Properties of voltage-gated potassium currents in nucleated patches from large layer 5 cortical pyramidal neurons of the rat

Abstract

1. Voltage-gated potassium currents were studied in nucleated outside-out patches obtained from large layer 5 pyramidal neurons in acute slices of sensorimotor cortex from 13- to 15-day-old Wistar rats (22–25 °C).

2. Two main types of current were found, an A-current (I_A) and a delayed rectifier current (I_K), which were blocked by 4-aminopyridine (5 mm) and tetraethylammonium (30 mm), respectively.

3. Recovery from inactivation was mono-exponential (for I_A) or bi-exponential (for I_K) and strongly voltage dependent. Both I_A and I_K could be almost fully inactivated by depolarising prepulses of sufficient duration. Steady-state inactivation curves were well fitted by the Boltzmann equation with half-maximal voltage (V_½) and slope factor (k) values of −81.6 mV and −6.7 mV for I_A, and −66.6 mV and −9.2 mV for I_K. Peak activation curves were described by the Boltzmann equation with V_½ and k values of −18.8 mV and 16.6 mV for I_A, and −9.6 mV and 13.2 mV for I_K.

4. I_A inactivated mono-exponentially during a depolarising test pulse, with a time constant (∼7 ms) that was weakly dependent on membrane potential. I_K inactivated bi-exponentially with time constants (∼460 ms, ∼4.2 s) that were also weakly voltage dependent. The time to peak of both I_A and I_K depended strongly on membrane potential. The kinetics of I_A and I_K were described by a Hodgkin-Huxley-style equation of the form m^Nh, where N was 3 for I_A and 1 for I_K.

5. These results provide a basis for understanding the role of voltage-gated potassium currents in the firing properties of large layer 5 pyramidal neurons of the rat neocortex.

The basic computational task of most neurons is to summate synaptic inputs and generate a coded output, represented as patterns of action potentials. In order to fully characterise this process, called synaptic integration, it is necessary to know the types and distribution of ionic conductances found in the neuronal membrane (Johnston et al. 1996). This information can then be used to build a numerical model of the neuron, by which the action potential output might be calculated for any arbitrary pattern of synaptic inputs (Destexhe & Paré, 1999).

Voltage-gated potassium currents are important members of the repertoire of ionic conductances expressed by neurons. Potassium currents help to shape firing patterns: they repolarise action potentials, set interspike intervals, and terminate bursts (Hille, 1992). Reflecting their importance, a large body of information is available about both the physiology (Storm, 1993) and molecular biology (Coetzee et al. 1999) of potassium channels. However, much of the electrophysiological data has been acquired for a few standard preparations, notably hippocampal pyramidal neurons. In recent years the large pyramidal neurons in layer 5 of rat neocortex, with their conveniently thick apical dendrites, have emerged as a powerful system for the study of neuronal excitability (Stuart & Sakmann, 1995; Markram et al. 1997; Schiller et al. 1997; Larkum et al. 1999). Despite this, and in contrast to the situation for hippocampal pyramidal neurons, the voltage-gated potassium channels in large layer 5 neurons have been little characterised. This has hindered interpretation of the firing properties of these cells. The goal of this paper and its companion (Bekkers, 2000) was to build up a profile of the types of voltage-gated potassium channels found in large layer 5 cortical pyramidal neurons of the rat.

Molecular techniques have revealed a large family of genes encoding voltage-gated potassium channels in mammals (Jan & Jan, 1997; Coetzee et al. 1999). Although a great deal is known about the expression patterns of channel subtypes and their properties in expression systems, it is often unclear how this information relates to native channels in neurons. Alternative splicing, heteromeric assembly of different subunits, and post-translational modifications may all generate complexity, altering the properties of native channels from what is observed in expression systems. For this reason a purely electrophysiological approach, as used here, is still preferred for working out the functionally distinct classes of potassium channels that are present in neurons.

This paper uses nucleated outside-out patches to study the macroscopic properties of voltage-gated potassium channels found in somatic membrane. The following paper uses cell-attached and conventional outside-out patches to map the dendritic distribution of potassium channels and to examine their activation by backpropagating action potentials. It is concluded that these neurons contain two main types of voltage-gated potassium current, an A-current (I_A) and a slowly inactivating delayed rectifier current (I_K), which resemble the corresponding currents seen in other types of pyramidal neurons (Storm, 1993). Use of nucleated patches permits the study of membrane conductances under very accurate voltage control (Martina & Jonas, 1997; Martina et al. 1998). Hence, this paper also presents a detailed analysis of the kinetics and voltage dependence of I_A and I_K, as a prerequisite for numerical modelling.

Some of these results have been published as an abstract (Bekkers & Stuart, 1998).

METHODS

Slice preparation

Neocortical slices were prepared from 13- to 15-day-old Wistar rats using standard procedures that were approved by the Animal Experimentation Ethics Committee of the Australian National University (Stuart et al. 1993). Animals were killed by decapitation using a small-animal guillotine. Slices (300 μm thick) were cut under ice-cold slicing solution (composition below) using a Campden vibrating slicer (Loughborough, UK). They were maintained at room temperature in a holding chamber until use (1-5 h after slicing).

Solutions

The basic external solution for recordings contained (mM): 125 NaCl, 3 KCl, 25 NaHCO₃, 1.25 NaH₂PO₄, 1 MgCl₂, 1 or 2 CaCl₂, 10 glucose, 0.5 μM tetrodotoxin (TTX); 300 mosmol kg⁻¹, pH 7.4 when bubbled with carbogen. In some experiments 50 μM to 5 mM 4-AP was added; in others the basic solution was modified to contain 95 mM NaCl, 30 mM TEA-chloride, all other components remaining the same. External solutions were changed by perfusing > 15 times the bath volume. The slicing solution was the same as the basic external solution except that it contained 6 mM MgCl₂ and 1 mM CaCl₂. The electrode solution comprised (mM): 140 potassium methylsulphate (KMeSO₄), 7 NaCl, 5 EGTA, 2 Mg-ATP, 10 Hepes; 280 mosmol kg⁻¹, pH 7.2 when adjusted with KOH. All compounds were obtained from Sigma, except KMeSO₄ (ICN, Cleveland, OH, USA) and TTX (Alomone, Jerusalem, Israel).

Nucleated patch recording

Neocortical slices were perfused continuously with carbogen-bubbled basic external solution at 1.5 ml min⁻¹. Neurons were visualised using infrared-differential interference contrast (IR-DIC) optics with an Olympus BX50WI microscope (Olympus, Tokyo, Japan) and a Hamamatsu C2400 video camera (Hamamatsu Photonics, Japan). Large layer 5 cortical pyramidal neurons were identified by their large soma (∼30 μm long) and prominent apical dendrite that could often be seen coursing for hundreds of micrometres towards the pial surface (Stuart et al. 1993). All neurons used for experiments were in the sensorimotor cortical region.

Patch pipettes were made from thick-walled borosilicate glass (GC150F, Clark Electromedical, Pangbourne, UK), were unpolished, and had resistances of 3–5 MΩ when filled with internal solution. Nucleated outside-out patches were pulled using standard methods (Sather et al. 1992). Patches were near-spherical with mean diameter 11.5 ± 0.1 μm (±s.e.m., measured for 6 patches) and resistances > 1 GΩ. Using an Axopatch 200A amplifier (Axon Instruments, Foster City, CA, USA) the capacitance transients following a test pulse applied to the patch could be fully compensated, although a residual fast transient emerged after setting series resistance (R_s) compensation (e.g. Fig. 7A). The mean whole-patch capacitance was 2.8 ± 0.1 pF (n= 117 patches) and mean R_s was 8.8 ± 0.4 MΩ. R_s compensation of 80–90 % was used, with a lag of 10 μs, and was periodically checked during the course of the experiment. With typical peak currents of < 1 nA, voltage errors were < 1 mV.

