INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Pyramidal cells are the main excitatory elements of neocortex. They are contacted by many other excitatory and inhibitory neurons via synapses, which are distributed over their somatodendritic membrane (DeFelipe and Farias 1992). The ultimate output of pyramidal cells consists of action potentials, which are initiated mainly at the initial segment of the axon as trains of individual spikes or spike bursts (Connors and Gutnick 1990; Stuart and Sakmann 1994). Knowledge of the precise rules by which synaptic inputs are converted into spike output is of key relevance for our understanding of neural function. Dendrites have long been thought to play an important role in processing synaptic signals, because their elongated cable-like structures allow for nonlinear interactions (Rall 1964), which may be computationally relevant (Mel 1994). The apical dendrite of pyramidal cells has been intensively investigated and serves as a paradigm for dendritic integration. A variety of active membrane conductances have been found in dendritic recordings (reviewed in Johnston et al. 1996), which allow for retrograde propagation of action potentials as well as for boosting or attenuation of individual synaptic signals (reviewed in Häusser et al. 2000; Magee 2000). While individual synaptic signals have very fast frequency components, neurons in vivo also encounter slower input fluctuations due to the time-varying synaptic background activity in the surrounding neural network (e.g., Steriade et al. 2001). Because it is largely unknown how dendrites respond to different temporal components of their synaptic inputs, I determine in this study the transfer impedance of the apical dendrite in layer V pyramidal cells over a physiologically relevant frequency range.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Tissue preparation and recordings

Wistar rats of either sex (postnatal day 19-22) were killed by decapitation. Individual cerebral hemispheres were glued on a stage tilted forward by 15°. Parasagittal slices of 300-µm thickness were cut on a Microtome (Leica VT 1000 S, Nussloch, Germany) and incubated at 35°C. Slices were transferred to a recording chamber and superfused at 4 ml/min (T = 35 ± 1 °C) with standard artificial cerebrospinal fluid containing (in mM) 125 NaCl, 1.25 NaH₂PO₄, 25 NaHCO₃, 2.5 KCl, 1 MgCl₂, 2 CaCl₂, and 10 glucose, pH 7.5 adjusted with 5% CO₂-95% O₂. Patch pipettes were filled with a solution containing (in mM) 125 K-Gluconate, 5 NaCl, 1 MgCl₂, 1 CaCl₂, 10 HEPES, and 11 EGTA, osmolarity: 280 mosmol., pH 7.2 adjusted with KOH (in some experiments EGTA and CaCl₂ were omitted). Patch pipettes used for somatic or dendritic recordings had a tip resistance of about 5 and 10 M, respectively. Pyramidal cells were visualized in layer V of somatosensory cortex with infrared differential interference contrast (DIC) video microscopy (Dodt and Zieglgänsberger 1990). Sinusoidal current waveforms of linearly increasing or decreasing frequencies were generated digitally between 0.1 and 25 Hz (Puil et al. 1986; Ulrich and Stricker 2000). Electrode resistance and capacitance were minimized by electronic compensation. Membrane voltage was recorded in Bridge mode with Axoclamp-2B amplifiers (Axon Instruments, Foster City, CA). Voltage and current traces were low-pass filtered at 1 kHz and digitized at 2 kHz (12 bits) with a Labmaster LM-12 A/D converter (Scientific Solutions, Solon, OH). A liquid junction potential of approximately 10 mV was left uncorrected.

