INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

The modulation of ion channel activity by neurotransmitters and hormones, either through a direct G-protein coupling or through a covalent modification resulting from the production of second messengers and activation of phosphorylation pathways, has been extensively documented in many excitable tissues (for reviews, see Nicoll et al., 1990; Catterall, 1992). Although such modulations have been mostly described for potassium and calcium currents, a growing number of reports have now pointed out that voltage-gated Na⁺ channels could be also subjected to modulation (for review see Caterall, 1992; Cukierman, 1996). Voltage-gated Na⁺ channels are responsible for the initiation and propagation of the action potential (Hille, 1992). Modulation of their activity is therefore expected to dramatically affect neuronal excitability through a modification of the threshold for generation of action potential, a reduction of action potential duration or an alteration in the frequency at which the cell is capable of generating these action potentials. Brain Na⁺ channels are phosphorylated by cyclic AMP-dependent protein kinase (PKA) and protein kinase C (PKC) in vitro and in intact neurons (Costa and Catterall, 1984; Costa et al., 1982; Rossie and Catterall, 1987; Catterall, 1992), and phosphorylation by either kinase results in channel activity inhibition (Numann et al., 1991; West et al., 1991; Gershon et al., 1992; Li et al., 1992; Smith and Goldin, 1992; Li et al. 1993; Hebert et al., 1994; Schiffmann et al., 1995; Smith and Goldin, 1997; Cantrell et al., 1997). For instance, in striatal neurons, stimulation of dopamine D₁ receptors inhibits voltage-gated Na⁺ currents (Surmeier et al., 1992; Schiffmann et al., 1995) through an increase in cAMP and the stimulation of PKA, and leads to a reduction in neuronal excitability by increasing the threshold for generation of action potentials (Schiffmann et al., 1995; Zhang et al., 1998). Na⁺ currents could be also regulated through additional pathways involving arachidonic acid (Fraser et al., 1993) or inhibition of protein phosphatase (Schiffmann et al., 1998). In some circumstances, activators of PKC (Godoy and Cukierman, 1994b) or activation of PKA (Li et al. 1993) may rather increase the Na⁺ current amplitude.

Peptides mapping had shown that four sites located in the cytoplasmic loop between domains I and II of the -subunit of the Na⁺ channel could be phosphorylated by PKA (Murphy et al., 1993). However, Smith and Goldin (1997) have recently demonstrated for the rat brain Na⁺ channel (RIIA), that the phosphorylation of one of these sites by PKA, the serine-573, is necessary and sufficient to reduce the Na⁺ current amplitude. Therefore, this suggests that only two functional states of the channel could be present in the cell following activation of PKA depending on whether the specific phosphorylation site is or is not phosphorylated.

The molecular mechanism leading to the PKA-induced reduction of whole-cell Na⁺ current amplitude is poorly understood. It has been repeatedly claimed that the gating dynamics of the channel was not modified in this condition (see, for instance, the recent review of Marban et al., 1998). This statement results from the observation that the phosphorylation of brain Na⁺ channels reduced the whole-cell current amplitude without significantly affecting the voltage dependence of the current-voltage relationship, the voltage dependence of the steady-state activation and inactivation, the kinetics of the time-dependent inactivation, and the kinetics of recovery from inactivation (Li et al., 1992; Schiffmann et al., 1995). This interpretation has been also reinforced by the very similar shapes of current traces corresponding to control and phosphorylated conditions. Such observations suggest that phosphorylated channels could not open upon depolarization, and thus, the effect of phosphorylation would consist of an apparent decrease of the channel population capable to open. However, the analysis of single channel data clearly indicated that phosphorylated channels may open with an unchanged conductance, but with a decreased open time fraction (Li et al., 1992), suggesting that one or several gating kinetics are affected in case of channel phosphorylation by PKA.

The gating kinetics of ion channels have been described by models that assume that channels exist in a number of discrete conformational states. Several studies have proposed models describing the gating mechanism of the Na⁺ channel (Armstrong, 1981; Aldrich et al., 1983; Horn and Vandenberg, 1984; Stimers et al., 1985; Patlak, 1991; Vandenberg and Bezanilla, 1991) and containing an open state and several closed and inactivated states. The decrease in open time fraction of PKA-phosphorylated channels can be due to alteration of different kinetic rate constants, alone or in combination. However, no study has fully addressed this question so far.

