Home | Help | Feedback | Subscriptions | Archive | Search | Table of Contents

This Article Abstract PDF (Full Text) PPT slides of all figures Alert me when this article is cited Citation Map Services Email this article Similar articles in this journal Similar articles in PubMed Alert me to new content in the JGP Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via CrossRef Citing Articles via Google Scholar Google Scholar Articles by Magistretti, J. Articles by Alonso, A. Search for Related Content PubMed PubMed Citation Articles by Magistretti, J. Articles by Alonso, A. Social Bookmarking                      What's this?

¹ Department of Neurology and Neurosurgery, McGill University and Montreal Neurological Institute, Montréal, Québec H3A 2B4, Canada
² Dipartimento di Scienze Fisiologiche-Farmacologiche Cellulari-Molecolari, Università degli Studi di Pavia, 27100 Pavia, Italy

Address correspondence to Dr. Jacopo Magistretti, Dipartimento di Scienze Fisiologiche-Faramacologiche, Cellulari-Molecolari Sezione di Fisiologia Generale e Biofisica Cellulare, Università degli Studi di Pavia, Via Forlanini 6, 27100 Pavia, Italy. Fax: (39) 0382-507527; E-mail: jmlab1{at}unipv.it

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
The gating properties of channels responsible for the generation of persistent Na⁺ current (I_NaP) in entorhinal cortex layer II principal neurons were investigated by performing cell-attached, patch-clamp experiments in acutely isolated cells. Voltage-gated Na⁺-channel activity was routinely elicited by applying 500-ms depolarizing test pulses positive to -60 mV from a holding potential of -100 mV. The channel activity underlying I_NaP consisted of prolonged and frequently delayed bursts during which repetitive openings were separated by short closings. The mean duration of openings within bursts was strongly voltage dependent, and increased by e times per every 12 mV of depolarization. On the other hand, intraburst closed times showed no major voltage dependence. The mean duration of burst events was also relatively voltage insensitive. The analysis of burst-duration frequency distribution returned two major, relatively voltage-independent time constants of 28 and 190 ms. The probability of burst openings to occur also appeared largely voltage independent. Because of the above "persistent" Na⁺-channel properties, the voltage dependence of the conductance underlying whole-cell I_NaP turned out to be largely the consequence of the pronounced voltage dependence of intraburst open times. On the other hand, some kinetic properties of the macroscopic I_NaP, and in particular the fast and intermediate I_NaP-decay components observed during step depolarizations, were found to largely reflect mean burst duration of the underlying channel openings. A further I_NaP decay process, namely slow inactivation, was paralleled instead by a progressive increase of interburst closed times during the application of long-lasting (i.e., 20 s) depolarizing pulses. In addition, long-lasting depolarizations also promoted a channel gating modality characterized by shorter burst durations than normally seen using 500-ms test pulses, with a predominant burst-duration time constant of 5–6 ms. The above data, therefore, provide a detailed picture of the single-channel bases of I_NaP voltage-dependent and kinetic properties in entorhinal cortex layer II neurons.

Key Words: persistent Na⁺ current • single channel • entorhinal cortex • stellate cells • patch clamp

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
The persistent Na⁺ current (I_NaP) is widely expressed in a variety of neuronal populations of the central nervous system (CNS)^* (French and Gage, 1985; Stafstrom et al., 1985; French et al., 1990; Chao and Alzheimer, 1995; Uteshev et al., 1995; Kay et al., 1998; Magistretti and Alonso, 1999). Its distinctive biophysical properties consist of a scarce, or absent, tendency to inactivate during sustained depolarizations and a low threshold of activation (for review see Taylor, 1993; Crill, 1996). I_NaP has recently been the object of considerable interest in both biophysical and functional studies on central neurons. It is now well established that, due to its persistent nature and its recruitment as a consequence of small depolarizations, I_NaP significantly contributes to basic aspects of neuronal integrative functions, such as amplification and processing of synaptic inputs (Deisz et al., 1991; Schwindt and Crill, 1995; Stuart and Sakmann, 1995; Lipowsky et al., 1996), and is implicated in the generation of specific patterns of neuronal electrical activity and responsiveness, including subthreshold oscillations (Alonso and Llinás, 1989; Amitai, 1994; Takakusaki and Kitai, 1997; Pape and Driesang, 1998), spontaneous firing (Pennartz et al., 1997; Takakusaki and Kitai, 1997; Bevan and Wilson, 1999; Bennett et al., 2000; Taddese and Bean, 2002), burst firing (Franceschetti et al., 1995; Parri and Crunelli, 1998; Brumberg et al., 2000), depolarizing afterpotentials (Azouz et al., 1996), and plateau potentials (Llinás and Sugimori, 1980; Jahnsen and Llinás, 1984; Sandler et al., 1998). Given the fundamental integrative functions of dendrites (Johnston et al., 1996; Reyes, 2001), the demonstration that the conductance and channels underlying I_NaP are expressed by dendrites of central neurons (Schwindt and Crill, 1995; Lipowsky et al., 1996; Magistretti et al., 1999b) further emphasizes the importance of the same current in information processing and integration.