Figure 7. Prepulse methods for isolating I_A and I_K, and peak current activation plots.

A, prepulse method for separating I_A. The membrane potential was alternately stepped to either -117 or -37 mV for 50 ms immediately before stepping to the test potential. The resultant membrane currents (thick trace: prepulse -117 mV; thin trace: prepulse -37 mV) were pair-wise subtracted to isolate I_A (V_test=+63 mV in the example illustrated). Remaining leak and capacitance currents, which were constant for all test potentials, were removed by subtracting from all episodes the pair-wise subtracted episode for V_test=−77 mV, which elicited no potassium current (see text). B, family of I_A currents isolated using this method, shown expanded in the inset. The pulse protocol is shown in A. Each trace is an average of 20 episodes. The external solution also contained 30 mM TEA to minimise I_K. D, example from another patch for which the external solution did not contain TEA. The pulse protocol is the same as in A and B. Each trace is an average of 30 episodes. E, prepulse method for separating I_K. Following a strongly hyperpolarising conditioning pulse (-117 mV for 450 ms) the membrane potential was stepped to -37 mV for 50 ms to inactivate I_A, then stepped to V_test. A family of the resultant leak-subtracted currents is illustrated. Each trace is an average of 20 episodes. The external solution did not contain any blockers apart from TTX. C, averaged, normalised peak activation plots for I_A, obtained in external solution containing 30 mM TEA (•; n= 12), in external solution containing 100 μM Cd²⁺ plus TEA (□; n= 9), or in external solution containing neither (○; n= 8). The prepulse method was used in all experiments. Error bars (±s.e.m.) are mostly smaller than the symbol size. The superimposed curves are Boltzmann functions with the indicated fit parameters. F, averaged, normalised peak activation plots for I_K, obtained in external solution containing 5 mM 4-AP (•; n= 9) or without 4-AP (○; n= 8). Adding external Cd²⁺ had no effect (not illustrated). The superimposed curves are fitted Boltzmann functions with the indicated fit parameters.

Patches were voltage clamped at a holding potential of -67 mV. The process of pulling the patch and setting up for recording typically took > 5 min, during which time the Donnan potential between the cytoplasm and pipette solution presumably dissipated (Verheugen et al. 1999; Fricker et al. 1999). Voltage protocols were provided and currents recorded via an ITC-16 interface (Instrutech, Great Neck, NY, USA) controlled by in-house software running under Igor (Wavemetrics, Lake Oswego, OR, USA) on a Macintosh computer. In most experiments currents were filtered at 2 or 5 kHz (4-pole Bessel filter) and digitized at 10 or 20 kHz. Unless otherwise stated, linear leak and residual capacitance currents were subtracted online as follows. For each member of a family of voltage command steps, the step pattern was inverted and scaled down by factor S into a hyperpolarised voltage range, usually -67 to -97 mV. It was checked that steps in this voltage range elicited only constant leak current, i.e. there was no sag. The resultant membrane current was then scaled back up by S and added to the current elicited by the original command step. An advantage of this method over the more common P/-4 approach is that the leak pulses occur over a known, fixed voltage range for all command pulses. A disadvantage is that the noise in the leak current is scaled up by a variable amount S, although this was usually overcome by sufficient signal averaging. Command and leak pulses were alternated, and 2–30 such leak-subtracted pairs were averaged. The interval between these paired stimuli was 2–50 s, depending on the experiment.

In all experiments the stability of the patch was confirmed by repeating some of the earlier command potentials at the end of the sequence (‘bracketing’; e.g. filled symbols in Figs 3 and 4). After loss of the patch, the electrode offset was measured and found to be within the range ±1.5 mV. Membrane voltages have been corrected for the liquid junction potential, which was measured to be -7 mV for all of the solutions used here. Experiments were done at room temperature (22-25°C).

Figure 3. I_A inactivates and recovers from inactivation with single-exponential kinetics.

A, onset of steady-state inactivation of I_A at -57 mV. Following a 500 ms prepulse to -87 mV to reduce inactivation, membrane potential was stepped to -57 mV for varying durations (ΔT). The amount of activatible I_A was then assayed by a step to +53 mV. ΔT ranged from 0 to 500 ms. B, plot of the amplitudes of I_A from A, after subtracting residual I_K (Methods), versusΔT. Filled circle is a bracket to Δ T= 0 at the end of the sequence. The superimposed curve is a fitted single exponential, time constant 13.2 ms. C, recovery from inactivation of I_A at -97 mV. I_A was inactivated by a 500 ms prepulse to -47 mV, then recovery at -97 mV was monitored. D, plot of the I_A data in C. The superimposed single exponential fit has a time constant of 40.9 ms. Filled circle is a bracket as before. All data in this figure are from the same patch with 30 mM TEA external solution. Each trace is an average of 4 episodes. Leak currents have been subtracted.

Figure 4. I_K inactivates and recovers from inactivation with double-exponential kinetics.

Similar experiment to Fig. 3, except that the external solution contained 5 mM 4-AP to block I_A and ΔT ranged from 0 to 45 s. A and B, onset of inactivation at -57 mV, fitted with the sum of two exponentials with time constants 178 ms and 8.86 s. C and D, recovery from inactivation at -97 mV, with fitted time constants 213 ms and 1.91 s. Filled symbols in B and D are bracket measurements made at the end of the sequence. Each trace in A and C is a single episode, all recorded from the same patch. Leak currents were not subtracted.

Data analysis

All analysis was done using AxoGraph (Axon Instruments). Instantaneous current-voltage (I–V) data was obtained by fitting a single exponential to the tail current at each potential (Fig. 2). The fit started 0.3 ms after the step, a value chosen to avoid asymmetries in the leak subtraction, as determined by running the tail current protocol on a model patch. The instantaneous current was measured from the amplitude of the exponential fit extrapolated back to the time of the step. The reversal potential was estimated from the fit of a quadratic polynomial to the instantaneous I–V plot (Fig. 2). Alternatively, the raw current amplitude was measured 0.3 ms after the step, which gave very similar results.

Figure 2. Instantaneous I–V data reveal that I_K has a more hyperpolarised reversal potential than I_A.

A, tail current family for I_K, recorded in 5 mM 4-AP. Following a 100 ms step to +53 mV, the membrane potential was stepped to a level ranging from +53 to -117 mV in 10 mV increments. Each trace is an average of 12 interleaved episodes. Leak currents have been subtracted. B, plot of peak instantaneous I_K, from extrapolated exponential fits to the tail currents (Methods), versus tail potential for this patch. The superimposed curve is a quadratic polynomial. The reversal potential for this patch was -86.4 mV. C, tail current family for I_A, recorded in 30 mM TEA and shown expanded in the inset. The pulse protocol was as in A, except the duration of the prepulse to +53 mV was 1.5 ms. Each trace is an average of 6 interleaved episodes. Leak currents have been subtracted. The slowly rising trace in the inset is the estimated time course of the contaminating I_K at +53 mV in this patch. At 1.5 ms the contamination is about 10 % of I_A. D, plot of peak instantaneous I_Aversus tail potential for this patch. The fitted quadratic polynomial gives a reversal potential of -68.7 mV.

