1. Top of page
  2. Abstract
  6. Acknowledgements
  • 1
    The properties of glutamate receptor (GluR) channels in outside-out patches from the dendrites and somata of rat cerebellar Purkinje cells in brain slices were studied using fast agonist application techniques. Dendritic patches were isolated 40–130 μm from the soma.
  • 2
    Outside-out patches from both dendrites and somata of Purkinje cells responded to application of glutamate with a current which desensitized rapidly and nearly completely. Currents evoked by glutamate application were blocked by 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), were mimicked by l-α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA), and were modulated by cyclothiazide. Kainate produced small, non–desensitizing currents. No currents were observed in response to aspartate application. Responses characteristic of NMDA receptor activation were not observed. These findings indicate that glutamate-activated currents were mediated by the AMPA subtype of GluR.
  • 3
    Deactivation of the GluR channels following 1 ms pulses of glutamate occurred with a time constant of 1.23 ± 0.07 ms in dendritic and 1.12 ± 0.04 ms in somatic patches. Desensitization occurred with a time constant of 5.37 ± 0.26 ms in dendritic and 5.29 ± 0.29 ms in somatic patches. The time constant of recovery from desensitization caused by a 1 ms application of 1 mm glutamate was 36 ms in dendritic patches and 33 ms in somatic patches.
  • 4
    Half-maximal activation of the GluR channels was achieved at a glutamate concentration of 432 μm. Deactivation kinetics were not dependent on the glutamate concentration, while desensitization became slower at lower glutamate concentrations.
  • 5
    Pre-equilibration of patches with low concentrations of glutamate reduced the peak current activated by 1 mm glutamate. The IC50 for this effect was 8.7 μm. Equilibrium desensitization did not affect the kinetics of the current activated by 1 mm glutamate.
  • 6
    The current–voltage relationship of the peak current was linear in normal Na+-rich external solution, with a reversal potential near 0 mV. In Ca2+-rich external solution, the reversal potentials were −51.4 ± 2.9 and −51.5 ± 2.8 mV for dendritic and somatic patches, respectively, indicating that these glutamate channels have a low permeability to Ca2+ (PCa/PCs= 0.053).
  • 7
    The mean single-channel conductance of the GluR channels measured using non–stationary fluctuation analysis was ∼8 pS in dendritic and somatic patches, and the maximum open probability was at least 0.7 with 5 mm glutamate.
  • 8
    GluR channel kinetics in patches excised from the soma of neonatal (postnatal day 4; P4) Purkinje cells, before the development of the dendritic arborization of the Purkinje cell, were similar to those in patches excised from more mature (P12–18) Purkinje cells.
  • 9
    Dendritic and somatic GluR channels in Purkinje cells appear to be functionally identical, are AMPA-subtype receptors containing the GluR-B subunit, and have rapid kinetics and low permeability to Ca2+. A kinetic model was constructed which faithfully reproduces the gating characteristics of the GluR channels.

The Purkinje cell is central to the cerebellar network, integrating excitatory and inhibitory synaptic signals to generate the sole output of the cerebellar cortex. Each Purkinje cell receives excitatory input from a single climbing fibre and from approximately 200 000 parallel fibres; both pathways are thought to release glutamate as a transmitter. Climbing fibre activity leads to the down-regulation of parallel fibre synapses which are concurrently active, a process known as long-term depression (LTD), which has been proposed to play an important role in the storage and processing of information in the cerebellum (Linden, 1994). The mechanism of LTD remains unknown, although it has been suggested to be due to a reduction in efficacy of the glutamate receptor (GluR) channels at parallel fibre synapses (Linden, 1994). In order to understand the process of synaptic transmission at these synapses, and shed light on the possible changes occurring during LTD, a detailed description of the functional properties of the synaptic GluR channels is essential.

The properties of GluR channels in Purkinje cells have been studied previously using outside-out patches excised from the soma (Farrant & Cull-Candy, 1991; Barbour, Keller, Llano & Marty, 1994). Since few excitatory synapses are located at the soma of Purkinje cells (Palay & Chan-Palay, 1974), these receptors are likely to be extrasynaptic, and as such may have properties different from those in the synaptic membrane. We have therefore studied the properties of GluR channels in outside-out patches from the dendrites of Purkinje cells, where the probability of the receptors being synaptic is considerably higher. These properties were compared with those of receptors in somatic membrane in order to determine whether differences exist between extrasynaptic and synaptic receptors. The results from these experiments show that dendritic GluRs in Purkinje cells are of the AMPA (l-α-amino-3-hydroxy-5-methyl-4-isoxazole-propionate) subtype and have rapid kinetics and relatively low permeability to Ca2+. No differences were found between receptors in dendritic and somatic membrane, suggesting that synaptic and extrasynaptic receptors may be identical.


  1. Top of page
  2. Abstract
  6. Acknowledgements

Slice preparation and visualization

Methods for preparation of cerebellar slices were similar to those described previously (Llano, Marty, Armstrong & Konnerth, 1991; Stuart & Häusser, 1994). Brains were removed from 12- to 18-day-old Wistar rats killed by decapitation and parasagittal slices (250–350 μm) were cut in cold (∼4 °C) physiological saline using a vibrating slicer (FTB, Weinheim, Germany); for some experiments 4-day-old rats were used where indicated. Physiological saline contained (mm): 125 NaCl, 25 NaHCO3, 25 glucose, 2.5 KCl, 1.25 NaH2PO4, 2 CaCl2, 1 MgCl2; and was bubbled continuously with 95% O2–5% CO2. Slices were then incubated at 33–35 °C for 30–60 min and subsequently at room temperature (21–23 °C). Experiments were done under visual control using an upright microscope (Axioskop FS; Zeiss, Göttingen, Germany) with a × 40 Achroplan water-immersion objective. Dendrites and somata of Purkinje cells were visualized using infrared differential interference contrast (IR-DIC) videomicroscopy (Stuart, Dodt & Sakmann, 1993). An infrared filter (RG-9; Schott, Mainz, Germany) was placed between the light source and the condensor and the tissue was observed using a Newvicon camera (C2400-07-C; Hamamatsu, Joko-cho, Japan). All experiments were performed at room temperature (21–23 °C).

Outside-out patch recording

Dendritic and somatic patch-clamp recordings were made using the methods described by Stuart et al. (1993). Patch pipettes were pulled from borosilicate glass tubing (Hilgenberg, Malsfeld, Germany; 2.0 mm outer diameter, 0.5 mm wall thickness) and had resistances of 4–10 MΩ when filled with internal solution, which contained (mm): 140 KCl, 10 EGTA, 10 Hepes, 2 MgCl2, 2 Na2ATP; pH adjusted to 7.3 with KOH. In some recordings Cs+ replaced K+ as the major internal cation. Internal solutions containing Lucifer Yellow were prepared by dissolving 8 mg of solid (Sigma, St Louis, MO, USA) in 50 μl of 100 mm LiCl followed by the addition of 2 ml of internal solution. Following establishment of the whole-cell configuration, the membrane properties of the cell being recorded were investigated to ensure that it was a Purkinje cell. The pipette was then withdrawn to form an outside-out patch and positioned near the mouth of the application pipette. Pulses of glutamate (1–100 ms) were applied to the patch every 3–5 s, and the patch voltage was either held at a constant value or stepped from 0 mV to the desired value 100 ms preceding the glutamate pulse. Patch recordings often lasted 30 min and occasionally longer. No appreciable changes in the kinetics of the glutamate-activated currents were observed during this time, although some run-down of the peak current usually occurred.