The aim of the present study was therefore to identify the putative modification(s) of the gating mechanism of Na⁺ channels in condition of phosphorylation by PKA, through the computer fitting of a molecular model to whole-cell Na⁺ currents.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Primary culture of striatal neurons

Three- to five-day-old Wistar pups (P3-P5) (Iffacredo, Brussels, Belgium) were aseptically decapitated and brains were placed in phosphate buffered saline containing 33 mM D-glucose. After the removal of the brains from the crania, the dorsal striata were dissected in cold phosphate buffered saline-glucose. The minced striata were pooled and gently triturated using fire-polished Pasteur pipettes. The resulting suspension was allowed to settle to remove cellular debris and the supernatant was again gently triturated. Cells were then plated on 35 mm petri dishes containing coverslips at a density ranging between 0.8 and 1 × 10⁶ cells per dish. Coverslips inside petri dishes had been previously coated with 1.5 µg/mL polyornithine, rinsed with sterile water and thereafter coated with 3 µg/mL laminin. The culture medium consisted of Eagle's minimal essential medium supplemented with sodium bicarbonate (2.2 g/L), L-glutamine (0.73 g/L), glucose (3.6 g/L), penicillin (100 U/mL), streptomycin (100 µg/mL) and 10% horse serum. Two days after plating, cytosine arabinoside (2 µM) was added to the medium to prevent non-neuronal proliferation. Cultures were maintained in a humid, 5% CO₂ atmosphere at 37°C and half of the medium was changed once a week. Culture medium and sera were obtained from Gibco; all other salts and drugs were purchased from the Sigma Chemical Company (St. Louis, MO).

Whole-cell voltage-clamp recording of the sodium current

Striatal neurons 6 to 15 days in vitro were recorded using the tight-seal whole-cell mode of the patch-clamp technique (Hamill et al., 1981) with a high-gain voltage-clamp amplifier (Visual-Patch 500, Bio-logic, Claix, France). For recording, the coverslip supporting the cultured neurons was fixed on the stage of an inverted Nikon Diaphot 200 microscope (Nikon, Namur, Belgium). Patch pipettes were fabricated from borosilicate capillary tubing (1.0 mm OD borosilicate tubing, GC100F-10, Clark Electrical Instruments, Reading, UK) and pulled on a P-2000 micropipette puller (Sutter Instrument Co., Novato, CA). They presented resistances of 2.5-8 M when filled with the patch pipette solution (see below). Junction potential between the electrode solution and the bath was adjusted to zero, and membrane potential values were not corrected with respect to this liquid junction potential. Series resistances and cell capacitances were compensated using the procedure described in the Visual Patch 500 manual.

Membrane currents were filtered using an inbuilt five-pole Bessel low-pass filter at 5 kHz of the Visual Patch 500, and each current trace was an average of two consecutive records elicited at 0.7 Hz.

Patch-clamp experiments were conducted at room temperature (21-24°C). To isolate the sodium current, the extracellular recording solution contained 50 mM NaCl, 100 mM tetraethylammonium chloride, 1 mM MgCl₂, 1 mM CaCl2, 1 mM CoCl₂, 5 mM CsCl₂, 10 mM D-glucose, and 10 mM HEPES adjusted to pH 7.3 and 295-330 mOsmol/L. The pipette solution contained 65 mM di(Tris)phosphate, 40 mM Tris-base, 5 mM CsCl, 11 mM EGTA, 1 mm CaCl₂, 1 mM MgCl₂, 0.4 mM Na₃GTP, 4 mM Na₂ATP, 0.2 mM cAMP, 20 mM phosphocreatine, 50 U/mL creatine phosphokinase, 0.1 mM leupeptin, 10 mM D-glucose, and 10 mM HEPES adjusted to pH 7.3 and 260-275 mOsmol/L. To reach the gigaseal cell-attached configuration, the tip of the pipette was back-filled with the intracellular solution without creatine phosphokinase, leupeptin, phosphocreatine in all experiments.