Data analysis

Impedance magnitude (|Z|) and phase shift () were calculated by Fourier transformation of digitally averaged (n = 10) current and voltage traces (Matlab, The Mathworks, Natick, MA). The complex impedance is Z(f) = V(f)/I(f) with a real and imaginary part: Z = Re(Z) + i * Im(Z), and (f) is frequency (in Hz). |Z| and  were obtained as |Z| = [Re(Z)² + Im(Z)²] and tan¹  = [Im(Z)/Re(Z)], respectively. To avoid boundary effects, which may have been introduced by the finite sampling window, only frequencies between 1 and 20 Hz were considered for analysis. The strength of the resonance is Q = |Z|_fres/|Z|_fmin (Koch 1984) (cf. Fig. 2), where |Z|_fres and |Z|_fmin are the impedance magnitude at the resonance or lowest frequency, respectively.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

To investigate the transfer impedance of the apical dendrite in layer V pyramidal neurons, dual whole cell patch-clamp recordings were obtained simultaneously from the soma and apical dendrite with interelectrode distances of 120-270 µm. The cells had a mean resting potential of 60 ± 4 mV (mean ± SD; n = 16) and fired adapting sequences of action potentials, when stimulated by somatic step current injections. However, ~30% of these putative regular spiking cells fired bursts of action potentials after step current injections via the dendritic electrode and were therefore disclosed as intrinsic bursters (not shown; cf. Williams and Stuart 1999). Because the results were independent of the firing mode, data from all experiments were pooled.

Transfer impedance of the apical dendrite

In the experiment of Fig. 1A a sinusoidal current waveform, which changed its frequency linearly between 0.1 and 25 Hz (chirp), was injected via the dendritic pipette. A second electrode measured the voltage response at the soma. The amplitude of the somatic voltage oscillations initially increased and peaked after around 400 ms (arrow), followed by a steady decline at higher frequencies. The reverse experiment in the same cell is shown in Fig. 1B. Here, the chirp current was injected via the somatic pipette and the voltage response recorded by the dendritic patch electrode. Again, the voltage amplitude at the dendrite is maximal after ~400 ms (arrow). Somatodendritic and dendrosomatic transfer impedances were calculated after Fourier transformation of digitally averaged current and voltage traces. Figure 2 (A and B) shows transfer impedance magnitude (A) and phase shift (B) for dendrosomatic (continuous line) and somatodendritic (dashed line) current flow (cf. Fig. 1). Both traces are well superimposed. The impedance magnitude has a maximum (Z_max) of ~30 M at a frequency (f_res) of ~6 Hz (Fig. 2A, arrow). Analysis of phase shift indicates that voltage leads current up to a frequency of ~3 Hz (_0; Fig. 2B, arrow), followed by a voltage lag. At higher frequencies the voltage lag asymptotically approaches /2 (i.e., a quarter-cycle). Similar results were obtained in all other cells with f_res = 5.5 ± 1.0 Hz and ₀ = 2.3 ± 0.9 Hz (mean ± SD, n = 16).

View larger version (58K): [in this window] [in a new window]   Fig. 1. Dendritic transfer impedance. A: a sinusoidal current waveform of linearly changing frequency (chirp) was injected via the dendritic patch electrode and the resulting voltage response recorded by the somatic electrode. Note the fusiform envelope of the voltage response at the soma with a maximal amplitude after ~400 ms (arrow). B: in the same neuron, a chirp current was injected into the soma and the voltage recorded by the dendritic patch electrode. Again, the voltage amplitude in the dendrite is maximal after ~400 ms (arrow). All traces are averages of 10 consecutive sweeps. The schematic representation of a pyramidal cell shows the relative positions of the current and voltage electrodes, respectively.

View larger version (17K): [in this window] [in a new window]   Fig. 2. Dendritic resonance. A: transfer impedance magnitude. B: phase shift for dendrosomatic (straight line) and somatodendritic (dashed line) voltage transfer. Note the close superposition of the 2 traces. A: the impedance magnitude has a maximum at ~6 Hz (Zmax; arrow) and falls off for de- and increasing frequencies. B: voltage leads current up to ~3 Hz (0; arrow) followed by current leading voltage for higher frequencies.