Episodes were baselined over a 50–1000 ms window, usually immediately before the test potential was applied. Peak amplitudes were measured by averaging over ±0.2 ms around the peak (for I_A) or ±5 ms (for I_K). Current (I) was converted to conductance using G = I/(V_t- E_K), where V_t is the test potential and E_K is the measured reversal potential for I. Activation and inactivation plots were fitted to the Boltzmann relation:

where G_max is the maximal conductance, V_½ is the voltage at which activation or inactivation is half-maximal, and k is the slope factor (a positive number for activation, a negative one for inactivation). These parameters were determined from a fit to each experiment, then averaged together to give the mean values (±s.e.m.) cited in this paper. To generate averaged, normalised activation and inactivation plots (Figs 6 and 7), the plots for individual experiments were normalised by dividing by the fitted G_max and averaged together. These were refitted to the Boltzmann equation (fits shown in Figs 6 and 7); estimates of V_½ and k obtained from these fits differed from the means mentioned above by < 1 mV.

Figure 6. Steady-state inactivation data for I_A and I_K.

A, inactivation family for I_A, recorded in 30 mM TEA. The prepulse voltage ranged from -127 to -27 mV in 10 mV increments, and its duration was 500 ms. Each trace is an average of 16 episodes. Leak currents have been subtracted. B, averaged, normalised steady-state inactivation plot for peak I_A, after subtracting the residual I_K (Methods). Data were obtained in control external solution (•; n= 8) or in external solution containing 100 μM Cd²⁺ (□; n= 12). Error bars (±s.e.m.) are mostly smaller than the symbol size. The superimposed curves are Boltzmann functions with the indicated fit parameters. C, inactivation family for I_K, recorded in 5 mM 4-AP. The holding potential was set at -117 to -7 mV in 10 mV increments for times varying from 1 to 30 s prior to the test pulse to +53 mV (see text). Each trace is an average of 8 episodes. Leak currents have been subtracted. D, averaged, normalised steady-state inactivation plot for peak I_K (n= 8). The superimposed curve is the Boltzmann function. Adding external Cd²⁺ had no effect (not illustrated).

External solution containing 30 mM TEA reduced but did not eliminate the slowly decaying component of potassium current (Fig. 1C). This residual slow current was assumed to be incompletely blocked I_K, rather than a slow component of I_A, because I_A decayed to the baseline with a single fast exponential when measured in cell-attached patches that contained only I_A channels (Bekkers, 2000). The contaminating I_K was subtracted as follows. A single exponential plus a constant was fitted to I_K over the range 50–500 ms after the start of the test pulse (I_A had fully relaxed by 50 ms; Fig. 8). The fit was extrapolated to the start of the test pulse and subtracted from the total measured current. The peak of the residual current, pure I_A, was then measured. This subtraction method was accurate for inactivation and recovery experiments because the test potential, and so current kinetics, was constant (Figs 3 and 6). However, it introduced errors in activation experiments, because the relative times to peak of I_A and I_K changed with membrane potential (Figs 8 and 9). Accordingly, I_A activation was measured in two different ways: (i) from the peak current without subtracting I_K, with the rationale that I_A was little contaminated by I_K because the time to peak of I_A was faster (Fig. 2C, inset); and (ii) from the peak current after subtracting the fitted slow component of current mediated by I_K. The former method overestimated the size of I_A, whereas the latter underestimated it. In practice, both methods gave very similar results. The contamination of I_A by I_K was also reduced by using a prepulse subtraction protocol (Results; Fig. 7).

Figure 1. Delayed rectifier (I_K) and A-current (I_A) can be pharmacologically distinguished in nucleated patches from large layer 5 cortical pyramidal neurons.

Voltage clamp families of potassium currents recorded in three different external solutions (A–C). Following a 500 ms prepulse to -117 mV, the membrane potential (V_m) was stepped to a level ranging from -67 to +73 mV in 20 mV increments (protocol at top). Capacitance transients and linear leak currents have been subtracted using an online subtraction protocol (Methods). A, control external solution, without potassium channel blockers. B, external solution with 5 mM 4-AP. The remaining current is I_K. C, external solution with 30 mM TEA. I_K is reduced, emphasising I_A. All external solutions also contained 0.5 μM TTX. Each trace is an average of 4 (A) or 8 (B and C) episodes. Each patch is from a different neuron, but the current waveform was stereotypical in each solution.

Figure 8. I_A kinetics are well fitted by an equation of the form m^Nh.

A, voltage dependence of parameters describing the kinetics of I_A. Data are from currents recorded in 30 mM TEA to reduce I_K (•) or in the absence of TEA, using a prepulse method (Fig. 7A) to reduce I_K (○). Aa, time from the foot of I_A to its peak. Ab, inactivation time constant obtained from the fit of a single exponential plus a constant (to account for residual I_K) to the decay phase of I_A. Ac, order (N) obtained from a fit of the equation m^Nh to families of I_A currents, as shown in B and C. Here m incorporates a single exponential rise and h a single exponential decay, and N was allowed to vary. Each point is mean ±s.e.m. (n= 14 for filled circles; n= 4-9 for open circles). The smooth curves superimposed on the filled circles are fits of the TEA data to empirical functions that are summarised in Table 1. The horizontal dashed line in Ac indicates the value of N chosen to calculate the fits summarised in Fig. 10A. B, activation family of I_A (dots) with superimposed fits to the equation m^Nh (smooth curves). Each trace is an average of 8 episodes. Leak currents were subtracted and the external solution contained 30 mM TEA. C, the same family on an expanded time scale.

Figure 9. I_K kinetics are well fitted by m^Nh.

A, voltage dependence of parameters describing the kinetics of I_K. Data are from currents recorded in 5 mM 4-AP to reduce I_A (•) or in the absence of 4-AP, using a prepulse method (Fig. 7E) to reduce I_A (○). Aa, time to peak, obtained from short timebase leak-subtracted I_K families, like those in B. Ab, decay time constants and the ratio of their amplitudes (Ac) obtained from fits to long timebase I_K families without leak subtraction, like those in C. Each point is mean ±s.e.m. (n= 7). The superimposed smooth curves are fits to empirical functions that are summarised in Table 2. The horizontal dashed line in Ad indicates the value of N chosen to calculate the fits summarised in Fig. 10B. B, activation family of I_K currents (dots) with superimposed fits to the equation m^Nh (smooth curves, mostly obscured by the data). Each trace is an average of 8 episodes. Leak currents were subtracted and the external solution contained 5 mM 4-AP. C, I_K family from a different patch, using a long (20 s) step to the test potential (cf. 500 ms in B). The decay phase was fitted to the sum of two exponentials, plus a constant offset to account for leak current, which was not subtracted in this experiment. Inset shows the currents on an expanded time scale. Each trace is an average of 2 episodes.

Curve fits were done using the Simplex algorithm built into AxoGraph, with the sum of squared errors as the minimisation parameter. Measurement errors are given as ±s.e.m., with n equal to the number of patches.

Hodgkin-Huxley modelling

The data in most of the figures in this paper were fitted to empirical equations (listed in Tables 1 and 2) to facilitate model-independent comparison with other work. The exceptions are in Figs 8–10, where a Hodgkin-Huxley-style model was used.

Table 1.

