Calcium ion and muscle contraction.

Diversity and ubiquity of K channels.

Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecule...

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Diffusion in brain extracellular space.

It is suggested that a link in excitation-contraction coupling involves the movement of a fixed amount of charge free to move between different locations across the membrane.

Voltage Dependent Charge Movement in Skeletal Muscle: a Possible Step in Excitation–Contraction Coupling

1. Acetylcholine produced end-plate current (e.p.c.) noise is shown to be the results of statistical fluctuations in the ionic conductance of voltage clamped end-plates of Rana pipiens.

2. These e.p.c. fluctuations are characterized by their e.p.c. spectra which conform to a relation predicted from a simple model of end-plate channel gating behaviour.

3. The rate constant of channel closing α is determined from e.p.c. spectra and is found to depend on membrane potential V according to the relation α = BeAV (B = 0·17 msec−1±0·04 S.E., A = 0·0058 mV−1±0·0009 S.E. at 8° C) and to vary with temperature T with a Q10 = 2·77, at −70 mV. A and B in this expression both vary with T and therefore produce a membrane potential dependent Q10 for α.

4. Nerve-evoked e.p.c.s and spontaneous miniature e.p.c.s decay exponentially in time with a rate constant which depends exponentially on V. The magnitude and voltage dependence of this decay constant is exactly that found from e.p.c. spectra for the channel closing rate α.

5. The conductance γ of a single open end-plate channel has been estimated from e.p.c. spectra and is found not to be detectibly dependent on membrane potential, temperature and mean end-plate current. γ = 0·32±0·0045 ( S.E.) × 10−10 mhos. Some variation in values for γ occurs from muscle to muscle.

6. It is concluded that the relaxation kinetics of open ACh sensitive ionic channels is the rate limiting step in the decay of synaptic current and that this channel closing has a single time constant. The relaxation rate is independent of how it is estimated (ACh produced e.p.c. fluctuations, e.p.c., m.e.p.c.), and is consistent with the hypothesis that individual ionic channels open rapidly to a specific conductance which remains constant for an exponentially distributed duration.

7. The voltage and temperature dependence of the channel closing rate constant agree with the predictions of a simple dipole-conformation change model.

Voltage clamp analysis of acetylcholine produced end-plate current fluctuations at frog neuromuscular junction

1. Membrane currents during step depolarizations were determined by a method in which three electrodes were inserted near the end of a fibre in the frog's sartorius muscle. The theoretical basis and limitations of the method are discussed.

2. Measurements of the membrane capacity (CM) and resting resistance (RM) derived from the current during a step change in membrane potential are consistent with values found by other methods.

3. In fibres made mechanically inactive with hypertonic solutions (Ringer solution plus 350 m M sucrose) step depolarizations produced ionic currents which resembled those of nerve in showing (a) an early transient inward current, abolished by tetrodotoxin, which reversed when the depolarization was carried beyond an internal potential of about +20 mV, (b) a delayed outward current, with a linear instantaneous current—voltage relation, and a mean equilibrium potential with a normal potassium concentration (2·5 m M) of −85 mV.

4. The reversal potential for the early current appears to be consistent with the sodium equilibrium potential expected in hypertonic solutions.

5. The variation of the equilibrium potential for the delayed current (V′K) with external potassium concentration suggests that the channel for delayed current has a ratio of potassium to sodium permeability of 30:1; this is less than the resting membrane where the ratio appears to be 100:1. V′K corresponds well with the membrane potential at the beginning of the negative after-potential observed under similar conditions.

6. The variation of V′K with the amount of current which has passed through the delayed channel suggests that potassium ions accumulate in a space of between ⅓ and ⅙ of the fibre volume. If potassium accumulates in the transverse tubular system (T system) much greater variation in V′K would be expected.

7. The delayed current is not maintained but is inactivated like the early current. The inactivation is approximately exponential with a time constant of 0·5 to 1 sec at 20° C. The steady-state inactivation of the potassium current is similar to that for the sodium current, but its voltage dependence is less steep and the potential for half inactivation is 20 mV rate more positive.

8. Reconstructions of ionic currents were made in terms of the parameters (m, n, h) of the Hodgkin—Huxley model for the squid axon, using constants which showed a similar dependence on voltage.

9. Propagated action potentials and conduction velocities were computed for various conditions on the assumption that the T system behaves as if it were a series resistance and capacity in parallel with surface capacity and the channels for sodium, potassium and leak current. There was reasonable agreement with observed values, the main difference being that the calculated velocities and rates of rise were somewhat less than those observed experimentally.

Voltage clamp experiments in striated muscle fibres.

