INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Since the classical view of passive dendritic integration was proposed for motoneurons 30 years ago (Fatt 1957), the introduction of new experimental techniques such as intradendritic recordings (Llinás and Nicholson 1971; Wong et al. 1979), and visually guided patch-clamp recording (Stuart et al. 1993; Yuste and Tank 1996) has revolutionized this area. These new approaches revealed that the dendrites of pyramidal neurons are involved actively in the integration of excitatory postsynaptic potentials (EPSPs) and that the activation of few synapses has powerful effects at the soma in brain slices (Markram et al. 1997; Mason et al. 1991; Thomson and Deuchars 1997). Although remarkably precise data have been obtained in slices, little is known about the integrative properties of the same neurons in vivo.

The synaptic connectivity of the neocortex is very dense. Each pyramidal cell receives 5,000-60,000 synapses (Cragg 1967; DeFelipe and Fariñas 1992), 70% of which originate from other cortical neurons (Gruner et al. 1974; Szentagothai 1965). Given that neocortical neurons spontaneously fire at 5-20 Hz in awake animals (Evarts 1964; Hubel 1959; Steriade 1978), cortical cells must experience tremendous synaptic currents that may have a significant influence on their integrative properties. This theme was explored by several modeling studies (Barrett 1975; Bernander et al. 1991; Holmes and Woody 1989), where it was predicted that synaptic activity may have a profound impact on dendritic integration. However, despite its possible importance for understanding neuronal function, the conductance due to synaptic activity was never measured in awake animals because of the paramount technical difficulties related to intracellular recordings in conscious animals.

To circumvent these difficulties, we constrained computational models of neocortical pyramidal neurons with in vivo intracellular data obtained in ketamine-xylazine-anesthetized cats before and after local perfusion of tetrodotoxin (TTX) (Paré et al. 1998b). The interest of this approach derives from the fact that under ketamine-xylazine anesthesia, cortical neurons oscillate (<1 Hz) between two states, one where the network is quiescent and another where it displays a pattern of activity similar to the waking state (Steriade et al. 1993a,b) (Fig. 1,A and B). Indeed, during these active periods (Fig. 1B, underlined epochs), as in the waking state (Fig. 1A), the electroencephalogram (EEG) is dominated by waves of low amplitude and high frequencies (20-60 Hz) and neocortical pyramidal neurons fire spontaneously at 5-20 Hz. Moreover, electrical stimulation of brain stem activating systems that are believed to maintain the awake state in normal circumstances elicits periods of desynchronized EEG activity with similar characteristics under ketamine-xylazine anesthesia (Steriade et al. 1993a).

View larger version (32K): [in this window] [in a new window]   Fig. 1. Electrophysiological properties of neocortical pyramidal neurons during periods of intense synaptic activity. A: extracellularly recorded cortical neuron of the suprasylvian gyrus in an awake cat. This cell fired tonically at 7.1 Hz (Extracellular) while the electroencephalogram (EEG) displayed low-amplitude fast activity (20-60 Hz). B: intracellularly recorded cortical neuron of the same cortical area under ketamine-xylazine anesthesia using a K-acetate-filled pipette. "Active" periods (bars) alternate with deep hyperpolarizations. During active periods, this cortical neuron fired at ~7.3 Hz while the EEG showed low-amplitude fast activities. C: low Rin during active periods. Top: during active periods, the voltage responses to intracellularly injected current pulses (0.1 nA) were highly variable (cell maintained hyperpolarized just below firing threshold). Avg: average of 50 pulses. D: same cell and current pulse amplitude as in C after application of TTX. Top: TTX suppressed most spontaneous events and produced a marked increase in Rin and time constant. Avg: average of 20 pulses. E: Vm distribution before and after TTX. During active periods (Active), Vm values were distributed between 70 and 55 mV, and the standard deviation was high (v = 3.5 mV in this case). TTX produced a marked hyperpolarization (to around 80 mV) and a drop of v (to ~0.4 mV). F: graph plotting the percentage decrease in Rin (normalized to the Rin under TTX) as a function of v for several cells during active periods and after TTX.

Thus we estimated the synaptic activity required to account for the differences in neuronal properties observed in vivo during synaptic quiescence (i.e., in the presence of TTX) and during these active periods, here considered as a model of the spontaneous synaptic bombardment occurring in the waking state. The model then was used to infer the impact of this intense synaptic activity on dendritic integration.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Intracellular recordings in vivo

We reanalyzed intracellular data obtained from neocortical pyramidal cells recorded in a previous study (Paré et al. 1998b). Unpublished intracellular recordings obtained with K-acetate-filled pipettes (n = 2) also were included in the analysis. Briefly, intracellular recordings were obtained from morphologically identified neocortical pyramidal cells in the suprasylvian gyrus (area 5-7) of cats deeply anesthetized with a ketamine-xylazine mixture (11 and 2 mg/kg im), paralyzed with gallamine triethiodide, and artificially ventilated. The level of anesthesia was determined by continuously monitoring the EEG, and supplemental doses of ketamine-xylazine (2 and 0.3 mg/kg, respectively, iv) were given to maintain a synchronized EEG pattern. Lidocaine (2%) was applied to all skin incisions. End-tidal CO₂ concentration was kept at 3.7 ± 0.2% (mean ± SE) and the body temperature was maintained at 37°C with a heating pad. To ensure recording stability, the cisterna magna was drained, the cat was suspended, and a bilateral pneumothorax was performed. Intracellular recording electrodes consisted of glass capillary tubes pulled to a tip diameter of ~0.5 µm (~30 M) and filled with K-acetate or KCl (2.5 M). Details about experimental procedures and cell identification were given previously (Paré et al. 1998a,b). Experiments were conducted in agreement with ethics guidelines of the Canadian Council on Animal Care.

