Targeted dendrotomy reveals active and passive contributions of the dendritic tree to synaptic integration and neuronal output

Abstract

Neurons typically function as transduction devices, converting patterns of synaptic inputs, received on the dendrites, into trains of output action potentials in the axon. This transduction process is surprisingly complex and has been proposed to involve a two-way dialogue between axosomatic and dendritic compartments that can generate mutually interacting regenerative responses. To manipulate this process, we have developed a new approach for rapid and reversible occlusion or amputation of the primary dendrites of individual neurons in brain slices. By applying these techniques to cerebellar Purkinje and layer 5 cortical pyramidal neurons, we show directly that both the active and passive properties of dendrites differentially affect firing in the axon depending on the strength of stimulation. For weak excitation, dendrites act as a passive electrical load, raising spike threshold and dampening axonal excitability. For strong excitation, dendrites contribute regenerative inward currents, which trigger burst firing and enhance neuronal excitability. These findings provide direct support for the idea that dendritic morphology and conductances act in concert to regulate the excitability of the neuron.

Most of the synaptic inputs to neurons are received on the dendritic tree, whereas the output signal of the neuron, the action potential (AP), is normally initiated in the axon, which originates from the soma. The input–output relationship of neurons depends not only on the individual properties of the axon and dendrites, but also on the interaction between them. It is essential to understand this interaction to determine its effect on the neuron's AP output.

Recent advances in electrophysiological, immunocytochemical, and imaging techniques have shown that dendrites are electrically excitable and express a wide range of voltage-gated channels in a nonuniform and cell-specific manner (1, 2). In addition to supporting active backpropagation of Na APs from the axon, dendrites can initiate their own Na and Ca spikes under some circumstances (3, 4). However, dendrites also express high densities of voltage-gated K channels, which can dampen excitability (5, 6). These findings have raised the question of how this mixture of active currents affects the excitability of the soma and axon, and thus the output of the neuron. This question is complicated by the fact that the interaction between soma/axon and dendrites is mutual, even on short time scales. For example, in layer 5 pyramidal cells, single backpropagating APs lower the threshold for initiation of dendritic Ca spikes, which can in turn deliver a depolarizing voltage envelope to the soma that enhances AP firing (7).

One approach to studying the contribution of dendritic electrogenesis to axonal output is to locally apply channel blockers, like tetrodotoxin or nickel (8, 9). When used in brain slices, this method suffers from uncertainties about the specificity and localization of the block. Another approach is to study the behavior of isolated somata, where the dendrites have been acutely removed (10–12). In such experiments, however, it is not possible to examine the behavior of the same soma before and after removal of the dendrites to make a careful quantitative comparison of dendritic influence.

We have overcome these limitations by developing a new method for reversibly uncoupling somata and dendrites in single identified neurons in brain slices. This approach allows us to directly assess the immediate functional consequences of dendrite removal in single neurons. Our experiments focused on cerebellar Purkinje cells and neocortical layer 5 pyramidal cells, which both have prominent excitable dendritic trees. Our results show that the dendritic tree either inhibits or enhances axosomatic excitability depending on the strength of stimulation.

Results

Dendrites Can Be Removed or Occluded by Dendrotomy or Pinching.

We developed two complementary methods that allowed us to record from the same identified neuron before and after physical removal or occlusion of its dendrites: dendrotomy, which involves permanent physical removal of the dendrites; and dendritic pinching, or occlusion of a dendrite, which is reversible. These approaches were optimized by using cerebellar Purkinje cells, which have a large, extensively branched dendritic tree that is connected to the soma by a single dendritic trunk (Fig. 1A Left). Thus, the entire dendritic tree can be removed by amputation or occlusion at a single location, maximizing the consequences of dendritic removal. Both dendrotomy and pinching were carried out by using two pincer pipettes, one placed just under and the other just above the dendritic trunk ≈20 μm from the soma (Fig. 1A Right). Dendrotomy was performed by slowly (over 5–8 min) raising the lower pincer, which stretched out the membrane, until the dendritic trunk separated and the membrane resealed. This manipulation was successful in ≈70% of experiments.

Fig. 1.