A well-characterized role of I_NaP in controlling the subthreshold electrical activity of central neurons is found in the stellate cells of entorhinal cortex (EC) layer II. The I_NaP expressed by these neurons (Magistretti and Alonso, 1999) has been demonstrated to interplay with the hyperpolarization-activated cation current, I_h (Dickson et al., 2000), to generate subthreshold membrane-potential oscillations in a frequency range corresponding to the theta band (Alonso and Llinás, 1989; Klink and Alonso, 1993; Dickson et al., 2000). These subthreshold theta oscillations critically influence spike patterning in response to small, sustained depolarizations (Alonso and Klink, 1993). Theta-patterned spike discharge underlain by subthreshold oscillations generated at the single-cell level is likely to be propagated, at the EC-network level, by the reciprocal connections developed by layer II stellate cells (Lingenhöhl and Finch, 1991; Klink and Alonso, 1997). Indeed, a local generator of theta rhythmicity has been demonstrated to exist in EC layer II (Alonso and García-Austt, 1987a,b), and theta population activity is prominently expressed in the EC and other parahippocampal structures (Bland and Colom, 1993). In turn, the theta rhythm is believed to be required for the proper implementation of the memory function of the parahippocampal region (PHR) (Winson, 1978; Buzsaki, 1996), and, in particular, to exert major modulatory effects on cellular events, such as long-term potentiation, that may represent elementary correlates of the ongoing PHR memory processes (Larson and Lynch, 1986; Larson et al., 1986; Greenstein et al., 1988; Alonso et al., 1990; Huerta and Lisman, 1996; Hölscher et al., 1997).

Due to the ability of I_NaP to generate membrane bistability and plateau potentials (e.g., Klink and Alonso, 1993; Johnston et al., 1994), this current has also been implicated in the basic pathophysiological mechanism of epileptogenesis (Segal, 1994; for review see Ragsdale and Avoli, 1998). In addition, since I_NaP can sustain long-lasting Na⁺ influxes, thus promoting steady increases of intracellular Na⁺ (and secondarily also Ca²⁺) concentration, considerable attention has been devoted to its possible contributions to neurodegeneration processes (Taylor and Meldrum, 1995).

Despite the major interest raised by I_NaP properties and functions, the single-channel correlates of this current have long remained elusive. This is not entirely surprising, since I_NaP is normally only a minimal fraction of total voltage-dependent Na⁺ currents expressed by neuronal membranes (Taylor, 1993; Crill, 1996), which is likely to hamper attempts to identify the underlying single-channel activity. In a recent study performed in EC layer II principal neurons (Magistretti et al., 1999a), the single-channel activity responsible for the I_NaP expressed by the same cells has been found to consist in channel openings characterized by: (a) relatively high opening probability, maintained for long periods of time (tens of minutes), during prolonged (500-ms) depolarizing test pulses; and (b) a single-channel conductance of 20 pS, significantly higher than observed in channel openings underlying the classical, transient voltage-dependent Na⁺ current (I_NaT).

In the present work we further developed our previous studies on the channels responsible for I_NaP generation by undertaking a thorough analysis of their fine gating properties in EC layer II principal neurons. Our results allowed us to provide a detailed description of the single-channel bases of I_NaP voltage dependence and kinetic properties.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Cell Preparation
Young-adult Long-Evans rats (P25-P35) were killed by decapitation according to a procedure approved by the Animal Care Committee of the Montreal Neurological Institute, and compliant with the Canadian and international laws on animal research. The brain was quickly removed under hypothermic conditions, blocked on the stage of a vibratome (Pelco), and submerged in an ice-cold cutting solution containing (in mmol/l): 115 NaCl, 5 KCl, 4 MgCl₂, 1 CaCl₂, 20 PIPES, and 25 D-glucose (pH 7.4 with NaOH, bubbled with pure O₂). Horizontal slices of the retrohippocampal region were cut at 350–400 µm. Layer II of medial EC was then dissected from each slice. Neurons were acutely isolated from the tissue fragments thus obtained following an enzymatic and mechanical dissociation procedure described elsewhere (Magistretti and de Curtis, 1998).

Single-channel Recordings
The recording chamber was mounted on the stage of an inverted microscope (see below). After seeding into the recording chamber, cells where initially perfused with a standard HEPES buffer containing (in mmol/l): 140 NaCl, 5 KCl, 10 HEPES (free acid), 2 CaCl₂, 2 MgCl₂, 25 glucose, pH 7.4 with NaOH, bubbled with pure O₂. The pipette solution contained (in mmol/l): 130 NaCl, 35 TEA-Cl, 10 HEPES-Na, 2 CaCl₂, 2 MgCl₂, 5 4-AP, pH 7.4 with HCl. Single-channel patch pipettes had resistances ranging from 10 to 35 M when filled with the above solution, and were always coated with Sylgard^® (Dow Corning) from the shoulder to a point as close as possible to the tip, so as to minimize stray pipette capacitance. After obtaining the cell-attached configuration, the extracellular perfusion was switched to a high-potassium solution containing: 140 K-acetate, 5 NaCl, 10 HEPES (free acid), 4 MgCl₂, 0.2 CdCl₂, 25 glucose, pH 7.4 with KOH, so as to hold the neuron resting membrane potential at near 0 mV. Recordings were performed at room temperature using an Axopatch 200B amplifier (Axon Instruments, Inc.). Capacitive transients and linear current leakage were minimized online by acting on the respective built-in compensation sections of the amplifier. To elicit voltage-gated Na⁺-channel currents, 50-, 500-, or 20-s depolarizing voltage steps were delivered one every 5, 5.6, or 40 s, respectively. The holding potential was -100 mV.

