Dendrosomatic Voltage and Charge Transfer in Rat Neocortical Pyramidal Cells In Vitro

Daniel Ulrich and Christian Stricker

Institute of Neuroinformatics, University of Zürich and Federal Institute of Technology, CH-8057 Zurich, Switzerland


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Ulrich, Daniel and Christian Stricker. Dendrosomatic Voltage and Charge Transfer in Rat Neocortical Pyramidal Cells In Vitro. J. Neurophysiol. 84: 1445-1452, 2000. Most excitatory synapses on neocortical pyramidal cells are located on dendrites, which are endowed with a variety of active conductances. The main origin for action potentials is thought to be at the initial segment of the axon, although local regenerative activity can be initiated in the dendrites. The transfer characteristics of synaptic voltage and charge along the dendrite to the soma remains largely unknown, although this is an essential determinant of neural input-output transformations. Here we perform dual whole-cell recordings from layer V pyramidal cells in slices from somatosensory cortex of juvenile rats. Steady-state and sinusoidal current injections are applied to characterize the voltage transfer characteristics of the apical dendrite under resting conditions. Furthermore, dendrosomatic charge and voltage transfer are determined by mimicking synapses via dynamic current-clamping. We find that around rest, the dendrite behaves like a linear cable. The cutoff frequency for somatopetal current transfer is around 4 Hz, i.e., synaptic inputs are heavily low-pass filtered. In agreement with linearity, transfer resistances are reciprocal in opposite directions, and the centroids of the synaptic time course are on the order of the membrane time constant. Transfer of excitatory postsynaptic potential (EPSP) charge, but not peak amplitude, is positively correlated with membrane potential. We conclude that the integrative properties of dendrites in infragranular neocortical pyramidal cells appear to be linear near resting membrane potential. However, at polarized potentials charge transferred is voltage-dependent with a loss of charge at hyperpolarized and a gain of charge at depolarized potentials.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Neocortical pyramidal cells receive the majority of excitatory synaptic input onto their dendrites (DeFelipe and Fariñas 1992). A variety of active conductances have been found in dendritic recordings (Amitai et al. 1993; Huguenard et al. 1988; Kim and Connors 1993) and these are likely to influence the propagation of synaptic signals to the soma (Deisz et al. 1991; Markram and Sakmann 1994; Schwindt and Crill 1998; Stafstrom et al. 1985; Stuart and Sakmann 1994, 1995). Sodium-dependent action potential generation is thought to occur mainly at the axon hillock (Stuart and Sakmann 1994). Knowledge of the relationship between synaptic input and spike output in individual neurons is essential for theories of cortical circuits (e.g., Douglas et al. 1995). The size of current flow at the soma after stimulation of dendritic synapses has been estimated under steady-state conditions, involving a large and unknown number of synaptic contacts (Ahmed et al. 1998; Schwindt and Crill 1996). However, the exact contribution of individual synapses to current arriving at the soma remains largely unknown. While passive dendrites are expected to act as low-pass filters, active dendritic properties may either boost or attenuate certain signal components. This could potentially lead to a complex relationship between neural input and output. In these experiments, we use an experimental design that circumvents the stochastic nature of transmitter release. We mimic a synaptic conductance on the apical dendrite with a dynamic current-clamp and measure somatic voltage and charge with a second electrode at the soma. This allows us to quantitatively correlate simulated synaptic input with the current arriving at the soma.


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Sprague-Dawley rats of either sex (P12-P18) 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 Vibratome (TPI, St. Louis, MI) and incubated at 34°C. Slices were transferred to a recording chamber and superfused at room temperature with standard artificial cerebrospinal fluid containing (in mM) 125 NaCl, 1.25 NaH2PO4, 25 NaHCO3, 2.5 KCl, 1 MgCl2, 2 CaCl2, 10 glucose, pH adjusted to 7.4 with 5% CO2-95% O2.