Depending on experimental protocols, the basic solutions were modified by addition of compounds and drugs. Forskolin and 1,9-dideoxy-forskolin (RBI, Natick, MA) dissolved in ethanol at 10 mM were added to the bath solution to give the adequate final concentration (50 µM). Bath solutions were exchanged using the Watson Marlow 205U pump (Watson Marlow, Leuven, Belgium).

Previous published data demonstrating the effects on Na⁺ current of PKA and phosphorylated DARPP-32, an inhibitor of protein phosphatase 1, as well as its inactive form, non-phosphorylated DARPP-32 (Schiffmann et al., 1995; Schiffmann et al., 1998) were also analyzed as described below.

Data analysis

Na⁺ current traces experimentally obtained (as shown, for instance, in Fig. 1 A) were analyzed by curve fitting (nonlinear regression based on Marquardt-Levenberg algorithm) using a model describing the gating mechanism of the Na+ channel, as follows. The model, defined by kinetic transitions between different channel states (closed, open, or inactivated), was mathematically described by a system of first order differential equations

(1)

where X_i was the fraction of channel population in state i, and k_ij was the first order kinetic constant characterizing the conversion of state i to state j. These differential equations were numerically integrated by using Runge-Kutta algorithm. Thus, this procedure gave the time course of the fraction of channel population in the open state, i.e., the open probability P_o(t). To fit the model to the experimental data, the measured Na⁺ current (I) had to be numerically transformed in open probability, using the theoretical relationship

(2)

where N and i referred to the total number of channels and to the current of a single open channel, respectively. Practically, the value of the scaling factor iN could not be determined, because N was unknown in our experiments. To circumvent this problem, we have referred to studies showing the voltage and time dependencies of the open probability (Patlak, 1991), and assumed that, at a chosen membrane potential, the maximal open probability with respect to time (P_o,max) corresponded to the peak amplitude of Na⁺ current (I_max). Thus, the normalization

(3)

with

(4)

was applied. For instance, the curve I(t) (Fig. 1 A) which was obtained using a depolarization step from 90 mV to 0 mV, was transformed in the curve P_o(t) (Fig. 1 B) using a P_o,max of 0.35 (Patlak, 1991). The kinetic parameters k_ij of the model were estimated by an iterative procedure searching for the set of parameter values generating the minimal deviation (least square fitting) between the experimental curve P_o(t) and the theoretical curve given by numerical integration of the differential equations.

View larger version (13K): [in this window] [in a new window]   FIGURE 1   The Na+ current of striatal neurons in primary culture. (A) In voltage-clamp and in conditions allowing the isolation of Na+ currents, depolarizing voltage step from a holding potential of 80 mV to a potential of 0 mV, evoked an inward current. (B) Open probability of the Na+ channel, corresponding to the normalized Na+ current for which the open probability peak is fixed at 0.35 (the scaling factor S, as defined in Eq. 4, is equal to 608 pA).

Statistical analysis

To compare the parameter estimates corresponding to the curves obtained in control and phosphorylation conditions, we used a two-tailed paired t-test and considered the difference significant if p < 0.05.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Gating mechanism modeling

Several studies have proposed models describing the gating mechanism of the Na⁺ channel (Armstrong, 1981; Aldrich et al., 1983; Horn and Vandenberg, 1984; Stimers et al., 1985; Patlak, 1991; Vandenberg and Bezanilla, 1991). Generally, these models contained several closed and inactivated states. Preliminary simulations indicated that our experimental data required the presence of at least three closed states, one open state, and two inactivated states. In fact, models with one or two closed states were not able to accommodate quantitatively the delayed activation of the channel causing the apparent lag in the current onset subsequent to depolarization; likewise, one inactivated state was not sufficient to account for the apparent existence of two kinetic components in the relaxation of Na⁺ current during the depolarization. This description was in general accordance with several proposed models based on the existence of three closed states (Vandenberg and Bezanilla, 1991) and two inactivated states (Patlak, 1991; Sarkar et al., 1995). Furthermore, it has been repeatedly suggested that the inactivation of a channel was not necessarily preceded by its opening (Bean, 1981; Horn et al., 1981; Vandenberg and Horn, 1984; Goldman 1995). The minimal model compatible with our data and in good agreement with the literature could be qualitatively described by

