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Characterization of Synaptic Conductances and Integrative Properties During Electrically Induced EEG-Activated States in Neocortical Neurons In Vivo

¹Unité de Neurosciences Intégratives et Computationnelles, Centre National de la Recherche Scientifique, Gif-sur-Yvette, France; and ²Rutgers University, Center for Molecular and Behavioral Neuroscience, Newark, New Jersey

Submitted 20 December 2004; accepted in final form 9 July 2005

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGMENTS REFERENCES

 
The activation of the electroencephalogram (EEG) is paralleled with an increase in the firing rate of cortical neurons, but little is known concerning the conductance state of their membrane and its impact on their integrative properties. Here, we combined in vivo intracellular recordings with computational models to investigate EEG-activated states induced by stimulation of the brain stem ascending arousal system. Electrical stimulation of the pedonculopontine tegmental (PPT) nucleus produced long-lasting (20 s) periods of desynchronized EEG activity similar to the EEG of awake animals. Intracellularly, PPT stimulation locked the membrane into a depolarized state, similar to the up-states seen during deep anesthesia. During these EEG-activated states, however, the input resistance was higher than that during up-states. Conductance measurements were performed using different methods, which all indicate that EEG-activated states were associated with a synaptic activity dominated by inhibitory conductances. These results were confirmed by computational models of reconstructed pyramidal neurons constrained by the corresponding intracellular recordings. These models indicate that, during EEG-activated states, neocortical neurons are in a high-conductance state consistent with a stochastic integrative mode. The amplitude and timing of somatic excitatory postsynaptic potentials were nearly independent of the position of the synapses in dendrites, suggesting that EEG-activated states are compatible with coding paradigms involving the precise timing of synaptic events.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGMENTS REFERENCES

 
In the neocortex, pyramidal cells are embedded in a very dense network, each cell receiving thousands of synaptic inputs from other neurons. In the parietal cortex of awake cats, neurons fire spontaneously at relatively high rates (1–20 Hz on average; Steriade 1978; Steriade et al. 2001). These cells are subjected to a sustained synaptic bombardment, which results in a high-conductance state characterized by highly fluctuating intracellular activity (reviewed in Destexhe et al. 2003). To circumvent the technical difficulty of recording in awake and conscious animals, one possibility is to use anesthetics that induce spontaneous periods ("up-states"), during which the electroencephalogram (EEG) is desynchronized, similar to the EEG of awake animals. Using this paradigm, it was possible to compare the same neurons during EEG-activated states and after suppressing network activity by microperfusion of tetrodotoxin (TTX) in the cortex (Destexhe and Paré 1999; Paré et al. 1998). This analysis revealed that during activated states, pyramidal neurons have a dramatically higher (about 500%) total conductance (i.e., a five times smaller input resistance, R_in) compared with the resting state after TTX. Synaptic activity was also responsible for a marked depolarization (average membrane potential of = –65 ± 2 mV, compared with –80 mV after TTX) and large-amplitude membrane potential (V_m) fluctuations (V_m SD of _V = 4 ± 2 mV during up-states). Recordings during EEG-activated states in other preparations also reported similar depolarized states and low input resistance (Baranyi et al. 1993; Borg-Graham et al. 1998; Matsumara et al. 1988; Steriade 2001).

Although during up-states, the EEG is desynchronized and neurons display intracellular features similar to recordings obtained in awake animals (Matsumara et al. 1988; Steriade et al. 2001), the presence of anesthetics likely affects the network state. Consistent with this, intracellular recordings in nonanesthetized animals have revealed that the input resistance during periods of wakefulness is higher than that during the up-states of slow-wave sleep (Steriade et al. 2001). There is therefore a need to further characterize the conductance state of cortical neurons during EEG-activated states.

A well-known paradigm to obtain EEG-activated states during anesthesia consists in stimulating the brain stem ascending arousal system, which is believed to maintain the wake state in physiological conditions (Moruzzi and Magoun 1949). Electrical stimulation of specific structures of the brain stem or basal forebrain is known to induce periods of EEG desynchronization. This is the case of the pedonculopontine tegmental (PPT) nucleus, which participates in brain arousal in part by its cholinergic projections to the thalamus (Paré et al. 1988; Steriade et al. 1987). The PPT also sends projections to the portions of the basal forebrain containing corticopetal cholinergic neurons (Hallanger and Wainer 1988; Semba et al. 1988; Woolf and Butcher 1986). In particular, there is a possibility that some of these projections are glutamatergic because horseradish peroxidase injections in the basal forebrain retrogradely labeled only noncholinergic cells of the PPT (Carnes et al. 1990; Steriade and Buzsaki 1990). It is therefore possible that PPT-induced EEG activation occurs through cholinergic effects in both thalamus and cortex, the latter being disynaptically caused by the basal forebrain. This duality of pathways does not seem strictly necessary, however, because PPT stimulation still evokes EEG desynchronization after large excitotoxic lesions of either the basal forebrain (Steriade et al. 1991, 1993) or the thalamus (Steriade et al. 1993). The role of acetylcholine (ACh) in mediating the activating effect of PPT was also confirmed by its blockade by systemic administration of muscarinic antagonists, such as scopolamine (Steriade et al. 1993).

During ketamine–xylazine anesthesia, electrical stimulation of the PPT nucleus induces 10- to 30-s periods of EEG desynchronization similar to the up-states (Steriade et al. 1993). In the present paper, we used intracellular recordings of morphologically identified pyramidal neurons to study EEG-activated states evoked under ketamine–xylazine anesthesia by PPT stimulation. In combination with computational models, we estimated the conductances underlying PPT-induced states, by reference to the up-states of ketamine–xylazine anesthesia characterized previously (Destexhe and Paré 1999; Paré et al. 1998). We then used these conductance estimates to evaluate the impact of this network activity on the integrative properties of cortical neurons.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGMENTS REFERENCES

 
In vivo recordings

Cortical neurons were recorded intracellularly in areas 5–7 of cats anesthetized with ketamine–xylazine. Under this anesthesia, cortical neurons display recurrent periods of activity ("up-states") similar to the wake state. Stimulating electrodes were placed in the PPT nucleus. PPT stimulation evoked periods of low-amplitude, fast-frequency EEG activity ("post-PPT states") lasting 20–30 s, during which the input resistance (R_in) and membrane potential (V_m) fluctuations were measured.