Patch pipettes were pulled from thick-walled borosilicate glass (Hilgenberg, Malsfeld, Germany) and filled with a solution containing (in mM) 125 K-gluconate, 5 KCl, 1 MgCl2, 1 CaCl2, 10 HEPES, 11 EGTA; osmolarity 280 mOsmol, pH 7.2 adjusted with KOH. Pipettes used for somatic or dendritic recordings had a tip resistance of about 5 and 15 MOmega , respectively. Pyramidal cells in layer V of somatosensory cortex were visualized with infrared differential interference contrast video microscopy (Dodt and Zieglgänsberger 1990).

Time-varying sinusoids of a linearly increasing frequency (chirps) with 20 pA peak-to-peak amplitude, I0, were generated digitally between 0.1 and 20 Hz (Hutcheon et al. 1996). The frequency was varied at eight octaves per second. The implementation is such that the instantaneous frequency, nu , of the chirp starts at time t = 0, increases linearly with time, and covers the range between the initial frequency nu 0 and the final frequency nu 1, i.e.
&ngr;(<IT>t</IT>)<IT>=&ngr;<SUB>0</SUB>+</IT><FR><NU><IT>&ngr;<SUB>1</SUB>−&ngr;<SUB>0</SUB></IT></NU><DE><IT>t</IT><SUB><IT>1</IT></SUB></DE></FR> <IT>t</IT>
Therefore the angle that must be supplied to the electrode is
2&pgr;&ngr;<IT>t</IT><IT>=2&pgr; </IT><LIM><OP>∫</OP><LL><IT>t</IT><SUB><IT>0</IT></SUB><IT>=0</IT></LL><UL><IT>t</IT><SUB><IT>1</IT></SUB></UL></LIM> <FENCE><IT>&ngr;<SUB>0</SUB>+</IT><FR><NU><IT>&ngr;<SUB>1</SUB>−&ngr;<SUB>0</SUB></IT></NU><DE><IT>t</IT><SUB><IT>1</IT></SUB></DE></FR><IT> t</IT></FENCE><IT>d</IT><IT>t</IT><IT>=2&pgr;</IT><FENCE><IT>&ngr;<SUB>0</SUB></IT><IT>t</IT><IT>+</IT><FR><NU><IT>&ngr;<SUB>1</SUB>−&ngr;<SUB>0</SUB></IT></NU><DE><IT>2</IT><IT>t</IT><SUB><IT>1</IT></SUB></DE></FR> <IT>t</IT><SUP><IT>2</IT></SUP><IT>+</IT><IT>C</IT></FENCE>
where C contains information on the phase lag. For zero phase lag, the current amplitude, I, of the chirp then takes the form
<IT>I</IT><IT>=</IT><IT>I</IT><SUB><IT>0</IT></SUB><IT> cos </IT><FENCE><IT>2&pgr;</IT><FENCE><IT>&ngr;<SUB>0</SUB>+</IT><FR><NU><IT>&ngr;<SUB>1</SUB>−&ngr;<SUB>0</SUB></IT></NU><DE><IT>2</IT><IT>t</IT><SUB><IT>1</IT></SUB></DE></FR> <IT>t</IT></FENCE><IT>t</IT></FENCE>
A dynamic current-clamp (Robinson and Kawai 1993; Sharp et al. 1993) was applied through an Axoclamp 2B amplifier (Axon Instruments, Foster City, CA) in bridge mode via a Labmaster A/D converter (Scientific Solutions, Solon, OH) as described previously (Ulrich and Huguenard 1996, 1997). The effects of electrode resistance and capacitance were minimized by electronic compensation. Due to the fast rise times of excitatory synaptic conductances, AD/DA conversions were executed at up to 25 kHz. Synaptic current was calculated from the dynamic current-clamp protocol. To avoid contamination by high-frequency noise, voltage traces were low-pass filtered with a custom-made eight-pole Bessel filter (design JCSMR-ANU, Australia) at 2 kHz, i.e., well below the limits given by the sampling theorem. A liquid junction potential of -8 mV was subtracted off-line.