TTX microperfusion in vivo

An injection micro-pipette (75 µm tip diameter) was inserted ~2 mm rostral to the recording micropipette to a depth of 1.5 mm. A solution (Ringer or Ringer + TTX, 50 µM) was pumped continuously through the injection pipette (1-1.5 µl/min) for the duration of the recording session; the dialyzing solution was changed using a liquid switch system. The Ringer solution contained (in mM) 126 NaCl, 26 NaHCO₃, 3 KCl, 1.2 KH₂PO₄, 1.6 MgSO₄, 2 CaCl₂, 5 HEPES, and 15 glucose. The blockade of synaptic activity by TTX was evidenced by the disappearance of responses to electrical stimuli applied to the cortex using tungsten microelectrodes inserted 2 mm caudal to the recording pipette (see Paré et al. 1997, 1998b for more details).

Estimation of membrane parameters

Membrane potential (V_m) distributions were computed from concatenated epochs of intense synaptic activity totaling ~1 min. The signal was sampled at 5 kHz (for a total of ~300,000 data points), and the positive phase of action potentials was deleted digitally. The values of these data points (usually 2) were replaced by that of points immediately preceding the action potentials. No attempt was made to delete spike afterpotentials because they were distorted by spontaneous synaptic events. The average V_m (V_m) and the standard deviation (_v) were computed from such distributions.

Geometry for computational models

Simulations of cat layer II-III, layer V, and layer VI neocortical pyramidal cells were based on cellular reconstructions obtained from two previous studies (Contreras et al. 1997; Douglas et al. 1991). The cellular geometries were incorporated into the NEURON simulation environment (Hines and Carnevale 1997). The dendritic surface was corrected for spines, assuming that spines represent ~45% of the dendritic membrane area (DeFelipe and Fariñas 1992). Surface correction was made by rescaling C_m and conductances by 1.45 as described previously (Bush and Sejnowski 1993; Paré et al. 1998a). An axon was added, consisting in an initial segment of 20 µm length and 1 µm diam, followed by 10 segments of 100 µm length and 0.5 µm diam each.

Passive properties

Passive properties were adjusted to experimental recordings in the absence of synaptic activity: to block synaptic events mediated by glutamate -amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and -aminobutyric acid type-A (GABA_A) receptors, the microperfusion solution contained: Ringer + TTX (50 µM) + 1,2,3,4-tetrahydro-6-nitro2,3-dioxo-benzo[f]quinoxaline-7-sulfon amide disodium (NBQX, 200 µM) + bicuculline (200 µM). This procedure suppresses all miniature synaptic events, as demonstrated in a previous study (Paré et al. 1997).

Fitting of the model to passive responses obtained in such conditions of absence of synaptic activity was performed using a simplex algorithm (Press et al. 1986). Fitted parameters were leak conductance and reversal potential, whereas other passive parameters were fixed (membrane capacitance of 1 µF/cm² and axial resistivity of 250 cm). Other combinations of passive parameters were also considered, including a supplementary leak in the soma (10 nS) due to electrode impalement, combined with a lower leak conductance of 0.015 mS cm² (Pongracz et al. 1991; Spruston and Johnston 1992) and/or a lower axial resistivity of 100 cm.

In some simulations, a nonuniform distribution of leak parameters was used based on estimations in layer V neocortical pyramidal cells (Stuart and Spruston 1998). As estimated by these authors, the axial resistance was low (80 cm) and the leak conductance was low (g_leak = 0.019 mS cm²) in soma but high (g_leak = 0.125 mS cm²) in distal dendrites. g_leak was given by a sigmoid distribution 1/g_leak = 8 + 44/{1 + exp[(x  406)/50]} where x is the distance to soma. The exact form of this distribution was obtained by fitting the model to passive responses as described above.

Synaptic inputs

The densities of synapses in different regions of the cell were estimated from morphological studies of neocortical pyramidal cells (DeFelipe and Fariñas 1992; Fariñas and DeFelipe 1991a,b; Larkman 1991; Mungai 1967; White 1989). These densities (per 100 µm² of membrane) were as follows: 10-20 GABAergic synapses in soma, 40-80 GABAergic synapses in axon initial segment, 8-12 GABAergic synapses, and 55-65 glutamatergic (AMPA) synapses in dendrites.

The kinetics of AMPA and GABA_A receptor types were simulated using two-state kinetic models (Destexhe et al. 1994)

(1)

(2)

where I_syn is the postsynaptic current, _syn is the maximal conductance, m is the fraction of open receptors, E_syn is the reversal potential, [T] is the transmitter concentration in the cleft, and  and  are forward and backward binding rate constants of T to open the receptors. E_syn = 0 mV,  = 1.1 × 10⁶ M¹s¹,  = 670 s¹ for AMPA receptors; E_syn = 80 mV,  = 5 × 10⁶ M¹s¹,  = 180 s¹ for GABA_A receptors. When a spike occurred in the presynaptic compartment, a pulse of transmitter was triggered such that [T] = 1 mM during 1 ms. The kinetic parameters were obtained by fitting the model to postsynaptic currents recorded experimentally (see Destexhe et al. 1998). N-methyl-D-aspartate (NMDA) receptors are blocked by ketamine and were not included.

