the transverse plane (parallel fiber axis) and somewhat longer (500-600 µm) in the sagittal plane. Most varicosities are asymmetrically distributed within 200-400 µm around the parent cell. The terminals of Purkinje cell collaterals in the granular layer form a nestlike structure around large cell bodies there, most likely Golgi cells. In the molecular layer, they innervate the molecular layer interneurons and other Purkinje cells. However, physiological studies have not succeeded in demonstrating inhibition of Purkinje cells by other Purkinje cell collaterals (Eccles et al. 1966; Llinas and Precht 1969). The spatial distribution of the inhibitory output of Purkinje cell collaterals, like that of Golgi cell inhibition, is limited to the area activated by parallel fibers.

Although the individual components of the inhibitory systems in the cerebellar cortex are well known, as are some of their properties, little is known about their functional organization. Here we demonstrate that the inhibitory systems of the cortex comprise at least two physiologically distinct components. Although both types of inhibitory responses are blocked by bicuculline (Cohen and Yarom 1998, 1999), they differ in their mode of activation, spatial distribution, time course, and dynamic properties. These results shed new light on the role of the inhibitory interneurons in intermodule communication.


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Optical measurement from the isolated guinea pig cerebellar preparation has been described in detail elsewhere (Cohen and Yarom 1999). Briefly, the intact cerebellum and the brain stem are removed from the animal, and a cannula is inserted into one of the vertebral arteries. Physiological solution is perfused via the vertebral artery at a rate of 0.5 ml/min using a peristaltic pump. The intravascular solution consists of (in mM) 124 NaCl, 5 KCl, 1.3 MgSO4, 1.2 KH2PO4, 26 NaHCO3, 10 glucose, 2.4 CaCl2, and 5% dextran. A similar solution without dextran is used for the external solution. The preparation was maintained at 28°C.

The voltage-sensitive dye RH-414 (2 µg/µl) was injected into one of the cerebellar folia using a glass micropipette. Optical signals were monitored by 128 photodiodes organized in a 12 × 12 array. Each element of the array detects light from a surface of 100 × 100 µm or 50 × 50 µm when using ×20 or ×40 objectives, respectively. The signals were amplified in two AC-coupled stages, with a time constant of 200 ms, and then sampled and digitized with 12-bit accuracy at maximal resolution of 50 µs (Microstar, DAP 3400a). Data were usually displayed as traces of absolute change in fluorescence as a function of time at each location. However, when the signals at two locations were compared, the relative fluorescence was used. To that end, the amplitude of the response was divided by the DC level measured at these locations. Concentric metal electrodes with a diameter of 200 µm were used to stimulate (0.1-ms pulses of 0.5-5 V) the cerebellar surface (parallel fibers).

When interpreting optical signals generated by voltage-sensitive dyes, one should be aware that the signals represent a weighted sum of all the changes in fluorescence detected by each photodiode. The weights are determined by factors like membrane area, the depth of the signals' source, and the amount of dye adhered to the membranes. Thus the absence of a negative component does not necessarily imply lack of inhibition. Furthermore, the size and shape of the signal cannot be used to determine its functional importance. However, in a previous study (Cohen and Yarom 1999) we have demonstrated that in our system all the negative signals generated by surface stimulation represent postsynaptic inhibitory signals, whereas positive responses reflect excitatory postsynaptic activity, composed of synaptic and regenerative responses. The parallel fiber action potential and the glial cells do not contribute significantly to the optical responses. Unstained preparation does not generate any signal, suggesting that "intrinsic signals" are insignificant in our system.


    RESULTS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Surface stimulation of the cerebellar cortex activates, in addition to an excitatory beam of activity, two types of inhibitory responses: lateral inhibition and on-beam inhibition. The spatial distribution of these inhibitory responses is shown in Fig. 1. Lateral inhibition is evoked by a single surface stimulation and appears on both sides of the activated beam (Fig. 1A). Large depolarizing responses were recorded at the 8th to 10th photodiodes rows, whereas the response in other areas consisted of a depolarization followed by a prolonged hyperpolarization. The ratio between the depolarization and hyperpolarization gradually decreased with the distance from the center of activity. Prolonged hyperpolarization was observed only in the most distant locations (top 2 rows).