Time centroids of current or voltage transients were calculated from the first and zeroth moments of current and voltage records as described by Agmon-Snir and Segev (1993). Data are presented as mean ± SE and "n" designates the number of recordings.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Dual whole-cell recordings were obtained from large layer V pyramidal cells in rat somatosensory cortex to characterize voltage and charge transfer from the dendrite to the soma and vice versa. Figure 1A shows an example of simultaneous recordings with somatic and dendritic patch electrodes separated by 200 µm. The average dendritic recording distance from the soma was 112 ± 14 µm. All cells were of the regular spiking type (Connors and Gutnick 1990) and had a mean resting membrane potential at the soma of -62 ± 1.5 mV (n = 12). In a linear system, charge transfer and steady-state voltage decay are equal in opposite directions (Carnevale and Johnston 1982; Rall and Segev 1985). Therefore we first investigated the spread of somatic voltage into the dendrite. At rest, small hyperpolarizing current steps were injected into the soma and the membrane voltage deflections were recorded simultaneously by the somatic and dendritic patch electrodes (Fig. 1B). As previously shown in layer V pyramids, an apparent sag in membrane voltage was revealed for hyperpolarizing voltage transients at both recording sites (Fig. 1B, Stuart and Spruston 1998) and was even more pronounced in the dendrite. The mean somatofugal steady-state voltage transfer ratio (k12) was 0.75 ± 0.03 (n = 9; note that k12 is the reciprocal of attenuation). In a passive neuron, k12 is expected to decrease with electrotonic distance (X). We calculated the length constant (lambda ) of the proximal apical dendrite as lambda  = radical [(d/4) · (Rm/Ri)] with an axial resistivity (Ri) of 100 Omega cm (Stuart and Spruston 1998) and Rm = tau m/Cm. The membrane time constant (tau m) was estimated from fitting an exponential function to the late part of the current step response at the soma (Holmes et al. 1992; data not shown). The average tau m was 30 ± 3.6 ms. The specific membrane capacitance (Cm) was taken as 1 µF cm-2 (Curtis and Cole 1938). Figure 1C shows a scatter plot of k12 versus the electrotonic distance (X) of the two recording electrodes. As predicted, dendritic voltage deflections decrease with distance. In Fig. 1C the function {cosh (L - X)/cosh (L)} was fitted to the data points by a least-squares algorithm. This formula describes the DC voltage decay in a uniform equivalent cylinder of electrotonic length L with a sealed end. The electrotonic length obtained from the fit (L = 1.7) is in agreement with previous estimates of L for the apical dendrite of layer V pyramidal cells based on morphological data (Larkman et al. 1992).



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Fig. 1. Somatodendritic steady-state voltage transfer. A: composite infrared videomicrograph of a layer V pyramidal cell in rat somatosensory cortex. A patch electrode is positioned at the apical dendrite and another electrode records from the soma. Scale bar corresponds to 10 µm. B: somatic current steps (top trace) and somatic (middle, S) and dendritic (bottom, D) voltage recordings were used to estimate the membrane time constant, the input resistance, and the somatofugal steady-state voltage transfer (k12). C: scatter plot of k12 versus the electrotonic interelectrode distance. The fitted line predicts the voltage profile in a homogeneous equivalent cylinder of electrotonic length 1.7 with a sealed end. D: somatofugal transfer resistances (R12) were obtained from data as in Fig. 1B and are plotted against their corresponding dendrosomatic values (R21) extrapolated from the chirps (cf. Fig. 2). The straight line was fitted by linear regression through the origin (Pearson's r = 0.89, P < 0.05). The (dashed) identity line is shown for reference.

The amplitude ratio between voltage and current at two different sites equals their transfer resistance (R). Figure 1D shows a scatter plot of somatofugal transfer resistances (R12) obtained from somatic current injections and corresponding dendrosomatic transfer resistances (R21). The latter were obtained from fitting an RC circuit to the chirp data by a least-squares algorithm and extrapolating the fit to DC. Note that at rest, transfer resistances in somatofugal and dendrosomatic directions are highly correlated as shown by the linear fit in Fig. 1D (Pearson's r = 0.89, P < 0.05). Reciprocity of transfer resistances is to be expected in a linear system.