Correlation of release events

In some simulations, N Poisson-distributed random presynaptic trains of action potentials were generated according to a correlation coefficient c. The correlation applied to any pair of presynaptic train, irrespective of the proximity of synapses on the dendritic tree and correlations were treated independently for excitatory and inhibitory synapses for simplicity. To generate correlated presynaptic trains, a set of N₂ independent Poisson-distributed random variables was generated and distributed randomly among the N presynaptic trains. This procedure was repeated at every integration step such that the N₂ random variables were redistributed constantly among the N presynaptic trains. Correlations arose from the fact that N₂  N and the ensuing redundancy within the N presynaptic trains. N₂ was chosen such as to generate a correlation of c = 0.05-0.2 calculated from the peak of the cross-correlation function. Typically, n = 16563 and N₂ = 400 gave a correlation value of c ~ 0.1.

Active currents

Active currents were inserted into the soma, dendrites, and axon with different densities in accordance with available experimental evidence in neocortical and hippocampal pyramidal neurons (Hoffman et al. 1997; Magee and Johnston 1995; Magee et al. 1998; Stuart and Sakmann 1994). Active currents were expressed by the generic form
where _i is the maximal conductance of current I_i and E_i is its reversal potential. The current activates according to M activation gates, represented by the gating variable m. It inactivates with N inactivation gates represented by the gating variable h. m and h obey to first-order kinetic equations.

The voltage-dependent Na⁺ current was described by (Traub and Miles 1991)






where V_T = 58 mV was adjusted to obtain a threshold of around 55 mV as in our experiments, and the inactivation was shifted by 10 mV toward hyperpolarized values (V_S = 10 mV) to match the voltage dependence of Na⁺ currents in neocortical pyramidal cells (Huguenard et al. 1988). The pattern and kinetics of Na⁺ channels was similar to a previous study on hippocampal pyramidal cells (Hoffman et al. 1997): the density was low in soma and dendrites (120 pS/µm²) and was 10 times higher in the axon.

The "delayed-rectifier" K⁺ current was described by (Traub and Miles 1991)



K⁺ channel densities were of 100 pS/µm² in soma and dendrites, and 1,000 pS/µm² in the axon.

A noninactivating K⁺ current was described by (Mainen et al. 1995)



This current was present in soma and dendrites (density of 2-5 pS/µm²) and was responsible for spike frequency adaptation, as detailed previously (Paré et al. 1998a).

It was reported that some pyramidal cell have a hyperpolarization-activated current termed I_h (Spain et al. 1987; Stuart and Spruston 1998). However, most cells recorded in the present study had no apparent I_h (see passive responses in Figs. 1 and 2). Occasionally, cells displayed a pronounced I_h, but these cells were not included in the present study. This current was therefore not included in the model.

View larger version (25K): [in this window] [in a new window]   Fig. 2. Calibration of the model to passive responses and miniature synaptic events recorded intracellularly in vivo. A: morphology of a layer VI neocortical pyramidal cell from cat cerebral cortex, which was reconstructed and incorporated into computational models. Passive responses of the model were adjusted to somatic (Soma; 0.1 nA current pulse) and dendritic recordings (Dendrite; 0.2 nA current pulse) obtained in vivo in the presence of TTX and synaptic blockers (see METHODS). B: miniature synaptic potentials in neocortical pyramidal neurons. Left: TTX-resistant miniature events in somatic (Soma) and dendritic (Dendrite) recordings. Histograms of mini amplitudes are shown in the insets. Right: simulated miniature events; 16,563 glutamatergic and 3,376 GABAergic synapses were simulated with Poisson-distributed spontaneous release. Quantal conductances and release frequency were estimated by matching simulations to experimental data. Best fits were obtained with an average release frequency of 0.01 Hz and conductances of 1,200 and 600 pS at glutamatergic and GABAergic synapses, respectively.

All simulations were done using NEURON (Hines and Carnevale 1997) on a Sparc-20 work-station (Sun Microsystems, Mountain View, CA).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Membrane properties of neocortical pyramidal neurons during active periods

In a previous study (Paré et al. 1998b), the properties of pyramidal neurons were compared before and after local TTX application, revealing that differences in background synaptic activity account for much of the discrepancies between in vivo and in vitro recordings. Intracellular recordings were performed under barbiturate and ketamine-xylazine anesthesia, and the input resistance (R_in) was estimated before and after TTX application (Paré et al. 1998b). However, these properties were never measured specifically during active periods. Here, we have reexamined and quantified these data by focusing specifically on active periods occurring under ketamine-xylazine anesthesia (Fig. 1B, bars). These active periods were identified as follows: neurons fire at ~5-20 Hz, their membrane potential (V_m) is around 65 to 60 mV, and the EEG displays low-amplitude waves of fast frequency in the gamma range. Active periods usually lasted ~0.4-2 s, although periods lasting up to several seconds occasionally occurred (Steriade et al. 1993a).