Fast application of agonists

The fast application of agonists was carried out as described by Colquhoun, Jonas & Sakmann (1992). Double-barrelled application pipettes were fabricated from theta glass tubing (Hilgenberg; 2 mm outer diameter, 0.3 mm wall thickness, 0.1167 mm septum). Solutions were perfused through control and agonist barrels from two independent, pressurized (20–50 h Pa) reservoirs each with two compartments, allowing exchange of solutions during an experiment; the time required to wash in new solutions was about 15 s, but longer times (1–2 min) were allowed to achieve complete wash-out. The tip of the patch pipette was positioned close to the sharp interface between the two solutions. The application pipette was mounted on a piezoelectric device (P-245.70; Physik Instrumente, Waldbronn, Germany) allowing fast translation of the interface. The properties of individual application pipettes were tested at the beginning of each day of experiments and after every successful recording by perfusing the two barrels with normal rat Ringer (NRR) solution and 10% NRR solution, respectively, and measuring the change in holding current using an open patch pipette. The 20–80% exchange times ranged between 50 and 150 μs.

Data acquisition and analysis

Currents were recorded using an EPC-7 amplifier (List Electronic, Darmstadt, Germany) and filtered at 2–3 kHz (−3 dB) using an 8-pole low-pass Bessel filter (Frequency Devices, Haverhill, MA, USA), except for the experiments used for non-stationary fluctuation analysis, where the corner frequency was 5 kHz. All records were digitized at at least twice the corner frequency using an AD/DA converter board (CED 1401-plus; Cambridge Electronic Design, Cambridge, UK), connected to a personal computer (Dell, Austin, TX, USA). Analysis of currents was performed using interactive programs written by D. Colquhoun (Department of Pharmacology, University College London, UK). Single- and double-exponential fitting were performed using an unweighted least-squares criterion, and concentration–response curves were fitted with the Hill equation using a weighted least-squares criterion. The traces shown represent averages of three to fifteen individual sweeps, unless otherwise indicated. Different measurements were compared using Student's two-tailed t test and differences were considered significant at the P < 0.05 level; the lowest P value is given when reference is made to multiple comparisons. All values are reported as means ±s.e.m. (n, number of patches tested).

The single-channel conductance of the GluR channels was estimated using non-stationary fluctuation analysis (Sigworth, 1980; Spruston, Jonas & Sakmann, 1995). Variances and means (using intervals of 90 ms, starting at the peak of the current) were calculated for groups of ten traces to minimize errors due to run-down of the peak, which was always less than 15% in the patches analysed. The mean variance (σ2) from four to twelve such groups was plotted against the mean current (I), and the data were then fitted with the function:

  • image(1)

where i represents the apparent single-channel current, N is the number of available channels, and σb2 is the background noise variance. Single-channel conductance was calculated as the chord conductance assuming a reversal potential of 0 mV, and maximum open probability was calculated as peak current divided by iN.

The apparent relative permeability of Ca2+versus Cs+, PCa/PCs, was calculated from mean reversal potentials in Ca2+-rich external solutions using the following modified Goldman–Hodgkin–Katz (GHK) equation (Iino, Ozawa & Tsuzuki, 1990):

  • image(2)

where R, T and F have their standard thermodynamic meanings, the concentrations have been corrected using activity coefficients of 0.515 and 0.71 for Ca2+ and Cs+, respectively (see Koh, Geiger, Jonas & Sakmann, 1995), and the reversal potential (Vrev) is corrected for the 10.4 mV junction potential. The fraction of current flowing through the GluR channel carried by Ca2+ (Pf) under physiological conditions was calculated from permeability ratios using a prediction of Pf based on the GHK current equation (Schneggenburger, Zhou, Konnerth & Neher, 1993; Spruston et al. 1995), assuming zero internal and 1.8 mm external Ca2+ concentration, corrected for activity using the coefficient 0.58.

Solutions and drugs

The NRR solution used for perfusion of the application pipette contained (mm): 135 NaCl, 5.4 KCl, 1.8 CaCl2, 1 MgCl2, 5 Hepes; pH adjusted to 7.2 with NaOH. In experiments designed to maximize the probability of NMDA channel activation, 10 μm glycine was added to the solutions in both barrels of the application pipette, and Mg2+ was also omitted from the extracellular solution. The Ca2+-rich external solution used in experiments measuring Ca2+ permeability contained 100 mm CaCl2 and 5 mm Hepes (pH adjusted to 7.2 with Ca(OH)2).

AMPA (Tocris Cookson, Bristol, UK) was stored as a 10 mm stock solution in NRR at −20 °C. 6-Cyano-7-nitroquinoxaline−2,3-dione (CNQX; Tocris Cookson) was stored as a 20 mm stock solution in 0.1 M NaOH at 4 °C, and when used was included in the solutions in both barrels of the application pipette. l-Glutamate, l-aspartate and kainate (Sigma) were stored as 100 mm stock solutions in distilled water at −20 °C. Solutions containing these drugs were prepared freshly each day. Cyclothiazide was from Eli Lilly (Indianapolis, IN, USA), and all other chemicals were from Merck (Darmstadt, Germany), Roth (Karlsruhe, Germany) or Sigma.

Kinetic model

Modelling was carried out using Mathematica 2.2 (Wolfram Research, Champaign, IL, USA) running on a Macintosh computer or a SUN workstation (SUN Microsystems, Mountain View, CA, USA). The mean current response of the model to the various glutamate concentration pulse protocols was computed by solving the occupancy equation (Colquhoun & Hawkes, 1977) using matrix exponentials. The matrix exponential was computed once for each glutamate concentration to give a sum of exponentials with numerical coefficients. Time was left as a symbolic parameter. The extraction of time constants and peak amplitudes from the simulated current responses was done using built-in Mathematica functions for non-linear fitting and minimization of functions, and fitting procedures matched those used on the experimental data as closely as possible.

Unlike the problem of solving the occupancy equation given the rate constants, the inverse problem of estimating a set of rate constants for a kinetic model that optimally represents AMPA receptor kinetics may not have a unique solution. However, it is possible to find a solution that is at least locally optimal. Starting from the initial estimates of the rate constants, some of these were changed by trial and error in order to minimize the difference between experimental observables and model predictions. When improving the model by hand became more and more difficult, a second, automated phase of optimization was begun. For every observable marked with an asterisk in Table 2, the difference between the value predicted by the model and the value measured by experiment was squared and divided by the variance of the experimental value. These terms were summed over the observables to yield the standard chi-square merit function. The chi-square function was minimized over the rate constants subject to the condition of microscopical reversibility of the model. For this purpose we employed the multidimensional minimization algorithm built into Mathematica (FindMinimum), which uses a variant of Powell's conjugate direction set method. Powell's method is very efficient in terms of the number of chi-square function evaluations necessary if, as in our case, the minima are situated in long, narrow ‘valleys’ in parameter space. The termination criteria of the optimization were those of FindMinimum.

Table 2.  Comparison of experimental data with values generated using the model (Scheme 1)
  1. The experimental observables against which model optimization was carried out are indicated by an asterisk; the individual values from the somatic recovery series (see Fig. 12) were also used in the optimization. In the case of double-exponential fits, relative amplitudes (in %) of the fast component are give in parentheses. Model values corrected for finite solution exchange time and low-pass filtering are given in square brackets. Values in A were obtained using 1 mm glutamate.

