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Concept conflicts in the Goldman-Hodgkin-Katz equation and action...
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Adrian Hum
Concept conflicts in the Goldman-Hodgkin-Katz equation and action...
Hi, In the GHK equation, it is assumed the Electric field reamains constant. Thus, during an AP, we get gNa and gk that are positive but K is leaving the cell when Na is entering the cell. You get POSITIVE ions that go in reverse directions in a CONSTANT ELECTRIC field. Positive ions in a constant field go in the SAME direction. There is a flaw in the theory!
Hi, In the GHK equation, it is assumed the Electric field reamains constant. Thus, during an AP, we get gNa and gk that are positive but K is leaving the cell when Na is entering the cell. You get POSITIVE ions that go in reverse directions in a CONSTANT ELECTRIC field. Positive ions in a constant field go in the SAME direction. There is a flaw in the theory!
No, the *resting* (but not the actual) membrane potential changes instantaneously when changing the concentrations and thereby Nernst potentials of either or both of K+ and Cl-. Sorry, Angelo, but your explanation is at least confusing.
No, the *resting* (but not the actual) membrane potential changes instantaneously when changing the concentrations and thereby Nernst potentials of either or both of K+ and Cl-. Sorry, Angelo, but your explanation is at least confusing.
Hey Marco, how are you? That idea is common, but perhaps only true for giant squid axons. Based on the estimations of Attwell et al. 2012 http://www.ncbi.nlm.nih.gov/pubmed/22434069 of potassium release and concomitant energy expenditure in rodents, I calculated that a single action potential typically increases the extracellular potassium concentration by 1 mM. (section 2.3 of my thesis).
These are rough estimates, and there is very good potassium homeostasis in the brain, but still it shows that this is not a small effect.
Hey Marco, how are you? That idea is common, but perhaps only true for giant squid axons. Based on the estimations of Attwell et al. 2012 http://www.ncbi.nlm.nih.gov/pubmed/22434069 of potassium release and concomitant energy expenditure in rodents, I calculated that a single action potential typically increases the extracellular potassium concentration by 1 mM. (section 2.3 of my thesis).
These are rough estimates, and there is very good potassium homeostasis in the brain, but still it shows that this is not a small effect.
If the above have not helped, I think I can simplify. Opening K channels does not hyper polarize or depolarize per se. It drives the membrane toward Ek (the Nernst potential for K). When [K] in and out are normal, this potential (Ek) is quite negative. When extracellular [K] rises, Ek also becomes somewhat more positive.
If the above have not helped, I think I can simplify. Opening K channels does not hyper polarize or depolarize per se. It drives the membrane toward Ek (the Nernst potential for K). When [K] in and out are normal, this potential (Ek) is quite negative. When extracellular [K] rises, Ek also becomes somewhat more positive.
Dear Kevin, I hope I understood your question. At rest conditions, the permeability to K+ is already high, so the the resting membrane potential (RMP: -70 mV c.a.) is very close to the Ke (Nernst potential for K: -90mV c.a.). So, at rest, you have a slow but continuous efflux of K+, due to the high permeability and to the low electrochemical force. This efflux is continuously compensated by the action of the Na/K ATPase pumps. During the action potential, the permeability to Na+ increases explosively and, as quickly, it decreases because of the very fast deactivation kinetics of Na+. This results in the Vm depolarisation towards the Nae (Nernst potential for Na: +50 mV c.a.). More slowly, voltage gated potassium conductances are activated, generating an outward current which compensates the depolarization: the electrochemical force generating this current gets stronger as the Vm is depolarised. In all this, the Nae and the Ke don't change and the intracellular and extracellular concentrations of Na+ and K+ DO NOT CHANGE significantly and the driving force generating Na and K currents keeps being intact, thanks to the continuous action of Na/K pump and of the quick activation/deactivation kinetics of Nav and Kav. For this reason, after the deactivation of Navs, the slower massive outward K current drives the Vm back towards Ke (i.e. -90), which tends to be reached during the AHP phase, when the Kavs are still not fully de-activated.
The Goldman equation is there to describe how to predict the Vm starting from internal and external ion concentrations and respective permeability of the membrane to that ion.
During an action potential, the membrane permeability to K and Na changes in time. So, the goldman equation keeps being valid at each point, in time, but considering that the permeability to the ions (not the concentrations) constantly changing during the spike it is not the best model to describe the Vm change during the AP. A better way to think about it is to think about the Nerst potential for each ion: as the permeability to that ion increases, the Vm will tend to the Nernst potential for that ion. Here there is a nice scheme that might help you to figure it out.