During active periods, neocortical neurons had a low R_in, as shown by the relatively small voltage responses to intracellular current injection (Fig. 1C, top). Averaging >50 pulses during active periods led to R_in of 9.2 ± 4.3 M (n = 26), consistent with previous observations (Contreras et al. 1996).

The total conductance change due to synaptic activity was quantified by comparing the R_in of the cells during active periods to that measured after blocking synaptic transmission using microperfusion of TTX. Under TTX, injection of current pulses led to larger responses (Fig. 1D) and larger R_in values (46 ± 8 M; n = 9). This was paralleled by a marked decrease in the amplitude of V_m fluctuations, as quantified by the standard deviation of the V_m(_v; Fig. 1E). In nine different cells recorded successively during active periods and after TTX application, _v was reduced from 4.0 ± 2.0 mV to 0.4 ± 0.1 mV, respectively (Fig. 1F). Figure 1E also shows that the V_m dropped significantly to 80 ± 2 mV, as reported previously (Paré et al. 1998b). During active periods, the average V_m (V_m) was 65 ± 2 mV in control conditions (K-acetate-filled pipettes) and 51 ± 2 mV with chloride-filled recording pipettes. These conditions correspond to chloride reversal potentials (E_Cl) of 73.8 ± 1.6 mV and 52.0 ± 2.9 mV, respectively (Paré et al. 1998a).

Normalizing R_in changes with reference to the R_in measured in the presence of TTX revealed that in all cells where active periods could be compared with an epoch of suppressed synaptic activity (n = 9), the R_in was reduced by approximately the same relative amount (81.4 ± 3.6%; Fig. 1F; data summarized in Table 1), independently of absolute values. Similar values were obtained by repeating this analysis at different V_ms, either more depolarized, by using chloride-filled pipettes (n = 7), or more hyperpolarized, by steady current injection (1 nA; n = 2). Taken together, these data show that active periods are characterized by an about fivefold decrease in R_in, a significant depolarization of 15-30 mV depending on the recording conditions;, and a ~10-fold increase in the amplitude of V_m fluctuations.

Model of high-frequency release

Computational models of cat neocortical pyramidal cells were used to estimate the release conditions and conductances necessary to account for these experimental measurements. A layer VI neocortical pyramidal cell (Fig. 2A) was reconstructed and incorporated in simulations (see METHODS). As both somatic and dendritic recordings are critical to constrain, the simulations of synaptic activity (see following text), passive responses from both types of recordings (Paré et al. 1997) were used to constrain the passive parameters of the model. The fitting was performed such that the same model could fit both somatic and dendritic recordings obtained in deep pyramidal cells in the absence of synaptic activity (TTX + synaptic blockers; see METHODS). The same model could fit both traces (Fig. 2A) with the following optimal passive parameters: g_leak = 0.045 mS cm², C_m = 1 µF/cm², and R_i = 250 cm (see METHODS). Another fit was performed by forcing R_i to 100 cm (C_m = 1 µF/cm² and g_leak = 0.039 mS cm²). Although the latter set of values were not optimal, they were used to check for the dependence of the results on axial resistance. A passive fit also was performed with high membrane resistance, based on whole cell recordings (Pongracz et al. 1991; Spruston and Johnston 1992), and a somatic shunt due to electrode impalement. In this case, the parameters were as follows: 10 nS somatic shunt, g_leak = 0.0155 mS cm², C_m = 1 µF/cm², and R_i was of either 250 or 100 cm. A nonuniform leak conductance, low in soma and a high in distal dendrites (Stuart and Spruston 1998), also was tested (see METHODS). No further effort was made to optimize passive parameters as models and experiments were based on different cellular morphologies. This fitting procedure ensured that the model had an R_in and a time constant consistent with both somatic and dendritic recordings free of synaptic activity.

The next step was to simulate TTX-resistant miniature synaptic potentials occurring in the same neurons. These miniature events were characterized in somatic and dendritic intracellular recordings after microperfusion of TTX in vivo (Paré et al. 1997) (Fig. 2B, left). To simulate them, a plausible range of parameters was determined based on in vivo experimental constraints. Then, a search within this parameter range was performed to find an optimal set that was consistent with all constraints. These constraints were the densities of synapses in different regions of the cell, as derived from morphological studies of neocortical pyramidal cells (DeFelipe and Fariñas 1992; Fariñas and DeFelipe 1991a,b; Larkman 1991; Mungai 1967; White 1989) (see METHODS); the quantal conductance at AMPA and GABA_A synapses, as determined by whole cell recordings of neocortical neurons (Markram et al. 1997; Salin and Prince 1996; Stern et al. 1992); the value of _v during miniature events after TTX application in vivo (~0.4 mV for somatic recordings and 0.6-1.6 mV for dendritic recordings) (Paré et al. 1997); the change in R_in due to miniature events, as determined in vivo (~8-12% in soma and 30-50% in dendrites) (Paré et al. 1997); and the distribution of mini amplitudes and frequency, as obtained from in vivo somatic and dendritic recordings (Fig. 2B, insets).

