Nomograms of the Goldman equation

1985 ◽  
Vol 404 (2) ◽  
pp. 178-184 ◽  
Author(s):  
J. P. Ruppersberg ◽  
R. R�del
Keyword(s):  
Goldman Equation

scholarly journals Permeability of the sodium channel in Myxicola to organic cations.

1976 ◽  
Vol 68 (5) ◽  
pp. 551-562 ◽  
Author(s):  
L Binstock
Keyword(s):  
Sodium Channels ◽  
Organic Cation ◽  
Reversal Potential ◽  
Node Of Ranvier ◽  
Ionic Currents ◽  
Giant Axon ◽  
Organic Cations ◽  
Relative Permeabilities ◽  
Potential Control ◽  
Goldman Equation

The relative permeability of sodium channels to organic cations was determined in the Myxicola giant axon. Ionic currents under potential control were measured in seawater and in sodium-free solutions containing the organic cation. The measured reversal potential and the Goldman equation were used to obtain the relative permeabilities. The permeability sequence was found to be: sodium greater than hydroxylamine greater than hydrazine greater than ammonium greater than guanidine greater than formamidine greater than aminoguanidine greater than methylamine. Measurements were also made on sodium and several of the organic cations at different concentrations. The relative permeabilities of the ions were found to be independent of concentration. Qualitatively, the permeability sequence for the Myxicola giant axon was similar to that of the frog node of Ranvier.

scholarly journals Responses of Regularly-Firing Aplysia R3-R13 Neurones to Normoxia and Hypoxia

1983 ◽  
Vol 107 (1) ◽  
pp. 1-8
Author(s):  
PHILIP E. COYER
Keyword(s):  
Steady State ◽  
Membrane Resistance ◽  
Chloride Ions ◽  
Membrane Potentials ◽  
Potassium Ion ◽  
Ion Permeability ◽  
Intracellular Potassium ◽  
Permeability Changes ◽  
Goldman Equation ◽  
Ion Activities

1. Exposure of 10 R3-R13 neurones to a 115-min period of hypoxia resulted in depolarization of their membrane potentials (EM) from a mean of −46.9±3.1 to −20.8±4.4mV (S.E.). 2. Intracellular potassium ion activities (aiK) decreased significantly from 118.9±5.1 to 67.7±8.5mM-K+. This is equivalent to a change in EK from −70.9 mV to −54.5 mV, which is insufficient to account for depolarization of approximately 26 mV. 3. During reoxygenation of the saline surrounding the ganglion, there was a continued depolarization of EM to −11.5 ± 3.2 mV and progressive fall in aiK to 49.2 ± 4.9 mM. 4. Decreases in the membrane slope resistance were also observed in these depolarizing neurones. The depression in resistance remained irreversible for as long as experiments were conducted. 5. Computations of PNa/PK ratios were made using a steady-state calculation. Increases in the PNa/PK ratio from 0.030 to 0.045 were observed during hypoxic depolarization using a modification of the Goldman equation which neglects the contribution of chloride ions. Subsequent depolarization and loss of aiK during reoxygenation elevated this value to 0.183. Whether or not the observed depression of the membrane resistance is linked to a change in either the sodium or potassium ion permeability is unknown. Release of neuro transmitter and related permeability changes cannot be ruled out as an effect of hypoxia.

Relationships Between Chloride Transport and Electrical Potential Differences in Carrot Root Cells

1975 ◽  
Vol 2 (3) ◽  
pp. 301 ◽  
Author(s):  
WJ Cram
Keyword(s):  
Chloride Transport ◽  
Electrical Potential ◽  
External Solution ◽  
Potential Difference ◽  
Electrical Potential Difference ◽  
Cell Potential ◽  
Root Cells ◽  
Goldman Equation ◽  
K Concentration ◽  
Small Change