Whole-cell Recordings
For these experiments, dissociated cells were initially perfused with the same solution as described in the previous paragraph. After washout of cell debris, cell perfusion was switched to a solution suitable for Na⁺-current isolation, containing: 100 NaCl, 40 TEA-Cl, 10 HEPES (free acid), 2 CaCl₂, 3 MgCl₂, 0.2 CdCl₂, 5 4-AP, 25 glucose, pH 7.4 with NaOH, bubbled with pure O₂. The intrapipette solution contained (in mmol/l): 110 CsF, 10 HEPES-Na, 11 EGTA, 2 MgCl₂, pH 7.25 with CsOH. When filled with the above solution, the patch pipettes had a resistance of 3–5 M. Cells were observed at 400x magnification with an Axiovert 100 microscope (ZEISS). Tight seals (>100 G) and the whole-cell configuration were obtained by suction (Hamill et al., 1981). Series resistance was on average 13.5 ± 3.1 M (n = 5), and was always compensated by 70% with the amplifier's built-in compensation section. Voltage-clamp recordings were performed at room temperature (22°C) using an Axopatch 1D amplifier (Axon Instruments, Inc.). The holding potential was -80 mV.

Data Acquisition
Voltage protocols were commanded and current signals were acquired with a Pentium PC interfaced to an Axon TL1 interface, using the Clampex program of the pClamp 6.0.2 software package (Axon Instruments, Inc.). Current signals were filtered on-line (using the amplifier's built-in low-pass filter) and digitized at different frequencies according to the specific experimental aim. In single-channel experiments, filtering and acquisition frequencies were 5 and 100 kHz, respectively, for 50-ms depolarizing protocols; 2 and 10 kHz, respectively, for 500-ms depolarizing protocols; 1 and 2 kHz, respectively, for 20-s depolarizing protocols. In whole-cell experiments, filtering and acquisition frequencies were 10 and 20 kHz, respectively.

Data Analysis
Single-channel recordings were analyzed using Fetchan, pStat, and Clampfit (from the pClamp 6.0.5 software package; Axon Instruments, Inc.). Residual capacitive transients were nullified by off-line subtracting fits of average blank traces. Residual leakage currents were carefully measured in trace regions devoid of any channel openings, and digitally subtracted.

Channel dwell times were determined by applying a standard half-amplitude crossing protocol using Fetchan. No minimum-duration threshold for detection of state transitions was imposed. Dwell-time histograms were constructed, in some cases, as double-linear plots. However, logarithmic plots represent a suitable and powerful tool for data display and analysis in the presence of different exponential components widely separated in terms of time constants, and the slowest of which are represented by relatively few samples (see Blatz and Magleby, 1986; Sigworth and Sine, 1987; McManus et al., 1987). Hence, logarithmic plots were routinely used for the analysis of intraburst open and closed times as well as burst duration, and in these cases data were binned logarithmically. To do this, lower and upper bin limits were first set according to a logarithmic scale that yielded 11.4 bins/decade. To avoid arbitrary over- or underestimations of the calculated numbers of events per millisecond, upper limit values were then approximated to the nearest tenth of a millisecond above, so as to make each bin width equal an integer multiple of the sampling interval routinely used (100 µs). After data binning, numbers of events (n_i) were divided by the corresponding bin widths (t_i), and the natural logarithm of n_i/t_i ratios was calculated. The values thus obtained were plotted as a function of x = ln t to construct log–log frequency-distribution graphs (see Fig. 2 A2 and B2). Exponential fitting of log-log histograms was performed by applying the following function (McManus et al., 1987):

(1)

where x_0j = ln _j, and W_j and _j are the weight coefficient and time constant, respectively, of each exponential component. Therefore, Eq. 1 corresponds to a double logarithmic transform of a sum of exponential functions. The above fittings were performed using the fitting routine of Origin 6.0 (MicroCal Software), based on a minimum ² method. To better highlight single exponential components as straight lines, logarithmically binned histograms constructed as described above were also displayed on a linear, rather than logarithmic, time scale, thereby obtaining log-linear graphs (see Fig. 2 A3 and B3). Theoretical mean dwell times () were derived from the exponential fitting functions according to the relationship:

(2)

View larger version (30K): [in this window] [in a new window]   FIGURE 2. Display and analysis of intraburst open- and closed-time data. (A) Frequency-distribution diagrams of intraburst open times at -10 mV. Data were collected from nine different patches. (B) Frequency-distribution diagrams of intraburst closed times at -10 mV. Data were from the same nine patches used for A. A1 and B1 show histograms constructed after linear binning of original data and displayed on a double-linear scale (bin width, 0.4 ms in A1; 0.1 ms in B1). A2 and B2 are log-log histograms. Data were binned logarithmically (11.4 bins/decade), and the natural logarithm of the numbers of observations per ms [ln(n/ms)] was plotted as a function of time in a logarithmic scale. Smooth, enhanced lines are third (A2) or second (B2) order exponential functions obtained by applying the fitting function of Eq. 1 (MATERIALS AND METHODS). Smooth, dotted lines are the single exponential components shown separately. Fitting parameters are specified in Table I. A3 and B3 are log-linear plots of the same data. Data were binned logarithmically as above, and the quantity ln(n/ms) was plotted as a function of time in a linear scale. The x value of each point is the logarithmic midpoint of the corresponding bin. Continuous and dotted lines are the same functions as in the two previous panels: single exponential components appear here as straight lines.