An extensive search in this parameter range was performed and a narrow region was found to satisfy the above constraints. The optimal values found were a density of 20 GABAergic synapses per 100 µm² in the soma, 60 GABAergic synapses per 100 µm² in the initial segment, 10 GABAergic synapses and 60 glutamatergic (AMPA) synapses per 100 µm² in the dendrites; a rate of spontaneous release (assumed uniform for all synapses) of 0.009-0.012 Hz; and quantal conductances of 1,000-1,500 pS for glutamatergic and 400-800 pS for GABAergic synapses. In these conditions, simulated miniature events were consistent with experiments (Fig. 2B, right), with _v of 0.3-0.4 mV in soma and 0.7-1.4 mV in dendrites, and R_in changes of 8-11% in soma and 25-37% in dendrites.

To simulate the intense synaptic activity occurring during active periods, we hypothesized that miniature events and active periods are generated by the same population of synapses with different conditions of release for GABAergic and glutamatergic synapses. The preceding model of miniature events was used to simulate active periods by increasing the release frequency at all synaptic terminals. Poisson-distributed release was simulated with identical release frequency for all excitatory synapses (f_e) as well as for inhibitory synapses (f_i). The release frequencies f_e and f_i affected the R_in and average V_m (V_m) (Fig. 3A). These aspects were constrained by the following experimental measurements (see preceding section): the R_in change produced by TTX should be ~80%; the V_m should be around 80 mV without synaptic activity; the V_m should be about 65 mV during active periods (E_Cl = 75 mV); and the V_m should be around 51 mV during active periods recorded with chloride-filled electrodes (E_Cl = 55 mV). Here again an extensive search in this parameter space was performed, and several combinations of excitatory and inhibitory release frequencies could reproduce correct values for the R_in decreases and V_m differences between active periods and after TTX (Fig. 3A). The optimal values of release frequencies were f_e = 1 Hz (range 0.5-3 Hz) for excitatory synapses and f_i = 5.5 Hz (range 4-8 Hz) for inhibitory synapses.

View larger version (41K): [in this window] [in a new window]   Fig. 3. Constraining the release parameters of the model to simulate periods of intense synaptic activity. A: effect of release frequencies on Rin (A1) and average Vm (Vm) for 2 values of chloride reversal potential ECl (A2 and A3). Both excitatory (fe) and inhibitory (fi) release frequencies were varied; each curve represents different ratios between them: fe = 0.4 fi (), fe = 0.3 fi (), fe = 0.18 fi (), fe = 0.1 fi (). , range of values observed during in vivo experiments using either KAc- or KCl-filled pipettes. Optimal value was fe = 1 Hz and fi = 5.5 Hz. B: increasing the release frequency can account for the experimentally observed Rin decrease but not for the standard deviation of Vm (v). B1-B4: effect of increasing the release frequency up to fe = 1 Hz, fi = 5.5 Hz (B4). Different symbols in the graph (B5) indicate different combinations of release frequencies, synaptic conductances and densities. C: several combinations of conductance and release frequencies could yield correct Rin decrease but failed to reproduce v. C1-C4: different parameter combinations giving the highest v. All parameters were varied within 50-200% of their value in B4 and are shown by crosses in C5. D: introducing a correlation between release events led to correct Rin and v. D1-D4: these correspond to fe = 1 Hz and fi = 5.5 Hz, as in B4, with increasing values of correlation (0.025, 0.05, 0.075, and 0.1 from D1 to D4). D5: , , , and , Rin and v obtained with different values of correlation (between 0 and 0.2) when all inputs (), only excitatory inputs () or only inhibitory inputs () were correlated.

An additional constraint was the large V_m fluctuations experimentally observed during active periods, as quantified by _v (see preceding section). As shown in Fig. 3B (, , , ), increasing the release frequency of excitatory or inhibitory synapses produced the correct R_in change but always gave too small values of _v. High release frequencies led to membrane fluctuations of small amplitude, due to the large number of summating random events (Fig. 3B4). Variations within 50-200% of the optimal value of different parameters, such as synapse densities, synaptic conductances, frequency of release, leak conductance, and axial resistance, could yield approximately correct R_in changes and correct V_m but failed to account for values of _v observed during active periods (Fig. 3C, ×).

One additional assumption had to be made to reproduce V_m fluctuations comparable to those occurring in vivo. In the cortex, action potential-dependent release is clearly not independent at different synapses, as single axons usually establish several contacts in pyramidal cells (Markram et al. 1997; Thomson and Deuchars 1997). More importantly, the presence of oscillatory amplitude fluctuations in the EEG (see Fig. 1, A and B) implies correlated activity in the network. A correlation therefore was included in the release of different synapses (see METHODS). For the sake of simplicity, the correlation was irrespective of the proximity of synapses on the dendritic tree and correlations were treated independently for excitatory and inhibitory synapses. Figure 3D shows simulations of random synaptic bombardment similar to Fig. 3B4 but using different correlation coefficients. The horizontal alignment of the open symbols in Fig. 3D5 shows that the degree of correlation had a negligible effect on the R_in because the same amount of inputs occurred on average. However, the degree of correlation affected the standard deviation of the signal. Several combinations of excitatory and inhibitory correlations, within the range of 0.05-0.1, gave rise to V_m fluctuations with comparable _v as those observed experimentally during active periods (Fig. 3D5; compare with Fig. 1F; see also Table 1). Introducing correlations among excitatory or inhibitory inputs alone showed that excitatory correlations were most effective in reproducing the V_m fluctuations (Fig. 3D5, ).