Frequency-dependent voltage transfer from the dendrite to the soma was investigated by sinusoidal current injections through the dendritic electrode (Fig. 2A). The resulting voltage was recorded simultaneously by the dendritic and somatic pipettes at resting membrane potential (Fig. 2A). Figure 2, B and C, shows an example of transfer impedance and phase shift between dendritic current and somatic voltage after fast Fourier transformation. The data points were fitted by an equivalent cable with sealed ends (Butz and Cowan 1974): V(f) = I(f) · Z(gamma ) · cosh (gamma x) · cosh {gamma (l - d)}/sinh (gamma l). V(f) and I(f) are the Fourier transforms of somatic voltage and dendritic current, and f indicates the frequency. Z(gamma ) and l are the input impedance and length of the equivalent cable, respectively. The relative positions of the recording (x) and stimulation (d) electrodes require that 0 < x < d < l. The propagation constant (gamma ) depends on lambda  and tau : gamma  = radical {(2pi iftau  + 1)/lambda } and Z(gamma ) is defined as Z = r/tau , where r corresponds to the axial resistance of the cable. The model was fitted to the complex numbers by a least-squares algorithm. The resulting tau  and lambda  from five different cells were 30 ± 4 ms and 400 ± 112 µm. The average length and diameter of the cable are 1169 ± 131 and 2 ± 0.5 µm, respectively. The fitted function in Fig. 2, B and C, falls monotonically for increasing frequencies. The inflection point is at 4 Hz and coincides approximately with the -3 dB point (5.3 Hz). The maximal initial roll-off is -17 dB per decade, which approaches -10 dB per decade at higher frequencies. Therefore at rest, transient synaptic input will be low-pass filtered by the dendritic cable properties.



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Fig. 2. Frequency dependence of dendrosomatic voltage transfer. A: a frequency-modulated sinusoidal current (chirp) was injected into the cell through the dendritic electrode. The resulting membrane voltage oscillations were recorded at the dendrite (VD) and the soma (VS). Transfer impedance (B) and phase shift (C) in frequency domain were obtained from a single, representative example. An equivalent cable with sealed ends was fitted to the data points by a least-squares algorithm. The parameters of the model cable for this cell are tau  = 32 ms, lambda  = 801 µm, l = 1,160 µm, d = 710 µm, x = 450 µm, and r = 2.1 GOmega /cm. Given this value for r and assuming an Ri of 100 Omega cm, a diameter of 2.5 µm for the equivalent cable can be calculated (cf. text for details).

Contrary to simple current injections, real synaptic inputs are generated by transmembrane conductances. The resulting current flow is a nonlinear function of the membrane potential. Experimentally, membrane conductances can be mimicked by a hybrid computer system, a dynamic current-clamp. Control experiments were carried out to show that the current generated by the conductance imposed at the soma corresponds to the current that was recovered under voltage-clamp conditions with a second electrode. Double somatic recordings (n = 4) were performed on thick-tufted layer V pyramidal cells as illustrated in Fig. 3A. With one electrode in current-clamp and the bridge balanced, the conductance time course was imposed. A second electrode in voltage-clamp measured the actual current delivered. Such an experiment is shown in Fig. 3B, where the conductance time course corresponded to an alpha -function with alpha  = 30, an amplitude of 2 nS, and a reversal potential of 0 mV. The top trace (a) is the membrane potential as measured by the electrode in current-clamp. The command potential of the second electrode was set at the resting membrane potential of this cell (-63 mV). At the peak of the conductance, a voltage escape of 1.5 mV was measured. The second trace (b) illustrates the current that passed through the electrode in current-clamp. Note the step-like increments in the tail of the excitatory postsynaptic current (EPSC) that are due to the finite resolution achieved with the analog-to-digital converter board. The third time course (c) is the current measured by the voltage-clamp electrode. Bottom trace, the two current time courses are superimposed (b + c). The figure indicates an excellent match between the two currents, except for a small lag during the rising phase (0.7 ms). This is due to incomplete compensation of the series resistance and neutralization of the electrode capacitance.



