| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
The Journal of Neurophysiology Vol. 80 No. 2 August 1998, pp. 504-519
Copyright ©1998 by the American Physiological Society
Born-Bunge Foundation, University of Antwerp-UIA, B2610 Antwerp, Belgium
 |
ABSTRACT |
|---|
 Abstract
 Introduction
Methods
Results
Discussion
References
|
|---|
De Schutter, Erik. Dendritic voltage and calcium-gated channels amplify the variability of postsynaptic responses in a Purkinje cell model. J. Neurophysiol. 80: 504-519, 1998. The dendrites of most neurons express several types of voltage and Ca2+-gated channels. These ionic channels can be activated by subthreshold synaptic input, but the functional role of such activations in vivo is unclear. The interaction between dendritic channels and synaptic background input as it occurs in vivo was studied in a realistic computer model of a cerebellar Purkinje cell. It previously was shown using this model that dendritic Ca2+ channels amplify the somatic response to synchronous excitatory inputs. In this study, it is shown that dendritic ion channels also increased the somatic membrane potential fluctuations generated by the background input. This amplification caused a highly variable somatic excitatory postsynaptic potential (EPSP) in response to a synchronous excitatory input. The variability scaled with the size of the response in the model with excitable dendrite, resulting in an almost constant coefficient of variation, whereas in a passive model the membrane potential fluctuations simply added onto the EPSP. Although the EPSP amplitude in the active dendrite model was quite variable for different patterns of background input, it was insensitive to changes in the timing of the synchronous input by a few milliseconds. This effect was explained by slow changes in dendritic excitability. This excitability was determined by how the background input affected the dendritic membrane potentials in the preceding 10-20 ms, causing changes in activation of voltage and Ca2+-gated channels. The most important model variables determining the excitability at the time of a synchronous input were the Ca2+-activation of K+ channels and the inhibitory synaptic conductance, although many other model variables could be influential for particular background patterns. Experimental evidence for the amplification of postsynaptic variability by active dendrites is discussed. The amplification of the variability of EPSPs has important functional consequences in general and for cerebellar Purkinje cells specifically. Subthreshold, background input has a much larger effect on the responses to coherent input of neurons with active dendrites compared with passive dendrites because it can change the effective threshold for firing. This gives neurons with dendritic calcium channels an increased information processing capacity and provides the Purkinje cell with a gating function.
Single neuron physiology and the functional properties of voltage-gated channels usually are studied in the slice preparation. It is not always clear, however, how such studies apply to the in vivo situation, where neurons may very well behave differently due to the presence of continuous background synaptic input (for Purkinje cells, see Fig. 1 of Jaeger and Bower 1994 Purkinje cell model
The compartmental Purkinje cell model has been described in detail elsewhere (De Schutter and Bower 1994a Synaptic input
Because of computational constraints, only a fraction of the parallel fiber inputs are represented in the model (De Schutter and Bower 1994b Data analysis
Responses to synchronous input were measured as the amplitude of the EPSP in the passive soma, i.e., the difference between somatic peak membrane potential and baseline membrane potential at the time of synaptic activation. Other commonly used measures, like the EPSP integral and half-width, showed similar variability as the EPSP amplitude. A dendritic spike was defined as a transient change of the somatic membrane potential that crossed Autocorrelations
Part of the analysis in this report was based on the use of two different autocorrelations over time (Fig. 7B). The autocorrelation over time of the baseline membrane potential was computed by selecting consecutive reference points in the somatic membrane potential computed during a particular simulation run and correlating them to data points generated later by the same simulation. This was repeated over 400 different simulations, resulting in n = 300,000 for each point in Fig. 7B. Data for the autocorrelation over time of the peak EPSP potential were generated by first simulating a reference EPSP and then repeating the simulation with identical background input while activating the synchronous input at later times (Fig. 7A). The reference peak EPSP potential was then autocorrelated with the peak potentials of the later triggered EPSP (n = 400).
Suprathreshold EPSPs
In the discussion, I present a simple analysis of how postsynaptic variability determines the likelihood of an EPSP being suprathreshold, which is expressed as the fraction of suprathreshold EPSPs (Fig. 10). To emphasize the dendritic contribution to differences between active and passive dendrite models, a similar effective voltage threshold for the peak amplitude of the EPSP was used for both models (3.5 mV above the mean somatic baseline potential). Using a realistic voltage threshold for the passive model (taking into account the low baseline membrane potential: 13 mV) resulted in a shift of the response curve to the right (800 inputs required for a suprathreshold response) without changing the slope of the curve. The use of a voltage threshold for the peak amplitude of the EPSP underestimated the number of spikes that the full spiking model would generate (Koch et al. 1995
This report studies the interaction between dendritic voltage and Ca2+-gated channels and the continuous background synaptic input that neurons are assumed to receive in vivo, and how this interaction affects the integration of suprathreshold synaptic inputs. In a model as complex as the Purkinje cell model (De Schutter 1994
Difference between membrane potential in active and passive dendrites
The somatic membrane potential was always more depolarized in the active dendrite model than in the passive model: mean Voltage dependency of the amplification of variability
If the increased variability of the membrane potential is due to the activation of dendritic voltage-gated channels, it should be voltage dependent. Figure 2 compares the SD of the membrane potential of the active model versus that of the passive model for different mean somatic membrane potentials. Whenever the mean somatic membrane potential was between
Variability of the somatic EPSPs
Next the suprathreshold response caused by the synchronous activation of 200 excitatory inputs was examined. It was shown previously that dendritic P-type Ca2+ channels amplify the somatic response of the model to such synchronous inputs (De Schutter and Bower 1994c Size of the synchronous input
A first parameter that was studied is the number of synchronous inputs activated (Fig. 3). In both models, the response amplitude increased linearly over the range of activated inputs studied, which represented <1% of the parallel fibers contacting a Purkinje cell (Harvey and Napper 1991
Robustness of results for changes in background input
The wide range of membrane potentials shown in Fig. 2 was produced by systematically changing the frequencies of the background excitatory and inhibitory input. The effect of these changes on the size and variability of the somatic EPSP in response to a synchronous activation of 200 excitatory inputs is shown in Fig. 4. Remember that the input frequencies of background input used in the model do not represent the firing rate of individual axons (see MODEL AND METHODS).
