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Recordings from two patches with large numbers of sodium channels are shown on the left side of Figure 3. The currents have kinetics similar to the averaged single­ channel currents shown in Figure 1, and to the TTX-sensitive current (see Figure 3 of Chapter 3). With increasing depolarisation, the Na"*" currents increase and then decrease in amplitude, reversing at the most positive potentials. Peak currents from this patch and two others are shown plotted against the potential of the depolarising pulse in the right panel of Figure 3. The reversal potentials are around

-1 33m V 40pA +97mV -83mV -1 0 0

\

Figure 3

(left) Na"^ currents in two outside-out patches originating from near the node in two different human axons. The pulse protocol, shown at the top, was similar to that used to record the currents in Figure 1. The lower currents are averages from ten runs of the same pulse protocol, and the capacitance transients, which were unusually large in this patch, have been blanked for clarity.

(right) The amplitude of peak sodium currents from three outside-out patches, including the two in the left panel of this Figure, plotted against pulse potential. The largest peak current occurs at potentials between -20 mV and -30 mV, and the reversal potential is around +60 mV.

+60 mV, close to the equilibrium potential for Na'^ ions, and the largest peak currents are seen at potentials around -20 mV or -30 mV. The peak currents of 40 - 60 pA correspond to a maximum of 35 - 55 channels simultaneously open in each patch. These patches were made with pipettes with bubble numbers of 2 - 3 (Corey & Stevens 1983).

2.1 Activation o f multi-channel sodium currents

2.1.1 Voltage dependence o f activation

In a rapidly inactivating current like the sodium current, where peak current amplitudes are influenced by inactivation as well as by activation, it is difficult to analyse the voltage dependence of activation in isolation. One approach is to assume that activation and inactivation are independent processes, and to fit the falling phase of the current with one or two exponential functions. However, activation and inactivation are not independent (Patlak 1991), and such approaches introduce model-dependent assumptions which might distort the data.

The voltage dependence of the maximum open probability (Popen) of the Na"^ current was therefore assessed instead; this measure includes effects from activation and inactivation, but is independent of assumptions about the nature of these processes. The peak currents in Figure 3 and the single-channel conductance in Figure 2 were brought together to calculate the relative Popen at the peak of the Na"^ current, which is shown in Figure 4. The open probability increases in a steeply voltage-dependent manner between -60 and -20 mV.

E I o _ 0 4 — -1 0 0 - 5 0 0 50 E (mV)

Figure 4

Voltage dependence of the open probability Popen at the peak of the Na"^ currents in the three outside-out patches featured in Figure 3 (represented by the same symbols).

Popen was calculated by dividing the current amplitude in that figure by the single-channel current amplitude at the same potential in Figure 2. Points from each patch were then fitted with the Boltzmann function:

/=W (’+“p((^o.5-£)A))

and normalised by dividing by /max- The values obtained from each fit were:

circles, Fq.s = -55.1 mV, k = 4.3 mV; squares, Fq.s = -46.8 mV, k = 5.5 mV; triangles, Fq.s = -47.0 mV, A = 6.1 mV.

2.2 Inactivation o f multi-channel sodium currents

2.2.1 Voltage dependence o f inactivation

When a voltage pulse which activates sodium current is preceded by a depolarising prepulse, voltage-dependent steady-state inactivation is seen; this is shown in Figure 5. The left panel shows the pulse protocol and the currents recorded. Each episode began with a 50 ms prepulse to -133 mV, to remove inactivation which may be present at the holding potential of -93 mV. This was followed by a 50 ms prepulse to potentials between -153 mV and -43 mV, to induce steady-state inactivation. Finally, the Na"^ current which could still be activated was measured with a 50 ms

-93mV E pre -43m V 50pA -133m V 25ms

1

1

Figure 5

(left) Effect of a 50 ms depolarising prepulse on sodium currents in response to a test pulse to -43 mV. 50 ms hyperpolarising prepulses to -133 mV were given to remove resting inactivation; 50 ms prepulses to potentials between -153 mV and -43 mV were then applied to induce steady-state inactivation, followed by 50 ms pulses to -43 mV to activate the remaining sodium current. Only the episodes with prepulses to -103, -83 and -63 mV are shown. No correction has been made for leak and capacity currents.

(right) Currents at the beginning of the -43 mV pulse after prepulses between -133 and -53 mV, after correction for leak and capacity currents.

pulse to -43 mV. The right panel of Figure 5 shows the currents at the beginning of the -43 mV test pulse, following prepulses between -133 mV and -53 mV, after correcting for leak and capacity currents. The voltage dependence of inactivation is shown in Figure 6; it is fitted well by a Boltzmann function.

- 1 5 0 - 1 0 0 - 5 0

E (mV)

Figure 6

Peak currents in Figure 5 during the -43 mV test pulse, plotted against the potential of the prepulse which induced inactivation, and normalised. 20 measurements were made at each potential in one patch (mean ± SEM shown). Currents recorded from each run of the pulse protocol were divided by the current recorded in the same run after the pulse to -150 mV; the normalised currents were then averaged across runs to produce the mean ± SEM. Mean currents were then fitted with the Boltzmann function:

l = l ^ / { l + e x p ( ( E - E j / k ) )

and then re-normalised by dividing all means and SEMs by /max- The parameters of the final fit were:

Eq.5 = -88.0 mV; = 9.32 mV.

2.2.2 Time course o f inactivation

At potentials negative to -13 mV, the inactivation phase of the multi-channel sodium current is not fitted well by a single exponential. Figure 7 shows averaged multi-channel Na"^ currents from the patch in Figure 3 (left, lower); the averages are smooth enough to allow the quality of the fit to be reliably assessed. Between -43 and -13 mV, a good fit is obtained using the sum of two exponentials, but the fit with a single exponential is clearly bad. At -3 mV, however, the slower component is much smaller, and the fit with a single exponential is reasonably good. The averages of the single-channel currents in Figure 1 can also be fitted using either one or two exponentials, although it is not easy to assess the quality of the fit.

The time constants obtained from fitting single and double exponential functions to the current in multi-channel patches, and to the averaged current from the patch with 3 Na"^ channels in Figure 1, are plotted against pulse potential in Figure 8. Measurements from averaged single-channel currents or from multi-channel currents produce very similar time constants.

-133mV_r 20pA -43 m V T = 1.56ms T] = 0.88ms T2 = 8.4ms 5ms

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Figure 7

Inactivation of multi-channel sodium currents fitted with one or two exponential terms. The currents are those shown in Figure 3 (left, lower). Time constants of single (above) and double (below) exponential fits are shown at three potentials (-43, -23 and -3 mV). Dotted lines show the fitted curves.

15i 50 - 5 0 0 1 5 i - 5 0 0 5 0 E (mV) E (mV)

Figure 8

Time constants from single exponential fits (left) and double exponential fits (right) to the inactivation phase of multi-channel sodium currents in 3 patches (open symbols; mean ± SEM shown) and to the averaged single-channel currents from the patch in Figure 1 (filled symbols).

CHAPTER 5