scholarly journals Sodium and potassium conductances in principal neurons of the mouse piriform cortex: a quantitative description

2018 ◽  
Vol 596 (22) ◽  
pp. 5397-5414 ◽  
Author(s):  
Kaori Ikeda ◽  
Norimitsu Suzuki ◽  
John M. Bekkers
Keyword(s):  
Piriform Cortex ◽  
Quantitative Description ◽  
Potassium Conductances ◽  
Sodium And Potassium

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 A quantitative description of the mouse piriform cortex

2017 ◽  
Author(s):  
Shyam Srinivasan ◽  
Charles F Stevens
Keyword(s):  
Piriform Cortex ◽  
Quantitative Description

AbstractIn this report, we provide a quantitative description for 2 aspects of the mouse piriform cortex. First, we give volumetric estimates of regions within the anterior and posterior piriform cortex. Second, we estimate the neuronal densities in each of these regions. From these two estimates, we calculate that the mouse piriform contains around half a million neurons equally distributed over the anterior and posterior piriform cortex. Quantitative descriptions such as these are important because they make it possible to construct realistic models and provide a constraint that theories of the olfactory circuit must fulfil. We show how quantitative descriptions can be useful for modelling by using our data to refine and improve earlier models of piriform cortex activity.

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 Sensitivity of the sodium and potassium channels of Myxicola giant axons to changes in external pH.

1976 ◽  
Vol 67 (2) ◽  
pp. 185-195 ◽  
Author(s):  
C L Schauf ◽  
F A Davis
Keyword(s):  
Giant Axons ◽  
Full Effect ◽  
Activation Rate ◽  
Potassium Conductances ◽  
Negative Surface ◽  
Negative Surface Charge ◽  
Acidic Conditions ◽  
Sodium And Potassium ◽  
Voltage Axis ◽  
External Ph

Myxicola giant axons were studied using standard voltage-clamp techniques in solutions whose pH values ranged from 3.9 to 10.2. Buffer concentrations of 50 mM or greater were necessary to demonstrate the full effect of pH. In acidic solutions the axon underwent a variable depolarization, and both the sodium and potassium conductances were reversibly depressed with approximate pKa's of 4.8 and 4.4, respectively. The voltage dependence of GNa was only slightly altered by acidic conditions, whereas there occurred large shifts in GK along the voltage axis consistent with a substantial decrease in net negative surface charge in the vicinity of the K+ channels. The sodium and potassium activation rate constants were decreased by acidic conditions, but the results could not be described as a simple translation along the voltage axis.

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 A Kinetic Model for the Action of Xylocaine on Receptors for Acetylcholine

1968 ◽  
Vol 52 (1) ◽  
pp. 162-180 ◽  
Author(s):  
A. B. Steinbach
Keyword(s):  
Acetylcholine Receptor ◽  
Kinetic Scheme ◽  
Rate Coefficients ◽  
Analogue Computer ◽  
End Plate ◽  
Rapid Formation ◽  
Potassium Conductances ◽  
Transmembrane Currents ◽  
Sodium And Potassium ◽  
Drug Complex

A kinetic scheme postulating the rapid formation of a partially active acetylcholine-receptor-drug complex from Xylocaine (or a derivative) and the active acetylcholine-receptor complex can account for the effects of Xylocaine and its derivatives at the neuromuscular junction. Transmembrane currents generated by an analogue computer programmed according to the scheme can exactly match end plate currents produced by nerve stimulation in the presence of the drugs. The scheme also accounts for the qualitatively different effects of the drugs on the end plate potential and on responses to iontophoretically applied acetylcholine. The analysis presented is consistent with very rapid reactions between acetylcholine and receptors, characterized by rate coefficients in the range 104 to 106 sec-1. It is based on the hypothesis that the activation of receptors by acetylcholine changes the structure of the receptors and thus their affinity for Xylocaine. The analysis does not require pharmacological separability of sodium and potassium conductances during the end plate current.

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.

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