A.20–80% rise time (ms)*0.28 ± 0.010.24 [0.27]
 Deactivation τ (ms)*1.12 ± 0.041.11
 Desensitization τ1 (ms)*3.44 ± 0.18 (74 %)3.37 (76 %)
 Desensitization τ2 (ms)*14.88 ± 1.1114.04
 Non-desensitizing current (%)*2.3 ± 0.32.14
 Recovery τ from brief-pulse desensitization (ms)33.343.8
 Maximal depression of second pulse (%)4342.6
B.Po,max (5 mm glutamate)*0.74 ± 0.030.71
 Dose–response EC50 (μM)*432441
 Dose–response Hill coefficient*1.161.25
 Equilibrium desensitization IC50 (μM)*8.668.99
 Equilibrium desensitization Hill coefficient*1.081.18
 Desensitization τ at 30 μm glutamate (ms)*20.619.6
 20–80% rise time at 30 μm glutamate (ms)*2.581.31
 Desensitization τ1 at 100 μm glutamate (ms)*6.62 (76 %)6.43 (76 %)
 20–80% rise time at 100 μm glutamate (ms)*1.140.92
 Desensitization τ2 at 200 μm glutamate (ms)4.34 (79 %)4.63 (79 %)
 20–80% rise time at 200 μm glutamate (ms)0.790.67
 Desensitization τ1 at 500 μm glutamate (ms)*3.78 (70 %)3.64 (77 %)
 20–80% rise time at 500 μm glutamate (ms)0.480.39 [0.40]
 Desensitization τ2 at 3 mm glutamate (ms)3.33 (73 %)3.35 (75 %)
 20–80% rise time at 3 mm glutamate (ms)0.250.12 [0.17]
 Desensitization ττ at 10 mm glutamate (ms)3.60 (71 %)3.39 (75 %)
 20–80% rise time at 10 mm glutamate (ms)0.210.07 [0.14]
 Desensitization ττ at 30 mm glutamate (ms)*3.41 (70 %)3.40 (75 %)
 20–80% rise time at 30 mm glutamate (ms)0.200.06 [0.13]


  1. Top of page
  2. Abstract
  6. Acknowledgements

Whole-cell and outside-out patch-clamp recordings were made from the dendritic and somatic membrane of Purkinje cells under direct visual control (Stuart et al. 1993; Stuart & Häusser, 1994). Dendritic recordings were made at distances ranging from the first branch point (typically 40–50 μm from the soma) up to 130 μm from the soma. Most of these recordings were made from the large primary and secondary dendrites, which receive synaptic input predominantly from climbing fibres (Palay & Chan-Palay, 1974). That recordings were in fact made from Purkinje cell dendrites was always verified by testing whether the cells displayed the distinctive electrophysiological properties characteristic of these neurones (Stuart & Häusser, 1994). This was also confirmed in seven out of seven dendritic recordings where the fluorescent dye Lucifer Yellow was included in the pipette solution, which always resulted in filling of the entire dendritic tree of a Purkinje cell (Fig. 1).


Figure 1. Whole-cell patch-clamp recording from a Purkinje cell dendrite

Photomicrograph of a Purkinje cell in a cerebellar slice filled with Lucifer Yellow via a dendritic recording pipette located 80 μm from the soma. Scale bar, 20 μm.

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Pharmacological properties of dendritic GluRs

All patches excised from the dendritic and somatic membrane responded to 100 ms pulses of 1 mm glutamate with a current which rose rapidly to a peak and desensitized rapidly and nearly completely (Fig. 2A). The GluR subtype mediating the glutamate-activated current was investigated by applying several GluR agonists to dendritic and somatic patches. Responses to 1 mm AMPA were very similar in amplitude and time course to those elicited by 1 mm glutamate in the same patches (Fig. 2B); the peak current relative to thatevokedby1 mm glutamate in the same patch was 104.7 ± 2.5% (n= 4) and 101.7 ± 3.4% (n= 4) for dendritic and somatic patches, respectively. The current activated by 1 mm kainate was usually non-desensitizing and the amplitude of the current was much smaller than the peak but always larger than the steady-state desensitized current generated by glutamate or AMPA (Fig. 2C). The peak current evoked by 1 mm kainate was 24.9 ± 3.5% (n= 5) and 23.9 ± 2.8% (n= 5) of the peak current evoked by 1 mm glutamate in the same dendritic and somatic patches, respectively. In a few patches, the kainite-activated current showed a small desensitizing component, which persisted when kainate was applied at a higher frequency (1–2 Hz). Cross-desensitization of AMPA and kainate was performed by first exposing the patch to 1 mm AMPA for 30 s and then applying 1 mm kainate; AMPA pre-desensitization nearly completely abolished the kainite-activated current (n= 3), suggesting that the kainate response is mediated by activation of AMPA receptors.


Figure 2. Pharmacological properties of dendritic GluRs

Currents evoked in a dendritic membrane patch by 100 ms pulses of 1 mm glutamate (A), 1 mm AMPA (B), 1 mm kainate (C), and 1 mm glutamate in the presence of 5 μm CNQX in both control and test solutions (D). All traces were obtained from the same patch. Here and in subsequent figures, the period of application of agonist to the patch is represented by the rectangular pulse at the top of the figure. In D, all solutions contained 10 μm glycine and had no added Mg2+.

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The glutamate-activated current was potently modulated by cyclothiazide, a modulator with a high specificity for AMPA-preferring over kainite-preferring GluR channels (Partin, Patneau, Winters, Mayer & Buonanno, 1993). A low concentration of cyclothiazide (20 μm) substantially reduced desensitization, increasing the steady-state current remaining at the end of a 100 ms pulse of glutamate from < 4% of the peak current in control to 48.3 ± 4.8% in the presence of the drug (n= 3). By contrast, desensitization of glutamate-activated currents in cells expressing recombinant kainite-preferring GluR subunits is unaffected by 100 μm cyclothiazide (Partin et al. 1993).

To test for the presence of NMDA receptor channels, glutamate was applied in the presence of 10 μm glycine and in the absence of added Mg2+, conditions expected to maximize NMDA receptor activation. Under these conditions, the current activated by glutamate could be completely abolished by 5 μm CNQX (n= 4; see Fig. 2D), indicating that it was mediated exclusively by AMPA/kainate receptors. Channel openings consistent with the large-conductance state characteristic of the NMDA receptor channel were never observed in either dendritic or somatic patches. Furthermore, when 1 mm aspartate (n= 4) or 100 μm NMDA (n= 3) were applied to dendritic patches under the same conditions, no response was detected.

These findings suggest that the glutamate-activated currents in patches from Purkinje cells are mediated largely or exclusively by AMPA-preferring receptors assembled from GluRA to D subunits (GluR-1 to 4 subunits).

Kinetics of GluR channels in dendritic patches

The responses of a dendritic patch to pulses of 1 mm glutamate of varying duration are shown in Fig. 3A. The peak currents in response to 1 and 100 ms pulses of 1 mm glutamate were identical, indicating that at this concentration the receptors reach maximum open probability in less than 1 ms. The peak current was variable from patch to patch, and did not appear to depend on the distance from the soma at which the patch was excised, as shown in Fig. 3D; the peak amplitudes of currents evoked in dendritic and somatic patches were comparable when similar-sized pipettes were used. The 20–80% rise time of the current activated by 1 mm glutamate was 0.28 ± 0.01 ms (n= 22) for dendritic patches and 0.28 ± 0.01 ms (n= 33) for somatic patches.


Figure 3. Kinetic properties of dendritic GluR channels

A, overlaid responses of a dendritic patch to 1, 5, 10 and 100 ms applications of 1 mm glutamate. In B and C, the deactivation (1 ms pulse) and desensitization (100 ms pulse) have been fitted with a single exponential function; the individual sampling points are shown to allow better evaluation of the quality of the fit. D–F, relationship of the peak current evoked by 1 mm glutamate at −50 mV (D), the deactivation time constant (deactivation τ; E), and the faster time constant of a double-exponential fit to desensitization (desensitization τ1; F) with distance from the soma at which the patch was excised. The mean ±s.e.m. values from somatic patches are shown as open circles. Linear regression (continuous lines) gave correlation coefficients of −0.05, 0.06 and 0.06 in D, E and F, respectively. All data shown in this figure were obtained from outside-out patches made with electrodes of similar size (∼7 MΩ).