Experiments were conducted in agreement with ethics guidelines of the Canadian Council on Animal Care. Cats (2.5–3.5 kg) were anesthetized with a ketamine–xylazine mixture (11 and 2 mg/kg, intramuscularly). Further, lidocaine (2%) was applied to all skin incisions and pressure points. The level of anesthesia was determined by continuously monitoring the EEG ipsilateral to the intracellular recording site. Supplemental doses of ketamine–xylazine (2 and 0.3 mg/kg, respectively, intravenously [iv]) were given to maintain a synchronized EEG pattern. The animals were paralyzed with galamine triethiodide (33 mg/kg, iv) and artificially ventilated only after the EEG displayed the usual pattern of deep general anesthesia. End tidal CO₂ concentration was kept at 3.7 ± 0.2% and the temperature at 37–38°C with a heating pad. A lactated Ringer solution was administered (20 ml, subcutaneously) twice during the experiment for fluid replacement. To ensure recording stability, the cisterna magna was drained, the cat suspended, and a bilateral pneumothorax performed. The bone and dura overlying the suprasylvian gyrus (areas 5–7) and mesencephalon were removed. In two animals, we tested the effects of PPT in the absence of flaxedil and saw no overt signs that the animals were coming out of the anesthesia: they remained immobile and unresponsive to toe pinch.

EEG recordings were obtained using pairs of tungsten electrodes (0.5 M) whose tips were separated by 1.5 mm in the vertical axis, with the superficial electrode located on the brain surface. Similar electrodes were stereotaxically aimed to the PPT. Intracellular recordings were made with glass micropipettes containing 3.5 M K-acetate and 1% neurobiotin (tip <0.5 µm, about 45 M resistance) using a high-impedance amplifier with active bridge circuitry. Typically, cells were recorded from for 30–120 min. Bridge balance was checked regularly during the recordings. The bridge was adjusted so that the onset and offset of the voltage responses to the intracellular current pulses were devoid of instantaneous resistive components. The intracellular and EEG signals were stored on tape. Analysis was performed off-line using the software IGOR (Wavemetrics, Lake Oswego, OR).

To test the effect of PPT stimulation on the R_in of cortical neurons, we applied repetitive current pulses of constant amplitude before and after the PPT stimulation while maintaining the V_m at particular membrane potentials with intracellular current injection.

Histological controls were performed to confirm the depth and morphology of the recorded cells, as revealed by intracellular injection of neurobiotin. The presence of neurobiotin did not appear to alter the electrophysiological properties of the recorded neurons. At the conclusion of the experiments, the animals were administered a lethal dose of pentobarbital and perfused with 500 ml of chilled saline (0.9%) followed by 1 liter of a solution of 2% paraformaldehyde and 1% glutaraldehyde in 0.1 M phosphate-buffered saline (PBS, pH 7.4). The brain was stored in 30% glucose solution overnight and then transferred to PBS. Sagittal sections (80 µm) were cut on a freezing microtome. Neurobiotin-filled cells were visualized by incubating the sections in the avidin–biotin–horseradish peroxidase (HRP) solution (ABC Elite Kit, Vector Labs) and processed to reveal the HRP staining (Horikawa and Armstrong 1988).

Models of cortical neurons and synaptic noise

Under the assumptions that synaptic noise constitutes the main source of membrane potential fluctuations in EEG-activated states in vivo, and that other potential noise sources, such as channel noise, provide here only very little contribution (see Manwani and Koch 1999) and are thus negligible, we constructed several models to characterize cortical network activity and investigate integrative properties during such active states. These models are distinguished by their level of complexity and can be used to address different aspects of neuronal dynamics.

A first type of model, the point-conductance model (Destexhe et al. 2001), represents the membrane potential fluctuations by stochastic processes. The advantage of this representation is that synaptic activity can be characterized by a few parameters (mean conductance, variance, decay time). In addition, the V_m distribution can be assessed analytically (Rudolph and Destexhe 2003b), which enables a direct estimate of these parameters from experimental recordings (Rudolph et al. 2004; see RESULTS).

The point-conductance model consisted in a single-compartment neuron described by the passive membrane equation

(1)

subject to a total synaptic current I_syn(t) = g_e(t)[V(t) – E_e] + g_i(t)[V(t) – E_i] and constant external (stimulating) current I_ext. In Eq. 1, V(t) denotes the membrane potential, C = C_ma is the membrane capacitance (membrane area a, specific membrane capacitance C_m = 1 µF/cm²), and G_L = 1/R_in and E_L denote the leak conductance (input resistance R_in) and reversal potential, respectively. g_e(t) and g_i(t) are time-dependent global excitatory and inhibitory conductances described by one-variable stochastic processes similar to the Ornstein–Uhlenbeck process (Uhlenbeck and Ornstein 1930)

(2)

with respective reversal potentials E_e = 0 mV and E_i = –80 mV. These two synaptic contributions represent respectively the glutamate -amino-3-hydroxy-5-methyl-4-isoxazolepropionic (AMPA) and -aminobutyric acid type A (GABA_A) postsynaptic receptors. Here, g_e0 and g_i0 are the mean conductances, _e = 2.73 ms and _i = 10.49 ms denote the noise time constants (Destexhe et al. 2001), _e and _i are the noise SDs. _e(t) and _i(t) denote independent Gaussian white-noise processes of unit SD and zero mean. Values for the passive cellular properties, E_L and G_L, as well as effective synaptic conductances, the means g_e0 and g_i0 and SDs _e and _i, were estimated from experiments (see RESULTS).