Summary of equations describing voltage-dependent properties of I_A

			Parameters
Experiment	Figure	Equation	a	b	c	d
Recovery from inactivation τ (ms)	5A	1/(a exp(bV) +cexp(dV))	2.13	0.065	0.00026	−0.044
Time to peak (ms)	8Aa	a/(1 + exp((b–V)/c)) +d	5.5	−43	−25	1.8
Decay τ (ms)	8Ab	aV + b	0.01	6.7	—	—
Order (N)	8Ac	aV + b	−0.028	3.7	—	—
τm (ms) (V < −50 mV)	10Aa	1/(a exp(bV) +cexp(dV))	0.026	−0.026	35	0.136
τm (ms) (V > −40 mV)	10Aa	a/(1 + exp((b–V)/c)) + d	1.7	−42	−26	0.34

V is the membrane potential in mV

Table 2.

Summary of equations describing voltage-dependent properties of I_K

			Parameters
Experiment	Figure	Equation	a	b	c	d
Inactivation recovery τfast (s)	5Ba	1/(a exp(bV) +cexp(dV))	43	0.04	3.5 × 10−4	−0.1
Inactivation recovery τslow (s)	5Ba	1/(a exp(bV) +cexp(dV))	10	0.09	0.0057	−0.05
Inactivation recovery (Ampfast/Ampslow)	5Bb	aV + b	−0.015	0.2	—	—
Time to peak (ms)	9Aa	a/(1 + exp((b—V)/c)) + d	100	−0.4	−19	16
Decay τfast (ms)	9Ab	aV + b	−0.001	0.5	—	—
Decay τslow (ms)	9Ab	aV + b	−0.0014	4.5	—	—
Decay (Ampfast/Ampslow)	9Ac	aV + b	−0.011	3.1	—	—
Order (N)	9Ad	a/(1 + exp((b–V)/c)) + d	1.8	−18	−10	0.95
τm (ms)	10Ba	1/(a exp(bV) +cexp(dV))	0.018	−0.022	0.046	0.032

V is the membrane potential in mV.

Figure 10. Parameters for a Hodgkin-Huxley model of I_A and I_K.

A, mean τ_m (a) and m_∞³ (b) for I_A, plotted against membrane potential. Filled symbols in a were obtained by fitting eqn (1) (Methods) with N= 3 to plots of I_Aversus time. Open symbols in a were obtained as 3 ×τ_tail, where τ_tail was obtained by fitting a single exponential to the I_A tail currents recorded in instantaneous current-voltage experiments (Fig. 2A). The superimposed smooth curve is described in Table 1. Filled symbols in b were obtained from the above fit of eqn (1), which gave I_max (the extrapolated maximal current in the absence of inactivation). I_max was converted to conductance (Methods) and plotted against membrane potential. The superimposed continuous curve is the Boltzmann function raised to the power 3. The dashed curve is the cube root of the continuous curve and thus represents m_∞; the Boltzmann fit parameters for the dashed curve are given in the figure. Ba and b, the same model parameters for I_K. These were obtained as for I_A, except N= 1, and the factors 3 were replaced by 1. The superimposed smooth curve in a is described in Table 2; that in b is the Boltzmann function with the indicated parameters.

Plots of I_A and I_Kversus time were fitted to a Hodgkin-Huxley equation of the form:

(1)

where m(t,V) = 1 – exp(-t/τ_r), and h(t,V) = exp(-t/τ_d) for I_A (Fig. 8) and h(t,V) = a exp(-t/τ_d1) + exp(-t/τ_d2) for I_K (Fig. 9). Here I_max is the maximal current, N is the ‘order’, which gives an inflection to the rising phase, a is an amplitude constant, τ_r is the rise time constant, and the τ_ds are decay time constants. The parameter N is typically given a fixed integer value of 4 for I_A (Connor & Stevens, 1971) and 1–4 for I_K (Hodgkin & Huxley, 1952; Sah et al. 1988). These restrictions gave sub-optimal fits to I_A and I_K in these patches, whereas allowing N to vary with membrane potential gave excellent fits over the entire voltage range (Figs 8Ac and B, and 9Ad and B).

Although the best fit to the kinetics of I_A and I_K was obtained with a voltage-dependent N, this freedom causes difficulties for the standard Hodgkin-Huxley model. Accordingly, N was fixed at 3 for I_A and 1 for I_K (dashed lines in Figs 8Ac and 9Ad) for the analysis presented in Fig. 10. These constraints gave acceptable fits to the time courses of both I_A and I_K, particularly at more strongly depolarised membrane potentials (not illustrated).

The Hodgkin-Huxley model assumes that an ion channel is controlled by one or more voltage-sensitive gates, each of which can occupy two states, closed and open. Knowing the time- and voltage-dependent probabilities, m(t,V) and h(t,V), that the activation and inactivation gates, respectively, are in the open state, the probability of the channel being open can be calculated from eqn (1). Classically, m(t,V) and h(t,V) are found from the opening (α) and closing (β) rates for the ‘m’ and ‘h’ gates, which can be extracted from fits to the data (Hodgkin & Huxley, 1952). An alternative approach has been presented by Connor & Stevens (1971). The equation describing the probability that the ‘m’ gate is in the open position can be written:

(2)

where m₀ and m_∞ are the initial and final probabilities, respectively, that the ‘m’ gate is open, and τ_m is the relaxation time constant between the closed and open states. (All parameters are also functions of membrane potential.) Thus, rather than estimating the α and β rates, an equivalent approach is to measure the activation time constant (τ_m) and the steady-state activation function (m₀, m_∞) as functions of voltage, and substitute into eqn (2) (Connor & Stevens, 1971; Huguenard & McCormick, 1992; Lockery & Spitzer, 1992). Similar arguments apply to the inactivation process. This approach was used to generate Fig. 10.

Consider I_A (with N= 3) as an example. The activation time constant, τ_m, was equated to the parameter τ_r obtained from the fits shown in Fig. 8B and C (eqn (1); Fig. 10Aa, filled symbols). For membrane potentials more negative than about -50 mV, τ_m was determined as 3 τ_tail, where τ_tail was obtained by fitting a single exponential to the tail currents obtained in instantaneous I–V experiments (Fig. 2; Fig. 10Aa, open symbols). The factor 3 arises because, when three ‘m’ gates are gating in parallel, the apparent deactivation time constant is one-third of that for only one such gate (Huguenard & McCormick, 1992). The fitted I_max in eqn (1) was converted to a conductance and plotted against test potential; this gave m_∞³ (Fig. 10Ab, filled symbols). The power 3 arises from the combination of steady-state activation curves for three separate ‘m’ gates operating in parallel (Huguenard & McCormick, 1992). Thus, m_∞ was calculated as the cube root of this curve (dashed curve, Fig. 10Ab). A similar analysis was applied to I_K, for which N= 1 (Fig. 9B).

In principle, the same procedure can be used for modelling the inactivation properties of I_A and I_K, to obtain h(t,V). This is more complex for I_K because inactivation proceeds with two time constants (Fig. 9Ab), necessitating ‘h’ gates with more than two states. However, since the inactivation of I_A and I_K is nearly voltage independent over most of the interesting range of membrane potentials (Figs 8Ab and 9Ab) the inactivation term in eqn (1) can be simplified to a function that depends only on time at depolarised membrane potentials.

RESULTS

Pharmacological separation of voltage-gated potassium currents

Figure 1A shows typical currents recorded under voltage clamp in a nucleated outside-out patch from a large layer 5 cortical pyramidal neuron in control external solution. The external solution contained 0.5 μM TTX to block sodium channels but no other blockers. The internal solution contained 140 mM K⁺ and included 5 mM EGTA to block calcium-dependent potassium currents. Capacitance transients and linear leak currents have been subtracted using an online subtraction protocol (Methods). Following a 500 ms hyperpolarising prepulse to -117 mV to remove resting inactivation, the membrane potential was stepped to a range of test potentials (-67 to +73 mV; Fig. 1, top). The resultant family of putative potassium currents appears to contain two distinct components, decaying with fast and slow time courses.