To check if these results were affected by voltage-dependent currents, we estimated the voltage-dependent currents present in cortical cells from their current-voltage (I-V) relationship. The I-V curve of a representative neocortical cell after TTX microperfusion is shown in Fig. 4A. The I-V curve was approximately linear at V_ms more hyperpolarized than 60 mV but displayed an important outward rectification at more depolarized potentials similar to in vitro observations (Stafstrom et al. 1982). The R_in was of ~57.3 M at values around rest (about 75 mV) and 30.3 M at more depolarized V_m (greater than 60 mV), which represents a relative R_in change of 47%. This cell had the strongest outward rectification in six cells measured after TTX (relative R_in change of 30 ± 11%, n = 6).

View larger version (24K): [in this window] [in a new window]   Fig. 4. Outward rectification of neocortical pyramidal neurons. A: current-voltage relation of a deep pyramidal neuron after microperfusion of TTX. This cell had a resting Vm of 75 mV after TTX and was maintained at 62 mV by DC current injection. Current-voltage (I-V) relation obtained by additional injection of current pulses of different amplitudes. I-V relation revealed a significant reduction of Rin at depolarized levels (straight lines indicate the best linear fits). B: simulation of the same protocol in the model pyramidal neuron. Model had 2 voltage-dependent K+ currents, IKd (100 pS/µm2) and IM (2 pS/µm2). I-V relation obtained in the presence of both currents (circles) and compared with the same model with IM removed (+). Model displayed a comparable rectification as experiments, although more pronounced (straight lines indicate the same linear fits as in A for comparison).

In the model, this type of I-V relation was simulated by including two voltage-dependent K⁺ currents, I_Kd and I_M (see METHODS). In the presence of these two currents, the model displayed a comparable rectification as the cell showing the strongest rectification in experiments under TTX (Fig. 4B; the straight lines indicate the same linear fits as in A for comparison).

The constraining procedure described above then was used to estimate the release conditions in the presence of voltage-dependent currents. First, the model including I_Kd and I_M was fit to passive traces obtained in the absence of synaptic activity to estimate the leak conductance and leak reversal (similar to Fig. 2A). Second, the release rate required to account for the _v and R_in change produced by miniature events was estimated as in Fig. 2B. Third, we estimated the release rates that could best reproduce the R_in, V_m and _v (see Fig. 3).

The presence of voltage-dependent currents produced smallbut detectablechanges in the optimal release conditions. For example, the same R_in change, V_m and _v as the passive model with f_e = 1 Hz and f_i = 5.5 Hz was obtained with f_e = 0.92 Hz and f_i = 5.0 Hz (8-9% lower) in a model containing I_Kd and I_M. Both models gave nearly identical _v values for the same value of correlation. A similar constraining procedure also was performed using a nonuniform leak distribution with high leak conductances in distal dendrites (see METHODS), in addition to I_Kd and I_M, and nearly identical results were obtained (not shown). We therefore conclude that leak and voltage-dependent K⁺ currents have a small contribution to the R_in and _v of active periods, which are mostly determined by synaptic activity.

Impact of synaptic activity on integrative properties

The experimental evidence for a ~80% decrease in R_in due to synaptic bombardment betrays a massive opening of ion channels. In the model, the total conductance due to synaptic activity was 7-10 times larger than the leak conductance. In conditions of high membrane resistance based on whole cell recordings (Pongracz et al. 1991; Spruston and Johnston 1992), the conductance due to synaptic activity was 20-30 times larger than the dendritic leak conductance.

The impact of this massive increase in conductance on dendritic attenuation was investigated by comparing the effect of current injection in active periods and synaptic quiescence (Fig. 5). In the absence of synaptic activity (Fig. 5B, smooth traces), somatic current injection (Fig. 5B, left) elicited large voltage responses in dendrites, and reciprocally (Fig. 5B, right), showing a moderate electrotonic attenuation. By contrast, during simulated active periods (Fig. 5B, noisy traces), voltage responses to identical current injections were reduced markedly, betraying a greatly enhanced electrotonic attenuation. In these conditions, the relative amplitude of the deflection induced by the same amount of current with and without synaptic activity, as well as the difference in time constant, were in agreement with experimental observations (compare Fig. 5B, Soma, with Fig. 1, C and D). The effect of synaptic bombardment on the time constant was also in agreement with previous models (Bernander et al. 1991; Holmes and Woody 1989; Koch et al. 1996).

View larger version (23K): [in this window] [in a new window]   Fig. 5. Passive dendritic attenuation during simulated active periods. A: layer VI pyramidal cell used for simulations. B: injection of hyperpolarizing current pulses in the soma (left, 0.1 nA) and a dendritic branch (right, 0.25 nA). Dendritic voltage is shown at the same site as the current injection (indicated by a small arrow in A). Activity during simulated active periods (noisy traces; average of 50 pulses) is compared with the same simulation in the absence of synaptic activity (smooth lines). C: somatodendritic Vm profile along the path indicated by a dashed line in A. Vm profile is shown at steady state after injection of current in the soma (+0.8 nA). In the absence of synaptic activity (Quiet), there was moderate attenuation. During simulated active periods (Active), the profile was fluctuating (100 traces shown) but the average of 1,000 sweeps (Active, avg) revealed a marked attenuation of the steady-state voltage.