Dendrotomy of a cerebellar Purkinje cell. (A) (Left) Biocytin-filled rat cerebellar Purkinje cell showing the dendritic tree attached to the soma by a single apical trunk. (Right) Infrared image of a different Purkinje cell (P19) during somatic whole-cell recording. The two pincer pipettes (arrows) are visible in their starting positions before dendrotomy. (B) Monitoring the progress of the dendrotomy (same cell as A Right). (Ba) (Left) Responses to a 5-mV hyperpolarizing voltage-clamp step before (control) and after (dendrotomy) amputation. (Right) Input resistance calculated from the step response plotted against time. The heavy dashed line indicates the period when the lower pincer was being raised. In this experiment, the apparent total capacitance of the cell decreased from 585.7 pF (before dendrotomy) to 21.9 pF (after dendrotomy). (Bb) (Left) Before and after responses to a 30-mV hyperpolarizing voltage-clamp step in the same cell, activating I_h. (Right) Time course plot showing the decline in I_h with dendrotomy. (Bc) (Left) Before and after responses to stimulation of parallel fiber inputs onto the distal dendrites. (Right) Time course plot showing the loss of synaptic input to the dendrites during dendrotomy. (C) (Left) Time course plot showing reversible pinching in a different Purkinje cell. Heavy dashed lines indicate the times during which the lower pincer was raised (≈1–9 min) and then lowered (≈44–51 min). Filled squares indicate the values of R_in and I_h measured 6 min before time 0 on the abscissa, confirming stability. Large filled circles indicate the values of R_in and I_h at time 39 min, during the period the pincers were stationary (≈9–44 min). (Right) Example traces at the numbered time points.

Dendrotomy was monitored electrically under somatic voltage clamp by using three different types of measurement. (i) The cell's input resistance (R_in) increased from 81 ± 9 MΩ to 355 ± 92 MΩ (P = 0.006, n = 7), and its apparent total capacitance (C_m) decreased from 622 ± 85 pF to 22 ± 2 pF (P < 0.001, n = 7) during dendrotomy, compatible with the removal of a large area of dendritic membrane (Fig. 1Ba). (ii) The amplitude of the hyperpolarization-activated cation current (I_h, present in the dendrites; ref. 13) was markedly reduced, again consistent with removal of the dendritic membrane (Fig. 1Bb). Removal of I_h was also accompanied by an expected hyperpolarization in resting membrane potential (control, −64.2 ± 1.5 mV with −480 ± 120 pA holding current; dendrotomy, −77.1 ± 3.5 mV without holding current; P < 0.01, n = 6). (iii) EPSCs evoked by distal parallel fiber stimulation were completely abolished by dendrotomy, as expected with dendritic removal (Fig. 1Bc). Additional confirmation of dendrotomy was obtained in experiments where confocal microscopy was used to monitor the dendritic Ca²⁺ transient elicited by a depolarizing current step at the soma. Dendrotomy abolished the Ca²⁺ transient distal to the cut (n = 7 cells; see below).

The large increase in R_in observed after dendrotomy suggests that the severed dendrite was able to reseal. To confirm that damage caused by the dendrotomy procedure was minimal, we also performed reversible pinching of the apical trunk rather than complete amputation. Pinching was done by raising the lower pincer pipette until the dendrite was compressed against the upper pipette but remained intact, as apparent from the fluorescent dye fill of the cell, increase in R_in, and reduction in I_h (Fig. 1C). These changes in R_in and I_h were partially reversed after lowering the pincer to its starting position (Fig. 1C). Pinching increased R_in from 88 ± 8 MΩ to 203 ± 50 MΩ (P = 0.03, n = 16) and reduced C_m from 499 ± 35 pF to 397 ± 36 pF (P < 0.001, n = 16). These changes are smaller than those observed after complete amputation, indicating that pinching only partially occludes electrical access to the dendrite.

Dendrotomy or Pinching Increases the Neuronal Excitability of Purkinje Cells.

We next examined the effect of dendrite removal on sodium APs in Purkinje cells. Trains of APs were elicited by applying a 1-sec current step to the same cell before and after dendrotomy (Fig. 2Aa). Dendrotomy dramatically hyperpolarized the absolute voltage threshold for initiating an AP (by 12.9 ± 2.2 mV); increased the height of the AP, measured from its voltage threshold to its peak (by 26.1 ± 6.3 mV); and increased the afterhyperpolarization (AHP) that followed each AP (by 19.3 ± 2.2 mV; n = 6 cells, all P < 0.009; Fig. 2 Ab and Ac). The AP rise time was not significantly changed (decreased by 0.03 ± 0.01 msec; P = 0.053).

Fig. 2.