This separation was confirmed pharmacologically. Addition of 5 mM 4-AP to the external solution completely blocked the rapid component, leaving a slowly rising and decaying current (Fig. 1B). Replacement of part of the NaCl in the external solution by 30 mM TEA reduced the slowly decaying current, leaving the fast component more prominent (Fig. 1C). There was little change in the current measured in the same patch before and after addition of 50–100 μM 4-AP to the external solution (-4 ± 3 %; mean ±s.e.m., n= 10, not illustrated).

The slow, 4-AP-resistant current (Fig. 1B) resembles the delayed rectifier potassium conductance I_K (Storm, 1993). I_K is little affected by 5 mM 4-AP but is reduced by 5–30 mM TEA in a variety of neurons (Sah et al. 1988; Storm, 1993; Klee et al. 1995; Zhang & McBain, 1995). The fast, TEA-resistant current (Fig. 1C) resembles the A-current, I_A, which is blocked by 1–5 mM 4-AP and not by TEA (Storm, 1993; Klee et al. 1995; Zhang & McBain, 1995). The residual slowly decaying current in TEA (Fig. 1C) is most probably incompletely blocked I_K, rather than a slow component of I_A (Huguenard & McCormick, 1992), since on-cell patches from these neurons often contained a pure I_A which decayed to the baseline with a single fast exponential (see Discussion; also, Bekkers, 2000). The fact that 50–100 μM 4-AP had little effect on the current in these patches excludes a significant contribution from the D-current, I_D (Storm, 1988).

Thus, nucleated patches from large layer 5 cortical pyramidal neurons appear to contain two types of voltage-gated potassium current, I_A and I_K. Further evidence for this separation comes from voltage pulse and single-channel experiments (see below; Bekkers, 2000).

Reversal potentials for I_K and I_A

To confirm that these were potassium currents, reversal potentials were measured using a tail current protocol (Fig. 2). For I_K, the external solution contained 5 mM 4-AP to block I_A (Fig. 2A). Following a 100 ms step to +53 mV, the membrane potential was stepped back to a range of voltages (+53 to -117 mV in 10 mV increments). The instantaneous I_K-V plot was calculated as described (in Methods; Fig. 2B). The mean reversal potential for I_K from a number of such experiments was -85.5 ± 1.1 mV (n= 14).

The same procedure was used for I_A, except that the external solution contained 30 mM TEA to reduce I_K and the test pulse to +53 mV was 1.5 ms long (Fig. 2C). This duration was chosen to minimise contamination by I_K, which is incompletely blocked by 30 mM TEA but which rises more slowly than I_A. Superimposing the estimated time course of I_K on the I_A tail currents (Fig. 2C, inset) shows that the amplitude of I_K is only about 10 % of that of I_A at the time of the tail voltage step. The mean reversal potential for I_A, estimated from instantaneous I_A-V experiments of this sort (Fig. 2D), was -69.9 ± 1.5 mV (n= 7).

The Nernst potential for K⁺ for these solutions (E_K) was -98 mV. The measured reversal potentials for I_K and I_A were thus depolarised to E_K, perhaps due to a non-zero permeability to Na⁺, as has been reported for these channels in other types of neuron (Sah et al. 1988). Surprisingly, the present results show that I_A reverses 16 mV depolarised to I_K, indicating that the channels underlying I_A are less K⁺ selective.

Inactivation onset and recovery kinetics

Before the activation and inactivation properties of I_A and I_K could be measured, it was necessary to establish the rate at which these currents achieved steady-state inactivation at each membrane potential in the hyperpolarised range. This information was used to choose appropriate prepulse durations.

Figure 3 illustrates the protocols used to measure inactivation onset and recovery for I_A. The external solution contained 30 mM TEA to minimise I_K. In one protocol (Fig. 3A) the membrane potential was first stepped to -87 mV for 500 ms to partially remove inactivation of I_A, then stepped to a test potential (e.g. -57 mV in Fig. 3A) for varying durations, ΔT, to follow the onset of inactivation at that potential. The extent of inactivation was probed by a step to a fixed potential (+53 mV) at the end of ΔT. This protocol was used for test potentials ≥-57 mV. A similar protocol was used to follow the recovery from inactivation at test potentials < -57 mV (e.g. -97 mV; Fig. 3C). In this case the membrane potential was first stepped to -47 mV to inactivate I_A, then stepped to a hyperpolarised test potential for ΔT to follow the recovery from inactivation at that potential (Fig. 3C).

For both protocols, the amount of I_A remaining was measured from the peak current evoked by the step to +53 mV, after subtracting the fitted slow component of current mediated by I_K (Methods). A plot of peak I_AversusΔT at each onset/recovery potential was well fitted by a single exponential (Fig. 3B and D). Figure 5A summarises the results of similar experiments on 7 patches at a range of test potentials (filled circles; mean ±s.e.m.). The superimposed continuous curve is a fit to an empirical function presented in Table 1. The time constant of inactivation onset and recovery for I_A was strongly voltage dependent. Also shown (open squares, dashed curve) are data obtained for the same experiment run in 100 μM Cd²⁺, discussed below.

Figure 5. I_A and I_K inactivate and recover from inactivation with voltage-dependent time constants.

A, mean time constants (±s.e.m.) for onset of or recovery from inactivation of I_A, plotted against membrane potential, for control external solution (•) and external solution containing 100 μM Cd²⁺ (□). Note the logarithmic ordinate. A single time constant described the inactivation onset/recovery of I_A at each membrane potential. Ba, a similar plot for I_K. Two time constants were needed to describe the inactivation onset/recovery of I_K, except at V_recov=−117 mV where a single exponential sufficed (○). External Cd²⁺ had no effect on I_K. Bb, mean ratio Amp_fast/Amp_slow for the onset/recovery of I_K, where Amp_fast is the amplitude of the fitted fast component and Amp_slow is that of the slow component. The continuous lines in all panels are fits to empirical functions that are summarised in Tables 1 and 2.

A similar experiment was done to measure inactivation onset and recovery for I_K (Fig. 4). The external solution contained 5 mM 4-AP to block I_A. The voltage protocols were as for I_A, except that ΔT ranged to 45 s to encompass the much slower kinetics of I_K (Fig. 4A and C). Plots of peak I_KversusΔT at each onset/recovery potential were well fitted by the sum of two exponentials (Fig. 4B and D), except at -117 mV where one exponential sufficed. Figure 5B summarises the results of such experiments on 6–12 patches at a range of potentials. This shows mean time constants (upper panel) and the ratios of their amplitudes (lower panel). The smooth curves are fits that are presented in Table 2. As for I_A, the inactivation onset and recovery kinetics of I_K were strongly voltage dependent.

Steady-state inactivation of I_A and I_K

Protocols for measuring the steady-state inactivation of I_A and I_K were designed in the light of the onset/recovery data in Fig. 5. For measuring inactivation of I_A, the duration of the inactivating prepulse was 500 ms (Fig. 6A), which is much longer than the slowest relaxation time constant for the onset of inactivation (45 ms at -77 mV; Fig. 5A). The external solution contained 30 mM TEA to minimise I_K, and leak currents were subtracted online. The peak amplitude of I_A was measured, after subtracting the fitted residual I_K (Methods), and was plotted versus prepulse potential for each patch (Fig. 6B). These plots were well fitted by the Boltzmann equation (Methods). Averaging the fits from all patches gave mean fit parameters V_½=−81.6 ± 1.1 mV and k=−6.7± 0.4 mV (n= 8). The plots for individual patches were normalised and averaged together (Fig. 6B, filled circles). This average was also well fitted by the Boltzmann equation (Fig. 6B, continuous curve). Similar experiments done in 100 μM Cd²⁺ (Fig. 6B, open squares) are discussed below.