View larger version (11K): [in this window] [in a new window]   Model 1

Definition of an operational model

Preliminary analyses of the proposed minimal scheme revealed acute over-parametrization of this model, in the sense that several parameters were highly correlated when the fitting procedure was applied to the experimental data. A dependence was clearly observed among the different kinetic parameters of the activation pathway, and between the parameters of the two inactivation pathways. Therefore, to eliminate these parameter dependencies, we have simplified the model in several respects by introducing some constraints, as follows.

Simplification of the activation pathway

Characterization of the transition between closed and inactivated states

(5)

(6)

View larger version (17K): [in this window] [in a new window]   FIGURE 2   Characterization of the inactivation from closed states. (A) The experimental conditions were: holding potential = 90 mV; conditioning potential = 40 mV; test pulse potential = 0 mV. The different traces of Na+ current begin at the initiation of the conditioning pulse (t = 0), and correspond to increasing durations of the conditioning pulse. (B)Inactivation from closed states for three different conditioning potentials. () normalized peak of the average current during the test pulse; the lines represent the fitting of Eq. 5 to the points. (C, D) () Estimates of the kinetic parameters kC1I2 and kI2C1 for the three different potentials. The lines represent the fitting of Eq. 6 to the points.

View larger version (9K): [in this window] [in a new window]   Model 2

1

1

1

1

1

1

View larger version (12K): [in this window] [in a new window]   FIGURE 3   Fitting of Model 2 to the experimental data (scaling factor S = 3814 pA). Data record for a test pulses to 0 mV from a holding potential = 90 mV. The parameter estimates are kC1C2 = kC2C3 = kC3O = 8070 s1, kOC3 = 0.027 s1, kOI1 = 4411 s1, kI1O = 816 s1 kI1I2 = 819 s1, and kI2I1 = 44 s1.

Effect of forskolin-induced channel phosphorylation

In agreement with previous results describing the partial inhibitory effect of PKA on Na⁺ channel activity (Gershon et al., 1992; Li et al., 1992; Smith and Goldin, 1992; Li et al. 1993; Hebert et al., 1994; Schiffmann et al., 1995; Smith and Goldin, 1997, Cantrell et al., 1997), the addition of forskolin (50 µM) in the bath depressed by 18% (mean of 10 independent observations) the peak amplitude of Na⁺ current evoked by a 90 mV to 0 mV step depolarization (see representative curves in Figs. 4 A and 6 A). This effect was reversed upon wash-out and was statistically significant (p < 0.05) as compared to that of the inactive analog 1,9-dideoxy-forskolin (n = 5), which did not affect the Na⁺ current amplitude (Fig. 4 B).

View larger version (39K): [in this window] [in a new window]   FIGURE 4   Effect of forskolin and 1,9-dideoxy-forskolin on voltage-gated sodium current, and effect of forskolin on steady-state inactivation and activation curves. (A) Typical experimental traces obtained either in the presence of forskolin or in the presence of the inactive analogue 1,9-dideoxy-forskolin. Holding potential = 90 mV; test pulse potential = 0 mV. (B) Normalized peak Na+ (mean ± SE, n = 3 to 5) during a 6-min application of 1,9-dideoxy-forskolin and forskolin (solid bar). (C) Activation and steady-state inactivation curves (fitted by Boltzmann equation (Eqs. 8 and 9)) were obtained before () and after () application of forskolin (n = 3). (D) Scatter plots of Vh (potential at mid-point) and k (slope factor) values for individual neurons show that forskolin did not significantly modify (p > 0.05) either the steady-state inactivation [Vh (control) = 35.3 ± 0.3 mV; Vh (forskolin) = 33.5 ± 2.0 mV; k(control) = 4.6 ± 1.2; k(forskolin) = 4.5 ± 1.1) or activation (Vh (control) = 30.4 ± 2.0 mV; Vh (forskolin) = 28.8 ± 6.5 mV; k (control) = 6.2 ± 2.7; k (forskolin) = 4.6 ± 3.2].

