Sodium Curr 2006

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Cellular/Molecular

Sodium Currents Activate without a Hodgkin and Huxley-

Type Delay in Central Mammalian Neurons

GytisBaranauskas1 andMarcoMartina2,31Psychiatric Institute, University of Illinois at Chicago, Chicago, Illinois 60612 and 2Department of Physiology, Feinberg School of Medicine, and 3Institute

for Neuroscience, Northwestern University, Chicago, Illinois 60611

Hodgkin and Huxley established that sodium currents in the squid giant axons activate after a delay, which is explained by the model ofa channel with three identical independent gates that all have to open before the channel can pass current (the HH model). It is assumed

that this model canadequately describe thesodium current activation time coursein allmammalian central neurons, althoughthereis no

experimental evidence to support such a conjecture. We performed high temporal resolution studies of sodium currents gating in threetypesof central neurons.The results show that,within thetested voltage rangefrom55to35mV,inalloftheseneurons,theactivationtime course of the current could be fit, after a brief delay, with a monoexponential function. The duration of delay from the start of the

voltage command to the start of the extrapolated monoexponential fit was much smaller than predicted by the HH model. For example,in prefrontal cortex pyramidal neurons, at46 mV and 12C, the observed average delay was 140s versus the 740s predicted by the

two-gate HH model and the 1180 s predicted by the three-gate HH model. These results can be explained by a model with two closedstates and one open state. In this model, the transition between two closed states is approximately five times faster than the transition

between thesecond closedstate andthe open state.Thismodelcaptures allmajor properties of thesodium current activation.In addition,the proposed model reproduces the observed action potential shape more accurately than the traditional HH model.

Keywords:dentate gyrus; granule cell;pyramidalcell; hippocampus; prefrontalcortex;sodium channel; CA1;action potential; activation;kinetics

IntroductionThe classical description of sodium currents is based on the ex-periments performed on the squid giant axon. Hodgkin andHuxley (1952) showed that, in this preparation, sodium currentsactivate after a delay. Because a simple two-state model predicts amonoexponential time course of current activation without anydelay, they proposed a gating model with three identical, inde-pendent gates (the HH model). Accordingto this model,all of thegates have to open before the channel can pass current; thus, thetime required for the three gates to open is responsible for the de-lay between the voltage command and the beginning of the cur-rent flow. The resulting activation time course of sodium cur-

rents is best describedby the cube of an exponential function (them 3 function).

Subsequent studies in large peripheral axons confirmed thatsodium currents activate after a delay (Goldman and Schauf,1973; Keynes and Rojas, 1976; Neumcke et al., 1976; Neumckeand Stampfli, 1982). In all of these experiments, the time courseof sodium current activation was best fit with the mn function in

which n varied from 2 to 4, implying the presence of two to fourindependent identical gates. More complex models are requiredto fully explain all experimental data (French and Horn, 1983;Patlak, 1991), but, because of its simplicity, the mn function (withn equal to 2 4) is universally used to describe the activation timecourse of sodium currents in all neuronal compartments of allcentral neurons (Traub and Milles, 1991; Mainen et al., 1995;Martina and Jonas, 1997).

Surprisingly, there is no direct evidence that sodium currentsactivate after a delay in neurons of the mammalian CNS. Thelackof such data can be attributed in part to the insufficient speed ofthe voltage clamp attained during the whole-cell recordings fromthe soma of central neurons. Most recordings fail to obtain reli-able data in the first 0.2 ms after the start of voltage step (Mainenet al., 1995; Sherman et al., 1999), which is the expected delay atroom temperature (Mainen et al., 1995;Martinaand Jonas,1997)(see Appendix). Therefore, the delay is usually beyond the nor-mal time resolution of voltage-clamp recordings.

Here we report that, in the prefrontal cortex, neurons cooledto 1214C, current whole-cell techniques allow the determina-tion of the sodium current activation kinetics. The actual timeresolution of these voltage-clamp recordings was verified by tailcurrent analysis (see Fig. 1). Surprisingly, within the tested volt-age range (55 to35 mV), sodium currents activated without

the m

n

type delay (n

2). Because this finding contradicts thecurrent consensus about sodium current activation kinetics, weperformed nucleated patch recordings from two additional cen-

Received June 4, 2005; revised Nov. 28, 2005; accepted Nov. 29, 2005.

ThisworkwasinpartsupportedbyaUniversityofIllinoisatChicagoCampusResearchBoardSpring2003award

(G.B.) and an Epilepsy Foundation Award (M.M.). We thank Bruce Bean and Svirskis Gytis for helpful comments on

previous versions of this manuscript.

Correspondenceshouldbe addressedtoGytis Baranauskas athis presentaddress:Departmentof Electronicsand

Information, Politecnico di Milano, Via Golgi 34/5, 20133 Milano, Italy. E-mail: [email protected]:10.1523/JNEUROSCI.2283-05.2006

Copyright 2006 Society for Neuroscience 0270-6474/06/260671-14$15.00/0

The Journal of Neuroscience, January 11, 2006 26(2):671684 671


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tral neuronal types. In these cells, at room temperature, the mea-sured delay of sodium current activation was approximatelymore than twofold shorter than what is predicted by the m 2

function.We conclude that, in mammalian central neurons, sodium

currents activate without a Hodgkin and Huxley-type delay. Inaddition, we discuss the consequence of such results on the elec-

trophysiology of central neurons.

Materials andMethodsElectrophysiology. The data presented in this paper were obtained fromexperiments performed using three types of electrophysiological tech-niques: whole-cell recordings of dissociated prefrontal cortex neurons,whole-cell recordings from prefrontal cortex slices, and nucleated patchrecordings of granule cells of the dentate gyrus and CA1 pyramidal cells.

For prefrontal cortexelectrophysiologyexperiments, acutebrain sliceswere obtained from 4- to 7-week-old rats following a standard protocoldescribed previously (Baranauskas, 2004). All procedures were reviewedby the University of Illinois at Chicago Animal Care Committee and metthe requirements outlined in the National Institutes of Health Guide forthe Care and Use of Laboratory Animals. In brief, rats were anesthetized

with sodium pentobarbital (50 mg/kg) and decapitated. The brains wererapidly removed, and the frontal part of the forebrain was sliced into400-m-thick coronal slices (cut at a slightly oblique angle of30) inice-cold oxygenated solution consisting of the following (in mM): 100NaCl,2.5KCl,2 MgCl2, 15HEPES, 1 CaCl2, 1 N a2HPO4, 15glucose,and26 NaHCO3, pH 7.35 with NaOH (osmolarity, 295305 mOsm/L). Theslices were then placed in the same solution with added 3 m M sodiumpyruvate and 1 mM ascorbic acid and kept at 36C.

For current-clamp recordings in prefrontal cortex slices, the internalsolution consisted of the following (in mM): 90 K2SO4, 2 MgCl2, 30HEPES, 0.5 EGTA, and 5 Na2ATP, pH 7.2 with15 NaOH (osmolarity,260270 mOsm/L). Theexternalsolution wasthe same as theone used toprepare slices. All recordings in slices were performed at room tempera-ture (2224C).

Pyramidal neurons from the dorsal part of the prelimbic area (Groe-

newegen and Uylings, 2000) were selected according to their shape andthe presence of a long apical dendrite. Staining with Lucifer yellow con-firmed the presence of long apical dendrite, reaching the pial surface ofthe slice (n 4; data not shown).

For acutely dissociated cells, the internal solution consisted of thefollowing (in mM): 75 K2SO4, 2 MgCl2, 30 HEPES, 10 EGTA, and 5Na2ATP or 5 K2ATP, pH 7.2 with 15 NaOH (osmolarity, 260270mOsm/L). The external solution consisted of the following (in mM): 2BaCl2, 30HEPES,110 CsCl,0.1CdCl2, 10 NaCl, and20 tetraethylammo-nium (TEA)-Cl. Osmolarity was 300 310 mOsm/L, pH adjusted to 7.35with CsOH. Solutions were applied by a gravity-fed sewer pipe system.

Prefrontal cortex pyramidal neurons were visually identified as largepyramidal-shaped cells. In five cells, theneurontype was later confirmedby detection of calcium/calmodulin-dependent protein kinase II(CaMKII) mRNA and the absence of the 67 kDa isoform of glutamatedecarboxylase (GAD67) mRNA (see Fig. 1A and below, Single-cellRT-PCR).

Most of the recordings were performed at 1214C using the Dagan(Minneapolis, MN) TC100 temperature controller. The remaining ex-periments were performed at room temperature (2224C). Recordingswere obtained with a Dagan 3900 patch-clamp amplifier and controlledand monitored with personal computer running pClamp software (ver-sion 8.0) (Axon Instruments, Union City, CA). In working solution,electrode resistance was 1.53.0 M. Electrodes were coated with Semi-conductor Protective Coating (Dow Corning, Midland, MI). After sealrupture, series resistance (3.48.5 M) was compensated (5080%)and monitored periodically. A supercharge technique (Armstrong andChow, 1987) was used to minimize the time required for the membranecharging after the voltage step. This time was always 150 s for voltage

steps of30mV. A seriesof tests were used to verify thequality andspeedof the voltage clamp (see Fig. 1 and Results). Voltage-clamp recordingswere low-pass filtered at a cutoff frequency of 20 kHz using an eight-pole

filter. Current traces were leak subtracted using the following proce-dures. For tail currents, the sodium current was first inactivated by a 50

ms voltage step to36mV andthenfollowed by a tail current protocol asshown in Figure 1 B (without returning to 76 mV). For IVmeasure-

ments,leakcurrents were estimatedby steppingfrom85to80to55mV.