For measuring inactivation of I_K, much longer inactivating prepulses were required: I_K attained steady-state inactivation with time constants as slow as ∼7 s (at -57 mV; Fig. 5B). Accordingly, the holding potential was set to each prepulse potential, prior to applying the test pulse/leak pulse pair, for the following durations: 30 s for V_prepulse=−77 to -7 mV, 20 s for -87 mV, 10 s for -97 mV, and 1 s for -107 and -117 mV (Fig. 6C). The external solution contained 5 mM 4-AP to block I_A, and leak currents were subtracted online. Peak I_K was plotted versus holding potential. The plots were well fitted by the Boltzmann equation and gave fit parameters V_½=−66.6 ± 1.7 mV and k=−9.2± 0.5 mV (n= 8; Fig. 6D).

Note that, with a holding potential of -7 mV, a small non-inactivated current remained when measuring I_K (<3 % of the current with holding potential -117 mV; Fig. 6C and D). This current was too noisy and variable to be studied further.

Activation of I_A in TEA and I_K in 4-AP

The measurements of I_A described so far were made after subtracting an exponential fitted to the I_K that remained in 30 mM TEA (Methods). This subtraction method is accurate for inactivation and recovery experiments, where the test potential is kept constant, but is not accurate for activation experiments, where the test potential (and so the relative times to peak of I_A and I_K) varies. A prepulse protocol was therefore used to further reduce contamination of I_A by I_K.

From a holding potential of -67 mV, the membrane potential was stepped alternately to -117 or -37 mV for 50 ms before stepping to the test potential (Fig. 7A). Subtracting the resultant current traces partially removed I_K, owing to its slower inactivation kinetics. Knowing the steady-state inactivation curves (Fig. 6) and the rates of inactivation onset or recovery at different membrane potentials (Fig. 5), the relative sizes of I_A and I_K in the subtracted currents could be calculated as a function of the prepulse duration (ΔT). I_A was found to be largest relative to I_K at ΔT= 50 ms, which was the value used (Fig. 7). An advantage of this protocol was that hyperpolarising leak pulses were not necessary, because leak currents during the test pulse, with the two different prepulses, were subtracted (Fig. 7A). On the other hand, leak currents during the alternating prepulse were not subtracted with this procedure, distorting the early part of I_A. However, these distorting currents were identical for each test potential and could be removed by subtracting from all episodes the difference episode for the test potential to -77 mV, which elicited no potassium current. This yielded activation families as in Fig. 7B.

Since this protocol still did not completely remove contaminating I_K, I_A was measured in two different ways: (i) from the peak current; and (ii) from the peak current after subtracting a single exponential fitted to the residual I_K (Methods). The former method overestimated the size of I_A, whereas the latter underestimated it. The current amplitude at each test potential was converted to a conductance (Methods) using the measured reversal potential for I_A (-69.9 mV), plotted against test potential, and fitted to the Boltzmann equation (Fig. 7C). Method (i) gave V_½=−18.8 ± 1.5 mV and k= 16.6± 0.4 mV (n= 12; Fig. 7C, filled circles). Method (ii) gave V_½=−18.9 ± 1.8 mV and k= 16.4± 0.4 mV (n= 12; not shown).

The prepulse protocol systematically underestimated maximal I_A conductance because the prepulse duration (50 ms) was a compromise designed to minimise the proportion of I_K, but also reduced I_A. Accordingly, G_max was estimated from a separate series of experiments using a 500 ms-long prepulse protocol (Fig. 1C). The two methods for measuring I_A, described above, gave G_max values of 3195 ± 343 pS (method (i)) and 2061 ± 280 pS (method (ii); n= 14). When divided by the mean surface area of these nucleated patches (416 ± 10 μm²; Methods) the mean conductance density was 768 ± 18 μS cm⁻² and 495 ± 12 μS cm⁻², respectively.

Activation families for I_K were obtained by stepping from a 500 ms prepulse at -117 mV to a range of test potentials (Fig. 1B). This prepulse was sufficient to remove > 95 % of resting inactivation (Fig. 5B). The external solution contained 5 mM 4-AP to completely block I_A, and leak currents were subtracted online. The peak current amplitude at each test potential was converted to a conductance as before, using the measured reversal potential for I_K (-85.5 mV). The mean value for G_max was 5578 ± 723 pS (n= 13), giving a mean conductance density for I_K of 1341 ± 32 μS cm⁻². Thus, the density of I_K in these nucleated patches was about twice that of I_A. Plots of the I_K conductance versus test potential were well fitted by the Boltzmann equation, giving mean fit parameters V_½=−9.6 ± 1.5 mV and k= 13.2± 0.5 mV (n= 9; Fig. 7F, filled circles).

Activation of I_A and I_K without TEA or 4-AP

All of the experiments described so far were done in the presence of either TEA or 4-AP in order to partially isolate I_A or I_K. However, these blockers may have non-selective or voltage-dependent effects that could distort the measurements (Storm, 1993). Accordingly, another series of experiments was done in which TEA and 4-AP were omitted and prepulse protocols were instead used to partially separate I_A and I_K.

Activation families for I_A, without TEA in the bath, were measured using the protocol in Fig. 7A; an example of such a family is shown in Fig. 7D. Plots of I_A conductance versus test potential were well fitted by the Boltzmann equation, giving mean fit parameters V_½=−20.7 ± 2.2 mV and k= 16.4 ± 0.9 mV (n= 8; Fig. 7C, open circles). This is nearly identical to the activation plot for I_A measured in TEA (Fig. 7C, filled circles).

Activation families for I_K, without 4-AP in the bath, were measured using the prepulse protocol shown in Fig. 7E. A 50 ms prepulse to -37 mV was inserted in order to inactivate I_A, yielding an activation family for I_K (Fig. 7E). Mean Boltzmann fit parameters for experiments of this sort were V_½=−17.0 ± 1.6 mV and k= 14.9± 1.0 mV (n= 8; Fig. 7F, open circles). Thus, the I_K activation curve is depolarised by about 7 mV in the presence of 4-AP (Fig. 7F).

Kinetic properties of I_A and I_K

Kinetic properties of these currents were measured both in the presence of TEA or 4-AP (filled circles, Figs 8 and 9) or in the absence of these drugs, instead using the prepulse protocols described above to separate I_A and I_K (open circles, Figs 8 and 9).

The time to peak of both I_A and I_K varied strongly with membrane potential (Figs 8Aa and 9Aa). In contrast, the decay time constants of both currents were only weakly voltage dependent (Figs 8Ab and 9Ab). The decay of I_A was well fitted by a single exponential plus a constant (Fig. 8B), where the constant accounts for incompletely subtracted I_K on this fast time base. The sum of two exponentials was required to fit I_K (Fig. 9C). The two decay time constants were fitted to I_K during a long (20 s) test pulse to a range of potentials (Fig. 9C). Since leak subtraction was not used for these long pulses, the fitted function also incorporated a constant offset to account for the unsubtracted leak current. The ratio of the amplitudes of the two fitted exponentials was also only weakly voltage dependent (Fig. 9Ac).