The membrane potential dependence of the transfer impedance was examined by simultaneously shifting the membrane voltage at both electrodes via DC current injections. Figure 3A shows the somatic voltage response to dendritic chirp inputs at three different membrane potentials (V = 90, 80, and 70 mV). Transfer impedance magnitude (B) and phase shift (C) are shown for the three recordings in A. Note the successive decrease of impedance magnitude with hyperpolarization accompanied by a shift of f_res to higher frequencies. Figure 4A shows the voltage dependency of f_res in four different cells. For membrane voltages below threshold, there was an approximately linear relationship between f_res and the membrane voltage as indicated by the straight line, which was fitted to the data points by linear regression (Pearson's r = 0.6, P < 0.05). On average, the resonance frequency increased by 0.6 Hz/10 mV of hyperpolarization.

View larger version (44K): [in this window] [in a new window]   Fig. 3. Voltage dependence of dendritic transfer impedance. A: somatic voltage responses to current injections into the apical dendrite were recorded at 3 different membrane voltages (V = 70, 80, and 90 mV). The potential at the dendritic and somatic electrode was shifted by simultaneous DC current injections through both pipettes. Note the decreasing voltage amplitudes with successive hyperpolarization. B and C: transfer impedance magnitude (B) and phase shift (C) at the 3 recording voltages (solid line, V = 70 mV; dashed line, V = 80 mV; dotted line, V = 90 mV). Note the hyperpolarization-induced shift of the maximal impedance magnitude to higher frequencies.

View larger version (23K): [in this window] [in a new window]   Fig. 4. Parameters influencing dendritic resonance. A: the resonance frequency increases linearly with hyperpolarization. Data points from 4 different cells are fitted by a straight line (Pearson's r = 0.6, P < 0.05). Experiments are symbol coded ( was obtained in 1 µM TTX). B: the transfer impedance maximum (Zmax) decreases with dendritic distance. The straight line was fitted by linear regression (Pearson's r = 0.57, P < 0.05). C: the resonance frequency (fres) is plotted against interelectrode distance. No clear correlation between these parameters could be found. D: the strength of the resonance (Q) is plotted vs. distance. The straight line was fitted by linear regression analysis (Pearson's r = 0.62, P < 0.05) and shows an enhancement of Q with increasing somatofugal distance.

Next, the possible influence of electrode position on parameters of dendritic resonance was assessed. Figure 4B shows a scatter plot of dendrosomatic Z_max and dendritic electrode location. As expected for a linear cable, the transfer impedance decreases with increasing distance from the soma. This is underlined by the straight line, which was fitted to the data points by linear regression (Pearson's r = 0.57, P < 0.05). In Fig. 4C the resonance frequency (f_res) is plotted against dendritic distance. Here, no correlation was found between the two parameters, suggesting site independence of the resonance frequency. Figure 4D shows a plot of resonance strength (Q) against interelectrode distance. Linear regression reveals a significant increase of Q with somatofugal distance (Pearson's r = 0.62, P < 0.05). An increase of Q with distance is predicted for linear cables (Koch 1984) and is likely enhanced by an inhomogeneous distribution of I_h (see following text and DISCUSSION) (Berger et al. 2001; Williams and Stuart 2000). Linear models were fitted to the data in Fig. 4, B and D, to underline a significant correlation. However, fits from more accurate cable models did not converge, most likely due to the limited data set and the well-known cell-to-cell variability of electrical parameters.

I next aimed to characterize the pharmacological basis of the dendritic transfer impedance resonance. Neurons with passive membrane properties are characterized by low-pass filter behavior, i.e., the impedance decreases steadily with increasing frequency due to the capacitive properties of the lipid bilayer. For resonance to occur, low frequencies need additionally to be attenuated. This likely involves mechanisms other than simple passive cable properties. The subthreshold electrical properties of layer V pyramidal cells are considerably influenced by a hyperpolarization-activated cation current (I_h) (Stafstrom et al. 1984), which is also present in the apical dendrite (Berger et al. 2001; Williams and Stuart 2000). Figure 5A shows the somatic voltage response to dendritic chirp current injections under control conditions and in presence of 100 µM ZD 7288 (4-{N-ethyl-N-phenylamino}-1,2-dimethyl-6-{methylamino} pyrimidinium chloride), an irreversible h-channel blocker (Harris and Constanti 1995). Figure 5, B and C, shows transfer impedance magnitude (B) and phase shift (C) in control (solid line) and after ZD 7288 application (dashed line). Under control conditions, the transfer impedance shows a typical resonance behavior with a maximal impedance magnitude and voltage phase lead at low frequencies. After blockade of I_h with ZD 7288, the transfer impedance now follows low-pass behavior, i.e., the impedance magnitude decreases monotonically with frequency, and the phase shift asymptotically approaches a quarter cycle. Equivalent results were obtained in three cells. Together, these results show that the resonance of the dendritic transfer impedance is mediated by I_h.