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Fig. 1. Spatiotemporal organization of lateral and on-beam inhibition evoked by surface stimulation. A and C: responses to a single and twin pulse stimulation, respectively. Data are displayed as a change in absolute fluorescence as a function of time at 128 locations. Each trace represents the averaged response of 3 consecutive stimuli. The stimulating electrode was located to the left of the recording area. Shaded areas mark the borders of the excitatory beam of activity. B and D: the relative change in fluorescence recorded in a column of diodes marked by dashed rectangles in A and C, respectively. Data are presented as a function of the diode location from top to bottom within the column. Amplitudes of the excitatory wave are represented by squares; circles and triangles are the values measured 60 ms after the positive peak (at the peak of the on-beam inhibition). Triangles represent the subtraction of the circles in B from the circles in D.

The borders of the excitatory beam were determined by plotting the amplitude profiles of the excitation and inhibition measured in a randomly chosen column of diodes perpendicular to the direction of the parallel fibers. The largest excitatory response was measured at the 10th diode in the column, and it decreased monotonically on both sides (Fig. 1B, squares). The smallest inhibitory response was recorded at the ninth diode, and it increased on both sides until it reached a plateau starting at the sixth diode (Fig. 1B, circles). We therefore define the borders of the excitatory beam as the location where excitation equals inhibition. According to this definition, rows 7 to 11 in Fig. 1 compose the beam of activity (etched area).

On-beam inhibition is activated when a train of two or more stimuli is applied to the cerebellar surface (Fig. 1C) and is found within the borders of the excitatory beam (Fig. 1D). The amplitude profile of the excitation evoked by the train (Fig. 1D, squares) resembles that evoked by a single stimulus (Fig. 1B, squares). In contrast, the amplitude profile of the inhibition includes both the lateral and on-beam inhibitory responses. To reveal the contribution of the on-beam inhibition, we subtracted the inhibitory profile in Fig. 1B from the inhibitory profile in Fig. 1D. The result (Fig. 1D, triangles) demonstrates that the inhibition elicited by a train of stimuli is confined to the excitatory beam.

The two inhibitory responses have different time courses (Fig. 2A), the on-beam inhibition decaying faster than the lateral inhibition. The linear behavior of the logarithmic value of the decay (Fig. 2B) indicates that both decays are described by a single time constant (Fig. 2, C and D). In the example shown, the time constants were calculated as 66 and 136 ms for the on-beam and the lateral inhibition, respectively, and ranging in other experiments from 45 to 73 ms for the on-beam inhibition and 100 to 140 ms for the lateral inhibition. The variation in the values of time constants between different locations in one experiment is much smaller than that between experiments. It is not unlikely that variation between experiments reflects the excitability of the inhibitory interneurons. It is well documented that cortical inhibitory interneurons respond in a train of action potentials to a single stimulus (Eccles et al. 1967). The train duration will determine the time constant of the inhibitory responses. In our preparation, the excitability of the interneurons may vary between experiments, and therefore various durations of action potential will be generated.



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Fig. 2. Recovery time course of on-beam inhibition is faster than that of lateral inhibition. A: the on-beam inhibitory response and lateral inhibition were superimposed. Amplitudes of the responses were scaled, and their peaks were aligned. B: semi-log presentation of the decay time courses of on-beam and lateral inhibitions, using the absolute values of the data. The time constant of decay of the lateral inhibition was twice as long as the time constant of the on-beam inhibition. C: a single exponent fits the recovery time course of on-beam inhibition. The excitatory response was truncated. D: as in C, for lateral inhibition. It should be noted that these time constants are shorter than the time constant of the recording system. In fact, the same time courses were measured both in AC and DC modes of the system.

