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Real and simulated patch currents. Shown on the top row are patch currents obtained from muscle fibers near the endplate A and away from the endplate B.
The outward potassium current is larger away from the endplate. On the bottom row are patch currents simulated with parameters used previously to model muscle fiber action potentials Cannon et al.
Previously used parameters resulted in potassium currents that were too small and sodium currents that peaked too slowly. Holding potential—induced shifts in the voltage dependence of sodium channel activation and fast inactivation.
A Shown is the pulse protocol used to measure holding potential—induced changes in the voltage dependence of sodium current inactivation.
A series of pulses to measure the voltage dependence of fast inactivation are run at the first holding potential.
This series is repeated every 1—2 min to follow changes in the voltage dependence of fast inactivation. The holding potential is then changed and the measures of fast inactivation are repeated every 1—2 min.
B Time course of holding potential—induced changes in the midpoint of inactivation measured in a selected muscle fiber. C The time course of holding potential—induced changes in the midpoint of activation.
We initially used parameters that had been used previously to model action potentials in skeletal muscle Table I ; Cannon et al.
Note, we report the midpoint of NaCh channel activation and inactivation and K channel activation rather than the values for the voltage dependence of the parameters m, h, and n as was done previously.
This was done to make it easier to compare modeled data to values recorded from real muscle fibers. Internal resistivity was taken from Farnbach and Barchi Data for slow inactivation was taken from Rich and Pinter To improve modeling of action potentials, we recorded patch currents from muscle fibers and used these to derive a set of parameters for modeling sodium and potassium currents at various resting potentials.
One difficulty in modeling patch currents in muscle fibers is that the amount of potassium current present in a patch of membrane is highly variable.
In general, the amplitudes of these currents are large when recorded at locations away from the endplate, whereas near the endplate there is often little to no potassium current Fig.
For modeling of action potentials, we used parameters that yielded a potassium current density between that found near endplates and that found away from endplates.
Modeling of patch currents showed that action potentials were abnormally wide in our initial simulations because sodium and potassium currents activated too slowly Fig.
Using previous parameters Cannon et al. These changes resulted in currents that more closely resembled those obtained from intact muscle fibers.
A major difficulty in modeling action potentials is deciding values to use for the numerous other parameters in the model.
Previous estimates of maximal sodium conductance from muscle fibers in vivo vary by up to fivefold. In our initial simulation of action potentials we used a value for specific membrane resistance based on our previous measurements Rich et al.
Although myotonia was prevented by use of a low specific membrane resistance Fig. Choosing values for the voltage dependence of slow inactivation are also problematic since values for Nav1.
The threshold for action potential initiation was very close to the membrane potential, and both myotonia and anode break excitation were observed Fig.
The modeling studies above show that shifts in the voltage dependence of sodium channel activation and fast inactivation are needed to accurately simulate muscle fiber excitability during depolarization of the resting potential.
If such shifts occur in muscle fibers in vivo, they may be of crucial importance for regulating excitability. Holding potential—induced changes in the voltage dependence of activation and fast inactivation in skeletal muscle have been noted during studies of slow inactivation of sodium currents from rat muscles Simoncini and Stuhmer, ; Ruff et al.
However, the significance of the effect was unclear and because increased extracellular calcium reduced the effect, subsequent studies were performed in high extracellular calcium Simoncini and Stuhmer, ; Ruff et al.
Our modeling studies suggest that this effect might be necessary to appropriately regulate muscle fiber excitability, so we performed further studies using normal extracellular calcium levels.
To study the effects of holding potential on the voltage dependence of inactivation, we held fibers for up to 30 min at various holding potentials.
At each holding potential, we measured the midpoint of the voltage dependence of fast inactivation every 1 to 2 min using the voltage protocol shown in Fig.
We found that changing the holding potential caused a shift in the voltage dependence of fast inactivation Fig. A similar effect was observed for the voltage dependence of activation Fig.
Thus, data from muscle fibers studied in vivo support the prediction from our modeling study that the voltage dependence of sodium channel gating is modulated by resting potential.
The voltage dependence of inactivation and activation at various holding potentials. On the right is the plot of the voltage dependence of activation over the same range of holding potentials.