View larger version (37K): [in this window] [in a new window]   Fig. 5. A sag current underlies dendritic resonance. A: somatic voltage oscillations induced by dendritic chirp current injections are shown under control conditions and after bath application of the h-channel blocker ZD 7288 (100 µM). Note the transition of the voltage response from band-pass (top, control) to low-pass (bottom, ZD 7288) behavior. B and C: transfer impedance magnitude and phase shift are shown for the experiment in A. B: note that ZD 7288 transforms the convex frequency dependence of the transfer impedance magnitude under control conditions (solid line) into a monotonically decreasing relationship (dashed line). C: the positive phase shift for low frequencies under control conditions (solid line) is abolished by ZD 7288 (dashed line).

Sub- and suprathreshold responses

Despite their complex geometry and variety of ion channels present, dendrites were often found to behave linearly under subthreshold conditions (Berger et al. 2001; Cash and Yuste 1998, 1999; Ulrich and Stricker 2000). To test for linearity of the dendritic transfer function, amplitude and direction of the chirp input current were systematically varied. Figure 6A shows the somatic voltage response to two different dendritic chirp current injections. The chirp was either incrementally or decrementally swept through its frequency range. Figure 6, B and C, depicts the dendrosomatic transfer impedance magnitude (B) and phase shift (C) for an accelerating (solid line) and decelerating (dashed line) dendritic chirp input. Both graphs show close superposition, indicating independence of the transfer impedance from the sign of the chirp. In other experiments (n = 8), the amplitude of the chirp input was systematically varied. Figure 7A shows somatic voltage recordings to dendritic chirp inputs of two different amplitudes. Transfer impedance magnitude (B) and phase shift (C) are closely superimposed, indicating homogeneity of the dendritic transfer impedance. Figure 8A illustrates the somatic voltage response for somatic (dashed lines) or dendritic (solid lines) chirp current injections, together with the somatic response to a simultaneous somatodendritic input (dashed-dotted line). Figure 8, B and C, depicts the impedance magnitude (B) and phase shift (C) for somatic (dashed line), dendritic (solid line), and combined somatic-dendritic input (dashed-dotted line), together with the algebraically summed impedance of individual somatic and dendritic inputs (dotted line). The close match of the algebraically with the experimentally summed input indicates superposition (n = 3). Homogeneity and superposition are key properties of linear systems.

View larger version (52K): [in this window] [in a new window]   Fig. 6. Waveform invariance of dendritic transfer impedance. A: accelerating or decelerating chirp current waveforms were injected into the apical dendrite and the voltage responses recovered by a somatic electrode. B and C: impedance magnitude (B) and phase shift (C) for accelerating (solid lines) and decelerating (dashed lines) chirp inputs are superimposed. The close match of both graphs indicates that the electrical behavior of the dendrite is independent of the sign of the chirp.

View larger version (40K): [in this window] [in a new window]   Fig. 7. Homogeneity of dendritic transfer impedance. Two chirp current waveforms with nearly duplicating amplitude ratio were successively injected into the apical dendrite and the voltages oscillations recorded at the soma. B and C: transfer impedance magnitude (B) and phase shift (C) are plotted for both current inputs. Note the close superposition of the 2 traces, thus implying homogeneity.

