Repriming of Delayed Potassium Conductance in Frog Skeletal Musclex

Hodgkin and Huxley (1952) proposed a mathematical scheme for describing the transient increase in sodium conductance responsible for nerve cell excitability. In their model, sodium conductance was proportional to the product of a rapidly developing (activating) third-order rate parameter and a more slowly declining (inactivating) first-order rate parameter, each of which was a function only of the membrane potential and time. This type of scheme has been successfully used to describe transient conductances in many different membrane systems (Cole, 1968). However, in the last decade there have arisen several difficulties in interpreting inactivation phenomena using the Hodgkin-Huxley model, notably in experiments on the transient sodium conductance in Myxicola axons. The kinetics of inactivation (Armstrong, 1970; Goldman & Schauf, 1972 ; Schauf & Davis, 1975 ; Bezanilla & Armstrong, 1977) and of recovery from inactivation (repriming) (Schauf, 1974) are sigmoid rather than exponential, the time course of inactivation depends on the activating test-pulse (Goldman & Schauf, 1972, 1973), the ‘steady state’ inactivation level varies with conditioning prepulses and also depends on the activating test-pulse potential (Goldman & Schaur 1972), and inactivation takes place more rapidly than repriming at the same membrane potential (Schauf, 1976). These deviations from the inactivation scheme proposed by Hodgkin and Huxley have been interpreted in terms of coupling between activation and inactivation (Hoyt, 1968; Goldman, 1975). An alternative is to postulate a sequential kinetic model (Armstrong, 1969, 1971; Moore & Cox, 1976) in which inactivation is subsequent to activation (a form of coupling in that activation must precede inactivation). It has been suggested that biphasic kinetics observed in multipulse experiments might be explained by multiple inactivated states (Argibay & Hutter, 1973; Hille, 1976).

Relatively few studies of the inactivating delayed conductance of skeletal muscle have been reported. Heistracher and Hunt (1969) observed a sigmoid repriming time course in snake fibres maintained in Ringer containing 100 mM-K. Adrian, Chandler & Hodgkin (1970) also observed a sigmoid repriming time course in frog fibres in high potassium, in contrast to the exponential repriming they found in briefly ( < 10 s) depolarized fibres in 2·5 mM potassium Ringer. In a series of multi-pulse experiments on frog skeletal muscle fibres, Argibay & Hutter (1973) apparently detected multiple inactivated states. In one such experiment a brief repriming pulse was ineffective in eliciting recovery from a chronically inactivated membrane; after a long repriming pulse followed by a depolarization sufficient for full inactivation of conductance, the same brief repriming pulse did elicit some recovery of delayed conductance.

The purpose of this paper is to report voltage-clamp experiments on the repriming of frog skeletal muscle fibres with a chronically inactivated delayed conductance. In these experiments the temperature was varied in order to provide more detailed kinetic information. A dissection that permits good visualization of fibre terminations for use with the three-electrode voltage-clamp technique, using American frogs, is also described.

Adrian & Freygang (1962) first suggested measuring the potential difference between two points near the termination of a cylindrical cell to obtain an approximation of membrane current density. Refinements by Adrian etal. (1970) and Schneider & Chandler (1976) have made the three-electrode voltage clamp a standard technique in muscle electrophysiology. To apply the technique a cell is impaled by voltagerecording electrodes at distances x₁ and x_2≅2x₁ from the fibre terminus. A third microelectrode inserted at x₃ > x₂ receives the output of a feedback circuit designed to maintain V₁ (the potential difference across the membrane at x₁) at a chosen level.

Voltage-recording electrodes filled with 3 M-KCI had resistances of 6–15 MΩ and tip potentials of less than 5 mV. Current passing electrodes filled with 2 M potassium citrate had resistances of 5 – 12 MΩ. Electrodes were shielded just before mounting using colloidal silver paint (Valdiosera, Clausen & Eisenberg, 1974). After successful impalement of a fibre with three microelectrodes, the potential difference across the membrane at position x_i was clamped to its initial value. Command pulses could then be imposed on V₁, with 90% completion within about 0 · 5 ms.

Control studies confirmed the findings of Adrian et al. (1970), and Stanfield (1970), in showing that the ‘instantaneous’ conductance of the delayed rectifier is linear over the voltage range – 80 to + 20 mV. In a given experiment a fixed voltage step (typically from +10 to – 40 mV) was used for all conductance measurements, and the instantaneous change in current divided by the size of the voltage step was taken to be the membrane conductance. Conductance was routinely measured both before and after a hyperpolarizing pulse, and the difference (having leakage current subtracted) was recorded as the ‘reprimed’ conductance (G_re). Inactivation was allowed to redevelop for five minutes following each repriming protocol.

Accurate measurement of distances from the electrodes to the end of the cell is difficult in the sartorius muscle of Rana pipiens, so a new preparation using the semitendinosus muscle was developed. The two heads of the semitendinosus muscle are attached to opposite faces of the sheet-like distal tendon. Cutting away some of the fibres on the ventral side of this tendon resulted in excellent visualization of the fibre ends on the dorsal side of the sheet. A loose tie around the remaining ventral head fibres permitted effective spreading of the muscle in a small chamber. The region of muscle to be impaled by microelectrodes was supported by a Lucite pedestal coated with petroleum jelly. The muscle was usually mounted at about 1 · 3 times slack length.