Robustness of results for changes in model parameters
After demonstrating the robustness of the variable amplification for changes in the background input, its sensitivity to model parameters will be described. In the original paper describing the model used (De Schutter and Bower 1994a
Time dependence of the variability
The somatic EPSP in response to a synchronous input was highly variable in the active model because its dendritic excitability was not constant (Figs. 1, 3, and 4). This raises the question of how fast this excitability changed. Figure 7A shows how the somatic EPSP changed when the synchronous input was provided at different times during an identical pattern of background input. In the active dendrite model, the first three EPSPs in this example had a similar amplitude, even though they started from very different baseline membrane potentials. The fourth and subsequent EPSPs clearly were reduced in amplitude. This example suggests that the dendritic excitability of the active model did not change fast. As expected, the differences in the passive dendrite were much smaller.
Does the membrane potential predict the amplitude of the response?
Finally we consider the factors causing the increased variability of somatic EPSPs in the active dendrite model. As the amplification process is voltage dependent (Fig. 2) (De Schutter and Bower 1994c Which dendritic channels are responsible for the variable amplification?
The higher correlation of variable amplification with the past dendritic membrane potential compared with that with the membrane potential at the time of the synchronous input (Fig. 8) suggests that activation of voltage and Ca2+-gated channels was involved, raising the question of which of these channels was most important in determining the excitability. The results of Fig. 5 already pointed to the importance of the CaP channel and of the two Ca2+-activated K+ channels in the model.
One of the central goals of neurobiology is to understand how neurons process synaptic input and transform it into action potential firing (Shepherd 1990 Limitations of the present modeling study
ACCURACY IN MODEL PROPERTIES.
A question that always arises with modeling is if the results have relevance to the real system. Of course the final answer to this is experimental verification (see further), but other arguments are relevant too. The main modeling result, i.e., the variable amplification of EPSPs, depended on only two conditions: the presence of amplification by dendritic Ca2+ channels and the presence of other voltage- and Ca2+-gated channels that could modulate their activation. It is beyond doubt that dendritic Ca2+ and K+ channels are present in Purkinje cells (Gruol et al. 1991 LIMITATIONS OF THE MODELING APPROACH.
Because a passive membrane soma was used in all simulations, synaptically evoked changes in somatic membrane potential and EPSP amplitude could be studied without interference of somatic voltage-gated processes. Although this facilitated the analysis of the modeling results (De Schutter and Bower 1994c Experimental evidence for variable amplification of EPSPs
Unfortunately the synaptic amplification mechanism in Purkinje cells has not yet been studied experimentally, although evidence for synaptic activation of dendritic Ca2+ channels exists (Denk et al. 1995 Functional consequences of variable amplification of EPSPs
CONSEQUENCES IN GENERAL.
What are the functional consequences of the amplification of postsynaptic variability? A simple analysis of the effect on spike initiation is presented in Fig. 10, where the thick lines show the fraction of suprathreshold responses caused by different sized synchronous stimuli in the passive dendrite model versus the active one. The slopes of these curves reflect the background induced variability in the system, as with a steady membrane potential and constant amplification, the fraction of suprathreshold responses would jump from 0 to 100%. The much more shallow response curve in Fig. 10B demonstrates that the active dendrite model behaved quite differently from the passive one. The 10-90% fraction suprathreshold responses spanned a difference of 160 synchronous inputs in the active dendrite model, compared with only 80 in the passive model. It should be noted that the data in Fig. 10 also can be interpreted as the mean response of a population of neurons receiving an identical synchronous input but different background input.
CONSEQUENCES FOR CEREBELLAR FUNCTION.
This leads to specific predictions on cerebellar function when the cerebellar anatomy is considered. A crucial question in understanding synaptic integration by Purkinje cells is the effectiveness of single parallel fiber inputs. Classic theories of cerebellar function (Albus 1971
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
; for other neurons, see Destexhe et al. 1996; Paré and Lebel 1997). Theoretical studies have shown that background input changes the passive cable properties of dendrites, thus affecting synaptic integration (Bernander et al. 1991; Holmes and Woody 1989; Rapp et al. 1992). It also has been suggested that synaptic integration by a passive dendrite cannot explain the irregular firing observed in neurons in vivo (Softky and Koch 1993). Recently, it has become clear that most dendrites are not passive. Instead, dendritic Ca2+ channels have been demonstrated in many neurons, including cerebellar Purkinje cells (Llinás and Sugimori 1980a) and neocortical (Amitai et al. 1993) and hippocampal (Regehr and Tank 1992) pyramidal neurons. Several groups have used the slice preparation to show that subthreshold excitatory inputs can activate dendritic Ca2+ channels (Denk et al. 1995; Eilers et al. 1995; Magee and Johnston 1995; Markram and Sakmann 1994; Regehr and Tank 1992). A combined experimental and modeling study demonstrated that background synaptic input can modify the bursting discharges caused by dendritic Ca2+ channels in thalamic reticular neurons (Destexhe et al. 1996).
,b) is based on all available experimental data and is not specifically tuned to simulate the responses to synaptic inputs. Because it is actually quite successful in reproducing such responses, the model can be considered to have predictive power (De Schutter and Bower 1994b). For example, in the model focal parallel fiber activation leads to localized voltage-gated Ca2+ inflow in the spiny dendrite (De Schutter and Bower 1993, 1994c). This model prediction was confirmed experimentally by others who used confocal imaging (Eilers et al. 1995) or dual photon microscopy (Denk et al. 1995) to demonstrate Ca2+ inflow in the spiny dendrite caused by parallel fiber activation. The same model also showed that background inhibition is essential to obtain the normal irregular in vivo firing pattern of Purkinje cells (De Schutter and Bower 1994b) and that, in fact, on average the inhibitory synaptic current in the Purkinje cell dendrite exceeds the total excitatory parallel fiber synaptic current (Jaeger et al. 1997). These predictions were confirmed by blocking inhibition in vivo, which changes the Purkinje cell firing pattern to the typical regular in vitro one (Jaeger and Bower 1994) and by the use of a dynamic clamp in vitro (Jaeger and Bower 1996). Recently others also showed the importance of inhibition for the irregular spiking of Purkinje cells (Häusser and Clark 1997).
; De Schutter and Bower 1992).
MODEL AND METHODS
Abstract
Introduction
Methods
Results
Discussion
References
,b). The model is based on a reconstructed Purkinje cell (Rapp et al. 1994), discretized into 1,600 compartments. Two versions of this model are used: a completely passive one and one with an active dendrite but passive soma (see also De Schutter and Bower 1994c). The active dendrite compartments contained two types of Ca2+ channels, a P type (CaP) (Llinás et al. 1989) and a T type (CaT) (Kaneda et al. 1990); two types of Ca2+-activated K+ channels, a BK type (KCa) (Latorre et al. 1989) and a K2 type (K2) (Gruol et al. 1991); and a persistent K+ channel. The proximal part of the dendrite contained in addition low densities of voltage-gated K+ channels, i.e., the delayed rectifier Kdr (Gähwiler and Llano 1989; Gruol et al. 1991) and the A current (KA) (Gruol et al. 1991; Hounsgaard and Midtgaard 1988).
) and K+ channels were absent from the model. This allowed measurement of excitatory postsynaptic potentials (EPSPs) in the soma instead of trains of action potentials, which simplifies the statistical analysis of responses to synaptic input (De Schutter and Bower 1994c).
). GENESIS 2.1 simulation scripts can be downloaded from http://bbf-www.uia.ac.be/CEREBELLUM (SYNCHROPASS9.g script).
). The 1,474 background parallel fiber inputs (onto the same number of passive spines) corresponded to ~1% of the total granule cell input onto a rat Purkinje cell (Harvey and Napper 1991). A standard approximation that may compensate for the reduced number of excitatory inputs modeled is to increase the firing rate of these synapses (Rapp et al. 1992). It was shown previously that such an approximation is valid for the interspike interval distributions in the Purkinje cell model (De Schutter and Bower 1994b) and that the necessary increase in rate scales linearly with the inverse of the fraction of inputs simulated. The number of inhibitory inputs onto the dendrite was 1,695 (De Schutter and Bower 1994b), which probably is close to the real number of inputs (Jaeger et al. 1997; Sultan et al. 1995).
. This state was evoked by background input consisting of random asynchronous excitatory (Poisson distribution, mean frequency 28 Hz) and inhibitory input (1 Hz). Such input caused the full model to fire simple spikes at a realistic rate of ~65 Hz. Note that the asynchronous input frequencies are arbitrary values, which need to be scaled for the number of inputs represented (see preceding text and De Schutter and Bower 1994b). The real activation rates of these inputs in vivo are not known. EPSPs were evoked by synchronously activating 200 excitatory synapses distributed equally over the dendrite after 400 ms of simulation (always denoted as time 0 in the figures).
20 mV.
View larger version (23K):
[in a new window]
FIG. 7.
Changes in dendritic excitability over time. A: somatic response produced by providing the synchronous excitatory input at different times (10-ms separation) during identical background input patterns in the active dendrite model (top) and passive model (bottom). B: autocorrelation over time for the baseline membrane potential in the soma (solid lines) and for the EPSP peak potential (dashed lines) for the active (thick lines) and the passive (thin lines) dendrite models.
) but required fewer simulations. Simulations with 250 different background input patterns were repeated for each number of synchronous inputs (range 0-320). The synchronous input was applied after 400 ms of simulation (denoted as time 0) or at 405 and 430 ms for a subset of 10 simulations. Identical background input patterns were used for each input size in both the passive and the active dendrite models.
View larger version (27K):
[in a new window]
FIG. 10.
Functional importance of amplification of postsynaptic variability by active dendrites. A: fraction of suprathreshold EPSPs evoked by different-sized synchronous inputs in the passive dendrite model. Fraction computed for a large sample of different background input patterns (n = 250, thick line) is shown together with the fractions for a smaller sample (n = 10) where the synchronous input was activated at different times (0 ms, 5 or 30 ms). B: fraction of suprathreshold EPSPs in the active dendrite model; same conventions as in A.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
), it is not easy to separate the effects of the synaptic input from those of the dendritic voltage-gated channels (Jaeger et al. 1997; see also later sections of this report). Therefore most of this study systematically compares the somatic responses of a purely passive Purkinje cell model to those of a model with an active dendrite. This strategy makes it possible to study the interactions between voltage-gated channels and background input without separating their respective effects and allows general statements about the properties of active dendrites to be made. In all simulations, both versions of the model received identical background and synchronous synaptic input so that any difference in the somatic response was entirely due to the presence of dendritic voltage- and Ca2+-gated channels in the active dendrite model. Moreover, the study was restricted to the differences in somatic membrane potential fluctuations and in somatic EPSPs caused by synchronous excitatory inputs evenly distributed over the dendritic tree. Background input was simulated as randomly activated subthreshold excitatory and inhibitory inputs (De Schutter and Bower 1994b), also evenly distributed over the dendritic tree.
View larger version (34K):
[in a new window]
FIG. 1.
Somatic membrane potential fluctuations and variability of the somatic excitatory postsynaptic potential (EPSP) in a passive membrane model (left) compared with an active dendrite model (right). A: examples of EPSPs recorded in the soma. Traces shown were selected to have similar membrane potentials at the time of the synchronous input. Note the large variability in amplitude and shape of EPSPs in the active dendrite model. B: distributions of somatic membrane potentials just before synchronous input (baseline membrane potential). Bars represent measured values; the mean ± SD is shown (n = 2,500). White curves show normal distribution with corresponding mean and SD. C: distributions of peak EPSP amplitudes, graphs as in B.
51.50 mV compared with 61.32 mV (n = 2,500; Fig. 1B). This reflected the activation of a dendritic plateau potential (Llinás and Sugimori 1980a) by the background input in the active dendrite model (De Schutter and Bower 1994b). We have demonstrated previously in this model that, under the conditions simulated here, the tonically activated dendritic voltage-gated currents exceed the currents caused by the background synaptic input (Jaeger et al. 1997).
2), while they were not in the active model (P < 0.001). These fluctuations were (indirectly) caused by the Poisson background input as it was the only source of randomness in the model. In the passive dendrite model, the membrane potential fluctuations were the summation of many subthreshold synaptic potentials as demonstrated by their normal distribution. In the active model, however, the fluctuations cannot be explained by simple synaptic summation as they were not normally distributed. Moreover, one would expect synaptic potentials to be smaller in the active model because of the decreased input impedance due to the activation of voltage-gated channels (Bernander et al. 1991; Jack et al. 1975; Rapp et al. 1992). Therefore, the larger membrane potential fluctuations in the active model were clearly caused by the (in)activation of dendritic voltage and Ca2+-gated channels due to their interaction with the background input. In other words, the active dendrite amplified the variability of the membrane potential compared with a passive dendrite.
65 and 46 mV, the variability of the membrane potential was much larger in the active dendrite model than in the passive one. This voltage range encompasses the activation threshold of the P-type dendritic Ca2+ channels present in the model (Regan 1991; Usowicz et al. 1992). But while the variability was voltage dependent, it was relatively constant within this voltage range. This was evident from the low correlation of the SD with somatic voltage in the active model (r = 0.43 in the range of 65 to 46 mV). Conversely, in the passive dendrite model these values were highly correlated (r = 0.96), which reflected the effect of the change in driving potential of (mainly the inhibitory) background input on the membrane potential fluctuations (e.g., Fig. 4A).
View larger version (17K):
[in a new window]
FIG. 2.
Relation of somatic membrane potential fluctuations, measured as the SD, to the mean somatic membrane potential (n = 80,000) for passive dendrite ( 
) and active dendrite models (
). Different membrane potentials were obtained by changing the excitatory (range 6-90 Hz) and inhibitory (range 0.5-2.0 Hz) background input frequencies.
View larger version (24K):
[in a new window]
FIG. 4.
Effect of changing background input frequency on the amplitude of the somatic EPSP (mean ± SD displayed, n = 200) for passive dendrite ( ) and active dendrite models (, 
). A: excitatory input frequency was increased from 6 to 90 Hz while the inhibitory frequency remained constant at 1 Hz. B: inhibitory input frequency was increased from 0.6 to 2.0 Hz while the excitatory frequency remained constant at 28 Hz. C: simulation of the effect of blocking background inhibitory input on EPSPs in slice. Two models received either no background synaptic input (top thick lines) or 1- or 2-Hz background inhibition (thin lines). Slice conditions were simulated by the absence of excitatory background input (Häusser and Clark 1997), traces at 78 mV were aligned by somatic injection of current.
). Here these results were confirmed: the mean amplitude of the EPSP was 4.59 mV in the active dendrite model compared with 3.44 mV in the passive one (Fig. 1C). But although the De Schutter and Bower study (1994c) considered only the averaged somatic EPSPs, it is clear from Fig. 1A that individual traces were quite noisy and variable in shape and amplitude. The variability was in both models completely and reproducibly determined by the background input patterns. A closer examination of Fig. 1A also shows that the EPSPs in the active dendrite model were much more variable in shape and amplitude than those in the passive model. For example, the EPSP peak membrane potential was 46.93 ± 1.36 mV in the active dendrite model and 57.88 ± 0.56 mV in the passive one (P < 0.001 for SD values, 2-sided F test). Moreover, the variability of the EPSP peak potential (SD 1.36 mV) was larger than that of the baseline for the active model (SD 1.14 mV, P < 0.001), whereas there was no significant difference for the passive model (P > 0.2). This means that the active dendrite model displayed a larger variability of the somatic response to synchronous input than the variability of the baseline membrane potential. In other words, the active dendrite amplified not only the size of the response but also its variability, whereas the passive dendrite amplified neither. The underlying mechanisms are explored later, but the difference in shapes of the EPSPs, in particular of the undershoot after the EPSP, already suggest that differential activation of Ca2+-activated K+ channels played an important role.
). In the passive dendrite, the SD of the response was constant (P > 0.5, 2-sided F test), i.e., independent of the size of the input and confirming the absence of any amplification. Therefore the interaction between background and synchronous inputs in the passive model can be described as additive or, in other words, as a coincidence effect. In the active dendrite model, however, the amplification mechanism increased both the mean response and its variability when 
100 excitatory inputs were activated. The SD of responses to small inputs was dominated by the baseline membrane potential fluctuations (e.g., 1.11 ± 0.62 mV for 50 inputs). When more inputs were activated, the SD of the active model increased with the mean, resulting in a close to constant coefficient of variation (0.17 for 200 inputs, 0.16 for 500 inputs). This constant coefficient of variation confirmed that the amplification of response amplitude and variability were intrinsically linked with each other in the active dendrite model, suggesting a common sensitivity to dendritic excitability.
View larger version (13K):
[in a new window]
FIG. 3.
Effect of number of synchronously activated excitatory inputs on the amplitude of the somatic EPSP (mean ± SD displayed, n = 200) for passive dendrite ( ) and active dendrite models ().
), increasing the background input frequency had two effects: it reduced the input impedance of the model (Bernander et al. 1991; Rapp et al. 1992) and changed the membrane potential to more depolarized (Fig. 4A: increasing excitatory frequency) or hyperpolarized (Fig. 4B: increasing inhibitory frequency) levels. The reduced input impedance combined with the reduced driving potential for excitatory inputs explains the progressive reduction of the passive dendrite EPSP amplitude in the case of increasing excitatory background frequency. In the case of increased inhibitory frequency, the two effects opposed each other: the reduced input impedance was more than compensated for by an increase in driving potential, causing a slowly increasing EPSP amplitude.
60 mV average baseline membrane potential (Fig. 4, ), the amplification mechanism was not very effective and the active membrane EPSP amplitude was close to the passive one. Above 60 mV (Fig. ), the amplitude of the EPSP was amplified to a variable extent, depending on the mean baseline membrane potential. In the case of increasing excitatory background frequency (Fig. 4A), the amplification mechanism initially overcame the reduced input impedance and driving potential, causing a progressively increasing EPSP amplitude in the active dendrite model (range 16-34 Hz, corresponding to 60 to 50 mV mean baseline membrane potential), whereas that in the passive dendrite model diminished. When the mean baseline membrane potential increased beyond 50 mV, however, the amplification mechanism saturated and the active EPSP amplitude also progressively declined.
60 mV, the EPSPs in the active and passive dendrite models were similar, but beyond 60 mV the somatic EPSPs in the active dendrite model were progressively more amplified. Below 0.6 Hz background inhibition, the active dendrite model started generating dendritic Ca2+ spikes in response to the synchronous input, like those seen during current injection in vitro (Llinás and Sugimori 1980a).
), it was concluded that removing background inhibition had a substantial effect on the decay time of the EPSP, roughly doubling it, whereas its amplitude changed only by a few percent. These experimental results confirm the theoretical prediction that background input should affect the time constant much more than it does the input impedance (Rapp et al. 1992; see also Holmes and Woody 1989). In Fig. 4C, it is demonstrated that similar results were obtained in both the passive and active dendrite models. Comparison of Fig. 4C with Fig. 7B of Häusser and Clark (1997) demonstrates that the active dendrite model replicated the experimental data better than the passive one. Specifically, the excitatory input caused a small activation of Ca2+ channels in the active dendrite model, which diminished the apparent decay constant compared with that of the passive model. Note, however, that because of the hyperpolarized membrane potential, the activation was insufficient to amplify the EPSP in the active dendrite model.
). As a consequence, the increase in inhibitory driving potential incremented the SD of the EPSPs in the passive membrane model with increasing excitatory input frequency (from 0.19 mV at 6 Hz to 0.32 mV at 90 Hz in Fig. 4A). But in Fig. 4B, the increase in inhibitory driving potential was more than compensated for by the decrease in inhibitory input frequency, resulting in a slowly decreasing SD (from 0.32 mV at 2 Hz to 0.28 mV at 0.6 Hz). It is also noteworthy that at 52 Hz excitatory background input, the somatic baseline potential of the passive dendrite model approximated that of the active model under standard conditions (51.2 mV, compare with Fig. 1B), but the amplitude of the passive EPSP and its variability (2.80 ± 0.33 mV, Fig. 4A) remained much smaller, confirming the fundamental differences between the active and passive models.
60 to 50 mV. This corresponded to the physiological range in vivo (Jaeger and Bower 1994; Jaeger et al. 1997). Although we have shown the robustness over only a limited range of background frequencies, the same was true for much higher or lower input background frequencies (results not shown), provided the membrane potential was in the physiological range (see also De Schutter and Bower 1994b; Jaeger et al. 1997).
), we described the robustness of the firing evoked by intracellular current injection to changes in the main free parameters of the model, i.e., the maximum conductances (
) of the voltage and Ca2+-activated channels. The sensitivity of the model synaptic responses to these parameters has never been described, mainly because these responses were considered to be emergent properties of a model that was not specifically tuned to reproduce them (De Schutter 1994). In the present context it is, however, important to demonstrate that the variable amplification mechanism does not depend critically on the fine tuning of the Purkinje cell model.
for a single channel type in all dendritic compartments of the active model for the Ca2+ channels (Fig. 5A) and for the K+ channels (Fig. 5B). Besides demonstrating the robustness of the model, this figure also indicates which channel types are important in causing the variable amplification. As shown in De Schutter and Bower (1994c), the P-type Ca2+ channel was responsible for the amplification of the somatic EPSP. Reducing its led to a progressive reduction of the amplification (Fig. 5A, ) until at 40% of the normal , the response could no longer be distinguished from that in a completely passive dendrite. As in Figs. 3 and 4, the variability of the response followed its amplitude, although the coefficient of variation (c.v.) did not remain constant as it did in Fig. 3. This is not surprising as the model c.v. dropped from that of the standard active model (0.19) to that of the standard passive model (0.09) when the of the CaP channels was set to zero. Only modest increases of the for the CaP channels were possible before the model responses became unphysiological. Similar to the effects described in De Schutter and Bower (1994a) increasing the CaP conductance by >30% changed the threshold for dendritic Ca2+ spike generation, causing the synchronous input to sometimes evoke full-blown dendritic spikes (
). This caused a large increase of the SD because the mean response included both normal EPSPs and dendritic spikes of 30 mV.
View larger version (22K):
[in a new window]
FIG. 5.
Effect of changing the densities ( ) of voltage-gated channels on the amplitude of the somatic EPSP (mean ± SD displayed, n = 200) for the active dendrite model. A: for the P-type (CaP; and ) and T-type (CaT; 
) Ca2+ channels were changed relative to their normal value. Increases of the CaP by >30% led to dendritic spiking (). B: same for the K+ channels in the model: the Ca2+-activated K+ channels, BK type (KCa; and ) and K2 type (K2; and 
), and the voltage-gated persistent K+ channel (
) and A current (KA; ). Large decreases of the KCa or K2 led to dendritic spiking ( and ). Note that for the latter, some of the SD bars are not displayed completely. For the simulations, the KA channel was present in the complete dendrite with a constant density indicated relative to the normal in the proximal dendrite (see text).
, the T-type Ca2+ channel in the model is not involved in the amplification mechanism and changing its had little effect on the amplitude or variability of the somatic EPSP (Fig. 5A, ). The small decrease of EPSP amplitude caused by increasing its can be explained by the progressive depolarization and the effect this had on the amplification mechanism (see Figs. 4 and 8).
View larger version (15K):
[in a new window]
FIG. 8.
Correlation of somatic EPSP amplitude with mean dendritic membrane potential at times indicated before the activation of the synchronous input in the active membrane model (thick line) and passive membrane model (thin line).
of K+ channels in the model is demonstrated. First, changing the density of voltage-gated K+ channels had very little effect on the variable amplification. This is demonstrated for the persistent K+ channel () and for the A-type K+ channel (). In the standard model, the A-type channel is present in the proximal smooth dendrite only (De Schutter and Bower 1994a), but because this channel has recently been shown to be important in regulating dendritic excitability in pyramidal cells (Hoffman et al. 1997) and a similar role has been suggested in Purkinje cells (Hounsgaard and Midtgaard 1988; Midtgaard et al. 1993), the simulations shown in Fig. 5B used a model with the KA channel present in every dendritic compartment (using the same as in the proximal dendrite for the standard case).
for the KA channels, however, led to a decreased amplification and variability, similar to the effects of decreasing CaP (Fig. 5A). A similar and stronger effect was observed for the two Ca2+-activated K+ conductances in the model, the KCa (Fig. 5B, ) and K2 channels (). The effect of these three channel types on the amplification mechanism can be explained by their role in dynamically setting the threshold for activation of the CaP channel, as described for the Ca2+-activated K+ conductances in De Schutter and Bower (1994a). In effect, decreasing the conductance for the Ca2+-activated K+ conductances had the opposite effect: it increased the amplification and its variability because it enhanced activation of the CaP channel. Eventually the lower threshold for CaP channel activation led again to the generation of full-blown dendritic Ca2+ spikes and this at relatively small decreases of for the KCa channel () compared with the decreases necessary for the K2 channel (). It is unlikely that this difference could be explained by the smaller of the K2 channel in the standard model, as the K2 channel actually generates the largest current when the dendrite is not actively spiking (De Schutter and Bower 1994a). A more probable cause was the intrinsic compensatory dynamics of the K2 channel described in De Schutter and Bower (1994a). Because the K2 channel is activated by small increases in the Ca2+ concentration, a decrease of its , which leads to more subthreshold CaP activation and more Ca2+ influx, will immediately cause a higher activation of the remaining K2 conductance, resulting in a comparatively small decrease in the K2 current.
of the model also modified the average membrane potentials of the model, which by itself will affect the amplification mechanism (Figs. 2 and 8). Therefore an additional series of simulations was run to measure the effect of changing the of the three channel types that caused the most pronounced effects in Fig. 5 (CaP, KCa, and K2) under the condition of a constant baseline membrane potential. The membrane potential was controlled by changing the frequency of the background excitatory input. The findings are shown in Fig. 6, where the white bars reprise the results of Fig. 5, i.e., with changing membrane potential but constant background input, whereas the gray bars show the effect of simultaneously changing the background input to keep the baseline potential constant. For all three conductances, the differences between the two conditions were minimal.