The putative effect of forskolin on steady-state inactivation and activation curves was investigated. The activation curve was constructed from the current-voltage curves obtained by applying 15 ms depolarizing pulses from a holding potential of 90 mV by 10 mV steps. The activation curve was obtained using the equation

(7)

where E_rev is the extrapolated reversal potential from the current-voltage curve, and G is the macroscopic conductance. The calculated conductances were normalized, plotted as a function of the test potential (Fig. 4 C) and the curves were fitted by the Boltzmann equation,

(8)

where V is the test potential, V_h is the voltage at half maximal activation, and k is the slope factor. The application of forskolin did not significantly modify the voltage-dependent activation parameters (Fig. 4 D).

The voltage-dependent steady-state inactivation was analyzed using a two-pulse protocol. The potential was held during 30 ms, successively from 120 to +20 mV before application of a constant test pulse to 0 mV. The steady-state inactivation curve was determined by normalizing the peak amplitude of the sodium current during the test pulse as a function of the conditioning potential (Fig. 4 C). These curves were fitted by the Boltzmann equation,

(9)

where V is the conditioning potential, V_h is the voltage at half maximal inactivation, and k is the slope factor. The application of forskolin did not significantly modify the steady-state inactivation parameters (Fig. 4 D).

If channel phosphorylation exerted its effect through modulation of one or several transition kinetic parameters, the statistical comparison of the parameter estimates resulting from the fitting of the curves obtained with control and forskolin treated cells should be able to identify the state transition that was sensitive to phosphorylation. Before trying to fit the operational model to these curves, it was necessary to analyze the possible effect of phosphorylation on the inactivation of the closed channel.

Forskolin effect on the inactivation of the closed channel

View larger version (15K): [in this window] [in a new window]   FIGURE 5   Effect of phosphorylation on the inactivation from closed states. The experimental protocol is the same as in Fig. 2. (A) Holding potential = 90 mV; conditioning potential = 50 mV; test pulse potential = 0 mV. The peak of the average current during the test pulse is shown as a function of conditioning duration. Closed and open circles refer to control and forskolin treated cells, respectively. (B, C) Scatter plots of paired kC1I2 and kI2C1 values for individual neurons. Paired t-test indicates no significant difference between the two situations.

Characterization of forskolin effect on the gating mechanism

View larger version (34K): [in this window] [in a new window]   FIGURE 6   Analysis of experimental traces (out of nine) obtained in the absence () or in the presence () of forskolin. (A) Typical experimental traces showing forskolin-induced current reduction. Holding potential = 90 mV; test pulse potential = 0 mV. (B) Open probability time course was calculated using a scaling factor S = 3814 pA. (C) Effect of forskolin-induced phosphorylation on the kinetic parameters. Scatter plots of kC1C2, kC2C3, kC3O, kOC3, kOI1, kI1O, kI1I2, and kI2I1 values for nine individual neurons. Only kOI1 exhibits a significant increase due to the forskolin treatment.

Analysis of the effect of channel phosphorylation directly induced by PKA

To confirm the results obtained with forskolin-induced phosphorylation, previously recorded current traces (Schiffmann et al., 1995), for which the phosphorylation was induced by the PKA catalytic subunit diffusing from the patch-pipette, were revisited. It must be noted that, for these experimental results, we were not able to estimate the individual k_C1I2 parameters, because the required protocol (Aldrich and Stevens, 1983; Goldman, 1995) was not applied at the time the traces were recorded; therefore, we extrapolated a k_C1I2 value at the correct test potential from the averaged k_C1I2 estimates found with the forskolin-treated cells. Figure 7 shows the results obtained from 80 mV to 20 mV depolarization experiments. The analysis of a total of six records confirmed that only the k_OI1 parameter was significantly increased (p = 0.017).

View larger version (31K): [in this window] [in a new window]   FIGURE 7   Analysis of experimental traces obtained with () or without () the addition of the PKA catalytic unit. (A) Typical experimental traces (out of six) showing PKA-induced current reduction. Holding potential = 80 mV; test pulse potential = 20 mV. (B) Open probability time course was calculated using a scaling factor S = 4102 pA. (C) Effect of PKA-induced phosphorylation on the kinetic parameters. Scatter plots of kC1C2, kC2C3, kC3O, kOC3, kOI1, kI1O, kI1I2, and kI2I1 values for six individual neurons. Only kOI1 exhibits a significant increase due to the addition of PKA catalytic unit.