Fittings to data points made by applying other nonlinear functions, including the Boltzmann relation in the form: y = A/{1 + exp[(V_m - V_1/2)/k]}, were performed using Origin 6.0. Average values are expressed as mean ± SE. Statistical significance was evaluated by means of the two-tail Student's t test for paired or unpaired data.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Na⁺-channel activity was studied in cell-attached membrane patches of entorhinal cortex layer II principal neurons. The cell-attached configuration was chosen in order to preserve the intracellular environment existing in intact cells, thus obtaining recording conditions closer to the physiological situation. Channel openings were routinely elicited by delivering 500-ms depolarizing pulses at variable test potentials (-50 to 0 mV). The application of these depolarizing protocols evoked, in most patches, a prominent, early Na⁺-channel activity that decayed within a few ms after the start of the test pulse. In addition to these expected, transient Na⁺-channel openings, in 56 out of 68 patches prolonged early openings and/or late openings were frequently observed (see Fig. 1). We have shown elsewhere that this "persistent" Na⁺-channel activity represents an elementary correlate of the macroscopic persistent Na⁺ current (I_NaP) expressed by these cortical neurons (Magistretti et al., 1999a; Magistretti and Alonso, 1999). The persistent Na⁺-channel activity consisted of more or less prolonged burst events in which repetitive openings of variable duration were separated by brief closings. The analysis of closed times at various test voltages (see below) revealed the existence of two relatively fast time constants (_c(fast)1 and _c(fast)2) plus a much slower time constant (_c(slow)). _c(slow) values were 65–95 times larger than the slowest _c(fast)2 values observed, and therefore _c(slow) was considered as related to the interburst closing process. The average values of _c(fast)2 and _c(slow) were such that the duration threshold between intraburst and interburst closing events was set at 10 ms (namely, an interval 6–10 times higher than the slowest _c(fast)s observed). Since most recordings were obtained from multichannel patches, only those bursts in which no sign of superimposed (multiple) openings was apparent were considered. Among these, only bursts of >10 ms in duration were selected for analysis (Fig. 1, arrows). This was done to exclude from our analysis late openings of brief duration that classical, fast Na⁺ channels can occasionally produce (Alzheimer et al., 1993).

View larger version (25K): [in this window] [in a new window]   FIGURE 1. Persistent Na+ channel activity consists in prolonged and/or delayed burst openings. The figure shows twelve consecutive current sweeps recorded in response to 500-ms depolarizing pulses at -10 mV (top trace) in a representative cell-attached patch (patch A8716). The interpulse interval was 5.1 s. The arrows point to burst openings that were selected for analysis due to their characteristics (see the text for details). Calibration bars, 2 pA, 50 ms.

Fig. 3 illustrates the results of open-time analysis. The repetitive openings within individual bursts appeared to be short and frequent at negative membrane potentials (V_ms), and more prolonged and stable at increasingly positive V_ms (Fig. 3 A, insets). The analysis of open-time frequency distributions allowed for a precise quantification of this behavior. Inspection of log-linear plots clearly revealed, at all test potentials, the presence of three exponential components (see Fig. 2 A3). Fittings of log-log plots performed applying Eq. 1 (see MATERIALS AND METHODS) confirmed that the best concordance with experimental data was achieved using a third-order exponential function (see Fig. 2 A2). Application of higher-order exponential functions did not add to the quality of fit. Fig. 3 (main panels) shows the open-time histograms obtained at all test potentials, here displayed as double-linear plots to highlight the actual numbers of observations, along with fitting functions derived as explained above. All of the three time constants found (_o(b)1 - _o(b)3)¹ proved to be prominently voltage dependent (Table I) and increased by 12 (_o(b)1), 20 (_o(b)2), or 8 (_o(b)3) times from -50 to 0 mV. The mean open time (_o(b)), calculated on the basis of fitting parameters as explained in MATERIALS AND METHODS (Eq. 2), was also strongly voltage dependent (Fig. 3 B, open symbols), showing an e-fold increase (over an estimated pedestal level of 0.47 ms) per every 11.8 mV of depolarization.

View larger version (47K): [in this window] [in a new window]   FIGURE 3. Open times are strongly voltage dependent. (A) Frequency distributions of open times at six different membrane potentials (-50 to 0 mV). Each histogram has been constructed pooling together data from 4 to 10 different patches. Data are shown binned linearly and plotted on a double-linear scale (bin width = 0.1 ms at -50 to -30 mV; 0.2 ms at -20 mV; 0.4 ms at -10 and 0 mV). Note the different time scales used. Smooth lines are best third order exponential fittings obtained applying Eq. 1 to log-log plots of the same data binned logarithmically (see MATERIALS AND METHODS, and Fig. 2). Fitting parameters are specified in Table I. For each test potential, exemplary 210-ms current-trace segments were selected from 500-ms sweeps recorded in a single representative patch (patch B8708), and are shown in the inset of the corresponding panel (calibration bars: 1 pA, 25 ms). (B) Plot of mean open time (, calculated from fitting parameters as explained in the text) as a function of membrane potential (open circles). The continuous line is the best fitting to data points obtained applying the exponential function = A · exp(Vm/h) + C, which returned the following fitting parameters: A = 7.0 ms, h = 11.8 mV, C = 0.47 ms. Filled circles are mean intraburst closed times (: see Fig. 4) measured in the same patches, shown here for comparison. (C) Voltage dependence of average intraburst opening probability (Po(b)), calculated from and as explained in the text. The continuous line is the best Boltzmann fitting to data points. Fitting parameters are: A = 0.869, V1/2 = -44.5 mV, k = -5.02 mV.

View larger version (36K): [in this window] [in a new window]   FIGURE 4. Intraburst closed times are scarcely voltage dependent. (A) Frequency distributions of intraburst closed times at two exemplary membrane potentials (-40 mV in A1, -20 mV in A2). The histograms have been constructed pooling together data from seven (-40) or nine (-20) different patches. Data are shown binned linearly and plotted on a double-linear scale (bin width = 0.1 ms). Smooth lines are the best second-order exponential fittings obtained applying Eq. 1 to log-log plots of the same data binned logarithmically (see the MATERIALS AND METHODS, and Fig. 2). Fitting parameters are specified in Table I. For both test potentials, exemplary 100-ms current-trace segments were selected from 500-ms sweeps recorded in a single representative patch (patch D8716), and are shown in the inset of the corresponding panel over an expanded time scale (calibration bars: 1 pA, 10 ms). (B) Plot of mean intraburst closed time (, calculated from fitting parameters as explained in the text) as a function of membrane potential.