In a second type of model, the one-compartment model with multiple synaptic inputs, V_m fluctuations were caused by a large number of individual synaptic conductances. Despite the large number of parameters describing the kinetics of each synaptic terminal, the simple spatial structure of the model neuron allows one to treat this type of model in the context of discrete stochastic calculus (see e.g., Rice 1945). The advantage of this level of description is that it establishes a link between the dynamics of V_m fluctuations and the dynamics of the activity at synaptic terminals and thus provides a framework for linking intracellular recordings with the activity of the surrounding network (Rudolph and Destexhe 2005).

We considered two-state kinetic models of AMPA and GABA_A postsynaptic receptors (Destexhe et al. 1998). The synaptic current resulting from N_AMPA = 10,018 and N_GABA = 2,249 synapses was given by

(3)

where g_AMPA and g_GABA are the quantal conductances, and the variables m_e⁽ⁿ⁾(t) and m_i^(m)(t) represent the fractions of postsynaptic receptors in the open state at each synapse. These variables were described by the kinetic equation

(4)

Here, [T](t) denotes the transmitter concentration in the synaptic cleft ([T] = T_max for a time period t_dur after a spike occurred and [T] = 0 until the next release), _{e,i} and _{e,i} are forward and backward binding rate constants for excitation and inhibition. Kinetic parameters obtained by fitting the model to postsynaptic currents recorded experimentally (Destexhe et al. 1998) were g_AMPA = 1.2 nS, g_GABA = 0.6 nS, _e = 1.1 x 10⁶ M^–1 s^–1, _e = 670 s^–1 for AMPA receptors, _i = 5 x 10⁶ M^–1 s^–1, _i = 180 s^–1 for GABA_A receptors, T_max = 1 mM, and t_dur = 1 ms. To simulate synaptic background activity, all synapses were activated randomly according to independent but temporally correlated (correlation measure c; see Rudolph and Destexhe 2001) Poisson processes with mean rates of _exc and _inh as well as equal temporal correlation c for AMPA and GABA_A synapses, respectively. Values for the temporal correlation c and release rates _exc, _inh at excitatory and inhibitory synaptic terminals, respectively, were estimated from experiments (see RESULTS). N-Methyl-D-aspartate (NMDA) receptors were not included because all experiments were obtained under ketamine–xylazine anesthesia, and ketamine is an NMDA blocker (e.g., Liu et al. 2001). GABA_B receptors were not incorporated either because no GABA_B inhibitory postsynaptic potential (IPSP) could be observed in an in vivo intracellular study of the laminar distribution of IPSPs in cat areas 5–7 (Contreras et al. 1997).

A third type of model, the detailed biophysical model, is intended to simulate neuronal dynamics as faithfully as possible by incorporating a realistic distribution of numerous synaptic terminals across spatially extended active or passive dendritic structures. We used this type of model to address questions of dendritic integration as well as subthreshold and suprathreshold responses to spatiotemporally distributed synaptic inputs. The detailed biophysical model considered here consisted of a compartmental model of a morphologically reconstructed cortical pyramidal neuron from lower layer V of cat parietal cortex. The cell was stained with neurobiotin and its morphology was reconstructed with a Neurolucida system (MicroBrightField, Williston, VT), using a x100 objective and correction for tissue shrinkage. The three-dimensional (3D) geometry was incorporated into the NEURON simulation environment, and included a dendritic surface correction for spines (assuming that spines constitute 45% of the dendritic membrane area). The corrected membrane area of this cell was a = 34,598 µm. The passive properties (E_L = –78.03 mV and R_in = 62.3 M) were estimated from intracellular recordings of the reconstructed cell (see following text) and were the same for all models of this cell.

In some simulations, voltage-dependent conductances were inserted in the soma, dendrites, and axon and were described by Hodgkin and Huxley (1952) type models. The latter model included two voltage-dependent currents, a fast Na⁺ current I_Na and a delayed-rectifier K⁺ current I_Kd, for action potential generation (Traub and Miles 1991), and which were modified to match voltage-clamp measurements in neocortical neurons (Huguenard et al. 1988). The conductance densities used were of 8.4 and 7 mS/cm² throughout soma and dendrites, and were ten times higher in the axon. To account for the spike-frequency adaptation and afterhyperpolarization commonly observed in "regular-spiking" neurons (Connors and Gutnick 1990), a slow voltage-dependent K⁺ current I_M (muscarinic potassium current; Gutfreund et al. 1995) with conductance densities of 0.35 mS/cm² (soma and dendrites, no I_M in axon) was added. To test for robustness of the results, simulations with additional fast inactivating A-type K⁺ current I_KA (model from Migliore et al. 1999; conductance density from Bekkers 2000), T-type (low-threshold) Ca²⁺ current I_CaT (model from Traub et al. 2003; conductance density from Hamill et al. 1991), hyperpolarization-activated current I_h (model and nonuniform conductance density from Stuart and Spruston 1998), as well as the voltage-dependent cation nonselective current I_CAN activated by muscarinic receptor stimulation (Haj-Dahmane and Andrade 1996) were used. AMPA and GABA_A synaptic terminals (kinetic models as described above) were inserted into dendrites with densities as estimated from morphological studies (see DeFelipe and Fariñas 1992; DeFelipe et al. 2002; N_AMPA = 10,018 and N_GABA = 2,249). Details of this model can be found in previous papers (Destexhe and Paré 1999; Rudolph and Destexhe 2003a).

All simulations were performed using the NEURON simulation environment (Hines and Carnevale 1997) and were run on PC-based workstations under the LINUX operating system. Simulations were performed with a temporal resolution of 0.1 ms (detailed biophysical model) and 0.05 ms (point-conductance and one-compartment model). For each parameter set, 200 s of neural activity were simulated.