For nucleated patch recordings from dentate gyrus granule cells and

CA1 pyramidal cells, 16-to 18-d-old rats were anesthetized with isoflu-

rane and killed by decapitation in accordance with national and institu-tional guidelines. Transverse 300-m-thick hippocampal slices were cutusing a vibratome (Dosaka, Kyoto, Japan). Granule cells of the dentate

gyrus andCA1 pyramidal cells were identified visually by infrared differ-

ential interference contrast video microscopy (Stuart and Sakmann,1994) using an upright microscope (Zeiss, Oberkochen, Germany)

equipped with a 60 water immersion objective (Olympus Optical, To-kyo, Japan) and by their characteristic action potential pattern during

sustained current injection.Patch pipettes were pulled from borosilicate glass tubing (2 mm outer

diameter, 0.5 mm wall thickness; Hilgenberg, Malsfeld, Germany), fire

polished immediately before use, and coated with thin stripes ofParafilm. Neurons were approached under visual control while applying

positive pressure (20 40 mmHg) to the pipettes. The pipette resistance

(inworking solution) was25 M, andthe seriesresistance in thewhole-cell configuration ranged from 4 to 14 M. Only neurons with initial

membrane potentials negative to 60 mV were accepted for recording.To isolate nucleated patches (Martina and Jonas, 1997), negative pres-

sure(40100 mmHg) was applied, andthe pipette was withdrawn slowlyunder visual control. Nucleated patches had input resistance 2 G,

almost spherical shape, and diameter of 59 m. A light negative pres-sure (35 mmHg) was maintained during the recordings.

Currents were recorded using an Axopatch 200 B amplifier (AxonInstruments).Signals were filtered at 100kHz using thebuilt-in low-pass

filter.Capacitivetransientswere minimized by maintaining the bath levelas low as possible and further reduced by the capacitive compensation

circuit of theamplifier. A Digidata 1300 interface connectedto a personalcomputer was used for stimulus generation and data acquisition. The

sampling frequency was 200 kHz. Nucleated patches were held at 90mV, and a pulse to120 mVwas applied beforeeachtestpulse to obtain

complete recovery from fast inactivation.Potassium currents were blocked by internal cesium and calcium cur-

rent by external CdCl2 (50 M). During recording, slices were continu-ously superfused with physiological extracellular solution containing the

following (in mM): 125 NaCl, 25 NaHCO3, 2.5 KCl, 1.25 NaH2PO4, 1.2CaCl2, 1 MgCl2, and 25 glucose (bubbled with 95% O2 and 5% CO2).

Pipettes internal solution contained the following (in m M): 140 CsCl, 2MgCl2,10EGTA,2Na2 ATP,0.3GTP,and10 HEPES,pH adjusted to7.3

with KOH. In some experiments, 10 mM TEA was added to the externalsolution. Because no differences were noticed in thecurrentsat themem-

brane potential values tested, data were pooled. In five cells, the currentswere completely blocked by the application of 500 nM TTX-containing

solution, confirmingthatthe observedcurrents were mediated by thefast

TTX-sensitive sodium channels. Leakage and capacitive currents weresubtracted online using a P/5 protocol.

The liquid junction potential was measured according to the method

described by Neher (1992) and by calculating with the pClamp tool. Theliquid junction potential was 6 mV for acutely dissociated cells, 9 mV for

the recordings in slices, and 4 mV for nucleated patches. These valueswere subtracted from the command voltages off-line, and the corrected

values are used in this paper.All data analysis was performed with Igor Pro (WaveMetrics, Lake

Oswego, OR). All averaged data are represented as an average SEM.Traces in the figures were filtered digitally (520 kHz) and represent the

average of up to 20 sweeps. Permeability voltage dependence was ob-tained from the corrected peak currentvoltage relationship using the

GoldmanHodgkinKatz equation (Hille, 2001). Peak current ampli-

tude correction was performed by extrapolating the exponential part ofthe current decay to the start of the test voltage command. Inactivationvoltage dependence was measured with 500-ms-long conditioning steps.

672 J. Neurosci., January 11, 2006 26(2):671 684 Baranauskas and Martina Sodium Currents Activate without a Delay


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All drugs were obtained from Sigma (St. Louis, MO), except for tetro-dotoxin, which was obtained from Alomone Labs (Jerusalem, Israel).

Single-cell reverse transcription-PCR. The reverse transcription (RT)-PCR procedure and the primers used have been described previously(Tkatch et al., 1998; Vysokanov and Flores-Hernandez, 1998; Baranaus-kas, 2004).

Briefly, neurons were recorded in a whole-cell mode with a minimalvolume of internal solution (3 l; see above) and aspirated into the

electrode for GAD67 and CaMKII mRNA detection. The RT was per-formedusing the SUPERSCRIPTFirst-Strand Synthesis System(Invitro-gen, Carlsbad, CA). All RT-PCR runs included negative and positivecontrols. Contamination from extraneous sources was checked by per-forming the RT-PCR procedure in exactly the same way as describedabove, except that no pipette content was expelled into the RT tube. Thecontribution of genomic DNA was checked by omission of the RT reac-tion. None of these negative controls resulted in a band on the gel. Thecell-harvesting process was visually controlled, and cells were not used ifanyadditional debrisenteredthe pipette.Highlydiluted tissue cDNA wasused as a positive control for PCR reaction.

Computer simulations. We constructed a six-state sodium currentmodel (see Fig. 5A). The transition rates from the second closed state tothe open state (2 and 2) and the transition rates to the inactivatedstates (3 and 3) were obtained from the fits shown in Figures 3, A andB, and 4 B. It was assumed that all of these rates saturate except 3. Thefollowing functions describe the voltage dependence of these rate con-stants: 2 2.8 ((T 13)/10) 11/(0.4 exp((V 6)/12)); 2 2.8((T 13)/10) 0.035/(0.0015 exp((V 6)/12));3 2.4((T 13)/10)2/(2 exp((V 6)/12)); and 3 2.4 ((T 13)/10) 0.00005 exp((V 6)/13). Here T is temperature in degrees Celsius, and V ismembrane voltage in millivolts. The units of the rate constants aremilliseconds.

Thetransition from thefirst to thesecond closed state helps to accountfor the observed steep voltage dependence of the sodium current ampli-tude and the presence of very brief delay (0.2 ms at 12C; see Results).Therefore, 1 was adjusted to reproduce the current amplitudes ob-servedduring voltage-clamp recordings at less than40 mV while main-taining the slowest time constant of this transition0.2 ms. The follow-

ing rates were used in the model: 1 2.8((T 13)/10)

10 exp((V6)/45); and 1 2.8 ((T 13)/10) 0.35 exp((V 6)/8).

Because in this model, the kinetics of sodium current activation isprimarily determined by a single transition from the second closed stateto the open state, we will refer to this model as the m 1 sodium currentmodel. For comparison, a widely used HH model with three gates(Mainen et al.,1995) will be referred to as the m 3 sodium current model.

All computations were performed using the simulation programNEURON (Hines, 1993). The fully implicit backward Euler integrationmethod was used with a time step of 25 s.

Voltage-clamp traces were simulated in a patch configuration assum-ing an internal sodium concentration of 34 mM and external sodiumconcentration of 10 mM. Current-clamp simulations used a model ofpyramidal cell that is available with the demonstration files of the pro-gram. The soma size was reduced to 32 19 m 2. The obtained somasurface area (32 19 3.14 1909 m2) is close to the surface areaestimated from the average capacity of 14 pF (n 36) obtained duringrecordings in slices (assuming 0.75 F/cm2, 14 pF corresponds to 1867m 2). Sodium currents were calculated according to the GoldmanHodgkinKatz equation, whereas potassium and leak currents were de-scribed using a classical Ohm law. This approach is justified by the factthat other authors reported their data in the terms of conductancedensities.

Twotypesof modelswere tested. In thefirsttype of model,we assumedthat the sodium channel density in the axonal and somatic compart-ments were the same. In the second type of model, the sodium channeldensityin theaxonal compartment wasapproximately eight times higherthan in the soma (Safronov et al., 2000). In this case, we were able toreproduce an asymmetrical time course of the depolarization speed (see

Fig. 5 I,J). Both types of models were used for simulations with the m1

sodiumchannel model andthe m 3 sodiumchannel model.Thus,in total,the results of four current-clamp simulations are reported in this paper.

The following parameters were used duringsimulations incorporatingthe m 1 sodium current model.

In thecase of thefirst type of model,the axoniccompartment includedthe sodium current (permeability, 3.2 104 cm/s), a slow potassiumcurrent (18 mS/cm 2) (Korngreen and Sakmann, 2000) (model providedby Migliore et al., 2001), a delayed rectifier current (30 mS/cm 2) (Durst-ewitz et al., 2000), and the leak current (0.02 mS/cm 2). The somaticcompartment contained the sodium current (permeability, 3.2 104

cm/s), theslow potassium current(12 mS/cm2), a fast potassium current(1 mS/cm 2) (Korngreen and Sakmann 2000) (model provided byMigliore et al., 2001), and the leak current (0.02 mS/cm 2). In the somacompartment, the used sodium channel permeability was within therange of the observed permeability values in prefrontal cortex pyramidalneurons. During voltage-clamp experiments in acutely dissociated cell,on average, the observed sodium channel permeability was 2.5 0.2104 cm/s (n 8; range from 1.2 104 to 3.9 104 cm/s). Thispermeabilityvalue correspondsto the60 mS/cm2 conductance densitymeasured at50mV (assumingthe reversal potentialof57mV)thatis10 times higher than the one reported by several groups (Stuart andSakmann, 1994; Martina and Jonas, 1997). One possible explanation ofthis difference is the use of adult animals (6 weeks old) for the currentstudy as opposed to the 2-week-old rats used by other groups. Alterna-tively, in dissociated cells, channel density is higher than in nucleatedpatches or cell-attached patches because of technical differences.