Dear Kevin, I hope I understood your question. At rest conditions, the permeability to K+ is already high, so the the resting membrane potential (RMP: -70 mV c.a.) is very close to the Ke (Nernst potential for K: -90mV c.a.). So, at rest, you have a slow but continuous efflux of K+, due to the high permeability and to the low electrochemical force. This efflux is continuously compensated by the action of the Na/K ATPase pumps. During the action potential, the permeability to Na+ increases explosively and, as quickly, it decreases because of the very fast deactivation kinetics of Na+. This results in the Vm depolarisation towards the Nae (Nernst potential for Na: +50 mV c.a.). More slowly, voltage gated potassium conductances are activated, generating an outward current which compensates the depolarization: the electrochemical force generating this current gets stronger as the Vm is depolarised. In all this, the Nae and the Ke don't change and the intracellular and extracellular concentrations of Na+ and K+ DO NOT CHANGE significantly and the driving force generating Na and K currents keeps being intact, thanks to the continuous action of Na/K pump and of the quick activation/deactivation kinetics of Nav and Kav. For this reason, after the deactivation of Navs, the slower massive outward K current drives the Vm back towards Ke (i.e. -90), which tends to be reached during the AHP phase, when the Kavs are still not fully de-activated.
The Goldman equation is there to describe how to predict the Vm starting from internal and external ion concentrations and respective permeability of the membrane to that ion.
During an action potential, the membrane permeability to K and Na changes in time. So, the goldman equation keeps being valid at each point, in time, but considering that the permeability to the ions (not the concentrations) constantly changing during the spike it is not the best model to describe the Vm change during the AP. A better way to think about it is to think about the Nerst potential for each ion: as the permeability to that ion increases, the Vm will tend to the Nernst potential for that ion. Here there is a nice scheme that might help you to figure it out.
Dear Kevin: You might find your answer by looking at Chapter 4 "Action Potentials" in Plonsey R. and Barr R.C. Bioelectricity: A Quantitative Approach. Second Edition. New York, NY: Kluwer Academic - Plenum Publishers, 2000. Particularly, look at the Sodium and Potassium currents - they reflect the changes in the conductances, and hence, the permeabilities of the two ions during the action potential. You may then apply derived values of permeabilities to the GHK equation.
Dear Kevin: You might find your answer by looking at Chapter 4 "Action Potentials" in Plonsey R. and Barr R.C. Bioelectricity: A Quantitative Approach. Second Edition. New York, NY: Kluwer Academic - Plenum Publishers, 2000. Particularly, look at the Sodium and Potassium currents - they reflect the changes in the conductances, and hence, the permeabilities of the two ions during the action potential. You may then apply derived values of permeabilities to the GHK equation.
The membrane potential does not change instantaneous upon adding extracellular KCl, but the resting (equilibrium) potential does (assuming the time for the KCl to distribute in the ECS is small). Since the reversal potentials change, the currents change and so the membrane potential moves towards the new resting potential.
The membrane potential does not change instantaneous upon adding extracellular KCl, but the resting (equilibrium) potential does (assuming the time for the KCl to distribute in the ECS is small). Since the reversal potentials change, the currents change and so the membrane potential moves towards the new resting potential.
In addition to the links and thoughtful discussion, a simple diagram of changes in conductance during the action potential can be useful as a visual reminder. It is the changes in these currents from "rest" that are particularly informative, as a simple model of the relative change in ionic currents being integrated accounts for the basic phenomenon. It may be entertaining to keep in mind, that Hodgkin-Huxley performed empirical fitting to arrive at the equations for the giant squid axon.
In addition to the links and thoughtful discussion, a simple diagram of changes in conductance during the action potential can be useful as a visual reminder. It is the changes in these currents from "rest" that are particularly informative, as a simple model of the relative change in ionic currents being integrated accounts for the basic phenomenon. It may be entertaining to keep in mind, that Hodgkin-Huxley performed empirical fitting to arrive at the equations for the giant squid axon.
APs are unlikely to change de concentrations of K, and also, during an AP the flux for K tends to move the membrane potential toward the Nernst potential for K (decrease for the most part).
APs are unlikely to change de concentrations of K, and also, during an AP the flux for K tends to move the membrane potential toward the Nernst potential for K (decrease for the most part).
Indeed, a potassium current induces a hyperpolarization. A prolonged potassium current is needed to change the extracellular concentration. Note that a prolonged current can only take place when it is balanced by an inward sodium flux, (or outward chlorine flux). In both cases, the nett current is approximately zero (else charge neutrality would be violated, or the membrane voltage would go extremely high/low). The resting membrane voltage slowly depolarizes however, because the Nernst/reversal potentials change.