Characterization of synaptic activity

To assess synaptic activity in different EEG-activated states, various methods based on the characterization of intracellular activity were used. In all cases, intracellular activity was characterized by the mean and variance of the membrane potential obtained from Gaussian fits of V_m distributions obtained at different levels of DC current injection. Passive parameters, in particular E_L and the total input resistance R_in, were obtained from linear fits of the I–V curves. Statistically, this approach is very robust and, with the restriction to the linear regime of the I–V curves, provided estimates whose error was <10%. Specifically, linear fits of the I–V curve obtained from intracellular recordings during down-states yield the leak reversal potential E_L for each cell. Fits to the I–V curve obtained during up-states yield values for the input resistance R_inup in these states. The passive input resistance R_in was then estimated for each cell under the assumption of a ratio R_inTTX/R_inup of 5.38 between the input resistance in the absence of synaptic activity, equaling the desired passive input resistance, and R_inup (Destexhe and Paré 1999). All estimated values are given as means ± SD, deduced from the statistical characterization of corresponding values for each individual cell.

A first method, referred to as the standard method, can be defined by taking the temporal average of the passive membrane equation (Eq. 1). Assuming that the average activity of the membrane potential remains constant (steady-state), the left-hand side of Eq. 1 vanishes, leading to

(5)

where denotes the average membrane potential and r_{e,i} = _{e_,i}/G_L defines the ratio between the average excitatory (inhibitory) and leak conductance. Denoting the ratio between the total membrane conductance (inverse of input resistance R_in) in activated states and in states without network activity (induced by application of TTX) with r_in, we obtain

(6)

This relation allows one to estimate the average relative contribution of inhibitory excitatory synaptic inputs in activated states. The value of r_in for up-states under ketamine–xylazine anesthesia was fixed to r_in = 5.38, corresponding to a relative change of the input resistance in this states of 81.4% compared with states under TTX (no network activity; see Destexhe and Paré 1999). The r_in for post-PPT states was estimated for each individual cell based on the ratio between the measured input resistance in up-states and post-PPT states as well as the assumption of a ratio of 5.38 between the input resistance under TTX and in up-states.

A second method, referred to as the VmD method, made use of the analytic expression of the steady-state V_m distribution (Rudolph and Destexhe 2003b). Based on this expression, the mean and variance of excitatory and inhibitory synaptic conductances can be estimated from the mean and variance of the membrane potential at two different injected current levels (Rudolph et al. 2004). The latter were obtained by Gaussian fits to the V_m distributions obtained experimentally. In all cases, intracellular activity at three or four different current levels in up-states, down-states, and post-PPT states constitutes the basis for application of the VmD method. Obtained values for the conductance mean and variance for each cell and state of activity (three pairings for three current levels, six pairings for four current levels) were averaged. Although the estimation of absolute synaptic conductance values depends on estimates or assumptions of the passive input resistance R_in (see Rudolph et al. 2004), in all cases presented here, the estimated synaptic conductance values was robust to variations of R_in (using variations severalfold larger than the the error of experimental measurements of the R_in; see above).

We also used a third method based on computational models. In this case, the release rates at inhibitory and excitatory synaptic terminals along with the temporal correlation in the synaptic activity were estimated by using computational models of a morphologically reconstructed pyramidal cell (see detailed biophysical model above). Here, _inh, _exc, and c were adjusted so that the model could match the intracellular activity of that cell, in particular the average V_m and its variance, as well as the input resistance (for details of this approach, see Destexhe and Paré 1999).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGMENTS REFERENCES

 
First, we describe the intracellular correlates of EEG-activated states as seen under ketamine–xylazine anesthesia in areas 5–7 cortical pyramidal neurons. Next, based on current-clamp recordings, we estimate the contribution of inhibitory and excitatory synaptic conductances using various methods. From these estimates, neuronal models of EEG-activated states with different levels of complexity are deduced. Finally, using a detailed biophysical model, the impact of EEG-activated states on mechanisms of dendritic integration is investigated.

Intracellular correlates of EEG-activated states

During these experiments, we obtained 12 stable recordings of areas 5–7 cortical neurons in six cats anesthetized with ketamine–xylazine. These cells had resting membrane potentials negative to –70 mV and generated overshooting action potentials. The following will be based on the detailed analysis of a subset of seven neurons that were morphologically identified by intracellular injection of neurobiotin as layer V pyramidal cells. All of these cells showed slow spontaneous membrane potential oscillations between periods of firing activity (up-states) and silent periods (down-states; frequency between 0.2 and 1 Hz). Up- and down-states occurred synchronously with changes in EEG activity: the down-states were associated with slow waves, and the up-states were paralleled with increased gamma power in the EEG (see gray bars in Fig. 1 A). In many respects, up-states are comparable to the activity seen in the wake state (see Destexhe et al. 2003 for a review): neurons fire tonically at 1 to 20 Hz, their membrane potential is depolarized by several millivolts with respect to the resting state ( = –72.85 ± 10.14 mV during up-states compared with = –85.21 ± 7.33 mV during down-states; Fig. 2 A, top) and displays large-amplitude, fast-frequency fluctuations (_V = 2.86 ± 0.84 mV; Fig. 2A, middle). Finally, the EEG is characterized by low-amplitude fast activity (Evarts 1964; Steriade 2001; Fig. 1B, left).

View larger version (49K): [in this window] [in a new window]   FIG. 1. Spontaneous and pedonculopontine tegmental (PPT)–induced electroencephalogram (EEG)–activated states under ketamine–xylazine anesthesia. A: cortical neuron recorded in cat parietal cortex (areas 5–7) displays up-states (gray bars) and down-states of activity that were paralleled by slow waves in the EEG. Electrical stimulation of the PPT (100 Hz for 0.1 s; see scheme) produced long periods of desynchronized EEG activity. Intracellularly, PPT stimulation induced periods characterized by a depolarized membrane potential as well as membrane potential fluctuations and discharge activity similar to that seen in the up-states. After 20–30 s, the slow waves progressively reappeared in the EEG, paralleled by the return to alternating up-/down-state patterns. B: expanded view of segments in gray shaded boxes of A.