All dendritic branches contained the leak conductance (0.025 mS/cm 2). In addition, the first 300 m of the apical dendrite containedsodium current (decreasing from 3.1 104 to 2.3 104 cm/s), slowpotassium current(decreasingfrom 12 to 8 mS/cm2), andfast potassiumcurrent (1 mS/cm2). It has been reported that, in cortical pyramidalneurons, the density of sodium and potassium channels slowly decreasesalong the apical dendrite (Huguenard et al., 1989; Stuart and Sakmann,1994; Korngreen and Sakmann, 2000). It has been assumed that similardistribution is valid for prefrontal cortex neurons. Dendritic sodiumcurrents helped to account for the observed amplitude of the actionpotential. The leak conductance value was adjusted so that a small cur-rent step (10 pA) would evoke membrane depolarization similar to theobserved depolarization in a real neuron.

The reversal potential of sodium current was set to 57 mV. The exter-nal potassium concentration was set to 3 mM and the internal potassiumconcentration was 180 mM, in agreement with the composition of solu-tions used for the slice recordings. The slow potassium current densitywas adjusted to obtain a spike width at 30 mV, similar to the oneexperimentally recorded in slices.

In the case of the second type of model, the axonic compartmentincluded the sodium current (19 104 cm/s), the slow potassiumcurrent (11 mS/cm2), the delayed rectifier current (80mS/cm2), and theleak current (0.02 mS/cm 2). The somatic compartment contained thesodium current (2.5 104 cm/s), the slow potassium current (11 mS/cm 2), the fast potassium current (0.5 mS/m2), and the leak current(0.02 mS/cm2). Current densities in dendrites were scaled in the samemanner as in the first model.

In the case of high axonalsodiumchannel density, theobservedactionpotential threshold could be obtained only after thesodiumcurrent half-activation voltage was shifted by 6 mV with respect to the data obtainedfrom the dissociated cells. This shift may be attributable to differences inthe phosphorylation state of the channels in dissociated cells comparedwithslices. Phosphorylation is known to affect thevoltage dependence ofsodium channels (Catterall, 2000). The second explanation can be asso-ciated with inaccurate description of potassium currents that were takenfromthe motor-cortex pyramidalneuron andmay notbe suitable for theprefrontal cortex neurons. Thus, the contribution of potassium currentto the setting of the spike threshold was not appropriate. Without thevoltage shift, the shape of action potential was very similar to the re-corded spike shape, with the only difference being the threshold of theaction potential.

The following parameters were used duringsimulations incorporating

the m3

sodium current model.In the case of the second type of model, all conductance densities were

the same as in the case of simulations with the m 1 model with the same

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sodium channel densityin theaxonal andsomatic compartments, exceptthat the sodium current permeability andthe conductance density of theslow potassium currents was increased by 10%. In these simulations, toobtain the observed threshold of the action potential, the voltage depen-dence of the sodium current was shifted by1 mV.

In the case of the second type of model, the axonic compartmentincluded the sodium current (2.4 104 cm/s), the slow potassiumcurrent (15 mS/cm 2), the delayed rectifier current (150 mS/cm 2), and

leak current (0.02 mS/cm2

). The somatic compartment contained thesodiumcurrent (permeability, 3.6104 cm/s),slow potassium current(15 mS/cm2), the fast potassium current (0.5 mS/cm 2), and a leak cur-rent (0.02 mS/cm 2). In both cases, the drop-off of dendritic sodium andslow potassium channel densities was qualitatively similar the one usedin the simulations with the m 1 sodium channel model. In these simula-tions, to obtainthe observed thresholdof theaction potential,the voltagedependence of the sodium current was shifted by 7 mV.

ResultsCurrents recorded at 12C had properties of typical fastsodium currentsElectrically compact neurons were obtained by acutedissociationof rat prefrontal cortex. Cells with pyramidal shape and a short(20 m) stump of the apical dendrite were selected for therecordings. In these neurons, the TTX-sensitive currents re-corded at 12C activated very rapidly (2 ms) and then decayedwith time constants ranging from 1 to 35 ms (Fig. 1A).Hence, the recorded current was similar to the fast TTX-sensitivesodium current described in prefrontal cortex pyramidal neu-rons (Maurice et al., 2001).

Because several types of neurons arefoundin thelayerV of therat frontal cortex (Kawaguchi, 1993), we used single-cell RT-PCRto characterize the cell type in a subset of the recorded neurons(n 5). In these neurons, cell identification was performed bytesting the presence of the CaMKII and GAD67 mRNAs. Asshown in Figure 1A (inset), all neurons were GAD67 negative but

positive for CaMKII, demonstrating that all of these neuronswere glutamatergic. All five neurons satisfied the below describedrequirements for the voltage-clamp speed and were used for thesodium current analysis.

Voltage-clamp quality was sufficient to determine theactivation time course of sodium currentsBecause the goal of these experiments was to establish the activa-tion kinetics of sodium currents, it was critical to verify the qual-ity of voltage clamp in our experimental conditions. To this aim,tail currents representing the deactivation kinetics were recorded(Fig. 1 B, C). At constant voltage, the time course of sodiumchan-nel closure can be usually fit with a monoexponential function

(Hodgkin and Huxley, 1952). Because the time constant of themonoexponential function is voltage sensitive, any loss of voltagecontrol will result in a non-monoexponential decay of the cur-rent. In addition, suboptimal voltage control will translate intounstable driving force for sodium ions, thus affecting the ampli-tude of the sodium current and additionally deteriorating themonoexponential time course of the current decay. The currenttime course matched very closely the monoexponential fit func-tion after 120 s from the start of the voltage step (Fig. 1 D).Hence, there is a reasonable voltage control of the current after120 s from the start of the voltage command for voltage stepsof30 mV.

An additional control for the speed and quality of the voltage

clamp can be made by plotting the peak amplitude of the tailcurrent against the voltage of the command step. In this case, thefraction of open channels at the beginning of the voltage com-

mand is the same for all test voltages, and the peak current am-plitude must be proportional to the driving force for sodiumions. Figure 1, E and F, shows that the sodium ion reversal poten-tial estimated from the tail currents was similar to the reversal

potential obtained from the peak current measurements in thesame cell. The value of the measured reversal potential for thesodium current was close to the calculated reversal potential of

Figure 1. The speed of voltage clamp in acutely dissociated prefrontal cortex neurons issufficientto investigate activationkineticsof sodiumcurrent at 12C.A, Anexample of currenttraces evoked by the voltage-clamp protocol shown above the traces. The inset shows a gelobtained after the RT-PCR analysis of the recorded neuron, and its current traces are shown inADand F. CaMKII mRNA but not GAD

67mRNA was detected in this neuron. B, The voltage-

clamp protocol shown above the traces was used to study the deactivation kinetics of sodiumcurrents(tailcurrents). Thedarkthicktracecorrespondsto the56 mVvoltage step, thedarkthintracecorrespondstothe46mV voltage step,and thelight thicktracecorrespondsto the

36 mV voltage step. C,ThesametracesofB areshownon anexpanded time scale.Notetheincreaseinthepeakamplitudeofthetailcurrentatmorehyperpolarizedmembranepotentials.The first100 s after the start of the test voltage step were blanked for clarity. D, A semi-logarithmic plot of the fast component of the traces shown in Cdemonstrates the monoexpo-nential decayof thetail currents starting100safterthestartofthevoltagestep.Theslowcomponent of the traces was subtracted as shown in Figure 2G. Dashed lines represent the

monoexponentialfits. E,Totalamplitudeof thetailcurrentmeasuredatthestartoftheteststep(120220 s after the start of the test pulse) plotted versus the voltage of the test step. Thethin line represents the GoldmanHodgkinKatz equation fit of the data points. The arrowpoints to the extrapolated reversal potential of the tail currents (30.5 mV). F, The reversal

potential of approximately30 mV was obtained by direct measurement. All traces are fromthesameneuronandwereobtainedbysubtractingthecurrentsobtainedinthepresenceof0.5M TTXfromthe control traces. Alltraces were digitally filtered forclarity(2 kHzforA, B, F; 10kHz for C, D). Traces inADare the averages of four sweeps.



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22 mV for the solutions used during these recordings (10 mMNa in the external solution and 25 mM of Na in the pipettesolution; see Materials and Methods).

Similar analysis indicated that an acceptable voltage-clampcontrol was achieved after 150 s in nine cells recorded at1214C (including five cells used for RT-PCR) and seven cellsrecorded at room temperature (2224C). Only these cells were

further analyzed.The time resolution of the currents (150 s) was sufficientto detect the delay of currents activation when theactivation timeconstants are0.5 ms (for details, see Appendix).

Sodium currents activate without themn type delay at 12C inprefrontal cortex neuronsFor traces obtained at 12C, a preliminary examination of thesodium current activation revealed no delay at less than40 mV(Fig. 2A). However, a more detailed examination of the timecourse of the sodium current activation can be performed by themathematical elimination of inactivation (Keynes and Rojas,1976). In this procedure, the current trace is treated as a multipleof two components: the raising phase or activation component1 exp(t/act)

n, where n 13, and the decaying phase orinactivationcomponent exp(t/inact). By dividing the currenttrace by the decaying component exp(t/inact), the raising phaseor activation component 1 exp(t/act) is revealed as a non-decaying trace (Fig. 2 D, inset) (for details, see Appendix). Hence,following this procedure, the time course of current raising phaseshould be determined solely by the function of exp(t/act).

