Action potential of striated muscle fiber (Adrian et al 1970)

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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 mM 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¡Xvoltage relation, and a mean equilibrium potential with a normal potassium concentration (2¡P5 mM) 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 1/3 and 1/6 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¡P5 to 1 sec at 20¢X 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¡XHuxley 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.
1 . Adrian RH, Chandler WK, Hodgkin AL (1970) Voltage clamp experiments in striated muscle fibres. J Physiol 208:607-44 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Sodium; I Potassium;
Gap Junctions:
Simulation Environment: XPP;
Model Concept(s): Action Potentials;
Implementer(s): Wu, Sheng-Nan [snwu at]; Chen, Chien-Liang;
Search NeuronDB for information about:  I Sodium; I Potassium;
% Model for action potential of skeletal muscle fiber
% Adrian RH, Chandler WK, Hodgkin AL. Voltage clamp experiments in striated muscle
% fibres. J Physiol 208:607-44, 1970.
% implemented by Dr. Sheng-Nan Wu

% Initial values
Initial Vm=-95, Vt=-95, m=0.0, h=1.0, n=0.0

% Stimulus
Param period=200, iStim_mag=3, iStim_beg=1, iStim_dur=0.5
iStim=  iStim_mag * heav(mod(t,period)-iStim_beg) * heav(iStim_beg+iStim_dur-mod(t,period))

% Values of the model parameters
Param gNa_max=1.0, gK_max=0.415, gL_max=0.0024
Param ENa=50.0, EK=-70.0, EL=-95.0, Cm=0.0090, Ct=0.04, Rs=15.0
Param alpha_m_max=0.208
Param beta_m_max=2.081
Param alpha_n_max=0.0229
Param beta_n_max=0.09616
Param alpha_h_max=0.0156
Param beta_h_max=3.382
Param Em=-42.0, En=-40.0, Eh=-41.0
Param v_alpha_m=10.0, v_alpha_h=14.7, v_alpha_n=7.0
Param v_beta_m=18.0, v_beta_h=7.6, v_beta_n=40.0

% Expressions

Ina= (gNa_max * m * m * m * h * (Vm - ENa))
beta_n= (beta_n_max * exp(((En - Vm) / v_beta_n)))
beta_m= (beta_m_max * exp(((Em - Vm) / v_beta_m)))
beta_h= (beta_h_max / (1.0 + exp(((Eh - Vm) / v_beta_h))))
IT= ((Vm - Vt) / Rs)
IL= (gL_max * (Vm - EL))
IK= (gK_max * n * n * n * n * (Vm - EK))
alpha_n= (alpha_n_max * (Vm - En) / (1.0 - exp(((En - Vm) / v_alpha_n))))
alpha_m= (alpha_m_max * (Vm - Em) / (1.0 - exp(((Em - Vm) / v_alpha_m))))
alpha_h= (alpha_h_max * exp(((Eh - Vm) / v_alpha_h)))

% Differential equations 
dVm/dt= ((iStim - (INa + IK + IL + IT)) / Cm)
dm/dt= ((alpha_m * (1.0 - m)) - (beta_m * m))
dh/dt= ((alpha_h * (1.0 - h)) - (beta_h * h))
dn/dt= ((alpha_n * (1.0 - n)) - (beta_n * n))
dVt/dt=((Vm - Vt) / (Rs * Ct))

% Numerical and plotting parameters for xpp
@ meth=Euler, dt=0.01, total=25
@ yp=v, yhi=50, ylo=-110, xlo=0, xhi=25, bounds=5000


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