Dependence on stimulus intensity

LATERAL INHIBITION. As shown in Fig. 1, the lateral inhibition appears on both sides of the activated beam, the width of the inhibited area increasing with stimulus intensity and spread up to 800 µm from the center of the beam. The amplitude of the inhibitory response thus depends on both stimulus intensity and distance from the center of the activated beam (Fig. 3). Distally (Fig. 3A), where there were mainly prolonged negative signals, the response increased monotonically to a saturated level as stimulus intensity increased (Fig. 3D, squares). At the center of the beam (Fig. 3C), increasing the stimulus intensity resulted in an initial increase in amplitude of the negative component followed by a decrease (Fig. 3D, circles). At low stimulus intensity, the negative response dominated the center of the beam, although it was always preceded by a positive response (Fig. 3C, thick line). At distal areas, the positive component of the response was rather small and hardly changed with stimulus intensity (Fig. 3E, squares), but closer to the center of the beam (Fig. 3B) it increased monotonically with stimulus intensity (Fig. 3E, triangles). The steepest slope was observed at the center of the beam (Fig. 3E, circles).



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Fig. 3. Dependence of the lateral inhibition on stimulus intensity. A-C: responses to a single stimulus at 3 intensities measured at 3 locations were superimposed. Locations are marked in the inset by a triangle, a square, and a circle for A, B, and C, respectively. D: the amplitude of the inhibitory responses measured in these locations as a function of stimulus intensity. Each value is an average of the responses in 3 diodes located at the same distance from the center of the beam. Responses were normalized by the highest average value. Amplitudes increased with stimulus intensity at low intensities and reached saturation (squares) or declined (circles) at higher stimulus intensities. E: as in D, for the amplitude of the excitation. Amplitudes of the excitatory responses measured closer to the beam increased with stimulus intensity (triangles and circles), whereas the response was independent of stimulus intensity at distal locations (squares). F: inhibition as a function of excitation at the center of the beam (circles) and at a distal location (squares). Stars denote the inhibition at the distal location as a function of the excitation measured at the location marked by a triangle. Note the linearity of the latter.

The overall relationship between positive and negative responses is shown in Fig. 3F, where the amplitude of the negative component is plotted as a function of the positive component. At distal locations, the amplitude of the lateral inhibition is independent of the amplitude of the positive wavelet that precedes it (Fig. 3F, squares). Both excitatory and inhibitory responses within the beam increase with stimulus intensity until the point at which inhibition saturates and further increase of stimulus intensity results in masking of the inhibitory response by the excitatory response (Fig. 3F, circles). This masking effect has been demonstrated in a previous publication (Cohen and Yarom 1999), where blocking the inhibition with bicuculline increases the amplitude and duration of a depolarizing (positive) response measured at the center of the beam. A linear relationship was obtained when the amplitude of the distal inhibitory response was plotted as a function of the excitatory response recorded closer to the beam (Fig. 3F, stars). This linear relationship implies that most of the cell bodies generating the lateral inhibition are located closer to the center of the beam.

ON-BEAM INHIBITION. A train of three stimuli elicited the superimposed responses shown in Fig. 4A. These responses, measured in two representative diodes located along the center of the beam, were elicited by different stimulus intensities. The amplitude of both the positive and negative components increased with stimulus intensity. To quantify this increase, we measured the amplitude of the first positive component and the amplitude of the last negative component and plotted them as a function of stimulus intensity. As shown in Fig. 4, B and C, both components depend similarly on stimulus intensity. As a result, the amplitude of the negative component is linearly related to the amplitude of the positive component measured at four stimulus intensities (Fig. 4D). The same linear relationship was found when the positive and negative responses were measured at all the diodes located within the beam, independent of the stimulus intensity (Fig. 4E).