This change in extracellular potassium plays a major role in epilepsy and cortical spreading depression. This is modeled and explained in e.g.
Indeed, a potassium current induces a hyperpolarization. A prolonged potassium current is needed to change the extracellular concentration. Note that a prolonged current can only take place when it is balanced by an inward sodium flux, (or outward chlorine flux). In both cases, the nett current is approximately zero (else charge neutrality would be violated, or the membrane voltage would go extremely high/low). The resting membrane voltage slowly depolarizes however, because the Nernst/reversal potentials change.
This change in extracellular potassium plays a major role in epilepsy and cortical spreading depression. This is modeled and explained in e.g.
There is always a confusion thinking on AP. During AP the concentration of the key ions (Na+ and K+) on the cytoplasmic and the extracellular sides of the membrane does not change very much. This is actually very important because it allows fast repolarisation and repetitive AP. During AP what change is the possibility of the ion to move through the membrane, which is refered to as permeability coefficient. This coefficient (for each ion) changes very much because the open probability of the ion channels increase. Using the Goldman equation to calculate the membrane potential during the AP, it is not necessary to consider changes in the concentration of the ions. one considers only the changes in the permeability. This is a very beautiful consideration of the membrane and the Goldman equation.
There is always a confusion thinking on AP. During AP the concentration of the key ions (Na+ and K+) on the cytoplasmic and the extracellular sides of the membrane does not change very much. This is actually very important because it allows fast repolarisation and repetitive AP. During AP what change is the possibility of the ion to move through the membrane, which is refered to as permeability coefficient. This coefficient (for each ion) changes very much because the open probability of the ion channels increase. Using the Goldman equation to calculate the membrane potential during the AP, it is not necessary to consider changes in the concentration of the ions. one considers only the changes in the permeability. This is a very beautiful consideration of the membrane and the Goldman equation.
Hi,
In the GHK equation, it is assumed the Electric field reamains constant.
Thus, during an AP, we get gNa and gk that are positive but K is leaving the cell when Na is entering the cell.
You get POSITIVE ions that go in reverse directions in a CONSTANT ELECTRIC field.
Positive ions in a constant field go in the SAME direction.
There is a flaw in the theory!
Hi,
In the GHK equation, it is assumed the Electric field reamains constant.
Thus, during an AP, we get gNa and gk that are positive but K is leaving the cell when Na is entering the cell.
You get POSITIVE ions that go in reverse directions in a CONSTANT ELECTRIC field.
Positive ions in a constant field go in the SAME direction.
There is a flaw in the theory!
More
VOTE
No, the *resting* (but not the actual) membrane potential changes instantaneously when changing the concentrations and thereby Nernst potentials of either or both of K+ and Cl-. Sorry, Angelo, but your explanation is at least confusing.
No, the *resting* (but not the actual) membrane potential changes instantaneously when changing the concentrations and thereby Nernst potentials of either or both of K+ and Cl-. Sorry, Angelo, but your explanation is at least confusing.
More
VOTE
Hey Marco, how are you? That idea is common, but perhaps only true for giant squid axons. Based on the estimations of Attwell et al. 2012 http://www.ncbi.nlm.nih.gov/pubmed/22434069 of potassium release and concomitant energy expenditure in rodents, I calculated that a single action potential typically increases the extracellular potassium concentration by 1 mM. (section 2.3 of my thesis).
These are rough estimates, and there is very good potassium homeostasis in the brain, but still it shows that this is not a small effect.
Hey Marco, how are you? That idea is common, but perhaps only true for giant squid axons. Based on the estimations of Attwell et al. 2012 http://www.ncbi.nlm.nih.gov/pubmed/22434069 of potassium release and concomitant energy expenditure in rodents, I calculated that a single action potential typically increases the extracellular potassium concentration by 1 mM. (section 2.3 of my thesis).
These are rough estimates, and there is very good potassium homeostasis in the brain, but still it shows that this is not a small effect.
More
VOTE
If the above have not helped, I think I can simplify. Opening K channels does not hyper polarize or depolarize per se. It drives the membrane toward Ek (the Nernst potential for K). When [K] in and out are normal, this potential (Ek) is quite negative. When extracellular [K] rises, Ek also becomes somewhat more positive.
If the above have not helped, I think I can simplify. Opening K channels does not hyper polarize or depolarize per se. It drives the membrane toward Ek (the Nernst potential for K). When [K] in and out are normal, this potential (Ek) is quite negative. When extracellular [K] rises, Ek also becomes somewhat more positive.