View larger version (25K): [in this window] [in a new window]   FIG. 2. Characteristics and time evolution of intracellular activity during EEG activation. A: up-states and post-PPT states are characterized by a marked depolarization (top: average membrane potential ) and large membrane potential (Vm) fluctuation amplitudes (middle: Vm SD V). Input resistance (Rin) was smaller in up-states (bottom) compared with post-PPT states (for values see text). Stars mark corresponding values obtained previously (Destexhe and Paré 1999; Paré et al. 1998). B: input resistance was estimated by injecting brief current pulses (0.4 nA in the example shown at top) in the linear portion of current–voltage (I–V) relations. Rin was always smaller during the up-states compared with the state induced by PPT stimulation, as indicated by the steeper slope in the I–V plot (bottom). C: SD of membrane potential V (top) and normalized Rin (bottom) as a function of time after PPT stimulation (average of 7 cells; consecutive windows of 500 and 300 ms, respectively). First point in the V graph indicates the value calculated over a long period of slow oscillations. Reference Rin (bottom) was the average input resistance during up-states (gray).

Previously (Destexhe and Paré 1999; Paré et al. 1998), we measured the effect of network activity on the input resistance (R_in) of cortical neurons by comparing intracellularly recorded cells under ketamine–xylazine anesthesia, before versus after microperfusion of TTX in the cortex. It was found that R_in was about five times higher under TTX. Here, the R_in was always significantly lower during the up-states (R_in = 10.08 ± 3.87 M; Fig. 2A, bottom) compared with the down-state (R_in = 14.91 ± 2.28 M; paired t-test, P < 0.006). After PPT stimulation, the R_in increased significantly (R_in = 18.03 ± 9.44 M; Fig. 2, A, bottom and B) by 44 ± 16%, yielding the R_in ratio of 2.09 ± 1.23 between up-states and post-PPT states. Assuming a fixed ratio between the R_in in up-states versus in the presence of TTX (R_inTTX/R_inup = 5.38), it follows that, on average, the R_in in post-PPT states is about three times smaller (R_inTTX/R_inPPT = 2.58 ± 1.52) than when the network is silent (Fig. 2C, bottom). Note that all R_in estimates given here were obtained by linear fits of the I–V curves in the corresponding states, and gave values that were in good agreement with estimates obtained by injection of short current pulses.

After PPT stimulation, the SD of the membrane potential was stable for 20 s (Fig. 2C, top), before increasing as a result of the alternating pattern of up- and down-states (slow oscillations). In contrast, the R_in showed higher values only for shorter periods (around 7 s) before returning back to the values typical of up- and down-states (Fig. 2C, bottom).

Estimation of synaptic conductances during EEG-activated states

To estimate the respective contribution of excitatory and inhibitory conductances, we first used the standard method (see METHODS). We integrated the V_m measurements into the expression of the passive membrane equation at steady state (Eq. 5), which yields the respective ratios of the mean inhibitory and excitatory synaptic conductances to the leak conductance (Eq. 6). Such estimates were performed for each current level in the linear I–V regime and for each cell. An example is shown in Fig. 3 A. The pooled results for all available cells indicate that the relative contribution of inhibition is severalfold greater than that of excitation (Fig. 3B). This holds for both up-states and post-PPT states, although inhibition appeared to be less pronounced for post-PPT states (paired t-test, P < 0.015; Fig. 3, B and C). Average values are r_i = 3.71 ± 0.48, r_e = 0.67 ± 0.48 for up-states, and r_i = 1.98 ± 1.65, r_e = 0.38 ± 0.17 for post-PPT states. From this, the ratio between the mean inhibitory and excitatory synaptic conductances can be estimated: 10.35 ± 7.99 for up-states and 5.91 ± 5.01 for post-PPT states (Fig. 3C).

View larger version (20K): [in this window] [in a new window]   FIG. 3. Contribution of excitatory and inhibitory conductances during activated states as estimated by application of the standard method. A: representative example for estimates of the ratio between mean excitatory and leak conductance (left) as well as mean inhibitory and leak conductance (middle) in up-states (light gray) and post-PPT states (dark gray). These estimates were obtained by incorporating measurements of the average Vm into the passive membrane equation (see METHODS; estimated values: ri = 4.18 ± 0.01 and re = 0.20 ± 0.01 for up-state, ri = 2.65 ± 0.09 and re = 0.28 ± 0.09 for post-PPT state), and yield a severalfold greater mean for inhibition than for excitation (right; i/e = 20.68 ± 1.24 for up-state, i/e = 9.81 ± 3.23 for post-PPT state). B: pooled results for 6 cells. In all cases, a larger inhibitory contribution was found (dashed line indicates equal contribution). C: average ratio between inhibitory and excitatory synaptic conductances was about 2 times larger for up-states (for values see text).

To determine the absolute values of conductances and their variance, we used a second approach, called the VmD method (Rudolph et al. 2004; see METHODS). This analysis makes use of an analytic expression of the steady-state V_m distribution, given as a function of effective synaptic conductance parameters, which can be fit to experimentally obtained V_m distributions. Figure 4 A illustrates this method for a specific example of up-state and post-PPT state. Restricting to a linear regime of the I–V relation (see Fig. 4A, insets), by fitting the V_m distributions (V) obtained at different current levels with Gaussians (Fig. 4B, left), the mean and variance of excitatory and inhibitory synaptic conductances can be deduced (Fig. 4B, right). Because the VmD method requires two different current levels, the available experimental data for three (or four) current levels allowed three (or six) possible pairings. For each investigated cell, the values obtained from all pairings were averaged (see METHODS). In a first analysis, we estimated synaptic conduc-tances by reference to the estimated leak conductance in the presence of TTX. This analysis yielded the following absolute values for the mean and variance of inhibitory and excitatory synaptic conductances (see Fig. 5, A and B): g_i0 = 70.67 ± 45.23 nS, g_e0 = 22.02 ± 37.41 nS, _i = 27.83 ± 32.76 nS, _e = 7.85 ± 10.05 nS for up-states; and g_i0 = 37.80 ± 23.11 nS, g_e0 = 6.41 ± 4.03 nS, _i = 8.85 ± 6.43 nS, _e = 3.10 ± 1.95 nS for post-PPT states. In agreement with the results obtained with the standard method (see above), these values show a much greater contribution of inhibitory conductances, albeit less pronounced in post-PPT states (paired t-test, P < 0.07 for ratio of inhibitory and excitatory mean, P < 0.05 for ratio of inhibitory and excitatory SD in both states). Ratios between inhibitory and excitatory mean conductances were 14.05 ± 12.36 for up-states and 9.94 ± 10.1 for post-PPT states (Fig. 5B, right). Moreover, inhibitory conductances displayed the greatest variance (the SD of the inhibitory synaptic conductance _i was 4.47 ± 2.97 times larger than _e for up-states and 3.16 ± 2.07 times for post-PPT states; Fig. 5B, right) and thus have a determinant influence on V_m fluctuations.