It should be noted that, for such analysis, we assume thatmacroscopic inactivation time constants correspond to the mi-croscopic inactivation time constants and that inactivation andactivation processes are independent. Single-channel recordingshave shown that macroscopic inactivation rates may not corre-spond to the microscopic inactivation rates (Aldrich et al., 1983);

since then, the sodium channel inactivation process is usuallyassumed to be either voltage independent (Kuo and Bean, 1994)or little voltage dependent (Vandenberg and Bezanilla, 1991).The relevance of these models to the data presented here is dis-cussed in the section of the model selection for computer simu-lations. Nevertheless, computer simulations show that,in most ofthe cases, the mathematical procedure used in this study to re-move inactivation is suitable to reveal the kinetics of the step(s)controlling activation process. For instance, in the case of thesequential model closed state 7 open state 7 inactivatedstate in which the first transition is slow whereas the second isfast (Hille, 2001), this procedure will identify the second transi-tion time constant,the onethat determines theactivation kinetics

in this model. Moreover, for voltage steps to less than 40 mV,the correction is minimal and unlikely to introduce any artifacts.

Nevertheless, we realize that it is a purely mathematical pro-cedure, andcaution shouldbe used while applying theprocedure.Hence, we used a double-pulse protocol to detect possible pres-ence of a rapid inactivation that may interfere with the activationprocess (Hille, 2001). Figure 2C shows that there was a goodmatch between the current decay after a step to46 mV and theestimated inactivation time course measured with a protocolshown in Figure 2 B. Importantly, there is no additional rapiddecay phase during the first 2 ms after the start of the test com-mand. In both cases, the time course could be fit with a monoex-ponential function, and the obtained time constants differed by

30%. This difference may be attributable to the relatively briefduration of the test command (two to three times that of theinactivation time constant).

Figure 2. Sodium current activation can be fit with a monoexponential function at 12C. A,An example of the sodium current activation recorded from an acutely dissociated prefrontalcortexneuron.Currentswereevokedbythevoltage-clampprotocolshownabovethetraces. B,Voltage clamp protocol used to test the presence of a fast component of inactivation. Currentswere evoked by the protocol shown above the traces; the inactivation time course at46 mV

wasestimatedbymeasuringtheamplitudeofthepeakcurrentat 36mV.C,Therewasaclearoverlap between the inactivation time course obtained by the protocol shown in B and thedecay of sodium current evoked with a voltage step to 46 mV. No fast inactivation wasdetected during the first 25 ms. D, The inactivation of the current trace shown in Cwaseliminated mathematically by dividing the current trace by the following function: 28.8 pA134.5 pA exp(t/16.1 ms). The inset shows that this procedure converted the decayingcurrent to a nondecaying current. The main panel shows the same converted trace on an ex-panded time scale and after the subtraction of the trace from 1. The light line represents themonoexponential fit of the activation. Note the absence of any detectable delay. For details ofall procedures,see Appendix.E,AsemilogarithmicplotofthetracefromD.Themonoexponen-

tial fitis shown asa thickdashedline. Twosmooth linescorrespond to thequadrate(thin line)andthecube(thickline)ofanexponentialfunction. F,Tailcurrentevokedbythevoltage-clampprotocolshownabovethetraces.G,Asemilogarithmicplotofthetailcurrentshownin Frevealsthepresenceoftwodistinctcomponents.Theslowlydecayingcomponentwasfitwithamono-exponential functionwitha time constantof 18ms, whichis closeto theinactivationrateof thecurrent at46 mV (C). This slow component was subtracted from the original trace, and thesemilogarithmic plot of the fast component is shown in H. H, The monoexponential fit for

the fast component of the tail current (dark line) is shown as a light dashed line. Note that theobtainedrateoftailcurrentdecayissimilartotheactivationrateatthisvoltage(0.80vs0.85ms;E). For comparison, the activation current trace from Eis shown as a thin light line.



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The elimination of inactivation was performedby dividing thecurrent trace by the monoexponential fit function (see Appen-dix). The result is a nondecaying trace (Fig. 2 D, inset). The ab-sence of any significant deviation of the obtained current ampli-tude from 1 (except during the activation process for the first 23ms) confirms that the original current trace decayed as a mono-exponential function. The same observation was made for all

nine neurons that were analyzed using this method for voltagesbetween56 and40 mV. At membrane potentials above 40mV, a second slower component of inactivation could be de-tected. However, this second component comprised30% of thetotal current amplitudeand wasvery slow (inactivation time con-stants20 ms at 1214C). Therefore, during the analysis of thesodium current activation time course, the slower inactivationcomponent was included into the non-inactivating term of theexponential function used to eliminate inactivation (for details,see Appendix).

Figure 2 D shows that the current activation time course couldbe fit with a monoexponential function. Therefore, the currenttrace obtained in the semilogarithmic plot follows a straight line

(Fig. 2 E). This linear portion of the trace was used to determinethe activation time constant m. For comparison, the lines corre-sponding to the square and the cube of an exponential functionwith the same time constant m have been added to this plot (Fig.2 E) (for details, see Appendix). It is obvious that the activationtime course is very different from the square or the cube of anexponential function.

Thesame clear difference between them 2 and them 3 functionandthe actualcurrent traceswas observed in allnine neurons thatsatisfied the above described criteria for the quality of the voltageclamp at 1214C. In Figure 2 E, the duration of the delay can bemeasured as the time interval between the start of the voltagecommand and the time when the extrapolated monoexponential

fit function is equal to 1 (Fig. 2 E) (for details, see Appendix). Forcurrent traces obtained at the test voltage of46 mV (holdingpotential of66 or 76 mV), the average delay was 140 s(0.13 0.02 m, ranging between 0.02 m and 0.19 m,where m is the time constant of the monoexponential fit; n 9).Similar observations were made for test voltages between 56and36 mV. In this range of voltages and for holding potentialsof either 76 or 66 mV, the delay never exceeded 270 s andwas always0.3 m. Because the estimated membrane charg-ing time is100150s (Fig. 1), such brief delays may be causedat least in part by membrane charging. However, these data donot exclude the existence of a brief delay (see below) similar towhat reported for the Kv3 potassium currents (Lien and Jonas,2003).

For holding potentials of76 or 66 mV, it is possible thatthe delay in the activation of the sodium current is reduced be-cause, at such depolarized potentials, a large fraction of the gatesis already in the open position and therefore the sodium currentcan be generated much faster. However, for the test voltage stepsto36 mV, the delay was increased by100 s when a 500 msconditioning step to 116 mV instead of the step to 66 mVpreceded the test pulse (n 3) (for the protocol, see Fig. 4C).Such a small increase in the delay may be attributable to thelongertime required to charge themembrane after a large voltagestep. In any case, for the test voltage steps to 36 mV, the delay

after the

116 mV conditioning step never exceed 0.4m (n

3) and was significantly shorter than the m 2 function delay of the0.69 m (for the formula, see Appendix).

Most of the sodium current kinetic properties are consistentwith a single transition modelThe monoexponential activation time course suggests that a sin-gle transition controls the kinetics of sodium current activation.If this is the case, for a test step to a given voltage, activation anddeactivation time constant of the current should be the same. Totest this hypothesis, we analyzed the tail currents obtained with a

two-step protocol in the same cell (Fig. 2 F, G).Voltage steps to46 mV that were preceded by a condition-ing step to 36 mV evoked currents with a two-component de-cay(Fig.2F, G). We assumed that theslowly decaying componentrepresents the inactivation of the activated current, whereas therapidly decaying component represents the deactivation process(Oxford, 1981) (for an additional analysis, see below). As shownin Figure 2 H, the time constant of the monoexponential fit of therapidly decaying component was similar to the current activationtime constant (Fig. 2 E), and, consequently, the traces overlapafter normalization.

The close match of activation and deactivation time constantswas evident for all of the voltages investigated (Fig. 3A). Becauseof technical difficulties, only a limited range between 56 and31 mV could be tested. The same close match of activation anddeactivation time constants could be detected also at room tem-perature (Fig. 3B). The voltage dependence of the time constantsremained essentially unaltered at both temperatures: the fits usedfor the time constants obtained at 1214C could be used for thetime constants measured at 2224C after division of the fit func-tion by 2.8, a value close to the expected Q10 value (Hille, 2001).These results suggest that no unusual changes in the kinetics ofsodium channels occur between 1214C and 2224C. At roomtemperature, a direct test of the presence of the delay was lessaccurate because the first 100150 s of the recordings after thevoltage step were unreliable, and this time is comparable with thetime range obtained for the activation time constants (150400

s) (Fig. 3B) (but see below, section about nucleated patch re-cordings at room temperature in hippocampal CA1 pyramidalneurons and dentate gyrus granule cells). Nevertheless, at roomtemperature, in prefrontal cortex pyramidal neurons, there wasno indication that sodium currents activate after the mn (n 2)type delay.

In a two-state model, the voltage dependence of the currentamplitude is usually tied to the voltage dependence of transitionrates (Hille, 2001). In prefrontal cortex pyramidal neurons, theactivation and deactivation rates increased e-fold for each 12mV (this value tended to increase at membrane potentials below60 mV and above 10 mV). This voltage dependence of theactivation/deactivation rates predicts a value of 6 mV for the

slope factor of the activation voltage dependence, which matchesthe observed slope value (Fig. 3C). For this graph, it was assumedthat current decay represents inactivation process, and the totalcurrent amplitude was obtained by extrapolation of the decay ofthe current to the start of the voltage command (for details, seeMaterials and Methods).