Plots of I_A and I_Kversus time were well fitted by a Hodgkin-Huxley-style equation of the form m^Nh (Methods, eqn (1)). N is typically given a fixed integer value of 4 for I_A (Connor & Stevens, 1971) and 1–4 for I_K (Hodgkin & Huxley, 1952; Sah et al. 1988). These restrictions gave sub-optimal fits to I_A and I_K in these patches, whereas allowing N to vary with membrane potential gave excellent fits over the entire voltage range (Figs 8B and 9B). The voltage dependence of N is summarised in Figs 8Ac and 9Ad. The smooth curves superimposed on the filled circles in the summary plots in Figs 8 and 9 are empirical equations that are listed in Tables 1 and 2.

In order to prepare these results for numerical modelling, two simplifications were made. First, N was given a fixed value of 3 (for I_A) or 1 (for I_K; dashed lines, Figs 8Ac and 9Ad). With these restrictions, reasonable fits could still be obtained, especially at the more depolarised membrane potentials (not illustrated). This simplification made possible a standard Hodgkin-Huxley-style analysis of activation behaviour (Methods; Fig. 10). Plots of the time constant of activation, τ_m, and the steady-state activation parameter, m_∞, are shown for both I_A and I_K (Fig. 10). The smooth curves are fits that are presented in Tables 1 and 2. The second simplification was to ignore the slight voltage dependence of inactivation of both I_A (Fig. 8Ab) and I_K (Fig. 9Ab) at membrane potentials more depolarised than about -40 mV. Thus, the time and voltage dependence of I_A and I_K could be approximated by application of eqns (1) and (2) (Methods).

Effect of external Cd²⁺ on I_A and I_K

In order to check for the presence of contaminating calcium currents, recordings were made with 100 μM Cd²⁺ added to the external solution, which is sufficient to completely block several subtypes of calcium channels (Reid et al. 1997). Solutions also contained either TEA or 4-AP. Little effect on the kinetics of the outward currents was observed, confirming that calcium current contamination is unlikely.

Although 100 μM Cd²⁺ did not alter the kinetics of potassium currents, it had dramatic effects on the peak activation and steady-state inactivation plots for I_A. The V_½ for I_A inactivation was depolarised by about 20 mV by Cd²⁺ (Fig. 6B, open squares), while V_½ for I_A activation was depolarised by about 10 mV (Fig. 7C, open squares). Cadmium also depolarised by about 20 mV the curve describing I_A inactivation onset and recovery kinetics at hyperpolarised membrane potentials (Fig. 5A, open squares), but had no effect on the decay time constant at depolarised potentials. Cadmium had no effect on any of the properties of I_K (not illustrated).

DISCUSSION

The aim of this work was to identify the functionally distinct kinds of voltage-gated potassium channels found in the somatic membrane of large layer 5 cortical pyramidal neurons. An important goal is to incorporate these channels into a realistic numerical model of layer 5 pyramids. Thus, a further aim of this paper was to produce accurate kinetic descriptions of the channels. This was accomplished by recording from nucleated outside-out patches of membrane pulled from the soma. These patches are large enough to produce sizeable, low-noise currents that can be reliably fitted. Furthermore, they can be accurately voltage clamped, owing to their spherical shape and low access resistance (Methods; Martina & Jonas, 1997). These factors facilitated a detailed kinetic analysis of the currents.

Two main types of voltage-gated potassium currents were found. These were identified as I_A and I_K, based on their pharmacology, kinetics and voltage dependence (Rudy, 1988; Halliwell, 1990; Storm, 1990, 1993). I_A was completely blocked by millimolar concentrations of 4-AP (Fig. 1), recovered rapidly from inactivation (Fig. 3), exhibited strongly hyperpolarised steady-state inactivation (Fig. 6), and had rapid, monoexponential activation and inactivation kinetics (Fig. 8). I_K was partially blocked by millimolar concentrations of TEA (Fig. 1), recovered slowly from inactivation (Fig. 4), exhibited less hyperpolarised steady-state inactivation (Fig. 6), and had slower kinetics, its decay being best described by the sum of two exponentials (Fig. 9).

Voltage-gated potassium currents in cortical pyramidal neurons have been little studied, although reports are available for cortical cultures (Zona et al. 1988; Massengill et al. 1997), slices (Spain et al. 1991; Banks et al. 1996) and acutely dissociated cells (Hamill et al. 1991; Foehring & Surmeier, 1993; Locke & Nerbonne, 1997). Far more information is available for potassium currents in hippocampal pyramidal neurons (e.g. Segal & Barker, 1984; Numann et al. 1987; Storm, 1988; Sah et al. 1988; Wu & Barish, 1992; Ficker & Heinemann, 1992; Klee et al. 1995; Hoffman et al. 1997; Martina et al. 1998; for review see Storm, 1993). Published data from both cortical and hippocampal pyramidal neurons, as well as thalamic relay neurons (Huguenard & Prince, 1991; Huguenard et al. 1991), will be cited in the following discussion.

Properties of I_A

I_A-like currents are consistently reported in pyramidal neurons, but these often vary in detail. The decay time constant varies between about 5 and 40 ms at depolarised potentials at room temperature (cf. ∼6-9 ms; Fig. 8Ab). In some cases the decay is reported to depend only weakly on voltage, as found here (cortex: Locke & Nerbonne, 1997; hippocampus: Wu & Barish, 1992; Klee et al. 1995); in other cases it varies strongly with voltage (hippocampus: Hoffman et al. 1997; Martina et al. 1998). The reported midpoint for activation varies between about -30 and +10 mV (cf. -18.8 mV; Fig. 7C), and that for inactivation between about -90 and -50 mV (cf. -81.6 mV; Fig. 6B). Some, but not all, of this variability may be explained by the presence of Cd²⁺ in the external solution of several studies (cortex: Zona et al. 1988; Albert & Nerbonne, 1995; Locke & Nerbonne, 1997).

The depolarising effect of 0.3-5 mM Cd²⁺ on I_A inactivation is well known (Mayer & Sugiyama, 1988; Klee et al. 1995) but it was surprising to find that concentrations as low as 100 μM also had a large effect (Figs 5A and 6B; cf. Albert & Nerbonne, 1995). The shift observed here (20 mV) was the same as that seen for 300 μM Cd²⁺ in hippocampus (Klee et al. 1995) suggesting that 100 μM is still a saturating concentration. Given that Cd²⁺ has its greatest effect on I_A inactivation, the most likely explanation is that Cd²⁺ binds to a specific site on the I_A channel, perhaps to a residue in the external mouth of the pore (Yellen et al. 1994; Talukder & Harrison, 1995).

A slow component of decay of I_A has been reported (Huguenard et al. 1991; Huguenard & McCormick, 1992; Wu & Barish, 1992). A slow current is also observed in Fig. 7B but this was attributed to partially recovered I_K. Cell-attached patches containing pure I_A-like current showed late channel openings, which would contribute to a slow component of I_A (Fig. 2; Bekkers, 2000). However, ensemble averages of these episodes decayed to the baseline with a single fast exponential, suggesting that any slow component of I_A must be small.

I_A has been most strongly correlated with the expression of the Kv4 family of potassium channel subunits, particularly Kv4.2, in a variety of neurons (Martina et al. 1998; Tkatch et al. 2000). In situ hybridization and immunocytochemistry have shown that Kv4 subunits are expressed at moderate levels in rat cortex (Serôdio & Rudy, 1998), with Kv4.2 concentrated in dendrites and somata (Sheng et al. 1992). This is consistent with the results obtained here and in the accompanying paper (Bekkers, 2000).