As the holding potential becomes more depolarized, the voltage dependence of both inactivation and activation shift to more depolarized potentials.
The voltage dependence of shifts in the midpoint of sodium channel gating. Shown on the left is the plot of the midpoint of fast inactivation versus holding potential.
On the right is the plot of the midpoint of activation versus holding potential. For the number of fibers at each holding potential refer to Table II.
Changes in the voltage dependence of the midpoint of activation K m act and fast inactivation K m inact for sodium channels in muscle fibers at various holding potentials V hold.
During the course of experiments, we noticed that different test potential amplitudes Fig. Similarly, changing the prepulse amplitude Fig. This was unexpected since evidence presented above suggested that shifts in the voltage dependence of activation and inactivation take minutes to occur.
Previously, a dependence of inactivation on the test pulse amplitude was observed during tight seal recording from cardiac myocytes, and the authors suggested this might be due to the presence of populations of sodium channels with differences in the voltage dependence of activation and inactivation Kimitsuki et al.
To further characterize these effects in skeletal muscle we determined the relationships between prepulse and test pulse amplitudes and the voltage dependence of activation and inactivation.
As shown in Fig. Similarly, as more depolarized prepulses were used, the measured voltage dependence of activation shifted toward more depolarized potentials Fig.
These results demonstrate that the measured voltage dependence of activation and inactivation is directly related to the amplitude of prepulses and test pulses used during the protocols.
Evidence presented above indicates that changes in voltage dependence require minutes to occur after changes in holding potential.
Thus, the results shown in Fig. The measured voltage dependence of sodium channel inactivation and activation depends on the pulse protocol used.
A Examples of two pulse protocols used to measure the voltage dependence of fast inactivation. In protocol 1, a depolarized test potential is used that activates all sodium channels.
Thus when prepulses are altered to measure the voltage dependence of fast inactivation, the measured voltage dependence of fast inactivation is affected by all Nav1.
In protocol 2, a more hyperpolarized activation pulse is used that only activates channels that gate at hyperpolarized potentials. In protocol 2, the voltage dependence of inactivation will preferentially measure the voltage dependence of inactivation of sodium channels that have a hyperpolarized voltage dependence of activation.
B Examples of two pulse protocols used to measure the voltage dependence of activation. In protocol 1, a depolarized prepulse preferentially inactivates sodium channels that inactivate at hyperpolarized potentials.
Thus protocol 1 will preferentially measure the voltage dependence of activation of sodium channels that have a depolarized voltage dependence of inactivation.
Protocol 2 will not inactivate any sodium channels so that the voltage dependence of activation includes both sodium channels that inactivate at hyperpolarized potentials and sodium channels that inactivate at depolarized potentials.
Use of more depolarized test pulses yielded more depolarized midpoints of inactivation. As the prepulse becomes increasingly depolarized, the measured voltage dependence of activation shifts toward depolarized potentials.
To study sodium channel gating in skeletal muscle in vivo, we used the loose patch technique to acquire the data presented above.
Loose patch studies have the advantage that they allow study of sodium channel gating in vivo with minimal perturbation of the muscle fiber.
However, loose patch studies in which the holding potential is altered are complicated by changes in the amplitude of the sodium current over time due to changes in the fraction of sodium channels that are slow inactivated.
Since the interior of the muscle fiber is not clamped during loose patch measurement of currents, large inward sodium current can cause depolarization of the fiber and underestimation of the voltage step.
Measures of the voltage dependence of activation, however, could be affected by lack of voltage control of the muscle fiber interior.
To determine whether depolarization of the muscle fiber was shifting our measurements of activation midpoint, we examined the effect of sodium current amplitude on the measured voltage dependence of sodium channel activation.
If an absence of interior voltage control was a contributing factor, we reasoned that patches in which currents were larger should have a more negative voltage dependence of activation.
It thus appears unlikely that lack of voltage control of the muscle fiber interior affected our measures of the voltage dependence of activation.
Holding potential—dependent shifts in sodium channel gating are not due to artifacts of the loose patch technique. There is no correlation between the amplitude of the current and the midpoint of inactivation.
The mean of the data shown is presented in Table II. For data included in Table II the patch with the maximal inward current of 55 nA was discarded. All recordings were performed in solution containing 12 mM potassium.
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