However, it is possible that the actual microscopic time con-stants do not correspond to the macroscopic time constants (Al-drich et al., 1983; Hille, 2001). For sodium channels, it has beenproposed that inactivation process is voltage independent andthe apparent voltage dependence of inactivation rate constants isattributable to coupling with activation process (Aldrich et al.,1983; Kuo and Bean, 1994). The following experiments were

aimed to test whether a model with a single open state andvoltage-independent inactivation can account for the sodiumcurrents behavior in prefrontal cortex pyramidal neurons.



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First, we investigated the voltage dependence of the sodiumcurrent at below 35 mV. To this end, in the same neuron, wemeasured the peak current amplitude (Fig. 1A protocol) anddivided it by the instantaneous tail current amplitude (Fig. 1 Bprotocol) at the same voltage. If our assumption that the activa-tion process is much faster than the inactivation process is cor-rect, most of the channels are already activated at the peak of the

current. Hence, we should obtain relative permeability numbersthat should match closely the data obtained in Figure 3C. Atmembrane voltages above 51 mV, the obtained data (Fig. 3D,filled circles) showed similar voltage dependence to the graph inFigure 3C. Interestingly, at membrane voltages less than 51mV, the peak current amplitude seemed to exhibit stronger volt-age dependence than at more depolarized membrane potentials.

In addition, we measured the amplitude of the slow tail cur-rent component normalized to the instantaneous tail current am-plitude at the same voltages. If the fast tail current componentrepresents deactivation process and the slow component repre-sents inactivation process, the normalized slow current ampli-tude should have voltage dependence similar to the voltage de-pendence of the peak current. The obtained data (Fig. 3D, opencircles) show that both datasets have similar voltage dependence,although some differences could be detected. Notably, the datapoints corresponding to the slow tail current component weresomehow lower than the data points corresponding to the peakcurrent measurements. However, similar behavior could be ob-served in the computer model described below.

It is important to notice that voltage dependence of both mac-roscopic activation and deactivation rates had clear peaks (Fig.3A). Although it was difficult to show a peak of deactivation ratesin a single cell(Fig. 3E), activation rates were clearly the slowest atapproximately40 mV and started to accelerated at more hyper-polarized membrane potentials as well as at more depolarizedpotentials (Fig. 3F). All of these observations will be discussed in

the next section while justifying the proposed sodium channelmodel.

The action potential shape in prefrontal cortex neurons canbe faithfully reproduced with computer simulationsThe activation kinetics of sodium currents affects the shape ofaction potential (Moore and Cox, 1976; Sangrey et al., 2004).Therefore, the validity of the model in which a single transitiondetermines the sodium current activation kinetics can be testedby comparing the shape of action potentials recorded in the pre-frontal cortex neurons with the shape of the computer-generatedaction potentials. To this aim, we developed a computer modelthat reproducesthe obtained current traces during voltage-clamp

experiments. Before we discuss the model selection, we presenthere the data on sodium current inactivation that are necessaryfor a complete model (Fig. 4).

As shown in Figure 2, Cand D, at membrane voltages below40 mV, the current decay could be fit by a monoexponentialfunction with a non-inactivating component, whereas at poten-tials above 40 mV, an additional slower component was de-tected. This component, however, accounted for 30% of thetotal current. Similarly, the recovery from inactivation could beusually fit with a monoexponential function. Because we wereinterested only in the shape of the action potential, we made noattempt to include such a slow current component into themodel. Figure 4 B shows the summary of the inactivation and

recovery from inactivation time constants corresponding to thefast component of each process (Fig. 4A, B). These time constantspeaked at approximately65 to70 mV, which was close to the

Figure 3. Summary of thepropertiesof sodiumcurrentactivationin prefrontal cortexpyra-midalneurons.A, Time constantsof activation(crosses)and deactivation (circles)at 12Cplot-tedasa functionof thetest voltage.AlltimeconstantsweremeasuredasshowninFigure2.Thethin line represents the fit function of 1/(11/(0.4 exp((V 6)/12)) 0.035/(0.0015exp((V 6)/12))), where Vis the membrane voltage in millivolts. This function was used forcomputer simulations(for details, see Materials and Methods).B, Time constantsof activation

(circles)anddeactivation (crosses)at 23C areplottedas a functionof thetestvoltage. Thethinline represents the fit obtained by dividing the fit function for the 12C by 2.8. C, Peak perme-ability is plotted as a function o f voltage. Permeability was obtained from the corrected peakcurrentamplitudesusingtheGoldmanHodgkinKatzequation.Thecorrectionofpeakcurrentamplitudewasperformedbyextrapolatingtheexponentialpartofthecurrentdecaytothestartof thetestvoltage command. Thin line represents a Boltzmannfunction fitof theform1/(1

exp[(Vh

V)/Vc],where

Vis themembranepotential,

Vh isthehalfactivationvoltage,and

Vc

istheslopefactor.D, Slowlydecaying componentof tail current (Fig.2G,opencircles)andpeakcurrentamplitude(Fig.1A,filled circles)areplottedas afunctionofthetestvoltage.Alldataarepresented as a relative permeability that was calculated by dividing current amplitude by theinstantaneous total tail current amplitude (Fig. 1 B protocol) at the same voltage. Thereafter,

the attained values were normalized to the relative permeability calculated for36 mV. Theamplitude of the slowly decaying component was obtained as shown in Figure 2, GandH. Thestraight linerepresentsthe monoexponentialfit to therelative permeabilityvalues of the slowtailcurrent component.Peak currents weremeasured duringvoltage-clampprotocol showninFigure1A. E, Deactivation timeconstants saturateat approximately36mV.Thefastcompo-nent of tail currents was obtained after peeling of the slow component as it is shown in Figure2 EH. The voltage-clamp protocol was the same as in Figures 1 B and 2G, except that theconditioning step was to26 mV. To facilitate deactivation rate comparison, tail current am-plitudesweresetto 1 atthebeginningof thetestvoltagecommand(100saftertheendoftheconditioning step). The first 100 s after the conditioning step to 26 mV are blanked for

clarity. F, There is an increase in the sodium current activation rates below41 mV. Currentswere evoked by the voltage-clamp protocol shown at the top. To facilitate activation ratecomparison, the amplitude of all currents was set to1 at the peak of the current.



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half-inactivation voltage (Fig. 4C,D). These results indicate that asingle transition between two states is sufficient to describe theinactivation/deinactivation process.

Based on these results, a six-state model was constructed (Fig.5A). Because a complete sodiumchannel model was notour goal,we selected the simplest model that could reproduce all key ob-servations reported here. First, at the same voltage, macroscopic

activation and deactivation rates were similar (Figs. 2 H, 3A).Second, there was a clear peak of activation rate voltage depen-dence (Fig. 3A, F) and good evidence that deactivation rates hada similar peak (Fig. 3A, E). Third, the total area under the currentnormalized to the driving force for the sodium ions decreases forvoltages more than 20 mV (data not shown) that contradictsthe predictions of a tight coupling between activation and inac-tivation (Bean,1981). Moreover, computer simulations (datanotshown) suggest that one open-state and multiple closed-statemodels with voltage independent inactivation (Kuo and Bean,1994) are unlikely to explain why, for membrane potentialchange from 41 to 51 mV, the macroscopic activation timeconstant decreased (Fig. 3F), whereas the macroscopic inactiva-tion time constants increased (Fig. 4 B). More sophisticatedschemes with several open states (Vandenberg and Bezanilla,1991) or a modified and more complex version of the Kuo andBean model (Kuo and Bean, 1994) could explain the observedcurrent behavior; however, we opted for a simpler scheme inwhich the parameters were more easily related to the observeddata.

In our model, the inactivation and activation processes areindependent, as it was proposed in the original Hodgkin andHuxley model. We did not use another alternative model that isthe one with slow activation and fast voltage-dependent inactiva-tion rates (Hille, 2001). Such a model can well reproduce most ofthe data presented here (Figs. 13). However, we did not see whyit should be preferred over an easily interpretable model pre-

sented here.In our model, the activation process was simulated by a two-

step process. There were several reasons for the addition of asecondclosed state.First, there was the5mV difference between the half-activationvoltage and the voltage at which activa-tion/deactivation time constants reachedtheir peak values (Fig. 3, compare A, C).Second, at membrane voltages below60mV, 12 mV corresponded to the e-foldchange in the deactivation time constant(Fig. 3A). Meanwhile, at membrane po-tentials below50 mV,the voltage depen-

dence of the current amplitude becamesteeper (Fig. 3D). This steeper voltage de-pendence was consistent with the low ac-tion potential threshold (Fig. 5D).Thead-dition of a fast voltage-dependenttransition between the two closed stateswas sufficient to account forboth observa-tions, although it could not explain allcomplex voltage dependence of the so-dium currents in prefrontal cortex pyra-midal neurons (for comparison, seebelow).