The Cl- influx across the tonoplast increases at about 3 days after excision, and is inhibited by carbonyl cyanide m-chlorophenylhydrazone in well-washed tissue, while the influx of Cl- across the plasmalemma and the cellular electrical potential difference both remain constant under these conditions. The transport of Cl- within the cell therefore appears not to be electrogenic. When SO42- is substituted for Cl-, keeping the external K+ concentration constant, the cell potential difference (p.d.) increases from - 54 mV in 10 mol m-3 KCl to -65 mV in 5 mol m-� KSO42- if the p.d. were solely a diffusion potential, then substituting SO42- for Cl- would be expected to reduce it. This prediction is based on the Goldman equation with a term for SO42- introduced, and various estimates of the parameters involved. It is therefore suggested that a small part of the p.d. in carrot may be due to the activity of a Cl- pump inwards across the plasmalemma, which is linked either to a larger cation influx or to a larger anion (e.g. OH-) efflux. During accumulation of KCl, the cell p.d. increases slightly, from - 54 mV in the non-loaded cell in 10 mol m-3 KCl to -59 mV in the KCl-loaded cell in 10 mol m-3 KCl. This small change is not inconsistent with the response of the p.d. to changes in external salt concentration. From these results, the electrochemical potential of Cl- in the vacuole is calculated to be greater than in an external solution of 1 mol m-3 KCl by 17 kJ mol-1 in non-loaded tissue and by 23 kJ mol-1 in KCl-loaded tissue. This increase in the gradient opposing Cl- entry is probably not sufficient to account for the fall in the active influx of Cl- during accumulation of KCl.

scholarly journals The Permeability of the Sodium Channel to Metal Cations in Myelinated Nerve

1972 ◽  
Vol 59 (6) ◽  
pp. 637-658 ◽  
Author(s):  
Bertil Hille
Keyword(s):  
Sodium Channels ◽  
Ionic Composition ◽  
Reversal Potential ◽  
Metal Cations ◽  
Ionic Currents ◽  
Giant Axon ◽  
Nerve Fibers ◽  
Myelinated Nerve ◽  
Bathing Medium ◽  
Goldman Equation

The relative permeability of sodium channels to eight metal cations is studied in myelinated nerve fibers. Ionic currents under voltage-clamp conditions are measured in Na-free solutions containing the test ion. Measured reversal potentials and the Goldman equation are used to calculate the permeability sequence: Na+ ≈ Li+ > Tl+ > K+. The ratio PK/PNa is 1/12. The permeabilities to Rb+, Cs+, Ca++, and Mg++ are too small to measure. The permeability ratios agree with observations on the squid giant axon and show that the reversal potential ENa differs significantly from the Nernst potential for Na+ in normal axons. Opening and closing rates for sodium channels are relatively insensitive to the ionic composition of the bathing medium, implying that gating is a structural property of the channel rather than a result of the movement or accumulation of particular ions around the channel. A previously proposed pore model of the channel accommodates the permeant metal cations in a partly hydrated form. The observed sequence of permeabilities follows the order expected for binding to a high field strength anion in Eisenman's theory of ion exchange equilibria.

scholarly journals The Passive Permeability of the Red Blood Cell to Cations

1966 ◽  
Vol 50 (1) ◽  
pp. 171-188 ◽  
Author(s):  
Paul L. LaCelle ◽  
Aser Rothstein
Keyword(s):  
Ionic Strength ◽  
Inflection Point ◽  
Ph Effect ◽  
Human Red Blood Cells ◽  
Low Concentrations ◽  
Goldman Equation ◽  
Low Ionic Strength ◽  
Straight Lines ◽  
The Relationship ◽  
Determining Factor

The efflux of salt from human red blood cells suspended in isotonic sucrose plus low concentrations of salt, was measured under steady-state conditions. The relationship between the efflux and the log of the salt concentration can be fitted by two straight lines with a sharp inflection point, the steeper slope occurring at concentrations below 0.2 mM NaCl. The determining factor in the rate of efflux is the ionic strength rather than the specific monovalent cations or anions and the effects are completely reversible. With an increase in temperature, the effects of reduced ionic strength are more pronounced and the inflection point is shifted toward higher salt concentrations. An increase in pH leads to an increased efflux at a given ionic strength, but the size of the pH effect is small at low ionic strength. At a given pH, the data can be fitted by a simplified form of the Goldman equation suggesting that with reduction in ionic strength, the permeability remains constant until the inflection point is reached. At that ionic strength, a sharp reversible transition to a new permeability state occurs. The permeability increases with an increase in the external but not the internal pH.

scholarly journals Ionic properties of the acetylcholine receptor in cultured rat myotubes.