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The decay of the current following the removal of glutamate, defined here as ‘deactivation’, was studied using 1 ms pulses. The time course of deactivation could be fitted with a single-exponential function with a time constant (τ) of 1.23 ± 0.07 ms (n= 16) or 1.12 ± 0.04 ms (n= 32) for dendritic and somatic patches, respectively. In some patches a double-exponential function provided a slightly better fit to the deactivation time course, the values of the time constants being 1.04 ± 0.08 ms (85% of fit amplitude) and 4.59 ± 0.68 ms (15%) for dendritic patches (n= 9) and 1.04 ± 0.08 ms (89%) and 5.60 ± 0.61 ms (11%) for somatic patches (n= 8). The deactivation time constant of the currents activated by AMPA was 3.01 ± 0.35 ms (n= 3), and that of the currents activated by kainate was 1.28 ± 0.11 ms (n= 4).

The time course of receptor desensitization in the continued presence of glutamate was fitted with a single time constant of 5.37 ± 0.26 ms (n= 8) for dendritic patches and 5.29 ± 0.29 ms (n= 21) for somatic patches. In most patches, the sum of two exponentials better described the time course of desensitization, with time constants of 3.58 ± 0.14 ms (70% of fitted amplitude) and 15.72 ± 0.91 ms (30%) for dendritic patches (n= 12), and 3.44 ± 0.18 ms (74%) and 14.88 ± 1.11 ms (26%) for somatic patches (n= 21). The desensitization of the receptors was almost complete, with only 0.8–4% of the peak current remaining at the end of the pulse (2.4 ± 0.4 and 2.3 ± 0.3%, respectively). Desensitization of the current activated by AMPA was also best fitted by two exponentials of 3.52 ± 0.46 ms (71%) and 17.85 ± 2.07 ms (29%) in dendritic patches (n= 4) and 3.28 ± 0.33 ms (71%) and 15.72 ± 1.87 ms (29%) in somatic patches (n= 5). As with glutamate, desensitization of the AMPA-activated current was nearly complete, with 3.0 ± 0.7 and 2.1 ± 0.7% of the peak current remaining at the end of a 100 ms pulse for dendritic and somatic patches, respectively.

None of the kinetic parameters of the glutamate-activated currents measured in dendritic patches were significantly different from those in somatic patches (P > 0.17). Furthermore, the kinetics of the receptors did not depend on the distance from the soma at which the patch was excised (P > 0.3), as shown in Fig. 3E and F.

Concentration dependence of GluR activation

To characterize the concentration dependence of the kinetic parameters measured above, large somatic patches containing many GluRs were used, making it easier to obtain quantitative information. The concentration dependence for the peak glutamate current was examined over the range 30 μm to 30 mm. Traces from a representative patch are illustrated in Fig. 4A and B. The pooled data from several patches, shown in Fig. 4C, were fitted with the Hill equation and gave a half-maximal activation concentration for glutamate of 432 μm and a Hill coefficient of 1.16. The deactivation time constant was independent of concentration over the range 0.1–30 mm, as shown in Fig. 5A. The rate of desensitization, however, was concentration dependent. As shown in Fig. 5C, over the range 0.1–1 mm the time constant of the fast component of desensitization (τ1) was halved, and it then remained relatively constant from 1–30 mm. The amplitude ratio of the two components was only weakly dependent on concentration (not shown). The concentration dependence of the 20–80% rise time of the current activated by long pulses of glutamate is shown in Fig. 5D; for concentrations above 1 mm, the rise time was ≤ 0.2 ms and became limited by the speed of solution exchange and low-pass filtering of the responses.


Figure 4. Concentration–response relationship of glutamate-activated currents in somatic patches

A, currents activated in a somatic patch by brief (1 ms) pulses of different concentrations of glutamate. B, currents activated by long pulses of glutamate at different concentrations in the same patch as in A. Note the increase in the time to peak at lower concentrations. C, concentration–response relationship of the peak current activated by long applications of glutamate. The Hill coefficient is 1.16 and the EC50 is 432 μm. The values on the ordinate represent the amplitude relative to the peak current at 1 mm; each data point is the mean of results from at least 5 patches.

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Figure 5. Concentration dependence of kinetic parameters of somatic GluR channels

Dependence on glutamate concentration of the deactivation τ measured from the decay of currents activated by 1 ms pulses (A); the desensitization τ from the decay of currents activated by 100 ms pulses (B); the (dominant) fast time constant (τ1) from a double-exponential fit of desensitization (C); and the 20–80% rise time from the current activated by 100 ms pulses (D). Data have been pooled from 4–7 patches. The continuous line in each panel shows the values predicted by the kinetic model (Scheme 1; see Discussion). In D, the dotted line represents the model values corrected for finite solution exchange time and low-pass filtering.

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Equilibrium desensitization

To determine whether concentrations of glutamate similar to those present in the extracellular space of the brain are sufficient to cause desensitization of GluRs, somatic patches were exposed to low concentrations of glutamate for at least 1 min before application of 1 mm pulses of glutamate. As shown in Fig. 6, pre-equilibration of the receptors with concentrations in the low micromolar range substantially reduced the response to the test pulse; the response was nearly completely abolished by pre-equilibration with 100 μm glutamate. Pre-equilibration with concentrations ≤ 10 μm did not appreciably alter the kinetics of the glutamate-activated current: in five patches preequilibrated with 5 μm glutamate, the deactivation time constant was 94.2 ± 5.3% of control, and the desensitization time constant was 108.9 ± 3.1% of control. The concentration–inhibition curve for equilibrium desensitization has been superimposed on the curve for activation of the receptors in Fig. 6D. Half-maximal desensitization was achieved at 8.7 μm and the Hill coefficient was 1.08.


Figure 6. Equilibrium desensitization of somatic GluR channels

A, currents activated in a somatic patch by 1 ms (thin trace) and 100 ms (thick trace) pulses of 1 mm glutamate. B, currents activated in the same patch by the same glutamate pulses after pre-equilibration of the patch with 5 μm glutamate for 45 s. C, recovery of the glutamate-activated currents several minutes after returning to glutamate-free solution in the control barrel. The fitted desensitization time constants were 4.90, 5.27 and 5.18 ms, respectively. The fitted deactivation time constants were 0.97, 1.04 and 1.09 ms, respectively, and the 20–80% rise times of the currents were 0.28 ms in each case. D, concentration–response relationship of the peak glutamate-activated current as shown in Fig. 4 (▪) and concentration–response relationship of equilibrium desensitization by glutamate of the current activated by a 1 mm test pulse (•). The half-maximal inhibitory concentration is 8.7 μm, and the Hill coefficient is 1.08; data have been pooled from 5 patches. The values on the ordinates represent the amplitude relative to the peak control current activated by 1 mm glutamate.