Dendrotomy and pinching of the dendritic tree alter the properties of APs in Purkinje cells and large layer 5 cortical pyramidal cells. (Aa) APs evoked by step depolarization in a Purkinje cell before (black) and after (red) dendritic amputation. (Ab) The first AP in the trains in a shown superimposed and expanded. (Ac) Summary of changes in AP voltage threshold (bar 1), AP height (bar 2), and AHP amplitude (bar 3) after dendrotomy of Purkinje cells (n = 6). (Ba) APs measured in a Purkinje cell before (black), during (red), and after (blue) pinching the dendritic trunk. (Bb) Summary of changes in AP threshold, AP height, and AHP amplitude during (red bars, n = 18) and after (blue bars, n = 3) pinching, all compared to values measured in the same cell before pinching. (Ca) APs evoked by step depolarization in a large layer 5 cortical pyramidal neuron before and during dendritic pinching. (Cb) The first AP from the trains in a superimposed and expanded. (Cc) Summary of changes in AP threshold, AP height, and AHP amplitude after pinching of layer 5 cells (n = 16).

Pinching, rather than amputation, caused similar but smaller effects, which were partially reversible (Fig. 2B), indicating that the changes caused by amputation were not because of damage. During the pinch, the AP threshold hyperpolarized by 5.9 ± 0.6 mV from control, the AP height increased by 16.7 ± 1.9 mV, and the AHP amplitude increased by 9.2 ± 0.7 mV (n = 18 cells, all P < 0.001; Fig. 2Bb, red bars). After releasing the pinch, all of these measures recovered toward control values (AP threshold −1.4 ± 0.9 mV, AP height 6.9 ± 1.2 mV, AHP amplitude −5.1 ± 2.3 mV, all relative to control values; Fig. 2Bb, blue bars; all P > 0.06; cf. control).

Effects of Dendritic Occlusion in Layer 5 Cortical Pyramidal Cells.

We hypothesized that these results could be explained by the dendritic tree acting as an electrical load on AP generation, decreasing excitability. Removal or occlusion of the tree would thus increase excitability. If so, similar but smaller effects should be seen in other types of neurons when only part of the dendritic tree is occluded. We tested this prediction in large layer 5 cortical pyramidal neurons by amputating or pinching the primary apical dendrite at 50 to 90 μm from the soma, leaving the basal dendrites intact.

Dendrotomy of layer 5 pyramids increased R_in from 77 ± 6 MΩ to 164 ± 16 MΩ (P = 0.026, n = 4) and reduced C_m from 167 ± 7 pF to 136 ± 12 pF (P = 0.09, n = 4). The resting potential was slightly hyperpolarized (control, −67.3 ± 0.7 mV; dendrotomy, −71.7 ± 2.2 mV; no holding current; P = 0.13, n = 4). Pinching, rather than amputating, the apical dendrite produced smaller changes in R_in (82 ± 7 MΩ to 131 ± 24 MΩ) and similar changes in C_m (162 ± 8 pF to 135 ± 8 pF; both P < 0.05, n = 20). These effects are less dramatic than those seen in Purkinje cells, compatible with the removal of a smaller proportion of the dendritic tree in pyramidal cells. Pinching the apical dendrite of layer 5 cells also had a smaller effect on the firing properties of these cells (AP threshold hyperpolarized by 3.0 ± 0.6 mV; AP height increased by 0.8 ± 1.4 mV; AHP amplitude increased by 3.1 ± 0.7 mV; n = 16 cells; Fig. 2C). Only the changes in AP threshold and AHP amplitude were significant (P < 0.001; Fig. 2Cc).

Pinching Alters the Input–Output Relation for APs in Purkinje Cells.

If removing the dendritic tree changes the properties of somatic APs, it might also change the manner in which the neuron converts input stimuli into AP outputs (its input–output relation). This hypothesis was tested by injecting a family of current steps into a Purkinje cell before and during pinching (Fig. 3A). The same current step elicited many more APs during pinching [leftward shift in the plot of AP frequency versus current step amplitude (f-I plot); Fig. 3B; same cell as in A; similar result in n = 5 cells]. This result is expected because pinching both lowers the threshold voltage for firing APs (Fig. 2Bb) and increases the input resistance of the cell. Surprisingly, pinching did not alter the asymptotic slope of the f-I plot (0.320 ± 0.028 Hz/pA before, 0.325 ± 0.029 Hz/pA after; ratio 1.02 ± 0.03; P > 0.6, n = 5 cells).

Fig. 3.