Finally, there was short delay (100

s) of the sodium current activation; im-perfect voltage-clamp might account forthis delay, but it is also possible that it was

Figure4. Inactivationpropertiesofsodiumcurrentsinprefrontalcortexpyramidalneurons.A, Current tracesevoked bythe voltage protocol used todeterminetherecovery from inactiva-tion time constants. The protocol is shown above the traces. B, Time constants of inactivationand recovery from inactivation plotted as a function of the amplitude of the conditioning volt-

agestep.Inactivationratesweremeasuredbyfittingthecurrentdecaywiththemonoexponen-tial or biexponentialfunction. Thebiexponential fitwas required only forvoltagesabove40mV.Inthesecases,thedominantfastcomponentwasusedfortheplot.Thethinlineforthedatapoints at 12C represents the fit function of 1/(2/(2 exp((V 6)/12)) 0.00005exp((V 6)/13)), where Vis the membrane potential in millivolts. The fit function for thedata points at 23C was obtained by dividing the fit function at 12C by 2.4. The parameters ofthefitfunctionwereusedforthecomputersimulations(fordetails,seeMaterialsandMethods).C, Currents evoked by the voltage-clamp protocol shown above the traces. The conditioningstep duration was500 ms.D, Amplitudeof thecurrentat36mVplottedasafunctionoftheconditioning step voltage. The thin line represents a Boltzmann function fit.

3

Figure5. Atwo-stepactivationmodelaccuratelyreproducesthesodiumcurrentbehaviorandtheshapeofactionpotentialsinprefrontalcortexpyramidalneurons.A,Statesandtransitionsschemeusedforthecomputersimulationsofthesodiumcurrent.C1

and C2 representthe closed states; I1I3representthe inactivated states; O representsthe openstate. For functionsdeterminingthe individual rates, see Materials and Methods. B, Simulated currents evoked by a voltage-clamp protocol shown above thetraces. Theinset showsthe startof theactivationof thesimulated(darklines) andrecorded(lightlines) currentsfor twovoltages(46 and41 mV). The dashed line represents the simulated current responseto the41 mV voltagestep obtained withthem

3 modelof Mainenetal. (1995). Thepeakcurrentamplitudewas normalized tothepeak current amplitudeof themodel showninA. Alltracescorrespond tothe 12C.C, Simulatedcurrents wereevoked by thevoltage-clamp protocol shownabove thetraces.D,Inthemodel,activation(graycircles)anddeactivation(graytriangles)ratesaresimilaratthesamevoltage.Crossescorrespondtoexperimentaldatafrom Figure3A. Linerepresentsdeactivationrates of them 3 model (13 of the timeconstantcorrespondingto the transition from the closed to the open state in the HH model). E, Activation voltage dependence obtained for simulatedcurrents.Dark thinline representsa Boltzmannfunctionfit. Lightthick linecorresponds to theexperimental datashown in Figure

3C. F, In the model, the voltage dependence of the tail current slow component amplitude (open circles) and the peak currentamplitude(filleddarkcircles)aresimilar.Experimentaldataofpeakcurrentamplitudeareshownasgrayfilledcircles.Alldataarepresentedasrelativepermeabilityobtainedbydividingcurrentamplitudesbytheinstantaneoustotaltailcurrentamplitudeatthestart of the test pulse at the same voltage. Thereafter, the attained values were normalized to the relative permeability valueobtained at26 mV. G, H, The simulated with the m 1 sodium channel model action potential (light thick line) is very similar inshape to the action potential recorded experimentally (thin dark line). In G, sodium channels density is the same in soma andaxons.InH,sodiumchannelsdensityisapproximatelyeighttimeshigherinaxonscomparedwithsoma.Forcurrentdensitiesusedduringsimulations,seeMaterialsandMethods.Forcomparison,anactionpotentialsimulatedwiththem 3modelisshown(dottedline).Noteasmoothertransitiontospikeinthismodel. I,J,Themembranepotentialdepolarizationspeedisreproducedwellinthemodelwith thehigher sodiumchanneldensityin axons.In I, sodiumchanneldensityis thesamein soma andaxons.In J,sodium

channel density isapproximately eighttimeshigherin axons compared with soma.Tracenotationis thesameas inGandH.Noteclearlyasymmetricaltimecourseofthedepolarizationspeedintherecordedspikeandinthemodelswithhigheraxonalchannelsdensity.



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not an experimental artifact (see below)(Lien and Jonas, 2003). Therefore, thepeak value of the time constants corre-sponding to the transition between twoclosed states was set to be 100 s.

Our model reproduces well both thevoltage dependence and kinetics of the so-

dium currents recorded from prefrontalcortex pyramidal neurons (Fig. 5 B, C).The inset of Figure 5B demonstrates thatthe time course of sodium current activa-tion matched well the time course of thesimulated currents. In contrast, at 41mV, the amplitude of the current simu-lated with the m 3 kinetics model [HHmodel (Mainen et al., 1995)] was approx-imately threefold smaller during the first0.5 ms after the start of the voltage step(Fig. 5B, inset), despite the fact that thereis only 30% difference between the timeconstant of the m3 model and the timeconstant of the model presented here.

Forasingletrace,itispossibletoobtaina much betterfit with theHH model;how-ever, in this model, there is a problem offitting currents at allvoltagesbecause volt-age dependence of activation and deacti-vation rates is tied to the voltage depen-dence of the amplitude of the current.According to the m 3 model, the voltagedependence of the amplitude of the cur-rent will be 3 2 times steeper than thevoltage dependence of activation and de-activation rates because of the presence of

the m 3 variable. Because the observedvoltage dependence of activation and de-activation rates is approximately twotimes less steep than the observed voltagedependence of the amplitude of the cur-rent (Fig. 3A, C), it is impossible to obtaina satisfactory match of the data reportedhere with the m 3 kinetics HH model. Inaddition, the m 3 kinetics HH model can-notexplain thesimilarity of activation anddeactivation rates at the same voltage. Forall of these reasons, we used the m3 kinet-ics model that was used by several groups

without any change in the parameters ofthe models.

As shown in Figure 5C, all essential in-activation features are reproduced by themodel. Although the simulated currentsdo not contain the more slowly decayingcomponent detected in the recorded cur-rents at potentials above 41 mV (com-pare Figs. 1A, 5B), this slower componentcould be added by extendingour model,asit has been done for the classical Hodgkinand Huxley model.

One of the key observations reported

here is the similarity of activation and de-activation rates at the same voltage overrelatively wide range of voltages (from



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46to31mV)(Fig.3A). Hence, it is crucial that our proposedmodel can reproduce this phenomenon as shown in Figure 5 D.Meanwhile, in the model, the same middle point of the voltagedependence of the current amplitude was attained, althoughthere was a large difference in the slope values between the modelandthe experimentaldata (3.7 vs 6.4mV) (Fig. 5E).Inourmodel,the increased shift of the half-activation voltage resulted in the

decrease of the slope factor. We selected to match the half-activation voltage while ignoring the slope factor of the Boltz-mann function fit. Such choice was dictated by the observationthat,for membrane voltages below40mV,therewasquitegoodcorrespondence between this model and the experimental data(Fig. 5F). In any case, these discrepancies between the model andthe experimental data indicate that our model is an oversimplifi-cation of the real channel behavior that is not entirelyunexpected.

Finally, we tested the models ability to reproduce the shape ofaction potential. Because the actual sodium channel density inaxons is still a matter of debate (Mainen et al., 1995; Safronov etal., 2000), we tested two channel distributions during simula-tions. First, we assumed that the sodium channel density is thesame in the axon and the soma. Under these conditions, a fairlygood reproduction of spike shape could be obtained with ourmodel, assuming a sodium channel density within the range ofthe experimentally observed values. For instance, the observedaverage sodium channel permeability was 2.5 104 cm/s(rang-ing from 1.8 104 to 3.9 104), whereas for this simulation,a 3.2 104 value was used (Fig. 5G,I). The main differencebetween the recorded and the simulated voltage traces is asmoother onset of the spike in the trace of the model (Fig. 5 G,inset). In the case of the m3 HH model, the simulated spike onsetwas even slower, although the sodium channel permeability wassimilar (Fig. 5G) (for the parameters of the model, see Materialsand Methods). The steep rising phase of the action potential is

attained in the model with approximately eight times higher so-dium channel density in the axonal compartment compared withthe soma (Fig. 5H, light thick trace). Interestingly, the simula-tions incorporating the m 3 sodium channel model showed littleimprovement in the steepness of the rising phase (Fig. 5H, dottedtrace). This result suggests that our model is more sensitive tolocal changes in the channels density, probably because of themuch faster activation kinetics.

Detailed information on the action potential shape can beobtained by examining the time course of the membrane poten-tial depolarization speed. As shown in Figure 5I,inthecaseofthesame sodium channel density in the soma and the axon, simula-tions with our model overestimated the maximal depolarization

speed, whereas simulations with the m3

sodium channel modelunderestimated the maximal depolarization speed (Fig. 5F). Inaddition, both simulations failed to reproduce the asymmetricalprofile of the experimentally observed time course of the depo-larization speed: the rise to the maximum was slow, whereas thesubsequent drop was much faster. However, in the case of highsodium channel density in the axonal compartment, simulationswith our model were able to closely reproduce both the timecourse and the amplitude of the depolarization speed (Fig. 5F,thick light trace), whereas simulation with the m3 sodium chan-nel model underestimated approximately two times the peak de-polarization speeds. In addition, the initial rising phase of thedepolarization speed was very slow compared with the experi-

mental data.Hence, the presented model is sufficient to reproduce accu-rately most of the properties of sodium currents and the shape of

the action potentials recorded in prefrontal cortex pyramidalneurons. In contrast, the shape of action potentials generated bythe model incorporating sodium currents with the m3 kineticsdiffered from the shape of the experimentally recorded actionpotential (Fig. 5GJ). In particular, the time course of depolar-ization speed could be matched only with simulations incorpo-rating our model. We conclude that the presented model can

reproduce the observed shape of action potential more faithfullythan the traditional Hodgkin and Huxley model.