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Recovery from desensitization

To determine the rate of recovery of dendritic GluR channels from desensitization, two brief (1 ms) pulses of 1 mm glutamate were applied at varying intervals. As shown in Fig. 7, even such a brief exposure of the receptors to glutamate produced a considerable depression of the subsequent response, with the receptors requiring several hundred milliseconds to recover completely. When the two pulses were separated by very short intervals (< 10 ms), two phenomena became apparent (Fig. 7B). First, the degree of depression of the second pulse was not maximal immediately following the end of the first pulse, but instead increased, reaching a maximum 3–5 ms following the end of the first pulse. Second, the peak of currents activated by pulses applied in the first few milliseconds following the end of the first pulse overlapped with the time course of desensitization of currents activated by a step application of glutamate, a phenomenon known as ‘enveloping’ (Raman & Trussell, 1995). These observations indicate that the receptors continue to desensitize from a closed state following the removal of glutamate (Hestrin, 1993; Raman & Trussell, 1995). The desensitization of the receptors following a 1 ms pulse of 1 mm glutamate could be fitted by a double-exponential function (Fig. 7C), with onset time constants of 2.2 and 1.4 ms, and decay time constants of 35.6 and 33.3 ms for dendritic and somatic receptors, respectively. The maximal extent of desensitization was 44% for dendritic receptors and 43% for somatic receptors.


Figure 7. Recovery from desensitization of dendritic GluR channels

A, superposition of 8 single sweeps from a dendritic patch exposed to two 1 ms applications of 1 mm glutamate separated by different intervals. The mean peak current activated by the first pulse is represented by the dashed line. B, superimposed responses from another dendritic patch to two 1 ms applications of 1 mm glutamate at brief intervals. The response to a step application of 1 mm glutamate has been superimposed as a thick line. C, depression of the response to the second pulse expressed as a percentage of the amplitude of the first pulse, plotted against the time interval of the two pulses. Pooled results from 9 dendritic patches. The data have been fitted with a double-exponential function (one for the rising phase and one for the decaying phase) with time constants of 2.2 and 35.6 ms, respectively; the maximal extent of desensitization was 44%.

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Calcium permeability

The voltage dependence of the peak glutamate current was examined in both dendritic and somatic patches, and was found to be essentially linear over the voltage range −100 to +60 mV, as shown in Fig. 8. With NRR solution as the external solution, the current reversed polarity near 0 mV in dendritic and somatic patches, indicating that these channels are approximately equally permeable to Na+ and Cs+ ions.


Figure 8. Current–voltage relationship of dendritic GluR channels

A, currents in a dendritic patch activated by 1 ms pulses of 1 mm glutamate at different holding potentials with external NRR solution and a Cs+-rich internal solution. Membrane potential was varied between −100 and 40 mV in steps of 20 mV. B, current–voltage relationship of the glutamate-activated peak current from the same patch as in A. The data were fitted using a second-order polynomial, giving a reversal potential of −5.2 mV.

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In order to determine the Ca2+ permeability of the GluR channels, reversal potential measurements were carried out with an external solution in which Ca2+ replaced all monovalent cations. As shown in Fig. 9, under these conditions the reversal potential of the glutamate-evoked current was considerably hyperpolarized with respect to that recorded in the standard Na+-rich external solution, and averaged −51.4 ± 2.9 mV (n= 4) in dendritic patches and −51.5 ± 2.8 mV (n= 4; P > 0.9) in somatic patches. From these values the relative permeability of these channels to Ca2+ and Cs+ was calculated using eqn (2), which gave a PCa/PCs of 0.053 for both dendritic and somatic GluR channels. By assuming that ions pass independently through the pore of the channel and that the permeability to monovalent cations is identical, it is possible to estimate the fractional Ca2+ current of the channels under physiological conditions (1.8 mm external Ca2+, at −60 mV; Schneggenburger et al. 1993; Spruston et al. 1995), which was calculated to be 0.23% for both dendritic and somatic channels. These findings suggest that the relative permeability of the GluR channels to Ca2+ is rather low in these neurones.


Figure 9. Calcium permeability of dendritic GluR channels

A, response of a dendritic patch to 100 ms pulses of 1 mm glutamate in Ca2+-rich external solution, using a Cs+-rich internal solution. Membrane potential was varied between −100 and 40 mV in steps of 20 mV. B, the current–voltage relationship of the peak current from the same patch. The data were fitted with a third-order polynomial, giving a reversal potential of −58.0 mV.

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Channel conductance

It was not possible to clearly resolve single-channel transitions corresponding to the opening and closing of the individual GluR channels, suggesting that their conductance must be relatively low. Therefore, the method of Sigworth (1980) was used to estimate the conductance from the variance around the mean of currents activated by successive applications of high concentrations of glutamate. Typically, 40–100 sweeps of responses to 5 mm glutamate were gathered (Fig. 10A), and from the relationship of the variance versus the mean current (Fig. 10B; eqn (1)) the single-channel conductance was determined to be 8.3 ± 0.8 pS (n= 5) for dendritic patches and 8.2 ± 0.8 pS (n= 7) for somatic patches. The probability of any given channel being open at the peak was as high as 0.83 and averaged 0.70 ± 0.03 (n= 5) and 0.74 ± 0.03 (n= 7) for dendritic and somatic patches, respectively.


Figure 10. Single-channel conductance of dendritic GluR channels

A, currents in a dendritic patch activated by 10 successive 100 ms applications of 5 mm glutamate at −70 mV. The average of the 10 responses has been superimposed (grey line). B, variance versus mean current plot from 5 ensembles of 10 sweeps each. The data have been fitted with eqn (1), giving a mean single-channel conductance of 8.1 pS and a maximum open probability at the peak of 0.80.

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A summary of the experiments performed on dendritic and somatic outside-out patches from Purkinje cells is given in Table 1. None of the measured parameters were significantly different between dendritic and somatic patches (P > 0.17).

Table 1.  Comparison of the properties of GluR channels in dendritic and somatic membrane patches from cerebellar Purkinje cells
  1. γ, single-channel conductance; Po,max, maximum open probability at the peak. All experiments (except those for the determination of γ and Po,max) were performed with 1 mm pulses of glutamate. Dendritic patches were excised 40–130 μm from the soma (mean = 72 μm). Values of n are given in parentheses. For double-exponential fits to desensitization the relative amplitudes of desensitization τ1 are given as a percentage.

20–80% rise time (ms)0.28 ± 0.01 (22)0.28 ± 0.01 (33)
Deactivation τ (ms)1.23 ± 0.07 (16)1.12 ± 0.04 (32)
Desensitization single τ (ms)5.37 ± 0.26 (8)5.29 ± 0.29 (21)
Desensitization τ1 (ms)3.58 ± 0.14 (70 %) (12)3.44 ± 0.18 (74 %) (21)
Desensitization τ2 (ms)15.72 ± 0.91 (12)14.88 ± 1.11 (21)
Non-desensitizing current (%)2.4 ± 0.4 (12)2.3 ± 0.3 (13)
Recovery τ from brief-pulse desensitization (ms)35.633.3
Maximal depression of second pulse (%)4443
Ca2+/Cs+ reversal (mV)−51.4 ± 2.9 (4)−51.5 ± 2.8 (4)
γ (pS)8.3 ± 0.8 (5)8.2 ± 0.8 (7)
Po,max0.70 ± 0.03 (5)0.74 ± 0.03 (7)

Glutamate receptor channel properties in neonatal Purkinje cells

The Purkinje cell dendritic tree is elaborated postnatally, with a period of explosive development between postnatal day 7 and 15 (P7 and P15) in the rat (Berry & Bradley, 1976). It is therefore of interest to study the GluR channels before the genesis of the dendritic tree to determine whether there is any difference in their properties associated with development. To address this question we examined the kinetics of glutamate-activated currents in outside-out patches excised from the soma of Purkinje cells in slices from P4 rats, which have virtually no dendrites (Berry & Bradley, 1976).