Analysis of the effect of the phosphatase inhibitor phospho-DARPP-32

The endogenous inhibitor of protein phosphatase 1, phosphorylated DARPP-32, has been demonstrated to reduce the Na⁺ current peak amplitude when loaded in neurons by diffusion from the patch pipette (Schiffmann et al., 1998). It has been proposed that this effect was mediated by an increase of the phosphorylation level of the Na⁺ channel. If this phosphorylation partially or totally involved the basal activity of PKA, one can expect that the addition of phospho-DARPP-32 might have an effect on the gating mechanism similar to the one obtained with the catalytic unit of the kinase A, i.e., an increase of k_OI1. To test this prediction, previously obtained current traces (Schiffmann et al., 1998) were analyzed (Fig. 8). It appeared that only the k_OI1 parameter was significantly changed in the presence of phospho-DARPP-32 (n = 3, p = 0.019), suggesting that in basal condition and in the case of phosphatase inhibition, PKA was the major active kinase. However, this effect was apparently less pronounced than when PKA was added, possibly because either phospho-DARPP-32 would lead to a lower phosphorylation level than added PKA, or other kinase(s) would also take a minor but significant part in the phosphorylation process. Fitting of current traces obtained at the beginning and the end of the recording (2-3 min and 8-10 min after reaching the whole-cell recording configuration, respectively) of nonphospho-DARPP-32-loaded neurons showed no significant change in the parameter estimates (data not shown).

View larger version (21K): [in this window] [in a new window]   FIGURE 8   Analysis of experimental traces obtained at the beginning () or the end () of recordings of phospho-DARPP-32 loaded neurons. (A) Open probability time course was calculated using a scaling factor S = 2661 pA. Holding potential = 80 mV; test pulse potential = 20 mV. (B) Effect of the addition of phospho-DARPP32 on the kinetic parameters. Scatter plots of kC1C2, kC2C3, kC3O, kOC3, kOI1, kI1O, kI1I2, and kI2I1 values for three individual neurons. Only kOI1 exhibits a significant increase due to the addition of phospho-DARPP-32.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

The inhibitory effect of PKA-induced phosphorylation of the Na⁺ channel has been widely documented (Gershon et al., 1992; Li et al., 1992; Smith and Goldin, 1992; Li et al. 1993; Hebert et al., 1994; Schiffmann et al., 1995; Smith and Goldin, 1997, Cantrell et al., 1997). Several potential sites of phosphorylation have been identified (Murphy et al., 1993). It now appears that the phosphorylation of only one of them is sufficient to induce channel inhibition (Smith and Goldin, 1997). The study of the inhibitory effect of PKA-induced phosphorylation of Na⁺ channels in excised membrane patches (Li et al., 1992) suggests that the reduction in Na⁺ current must be attributed primarily to reduction of the open probability. On one hand, null sweeps represent about 20% and 50% of the records before and after phosphorylation, respectively. On the other hand, the total channel open time during the stimulating pulse in responding sweeps significantly decreases by a factor of about 2.6 after phosphorylation (maximum likelihood fitting of the data taken from Fig. 2 C in Li et al., 1992). Thus, when the phosphorylated channel opening can be detected and measured, it is characterized by a lower half life as compared to the one observed in the control situation.