Sodium current activates with minimal delay in hippocampalCA1 pyramidal neurons and dentate gyrus granule cellsThe described lack of the Hodgkin and Huxley-type delay in thesodium current activation in the prefrontal cortex pyramidalneurons is at odds with the current prevailing view that most, ifnot all, fast sodium currents activate after the Hodgkin andHuxley-type delay. Therefore, to test whether the sodiumcurrentactivation time course in prefrontal cortex pyramidal neuronswas unique to this cell type or common to other mammalianbrain neurons, we recorded sodiumcurrents from twoadditionaltypes of CNS neurons. We selected hippocampal CA1 pyramidalneurons and dentate gyrus granule cells because they are two wellstudied and distinct neuron types.

These experiments were performed using the nucleated patchconfiguration, which provides, probably, the best voltage-clampconditions (Martina and Jonas, 1997).

In addition, the use of a different experimental approach gaveus the opportunity to test whether the observed properties ofsodium current activation in the prefrontal cortex neurons wereassociated with the acute dissociation procedure, which involvesprotease treatment, the age of animals (4 weeks for acutelydissociated neurons vs 1618 d for nucleated patch recordings),the type of used voltage compensation (hypercharge in acutelydissociated cells vs traditional exponential charging), or the spe-

cific solution composition used to record sodium currents (fordetails, see Materials and Methods). Finally, the 124 mV pre-pulse was used during nucleated patch recordings to boost therecorded current amplitude. At 120 mV, we expected all so-dium channels to be closed, preventing any possible complica-tions associated with the relatively depolarized holding potentialused in the previous experiments.

All experiments on nucleated patches were performed atroom temperature (2123C).

Despite the above-mentioned differences in the experimentaldetails, the properties of the sodium current activation in thehippocampal CA1 pyramidal neurons and dentate gyrus granulecells were qualitatively the same as in the prefrontal cortex pyra-

midal neurons. Figure 6A shows a typical set of traces obtainedfrom an hippocampal CA1 neuron. Looking at the expandedtime scale tracesshown in theFigure 6 B, at first glance, onemighthave the impression that sodium currents activate after a rela-tively long delay. However, because of the extreme speed of thesodium current activation, first we need to establish experimen-tally how quickly the voltage clamp was established after the volt-age step.

Most commercial amplifiers, including the Axopatch 200Bused for these experiments, in addition to the devices that speedup membrane charging at the beginning of the voltage command(active compensation according to the Axopatch 200B man-ual), have a circuitry that subtracts from the recorded trace the

membrane charging transient current (passive compensation).Hence, the absence of any charging current in the traces does notmean that the membrane charging process has been completed



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and the applied voltage is sensed by the membrane. Because weapplied test voltages of64 to44 mV from the holding poten-tial of124 mV,a 20%reduction in thevoltage command wouldresult in a voltage difference of10 mV. Figure 6A shows that,for the command step from124 to44 mV, no current wouldbe detected if the membrane sensed only 80% of the 80 mVvoltage difference, which translates into a membrane potential of

44mV 0.2 80mV60mV. Therefore, we need toknowthe time required to achieve80% of the voltage command stepamplitude on the cell membrane. This time can be estimatedfrom the tail currents by identifying the time point at which thecurrent trace deviates 20% from the monoexponentialfunction.

The amplitude of the voltage steps used to evoke tail currentswassimilar to theamplitude of thevoltage steps used forthe delaymeasurements (Fig. 6A, B). Figure 6 D shows tail current traceson an expanded semilogarithmic scale. It is clear that30s wasrequired to charge the membrane, because no tail currents weredetectable during the first 30 s. The arrow indicates the timepoint corresponding to the average membrane charging duration

that was sufficient to ensurethat thedeviation of thecurrent tracefrom the monoexponential time course was 20%. This timepoint was35s after the onset of the voltage step command. Inthis recording, the estimatedseries resistance was 10 M,andthepatch capacitance that corresponds to the patch area of70m2

was 1 pF. Hence, for uncompensated series resistance, the calcu-lated time constant would be 10 s. This estimate shows thatother factors, such as digital filter time constant (10softhe20kHz low-pass filter), command lag (5 s), compensation cir-cuitry lag (15 s), and pipette stray capacitance, have contrib-uted to a relatively slow onset of the tail current.

The arrow inthe Figure 6 B indicates thetime point 35s afterthe start of the voltage step. Now the detected delay is approxi-

mately two times shorter than one would measure without thecorrection derived from the tail current analysis. Following theprocedure described in Figure 2, a direct comparison of the ob-served delay and the expected delay can be performed (Fig. 6 E).The traces corresponding to the m2 and m 3 functions wereshifted to the right by 35 s. There are no obvious differencesbetween Figures 2 E and 6 E, except for much faster activationtime constant at 22C. In hippocampal CA1 pyramidal neurons,for voltage steps to44 mV, the average delay was 71 13 s or(0.16 0.04) m (n 4). Similarly, in dentate gyrus granulecells, for voltage steps to44 mV, the observed average delay was50 5 s or (0.18 0.02) m (n 4) (Fig. 6 FH).

Interestingly, the average delay changed little with voltage. Inhippocampal CA1 pyramidalneurons,the delay was71 s at44mV and 69 s at 29 mV (n 4). Meanwhile, in the sameneurons, the activation time constant differed 1.7 times forthese two membrane potentials (396 s at44mV and 237s at29 mV; n 4). This relative insensitivity to the membranevoltage in this range of membrane potentials is inconsistent withthe Hodgkin and Huxley model, which predicts a linear relation-ship between the delay and the activation time constant. Never-theless, there was a clear decrease in the delay for voltage steps toless than45 mV. For voltage steps to49 mV, the delay dura-tion observed in the currents from the hippocampal CA1 pyra-midal neurons was 41 s (n 3). Although the small current

amplitude complicated the analysis at these voltages, the ob-served trend is consistent with the proposed model of sodiumcurrent activation.

Figure 6. Sodium currents activated with minimal delay in hippocampal CA1 pyramidalneurons(AE) andthedentategyrusgranule cells (FH)at22C. A,B, Sodiumcurrentactiva-tion recorded in a nucleated patch obtained from a hippocampal CA1 pyramidal neuron. Cur-rentswereevokedbythevoltage-clampprotocolshownabovethetraces.In B,tracesareshown

on expanded time scale. An arrow indicates an estimated time point when the membranecharging was completed by80% as estimated from tail current traces shown in D. C, D, Tailcurrentsevokedbytheprotocolshownabovethetraces.In D,tracesareshownintheexpandedsemilogarithmicplot.Thelightarrowindicatestheonsetofthevoltagestepcommand,andthedark arrow indicates the time point when current traces differed20% from the monoexpo-nential fitof thelinearpartof thetrace inthesemilogarithmicplot. E,Asemilogarithmicplotofthemodifiedcurrenttracethatwasobtainedfrom A followingtheprocedureshowninFigure2.This procedure included two steps of modifications. First, inactivation of the current was elim-inatedmathematicallybydividingthecurrenttracebythefollowingfunction:17.8pA 227.4pA exp(t/2.22 ms). Second, the final trace was obtained after the subtraction of theobtainedtracefrom1.Fordetailsofallprocedures,seeAppendix.Thethicklightlinerepresents

the monoexponential fit. The two smooth lines correspond to the quadrate (thin line) and thecube (thick line) of an exponential function. The light arrow indicates the time point when themembrane charging wascompletedby80%asestimatedfromtailcurrenttraces. E,Sodiumcurrent activation recorded in a nucleatedpatchobtained from a dentate gyrus granulecell.F,Tail currentsplotted inthe semilogarithmicplotwereevokedby theprotocolshownabove thetraces. The light arrow indicates the onset of the voltage step command, and the dark arrowindicates the time point when current traces differed20% from the monoexponential fit of

thelinearpartofthetraceinthesemilogarithmicplot. H,Asemilogarithmicplotofthemodifiedcurrenttracethatwasobtainedfrom FfollowingtheprocedureshowninFigure2.Allnotationsare the same as in E.



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DiscussionAnalysis of the sodium current gating in three different types ofcentral neurons showed that, in all of them, sodium currentsactivatedwithout a Hodgkin and Huxley-typedelay. A brief delaythat could not be attributed to the experimental artifact was twoto five times shorter than the delay predicted by the Hodgkin andHuxleymodel. In addition,at thesame voltage, theactivation and

deactivation time constants were indistinguishable. These resultsare consistent with a model in which a single transition from theclosed to the open state determines the activation kinetics ofsodiumcurrents. Computer simulations with such a sodiumcur-rent model reproduced well the shape of the action potentialrecorded in the prefrontal cortex neurons. In contrast, computersimulations with the traditional Hodgkin and Huxley-typemodel failed to reproduce the sharp rising phase of the experi-mentally recorded action potentials (Fig. 5D).

Our results show that the usual assumption that, in the ma-jority of neurons, sodiumcurrents activate after the Hodgkin andHuxley-type delay (Traub and Milles, 1991; Mainen et al., 1995)is probably incorrect. Over the membrane voltage range tested in

this paper, the observed brief delay that cannot be attributed toexperimental artifacts is primarily voltage independent and toobrief to be fit with the mn function. For membrane voltages be-tween55 and25 mV, the observed delay was at least two tofive times shorter than is predictedby them 2 function and at leastthree to seven times shorter than is predicted by the m 3 function.

