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 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 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

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.

scholarly journals A Mathematical Model for the Cardiac Action Potential Based on Slow Inactivation of Sodium Conductance

1968 ◽  
Vol 21 (1) ◽  
pp. 37 ◽  
Author(s):  
L Munk ◽  
E PGeorge
Keyword(s):  
Mathematical Model ◽  
Action Potential ◽  
Action Potentials ◽  
Sodium Current ◽  
Potassium Conductance ◽  
Slow Inactivation ◽  
Squid Axon ◽  
Purkinje Fibres ◽  
Cardiac Action ◽  
Potassium Conductances

A mathematical model for the action potential in Purkinje fibres is developed. It is based on voltage-clamp results which show that inactivation of sodium current in these muscles is much slower than in squid axon and that the latent rise in potassium conductance is not present. Both the sodium and the potassium conductances are represented as a sum of slow and fast components. This is incorporated in the suitably adjusted Hodgkin-Huxley model for the squid axon. It is shown that such a model can account satisfactorily for the shape of the action potentials in Purkinje fibres.

scholarly journals Quantitative Description of Sodium and Potassium Currents and Computed Action Potentials in Myxicola Giant Axons

1973 ◽  
Vol 61 (3) ◽  
pp. 361-384 ◽  
Author(s):  
L. Goldman ◽  
C. L. Schauf
Keyword(s):  
Action Potentials ◽  
Initial Conditions ◽  
Sodium Current ◽  
Quantitative Description ◽  
Potassium Conductance ◽  
Giant Axons ◽  
Sodium Conductance ◽  
Potassium Conductances ◽  
The Right ◽  
Sodium And Potassium

All analysis of the sodium and potassium conductances of Myxicola giant axons was made in terms of the Hodgkin-Huxley m, n, and h variables. The potassium conductance is proportional to n2. In the presence of conditioning hyperpolarization, the delayed current translates to the right along the time axis. When this effect was about saturated, the potassium conductance was proportional to n3. The sodium conductance was described by assuming it proportional to m3h. There is a range of potentials for which τh and h∞ values fitted to the decay of the sodium conductance may be compared to those determined from the effects of conditioning pulses. τh values determined by the two methods do not agree. A comparison of h∞ values determined by the two methods indicated that the inactivation of the sodium current is not governed by the Hodgkin-Huxley h variable. Computer simulations show that action potentials, threshold, and subthreshold behavior could be accounted for without reference to data on the effects of initial conditions. However, recovery phenomena (refractoriness, repetitive discharges) could be accounted for only by reference to such data. It was concluded that the sodium conductance is not governed by the product of two independent first order variables.

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.

scholarly journals Propagation of action potentials in squid giant axons. Repetitive firing at regions of membrane inhomogeneities.

1979 ◽  
Vol 73 (5) ◽  
pp. 595-603 ◽  
Author(s):  
F Ramón ◽  
J W Moore
Keyword(s):  
Action Potentials ◽  
Potassium Conductance ◽  
Electric Activity ◽  
Repetitive Firing ◽  
Prolonged Action ◽  
Membrane Action ◽  
Duration Of Action ◽  
Giant Axons ◽  
Complex Interactions ◽  
Potassium Conductances

Effects of reduction in potassium conductance on impulse conduction were studied in squid giant axons. Internal perfusion of axons with tetraethylammonium (TEA) ions reduces G K and causes the duration of action potential to be increased up to 300 ms. This prolongation of action potentials does not change their conduction velocity. The shape of these propagating action potentials is similar to membrane action potentials in TEA. Axons with regions of differing membrane potassium conductances are obtained by perfusing the axon trunk and one of its two main branches with TEA after the second branch has been filled with normal perfusing solution. Although the latter is initially free of TEA, this ion diffuses in slowly. Up until a large amount of TEA has diffused into the second branch, action potentials in the two branches have very different durations. During this period, membrane regions with prolonged action potentials are a source of depolarizing current for the other, and repetitive activity may be initiated at transitional regions. After a single stimulus in either axon region, interactions between action potentials of different durations usually led to rebound, or a short burst, of action potentials. Complex interactions between two axon regions whose action potentials have different durations resembles electric activity recorded during some cardiac arrhythmias.

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 Effect of Ethanol on the Sodium and Potassium Conductances of the Squid Axon Membrane

1964 ◽  
Vol 48 (2) ◽  
pp. 279-295 ◽  
Author(s):  
John W. Moore ◽  
Werner Ulbricht ◽  
Mitsuru Takata
Keyword(s):  
Time Course ◽  
Sea Water ◽  
Squid Axon ◽  
Membrane Action ◽  
Axon Membrane ◽  
Gap Technique ◽  
Potassium Conductances ◽  
Steady State Inactivation ◽  
Sucrose Gap ◽  
Sodium And Potassium

The effects of ethanol on squid giant axons were studied by means of the sucrose-gap technique. The membrane action potential height is moderately reduced and the duration sometimes shortened by ethanol in sea water. Voltage clamp experiments showed that ethanol in sea water reduced the maximum membrane conductances for sodium (g'Na) and potassium (g'K). In experiments with multiple application of ethyl alcohol to the same spot of membrane, a reduction of g'Na to 82 per cent and of g'K to 80 per cent of their value in sea water was brought about by 3 per cent ethanol (by volume) while 6 per cent caused a decrease of g'Na to 59 per cent and of g'K to 69 per cent. Ethanol has no significant effect on the steady-state inactivation of gNa (as a function of conditioning membrane potential) or on such kinetic parameters as τh or the time course of turning on gi gNa and gK. It is concluded that ethanol mainly reduces gNa and gK in the Hodgkin-Huxley terminology.

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