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Fig. 3. Recovering the current resulting from a conductance change by voltage-clamp with a second electrode. A: experimental arrangement of paired somatic recordings. One electrode is in current-clamp, the other in voltage-clamp mode. The scale bar corresponds to 10 µm. B: top (a) indicates the membrane voltage measured by the electrode in current-clamp with the bridge balanced. The time course of the conductance corresponded to an alpha -function (alpha  = 30) with a reversal potential of 0 mV and an amplitude of 2 nS. The resting membrane potential was -63 mV, which was equivalent to the command potential of the voltage-clamp. The second trace (b) is the current passed through the electrode in current-clamp and the third (c) is the current recovered by the voltage-clamp electrode. Bottom, the two current traces are superimposed (b + c).

To estimate the charge arriving at the soma, the cell should be kept in voltage-clamp. However, somatic voltage-clamp would artificially force the membrane potential of the apical dendrite to stay near the command potential and would affect voltage-dependent conductances. As an approximation for the charge arriving at the soma under unclamped conditions, the somatic voltage integral can be divided by the somatic input resistance obtained by linear regression of current-voltage data similar to Fig. 1B (not shown). To validate this approach, we compared the charge delivered by the dynamic current-clamp electrode with the estimated charge of the voltage integral scaled by RN (Fig. 4A). In a series of six experiments, double somatic recordings as in Fig. 3A were obtained in current-clamp. In each case the membrane potential was held at around -70 mV to provide an equal driving force for the conductance in each of the cells. A dynamic current-clamp was imposed with the second electrode simulating a conductance time course using alpha -functions of different values (30, 200, 500, 1,000) and a magnitude of 2 nS. In Fig. 4A, the scaled voltage integral is plotted against the effective charge delivered through feedback from the dynamic current-clamp. The dashed line indicates equality in charge. The solid line is the linear regression forced through zero with a slope of 1.01 ± 0.01 and a Pearson's r = 0.996 (P < 0.001). This suggests that for double somatic recordings the somatic charge can be inferred from the scaled voltage integral with excellent accuracy. The scatter in the ordinate for values of alpha  = 30 is largely due to the spontaneous synaptic activity encountered in these cells, whereas the scatter in the abscissa is due to the inaccuracy of holding the cell at -70 mV in current clamp.



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Fig. 4. Assessment of excitaory postsynaptic potential (EPSP) charge estimates at the soma. A: scatter plot of charge calculated using the voltage integral divided by input resistance (RN) versus the effective charge (Qeff) based on the current injected during the dynamic current-clamp. The graph is based on measurements obtained from double somatic patch recordings from 6 cells as in Fig. 3. However, the cells were kept in current-clamp and Vm was held around -70 mV. For simplicity, alpha -functions of different values (alpha  = 30, 200, 500, 1,000) were used to model the synaptic conductances of 2 nS in each cell (symbol coded). Note that for values of alpha  = 200 to 1,000, the 6 data points per alpha -value overlap to form a single point. The error bars reflect the uncertainty with which RN could be determined. The dashed line is the prediction of equality. The solid line indicates the linear regression to the data forced through zero with a slope of 1.01 ± 0.01 (Pearson's r = 0.996; P < 0.001). This line is not different from the line of equality. B: input resistance as a function of membrane potential. Scatter plot of the data from 3 cells with comparable RN (symbol coded). A linear regression of the data revealed that RN changed at 4.8 ± 0.7 MOmega per mV polarization (Pearson's r = 0.89; P < 0.005).

In a further set of control experiments, we checked if membrane potential affects input resistance (RN) in layer V pyramidal cells. In Fig. 4B, RN is plotted as a function of membrane potential from three cells of similar input resistance. The result shows a significant linear correlation of RN with membrane potential, having a slope of 4.8 ± 0.7 MOmega per mV polarization (Pearson's r = 0.89, P < 0.005). Therefore because the scaled voltage integral as a predictor of charge arriving at the soma is multiplied by (1/RN), it is expected that with depolarization the actual charge is progressively underestimated (cf. Fig. 6C and the last paragraph of this section).