View larger version (47K): [in this window] [in a new window]   FIG. 4. Estimation of synaptic conductances during activated states using the VmD method. A: examples of intracellular activity during up-states (left; up-states indicated by gray bars) and post-PPT states (right). Insets: recorded cell (middle) and enlarged intracellular traces (gray boxes) as well as the I–V curves for the given cell. B: membrane potential distributions (V) (left) for up-states (left) and post-PPT states (right) at 2 different injected currents Iext1 = –1.04 nA and Iext2 = 0.04 nA. Most investigated Vm distributions were symmetric and values for the mean and SD V of the membrane potential were obtained by Gaussian fits (black). Right: estimations of the mean of excitatory and inhibitory synaptic conductances (ge0 and gi0, respectively) as well as their SDs (e and i, respectively). Estimated values: ge0 = 4.13 ± 4.29 nS, gi0 = 41.08 ± 34.37 nS, e = 2.88 ± 1.86 nS, i = 18.04 ± 2.72 nS, gi0/ge0 = 21.13 ± 16.57, i/e = 7.51 ± 3.9 for up-state; ge0 = 5.94 ± 2.80 nS, gi0 = 29.05 ± 22.89 nS, e = 2.11 ± 1.15 nS, i = 7.66 ± 7.93 nS, gi0/ge0 = 6.53 ± 5.52, i/e = 3.06 ± 2.09 for PPT-state. These estimates show a severalfold greater contribution of inhibition over excitation in both states, with a ratio between inhibitory and excitatory mean (i/e = 20.68 ± 1.24 for up-state, i/e = 9.81 ± 3.23 for post-PPT state) that compares to that found with the classical method (see Fig. 3A). C: impact of neuromodulators on the mean excitatory (left) and inhibitory (middle) conductance estimates. labels the neuromodulation-sensitive fraction of the leak conductance (see Eq. 7). Light gray area indicates the experimentally evidenced parameter regime of a contribution of down-regulated potassium conductances (Krnjevic et al. 1971). However, at hyperpolarized levels, the impact of neuromodulators is expected to be small (McCormick and Prince 1986) and changes in the conductance estimates are negligible (dark gray areas). Right: impact of neuromodulators on the ratio between excitatory and inhibitory mean conductances for the lower and upper limits of the experimentally evidenced parameter regime (gi0/ge0 = 6.51 ± 6.94 for = 0; 11.97 ± 11.48 for = 0.4).

View larger version (37K): [in this window] [in a new window]   FIG. 5. Characterization of synaptic conductances during activated states using the VmD method. A: pooled result of conductance estimates (mean ge0, gi0 and SD e, i for excitatory and inhibitory conductances, respectively) for all cells (light gray: up-states; dark gray: post-PPT states). Insets: data for smaller conductances. B: mean and SD of synaptic conductances (left) as well as their ratios (middle and left) averaged over whole population of available cells (for estimated values see text). C: pooled result for the impact of neuromodulator-sensitive potassium conductance on estimates of the mean excitatory (left) and inhibitory (middle) conductance as a function of the parameter (see Eq. 7). Light gray area indicates the experimentally evidenced parameter regime with a contribution of down-regulated potassium conductances (Krnjevic et al. 1971). Right: only minor impact of neuromodulators on the ratio between gi0 and ge0 for the lower and upper limits of the experimentally evidenced parameter regime (gi0/ge0 = 9.94 ± 10.1 for = 0; 11.61 ± 6.06 for = 0.4).

PPT-induced EEG-activated states are suppressed by systemic administration of muscarinic antagonists (Steriade et al. 1993). Thus after PPT stimulation, cortical neurons are in a different neuromodulatory state, likely stemming from the release of acetylcholine. Because muscarinic receptor stimulation blocks various K⁺ conductances in cortical neurons (McCormick 1992), thus leading to a general increase in R_in and depolarization (McCormick 1989), we assessed the contribution of K⁺ channels on the above conductance measurements. To this end, the leak conductance G_L was decomposed into a permanent (neuromodulation-insensitive) leak conductance G_L0, and a leak potassium conductance sensitive to neuromodulators G_KL

(7)

Moreover, denoting with E_K the potassium reversal potential, the passive leak reversal potential in the presence of G_KL takes the form

(8)

where E_L0 denotes the reversal for the G_L0 conductance. Introducing the scaling parameter (0 1) by rewriting G_KL = G_L, the impact of the neuromodulator-sensitive leak conductance can be tested. Here, = 0 denotes the condition where the effect of neuromodulators on leak conductance is negligible, whereas for = 1, the totality of the leak is suppressed by neuromodulators.