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Fig. 4. Amplitude of the on-beam inhibition increased with stimulus intensity. A: responses to 3 stimulus intensities at 2 locations along the excitatory beam (a square and a circle) were superimposed. B: amplitudes of the 1st excitatory responses at these locations (a square and a circle) as a function of stimulus intensity. C: as in B, for the amplitude of on-beam inhibition. D: the inhibition as a function of excitation at 4 intensities and 4 locations (different symbols). E: the inhibition as a function of excitation in all locations within the excitatory beam at a single stimulus intensity.

In summary, the on-beam and lateral inhibition depend differently on stimulus intensity. The lateral inhibition has a lower threshold for activation relative to the on-beam inhibition. This conclusion stems from the fact that at the center of the beam the excitation-inhibition relationship of the lateral inhibition (Fig. 3F) intersects the inhibition axis, whereas that of the on-beam inhibition (Fig. 4E) intersects the excitation axis. Thus the depolarizing response should exceed a minimum value to elicit on-beam inhibition, whereas lateral inhibition can be evoked with a negligible depolarizing response (Fig. 3C; thicker trace). In addition, the amplitude of the on-beam inhibition is linearly related to the preceding excitatory response recorded at the same location (Fig. 4E), whereas lateral inhibition can occur without a preceding excitatory response at the same location. These differences suggest that the two systems have different origins.

Temporal properties of the inhibitory responses

The most significant functional difference between the two inhibitory systems is that the on-beam inhibition increases with repetitive stimulation, whereas the lateral inhibition decreases. This difference is shown in Fig. 5, where responses to two consecutive stimuli delivered to the cerebellar surface at various interstimulus intervals were superimposed. Although the second stimulus elicited a depolarizing wavelet at lateral locations (Fig. 5A), it failed completely to elicit an inhibitory response when applied <50 ms after the first stimulus. The amplitude and duration of the depolarizing wavelet evoked by the second stimulus increased relatively to the wavelet generated by the first stimulus. At longer interstimulus intervals, the blockade of the inhibition was partially removed, and the amplitude of the depolarizing wavelet and the inhibitory response to the second stimulus gradually returned to the levels occurring in response to the first stimulus.



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Fig. 5. Temporal properties of lateral and on-beam inhibition. A: responses at a distal location to twin pulse stimuli at different interstimulus intervals were superimposed. Note the complete blockade of the 2nd inhibitory responses at intervals shorter than 50 ms. B: amplitudes of the inhibitory responses evoked by the 1st (squares) and 2nd (circles) stimuli as a function of the interstimulus interval. The amplitude of the 2nd inhibitory response was measured after subtracting the response to a single stimulus from the response to twin stimuli. All inhibitory responses were normalized relative to the 1st response at 100 ms. Triangles show the difference between the 1st and 2nd excitatory responses as a function of the interstimulus interval. The excitatory responses were normalized relative to the strongest response evoked by the 1st stimulus. C and D: as in A and B, for a diode located at the center of the excitatory beam. Note the appearance of on-beam inhibition at intervals shorter than 50 ms in C. Responses were normalized relatively to the inhibition at 20-ms interstimulus interval.

Quantitative analysis of these observations is given in Fig. 5B, where the normalized amplitude of the two inhibitory responses and the normalized difference in the depolarizing wavelet were plotted as a function of interstimulus interval. The amplitude of the first inhibitory response remained constant (squares), whereas the inhibitory response following the second stimulus was completely blocked for at least 50 ms (circles). The amplitude of the second inhibitory response recovered almost completely after 300 ms. Concomitantly, the difference between the amplitudes of the depolarizing wavelets of the first and second responses decreased with a similar time course (triangles).

A different behavior was observed at the center of the excitatory beam (Fig. 5C). Here, the response to the first stimulus is characterized by a depolarizing response followed by a prolonged and shallow hyperpolarization. The second stimulus elicits a pronounced inhibitory response at interstimulus intervals shorter than 70 ms. This response is strongest at shorter intervals (10-20 ms) and decreases with increasing interstimulus interval (Fig. 5D, circles). At longer intervals, the second stimulus fails to produce an inhibitory response, whereas the duration of the depolarizing component increases (Fig. 5C). Almost complete recovery of both components was observed at intervals longer than 200 ms (Fig. 5D).