The results presented in our study, which assumes that the phosphorylated channel exhibits modified gating kinetics, indicate that the phosphorylation-induced decrease in whole-cell Na⁺ current is explained by a faster channel inactivation, leading thus to a lower mean open time as observed in single channel experiments. The minimal operational model used to demonstrate this point is compatible with the current knowledge on the gating mechanism of the Na⁺ channel. It considers two inactivating pathways: an inactivated state is formed either from a closed state, or from an open state. Direct observation presented in this work shows that channel phosphorylation would not modify the kinetics of inactivation from the closed state. On the contrary, the statistical analysis of the quantitative characterization by curve fitting suggests that, within the framework of this model, the O to I₁ transition is significantly faster when the channel is phosphorylated. No significant difference was detected with the other kinetic parameters. A typical figure of the factor by which k_OI1 is multiplied due to channel phosphorylation is 2. However, it has been proposed that, under control conditions, the Na⁺ channel population would not be completely unphosphorylated, because more channel activity was elicited when the phosphorylation level was decreased (Gershon et al., 1992; Li et al., 1992). Therefore, the given k_OI1 estimates would rather characterize average situations corresponding to different levels of phosphorylation.

It must be stressed that the increased number of null sweeps obtained with excised membrane patches after phosphorylation (Li et al., 1992) can be entirely accounted for by a decreased mean open time of the channel, without any change in the number of openable channels. Assuming a mean open time of 0.23 ms in the control condition and an effective minimal duration of detectable openings of 0.15 ms (see the characterization of the wild type channel in McPhee et al., 1995; Horn and Vandenberg, 1984), a simple calculation based on the exponential distribution of the open times indicates that 48% of the openings are not detectable, leading to 23% of null sweeps if there are two channels in the patch (as suggested in Fig. 1 in Li et al., 1992). A similar calculation shows that, if channel phosphorylation decreases the mean open time by a factor of two, 53% of null sweeps are generated with a 2-channel patch: these figures for the expected number of null sweeps satisfactorily account for the values reported by Li and co-workers (1992). These simple calculations based on realistic experimental characteristics demonstrate that it is not necessary to invoke a phosphorylation-induced decrease of the number of openable channels for explaining the increased number of null sweeps.

The operational model was simulated by using typical parameter values obtained in this work. The two curves corresponding to control and phosphorylation conditions, respectively, were generated with the same parameter values except k_OI1, which was multiplied by a factor of 2 (Fig. 9 A). The two curves exhibit very similar shapes, as if they only differ in first approximation by a simple scaling factor. A possible intuitive interpretation, as previously proposed in the literature, is that channel phosphorylation would deplete the population of channels capable to open upon depolarization through an inactivation from the closed state. Interestingly, this interpretation can be supported by the analysis of experimental curves on the basis of a minimal model of Hodgkin-Huxley (1952) type compatible with our data. Indeed, when the six pairs of curves obtained in the experiments using PKA were fitted by the HH model (referring to a third-order activation process and a biexponential inactivation process),

(10)

no systematic and significant modification was observed in parameters characterizing both activation and inactivation kinetics (Fig. 10). It would have been concluded, on the basis of such an analysis, that phosphorylation of the channel would not alter the gating mechanism of the channel. Thus, it appears now that such an empirical model is unable to detect that the inactivation of the open state is actually accelerated by the phosphorylating treatment.

View larger version (18K): [in this window] [in a new window]   FIGURE 9   Simulation of Model 2 using typical parameter values. (A) The control curve was obtained using the following parameter values: kC1C2 = kC2C3 = kC3O = 6977 s1, kOC3 = 6664 s1, kOI1 = 3349 s1, kI1O = 203 s1, kI1I2 = 389 s1, kI2I1 = 262 s1, and kC1I2 = 411 s1. The curve corresponding to the phosphorylation conditions was obtained with the same parameter values, except kOI1, which was multiplied by a factor of 2, leading to a 29% reduction in the peak amplitude. (B) Control curve as in A; the curve corresponding to the phosphorylation conditions was obtained with the same parameter values, except kCO (= kC1C2 = kC2C3 = kC3O) which was divided by 1.5 to produce the same 29% reduction in the peak amplitude. (C) Time course of net charge accumulation in the three conditions. The net charge Q was calculated by integrating the current I(t) with respect to time, after conversion of PO(t) into I(t) by using a scaling factor S = 4000 pA.

View larger version (19K): [in this window] [in a new window]   FIGURE 10   Analysis of experimental traces obtained at the beginning () or the end () of recordings of PKA catalytic unit loaded neurons, using the Hodgkin and Huxley model (Eq. 10). (A) Typical experimental traces (out of six pairs) showing PKA-induced current reduction. Holding potential = 80 mV; test pulse potential = 20 mV. (B) Effect of PKA-induced phosphorylation on the kinetic parameters. Scatter plots of Iss, tm, t1, t2, h1, and h2 values for six individual neurons. No parameter exhibits any significant change due to the addition of PKA catalytic unit treatment.