Experiments indicate that the change of R_in of cortical neurons induced by ACh is <40% at a depolarized V_m between –55 and –45 mV (39% in Krnjevic et al. 1971; 26.4 ± 12.9% in McCormick and Prince 1986), and drops to about 5% at hyperpolarized levels between –85 and –65 mV (4.6 ± 3.8% in McCormick and Prince 1986). The range of V_m in our experiments corresponds in all cases to the latter values, so we would expect to be small, around 0.05 to 0.1 (i.e., 5 to 10% R_in change). We repeated the conductance analysis for different values of . Although this analysis shows that there can be up to twofold changes in the values of g_e0 and g_i0 (see Fig. 4C for a specific example and Fig. 5C for population result), for between 0.05 to 0.1 these changes are minimal. Moreover, the finding that synaptic noise is mainly inhibitory in nature is not affected by incorporating the effect of ACh on R_in and E_L (Figs. 4C and 5C, right).

Biophysical models of EEG-activated states

One of the neurons recorded in this study was reconstructed using a computerized tracing system. The reconstructed 3D pyramidal morphology, shown in Fig. 6 A, was integrated into the NEURON simulation environment (Hines and Carnevale 1997). The constructed model incorporated a realistic density of excitatory and inhibitory synapses, as well as quantal conductances adjusted according to previous estimates (see METHODS). The model was then compared with intracellular recordings obtained in the same cell. The parameters of synaptic background activity were varied until the model matched these recordings, by using a previously proposed search strategy that is based on matching of experimental constraints (Destexhe and Paré 1999), such as the average V_m (), its variance (_V), and the R_in (Fig. 6). This method allowed us to estimate the activity at excitatory and inhibitory synaptic terminals, such as the average release rate and temporal correlation (for an application of this method to up-states under ketamine–xylazine anesthesia, see Destexhe and Paré 1999).

View larger version (40K): [in this window] [in a new window]   FIG. 6. Estimation of synaptic activity in EEG-activated periods elicited by PPT stimulation using biophysically detailed models. A: morphologically reconstructed layer V neocortical pyramidal neuron of cat parietal cortex incorporated in the modeling studies. B: dependency of the input resistance Rin change on the inhibitory release rate inh and the ratio between inh and exc (ratios of inh/exc from 0.05 to 0.25 were considered). C: dependency of the average membrane potential on inh and the ratio between inh and exc (see B). D: dependency of changes in Rin and V on the level of temporal correlation c in the synaptic activity. For uncorrelated synaptic activity, changes in the release rates primarily have an impact on Rin while leaving the fluctuation amplitude nearly unaffected (white dots), whereas changes in the correlation for fixed release rates do not change Rin but appreciably affect V (black dots). In all cases the observed experimental and estimated values are indicated by gray horizontal and vertical bars (mean ± SD), respectively (for values see text).

To test whether the estimated synaptic release rates and correlation are consistent with conductance measurements, we applied both the standard method and the VmD method to the computational model (see METHODS). Results from intracellular activity at nine different current levels from –1 to 1 nA, yielding 36 pairings, were averaged. The intracellular activity (Fig. 7 A) as well as the estimates for the mean and SD of synaptic conductances (Fig. 7C; estimated values: g_e0 = 5.03 ± 0.20 nS, g_i0 = 24.57 ± 0.87 nS, _e = 2.12 ± 0.18 nS, _i = 4.74 ± 0.86 nS) matched well the corresponding experimental measurements in the post-PPT state (Fig. 7C, compare light and dark gray; estimated values: g_e0 = 5.94 ± 2.80 nS, g_i0 = 29.05 ± 22.89 nS, _e = 2.11 ± 1.15 nS, _i = 7.66 ± 7.93 nS). Only in the case of _i did the model yield a slight underestimation of the value deduced from experiments. This mismatch could reflect either an incomplete reconstruction or, simply, a larger error in the estimation of this parameter. Nevertheless, the ratios between the inhibitory and excitatory means (g_i0/g_e0 = 4.89 ± 0.15; model estimate using classical method: g_i0/g_e0 = 4.60 ± 1.51), as well as those between the SDs (_i/_e = 2.26 ± 0.53), matched closely the results obtained by applying the VmD method to experimental data (Fig. 7C, right; g_i0/g_e0 = 6.526 ± 5.518, _i/_e = 3.06 ± 2.09; experimental estimation using classical method: g_i0/g_e0 = 9.81 ± 3.23), thus cross-validating the different methods.

View larger version (38K): [in this window] [in a new window]   FIG. 7. Estimation of synaptic conductances in the detailed biophysical model. A: estimation of synaptic conductances using the VmD method (see METHODS). Intracellular activity at 2 different injected constant current levels (Iext1 and Iext2, middle) yields Vm distributions that match well with those seen in the corresponding experiments (right). B: an "ideal" voltage clamp (no series electrode resistance) inserted into the soma (left) allows decomposition of the time course of inhibitory and excitatory synaptic conductances (middle) based on pairing of current recordings obtained at 2 different voltage levels. Conductance histograms (right, gray), which show the example for one pairing, are compared with Gaussian conductance distributions with mean and SD taken from the VmD analysis of the experimental data. C: synaptic conductance parameters estimated from various methods applied to experimental results and the corresponding computational model. Whereas the mean conductances are in good agreement across the various methods, the detailed biophysical model shows a slight underestimation of inhibitory SD.

Robustness of synaptic conductance estimates

To test the robustness and applicability of the proposed method to more realistic situations with active dendrites capable of generating and conducting spikes, we incorporated voltage-dependent currents [I_Na, I_Kd for spike generation, and a slow voltage-dependent K⁺ current for spike-frequency adaptation, a hyperpolarization-activated current I_h, a low-threshold Ca²⁺ current I_CaT, an A-type K⁺ current I_KA (Fig. 8) as well as a voltage-dependent cation nonselective current I_CAN (Fig. 9) with densities typical for cortical neurons; see METHODS] into the detailed biophysical model. The presence of voltage-dependent ion currents yield, in general, nonlinear I–V curves (see Figs. 8B and 9B). However, restricting to the linear regime of the I–V curves (Figs. 8B and 9B, gray) provided synaptic conductance estimates using the VmD method (Figs. 8A and 9A, light gray), which were in good agreement with the estimates obtained with the passive model as well as experiments (Fig. 8A, diamonds and white bars, respectively). This suggests that the VmD method constitutes a robust way for estimating synaptic contributions to the membrane conductance even in situations where the membrane shows a nonlinear behavior arising from the presence of active conductances, but only if the linear portion of I–V curves is considered.