View larger version (44K): [in this window] [in a new window]   Fig. 8. Superposition of dendritic transfer impedance. A, left: a chirp was injected successively through the somatic or dendritic pipette, followed by a simultaneous current injection via both pipettes. The voltage responses at the soma are shown for the 3 input configurations (right). The middle trace (solid line) shows the somatic voltage response to the dendritic chirp input. A similar response of slightly higher amplitude results from the somatic chirp injection (bottom dashed trace). The combined dendritic and somatic input leads to the somatic voltage response shown in the top right graph (dashed-dotted line). B and C: impedance magnitude and phase shift for the 3 experiments in A. Dendrosomatic transfer impedance (solid line) and somatic point impedance (dashed line) are shown together with their algebraic sum (dotted) line. Superimposed is the transfer impedance for concomitant somatic and dendritic input (dashed-dotted line). Note the close superposition of the impedance for the summed current input with the algebraically summed impedances of either input alone.

To investigate the influence of the dendritic resonance on the generation of action potentials, sub- and suprathreshold chirp currents were injected into the dendrite and the somatic voltage responses measured. Figure 9A shows an example of a subthreshold dendritic chirp input, which led to an oscillatory somatic voltage response with the typical fusiform envelope. Successfully, the amplitude of the chirp input was slightly enhanced. Now, action potentials were detectable at the somatic electrode. Note that the time points of the maximal subthreshold voltage deflections and occurrence of spikes are coincident (arrow). Figure 9B shows a similar experiment in presence of ZD 7288. A subthreshold dendritic chirp input led to a monotonically decreasing voltage oscillation at the soma, in agreement with the low-pass filter properties of a passive dendrite. Successfully, the amplitude of the chirp input was increased, and spikes were now emitted at the peak of the lowest frequency oscillation (arrow). These results imply that under physiological conditions, pyramidal cells can behave as band-pass filters with preferential spike generation at the intrinsic resonating frequency.

View larger version (46K): [in this window] [in a new window]   Fig. 9. Band-pass spiking behavior. A: 2 chirp current waveforms of increasing amplitude were successively injected into the apical dendrite of a layer V pyramidal cell. A 2nd pipette measured the voltage at the soma. The smaller voltage response remained subthreshold and had a maximum amplitude after ~400 ms. The larger current input lead to the emission of action potentials. Note the coincidence of preferred spiking with the maximal subthreshold voltage deflections. Action potentials are truncated due to averaging. B: a similar experiment is shown in presence of the h-channel blocker ZD 7288 (100 µM). A subthreshold dendritic chirp input generates monotonically decreasing voltage oscillations at the soma. Another larger dendritic chirp input initiated action potentials at the 1st depolarizing voltage deflection (arrow). Again, spikes are truncated due to averaging.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

In the present study I show that the proximal apical dendrite of rat layer V pyramidal cells behaves linearly around resting potential and is endowed with a resonance, which favors input in the theta frequency band.

Characteristics of dendritic resonance

The dendritic resonance was abolished by the irreversible H-channel blocker ZD 7288 and thus depends on a hyperpolarization-activated cation current (I_h). Indeed, I_h was found in recordings from the apical dendrite with a density that increased with more distal locations (Berger et al. 2001; Williams and Stuart 2000). In previous studies in this cell type, it was found that dendritic I_h curtails excitatory postsynaptic potentials (EPSPs) and prevents their temporal summation (Berger et al. 2001; Nicoll et al. 1993; Williams and Stuart 2000). Blockade of I_h was also shown to enhance the flow of "tonic" excitation from the apical dendrite to the soma (Schwindt and Crill 1997). Our data suggest an additional role for I_h as a high pass filter of dendritic input, which together with the low-pass behavior of the passive membrane leads to dendritic resonance. Indeed, a resonance frequency of ~6 Hz is about halfway between the activation time constant of I_h (~30-100 ms) (Berger et al. 2001; Williams and Stuart 2000) and the passive membrane time constant in these cells (~14 ms; data not shown). However, it remains to be investigated to what degree this resonance frequency can be shifted by modulation of the membrane leak conductance or I_h (Destexhe and Paré 1999; Pape 1996).