More
VOTE
Dear Kevin, I hope I understood your question. At rest conditions, the permeability to K+ is already high, so the the resting membrane potential (RMP: -70 mV c.a.) is very close to the Ke (Nernst potential for K: -90mV c.a.). So, at rest, you have a slow but continuous efflux of K+, due to the high permeability and to the low electrochemical force. This efflux is continuously compensated by the action of the Na/K ATPase pumps. During the action potential, the permeability to Na+ increases explosively and, as quickly, it decreases because of the very fast deactivation kinetics of Na+. This results in the Vm depolarisation towards the Nae (Nernst potential for Na: +50 mV c.a.). More slowly, voltage gated potassium conductances are activated, generating an outward current which compensates the depolarization: the electrochemical force generating this current gets stronger as the Vm is depolarised. In all this, the Nae and the Ke don't change and the intracellular and extracellular concentrations of Na+ and K+ DO NOT CHANGE significantly and the driving force generating Na and K currents keeps being intact, thanks to the continuous action of Na/K pump and of the quick activation/deactivation kinetics of Nav and Kav. For this reason, after the deactivation of Navs, the slower massive outward K current drives the Vm back towards Ke (i.e. -90), which tends to be reached during the AHP phase, when the Kavs are still not fully de-activated.
The Goldman equation is there to describe how to predict the Vm starting from internal and external ion concentrations and respective permeability of the membrane to that ion.
During an action potential, the membrane permeability to K and Na changes in time. So, the goldman equation keeps being valid at each point, in time, but considering that the permeability to the ions (not the concentrations) constantly changing during the spike it is not the best model to describe the Vm change during the AP. A better way to think about it is to think about the Nerst potential for each ion: as the permeability to that ion increases, the Vm will tend to the Nernst potential for that ion. Here there is a nice scheme that might help you to figure it out.
http://mathbench.umd.edu/modules/cell-processes_nernst-potential/page17.htm#
Dear Kevin, I hope I understood your question. At rest conditions, the permeability to K+ is already high, so the the resting membrane potential (RMP: -70 mV c.a.) is very close to the Ke (Nernst potential for K: -90mV c.a.). So, at rest, you have a slow but continuous efflux of K+, due to the high permeability and to the low electrochemical force. This efflux is continuously compensated by the action of the Na/K ATPase pumps. During the action potential, the permeability to Na+ increases explosively and, as quickly, it decreases because of the very fast deactivation kinetics of Na+. This results in the Vm depolarisation towards the Nae (Nernst potential for Na: +50 mV c.a.). More slowly, voltage gated potassium conductances are activated, generating an outward current which compensates the depolarization: the electrochemical force generating this current gets stronger as the Vm is depolarised. In all this, the Nae and the Ke don't change and the intracellular and extracellular concentrations of Na+ and K+ DO NOT CHANGE significantly and the driving force generating Na and K currents keeps being intact, thanks to the continuous action of Na/K pump and of the quick activation/deactivation kinetics of Nav and Kav. For this reason, after the deactivation of Navs, the slower massive outward K current drives the Vm back towards Ke (i.e. -90), which tends to be reached during the AHP phase, when the Kavs are still not fully de-activated.
The Goldman equation is there to describe how to predict the Vm starting from internal and external ion concentrations and respective permeability of the membrane to that ion.
During an action potential, the membrane permeability to K and Na changes in time. So, the goldman equation keeps being valid at each point, in time, but considering that the permeability to the ions (not the concentrations) constantly changing during the spike it is not the best model to describe the Vm change during the AP. A better way to think about it is to think about the Nerst potential for each ion: as the permeability to that ion increases, the Vm will tend to the Nernst potential for that ion. Here there is a nice scheme that might help you to figure it out.
http://mathbench.umd.edu/modules/cell-processes_nernst-potential/page17.htm#
More
VOTE
Dear Kevin:
You might find your answer by looking at Chapter 4 "Action Potentials" in Plonsey R. and Barr R.C. Bioelectricity: A Quantitative Approach. Second Edition. New York, NY: Kluwer Academic - Plenum Publishers, 2000.
Particularly, look at the Sodium and Potassium currents - they reflect the changes in the conductances, and hence, the permeabilities of the two ions during the action potential. You may then apply derived values of permeabilities to the GHK equation.
Dear Kevin:
You might find your answer by looking at Chapter 4 "Action Potentials" in Plonsey R. and Barr R.C. