scholarly journals Sodium and potassium conductance changes during a membrane action potential

1970 ◽  
Vol 211 (3) ◽  
pp. 729-751 ◽  
Author(s):  
Francisco Bezanilla ◽  
Eduardo Rojas ◽  
Robert E. Taylor
Keyword(s):  
Action Potential ◽  
Potassium Conductance ◽  
Membrane Action ◽  
Conductance Changes ◽  
Sodium And Potassium

scholarly journals The exponential tracking and disturbance rejection of the propagated membrane action potential with conductance coefficient feedforward controllers

2021 ◽  
Author(s):  
Weijiu Liu
Keyword(s):  
Action Potential ◽  
Disturbance Rejection ◽  
Surface Membrane ◽  
Potassium Conductance ◽  
Initial Condition ◽  
Membrane Action ◽  
Feedback Controllers ◽  
Pde Model ◽  
Potassium Conductances ◽  
Sodium And Potassium

In the early 1950's, using their experimental data, Hodgkin and Huxley constructed the sodium and potassium conductance feedback controllers for their mathematical model of the flow of electric current through the surface membrane of a giant nerve fibre. In this paper, we re-formulate the construction as a problem of exponential tracking and disturbance rejection and then re-construct new conductance feedforward controllers in the more complicated case of a propagated action potential. The dynamics of the potential is governed by the Hodgkin-Huxley's partial differential equation (PDE) model. The problem is solved for any current disturbances and potential references and conductance coefficient feedforward controllers are designed by using the method of variable transform. It is proved that, under the designed feedforward controllers, the potential tracks exponentially a desired potential reference uniformly on an interval of one unit and the reference satisfies the controlled PDE model except an initial condition. A numerical example shows that the simulated action potential and sodium and potassium conductances are close to the experimental observations.

Demonstration of Sodium and Potassium Conductance Changes during a Nerve Action Potential

Nature ◽  
1970 ◽  
Vol 225 (5234) ◽  
pp. 747-748 ◽  
Author(s):  
E. ROJAS ◽  
F. BEZANILLA ◽  
R. E. TAYLOR
Keyword(s):  
Action Potential ◽  
Potassium Conductance ◽  
Nerve Action ◽  
Conductance Changes ◽  
Sodium And Potassium

scholarly journals The exponential tracking and disturbance rejection of the propagated membrane action potential with conductance coefficient feedforward controllers

2021 ◽  
Author(s):  
Weijiu Liu
Keyword(s):  
Action Potential ◽  
Disturbance Rejection ◽  
Surface Membrane ◽  
Potassium Conductance ◽  
Initial Condition ◽  
Membrane Action ◽  
Feedback Controllers ◽  
Pde Model ◽  
Potassium Conductances ◽  
Sodium And Potassium

In the early 1950's, using their experimental data, Hodgkin and Huxley constructed the sodium and potassium conductance feedback controllers for their mathematical model of the flow of electric current through the surface membrane of a giant nerve fibre. In this paper, we re-formulate the construction as a problem of exponential tracking and disturbance rejection and then re-construct new conductance feedforward controllers in the more complicated case of a propagated action potential. The dynamics of the potential is governed by the Hodgkin-Huxley's partial differential equation (PDE) model. The problem is solved for any current disturbances and potential references and conductance coefficient feedforward controllers are designed by using the method of variable transform. It is proved that, under the designed feedforward controllers, the potential tracks exponentially a desired potential reference uniformly on an interval of one unit and the reference satisfies the controlled PDE model except an initial condition. A numerical example shows that the simulated action potential and sodium and potassium conductances are close to the experimental observations.

scholarly journals Competitive Action of Calcium and Procaine on Lobster Axon

1966 ◽  
Vol 49 (5) ◽  
pp. 1043-1063 ◽  
Author(s):  
Mordecai P. Blaustein ◽  
David E. Goldman
Keyword(s):  
Calcium Concentration ◽  
Potassium Conductance ◽  
Membrane Conductance ◽  
Giant Axon ◽  
Sodium Conductance ◽  
Potassium Conductances ◽  
Conductance Changes ◽  
Sodium And Potassium ◽  
External Calcium