View larger version (23K):
[in a new window]
FIG. 6.
Effect of somatic membrane voltage on the amplitude of the somatic EPSP in models with changed densities for the voltage-gated channels. A: interaction between changes in CaP conductance and membrane voltage. , replicated data from Fig. 5; they represent, from left to right, the amplitude of the somatic EPSP (mean ± SD displayed, n = 200) for a that reduces the SD to ~50% of its normal value, the standard case, and a that doubles the SD. In each column the relative , the frequency of the background excitatory input, and the resulting average somatic membrane potential (in mV) are printed. Note that besides its effect on the amplification, changes of also influenced the baseline membrane potential. 
, effect shown of changing the frequency of the background excitatory input so as to bring the baseline membrane potential to the same level as in the standard case ( =1). B: same for changes in the KCa conductance. C: same for changes in the K2 conductance.
) of the Purkinje cell (46 ms) (Rapp et al. 1994). The faster decay of the autocorrelation function can be explained by the background synaptic input, which increased the membrane conductance of the model and therefore decreased its time constant. The effects of background synaptic input on the time constant of passive models have been analyzed in detail by others (Bernander et al. 1991; Holmes and Woody 1989; Rapp et al. 1992). Active membrane models do not have a true membrane time constant, but, because of their effect on membrane conductance, activation of ion channels should decrease the "effective" (continuously changing) membrane time constant (De Schutter and Bower 1994a; Jack et al. 1975), resulting in a faster decay of the autocorrelation function. Instead, during the first 12 ms, the autocorrelation function of the active dendrite model decreased more slowly than that of the passive model. This then was followed by a much faster decay resulting in a zero correlation after 40 ms. The initially high autocorrelation function of the active dendrite model indicates that changes of dendritic excitability were relatively slow.
), increasing the nonlinear effects on the autocorrelation curve.
), the membrane potential was examined first as a possible predictor of the amplitude of the somatic response to synaptic input. This was not the case for the membrane potential at the time of activation of the synchronous input, as it showed no correlation at all with the subsequent EPSP amplitude in the active dendrite model (r = 0.09, n = 2,500; the passive dendrite model showed a weak correlation with r = 0.31). This implies that the somatic baseline membrane potential did not reflect the immediate excitability level of the active dendrite.
) was examined. The mean dendritic membrane potential was, like the somatic membrane potentials, much more variable (P < 0.001, 2-sided F test) in the active dendrite (51.49 ± 1.26 mV, n = 74) than in the passive dendrite model (61.37 ± 0.53 mV). For both the active (r = 0.16) and the passive dendrite model (r = 0.25), the average dendritic membrane potential at the time of activation of the synchronous input showed a small negative correlation with the amplitude of the somatic EPSP. In the case of the passive dendrite model, this negative correlation reflected the increase in driving potential of synchronous excitatory input at more hyperpolarized levels. In the active dendrite model, it was more relevant to look at the correlation between somatic EPSP amplitude and mean dendritic membrane potential sometime before the synchronous input (Fig. 8). Although the correlation of the passive dendrite model remained relatively constant (up until the time constant, of 36 ms, no statistical difference compared with time 0 ms: P > 0.10, 2-sided F test), it increased in the active dendrite model from 0.16 at time 0 to 0.61 at time 18 ms before the synchronous input (P < 0.05). This increased correlation with dendritic potentials backward in time can be explained by the delays imposed by the (in)activation time constants of the voltage and Ca2+-gated channels. In other words, the background synaptic input had not an immediate effect on the excitability of the dendrite but worked indirectly by first changing the dendritic membrane potential and subsequently the activation of the ionic channels in the dendrite. Note also that both the autocorrelation curve of Fig. 7 and the correlation curve of Fig. 8 turned to zero at ~40 ms after or before the EPSP, respectively, suggesting that this is an important time frame in the variable amplification. Finally, the negative correlation of Fig. 8 shows that the amplification was increased by deactivation and deinactivation of dendritic channels, i.e., relative hyperpolarization increased the size of subsequent EPSPs.
40 ms before the synchronous input determine the size of the amplification (Fig. 8). Here we try to determine, however, if a single model variable can be found that accurately predicts (and controls) at the time of the synchronous input what will be the amplitude of the EPSP. Earlier it was shown that this is not the case for the somatic membrane potential and only poorly so for the average dendritic membrane potential (Fig. 7).
), the background synaptic input has only an indirect effect on the excitability of the dendritic tree, resulting in a low correlation between the activation of excitatory and inhibitory synaptic conductances and the somatic EPSP. For the voltage-gated channels, the correlation analysis of Table 1 would suggest that the most important variables were the voltage-dependent deactivation and deinactivation of the T-type Ca2+ channel, deactivation of the persistent K+ channel, and the Ca2+-deactivation of the Ca2+-activated K+ channels, because all of these correlations were significantly higher than the negative correlation with the mean dendritic membrane potential. This correlation analysis should be interpreted with caution, however, as the correlations may have been caused indirectly by the correlation with membrane potential (Fig. 8). In fact, it is noticeable that some of the highest correlations were with currents of very small amplitude in the model, i.e., the T-type Ca2+ channel and persistent K+ channel, which were previously shown not to be important for the variable amplification mechanism (Fig. 5). All of the (in)activation factors mentioned had, in the voltage range 60 to 50 mV, an activation time constant of ~10 ms (De Schutter and Bower 1994a). In other words, the most likely explanation for these high correlations is that a high negative correlation with membrane potential ~20 ms before the stimulus (Fig. 8) corresponded to a deactivation or deinactivation of these currents at the time of the synchronous input. It is unlikely that any of these four currents were a causal factor for the variability of amplification.
View this table:
TABLE 1.
Correlation and variable switching analysis of factors causing variable amplification
View larger version (10K):
[in a new window]
FIG. 9.