The inhibitory response at the center of the beam displays a different temporal behavior than that of the lateral inhibitory response. The on-beam inhibition undergoes a strong facilitation, whereas the lateral inhibition shows a robust and long-lasting depression. It should be noted, however, that the prolonged and shallow hyperpolarization elicited by the first stimulus (Fig. 5C) has the same properties as the lateral inhibition. First, it is completely absent in the response to the second stimulus (Fig. 5C), and second, it is activated by a low stimulus intensity (Fig. 3C; thicker trace). Therefore the term "lateral inhibition" is inaccurate, for this type of inhibition occurs all over the activated area.

The complete blockade of the lateral inhibitory response by a preceding stimulus (Fig. 5, A and B) can be attributed either to synaptic depression or inhibition of the inhibitory interneurons at the level of either their cell body (postsynaptic inhibition) or their axonal terminals (presynaptic inhibition). To distinguish between these two possibilities, we studied the reciprocal interactions between two lateral inhibitory responses elicited by different sources. Two stimulating electrodes were used to activate two excitatory beams 800 µm apart (stim 1 and stim 2, inset in Fig. 6). Both stimuli elicited an inhibitory response in the area between the two excitatory beams (top 2 traces in Fig. 6A). The two stimuli were applied sequentially with different interstimulus intervals. The second inhibitory response was always blocked by the first stimulus (Fig. 6A, bottom traces and 6B), regardless of the order of stimulation or the location within the activated area. To demonstrate the extent of the blockade, we superimposed, in Fig. 6A (bottom traces), the expected sum of the two top traces (thick lines). As shown in Fig. 6, B and C, a complete blockade occurred when the interval between the two stimuli was shorter than 70 ms, and gradual recovery was observed at longer intervals. Moreover, the time course of this recovery resembles the recovery time course of the second inhibitory response measured when a single beam elicited both responses (Fig. 5, A and B).



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Fig. 6. Heterosynaptic blockade of the 2nd inhibitory response. Two stimulating electrodes were placed on the cerebellar surface >800 µm apart (see inset). Both stimuli evoked lateral inhibition in the area between the stimulating electrodes. Representative responses were measured at the sites marked by a circle (left panel) and a square (right panel) in the inset. A, top 2 traces: responses to a single stimulus delivered via each of the stimulating electrodes. Bottom thin traces: the response to sequential activation of both beams at a 40-ms interstimulus interval. Note that the 2nd stimulus failed to activate an inhibitory response. Thick trace represents the sum of the 2 top traces in each column. B: superposition of the responses to 2 stimuli, each delivered via a different stimulating electrode, at several interstimulus intervals. Arrows mark the time of the 2nd stimulus. C: amplitudes of the 2nd inhibitory response (triangles) as a function of the interstimulus interval. Responses were normalized relative to the amplitude of the response to this stimulus applied alone (squares).

We therefore conclude that the blockade of the inhibitory response by a preceding lateral inhibition is independent of the location or the source of the lateral inhibition, which supports the possibility of interneurons inhibition rather than synaptic depression.

Dynamics of the on-beam inhibition

The dynamics of the on-beam inhibition were studied by analyzing the behavior of the on-beam inhibition as a function of the intratrain frequency and train duration (i.e., the number of stimuli in the train). Figure 7 shows the buildup of the on-beam inhibition at different train durations and frequencies. Each panel shows six superimposed traces, each with a different train duration ranging from one to six stimuli. The intratrain time interval is 10, 20, and 30 ms in A, B, and C, respectively. It is clear that the amplitude of the on-beam inhibition increases with both the train duration and intratrain frequency. However, saturating states are reached at lower frequencies (Fig. 7, B and C), the level of this saturation increasing with intratrain frequency. At higher intratrain frequency (Fig. 7A), train duration of up to six stimuli did not reach saturation. This behavior suggests that each stimulus makes a constant contribution to the buildup of the inhibition. Occasionally, when a long train duration was used, the on-beam inhibition was followed by a prolonged depolarizing wave that lasted hundreds of milliseconds. The source and properties of this wave were not studied here.