All patches responded to the application of 1 mm glutamate with a current which rose rapidly to a peak (20–80% rise time of 0.28 ± 0.02 ms). Deactivation was fitted with a time constant of 1.34 ± 0.24 ms (n= 7), and desensitization was fitted with either a single time constant of 4.97 ± 0.51 ms (n= 6) or with two exponentials of 3.57 ± 0.57 ms (71%) and 12.02 ± 2.10 ms (29%; n= 5). As in patches from more mature Purkinje cells, desensitization was relatively complete, with only 2.0 ± 0.8% of the peak current remaining at the end of a 100 ms pulse. Non-e of these values were significantly different from those found in more mature (P12–18) Purkinje cells (P > 0.13).

In some patches from neonatal Purkinje cells, application of glutamate in the presence of 10 μm glycine and no added Mg2+ produced occasional single-channel openings of an amplitude consistent with the 38 pS conductance NMDA receptor channels recently reported in neonatal Purkinje cells (Momiyama, Feldmeyer & Cull-Candy, 1996). These openings were infrequent and were not analysed in further detail.

These findings suggest that the development of the dendritic tree and the innervation by excitatory synapses are not accompanied by major changes in the kinetic properties of the AMPA/kainate GluR channels in Purkinje cells.


  1. Top of page
  2. Abstract
  6. Acknowledgements

The results presented here provide a detailed description of the properties of GluR channels in Purkinje cells. There were no appreciable differences in patches from dendritic and somatic membrane, suggesting that synaptic and extrasynaptic GluR channels are identical. These findings and their implications are discussed in detail below.

Synaptic and extrasynaptic GluR channels

It is difficult to assess the relative contribution of synaptic and extrasynaptic receptors to glutamate-activated currents measured in outside-out patches excised from dendritic membrane. Purkinje cells have one of the densest synaptic innervations of any neurone in the brain (Palay & Chan-Palay, 1974), and their dendrites are heavily covered with synapses, the majority of which are excitatory. Therefore it is likely that a substantial fraction of dendritic patch membrane is of synaptic origin. If this is correct, then one can conclude on the basis of the data presented here that synaptic and extrasynaptic receptors have similar properties and may be identical. This conclusion is in agreement with the anatomical distribution of GluR subunits demonstrated in Purkinje cells, as both GluR-A and GluR-B/C subunit immunoreactivity has been found in dendritic and somatic extrasynaptic membrane, as well as in the postsynaptic density (Baude, Molnar, Latawiec, McIlhinney & Somogyi, 1994; Nusser, Mulvihill, Streit & Somogyi, 1994). Similarly, no differences were found recently between GluRs in dendritic and somatic patches from hippocampal pyramidal cells (Spruston et al. 1995). Other evidence that synaptic and extrasynaptic channels are similar, at least in terms of channel conductance, has recently been obtained for glycine, GABA and NMDA receptor channels (Takahashi & Momiyama, 1991; Borst, Lodder & Kits, 1994; Clark, Farrant & Cull-Candy, 1997). The function of these extrasynaptic receptors is unclear. The resting ambient concentration of glutamate in the extracellular space is too low to activate AMPA receptors directly, except perhaps under pathological conditions. However, it is conceivable that these extrasynaptic receptors may be activated by synaptically released glutamate, particularly when many quanta are released synchronously from neighbouring synapses. Taken together, these findings suggest that the GluRs are not modified as they move from the soma towards the synapses in the dendritic membrane. Furthermore, it appears that somatic GluRs can be considered to be representative of those in the synaptic membrane.

AMPA receptors mediate the glutamate-activated current in outside-out patches

The responses mediated by glutamate in dendritic patches were mediated largely or exclusively by the AMPA subtype of GluR, composed of the GluR-A to -D subunits (GluR-1 to -4). This conclusion is based on several lines of evidence. First, the response to AMPA closely resembled the response to glutamate in the same patch. Second, responses to kainate were usually non-desensitizing, and when a desensitizing component was observed, it was small and did not show the frequency dependence characteristic of kainite-preferring GluR channels (Burnashev, 1993). Third, cross-desensitization with AMPA virtually abolished the kainite-activated current, suggesting that kainate is acting on AMPA-type receptors in these cells. Finally, cyclothiazide potently modulated desensitization of the glutamate-activated current, a characteristic selective for GluRs assembled from AMPA receptor subunits (Partin et al. 1993). It cannot be excluded, however, that a small fraction of the current evoked by glutamate is due to an action on kainite-preferring receptors, particularly when Purkinje cells have been shown to contain mRNA for the kainite-preferring subunits KA−1, KA-2 and GluR-5 (Ruano, Lambolez, Rossier, Paternain & Lerma, 1995).

The density of functional NMDA receptor channels in the dendritic and somatic membrane was judged to be very low or zero. This is in line with previous evidence that Purkinje cells lack functional NMDA receptors beyond the first postnatal week (Perkel, Hestrin, Sah & Nicoll, 1990; Farrant & Cull-Candy, 1991; Llano et al. 1991; Momiyama et al. 1996). The absence of aspartate-activated currents in dendritic patches is in agreement with recent observations made using somatic patches (Barbour et al. 1994), and is also consistent with previous evidence that aspartate is selective for NMDA receptors and has only low affinity for non-NMDA receptors (Patneau & Mayer, 1990).

Glutamate receptor channels in Purkinje cells have low permeability to Ca2+

The low average Ca2+ permeability of the dendritic GluR channels measured in these experiments is in agreement with imaging experiments demonstrating that currents generated by bath application of AMPA or kainate under voltage-clamp conditions are not associated with significant increases in intracellular Ca2+ (Tempia et al. 1996). AMPA/kainate receptors showing permeability to Ca2+ have been reported in Purkinje cells in cultures from embryonic rats (Brorson, Bleakman, Chard & Miller, 1992), indicating that the properties of these receptors may be different in culture. Recombinant GluR channels showing relative impermeability to Ca2+ display a linear current–voltage relationship (Burnashev, 1993), as do the glutamate-activated currents reported here; since the current–voltage relationship of the synaptic current is also linear in Purkinje cells (Perkel et al. 1990; Llano et al. 1991), this suggests that the synaptic GluR channels are also relatively impermeable to Ca2+. The low fractional Ca2+ current estimated for physiological concentrations of external Ca2+ is consistent with recent estimates from a combined fluorometric–electrophysiological approach in neonatal Purkinje cells (Tempia et al. 1996). This indicates that the large voltage-dependent dendritic Ca2+ signals resulting from synaptic stimulation in Purkinje cells (Eilers, Augustine & Konnerth, 1995; Denk, Sugimori & Llinás, 1995), which can lead to plastic changes such as LTD (Linden, 1994), arise primarily via the activation of dendritic voltage-sensitive Ca2+ channels, possibly also involving the release of Ca2+ from intracellular stores. Denk et al. (1995) have demonstrated a subpopulation of spines in Purkinje cells where the Ca2+ signals in response to synaptic stimulation increase rather than decrease upon hyper-polarization. This suggests that synaptic GluR channels are heterogeneous with respect to Ca2+ permeability, or that spines may have different relative densities of AMPA receptors and Ca2+ channels.