Properties of I_K

I_K-like currents are also commonly reported in pyramidal neurons, but there is less agreement about their defining properties, and even nomenclature, than for I_A. Such currents have variously been called I_K2 (thalamus: Huguenard & Prince, 1991), I_KS and I_KSS (cortex: Foehring & Surmeier, 1993), and fast and slow delayed rectifiers (hippocampus: Martina et al. 1998). Some of these currents inactivate slowly (over seconds) with double exponential kinetics (thalamus: Huguenard & Prince, 1991; hippocampus: Klee et al. 1995), while others are reported not to inactivate at all (hippocampus: Hoffman et al. 1997). The midpoint for activation varies between about -10 and +15 mV (cf. -17 mV without 4-AP; Fig. 7F), and that for inactivation between about -95 and -30 mV (cf. -66.6 mV; Fig. 6D). Incomplete inactivation of I_K has also commonly been reported (thalamus: Huguenard & McCormick, 1992; hippocampus: Ficker & Heinemann, 1992; Costa et al. 1994; Martina et al. 1998). This is explained by the use of insufficiently long conditioning prepulses (300 ms to 10 s, cf. up to 30 s here).

Some of this complexity stems from the presence, in some neurons, of an I_K-like current that is sensitive to low (∼100 μM) concentrations of 4-AP, sometimes called I_D (Storm, 1988) or I_K(AT) (Bossu et al. 1996). Even when present, this current is often a relatively minor component (∼10 %; cortex: Locke & Nerbonne, 1997; hippocampus: Martina et al. 1998) although I_K(AT) has been reported to be dominant in CA3 pyramidal neurons in organotypic slice cultures (Bossu et al. 1996). I_D, if present, was a very minor component of the currents in these nucleated patches because 50–100 μM 4-AP had little effect. Interestingly, the subunit Kv1.2, which encodes a delayed rectifier that is highly sensitive to 4-AP when expressed in Xenopus oocytes, is largely absent from the somata of large layer 5 cortical neurons (Sheng et al. 1994).

It remains possible that the I_K described here encompasses two or more subtypes of potassium channel. This may be suggested by the biexponential inactivation kinetics (Fig. 9) or the small non-inactivating component of current (Fig. 6C). Alternatively, only one class of channel may underlie I_K but different pools of channels may be differentially modulated. This will be discussed further in the companion paper (Bekkers, 2000).

Effects of TEA and 4-AP

Although TEA and 4-AP are commonly used for the pharmacological separation of potassium channel subtypes, they need to be regarded with caution. Incomplete blockade, lack of specificity, and the distortion of current kinetics by these compounds have all been reported (Storm, 1993). In this paper, an attempt was made to appraise some of these difficulties by separating I_A and I_K both pharmacologically and by means of pulse protocols (Fig. 7). The latter method is still not perfect, because the design of pulse protocols involves compromises.

In the experiments described here, 30 mM TEA had little effect on the activation properties and kinetics of I_A (compare filled and open circles, Figs 7C and 8A). The time to peak at depolarised potentials was slightly faster in TEA, compared with that measured without TEA using a prepulse protocol (Fig. 8Aa). This may reflect greater contamination by the more slowly rising I_K in the absence of TEA.

In contrast, 5 mM 4-AP produced a consistent depolarising shift of about 7 mV in the activation curve for I_K (Fig. 7F). Despite this, the time to peak of I_K was unaffected by 4-AP (Fig. 9Aa). The divergence in the fitted Hodgkin-Huxley parameter N (Fig. 9Ad) probably reflects not the effect of 4-AP but, rather, the difference between stepping from -117 mV (with 4-AP) or from -37 mV (without 4-AP). The prepulse potential has long been known to affect the activation sigmoidicity (N) of I_K in squid axons (Cole & Moore, 1960).

In summary, these results suggest that neither TEA nor 4-AP greatly affects the voltage-dependent properties of I_A or I_K. For this reason, the Hodgkin-Huxley kinetic analysis used the more complete data acquired in the presence of these compounds.

Kinetic modelling

The kinetic properties of I_A and I_K are presented in two different ways in this paper. First, plots of the time to peak, decay kinetics, and onset of and recovery from inactivation have been fitted to empirical equations describing the voltage dependence of these parameters (Tables 1 and 2). The equations provide model-independent descriptions of the data, to facilitate comparison with other work or the formulation of alternative models. Second, the currents have been fitted to a standard Hodgkin-Huxley-style model (Fig. 10). Although this model has limitations, it provides a useful starting point.

Hodgkin-Huxley models of I_A in other preparations always assume N= 4 (Huguenard & McCormick, 1992; Lockery & Spitzer, 1992; Hoffman et al. 1997), as was done in the original description (Connor & Stevens, 1971). In this paper N= 3 was chosen as a better compromise (Fig. 8Ac). The data presented here suggest that a fixed N is a simplification (Fig. 8): the activation of I_A has less inflection (smaller N) at depolarised membrane potentials and more inflection (larger N) at hyperpolarised potentials, than is predicted by a simple m^3or4h scheme. Other features of the data also highlight problems with this model. Inactivation of I_A at depolarised potentials is voltage independent (Fig. 8Ab), whereas onset of and recovery from inactivation at hyperpolarised potentials is strongly voltage dependent (Fig. 5A). Plots of time constants of inactivation versus membrane potential, obtained in these two ways, therefore do not lie on the same bell-shaped curve, as is classically the case (Hodgkin & Huxley, 1952). A similar problem applies to τ_m obtained from tail current kinetics or fits to the rising phase of I_A (Fig. 10Aa). This has required a segmental approach to modelling I_A, whereby activation and inactivation are discontinuous functions of membrane potential (Huguenard & McCormick, 1992; Lockery & Spitzer, 1992; Hoffman et al. 1997).

Hodgkin-Huxley models of I_K in pyramidal neurons use values of N equal to 1 or 4 (Sah et al. 1988; Huguenard & Prince, 1991; Hoffman et al. 1997). The data in Fig. 9A show that N= 1 is appropriate for membrane potentials > 0 mV, but N increases at hyperpolarised potentials. Again, inactivation is largely voltage independent at depolarised potentials (Fig. 9A), but onset and recovery are strongly voltage dependent (Fig. 5B). This necessitates a segmental equation for I_K inactivation, although activation is well described by a single smooth function for all membrane potentials (Fig. 10Ba). These considerations must be borne in mind when the conductances are incorporated into a future numerical model of large layer 5 neurons.

Implications for firing properties

The rapid kinetics of I_A suit it to the role of a fast ‘shock absorber’ of membrane potential, resisting sudden depolarisations (Hoffman et al. 1997). Its strongly hyperpolarised steady-state inactivation curve (Fig. 6B) means that small voltage perturbations around the resting potential, such as might be provided by synaptic inputs, will markedly affect the availability of I_A. Thus, a rapid depolarisation following inhibitory synaptic input will be most effectively dampened by I_A; other patterns of activity will be less affected.

The slow kinetics of I_K adapt it to the role of setting general levels of excitability, rather than responding to fast changes. For example, I_D, a current in CA1 pyramidal neurons with similar kinetic properties to I_K, has been shown to delay the onset to firing following a prolonged hyperpolarisation (Storm, 1988). The activation of I_K is still sufficiently rapid, however, for it to contribute to action potential repolarisation (Bekkers, 2000).

This discussion reveals only a part of the picture of excitability in large layer 5 pyramids; the distribution and density of conductances must also be considered. This is addressed in the following paper (Bekkers, 2000).