Pinching alters input–output relationships, and a compartmental model qualitatively replicates all effects of pinching. (A) APs evoked by a series of step current injections (values above the traces) applied to a Purkinje cell before (black) and during (red) dendritic pinching. (B) f-I plot for the Purkinje cell in A before and during pinching. (C) (Top Left) Purkinje cell used in the modeling. (Top Right) Calculated single AP in this cell before (black) and during (red) simulated pinching. (Middle and Bottom) Trains of simulated APs in response to current steps before and during pinching. (D) f-I plots calculated from simulations like those in C.

Effects of Dendrotomy Can Be Reproduced by an Active Compartmental Model.

How can the effects of dendrotomy on APs be explained? This question was addressed with simulations by using full 3D reconstructions of a cerebellar Purkinje cell (14) and a layer 5 neocortical pyramidal neuron (15) with active conductances. Similar results were also found in simplified equivalent cable models (16). As in the experiment, pinching in a model Purkinje cell hyperpolarized the spike threshold, increased the spike height, and increased the AHP amplitude (Fig. 3C Top). This effect depended most strongly on dendritic membrane capacitance (C_m): Increasing C_m in the model dramatically attenuated excitability, whereas setting C_m to zero produced similar effects on the AP as did complete removal of the dendritic tree. Similar but smaller effects on the AP were found in a model layer 5 pyramidal cell (data not shown), replicating the observed difference between pyramidal and Purkinje cells (Fig. 2). Although we did not attempt to tune the model to the data, the model also reproduced qualitatively the effect of pinching on the f-I plot, causing a leftward shift without changing the asymptotic slope (Fig. 3D). This effect depended on the presence of an AHP conductance after each AP (data not shown), confirming other studies showing the importance of the AHP for input–output gain (17).

Dendrotomy Blocks Burst Firing.

Some forms of burst firing in both Purkinje and layer 5 pyramidal cells have been linked to calcium electrogenesis in the dendritic tree (1). We examined this directly by recording APs in the same neuron before and after amputation of the apical dendrites. A strong depolarizing current step at the soma of an intact Purkinje cell elicited repetitive burst firing during the latter part of the step (control, Fig. 4Aa; expanded in Fig. 4Ab, arrow). This response was accompanied by a Ca²⁺ transient measured in the dendritic tree ≈50 μm from the soma (Fig. 4Aa). After dendrotomy, both the delayed burst firing observed at the soma and the dendritic Ca²⁺ transient distal to the cut were abolished (Fig. 4A, dendrotomy; same result in three cells). These data confirm that the delayed, repetitive burst firing requires conductances in the Purkinje cell dendritic tree. Interestingly, dendrotomy increased the transient burst firing of sodium APs elicited by a brief, large current step at the soma (Fig. 4Ac; n = 3 cells). This form of burst firing has been reported to persist in acutely isolated Purkinje cell somata (18), confirming its somatic origin.

Fig. 4.

Dendrotomy abolishes some forms of bursting in Purkinje cells and layer 5 pyramidal cells. (Aa) Simultaneous recordings of somatic membrane potential (Middle) and dendritic Ca²⁺ fluorescence (Bottom) before (black) and after (red) dendrotomy. The stimulus was a 500-msec-long 7-nA current step applied at the soma (Top). The Purkinje cell in which these recordings were made is shown at right before dendrotomy. Red line, location of the Ca²⁺-imaging line scan; dashed white line, approximate site of dendrotomy. (Ab) Expanded views of the somatic membrane potential recorded in this cell, showing the first and last 50 msec of the response to the current step. Before dendrotomy, there was a rapidly inactivating burst of sodium APs at the beginning of the step, followed by slower rhythmic bursting during the latter part of the step (Left, arrow). After dendrotomy, the fast initial burst remained, but the late rhythmic bursting was abolished (Right). (Ac) Response of a different Purkinje cell to a 1-msec-long current step applied before (Left, 1.4-nA step) and after (Right, 0.5-nA step) dendrotomy. A second, attenuated sodium AP appears after dendrotomy (arrow). (Ba) A similar experiment was done on the layer 5 pyramidal cell (Right). The stimulus was a 100-Hz train of five 3-msec-long 2.2-nA current steps (Top). This stimulus elicited both a train of five APs (Middle) and, in control conditions, a Ca²⁺ transient (Bottom Left) recorded in the primary apical dendrite ≈90 μm from the soma (at red line in fluorescence image). After dendrotomy (at the dashed white line in the fluorescence image), the Ca²⁺ transient was abolished (Bottom Right). (Bb) Voltage response of this cell to a 450-pA current step applied at the soma. In control conditions (Left), the cell showed an initial burst of APs (arrow). After dendrotomy, bursting was abolished (Right). (Bc) Expanded view of the first AP in a train elicited in the same layer 5 cell before (black) and after (red) dendrotomy, showing the reduction in amplitude of the afterdepolarization (arrows).