Clues to the molecular composition of GluR channels in Purkinje cells

GluR channels in Purkinje cells are unusual in that they display both low Ca2+ permeability and relatively rapid gating kinetics; GluR channels in other neuronal types with similarly rapid gating kinetics have a relatively high Ca2+ permeability (e.g. neocortical interneurones and hippocampal basket cells; Geiger et al. 1995; Koh et al. 1995), and those with similarly low Ca2+ permeability have much slower kinetics (e.g. neocortical and hippocampal pyramidal cells; Colquhoun et al. 1992; Spruston et al. 1995; Geiger et al. 1995). Given that low Ca2+ permeability appears to be determined by the edited version of the GluR-B subunit (Burnashev, 1993; Geiger et al. 1995), this suggests that the functional GluR channels in Purkinje cells incorporate this subunit, consistent with the high level of expression of the GluR-B subunit found using in situ hybridization (Keinänen et al. 1990), immunocytochemistry (Petralia & Wenthold, 1992), and single-cell reverse transcriptasepolymerase chain reaction (Lambolez, Audinat, Bochet, Crepel & Rossier, 1992; Tempia et al. 1996). As there is a strong positive correlation between the degree of expression of the flip version of GluR-B and the kinetics of the functional receptors (Geiger et al. 1995; Lambolez, Ropert, Perrais, Rossier & Hestrin, 1996), the rapid kinetics of the GluR channels in Purkinje cells suggests that in these neurones the GluR-B subunit exists predominantly in its flop form. There is also a negative correlation between receptor channel kinetics and the expression of the GluR-D subunit (Geiger et al. 1995; cf. Lambolez et al. 1996), but since in Purkinje cells this subunit is only expressed at a very low level, if at all (Keinänen et al. 1990; Lambolez et al. 1992; Tempia et al. 1996), it probably does not play a determining role. The results from Purkinje cells therefore suggest that Ca2+ permeability and gating kinetics of GluR channels can be determined independently, and that similar kinetic phenotypes can be generated by assembly of different subunit combinations. It remains to be determined whether other differences in the functional properties of the receptors, such as their single-channel conductance, can be traced to differences at the molecular level.

Number of GluR channels mediating excitatory synaptic events

The mean single-channel conductance estimated from non-stationary noise analysis was in the order of 8 pS in dendritic and somatic patches, which represents a weighted mean of all the possible conductance states that the GluR channels can adopt. Previous studies have shown that the GluR agonists AMPA, kainate and quisqualate can activate channels with a variety of conductances in Purkinje cells, ranging from 2.5 to 18 pS (Llano, Marty, Johnson, Ascher & Gähwiler, 1988; Farrant & Cull-Candy, 1991); it is still unclear whether these different conductances arise from a single channel or several different channel types. The mean conductance found here is somewhat lower than that found for pyramidal cells in the hippocampus and cortex (∼10 pS; Hestrin, 1993; Spruston et al. 1995) and is considerably lower than that found in nucleus magnocellularis neurons (∼18 pS; Raman & Trussell, 1995) and in hippocampal and cortical interneurones (∼25 pS; Hestrin, 1993; Koh et al. 1995) using similar techniques. Given that quantal excitatory synaptic currents in Purkinje cells have a peak conductance ranging from 70 to over 1000 pS (Barbour, 1993; M. Häusser, unpublished observations), this suggests that, on average, from 9 to over 125 GluR channels are open at the peak of these events.

Functional relevance of GluR desensitization

Aside from the possibility that desensitization may shape the decay of the synaptic current (see below), there are several ways in which desensitization of GluR channels may be of functional importance. Glutamate receptor channels in Purkinje cells appear to share a common kinetic phenotype with other GABAergic neurones in the brain; GABAergic interneurones in the neocortex (Hestrin, 1993; Geiger et al. 1995; Lambolez et al. 1996), hippocampal dentate gyrus (Koh et al. 1995) and cerebellum (Barbour et al. 1994) have GluR channels with similar kinetics to those of Purkinje cells. The rapid and nearly complete desensitization of these GluRs may help protect these GABAergic neurones under conditions in which the extracellular glutamate concentration rises to neurotoxic levels. Alternatively, the rapid kinetics of these channels may be necessary in order to help maintain a precise temporal relationship between presynaptic activity and postsynaptic firing via a rapidly rising and decaying quantal synaptic current, which is particularly important given the rapid firing rates that GABAergic neurones exhibit in vivo.

The recovery from desensitization of the GluR channels is also relevant to synaptic integration at single release sites. Climbing fibres have been shown to be active at rates up to 10 Hz in vivo (Montarolo, Palestini & Strata, 1982), and individual parallel fibres are occasionally active above 10 Hz (Merrill, Wall & Yaksh, 1978), frequencies at which cumulative postsynaptic depression of the GluRs can occur. If synaptic contacts release transmitter reliably then the rate of recovery from desensitization will limit temporal summation at climbing fibre and parallel fibre inputs. Evidence that the rate of recovery from desensitization may be relevant to synaptic depression in Purkinje cells is provided by paired-pulse stimulation of single climbing fibres, which produces comparable depression of the second EPSC to that observed in the patches (Konnerth, Llano & Armstrong, 1990; Perkel et al. 1990), although presynaptic factors are undoubtedly also involved. The response to successive activation of single parallel fibres has not yet been determined; although paired-pulse data are available for compound parallel fibre inputs, these involve the possibly unreliable stimulation of hundreds of fibres, which is difficult to interpret (Merrill et al. 1978).

Synaptically released glutamate may not only inhibit the response to subsequent release at the same release site, but also at neighbouring release sites to which glutamate diffuses in sufficient concentrations. The close spacing of synapses on the Purkinje cell (Palay & Chan-Palay, 1974) and the low concentrations required for significant desensitization (see Fig. 6) suggest that such ‘surround inhibition’ of the synapses adjacent to active release sites may occur, particularly when several neighbouring synapses are active concurrently.

Another important way in which desensitization of GluR channels will regulate the size of EPSCs is via equilibrium desensitization of GluRs by ambient glutamate. The concentration of ambient glutamate is unknown, but has been estimated to be around 1–3 μm (e.g. Lerma, Herranz, Herreras, Abraira & Martin del Rio, 1986); from the dose–response curve for equilibrium desensitization shown in Fig. 6, this predicts that up to 20–30% of the synaptic GluRs will be desensitized under resting conditions. Given that the ambient glutamate concentration in the cerebellum has been shown to be controlled by the tonic activity of glutamate uptake pumps (Barbour et al. 1994), small changes in the efficacy of uptake may therefore have a major impact on the efficacy of synaptic transmission to Purkinje cells. In support of this hypothesis, block of glutamate uptake has been shown to reduce the amplitude of climbing fibre and parallel fibre EPSCs, which may occur due to desensitization of synaptic GluRs via local elevation of extracellular glutamate (Barbour et al. 1994; Takahashi, Kovalchuk & Attwell, 1995).

A kinetic model for AMPA-type GluR channels in Purkinje cells

To better understand the kinetic behaviour of AMPA-type GluR channels in Purkinje cells, a detailed kinetic model of these channels was constructed. Such a model is useful for several reasons. First, it provides a compact representation

  • image(Scheme 1)

[Kinetic scheme of the model used to represent AMPA receptor channels in Purkinje cells. The rate constants of the respective transitions are given at the bottom. Glutamate concentration is denoted byc. For further details see text.] of the experimental data, which can be used in simulations. Second, it can suggest novel features of channel behaviour and thereby direct new experiments. Third, it is useful for examining conditions which are difficult or impossible to achieve experimentally, in particular the non-rectangular glutamate waveforms such as are likely to occur in the synaptic cleft. Finally, such a model is ultimately necessary to fully understand, on a quantitative basis, the processes generating the synaptic current.

The starting point of the kinetic model was the model for somatic AMPA/kainate receptor channels in hippocampal CA3 pyramidal cells described by Jonas, Major & Sakmann (1993). This model assumes two binding sites for glutamate, six closed states and one open state, and describes most aspects of the kinetics of AMPA receptor channels in CA3 cells satisfactorily. In order to reproduce the double-exponential desensitization in Purkinje cells, two more closed states were added at the right of the state diagram to yield Scheme 1. The model has a total of nine states, where C0 is the unliganded closed state, C1 is the singly liganded closed state, and C2 is the doubly liganded closed state (c denotes glutamate concentration). C3 to C7 are desensitized (closed) states, with C3 being singly liganded and C4 to C7 doubly liganded. O is the doubly liganded open (conducting) state. The initial estimates for the rate constants in this model were the values in set 1 of Jonas et al. (1993) together with estimates for the rates connecting to C6 and C7. The model data were compared with fast-application data obtained from somatic patches, for which a more complete range of parameters was available; since dendritic patches were not significantly different from somatic patches in the measured parameters, the model should reproduce the behaviour of dendritic GluRs as well. The model was initially improved by hand before starting an automated phase of optimization (see Methods).