The pharmacological profile of the dendritic transfer impedance resonance in this study is compatible with a 1- to 3-Hz resonance described previously at the soma of pyramidal cells (Hutcheon et al. 1996). The lower frequency of this somatic point impedance resonance and the apparent absence of a dendritic resonance in a previous study (Ulrich and Stricker 2000) are likely to be attributed to differences in recording temperature (room temperature vs. 35°C). I measured a Q₁₀ of ~4 for the temperature dependence of the resonance frequency in these cells (Q₁₀ = 3.8 ± 1.6, n = 3, data not shown), which is compatible with the results of Hutcheon et al. (1996). Likewise, a somatic point impedance resonance of ~6 Hz has been found in hippocampal pyramidal cells at a comparable elevated recording temperature (Leung and Yu 1998). The hyperpolarization induced decrease of Z_max and shift of f_res to higher frequencies is in agreement with previous findings in this cell type at the soma (Hutcheon et al. 1996), and is in line with the voltage dependency of I_h kinetics (Berger et al. 2001; Williams and Stuart 2000). While I_h is responsible for resonance in principal cells of cortex and thalamus, in other brain regions different ionic mechanisms can cause resonance phenomena (Hutcheon and Yarom 2000; Llinás 1988).

Resonance, dendritic integration, and physiological rhythms

The subthreshold voltage transfer along the dendrite at rest was independent of the time course or amplitude of the chirp input. In addition, the voltage response to a distributed current input was equal to the sum of the individual inputs. These are essential features of linear systems. This result is surprising in view of the plethora of dendritic conductances in pyramidal cell dendrites (cf. Johnston et al. 1996), but in agreement with previous studies on signal propagation along the apical dendrite (Berger et al. 2001; Cash and Yuste 1998, 1999; Ulrich and Stricker 2000). Theoretically, active membrane processes are not incompatible with linearity. Many conductances behave linearly over a certain voltage range, as do dendritic cables, which have those incorporated (Koch 1984). The distance dependencies of Z_max and Q are compatible with linear cable theory (Koch 1984) and may be pronounced due to the increased density of I_h at more distal dendritic segments (Berger et al. 2001; Williams and Stuart 2000). From these results it can be predicted that although the impact of distal input is weaker (smaller Z_max), the resonance frequency will be better discriminated (increased Q). Two limitations may restrict the generalization of this study to the overall input-output behavior of pyramidal cells. 1) Simple current injections were used to perturb the cells. This will leave nonlinearities associated with synaptic conductances undetected (Rall 1967). 2) Recordings were limited to relatively proximal segments of the apical dendrite. It has been shown that the distal apical dendrite has peculiar electrical properties, which may lead to a more complex input-output relationship for inputs to the apical tuft (e.g., Larkum et al. 2001). Also, it remains to be shown whether and under what conditions linearity applies to basal and oblique dendrites (cf. Oakley et al. 2001).

The increased impedance at the resonating frequency should favor the propensity of the neuron to generate action potentials at that frequency (Hutcheon and Yarom 2000). This has been confirmed in the present study for just threshold current amplitudes (Fig. 9). Preferred spiking of pyramidal cells around 6 Hz has been previously described in slices of rat somatosensory cortex (Silva et al. 1991). Given the strong temperature dependence of the resonance, such rhythmic spiking is more likely to occur around 9 Hz in vivo (extrapolated from 35°C to a body temperature of 38°C with a Q₁₀ ~4, see above), i.e., in the alpha band. In a recent study, associations of primary sensory input with signals from higher brain areas have been shown to occur through synchronizations in the alpha band (von Stein et al. 2000). Such associations could be favored by the resonance described in this study, particularly because the strength of the resonance increases with somatofugal distance. Rhythmic discharges in sensory cortex within the alpha frequency band were also found in rats before and during exploratory behavior (Nicolelis et al. 1995). Our data show that the frequency tuning of pyramidal cells, which results from their intrinsic input-output properties, is compatible with the behavior of the cortical network during sensory processing.