A similar experiment was done in intrinsically bursting, large layer 5 pyramidal cells. In an intact cell, somatic current steps (0.15–1 nA) elicited a burst of APs at the beginning of the step, together with a Ca²⁺ transient measured in the apical dendrite ≈90 μm from the soma (Fig. 4 Ba and Bb, control). After dendrotomy, this bursting was abolished for all current steps, as was the Ca²⁺ transient distal to the cut (Fig. 4B, dendrotomy; same result in four cells). Ca²⁺ transients in response to the stimulus were still present in an intact basal dendrite from the same cell (data not shown). The abolition of this burst firing was associated with a large reduction in the afterdepolarization (ADP) after the AP (amplitude reduced by 4.9 ± 0.5 mV, P = 0.002, n = 4; Fig. 4Bc). These data confirm directly that in large layer 5 pyramidal cells, as in Purkinje cells, some forms of intrinsic burst firing require the apical dendritic tree.

Discussion

We have developed a new approach for directly assessing the contribution of the dendritic tree to neuronal excitability. Our approach, which uses fine pincer electrodes to compress or sever the dendrite, can reversibly uncouple the dendritic tree from the soma, allowing the effect of the active and passive properties of the dendrite to be assessed in single identified neurons. Our experiments show that the dendritic tree can act as a passive load that dampens excitability, but at higher levels of excitation can also provide inward currents that promote axosomatic excitability.

This approach has a number of advantages over previous methods. First, it can be targeted to individual dendrites in identified neurons, in contrast to methods using surgical cuts to the tissue (19). Second, the pinching method is partly reversible, allowing the possibility of damage caused by the procedure to be assessed. This reversibility contrasts with a recent approach using a laser to permanently remove the axon (20). Third, being a physical method relying on the occlusion or removal of the dendrite, it allows both passive (particularly capacitive) and active (voltage-gated) contributions of the dendrites to be determined, in contrast to pharmacological (21) and electronic (22) approaches.

In principle, the method can be used to address a wide range of questions regarding the interaction between different cellular compartments, including basal dendrites and axons. For example, the method could be used to assess molecular traffic between different parts of the neuron (23) or measure the properties of axons and dendrites in isolation from the soma (24). It could also be used to manipulate propagation of events between different dendritic compartments, such as Ca spikes or waves (25), to address their contribution to synaptic integration and the spread of synaptic plasticity.

We have provided the first direct experimental evidence to confirm previous modeling predictions that the dendrites can act as a capacitive load that raises the threshold for AP initiation near the soma (16, 26). We demonstrate that dendritic occlusion can increase the excitability of the soma by lowering the threshold for AP initiation and increasing AP amplitude. Layer 5 pyramidal cells show smaller effects than Purkinje cells because a smaller fraction of their dendritic membrane was removed and their APs have slower kinetics, making them less susceptible to capacitive loading.

Dendrotomy also produces striking changes in the f-I curve in response to steady injected current. Although the leftward shift in this curve can readily be explained by the difference in input resistance, the lack of change in slope initially seems surprising. However, modeling shows that this is because of the effect of the AHP: The decrease in AP threshold is balanced by the increase in the AHP, normalizing the gain (17).

Our results also show that certain types of intrinsic bursting generated by somatic current injection require an intact apical dendrite because its removal could prevent bursting. This behavior could result from the presence of voltage-gated channels in the apical dendrite, as well as its geometry, enabling backpropagating APs to activate a slow inward current that is returned to the soma (27). Our findings also suggest that backpropagation into the basal dendrites of pyramidal cells is insufficient to drive bursting on its own (28).

In summary, we show here that the capacitive and ionic contributions of the apical dendrites can have opposing effects on neuronal excitability and are differentially engaged, depending on the strength of excitatory input. For small inputs, the capacitive properties of the dendrites predominate and impose a “cost” by providing an electrical load, inhibiting the initiation of APs. For large inputs, dendritic nonlinearities become recruited and predominate, such that the dendrites can increase axonal excitability by enhancing burst firing. Thus, dendrites exaggerate the nonlinearity of neurons as transduction devices, sharpening the distinction between their responses to weaker and stronger inputs.

Materials and Methods

Slice Preparation.