The gating model presented here, conversely, did reproducethat brief delay (Fig. 5B) by adding a transition between twoclosed states. For membrane voltages from45 to30 mV, thistransition was assumed to be much faster (more than approxi-mately five times) than the second transition from the closed tothe open state, whichdetermines the activation/deactivationtimeconstants of thecurrents(for details, seeMaterials andMethods).

In this range of membrane voltages, the approximately fivefolddifference in transition rates corresponds to the observed delayduration, ranging from 0.13 m to 0.25 m, where m is theactivationtimeconstant. Comparisonof simulatedcurrent traceswith the experimentally recorded currents (Figs. 1, 2, 5) suggestthat our model reproduces well most of the sodium current acti-vation properties observed in prefrontal cortex pyramidalneurons.

In addition, we tested the validity of our model by reproduc-ing current-clamp data obtained from the prefrontal cortex py-ramidal neurons. Although many currents shape neuronal re-sponses, the action potential shape is very sensitive to changes inthe sodium current activation time course (Moore and Cox,

1976; Clay, 1998; Sangrey et al., 2004). Therefore, we reasonedthat a good model should be able to reproduce spike shape withcurrent densities that are close to the experimentally observedvalues. For comparison, we selected the traditional m 3 sodiumchannel model (Mainen et al., 1995)that has been used by severalgroups. As shown in Figure 5GJ, the steep rising phase of therecorded action potential was reproduced significantly betterduring simulations with our model. In addition, during simula-tions with our model, we were able to attain a close match be-tween the simulated and experimental time course and ampli-tude of the membrane potential depolarization speed.

It is rather surprising that nobody attempted to carefully an-alyze the shape of the sodium currents activation time course in

central mammalian neurons. Although several papers reporteddata on sodium current activation and deactivation time con-stants in central neurons (for example, Mainen et al., 1995; Mar-

tina and Jonas, 1997), none of them attempted to identify theshape of the activation time course of the current as it was donefor the sodium currents recorded in the large peripheral axons(Goldman and Schauf, 1973; Keynes and Rojas, 1976; Neumckeet al., 1976; Neumcke and Stampfli, 1982). This fact could haveseveral explanations. First, it seems likely that researchers as-sumed that such an analysis is impossible because sodium cur-

rents activate extremely rapidly. A second possibility is that, withmost commercial amplifiers, the quality of the achieved voltageclamp may be deceiving, as is demonstrated in Figure 6. More-over, we discovered that, in some amplifiers such as Axopatch200B, the 20 kHz setting of the low-pass filter that was necessaryfor the analysis of our experiments is absent and a software-basedsignal filtering was used (see Materials and Methods).

Finally, we cannot exclude that, outside of the tested heremembrane potential range (above25 mV), the activation timecourse can be fitted with the mn function. We focused on therange of membrane voltages at which sodium current activationis the slowest (from 55 to 25 mV), and the duration of thedelay is clearly smaller than it is predicted by the mn function.Extrapolation of our data to more depolarized potentials suggestthat, at0 mV, the activation time course may be fit with the m 2

function. Nevertheless, this current behavior is primarily repro-duced by the computer model because, for the membrane poten-tials 0 mV, the two transition rates that describe the channelsopening differ less than two times, and the delay duration intro-duced by our model approaches the delay duration predicted bythe m 2 function (see Materials and Methods). Hence,the conclu-sions drawn from our computer simulations are not affected bythe relatively longer delays at more depolarized potentials.

Besides the differences in the predicted action potential shapeand the effects of sodium channel distribution, there are twoadditional important consequences of our observations.

First, our data show that, in sodium channels of central mam-

malian neurons, a single gate controls most of the channel kinet-ics. Such a conclusion is based on a number of observations,including the similarity between activation and deactivation timeconstants (Fig. 3A), the presence of the minimum in the voltagedependence of activation and deactivation time constants (Fig.3 E, F), and good correspondence between voltage dependence ofactivation kinetics and current amplitudes (Fig. 3AD). Hence, itis likely that a unique structural motif is responsible for most ofthekineticsgoverning theopening of sodiumchannels. Theiden-tification of this structural motif will require experiments in het-erologous expression systems. Interestingly, there is no detailedstudy on sodium current activation time course for currents re-corded in heterologous expression systems. Thus, our data sug-

gest a new venue for the structurefunction studies in sodiumchannels.

Second, it is known that the amplitude of current fluctuationsdepends on the current activation time course (Steinmetz et al.,2000). For the same channel density, the fluctuation amplitude islarger when the current activation time course is described by amonoexponential function than when it is described by the cubeof an exponential function. Because membrane potential fluctu-ations modulate coincidence detection, it is possible that the ab-sence of the HH-type delay of the sodium current activation willbe reflected in the coincidence detection (Wiesenfeld and Moss,1995).In other words,informationprocessing in neurons maybeinfluenced by the activation time course of sodium currents.

However, a detailed study is required to support this hypothesis.In conclusion, sodium currents in three types of central neu-rons activate with a brief delay, the duration of which is much



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smaller than predicted by the Hodgkin and Huxley-type model.The data presented here change our understanding of how so-dium currents determine the shape of action potentials and, con-sequently, influence calcium entrance during the spike, a crucialprocess for brain plasticity and memory (Deisseroth et al., 2003).

Appendix

A modified procedure used by Keynes and Rojas (1976) was usedto directly determine the activation time constant m and n in the[1 exp(t/m)]

n function (see below).According to the Hodgkin-Huxley model, the shape of so-

dium currents activated by a voltage step from hyperpolarizedmembrane potentials can be described by the following equation(Hodgkin and Huxley 1952, their Eq. 19): gNa gNamax [1 exp(t/m)]

3 exp(t/h), where gNa is the amplitude of the

sodium current, gNamax is the maximal amplitude of the sodiumcurrent at the test potential, t is the time from the start of thevoltage step, m is the activation time constant at the test voltage,and th is the inactivation time constant at the test voltage. A moregeneralized version of this function is the following:gNagNamax [1 exp(t/m)]

n exp(t/h).

Because is usually setto be equal to 2 or 3, this general functiondescribing sodium current activation is here referred to as the mn

function. The procedure consisted of the following steps.First, the TTX-sensitive currents were corrected for inactiva-

tion by dividing by gNamax exp(t/h) gnon-inac, in whichgnon-inac represents the non-inactivating term of the monoexpo-nential fit function or the non-inactivating plus slowly inactivat-ing terms of the biexponential fit function. The fit was performedin a semilogarithmic plot (Fig. 2G) using peeling procedure forthe non-inactivating and slowly inactivating components, if theywere present.

Following such a procedure, in the case of the m3 kinetics, theobtained current shape can be described by the following func-

tion: I1 [1 exp(t/m)]3.Second, the normalized current (Fig. 2 D, inset) was sub-

tracted from 1. In the case of the m 3 kinetics, following this pro-cedure, we obtain the following function: I2 1 [1 exp(t/m)]

3 1 1 3 exp(t/m) 3 [exp(t/m)]

2

[exp(t/m)]3 and I2 3 exp(t/m) 3 [exp(t/m)]

2

[exp(t/m)]3.

Because [exp(t/m)]2 and [exp(t/m)]

3 decay faster thanexp(t/m), for t m, I2 3 exp(t/m).

In the case of the m 2 kinetics, this procedure produces thefollowing function: I2 2 exp(t/m) [exp(t/m)]2.

For t m, it becomes the following: I2 2 exp(t/m).In the case of the m 1 kinetics, we obtain the following func-

tion: I2 exp(t/m). Therefore, in a semilogarithmic plot, for t m, the obtained current trace will approach the line corre-sponding to the slope of exp(t/m) (Fig. 2 E). The only differ-ence between the graphs corresponding to the m 3, m 2, and m 1

kinetics will be a delay that corresponds to the coefficient in frontof the exponential term, which is ln(3) m in the case of the m

3

kinetics, ln(2) m inthe case ofthe m2 kinetics, and no delay in

the case of the m 1 kinetics.Hence, this method permits a relatively independent way to

estimate m and n in the mn function. In addition, this procedure

provides an estimate of the maximal time allowed to attain thedesired voltage-clamp control after the voltage step so as not toimpair the identificationof the n inthe mn function. For example,

if we want to discriminate between the m

2

and m

1

kinetics, wehave to detect the ln(2) m delay ofI2. Because m is0.3 msat23C (Fig. 3B) (Martina and Jonas, 1997), the membrane poten-

tial should stabilize in0.3 ln(2) 0.2 ms. During the exper-iments described here, the estimated membrane potential stabi-lization times (Fig. 1) were 0.10.15ms, which is insufficientinmost of the recordings at room temperatures. However, at 13C,m can be0.5 ms (Fig. 3A), and the 0.15 ms membrane chargingtime allows the discrimination between the m 2 and m1 kinetics.

In the majority of studies using whole-cell recordings, no ex-

perimental data are provided to estimate the duration of mem-brane potential stabilization afterthe voltage step. Without directevidence, it is difficult to estimate the time required to establishthe desired voltage-clamp control after a voltage command. Atypical estimate based on the current transient in response to avoltage step does notprovide a good estimateof stabilization timefor most commercial amplifiers (Sherman et al., 1999). The esti-mated response time of the Axoptach 1D amplifier was always90 s (Sherman et al., 1999), and it is probably safe to say thatit takes0.10.2 ms to attain a sufficient voltage-clamp controlafter a voltage step. Therefore, during whole-cell recordings atroom temperature, it is nearly impossible to detect the m 2-typedelay of sodium currents.

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