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Fig. 7. On-beam inhibition increases with train frequency and duration. A: superimposed responses to 6 trains of stimuli, each consisting of a different number of pulses, ranging from 1 to 6, with a 10-ms interstimulus interval. B and C: as in A, but with 20- and 30-ms interstimulus intervals. Amplitude of the on-beam inhibition increases with both the train duration and frequency.

The buildup of the on-beam inhibition is quantitatively described in Fig. 8. The increase in inhibition as a function of the number of stimuli in the train (train duration) is given in Fig. 8A. As expected, the amplitude of the inhibitory response saturated and the steady-state level increased with the frequency of the train (, , and black-triangle). We have shown that the amplitude of the on-beam inhibition is linearly related to the amplitude of the first depolarizing response (Fig. 4, D and E). Hence here we describe the maximum inhibition as a function of the excitation in all locations for two frequencies (Fig. 8, B and C). Each of the panels shows this relation for three train durations (1, 3, and 6 pulses). The linear relationship is maintained with a similar level of significance in all cases, the slope of this relationship increasing with the number of stimuli in the train and with the intratrain frequency (cf. Fig. 8, B and C).



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Fig. 8. Quantitative analysis of on-beam inhibition. A: amplitude of the on-beam inhibition as a function of number of stimuli in the train. The interstimulus interval in the trains was 20, 30, and 40 ms (black-triangle, , and , respectively). B: the amplitude of the inhibitory response as a function of the amplitude of the 1st excitatory response. The interstimulus interval was 20 ms. Responses were evoked by a single stimulus (), a train of 3 stimuli () or 6 stimuli (black-triangle) and measured in all diodes within the excitatory beam. Solid lines are the linear regression curves calculated for all train durations. Note that a single stimulus failed to produce an inhibitory response. C: as in B, but with 30-ms interstimulus interval. Note the lower slope of the linear regression curves than in B. D and E: the facilitation process of the on-beam inhibition is characterized. D: 6 superimposed traces evoked by stimulation with trains ranging from 1 to 6 stimuli and interstimulus interval of 30 ms. E: calculating the contribution of each stimulus in the train to the on-beam inhibition. The response to a single stimulus was subtracted from the response to twin pulse (bottom trace). All consecutive responses were similarly subtracted from one another (4 top traces). Note that a maximal contribution to the inhibition is reached no later than the 3rd pulse, indicating a rapid saturation of the process of facilitation.

To start characterizing the process governing the buildup of the on-beam inhibition (Fig. 8D), we determined the contribution of the second stimulus in the train by subtracting the response to a single pulse from the response to twin pulses. The difference (Fig. 8E, bottom trace) gives the contribution of the response to the second stimulus to the on-beam inhibition. Similarly, we sequentially subtracted all consecutive responses, thus isolating the contribution of each stimulus in the train (Fig. 8E). The striking outcome is the identical contribution of each stimulus in the train to the buildup of the inhibition, except for the second stimulus whose contribution was smaller. Thus the facilitatory process that produces the on-beam inhibition has a rather short dynamic range that reaches saturation within two or three pulses.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Several lines of evidence were brought here to demonstrate for the first time that the activity in the cerebellar cortex is governed by two distinct inhibitory systems, which differ in their physiological properties. The differences are summarized in four points. 1) Lateral inhibition occurs throughout the area responding to a stimulus, whereas on-beam inhibition is confined to the region activated directly by the parallel fibers. 2) Both inhibitory responses increase with stimulus intensity, yet the lateral inhibition has a lower threshold and saturates at lower stimulus intensity. In addition, the amplitude of the on-beam inhibition is linearly related to the excitation at the same location, whereas the amplitude of the lateral inhibition at distal locations is linearly related to the excitatory response closer to the center of the beam. 3) The time course of the lateral inhibition is twice as long as that of the on-beam inhibition. 4) Repetitive stimulation is required to activate the on-beam inhibition, whereas long-lasting depression of the lateral inhibition occurs on repetitive stimulation.