Having measured intraburst mean open and closed times, we were able to directly derive the probability of a channel to be open within a bursting event (P_o(b)) by applying the following relation:

P_o(b) values thus obtained were then plotted as a function of membrane potential (Fig. 3 C), which revealed a progressive increase of P_o(b) at increasingly positive voltages, with a nearly saturating level at V_ms positive to -20 mV. Fitting the data points with a single Boltzmann function returned a plateau P_o(b) level of 0.87, a V_1/2 of about -44.5 mV, and a slope coefficient (k) of about -5 mV. Remarkably, the V_1/2 and k values thus found were extremely similar to those already reported for the activation voltage dependence of the whole-cell conductance underlying the macroscopic I_NaP (Magistretti and Alonso, 1999).

Analysis of Interburst Closed Times
The quantitative analysis of closing periods between bursts requires the isolation of channel activity that may be attributed to an individual channel only, or, alternatively, to a known number of channels behaving identically. As mentioned above, most patches recorded in this study were multichannel patches. In these cases no assumptions could be made as to the number of channels responsible for "persistent" openings (from this point on, "NaP channels" for brevity), and, hence, no analysis of interburst closings could be performed. In two patches, however, only one single NaP channel appeared to be present. Indeed, despite the relatively high opening probability found in these patches (0.18 ± 0.04 during 500-ms depolarizing pulses at -10 mV), superimposed persistent openings were never observed in a total of 180 sweeps.² In these patches, therefore, inter-burst closed times, in addition to intraburst closed times, could be analyzed. Current traces recorded in response to 500-ms depolarizing pulses were used for this analysis (Fig. 5 A). The overall closed-time distribution obtained for the test potential of –10 mV is shown in Fig. 5 B. The log-log histogram could be best fitted with a third-order exponential function (Fig. 5 B, inset), with two fast time constants (_c(fast)1 and _c(fast)2) of 0.351 and 1.215 ms, respectively, and a much slower one (_c(slow)) of 115.5 ms. Similar measurements could also be performed in the same patches for the test potentials of -20 and -30 mV (not depicted): exponential fittings of closed-time histograms returned _c(slow) values of 81.0 and 88.3 ms, respectively. The ratios between _c(slow) and the slowest _c(fast) were 95.1, 94.3, and 144.8 at -10, -20, and -30 mV, respectively. These data clearly indicate the existence of at least one long-lasting nonconductive state that interrupts and separates burst events generated by single NaP channels.³

View larger version (25K): [in this window] [in a new window]   FIGURE 5. Analysis of interburst closed times. (A) Selected 500-ms sweeps from a patch in which the activity of a single NaP channel was recorded in isolation (patch F8711). The traces have been chosen to show the occurrence of reopenings and illustrate inter-burst intervals. Test potential was -10 mV. Calibration bars, 1 pA, 50 ms. (B) Frequency distribution of total closed times at -10 mV. The graphs have been constructed pooling together data from two single-channel patches. Data were binned logarithmically and in the main panel are shown in a log-linear plot. In the inset, the same data are shown as a log-log histogram. In both panels, the smooth, continuous line is the best third-order exponential fitting obtained applying Eq. 1 to the log-log plot. Dotted lines are the single exponential components of the fitting function shown separately. Fitting parameters are: W1 = 1094.29, c1 = 351.2 µs; W2 = 291.57, c2 = 1.215 ms; W3 = 63.42, c3 = 115.53 ms.

View larger version (19K): [in this window] [in a new window]   FIGURE 9. Burst-duration time constants result in very similar macroscopic relaxation time constants in ensemble-average traces. (A) Kinetic properties of the ensemble-average current derived, for the test potential of -10 mV, from patches showing the activity of single NaP channels in isolation. A1 shows exemplary traces recorded in response to 500-ms depolarizing pulses at -10 mV in the same patch as in Fig. 5, A2 shows the trace obtained by averaging 34 such traces from the two single-channel patches available. The smooth, blank line in A2 is the best biexponential fitting to data points (time-constant values are specified nearby). Calibration bars, 1 pA, 50 ms (A1); 400 fA, 50 ms (A2). (B) Frequency distribution of burst durations at -10 mV for the two single-channel patches illustrated above. The graphs have been constructed pooling together data from the same two patches used for A2. Data were binned logarithmically and in the main panel are shown in a log-linear plot. In the inset, the same data are shown as a log-log histogram. In both panels, the smooth, continuous line is the best second-order exponential fitting obtained applying Eq. 1 to the log-log plot. Dotted lines are the single exponential components of the fitting function shown separately. Fitting parameters are: W1 = 90.21, b1 = 18.71 ms; W2 = 30.68, b2 = 111.92 ms.

View larger version (38K): [in this window] [in a new window]   FIGURE 6. Analysis of first latencies at -10 mV. (A) Selected sweeps showing persistent Na+ channel openings in isolation from a representative patch (patch H8710). Single-channel currents recorded in response to 50-ms depolarizing step pulses at -10 mV are shown in A1. A2 shows a detail, over an expanded time scale, of the first 15 ms of the same traces as in A1 (corresponding to the segments included in the dotted-line box of A1). The arrows in A1 remark two channel openings characterized by remarkably long first latencies. The filled bar in A2 indicates the first latency of the channel opening occurring in the top trace, determined starting from the depolarization's zero time point (dotted vertical line). Calibration bars, 1 pA, 5 (A1) or 1.5 (A2) ms. (B) Frequency distribution of first latencies at -10 mV. Data have been obtained in a total of 42 sweeps from two different patches, and are shown binned linearly and plotted on a double-linear scale. B1 highlights the initial part of the distribution (up to 1.75 ms). B2 shows the whole frequency distribution (with a different bin width).