To quantify synaptic voltage and charge transfer from dendrite to soma, a dynamic current-clamp was applied to the dendritic pipette. The kinetics of the conductance waveforms were described by two exponential functions with time constants characteristic for fast glutamatergic or GABAergic synapses (tau rise = 0.2 ms, tau decay = 1.5 ms and tau rise = 0.4 ms, tau decay = 7.5 ms, respectively). Peak conductance was varied between 1 and a few nS in agreement with estimates of quantal size (Forti et al. 1997; Stricker et al. 1996). The corresponding (uncorrected) reversal potentials were 0 mV for the EPSC and -65 mV for the inhibitory postsynaptic current (IPSC). Figure 5A shows an example of a dendritic dynamic current-clamp EPSP that was simultaneously recorded at the soma. Figure 5B depicts another experiment simulating an inhibitory postsynaptic potential (IPSP). Because the driving force for the IPSC is only a few millivolts at rest, the amplitude of the dendritic IPSP is relatively small. EPSP charge transfer and amplitude ratios for EPSPs and IPSPs are summarized in Fig. 5C. As expected in a linear system (Carnevale and Johnston 1982; Rall and Segev 1985), dendritic charge transfer at rest is on average comparable to somatodendritic steady-state voltage transfer (Fig. 5C). Due to the high-frequency components of a glutamatergic conductance, EPSP amplitude at the soma is significantly reduced (7.7 ± 1.5%, n = 7) compared with the EPSP at the input site. Because of the slower time course of the conductance, the IPSP peak amplitudes are reduced less (to about a quarter of the initial size, i.e., 27 ± 7%, n = 4). Note that, although data from different experiments are pooled in Fig. 5, C and D, comparisons were made by a Student's paired t-test, i.e., data from individual experiments were compared.



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Fig. 5. Synaptic voltage and charge transfer. A: excitatory conductance. The synaptic current (second trace) follows the time course of the conductance waveform (upper trace). Dynamic current-clamp EPSP generated at the dendrite (D) and simultaneously recorded at the soma (S). B: similar experiment as in A but with an inhibitory conductance. Note the small amplitude of the IPSP due to a much smaller driving force than in A (few millivolts at rest). C: histogram of pooled data of k12, Qrel (EPSP charge ratio), and EPSP and inhibitory postsynaptic potential (IPSP) peak-amplitude transfer ratio. k12 and Qrel were not significantly different from each other (P > 0.05, paired t-test). D: histogram of pooled data of the total delay (TD) and local delay (LD) of the EPSP in relation to the membrane time constant (tau ). tau  and TD were not significantly different from each other (P > 0.05, paired t-test).

Neuronal integration not only depends on amplitude transfer but also on propagation times (Agmon-Snir and Segev 1993). We determined the time centroids of dendritic EPSC/Ps and of the resulting somatic EPSPs by the method of moments. The centroid delay of synaptic EPSC and EPSP is called the local delay, whereas the time interval between the centroids of somatic EPSP and dendritic EPSC is termed the total delay. Figure 5D shows a summary histogram of calculated local and total delays in relation to the membrane time constant. As predicted for a passive neuron, the total delay of dendritic EPSPs was not significantly different from the corresponding membrane time constant. The local delay (2.7 ± 0.5 ms), which determines the integration time at the synapse, was on the order of a tenth of the membrane time constant, again in agreement with simulations of pyramidal cells with passive membrane properties (Fig. 5D, cf. Agmon-Snir and Segev 1993).