Voltage clamp studies with the squid giant axon have shown that changes in the external calcium concentration (Frankenhaeuser and Hodgkin, 1957) shift the sodium and potassium conductance versus membrane potential curves along the potential axis. Taylor (1959) found that procaine acts primarily by reducing the sodium and, to a lesser extent, the potassium conductances. Both procaine and increased calcium also delay the turning on of the sodium conductance mechanism. Calcium and procaine have similar effects on lobster giant axon. In addition, we have observed that the magnitude of the response to procaine is influenced by the external calcium concentration. Increasing external calcium tends to reduce the effectiveness of procaine in decreasing sodium conductance. Conversely, procaine is more effective in reducing the membrane conductance if external calcium is decreased. The amplitude of the nerve action potential reflects these conductance changes in that, for example, reductions in amplitude resulting from the addition of procaine to the medium are partially restored by increasing external calcium, as was first noted by Aceves and Machne (1963). These phenomena suggest that calcium and procaine compete with one another with respect to their actions on the membrane conductance mechanism. The fact that procaine and its analogues compete with calcium for binding to phospholipids in vitro (Feinstein, 1964) suggests that the concept of competitive binding to phospholipids may provide a useful model for interpreting these data.

How Gymnodinium breve red tide toxin(s) produces repetitive firing in squid axons

1977 ◽  
Vol 232 (1) ◽  
pp. 23-29 ◽  
Author(s):  
M. Westerfield ◽  
J. W. Moore ◽  
Y. S. Kim ◽  
G. M. Padilla
Keyword(s):  
Action Potential ◽  
Action Potentials ◽  
Red Tide ◽  
Potassium Conductance ◽  
Giant Axon ◽  
Resting Potential ◽  
Repetitive Firing ◽  
Gymnodinium Breve ◽  
Rate Of Recovery ◽  
Conductance Changes

Partially purified toxin(s), GbTX, extracted from Gymnodinium breve red tide organisms elicits a spontaneous train of action potentials in the squid giant axon. The spikes have a shape similar to that in the normal seawater control except for an increase in the rate of recovery from the afterhyperpolarization. With this more rapid recovery, the membrane potential overshoots the resting potential and threshold, triggers another spike, and thus produces repetitive firing. Voltage-clamp studies revealed that the toxin has no effect on the normal sodium or potassium conductance changes produced by step depolarization. However, consistent with the faster recovery after an action potential, GbTX speeds recovery of the “shut-off” currents to their steady-state values after a depolarization. The most likely mechanism by which the toxin accelerates recovery after an action potential (leading to repetitive firing) is the induction of a small additional inward current which was found to be reduced by prehyperpolarization. This toxin-induced current which speeds recovery is blocked by tetrodotoxin and hence presumably flows through the sodium channel.

scholarly journals Effects of Maximal Sodium and Potassium Conductance on the Stability of Hodgkin-Huxley Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yue Zhang ◽  
Kuanquan Wang ◽  
Yongfeng Yuan ◽  
Dong Sui ◽  
Henggui Zhang
Keyword(s):  
Experimental Data ◽  
Mathematical Method ◽  
Bifurcation Point ◽  
Potassium Conductance ◽  
Maximal Conductance ◽  
Computing Model ◽  
The World ◽  
Stability And Bifurcations ◽  
The Stability ◽  
Sodium And Potassium

Hodgkin-Huxley (HH) equation is the first cell computing model in the world and pioneered the use of model to study electrophysiological problems. The model consists of four differential equations which are based on the experimental data of ion channels. Maximal conductance is an important characteristic of different channels. In this study, mathematical method is used to investigate the importance of maximal sodium conductanceg-Naand maximal potassium conductanceg-K. Applying stability theory, and takingg-Naandg-Kas variables, we analyze the stability and bifurcations of the model. Bifurcations are found when the variables change, and bifurcation points and boundary are also calculated. There is only one bifurcation point wheng-Nais the variable, while there are two points wheng-Kis variable. The (g-Na,  g-K) plane is partitioned into two regions and the upper bifurcation boundary is similar to a line when bothg-Naandg-Kare variables. Numerical simulations illustrate the validity of the analysis. The results obtained could be helpful in studying relevant diseases caused by maximal conductance anomaly.

Dendrotoxin blocks accommodation in frog myelinated axons

1989 ◽  
Vol 62 (1) ◽  
pp. 174-184 ◽  
Author(s):  
M. O. Poulter ◽  
T. Hashiguchi ◽  
A. L. Padjen
Keyword(s):  
Action Potential ◽  
Computer Model ◽  
Action Potentials ◽  
Potassium Conductance ◽  
Constant Stimulus ◽  
Motor Axons ◽  
Myelinated Axons ◽  
Frequency Adaptation ◽  
Potassium Conductances ◽  
Slow Potassium