Example of variable switch analysis. A and B: somatic EPSP in response to identical synchronous inputs with different background input patterns (thick lines; amplitude 5.1 and 2.9 mV, respectively). Thin traces show the effect of switching the respective patterns of background input between the 2 simulations at the time of activation of the synchronous input. ···, effect of switching, in addition to the background, the Ca2+-activation of the Ca2+-activated KCa conductances; - - -, effect of switching both Ca2+-activated K+ conductances (KCa and K2). Amplitudes of the respective EPSPs are indicated.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
). The simplest description of this process is the integrate-and-fire model, but it is unlikely that such models capture the complexity of real neurons. For example, previous studies have demonstrated that the Purkinje cell model is not an integrate-and-fire model. In fact, the Purkinje cell dendrite is most of the time slightly hyperpolarized compared with the soma, so that the dendrite operates as a current sink (Jaeger et al. 1997). One exception is during the response to a synchronous excitatory input, which activates dendritic voltage-gated Ca2+ channels and actively charges the soma (De Schutter and Bower 1994c).
). An extensive analysis (Fig. 9, Table 1) demonstrated that the variability of dendritic excitability could not be attributed to a single channel type. Nevertheless, on average the Ca2+-gated K+ channels were more important than other ionic channels in the model. The effect of Ca2+-activated K+ channels also showed the importance of the dendritic Ca2+ concentration as a controlling factor of the excitability. This could not be studied in more detail in the present model because Ca2+ concentration was computed as a simple exponentially decaying pool (De Schutter and Bower 1994a). More realistic simulations including Ca2+ diffusion and buffering (De Schutter and Smolen 1998) will be required to fully investigate the relation between Ca2+ concentration and dendritic excitability.
; Llinás and Sugimori 1980a; Usowicz et al. 1992), but do they have the densities and kinetic properties required?
; Usowicz et al. 1992; see De Schutter and Bower 1994a), suggesting that these kinetics can indeed support the amplification of EPSPs (see also Fig. 2 of De Schutter and Bower 1994c). The kinetics of the Ca2+-activated K+ channels in the model are only approximative (De Schutter and Bower 1994a) and therefore may differ from those in real Purkinje cells. But as several K+ channels support the variable amplification (e.g., Fig. 5 and Table 1), it is likely that changes in their kinetics would change the modeling results only quantitatively (for example the time constants in Figs. 7 and 8), without affecting the main result.
), as in the model. The results from Figs. 5 and 6 suggest that the variable amplification was robust for changes in channel densities but that a minimum density of P-type Ca2+ channels was required, and sufficient K+ channels had to be present to prevent spontaneous dendritic Ca2+ spikes. The maximum Ca2+ current density in the model is actually lower than that reported experimentally in immature Purkinje cells (Llano et al. 1994), but this may be related to the high specific capacitance used for the model (see Jaeger et al. 1997). Nevertheless, the experimental data (Llano et al. 1994) support the high density of Ca2+ channels required for the amplification mechanism and, as predicted by the model (De Schutter and Bower 1994c), focal parallel fiber input can activate those channels (Denk et al. 1995; Eilers et al. 1995). The arguments for high densities of Ca2+-activated K+ channels is more indirect. It is known that Purkinje cells can be depolarized to fire somatic spikes without generating dendritic Ca2+ spikes (Häusser and Clark 1997; Llinás and Sugimori 1980b). It seems logical to expect that the Ca2+-activated K+ channels that are present in the dendrite (Gruol et al. 1991) and that can be activated by Ca2+ at membrane potentials lower than those used in this study (Wang and Augustine 1995) play an important role in suppressing dendritic spikes, though others have suggested that A-type K+ channels may be important too (Midtgaard et al. 1993).
), it does not allow for exact predictions of how the variable dendritic excitability changes simple spike firing. Several other voltage-dependent processes may influence action potential firing (Koch et al. 1995), e.g., the refractory period (Jack et al. 1975) and the large Na+ plateau potentials present in the soma of Purkinje cells (Callaway and Ross 1997; Llinás and Sugimori 1980b). Unfortunately in the model the Na+ plateau potentials are generated by the window current of the fast Na+ channel (De Schutter and Bower 1994a), making it impossible to study their effect in absence of spiking.
). Moreover, only one source of noise was considered in the model, i.e., the variability in timing of subthreshold excitatory and inhibitory input, also called the postsynaptic variability (Gossard et al. 1994). Other sources of noise in the preparation, like the stochastic opening of single channels (Hille 1991), stochastic transmitter release (Allen and Stevens 1994), and thermal noise, were not modeled. Because of computational constraints, it was not possible to include the stochastic mechanisms in the computer model, because this would require simulation of each single channel and of each synaptic contact. In experimental recordings, it has been demonstrated that noise can enhance the response to weak inputs (Collins et al. 1996; Pei et al. 1996) and stochasticity of single channel kinetics may be important in this context (Bezrukov and Vodyanoy 1995). Similarly, changes in stochastic transmitter release processes may play an important role in plasticity (Stevens and Wang 1994) and learning. Nevertheless, Fig. 10 demonstrates that the postsynaptic variability caused by subthreshold inputs also may be quite relevant to information processing by the nervous system.
; Eilers et al. 1995). These studies are limited, however, by the absence of excitatory background input in the cerebellar slice preparation (Häusser and Clark 1997) and by the relative hyperpolarized membrane potentials at which the cells are studied. A recent experimental study demonstrated, however, the importance of background inhibition in controlling interspike interval distributions (Häusser and Clark 1997), as was predicted by the model (De Schutter and Bower 1994b; Jaeger et al. 1997). Moreover, it was shown in this paper (Fig. 4C) that background inhibition had the same effect on the integration of excitatory synaptic input by the active dendrite model as in the experimental study (Fig. 7B of Häusser and Clark 1997).
; Markram and Sakmann 1994; Nicoll et al. 1993; Schwindt and Crill 1997; Seamans et al. 1997), and the resulting amplification is quite variable (Deisz et al. 1991). Other systems where amplification of excitatory synaptic inputs have been reported are hippocampal pyramidal cells (Gillessen and Alzheimer 1997; Lipowsky et al. 1996) and fly visual neurons (Haag and Borst 1996). More relevant to the present modeling study are in vivo intracellular recordings of neurons. Membrane potential fluctuations are very large in in vivo recordings of pyramidal neurons from cat visual cortex (Ferster and Jagadeesh 1992) and monkey sensorimotor cortex (Murthy and Fetz 1992). Moreover, these fluctuations "can distort the EPSP's shape" significantly (Ferster and Jagadeesh 1992), and the amplitude of EPSPs is quite variable (coefficient of variation of 58% reported by Matsumura et al. 1996).