Currents generated by the model in response to pulses of glutamate are shown in Figs 11 and 12, and a comparison of the behaviour of the model with the experimentally observed values for a wide variety of different parameters is shown in Table 2. In general, the model was able to reproduce the experimental data faithfully, with the differences between model and experiment usually being within a few per cent, i.e. within (random) experimental error. In particular, the concentration dependence of desensitization was well conserved, which had been a problem in the model proposed by Jonas et al. (1993). Many features of GluR channel gating, such as the degree of desensitization following a brief pulse of glutamate, the EC50 for activation and the IC50 for equilibrium desensitization, the ‘enveloping’ property at brief interpulse intervals (Fig. 12B), and the open probability with 5 mm glutamate were also well reproduced by the model. The fact that parameters against which optimization had not been carried out were determined equally successfully to parameters which had been optimized against provided further independent confirmation of the model. One feature of the experimental data was not optimally represented by the model, namely the rise times of currents activated by low concentrations of glutamate (< 100 μm), which were somewhat too rapid in the model. This may be due either to an intrinsic problem of the model, or because in the fast application experiments at these low concentrations glutamate equilibrates relatively slowly with the receptors in an outside-out patch, due, e.g. to microscopic ‘diffusion pockets’ or binding to other high-affinity glutamate binding sites such as transporters or metabotropic receptors.


Figure 11. Glutamate-activated currents simulated by the kinetic model

The currents in A–C were calculated using the kinetic model (Scheme 1) assuming 100 available GluR channels; all receptors were exposed to the same glutamate concentration. A, currents activated by 1, 5, 10 and 100 ms pulses of 1 mm glutamate. Compare with Fig. 3A. B, currents activated by long pulses of glutamate at different concentrations, indicated beside the traces. Compare with Fig. 4B. C, a simulated quantal EPSC in response to a biexponentially decaying pulse of glutamate. The glutamate pulse (see Clements, 1996) rises instantaneously to a peak concentration of 3.11 mm and decays with time constants of 0.1 ms (87%) and 2.1 ms (13%); the vertical scale of the glutamate concentration is the same in A and C. The decay of the current could be fitted by a single-exponential function with a time constant of 2.06 ms.

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Figure 12. Recovery of simulated glumate-activated currents from desensitization

A and B, currents activated by two 1 ms pulses of 1 mm glutamate at varying intervals. In B, the response to a long pulse of 1 mm glutamate has been superimposed (thick line). Compare with Fig. 7A and B. C, plot of the percentage depression of the peak current activated by the second pulse of 1 mm glutamate for somatic (○) and dendritic (•) receptors in outside-out patches. The corresponding curve (continuous line) from the kinetic model has been superimposed.

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Despite its faithfulness to the experimental data, the present model has several limitations. First, the chosen kinetic scheme is essentially arbitrary; although the addition of each state was based on a particular feature of the data, it is possible that there exist other schemes which may reproduce the experimental data equally well or better. However, in our opinion the model represents the simplest possible scheme which accurately reproduces all features of the available kinetic data (see also Jonas et al. 1993). Second, the model was based on values derived from macroscopic currents, and not on single-channel data. Since it is possible that GluRs in Purkinje cells are a heterogenous population (e.g. composed of different subunit combinations with different properties; see Geiger et al. 1995; Lambolez et al. 1996), the present model represents an ‘ensemble average’ of the behaviour of all the receptor types. Single-channel recording will help to resolve this question, and will also allow a more reliable determination of particular states of the model (e.g. the number of open states). Finally, there are certain effects which are not accounted for and/or easily represented by such a model, e.g. modulation of kinetic properties by phosphorylation or Ca2+.

The present model is very similar in structure to the CA3 model (Jonas et al. 1993) from which it was developed, as well as to a model for AMPA receptors in hippocampal basket cells (A. Roth & P. Jonas, unpublished results), which has the same states as the CA3 model but different rate constants. The robustness of the estimation of individual rate constants in the present model can be examined by comparing them with the analogous rate constants in these other optimized models. The estimated rate constants for glutamate binding to and unbinding from non-desensitized AMPA receptors in Purkinje cells (Scheme 1) typically differ by a factor of 1.2–4 from the corresponding rate constants found for the CA3 model and the basket cell model. The same holds for the rate constants describing transitions between the doubly liganded closed state (C2) and the open state (O). The relatively small differences in these rate constants primarily reflect the different properties of the AMPA receptors in each cell type; AMPA receptor currents in CA3 cells are approximately 2–3 times slower than those in Purkinje cells and basket cells, which have very similar kinetics, and up to 4-fold differences exist in the EC50 and IC50 values for the three cell types (Colquhoun et al. 1992; Koh et al. 1995; Spruston et al. 1995). Some other rate constants which are not directly associated with glutamate binding, unbinding, or channel opening are also well conserved between these three models, e.g. kC3C1, which is involved in determining the time constant of recovery from desensitization. The present model also bears some structural similarity to a model of AMPA receptors in cochlear nucleus neurones (Raman & Trussell, 1995), which have extremely fast gating kinetics, with the key difference being that the latter model has three open states. Both the present model and the model of Raman & Trussell (1995) have a relatively low value of kC1C3 to match the concentration dependence of desensitization; in the present model this is achieved without assuming very different affinities for C1 and C2, which was necessary in the Raman & Trussell (1995) model.

Comparison of GluR channel kinetics and EPSC time course

Climbing fibre and compound parallel fibre EPSCs have been reported to have a relatively slow decay time course, several times slower than EPSCs in most other neuronal types (Perkel et al. 1990; Llano et al. 1991; Barbour et al. 1994; Takahashi et al. 1995). One possible explanation for this discrepancy, that cerebellar Purkinje cells have synaptic GluR channels with unusually slow kinetics, is rendered unlikely by the present results, confirming the findings of Barbour et al. (1994) with somatic patches. To simulate the quantal synaptic current generated by a synaptic glutamate concentration waveform, we examined, as a first approximation, the response of the kinetic model to the glutamate transient estimated from experiments using displacement of a low-affinity antagonist to map the time course of glutamate in the synaptic cleft at cultured hippocampal synapses (Clements, 1996). This glutamate waveform produced a simulated quantal EPSC (Fig. 11C), which decayed with a single time constant of 2.06 ms, which is still considerably faster than the decay of climbing fibre and compound parallel fibre EPSCs reported previously. Assuming that the behaviour of the receptors in dendritic patches is similar to those at the synapse, this suggests three main possibilities. First, the EPSCs measured previously may have been distorted by poor space clamp. Second, asynchrony in the release of individual quanta may prolong the time course of EPSCs composed of many quanta. Alternatively, the time course of glutamate in the synaptic cleft may be prolonged at Purkinje cell synapses, such that desensitization of the receptors contributes significantly to shaping the EPSC decay.


  1. Top of page
  2. Abstract
  6. Acknowledgements

We thank Bert Sakmann for support, Peter Jonas and Jörg Geiger for helpful discussions, David Colquhoun for computer programs and advice, Philippe Ascher and Claudia Racca for their comments on the manuscript and Marlies Kaiser for expert technical assistance. M.H. was supported by a fellowship of the Alexander von Humboldt Foundation.