Sprague–Dawley or Wistar (17- to 25-day-old) rats were anesthetized with Isoflurane and rapidly decapitated in accordance with the Animals (Scientific Procedures) Act of 1986 (U.K.) or the Animal Experimentation Ethics Committee of the Australian National University. Slices (300 μm thick) were prepared from either the cerebellar vermis or the somatosensory cortex by using standard techniques (5, 29).

Electrophysiology.

Slices in the recording chamber were maintained at 32°C to 34°C in a continuous flow of carbogen-bubbled artificial cerebrospinal fluid comprising 125 mM NaCl, 3 mM KCl, 2 mM CaCl₂, 1 mM MgCl₂, 25 mM NaHCO₃, 1.25 mM NaH₂PO₄, and 25 mM glucose. Usually, 5 μM 6-cyano-7-nitroquinoxaline-2,3-dione and 10 μM bicuculline were added to inhibit spontaneous synaptic activity (except in Fig. 1). Internal solution contained 130 mM K-methylsulfate, 7 mM KCl, 1 mM EGTA, 2 mM Na₂ATP, 2 mM MgATP, 0.5 mM Na₂GTP, and 10 mM Hepes (pH 7.2). Pincer pipettes resembled sharp intracellular electrodes, with a shallow taper and very fine tips. A MultiClamp 700A amplifier (Molecular Devices, Union City, CA) was used to obtain whole-cell recordings from the somata of visually identified Purkinje neurons or large layer 5 cortical pyramidal neurons. In current-clamp recordings, pyramidal neurons were allowed to remain at their resting potential (approximately −67 mV), whereas Purkinje cells were hyperpolarized to approximately −65 mV by steady current injection to prevent spontaneous APs. In voltage-clamp recordings, the soma was clamped at −70 mV. Voltages have not been corrected for the liquid junction potential (−7 mV).

Confocal Microscopy.

Calcium imaging was done by using a Zeiss LSM 510 confocal microscope with a ×40/0.8 N.A. water-immersion objective (Carl Zeiss, Sydney, Australia). Oregon Green BAPTA-1 (100 μM) was added to the standard intracellular solution, which also contained 1 mM EGTA. The presence of EGTA slowed the decay of the Ca²⁺ transient (Fig. 4 Aa and Ba) compared to other reports (e.g., ref. 3). Line scans, repeated at 5-msec intervals, were done at the indicated dendritic locations (Fig. 4 A Right and B Right, red lines).

Analysis.

Analysis was done by using Axograph X (Axograph Scientific, Sydney, Australia). Input resistance before and after pinching/dendrotomy was determined from the current response to voltage-clamp test pulses (usually −1 mV for 100 msec) from a holding potential of −70 mV. Cell capacitance was found by integrating the off capacitance transient after this step. I_h was measured from the plateau current elicited by a 15- or 30-mV hyperpolarizing voltage step without correcting for leak current. For each cell, AP threshold, AP height, and amplitudes of the ADP and AHP were averaged from the APs in the first current step (increased in 50-pA increments) that generated at least four APs. Threshold was defined as the membrane potential, V_m, at which dV_m/dt = 50 mV/msec. AP height was defined as the difference between the threshold and peak of that AP. ADP peak was identified visually and expressed relative to the voltage threshold of the immediately preceding AP. AHP amplitude was measured at the (absolute) minimum V_m between adjacent APs. Results are given as mean ± SE, with n = number of cells. Groups were compared by using Student's t test.

Neuronal Modeling.

Simulations used morphologically realistic compartmental models of a Purkinje cell (ref. 14, fig. 2, cell 4) or a layer 5 neocortical pyramidal neuron (15) run under neuron. An equivalent cable model of a Purkinje cell was also used (16). For the morphologically realistic Purkinje cell, R_i, C_m, and R_m were uniform and set to 115 Ωcm, 1 μF/cm², and 40,000 Ωcm², respectively (14). Active conductances were taken from ref. 30. Resurgent Na current and three types of voltage-gated K channels (TEA-sensitive, low TEA-sensitive, and slow K) were placed at the soma at densities of 0.2, 0.05, 0.1, and 0.1 S/cm², respectively, whereas I_h channels were uniformly distributed over the soma and dendrites at a density of 3 × 10⁻⁵ S/cm². Layer 5 pyramidal cell simulations used the parameters as described in ref. 15.

Abbreviations

ADP

afterdepolarization

AHP

afterhyperpolarization

AP

action potential

f-I plot

plot of AP frequency versus current step amplitude.