1975 ◽  
Vol 65 (6) ◽  
pp. 751-767 ◽  
Author(s):  
A K Ritchie ◽  
D M Fambrough
Keyword(s):  
Equivalent Circuit ◽  
Reversal Potential ◽  
Electrical Circuit ◽  
Frog Muscle ◽  
Constant Field ◽  
Adult Rat ◽  
Wide Range ◽  
Goldman Equation ◽  
Alpha Bungarotoxin ◽  
External Ph

The acetylcholine reversal potential (Er) of cultured rat myotubes is -3mV. When activated, the receptor is permeable to K+ and Na+, but not to Cl- ions. Measurement of Er in Tris+-substituted, Na-free medium also indicated a permeability to Tris+ ions. Unlike adult frog muscle the magnitude of Er was insensitive to change in external Ca++ (up to 30 mM) or to changes in external pH (between 6.4 and 8.9). The equivalent circuit equation describing the electrical circuit composed of two parallel ionic batteries (EK and ENa) and their respective conductances (gK and gNa), which has been generally useful in describing the Er of adult rat and frog muscle, could also be applied to rat myotubes when Er was measured over a wide range of external Na+ concentrations. The equivalent circuit equation could not be applied to myotubes bathed in media of different external K+ concentrations. In this case, the Er was more closely described by the Goldman constant field equation. Under certain circumstances, it is known that the receptor in adult rat and frog muscle can be induced to reversibly shift from behavior described by the equivalent circuit equation to that described by the Goldman equation. Attempts to similarly manipulate the responses of cultured rat myotubes were unsussessful. These trials included a reduction in temperature (15 degress C), partial alpha-bungarotoxin blodkade, and activation of responses with the cholinergic agonist, decamethonium.

An upper limit for the electrogenic Na–K pump contribution to maximum diastolic potential in feline cardiac Purkinje fibers in steady state

1986 ◽  
Vol 64 (5) ◽  
pp. 641-648
Author(s):  
Joseph A. Hill Jr. ◽  
Joey L. Trantham ◽  
David J. Browning ◽  
Augustus O. Grant ◽  
Harold C. Strauss
Keyword(s):  
Steady State ◽  
Extracellular Space ◽  
Membrane Conductance ◽  
Initial Increase ◽  
High Concentration ◽  
Control Value ◽  
Upper Limit ◽  
Goldman Equation ◽  
Diastolic Potential ◽  
K Activity

We have estimated an upper limit for the electrogenic contribution of the Na–K pump to diastolic transmembrane potential. We simultaneously monitored the maximum diastolic potential and the extracellular space potassium activity during exposure to a very high concentration of ouabain. Exposure to ouabain caused a depolarization of approximately 3 mV (n = 33 experiments) over 34 ± 3 s (mean ± standard error) prior to any change in extracellular K activity. In four experiments, we monitored intracellular sodium activity and observed it to rise with approximately the same temporal lag (delay = 26 ± 7 s). We also measured relative membrane conductance in one series of experiments and observed it to decrease to 91 ± 2% of its control value by the time extracellular space K began to rise. Following the initial increase in extracellular space K activity the subsequent membrane depolarization is shown to be accurately predicted solely from the measured increase in extracellular space K activity as calculated from the Goldman equation. Limitations of the method and possible interpretations of the data are discussed. We interpret this ouabain-induced depolarization that occurs prior to the rise in external K to be an upper limit to the Na–K pump's electrogenic contribution to steady-state membrane potential.

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