1. Intracellular microelectrode recordings from large sensory and motor myelinated axons in spinal roots of Rana pipiens were used to study the effects of dendrotoxin (DTX), a specific blocker of a fast activating potassium current (GKf1). 2. Dendrotoxin reduced the ability of myelinated sensory and motor axons to accommodate to a constant stimulus. A depolarizing current step, which normally evoked only one action potential, after dendrotoxin treatment (200-500 nM) produced a train of action potentials. These spike trains lasted 29 +/- 2.8 (SE) ms on average in sensory fibers (n = 18) and 40.2 +/- 4.5 ms in motor fibers (n = 9). 3. After dendrotoxin treatment, in addition to a reduction in the ability to accommodate to a constant stimulus, a slowing in the rate of action potential generation was evident (spike frequency adaptation). 4. Dendrotoxin had no effect on the rising phase of conducted action potentials evoked by peripheral stimulation. Together with a lack of effect on the absolute refractory period, these results indicate that dendrotoxin does not affect sodium channel activity. 5. The steady-state voltage/current relationship was unchanged in response to hyperpolarizing current pulses; however, there was a significant increase in cord resistance in response to depolarizing current steps, demonstrating that DTX decreases outward rectification. 6. A computer model based on Hodgkin and Huxley equations was developed, which included the three voltage-dependent potassium conductances described by Dubois. The model reproduced major experimental results: removal of the conductance, termed GKf1, reduced the accommodation in the early phase of a continuous stimulus, indicating that this current could be responsible for the early accommodation. The hypothesis that the slow potassium conductance GKs regulates late accommodation and action potential frequency adaptation is also supported by the computer model. 7. In summary, these results suggest that in amphibian myelinated sensory and motor axons, the activity of potassium conductances can account for accommodation and adaptation without involvement of sodium conductance activity.

Multiple potassium conductances and their role in action potential repolarization and repetitive firing behavior of neonatal rat hypoglossal motoneurons

1993 ◽  
Vol 69 (6) ◽  
pp. 2150-2163 ◽  
Author(s):  
F. Viana ◽  
D. A. Bayliss ◽  
A. J. Berger
Keyword(s):  
Action Potential ◽  
Calcium Influx ◽  
Potassium Conductance ◽  
Firing Frequency ◽  
Neonatal Rat ◽  
Repetitive Firing ◽  
Firing Behavior ◽  
Hypoglossal Motoneurons ◽  
Potassium Conductances ◽  
Action Potential Repolarization

1. The role of multiple potassium conductances in action potential repolarization and repetitive firing behavior of hypoglossal motoneurons was investigated using intracellular recording techniques in a brain stem slice preparation of the neonatal rat (0-15 days old). 2. The action potential was followed by two distinct afterhyperpolarizations (AHPs). The early one was of short duration and is termed the fAHP; the later AHP was of longer duration and is termed the mAHP. The amplitudes of both AHPs were enhanced by membrane potential depolarization (further from EK). In addition, their amplitudes were reduced by high extracellular K+ concentration, suggesting that activation of potassium conductances underlies both phases of the AHP. 3. Prolongation of the action potential and blockade of the fAHP were observed after application of 1) tetraethylammonium (TEA) (1-10 mM) and 2) 4-aminopyridine (4-AP) (0.1-0.5 mM). Calcium channel blockers had little or no effect on the fAHP or action potential duration. 4. The size of the mAHP was diminished by 1) manganese, 2) lowering external Ca2+, 3) apamin, and 4) intracellular injection of ethylene glycol-bis(beta-aminoethyl ether)-N,N,N',N'-tetraacetic acid (EGTA) suggesting that influx of calcium activates the potassium conductance that underlies the mAHP. 5. The mAHP was unaffected by nifedipine (20 microM), but was strongly reduced by focal application of omega-conotoxin GVIA, suggesting that N-type calcium channels represent the major calcium influx pathway for activation of the calcium-dependent K+ conductance underlying the mAHP. 6. Repetitive firing properties were investigated by injecting long-duration depolarizing current pulses. Steady-state firing rose linearly with injected current amplitude. The slope of the firing frequency-current (f-I) relationship averaged approximately 30 Hz/nA in control conditions. Blockade of the conductance underlying the mAHP caused a marked increase in the minimal repetitive firing frequency and in the slope of the f-I plot, indicating a prominent role for the conductance underlying the mAHP in controlling repetitive firing behavior. 7. We conclude that action potential repolarization and AHPs are due to activation of pharmacologically distinct potassium conductances. Whereas repolarization of the action potential and the fAHP involves primarily a voltage-dependent, calcium-independent potassium conductance that is TEA- and 4-AP-sensitive, the mAHP requires the influx of extracellular calcium and is apamin sensitive. Activation of the calcium-activated potassium conductance greatly influences the normal repetitive firing of neonatal hypoglossal motoneurons.

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