The muscle in a cooling chamber was mounted under a Zeiss standard WL research microscope and viewed through a Leitz long working distance 20 × objective at a total magnification of 250. Striation spacings, visible in normal Ringer, usually disappeared several minutes after changing to hypertonic sucrose solution.

Extracellular bathing solutions are listed in Table 1. Muscles were dissected and mounted in normal Ringer, solution A (Adrian, 1956). Experimental solutions B and C had sulphate substituted for chloride to eliminate chloride conductance and 350 mM added sucrose to abolish movement. Solution B had the same ionic strength as A (Hodgkin & Horowicz, 1959). Rubidium-containing solution C was introduced at a later stage in the investigation to block currents through the ‘inward rectifier’ (Adrian, 1964) ; sucrose was reduced and ionic strength increased to retard the deleterious effects of sucrose, and so that the results would be more directly comparable to recent experiments of Adrian & Rakowski (1978).

Oscilloscope traces were photographed by a Grass Camera on Recordak film (Kodak). Results were projected on graph paper and measurements made directly on the projected image or on tracings. Instantaneous currents were measured by determining the current time course 5 – 15 ms after a voltage step and linearly extrapolating back to the end of the step, as the current was obscured by the capacity transient during the first few milliseconds.

Curve-fitting was carried out on a PDP 11/40 computer (Digital Equipment Corporation) using a random direction search method (Bremmerman, 1970).

The delayed potassium conductance in skeletal muscle fibres is activated in normally polarized fibres by voltage-clamp steps to membrane potentials above – 40 mV, and conductance reaches a maximum at positive membrane potentials (Adrian et al. 1970). With prolonged depolarization the system inactivates, and recovery at a polarized potential (repriming) is necessary before conductance can again be activated by depolarization (Heistracher & Hunt, 1969; Adrian et al. 1970; Stanfield, 1970). In the present experiments, fibres placed in solutions containing 80 mM potassium or rubidium spontaneously depolarized to membrane potentials of – 30 to – 20 mV. In these fibres the delayed conductance system is chronically inactivated. Voltage-clamp steps to membrane potentials of – 140 to – 90 mV resulted in recovery of the delayed conductance.

Fig. 1 shows records taken from a cell in solution C with a holding potential of – 20 mV. A small deflection in the current ( Δ V) trace accompanies the voltage step to + 4 mV, and very little ‘tail’ current is seen with a post-pulse to – 54 mV (Fig. 1 a). With an identical voltage sequence immediately following 34s repriming pulse to – 108 mV, a large delayed current accompanies the test-pulse to +4 mV, and a large tail current is seen with the post-pulse to – 54 mV (Fig. 1 b). Conductance was measured as the ratio of the ‘instantaneous’ current change to voltage change at the time of the step from the test-pulse voltage (IQ to the post-pulse voltage (PJ,) (arrows). The difference in conductance before and after a hyperpolarizing pulse, the ‘reprimed conductance’, was 22-2 mmho/cm².

Repriming of conductance by 90 s pulses to – 109 mV, between 2 · 5 and 20 °C, is shown in Fig. 2. Conclusions based on these data are limited since they reflect temperature effects on both the maximum conductance and the recovery rate. However, the absence of an abrupt drop in this range rules out a phase change effect such as has been reported in end-plate tissue culture (Lass & Fischbach, 1976), and suggests a reasonably smooth temperature dependence of both the maximum conductance and the recovery rate.

A repriming time course for relatively long pulses is shown in Fig. 3. Most of the pulses delivered to this fibre were to – 95 mV ; at this potential, an exponential fit resulted in a time constant of 75 seconds and an assymptote of 1 · 6 mmho/cm². Two measurements at more negative potentials indicate that this was not a true steady state value, however, and suggest the presence of a component requiring many minutes to develop at – 95 mV (Adrian & Rakowski, 1978). Other experiments using 20-100 s pulses to membrane potentials between – 90 and – 140 mV confirmed the multi-state character of repriming at long times, and demonstrated the difficulty of taking recovery to completion within a reasonable time.

Experiments at 20 °C were performed with a fixed repriming potential while varying else duration (t_Re). Figure 4 illustrates the time course of repriming at – 108 mV.

The least-squares fit of the data in Fig. 4 to a rising exponential (not shown) resulted in a time constant of 3· 9 s. Data from another cell studied at – 117 mV was fitted by a rising exponential with 33-13 time constant. Both fits deviated from the data at short times, however, since conductance appeared following an initial delay.

Cooling to 10 °C considerably slowed the early recovery from inactivation. The cell illustrated in Fig. 5 required hyperpolarizing pulses of several seconds in length to begin to elicit repriming, compared with the delay of 0· 1 s seen in Fig. 4. Data from another cell studied at three different temperatures are shown in Fig. 6. With cooling from 14· 5 to 9· 2 °C the initial delay appeared to become more pronounced.