Dendritic attenuation was characterized further by computing somatodendritic profiles of V_m with steady current injection in the soma: in the absence of synaptic activity (Fig. 5C, Quiet), the decay of V_m after somatic current injection was characterized by space constants of 515-930 µm, depending on the dendritic branch considered, whereas the space constant was reduced by about fivefold (105-181 µm) during simulated active periods (Fig. 5C, Active).

To estimate the convergence of synaptic inputs necessary to evoke a significant somatic depolarization during active periods, a constant density of excitatory synapses was stimulated synchronously in "proximal" and "distal" regions of dendrites (as indicated in Fig. 6A). In the absence of synaptic activity, simulated EPSPs had large amplitudes (12.6 mV for proximal and 6.0 mV for distal; Fig. 6B, Quiet). By contrast, during simulated active periods, the same stimuli gave rise to EPSPs that were barely distinguishable from spontaneous V_m fluctuations (Fig. 6B, Active). The average EPSP amplitude was 5.4 mV for proximal and 1.16 mV for distal stimuli (Fig. 6B, Active, avg), showing that EPSPs are attenuated by a factor of 2.3-5.2 in this case, with the maximal attenuation occurring for distal EPSPs. Figure 6C shows the effect of increasing the number of synchronously activated synapses. In quiescent conditions, <50 synapses on basal dendrites were sufficient to evoke a 10-mV depolarization at the soma (Quiet, proximal), and the activation of ~100 distal synapses was needed to achieve a similar depolarization (Quiet, distal). During simulated active periods, >100 basal dendritic synapses were necessary to reliably evoke a 10-mV somatic depolarization (Active, proximal), whereas the synchronous excitation of 415 distal synapses only evoked depolarization of a few millivolts (Active, distal).

View larger version (22K): [in this window] [in a new window]   Fig. 6. Somatic depolarization necessitates the convergence of a large number of excitatory inputs during simulated active periods. A: layer VI pyramidal cell was divided into 2 dendritic regions: "Proximal" included all dendritic branches laying within 200 µm from the soma (circle) and "Distal" referred to dendritic segments outside this region. B: attenuation after synchronized synaptic stimulation. Density of 1 excitatory synapse per 200 µm2 was stimulated in proximal (81 synapses) and distal regions (46 synapses). Responses obtained in the absence of synaptic activity (Quiet) are compared with those observed during simulated active periods (Active; 25 traces shown). In the presence of synaptic activity (Active), the evoked EPSP was visible only when proximal synapses were stimulated. Average EPSPs (Active, avg; n = 1000) showed a marked attenuation compared with the quiescent case. C: averaged EPSPs obtained with increasing numbers of synchronously activated synapses. Protocols similar to B were followed for different numbers of synchronously activated synapses (indicated for each trace). Horizontal dashed line indicates a typical value of action potential threshold.

To determine whether these results are dependent on the specific morphology of the studied cell, four different cellular geometries were compared, ranging from small layer II-III cells to large layer V pyramidal cells (Fig. 7A). In experiments, the absolute R_in values varied from cell to cell. However, the relative R_in change produced by TTX was similar in all cells recorded. Similarly, in the model, the absolute R_in values depended on the cellular geometry: using identical passive parameters, the R_in values of the four neurons shown in Fig. 7A ranged from 23 to 94 M. However, high-frequency release conditions had a similar impact on their membrane properties. Using identical synaptic densities, synaptic conductances, and release conditions as detailed above led to a decrease in R_in of ~80% for all cells (Fig. 7B). V_m fluctuations also depended critically on the degree of correlation between the release of different synapses. Uncorrelated events produced too small _v (Fig. 7B, ×), whereas a correlation of 0.1 could reproduce both the R_in change and _v (Fig. 7B, ). The value of _v was correlated with cell size (not shown), and the variability of _v values was relatively high compared with that of R_in decreases. The effect of synaptic activity on dendritic attenuation was also independent of the cell geometry: the space constant was reduced by about fivefold in all four cells (not shown). Moreover, for the two layer V neurons, stimulating several hundreds of synapses at a distance of >800 µm from the soma had undetectable effects during active periods (Fig. 7C). This result was also reproduced using low axial resistivities (Fig. 7C, dashed lines).

View larger version (28K): [in this window] [in a new window]   Fig. 7. Effect of dendritic morphology on membrane parameters during intense synaptic activity. A: 4 cellular reconstructions from cat neocortex used in simulations. All cells are shown at the same scale and their Rin was measured in the absence of synaptic activity (identical passive parameters for all cells). B: graph plotting the Rin decrease as a function of the standard deviation of the signal for these 4 cells. For all cells, the release frequency was the same (fe = 1 Hz, fi = 5.5 Hz). Results obtained without correlation (×) and with a correlation of c = 0.1 () are indicated. C: attenuation of distal EPSPs in 2 layer V cells. Excitatory synapses were stimulated synchronously in the distal apical dendrite (>800 µm from soma; indicated by dashed lines in A). EPSPs resulting from the stimulation of 857 (left) and 647 AMPA synapses (right, 23.1 M cell) are shown for quiescent (Quiet) and active conditions (Active). These EPSPs were ~2-3 mV in amplitude without synaptic activity but were undetectable during active periods. Same simulation, performed with low axial resistance (100 cm; dashed lines), gave qualitatively identical results.

These results show that intense synaptic activity has a drastic effect on the attenuation of distal synaptic inputs. However, voltage-dependent currents in dendrites may amplify EPSPs (Cook and Johnston 1997) or trigger dendritic spikes that propagate toward the soma (Stuart et al. 1997). Therefore the attenuation of EPSPs must be reexamined in models that include active dendritic currents.