View larger version (35K): [in this window] [in a new window]   FIGURE 7. Analysis of burst duration. (A) Selected current traces recorded in response to 500-ms depolarizing pulses at -40 mV (A1) or 0 mV (A2) in a representative patch (patch D8708). Calibration bars, 2 pA, 50 ms. (B) Frequency distributions of burst duration at Vm = -40 mV (B1) and 0 mV (B2). Each graph has been constructed pooling together data from five different patches. Data were binned logarithmically and in the main panels are shown as log-linear plots. In the insets, the same data are shown as log-log histograms. In all panels, the smooth, continuous line is the best second-order exponential fitting obtained applying Eq. 1 to log-log plots. Dotted lines are the single exponential components of fitting functions shown separately. Fitting parameters are: W1 = 192.16, b1 = 26.98 ms; W2 = 55.83, b2 = 177.47 ms (-40 mV); W1 = 258.22, b1 = 27.03 ms; W2 = 72.26, b2 = 210.83 ms (0 mV). (C) Plot of burst-duration time constants (bs) as a function of membrane potential. Filled and empty circles are b1 and b2 values, respectively. Note the logarithmic scale of the y axis. (D) Voltage dependence of mean burst duration (, calculated from fitting parameters as explained in the text).

where i_NaP is the amplitude of unitary persistent Na⁺-channel openings at a given potential, and n is the number of channels. The product of the two factors, P_b and P_o(b), expresses the probability of a NaP channel to be open at any time point. n · P_b can thus be derived as:

(3)

On the basis of Eq. 3, we reconstructed n · P_b values in the six patches used for burst-duration analysis. I_NaP amplitude was estimated from the amplitude of the persistent component of ensemble-average currents (I_avg; Fig. 8 A). Importantly, the voltage dependence of the I_avg thus obtained (Fig. 8 B) was very similar to that typical of the whole-cell I_NaP (Magistretti et al., 1999a; Magistretti and Alonso, 1999). Moreover, the voltage dependence of P_o(b) measured in these patches closely paralleled that observed analyzing all of the available patches (compare Fig. 8 C with Fig. 3 C). n · P_b was thus calculated applying Eq. 3 at each test potential, then n · P_b values were normalized for the maximum value observed in each patch and averaged among patches. The plot of average, normalized n · P_b as a function of V_m (Fig. 8 D) clearly shows that this parameter was basically constant over the whole voltage range considered (-50 to 0 mV).

View larger version (29K): [in this window] [in a new window]   FIGURE 8. The probability of NaP channels to dwell in a "bursting state" is largely voltage-independent. (A) Measurement of INaP amplitude from ensemble-average currents (EACs). A1 shows exemplary traces recorded in response to 500-ms depolarizing pulses at -30 mV in a representative multichannel patch (patch C8703), A2 shows the trace obtained by averaging 20 such traces from the same patch. The horizontal bar marks the part of the trace the points of which were averaged to derive the amplitude of EAC's persistent component (Iavg). Calibration bars, 2 pA, 50 ms (A1); 1 pA (A2). (B) Plot of average Iavg amplitude, measured in EACs, as a function of membrane potential (n = 6). The continuous line is the best fitting to data point obtained applying the following function: Iavg = A/{1 + exp[(Vm – V1/2)/k]} · (Vm – VNa), were VNa is the average, extrapolated reversal potential of persistent Na+-channel openings as derived from the same six patches (54.5 mV). Fitting parameters are: V1/2 = -42.2 mV, k = -6.8 mV. (C) Values of intraburst opening probability (Po(b)) were derived from each of the same six patches as in B, averaged, and plotted as a function of membrane potential. The continuous line is the best Boltzmann fitting to data points. Fitting parameters are: A = 0.92, V1/2 = -42.0 mV, k = -6.6 mV. (D) Voltage dependence of average, normalized nPb (see text). nPb values were derived for the same six patches as in B and C.

As a further step, we analyzed the decay kinetics of whole-cell I_NaPs. We considered the decay phase of Na⁺ currents recorded in response to 500-ms depolarizing steps starting from 20–30 ms after the test pulse's onset, so as to exclude fast decay components due to the classical, fast Na⁺ current, I_NaT. At test potentials positive to -55 mV, I_NaP decay could be consistently fitted by second-order exponential functions (Fig. 10, A and B). In the same voltage region, the decay time constants (_ds) showed no apparent voltage dependence and fluctuated around values of 24 ms and 120 ms, respectively (Fig. 10 D). These values are not far from those found, in single-channel experiments, for the two major burst-duration time constants, which is in agreement with the hypothesis that I_{NaP d}s mainly reflect mean burst durations. Consistently with this view, in the same membrane-potential region the overall I_NaP decay kinetics appeared remarkably voltage independent (Fig. 10 C), a behavior that paralleled the relative voltage independence of single-channel mean burst durations (see Fig. 7 C). At test potentials negative to -50 mV, whole-cell I_NaPs appeared much more sustained and largely nondecaying (Fig. 10 A, top trace). A similar behavior was also observed in ensemble-average traces from single-channel recordings (not depicted, but see Fig. 6 A in Magistretti et al., 1999a). Given the difficulty to obtain reliable measures of various single-channel kinetic parameters (i.e., first latencies, interburst closed times) at such negative voltage levels, the exact single-channel bases of the latter phenomenon could not be elucidated.