Origins of the inhibitory responses

Based on the specific properties of the two inhibitory responses described above, we suggest that each response reflects the activity of different neuronal elements. The properties of the lateral inhibition suggest that it is generated by the molecular layer interneurons. The spatial distribution of the lateral inhibition fits the distribution of the axons of the molecular layer interneurons, which are either restricted to the vicinity of their cell body or extend sagittally for different distances. In addition, these neurons are small and have high-input resistance, both imply a low threshold for activation as shown (Fig. 3C). Indeed, it has been reported that a single granule cell is sufficient to activate a stellate cell (Barbour 1993). Furthermore, the recent demonstration (Mann-Metzer and Yarom 1999) that these neurons form local inhibitory networks, whose neurons are electrotonically coupled, suggests that an input to one interneuron can activate, via the gap junctions, a group of interneurons, thereby inducing a relatively fast saturation of the inhibitory system.

Based on morphological data, the most likely source of on-beam inhibition is the Golgi cell inhibition of granule cells. The relatively large optical signals recorded during on-beam inhibition indicate that a large membrane area participates in the response. Although the granule cells are small and located deep below the surface, they outnumber Purkinje cells by 5 orders of magnitude and therefore can contribute to the on-beam inhibition. An alternative possibility is that the on-beam inhibition reflects hyperpolarization of Golgi cells. Namely, Purkinje cells, activated by the parallel fiber volley, induce, via their collaterals, hyperpolarization of Golgi cells and other molecular layer interneurons. The Golgi cells are relatively large and numerous (the Golgi cells to Purkinje cells ratio vary between 1:1.5 and 3) (Ito 1984) and therefore can produce a large optical signal without reaching saturation, whereas small cells, like the molecular layer interneurons, can account for only a small part of the response. The finding of Bishop and colleagues (Bishop 1988; O'donoghue and Bishop 1990) that Purkinje cell collaterals extend more sagittally than transversely cannot exclude this alternative possibility. In their measurements most of the synapses are within a distance of <400 µm from the parent Purkinje cell, and the difference between the sagittal and transverse distribution is <100 µm. It is difficult to detect such differences in our imaging system.

Both possibilities are in agreement with the linear relationship between the excitatory and inhibitory responses of the on-beam inhibition. If most of the excitation reflects the activity in Purkinje cells, then it should be linearly related to the inhibition produced by their collaterals. A linear relationship would also be predicted if the on-beam inhibition occurs at the granule cells level and is activated by the Golgi cells axons. The Golgi cells are of a similar size to Purkinje cells and are activated by the same beam of parallel fibers. Therefore their activity is expected to be linearly related to Purkinje cells activity, meaning that the inhibition produced by the Golgi cell axons will be linearly related to Purkinje cells activity.

Which cell type produces the on-beam inhibition is of considerable significance for our understanding of the functional organization of the cerebellar cortex. If on-beam inhibition reflects Golgi cell activity, then it would inhibit mossy fiber inputs. If, on the other hand, it reflects Purkinje cell collateral activity, then by inhibiting Golgi cells it would enhance mossy fiber inputs. The enhanced excitability could occur in the same module or in neighboring modules, depending on the extent of Purkinje cell collaterals.

Kinetics of the on-beam inhibition

Two physiological processes can account for the facilitation of the on-beam inhibition. The first is enhanced release of neurotransmitter, and the second is summation of synaptic potentials. Enhanced release of neurotransmitter may occur at the synapses formed by the parallel fibers on Purkinje cells and/or Golgi cells and also at the inhibitory terminals of Purkinje cell collaterals or Golgi cells axons. Summation of synaptic potentials may occur in Purkinje cells or in Golgi cells. Regardless of location, the pronounced facilitatory process has a rather short dynamic range; a single stimulus fails to evoke on-beam inhibition, whereas two stimuli at intervals shorter than 20 ms already reach saturation. Even at longer intervals of 30-40 ms, saturation is reached within few stimuli. The short dynamic range allows a complex temporal regulation of the activity in the cerebellar cortex, in which the first input signal is transferred unaffected, whereas the following inputs are either enhanced, if Purkinje cell collaterals are involved, or depressed, if Golgi cells are involved.