Various voltage-dependent membrane conductances can be activated by small voltage deflections from rest. Therefore the influence of membrane potential changes on dynamic current-clamp EPSP amplitude and charge transfer was assessed. Dendritic and somatic membrane voltages were simultaneously shifted by DC current injections. Figure 6A shows an example of simultaneously recorded somatic and dendritic dynamic current-clamp EPSPs at three different holding potentials (-56, -71, and -78 mV at the soma; single traces). There is a small scatter in membrane voltage between soma and dendrite due to the inability to perfectly clamp the membrane potential in current-clamp mode. As expected, the dendritic EPSP amplitude is diminished with depolarization due to a reduced driving force. At the same time, the somatic EPSP became prolonged. Figure 6, B and C, show scatter plots of pooled data (n = 5; results of each cell symbol coded). While the EPSP peak amplitude ratio was independent of the membrane potential (Fig. 6B), charge transfer was strongly voltage-dependent (Fig. 6C). Incomplete series resistance and electrode capacitance compensation and variable dendritic seal resistances from experiment to experiment may have contributed to the scatter of the data points in Fig. 6C. However, these cannot explain the significant linear relationship between membrane potential and charge transfer (Pearson's r = 0.44, P < 0.04), which results in a relative charge gain of 30 ± 13% for 10 mV of depolarization. Due to the voltage dependence of RN, the actual charge gain is expected to be more pronounced, i.e., our estimate is conservative. We recalculated the estimates in Fig. 6C for RN at different holding potentials. The new estimates are still fitted best with a line, but one with an increased slope of 51 ± 15% per 10 mV polarization (Pearson's r = 0.59; P < 0.01). With respect to charge transfer under passive conditions (horizontal dashed line in Fig. 5C), a disproportional loss of charge is found below rest, and a gain of charge between rest and spike threshold (vertical dashed line in Fig. 6C).



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Fig. 6. Voltage-dependent EPSP efficacy. A: dendritic (D) and somatic (S) EPSPs generated at the dendrite by a dynamic current-clamp at 3 membrane voltages, -56, -71, and -78 mV, respectively. B and C: scatter graphs of EPSP peak amplitude (B) and charge (C) ratio in relation to membrane potential from 5 cells. The straight line in C was obtained by linear regression (Pearson's r = 0.44, P < 0.04). The horizontal dashed line corresponds to the mean k12, i.e., the expected average electrotonic charge transfer. The vertical dashed line indicates the average action potential threshold in these cells. Data from individual cells in B and C are symbol coded.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The main findings of this study are 1) that synaptic charge transfer from dendrite to soma is voltage-dependent, whereas the transfer of peak amplitude is not, and 2) that at rest, voltage and charge transfer from dendrite to soma and vice versa depend on linear cable properties.

The sites of dendritic recordings in this study are relatively proximal (X < 0.7) compared with the total length (L ~ 1.7) of the apical dendrite. About 85% of all excitatory synapses are on spines (DeFelipe and Fariñas 1992; Larkman 1991b). The apical trunk of a thick layer V pyramidal cell has a spine density of 6.3/µm and a total of 3100 spines. Therefore our maximal recording distance is within the range of ~35% of all synapses on the apical trunk dendrite. However, a generalization to other synapses of similar distance on basal and oblique dendrites will have to await experimental verification. How well are synapses on spines represented by a dynamic current clamp on the stem dendrite? Recent findings suggest that spines are more likely to separate synapses biochemically rather than electrically (Svoboda et al. 1996). It is therefore reasonable to assume that our main conclusions about synaptic charge transfer are valid for synapses on spines and on shafts. This point of view is in agreement with modeling studies of synaptic conductance inputs on dendritic spines and shafts in pyramidal cells (Turner 1984).

It has recently been shown that somato-dendritic voltage attenuation can be best accounted for by a nonuniform Rm and Ih (Stuart and Spruston 1998). It is likely that Ih affects even small voltage deflections of a few millivolts, as shown by an omnipresent sag in our recordings. Therefore our estimates of Rm are unlikely to reflect strictly passive conditions. Nevertheless, the reciprocity of transfer resistances and of charge and voltage transfer holds under our resting conditions as expected for a linear system (Carnevale and Johnston 1982; Rall and Segev 1985). We conclude that within the voltage range of our observations the interplay of all open conductances still results in a linear albeit not passive membrane. A similar conclusion was drawn by studying spatial EPSP summation in hippocampal pyramidal cells (Cash and Yuste 1999).