-motoneurons show in vivo a "postsynaptic" variability of EPSP amplitudes that is caused by background synaptic input (Gossard et al. 1994). In these neurons, the activation of a dendritic plateau potential in vivo evokes a large increase of the somatic membrane potential noise (Hounsgaard et al. 1988). Although the origin of this increased membrane potential noise has not been determined, our simulation results suggest that it may be caused by increased membrane potential fluctuations due to the activation of the dendritic Ca2+ channels that cause the plateau potential and that move the neuron to an active dendrite state (e.g., Fig. 1B).
); this can lead to localized Ca2+ inflow in the dendrite (Markram and Sakmann 1994; Regehr and Tank 1992). Moreover, it was recently shown that a dendritic A-type K+ channel can control dendritic excitability in these cells (Hoffman et al. 1997). In the Purkinje cell model, Ca2+-activated K+ channels were more important in this regard than A channels (Fig. 5B).
10 ms have very small effects on the response, whereas delays by 30 ms completely reset the dendritic excitability (zero correlation). In other words, a small delay of a few milliseconds in the timing of a coherent input (e.g., Nelson et al. 1992) will not change the response, but shifts in timing of >30 ms can have a profound effect.
; Braitenberg et al. 1997; Marr 1969) propose that thousands of the 150,000 parallel fiber inputs onto a single Purkinje cell (Harvey and Napper 1991) have to be coactivated to cause a response. Such a large stimulus would be very reliable as it is outside of the range where variable amplification has any effect (Fig. 10). But recent experimental findings suggest that much smaller stimuli also might be adequate. Barbour (1993) estimated that 50 parallel fiber inputs might be sufficient to cause the Purkinje cell to fire a spike. Similarly, activation of a few (Eilers et al. 1995) or even a single (Denk et al. 1995) parallel fiber is enough to activate dendritic Ca2+ channels. But if the Purkinje cell is so sensitive to activation of a small number of its 150,000 excitatory synapses, what prevents it from firing continuously at maximum rate? Analysis of the Purkinje cell model has shown that the feed-forward inhibition by stellate cells, which also receive parallel fiber input (Ito 1984; Palay and Chan-Palay 1974), can cancel the constant component of parallel fiber activation (Jaeger et al. 1997). In fact under conditions of steady background input, the Purkinje model settles at an average membrane potential where the inhibitory current is larger than the excitatory one. I previously have proposed that long-term depression of the parallel fiber synapse may be important in fine-tuning this balance between excitation and inhibition (De Schutter 1995a, 1997).
) (Figs. 3 and 10B). Such synchronous inputs are presumably not canceled by inhibition because the feed-forward loop acts with a delay. Assuming that activation by small synchronous excitatory inputs is a correct representation of Purkinje cell function, its response will be very sensitive to the variable thresholds demonstrated in Fig. 10.
,c). Similarly, the synchronous input could be provided by the ascending branch of the granule cell axon (Bower 1997), which makes much more extensive synaptic contacts with close by Purkinje cells than has been generally assumed (Gundappa-Sulur et al. 1998), or by the parallel fibers (Braitenberg et al. 1997). Because of their long length (5 mm long) (Mugnaini 1983; Pichitpornchai et al. 1994), parallel fibers originate in many different patches of the fractured somatotopy of cerebellar cortex (Shambes et al. 1978) and consequently will carry information from many different sources, while ascending branches are expected to convey one particular receptive modality only (Bower 1997; Bower and Woolston 1983). If this functional separation of the granule axon in an ascending and parallel branch is correct, the parallel fiber system transmits heterogenous background input, which, by the variable amplification mechanism, can modulate the Purkinje cell response to synchronous excitation by the homogenous ascending branch input. As is demonstrated in Fig. 10B, the parallel fiber system (combined with feed-forward inhibition by stellate cells) can change the effective threshold for spike transmission by ascending branch inputs. In other words, the parallel fiber system may determine if a particular mossy fiber input can activate the overlying Purkinje cells by gating the ascending branch input.
; Braitenberg et al. 1997), which assume that the Purkinje cell operates as a detector of parallel fiber coincidences. It indeed can be shown that Purkinje cell responses to large synchronous activations of the parallel fiber tract in vitro are time locked (Heck 1994), but as argued above and elsewhere (Jaeger and De Schutter 1997) it is unlikely that these stimulation paradigms are physiological.
) is attractive, many unknowns remain. In particular, the timing of granule cell activation may be much less random than is generally assumed (Maex et al. 1996; Vos et al. 1997). Similarly, the activation patterns of the stellate cells, which are crucial in determining Purkinje cell spiking responses (Jaeger and Bower 1996; Jaeger et al. 1997), have not been determined in vivo.
| |
ACKNOWLEDGEMENTS |
|---|
I thank J. M. Bower for access to the Intel Touchstone Delta System operated by Caltech on behalf of the Concurrent Supercomputing Consortium and anonymous reviewers for valuable comments.
This work was supported by Fonds Wetenschappelijk Onderzoek (Flanders) and National Institute of Mental Health Grant MH-52903.
| |
FOOTNOTES |
|---|
Received 8 September 1997; accepted in final form 29 April 1998.
| |
REFERENCES |
|---|
|
Abstract
Introduction
Methods
Results
Discussion
References
|
|---|
-motoneurones in the decerebrate cat and in the acute spinal cat after intravenous 5-hydroxytryptophan.
J. Physiol. (Lond.)
405: 345-367, 1988.This article has been cited by other articles:
|
|
 |
|
  M. Häusser, N. Spruston, and G. J. Stuart Diversity and Dynamics of Dendritic Signaling Science, October 27, 2000; 290(5492): 739 - 744. [Abstract] [Full Text]
|
|
|
|
 |
|
 E. P. Cook and D. Johnston Voltage-Dependent Properties of Dendrites That Eliminate Location-Dependent Variability of Synaptic Input J Neurophysiol, February 1, 1999; 81(2): 535 - 543. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 B. P. Vos, R. Maex, A. Volny-Luraghi, and E. D. Schutter Parallel Fibers Synchronize Spontaneous Activity in Cerebellar Golgi Cells J. Neurosci., June 1, 1999; 19(11): RC6 - RC6. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