View larger version (41K): [in this window] [in a new window]   FIGURE 10. INaP fast and intermediate decay time constants closely parallel burst-duration time constants characteristic of persistent Na+-channel openings. (A) Whole-cell Na+ currents recorded in response to 500-ms depolarizing pulses at four different test potentials in a representative neuron (cell 96315). The traces are shown to highlight the INaP component (part of the peak transient component at -40 to -5 mV has been blanked). The decay phases of the three lower traces (starting at 20–30 ms from the onset of the depolarizing test pulse) have been best fitted with a second order exponential function (smooth, blank lines). The time constants values returned by fittings are specified close to each trace. Calibration bars, 100 (-60 mV) or 200 (the remaining potentials) pA, 50 ms. (B) The two lower traces of A and the corresponding fitting functions are shown sign-inverted, subtracted of their offset components, and plotted on a logarithmic y axis to highlight the correspondence between second order exponential fitting functions and the experimental traces. Smooth, enhanced lines are the total fitting functions, dotted lines are the single exponential components shown separately. (C) Average INaP traces obtained from five cells for three different test potentials (-45 mV, black trace; -25 mV, blank trace; -5 mV, gray trace) are shown normalized in amplitude and superimposed to highlight the similarities in their decay kinetics. Current traces were subtracted of their offset components and normalized for the amplitude measured at 40 ms from the onset of the depolarizing test pulse (the parts preceding the above time point have been omitted). Same time scale as in A. (D) Voltage dependence of INaP "fast" and "intermediate" decay time constants (d1 and d2: filled and open circles, respectively) as obtained from the protocol illustrated in A and B (n = 5). Note the logarithmic scale of the y axis.

View larger version (40K): [in this window] [in a new window]   FIGURE 11. Prolonged depolarizations induce longer interburst closings and shorter burst openings. (A) Single-channel recordings obtained applying long-lasting (20-s) depolarizing pulses at -20 mV in a representative patch (same patch as in Fig. 7 A). A1 shows six selected 20-s current sweeps in their entire length. 5-s segments were extracted from either the initial (dashed-line box) or the final (dotted-line box) part of the same sweeps, and shown in A2 over an expanded time scale to highlight the different mean duration of burst openings. Calibration bars, 2 pA, 2 s (A1) or 490 ms (A2). (B) Scatter plot of burst duration versus time during the application of 20-s depolarizing pulses at -20 mV. Data are from the same patch illustrated in A. Burst durations were plotted as a function of the starting point of each burst. The vertical, dotted lines mark the limits between the regions in which the plot was subdivided, and from each of which data values were extracted and used to construct burst-duration histograms (see D1 and D2). (C) Time course of mean burst duration, , during long-lasting (20-s) depolarizing pulses at -20 mV. Data points are values derived from burst-duration histograms (see D1 and D2) constructed for the five regions in which the experimental traces were subdivided (see B). The continuous line is the best exponential fitting to data points. Fitting parameters are: A = 15.61 ms, = 4.01 s, C = 6.95 ms. (D) Frequency distributions of burst duration in early (D1) and late (D2) phases of 20-s depolarizing pulses at -20 mV. Each graph has been constructed pooling together data from five different patches. The data shown in D1 and D2 were collected from the first and the last, respectively, of the periods in which burst-duration time courses were subdivided (see B). Data were binned logarithmically and in the main panels are shown as log-linear plots. In the insets, the same data are shown as log-log histograms. In all panels, the smooth, continuous line is the best third- (D1) or second- (D2) order exponential fitting obtained applying Eq. 1 to log-log plots. Dotted lines are the single exponential components of fitting functions shown separately. Fitting parameters are: W0 = 274.08, b0 = 6.01 ms; W1 = 118.19, b1 = 25.79 ms; W2 = 26.57, b2 = 151.4 ms (D1); W0 = 612.28, b0 = 5.83 ms; W1 = 34.09, b1 = 29.26 ms (D2).

Further, our analysis of burst duration as a function of time revealed, in the histograms constructed for "late" openings, the predominance of a fast time constant (_b0, equal to 6 ms) (Fig. 11 D2) that was much less represented in the histograms constructed for "early" openings (Fig. 11 D1). Indeed, in the last 10 s of 20-s depolarizing pulses, the relative amplitude coefficient of this fast exponential component was 0.947, as compared with a value of 0.654 observed during the first second.⁴ These results demonstrate that prolonged depolarizations promote the transition of NaP channels to short-duration "bursting" state(s). Consistently with these findings, we noticed that standard, 500-ms depolarizing test pulses delivered from holding potentials positive to -80 mV, rather than the usual level of -100 mV, evoked a NaP-channel activity characterized by markedly shorter burst openings than normally observed (not depicted). Data obtained with such experiments in four patches at V_m = -20 mV were used to construct an overall burst-duration histogram, which revealed the appearance of a predominant fast time constant equal to 5.41 ms, and therefore similar to the above _b0.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
The present study provides a detailed analysis of the gating properties of the channels mainly responsible for persistent Na⁺-current (I_NaP) generation ("NaP channels") in EC layer II neurons. The achievement of this aim was hindered by the extreme difficulty to encounter patches showing the activity of single NaP channels in isolation, and hence to obtain reliable estimations of some specific single-channel parameters. This is not unexpected, since I_NaP is normally a tiny fraction (0.002–0.02) of total whole-cell, voltage-gated Na⁺ currents (Taylor, 1993; Crill, 1996). Nonetheless, our results allowed us to unveil and describe in detail several basic properties of NaP channels, including their bursting behavior, and, perhaps most significantly, to elucidate the single-channel bases of I_NaP voltage dependence and kinetic properties.

Voltage Dependence of Intraburst Open and Closed Times
First of all, our data show that, differently from intraburst closed times, intraburst open times are characterized by a very pronounced voltage dependence, with an e-fold increase of mean open time per every 12 mV of depolarization. This observation may have implications of some importance in clarifying the mechanistic processes involved in I_NaP generation. In single-channel studies on native neurons, persistent Na⁺ channel openings underlying the macroscopic I_NaP have been proposed to derive from a specific population of "persistent" Na⁺ channels (on the basis of conductance data: Magistretti et al., 1999a), or, alternatively, from the occasional, transient switch of otherwise typical, "fast" Na⁺ channels to a noninactivating gating modality ("modal gating": Alzheimer et al., 1993). Open times of classical, neuronal Na⁺ channels, however, are known to be largely voltage independent and uniformly short over a wide range of V_ms (Aldrich et al., 1983; Barres et al., 1989; Kirsch and Brown, 1989). In the latter hypothesis, therefore, it should be assumed that the inactivation process, rather than becoming transient and extremely short-lived, does not proceed at all. For instance, in a "ball-and-chain" model of the inactivation process (Armstrong et al., 1973; Bezanilla and Armstrong, 1977; Armstrong and Bezanilla, 1977), the lack of inactivation could be the consequence of a failure of the inactivating ball either to maintain the inactivated state (the ball does reach its binding site but does not "stick" onto it for long), or, alternatively, to induce it (the ball does not have any tendency to reach its binding site any more). Only the latter possibility is compatible with our single-channel data. A voltage-dependent behavior of open times similar to that we describe here was observed in long-lasting burst events that are occasionally produced in membrane patches from skeletal muscle fibers (Patlak and Ortiz, 1986), ventricular myocytes (Ju et al., 1994), and neocortical neurons (Alzheimer et al., 1993), and that have been attributed to modal gating of classical Na⁺ channels by Patlak and Ortiz (1986) and Alzheimer et al. (1993). Also in these cases, it was concluded that only a transient failure of the inactivation process is a mechanism compatible with the kinetic properties of such bursting events (Patlak and Ortiz, 1986; Alzheimer et al., 1993). Indeed, removal of Na⁺ channels' fast inactivation, obtained with proteolytic treatment, animal toxins, or organic gating modifiers, unveils a prominent voltage dependence of open times within burst openings (Horn et al., 1984; Kohlhardt et al., 1987; Quandt, 1987; Cukierman, 1991). Hence, it seems that, under the "modal gating" hypothesis, prolonged periods of "persistent" activity of individual channels (that we did observe in our recordings: see Magistretti et al., 1999a,b) would require significant functional modifications (and, therefore, probably also structural rearrangements) of the molecular components that govern the inactivation process within the same channels. Interestingly, expression in Xenopus oocytes of various brain or skeletal muscle Na⁺ channel subunits (Nav1.2A, Nav1.3, Nav1.4) in the absence of ß subunits produces I_Nas with abnormally slow decay kinetics (discussed by Chang et al., 1996; Makita et al., 1996; Goldin, 1999) resulting from an exaggerated Na⁺ channel bursting activity (Moorman et al., 1990; Zhou et al., 1991), the normal phenotype being recovered by coexpression with ß₁ subunits.

An additional consequence of our data is that the closings occurring within bursts are not compatible with transient, short forays to a "classical" inactivated state, but rather represent transitions to different, short-lived closed states. Our analysis identified at least two distinct closed states, as well as three open states, within bursts. Because all of the dwell-time histograms used for this analysis were constructed pooling together data from several different patches, in most of which more than one channel was active, the question could be raised whether individual channels can generate the three open states and the two closed states corresponding to the time constants observed, or, rather, distinct channel subsets are responsible for these different kinetic states. This issue will be the subject of a separate paper (unpublished data).

Properties of Bursts
Differently from intraburst open times, the duration of burst openings, as well as the probability of NaP channels to be in a "bursting" state, were found to be largely voltage independent in the range of membrane potentials we investigated. The frequency distribution of burst durations could be described by two relatively voltage-independent time constants (_b1 and _b2) of 28 and 190 ms, the faster of which was typically much more represented. Therefore, most bursts were of "medium" duration, whereas long-lasting burst events (underlying the slow time constant, _b2) were of less frequent observation. "Medium-duration" burst openings were encountered in the majority of sweeps in >80% of the patches examined. By contrast, in frog skeletal muscle (Patlak and Ortiz, 1986) and mammalian neocortical neurons (Alzheimer et al., 1993), late Na⁺-channel activity has been reported to consist in either brief reopenings ("background activity") or rarely occurring, long-lasting bursts that often exceeded the duration of the depolarizing pulses applied (500 ms). In our recordings, "long-duration" bursting activity was prevalent in a minority of patches, and in such cases it appeared remarkably persistent (see Magistretti et al., 1999a,b). This diversity of bursting behaviors encountered in EC neurons and its bases will be also described in more detail elsewhere (unpublished data).

Whatever the mechanisms underlying the above diversity in bursting activity, the prevalence of "medium"-duration bursts (or, after prolonged depolarizations, short-duration bursts; see below) over long-lasting bursts is likely to add to the relatively high conductance of NaP channels in determining the "noisy" nature of I_NaP (White et al., 1998; Agrawal et al., 2001). Indeed, for given values of steady current and channel conductance, discontinuous openings would generate higher levels of stochastic channel noise than sustained openings. In turn, membrane-potential fluctuations resulting from channel noise may have major impacts on neur