The somatopetal current transfer properties of the apical dendrite could be satisfactorily approximated by a linear cable model. The independent estimates of L (1.7) and lambda  (400 µm) are in line with the morphological length of the apical trunk (~0.7 mm) in these cells (Larkman 1991a). The simple low-pass behavior of the apical dendrite agrees with similar findings from dendrites in spinal neurons (Buchanan et al. 1992). We did not find resonance phenomena in our transfer impedance measurements as described in neuroblastoma neurites (Moore et al. 1988). In neocortical pyramidal cells, somatic point impedance measurements revealed a resonance below 2.5 Hz at hyperpolarized potentials (Hutcheon et al. 1996). Because our measurements of transfer impedance were confined to resting conditions, deviations from linearity cannot be excluded at hyperpolarized membrane voltages.

Our data confirm previous experimental and modeling data (Cauller and Connors 1992; Markram et al. 1997) which demonstrated severe EPSP peak attenuation for unitary input even at moderate electrotonic distances from the soma. However, quantal current at the soma has been shown to be location independent (Jack et al. 1981; Stricker et al. 1996). This could either result from a location-scaled increase in input conductance (Stricker et al. 1996) or an appropriately balanced boosting mechanism (Cook and Johnston 1999). In our experiments, we did not scale the conductances of the dynamic current clamp for dendritic location.

Under unclamped conditions, measuring the charge arriving at the soma is not possible. However, we were able to show using double somatic recordings that the voltage integral scaled by RN is a surprisingly precise predictor for charge estimation with accuracy in the range of 1% (well within the errors of estimating RN). We also observed that RN was dependent on the membrane potential. This is in agreement with the observations of Connors et al. (1982) and Stafstrom et al. (1984) in other cortical slice preparations. This finding can most likely be explained by rectification in the depolarizing direction due to INaP (Stafstrom et al. 1982) and in the hyperpolarizing direction to Ih (Spain et al. 1987).

We further obtained evidence that voltage-dependent membrane nonlinearities influence the flow of charge from a synapse to the soma. No attempt was made to assess the nature of these conductances but likely candidates for the prolongation of the EPSP above -60 mV are INa,p (Stuart and Sakmann 1995) and/or INMDA (activated by ambient glutamate, Sah et al. 1989). Ih (Nicoll et al. 1993; Stuart and Spruston 1998) and/or IA (Hoffman et al. 1997) have the potential to cause the truncation of the EPSP below -60 mV. All four currents have been found in dendritic recordings; they activate/deactivate or inactivate in the appropriate voltage ranges and could lead to the required charge gain/loss.

What are the potential functional consequences of voltage-dependent charge transfer? Modeling studies suggest that the resting membrane voltage can be depolarized by moderate background activity of excitatory synapses (Bernander et al. 1991). From our data we predict that the additional inward current responsible for the enhanced charge transfer will increase the gain of the relationship between synaptic input and spike output under depolarized conditions. In addition, the time window for nonlinear EPSP summation will be increased for two reasons: the increase in RN and the charge gain that is predominantly in the tail of the EPSP.


    ACKNOWLEDGMENTS

We are very grateful to Prof. S. J. Redman for carefully reading the manuscript and for excellent advice. We thank Prof. R. J. Douglas, Dr. M. Carandini, and dipl. phys. A. Kern for help with the design, implementation, and analysis of the chirps and stimulating discussions. We are indebted to Dr. A. I. Cowan for experimental support with the double somatic recordings.

This work was supported by Swiss National Science Foundation Schwerpunk Programm Biotechnologie Grants 5002-242787 and 50-52085-97.


    FOOTNOTES

Present address and address for reprint requests: D. Ulrich, Dept. of Physiology, University of Bern, Bühlplatz 5, CH-3012 Bern, Switzerland (E-mail: Ulrich{at}pyl.unibe.ch).

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

Received 21 January 2000; accepted in final form 25 May 2000.


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