1. The kinetics of mechanical activation were examined in muscle fibres of the frog's sartorius muscle, using a voltage clamp to control membrane potential, tetrodotoxin to eliminate electrical activity and microscopic observations to determine the mechanical threshold.2. The strength-duration curve was determined over a range of membrane potentials varying between -52 mV (rheobase) and +90 mV. At 4 degrees C the critical duration was about 11 msec at -30 mV, 4 msec at 0 mV and 2 msec at +40 mV.3. For pulses where V > -10 mV the threshold criterion at 4 degrees C was that the ;area above -30 mV' must exceed about 120 mV msec.4. The effect of a brief subthreshold pulse declines with a time constant of about 3 msec at -100 mV and about 8 msec at -85 mV at 4 degrees C.5. Although the strength-duration curve is well fitted by assuming a first-order mechanism in which the rate of release of activator increases with membrane potential, other experiments show that the over-all mechanism is probably second order in time.6. A short pulse must be at least 50% threshold if it is to give a visible contraction when added to a long pulse which is just below rheobase.7. Delayed rectification was conspicuous with medium or long pulses which were just below the mechanical threshold, but short pulses could give contraction without turning on any appreciable potassium conductance.8. The Appendix extends Falk's (1968) treatment of the charging of the tubular system under a voltage clamp.

https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1969.sp008909

The kinetics of mechanical activation in frog muscle

1. Voltage clamp experiments on sartorius muscle fibres at 3° C showed that the potassium current is divisible into three components, namely:



(a) Current in the delayed rectifier channel, which reached a maximum in about 0·1 sec at −30 mV, and declined with a time constant of about 4 msec when the fibre was repolarized to −100 mV; this component had an approximately linear instantaneous current—voltage relation and an equilibrium potential E1 at 10–15 mV positive to the resting potential.



(b) A slow component which reached a maximum in about 3 sec at −30 mV, and declined with a time constant of about 0·5 sec when the fibre was repolarized to −100 mV; this component had an approximately linear instantaneous current—voltage relation and a mean equilibrium potential E2 at ‒83 mV in fibres where E1 averaged −75 mV.



(c) Current in the inward rectifier channel which decreased with a time constant of about 0·25 sec when the fibre was hyperpolarized to −150 mV. This component had an equilibrium potential close to the resting potential and an instantaneous current—voltage relation which was that of an inward rectifier.



2. The general characteristics of the late after-potential in muscles in hypertonic solutions at 3° C are consistent with those of the slow conductance change. The sign of the late after-potentials was reversed by depolarizing below −80 mV.



3. The decline of current during a maintained hyperpolarization cannot be attributed solely to a decrease in tubular potassium concentration, since there may be a large decrease in current without much alteration of equilibrium potential. The negative slope conductance often seen at −150 mV is also difficult to reconcile with the tubular depletion hypothesis.



4. Replacement of 10 m M-K by 10 m M-Rb abolished inward rectification but had less effect on the fast and slow components of the potassium conductance.

Slow changes in potassium permeability in skeletal muscle

The voltage clamp technique (Cole, 1949; Hodgkin, Huxley, and Katz, 1952) has been applied successfully to the analysis of ionic currents in a wide variety of excitable ceils. I t has proved difficult to apply this technique to striated muscle, both because it is hard to isolate a small area of membrane electrically and because the fiber contracts when depolarized. Takeuchi and Takeuchi (1959) applied voltage feedback at the end plate region of striated muscle fibers. Their method of controlling the voltage at a point produced an elegant method for measuring the currents of the muscle membrane at the end plate. Previous attempts to control the voltage of an area of membrane have been made by Adrian and Freygang (1962 b) and by Frankenhaeuser, Lindley and Smith (1965). In the present experiments (Adrian, Chandler, and Hodgkin, 1966) we have tried to control the voltage over a short length of a striated muscle fiber, by a technique which uses an internal microelectrode to deliver current and two additional microelectrodes to measure membrane current and voltage. The three electrodes are inserted near the pelvic end of a muscle fiber, in a frog sartorius muscle. Fig. 1 shows the positions of the microelectrodes and the arrangement of the feedback amplifier. The current through electrode 3 is controlled by feedback to give steady voltages or steps of voltage at electrode 1. The membrane current density at 1 is estimated by the difference in potential between electrodes 1 and 2. As a simple approximation, this potential difference can be considered to be produced by a longitudinal current flowing along the internal resistance between 1 and 2. The same current crosses the membrane between the end of the fiber and a point 3l/2 from the end of the fiber. On this basis the membrane current per unit length would be given by

https://rupress.org/jgp/article-pdf/51/5/188/1417596/188s.pdf

R. H. Adrian

Papers

Voltage clamp experiments in striated muscle fibres.

The kinetics of mechanical activation in frog muscle

Slow changes in potassium permeability in skeletal muscle

Voltage clamp experiments in striated muscle fibers.

Voltage clamp experiments in skeletal muscle fibres.