View larger version (50K): [in this window] [in a new window]   FIG. 8. Estimation of synaptic conductances from the membrane potential activity in the detailed biophysical model with active dendrites. Model with voltage-dependent currents for spike generation (INa, IKd), spike-frequency adaptation (IM), A-type K+ current (IKA), low-threshold Ca2+ current (ICaT), and hyperpolarization-activated current Ih in soma and dendrites with experimentally reported densities (see METHODS) were considered. A: means (ge0 and gi0; top) and SDs (e and i; bottom) for excitatory (left) and inhibitory (middle) conductances, and their corresponding ratios (right) for different active properties. Estimates using the VmD method (light gray) and "ideal" somatic voltage clamp (dark gray) are shown and compared with the corresponding passive model and experimental results (white bars). Despite huge variations in active properties, the estimates were in good agreement across the various methods, indicating the robustness of the proposed methods. B: I–V curves for models with active soma and dendrites. Linear regimes used for the estimation of synaptic conductance parameters in the VmD method are indicated with gray bars. C: membrane potential traces for the passive (left) and various active models. Gray arrows mark somatic spikelets generated by arriving dendritic spikes that fail to evoke somatic spikes. Such spikelets were absent in the passive model (left) and experimental recordings (e.g., Fig. 4) and led to small but systematic overestimation of excitatory conductances using the VmD method.

View larger version (40K): [in this window] [in a new window]   FIG. 9. Estimation of synaptic conductances from the membrane potential activity in the detailed biophysical model with the voltage-dependent cation nonselective current ICAN. A: estimates for the mean (ge0 and gi0; top) and SD (e and i; bottom) of excitatory (left) and inhibitory (middle) conductances as well as their corresponding ratios (right) for different somatic and dendritic densities of ICAN conductances, labeled as multiples of 0.02 mS/cm2 (Haj-Dahmane and Andrade 1996). Conductance estimates were obtained using the VmD method (light gray) and an "ideal" somatic voltage clamp (dark gray), and are compared with the corresponding passive model and experimental results (white bars). Only minimal variations in the estimated conductance parameters were found in the investigated parameter regime. B: I–V curves for models with different densities of ICAN conductances (same parameter regime as in A). Only for strong depolarizing current, does the I–V relation start to deviate from a linear behavior, indicating that in the subthreshold regime (gray bar) considered for estimating synaptic conductances the impact of ICAN is negligible. Inset: activation current for ICAN conductance density of 0.02 (1.0) and 0.04 mS/cm2 (2.0). C: membrane potential traces for 2 different conductance densities of ICAN (same as in B, inset) for identical synaptic activation pattern. Differences in the Vm time course are minimal in the subthreshold regime.

To evaluate the impact of a cholinergic modulation other than a K⁺ conductance block described above, we inserted in our models the voltage-dependent cation nonselective current I_CAN (Guérineau et al. 1995; Haj-Dahmane and Andrade 1996) with densities ranging from zero to two times the experimentally reported value of 0.02 mS/cm² (Haj-Dahmane and Andrade 1996; see Fig. 9). In this parameter regime, synaptic conductance estimates performed using the VmD method and an "ideal" somatic voltage clamp (Fig. 9A, light and dark gray, respectively) were again in good agreement with the results obtained from the corresponding experimental recordings and the passive model. Surprisingly, the estimated values for the means g_e0 and g_i0 as well as SDs _e and _i of excitation and inhibition, respectively, were affected only slightly by the I_CAN conductance density, which suggests that in the subthreshold regime considered for estimating synaptic conductances, the impact of I_CAN is negligible. This relative independence is a direct result of the activation current of I_CAN (see Fig. 9B, inset), which takes large values only at strongly depolarized levels, resulting in a nonlinear I–V relation for the membrane (Fig. 9B). Moreover, the subthreshold dynamics did not show spikelets (see above) and was nearly unaffected by the presence of I_CAN in a physiologically relevant regime of conductance densities (Fig. 9C).

Simplified models of EEG-activated states

To construct simplified models of cortical neurons in high-conductance states, we first analyzed the scaling structure of the power spectral density (PSD) of the V_m. For post-PPT states (Fig. 10 A), we found that the power spectral density S() followed a frequency-scaling behavior described by

(9)

where denotes an effective time constant, D is the total spectral power at zero frequency, and m is the asymptotic slope for high frequencies . The latter is a direct indicator of the kinetics of synaptic currents (Destexhe and Rudolph 2004) and the contribution of active membrane conductances (Manwani and Koch 1999). Consistent with this, the slope showed little variations as a function of the injected current (Fig. 10B, top) and of the membrane potential (Fig. 10B, bottom). It was nearly identical for up-states (slope m = –2.44 ± 0.31 Hz^–1; not shown) and post-PPT states (slope m = –2.44 ± 0.27 Hz^–1; see Fig. 10C). These results indicate that, in these cells, the subthreshold membrane dynamics are mainly determined by synaptic activity, less so by active membrane conductances.

View larger version (17K): [in this window] [in a new window]   FIG. 10. Power spectral densities (PSDs) of membrane potential fluctuations estimated from EEG-activated states. A: example of the spectral density in the post-PPT state for the cell shown in Fig. 4. Black line indicates the slope (m = –2.76) obtained by fitting the Vm power spectral density to a Lorentzian S() = D2/(1 + 2)m at high frequencies 10 < < 500 Hz. Dashed line shows the best fit using the analytic form of the Vm PSD (see Eq. 10; fitted parameters: C1 = C2 = 0.183; e = 3 ms, i = 10 ms, m = 6.9 ms). B: slope for all investigated cells as a function of the injected c