The three microelectrode voltage-clamp has emerged as a convenient and reliable technique for measuring membrane current density at a site of controlled membrane potential in preparations where space clamping is not feasible. Previous work using this method has mainly utilized the pelvic end of the sartorius muscle from the English frog, Rana temporaria, since pelvic terminations of sartorius muscle cells from Rana pipiens are poorly visualized (Schneider & Chandler, 1976). However, terminations of cells of the semitendinosus muscle from Rana pipiens are easily exposed and provide a convenient voltage-clamp preparation for investigators in the United States.

Although the instantaneous conductance is linear in this preparation, several difficulties interfere with simple application of Ohm’s law to determine membrane conductance from total current. Problems include current-dependent changes in concentration of permeant ions in the transverse tubules, the unreliability of absolute potential measurements using microelectrodes, and the uncertainty of the zero current level in the presence of gradually developing electrode leaks. The technique described in the Methods depends only on changes in current ( Δ P) simultaneous with a fixed voltage step. Uncertainties due to changes in ionic driving forces are eliminated since the method does not require determination of the channel reversal potential. Electrodes were chosen for small tip potentials to minimize errors in potential measurements.

The method of data analysis was chosen to minimize errors due to leakage current at the electrode impalement sites. The scaling factor (= 1/πar_i (x₂² – x₂²)) to convert ΔV/V₁ to conductance per unit surface area was determined by using small pulses at the beginning of each experiment. Since only this scaling factor is affected by leaks at x₂ and x₃, changing leakage at these sites will not affect measured conductances. Leakage at x_n which does result in ΔV errors, was corrected for in the procedure used to calculate reprimed conductance by subtracting leakage conductance (with no repriming) from the total conductance following the hyperpolarization protocol, to obtain reprimed conductance (G_Re). This correction assumes that leakage at x₁ is unchanged during the repriming protocol.

The present data do not reveal the full time course of repriming kinetics (Fig. 3). Reduced survival time of fibre subjected to strenuous repriming protocols made complete determinations impossible. Lacking steady-state measurements of reprimed conductance, data cannot be normalized and quantification of early sigmoidicity can only be regarded as tentative. However, some useful inferences can still be drawn from observations of recovery from inactivation made at short and intermediate times ( < 25 s).

The sigmoid character of equation 3 is monotonically related to the ratio of the smaller to the larger rate constant, with the largest delay for β₂/α₂ = 1. This is the case in Fig. 5 (10 °C), where the data would be better fit by a model allowing even more sigmoidicity. In Fig. 4 (20 °C) a good fit was obtained for β₂/α₂ = 0· 49. The fit to another time-course at 20° resulted in α₂/α₂ = 0· 059. These observations quantitatively support the suggestion that sigmoid time courses are more pronounced at lower temperatures.

Fits to repriming time courses at several temperatures (Fig. 6) were calculated by including temperature coefficients for ⁠, α₂, and β₂ as adjustable parameters. Parameter values resulting from these fits are of limited use since there were only about twenty data points and six adjustable parameters. Nevertheless, in Fig. 6, the ratio β/ αranged from 0· 054 at I4· 5° to ° 0· 105 at 9· 2°, corroborating the trend seen in experiments on separate fibres studied at different temperatures.

The results of this curve-fitting exercise show that for the limited data available, the sigmoid descriptions did exhibit increasing delays as the temperature was lowered. Delays were determined by comparing the ratios of two rate constants, a method that is independent of axis-scaling. It is therefore concluded that the repriming mechanism consists of at least two rate processes with different temperature dependences.

The present finding of a sigmoid repriming time course is consistent with the results of Adrian et al. (1970), Heistracher and Hunt (1969), and Argibay & Hutter (1973). Adrian and Rakowski (1978) observed an exponential repriming time course under similar conditions; however, their experiments were more concerned with steady-state recovery and the early time-course was not investigated in detail. Although the latter authors described repriming as a single-state exponential process, they also observed fibres that did not achieve a steady level of recovery after several minutes. Their interpretation in terms of a separate very slowly repriming conductance is supported by the present results (Fig. 3).

Adrian & Rakowski (1978, fig. 10) also found that the voltage dependence of repriming showed a marked shift towards more negative potentials compared to results obtained by Adrian et al. (1970, fig. 16) and Aimers (1976, pp. 19–20) in normally polarized cells. A shift in this direction is predicted by the proposed model. The kinetic differences between repriming in briefly and in chronically inactivated cells reported by Adrian et al. (1970) and Heistracher and Hunt (1969) are also predicted.

I would like to thank Dr R. F. Rakowski for suggestions and advice, Dr W. F. Pickard and the Biomedical Engineering Program for flexibility and support, and Dr C. B. Ballou for continued encouragement. This work constituted partial fulfillment of the requirements of the Doctor of Science degree in Electrical Engineering at Washington University, and was supported by P.H.S. grant number 5-T01-GM01827 to the Biomedical Engineering Program.