Although our study suggests that the phosphorylation of the channel would induce a significant acceleration of the inactivation from the open state, it is not able to demonstrate that the other transitions actually are unaffected. However, it is interesting to see how P_o, and thus, the current trace, would transform if the Na⁺ current attenuation induced by phosphorylation is due to a decrease of the activation rate. For that purpose, we simulated the model as in Fig. 9 A, except that the phosphorylation conditions were defined by a k_CO (= k_C1C2 = k_C2C3 = k_C3O) value divided by 1.5, leading to the same current value at the peak of the inhibited trace (Fig. 9 B). In agreement with other simulations (Godoy and Cukierman, 1994a), the decrease of k_CO has an obvious effect on the shape of the inhibited curve, which now intersects the control curve. This phenomenon results from the fact that the mean lag before channel opening is now increased by phosphorylation, but the mean open time remains unchanged. Thus, the mean net charge movement during an opening is also unchanged, though delayed, leading to a shift of the current trace to the right. This characteristic is clearly not compatible with the experimentally observed curves, suggesting that the phosphorylation-induced inhibition of the Na⁺ current cannot be explained by a decreased rate of channel activation.

Interestingly, if phosphorylation accelerates the inactivation from the open state, then the mean open time is decreased, as well as the mean net charge movement, contrary to the case in which the inhibition is due to a decreased rate of activation. The fact that the channel inhibition obeys one or another mechanism is not without physiological consequence, as shown in Fig. 9 C: for a same decrease of the peak amplitude, the cumulated amount of net charge going into the cell is drastically different depending on whether the inhibition is due to a decrease of k_CO or an increase of k_OI1. In the former case, the effect of the inhibition simply delays the rise of charge. In the latter case, corresponding to the actual situation, the net amount of charge passing through the channels markedly falls down at any time. These mechanisms would therefore result in subtle but important differences in the regulation of action-potential generation, duration, and frequency.

Two previous studies proposed, on the basis of fragmentary data, that the phosphorylation-induced inhibition of the Na⁺ channel does not involve any alteration of the mechanism of channel inactivation: on one hand, the inhibition apparently persisted in the presence of the batrachotoxin, which was known to block the inactivation process (Cukierman, 1996), and, on the other hand, the inhibition by phosphorylation was reported with a channel variant which did not exhibit inactivation (Smith and Goldin, 1997). In an attempt to reconcile our results with these observations, we could tentatively infer that, because the phosphorylation site recognized by the kinase A is situated in the I-II linker of the brain channel, different from the III-IV linker responsible for the classical channel inactivation, phosphorylation would induce the formation of an inactivated state different from the one which may be blocked either by the batrachotoxin or by the specific mutation. The proposed kinetic analysis developed in this study is certainly not capable of detecting the existence of a new inactivated state different from the classically described state. The observed increase of k_OI1 would simply reflect the acceleration of the global inactivation process.

Na⁺ channel has been demonstrated to be a substrate for PKC. The effects of phosphorylation by PKC are known to be different from those elicited by PKA because the voltage-dependence of the steady-state inactivation or the kinetics of the time-dependent inactivation were affected by PKC (Dascal and Lotan, 1991; Numann et al., 1991; West et al., 1991; Godoy and Cukierman, 1994a,b; O'Reilly et al., 1997). Godoy and Cukierman (1994a) have proposed that the PKC-induced phosphorylation of the channel accelerates the inactivation from the closed state. Our results suggest that this mechanism is not relevant in what concerns the effect of PKA phosphorylation. Indeed, after a conditioning potential pulse, the number of channels still susceptible to respond to depolarization appeared to be the same in the absence or in the presence of a phosphorylating treatment.

In brain, several neurotransmitters would be able to affect the activity of Na⁺ channels through a PKA-induced phosphorylation, which would lead to the presented proposed alteration in Na⁺ channel gating mechanism.