Firing properties during active periods

The response of the simulated neuron to depolarizing current pulses was tested in the presence of voltage-dependent Na⁺ currents, in addition to I_Kd and I_M. In the absence of synaptic activity (Fig. 8A), the model displayed pronounced spike frequency adaptation due to I_M, similar to "regular spiking" pyramidal cells in vitro (Connors et al. 1982). However, spike frequency adaptation was not apparent in the presence of correlated synaptic activity (Fig. 8B), probably due to the very small conductance of I_M compared with synaptic conductances. Nevertheless, the presence of I_M affected the firing behavior of the cell, as suppressing this current enhanced the excitability of the cell (Fig. 8B, No I_M). This is consistent with the increase of excitability demonstrated in neocortical slices (McCormick and Prince 1986) after suppression of I_M by application of acetylcholine.

View larger version (16K): [in this window] [in a new window]   Fig. 8. Model of spike frequency adaptation with and without synaptic activity. A: in the absence of synaptic activity, the slow voltage-dependent K+ current IM caused spike frequency adaptation in response to depolarizing current pulses (Control; 1 nA injected from resting Vm of 80 mV). Same stimulus did not elicit spike frequency adaptation in the absence of IM (No IM). B: in the presence of correlated synaptic activity, spike frequency adaptation was not apparent although the same IM conductance was used (Control; depolarizing pulse of 1 nA from resting Vm of approximately equal to 65 mV). Without IM, the excitability of the cortical pyramidal cell was enhanced (No IM).

In the presence of Na⁺ and K⁺ voltage-dependent currents, simulated active periods generated "spontaneous" firing at an average rate that depended on the action potential threshold, which was affected by Na⁺ current densities. Setting the threshold at about 55 mV in soma, based on our experiments, led to a sustained firing rate of ~10 Hz (Fig. 9A), with all other features consistent with the model described earlier. In particular, the R_in reductions and values of _v produced by synaptic activity were affected minimally by the presence of voltage-dependent currents (Table 1). However, this was only valid for R_in calculated in the linear region of the I-V relation (less than 60 mV; see Fig. 4). Thus at V_ms more negative than 60 mV, the membrane parameters are essentially determined by background synaptic currents with a minimal contribution from intrinsic voltage-dependent currents.

View larger version (33K): [in this window] [in a new window]   Fig. 9. Tonic firing behavior in simulated active periods. A1: in the presence of voltage-dependent Na+ and K+ conductances distributed in axon, soma, and dendrites, the simulated neuron produced tonic firing at a rate of ~10 Hz (action potential threshold of 55 mV, Vm = 65 mV, v = 4.1 mV). A2: same simulation as A1 shown with a faster time base. B: effect of a 3-fold increase in release frequency at excitatory and inhibitory synapses. Firing rate of the simulated cell also increased 3-fold (- - -). Rin is indicated before, during, and after the increase of release frequency. C: relation between firing rate and release frequency when the frequency of release was increased at both excitatory and inhibitory synapses () or solely at excitatory synapses ().

In these conditions, the firing rate of the cell was sensitive to the release frequency: a threefold increase in release frequencies led to a proportional increase in firing rate (from ~10 to ~30 Hz; Fig. 9B, - - -). Indeed, if all release frequencies were increased by a given factor, the firing rate increased by about the same factor (Fig. 9C, ). This shows that, within this range of release frequencies, the average firing rate of the cell reflects the average firing rate of its afferents. However, this relationship was broken if the release frequency was changed only at excitatory synapses: doubling the excitatory release frequency with no change in inhibition tripled the firing rate (Fig. 9C, ).

Surprisingly, in Fig. 9B there was only a 12% R_in difference between the 10 and 30 Hz conditions, although the release frequency was threefold higher. This is due to the saturation effect of the R_in change as a function of release frequency (Fig. 3A1). This property may explain the observation that visually evoked responses are not paralleled by substantial R_in changes in area 17 neurons (Berman et al. 1991).

Sharp events of lower amplitude than action potentials are also visible in Fig. 9, A and B. These events are likely to be dendritic spikes that did not reach action potential threshold in the soma/axon region, similar to the fast prepotentials described by Spencer and Kandel (1961). Similar events were reported in intracellular recordings of neocortical pyramidal cells in vivo (Deschênes 1981).

Integrative properties during active periods

The dendritic attenuation of EPSPs was examined in the presence of voltage-dependent Na⁺ and K⁺ dendritic conductances. Using the same stimulation paradigm as in Fig. 6B, proximal or distal synapses reliably fired the model cell in quiescent conditions (Fig. 10A, Quiet). The stimulation of distal synapses elicited dendritic action potentials that propagated toward the soma in agreement with a previous model (Paré et al. 1998a). During active periods (Fig. 10A, Active), proximal or distal stimuli did not trigger spikes reliably although the clustering of action potentials near the time of the stimulation (*) shows that EPSPs affected the firing probability. The evoked response, averaged from 1,000 sweeps under intense synaptic activity (Fig. 10A, Active, avg), showed similar amplitude for proximal or distal inputs. Average responses did not reveal any spiky waveform, indicating that action potentials were not precisely timed with the EPSP in both cases.

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