Depression of the lateral inhibition

In contrast to the classical view, our results suggest that the major role of lateral inhibition is to remove inhibition throughout the activated area. This disinhibition is a robust and pronounced phenomenon that lasts for up to 300 ms (Figs. 5 and 6). Thus the spread of lateral inhibition increases, by disinhibition, the responsiveness to incoming information for a significant period. In addition to its effect of disinhibition, lateral inhibition actually inhibits Purkinje cells and other molecular layer interneurons. However, the inhibitory effect is rather short lasting (<20 ms), and, although mediated via a bisynaptic pathway, it is strong enough to decrease the amplitude and duration of the preceding excitatory response. The increase in amplitude and duration of the excitatory response during disinhibition (Fig. 5B) emphasizes the efficiency and strength of this inhibitory effect.

A similar blockade of the inhibitory response accompanied by an increase in the excitatory response has been previously reported (Eccles et al. 1966). In this in situ set of experiments, Purkinje cells were intracellularly recorded, and the responses to surface stimulation, applied via two very close electrodes, were analyzed. The stimulus intensity was adjusted so that each electrode evoked similar inhibitory postsynaptic potentials (IPSPs) in the recorded Purkinje cell. As in our experiments, sequential activation of the two IPSPs resulted in a time-dependent depression of the second response. Eccles and his colleagues proposed that this was due either to a decrease in transmitter release, desensitization of synaptic receptors, or the proximity to equilibrium potential of the inhibitory synaptic currents.

In view of our results synaptic depression is less likely because disinhibition is present even when two separate populations of inhibitory interneurons are activated (Fig. 6). In addition, the increase in the excitatory wavelet during disinhibition (Fig. 5) argues against presynaptic inhibition at the parallel fiber synapses (Dittman and Regher 1997). Therefore the most likely explanation is interactions among the molecular layer interneurons, either at the cell bodies of these interneurons or at the presynaptic terminals of their axons. The latter seems more probable because the large distance between the two stimulating electrodes prevents axosomatic interactions. The presynaptic nature of the disinhibition is further supported by its long time course. The disinhibition may be mediated by GABAB receptors, which are known to have a slower time course relative to the activity in GABAA receptors, and are mostly located on presynaptic terminals (Misgeld et al. 1995).

Conclusions

The patchlike organization of the response to mossy fiber input (Cohen and Yarom 1998) and the powerful depression of the lateral inhibition have significant consequences for our understanding of the functional organization of the cerebellum. They imply that the basic independent modules of the cerebellar cortex consist of a localized group of granule cells and the overlaying group of Purkinje cells connected via excitatory synapses. The activity of this module is modulated by Golgi cell feedback inhibition and stellate cell feed-forward inhibition. Mutual interactions between modules occur via the parallel fibers in the mediolateral axis and via the long-range axons of the molecular layer interneurons in the sagittal axis. However, the mediolateral interaction via the parallel fibers is rather weak and occurs only during a narrow time window. Due to disinhibition, the sagittal interaction is far more significant and has a prolonged time window. Because of the large time tolerance provided by the disinhibition, it is more likely that activity be organized in parasagittal bands than in the mediolateral direction.


    ACKNOWLEDGMENTS

This study was supported by the US-Israel Binational Science Foundation, the Israel Academy of Sciences, and the European Commission. D. Cohen was the recipient of a Clore Fellowship.


    FOOTNOTES

Address for reprint requests: Y. Yarom, Dept. of Neurobiology, Life Science Institute, The Hebrew University, Jerusalem 91904, Israel.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 17 September 1999; accepted in final form 10 December 1999.


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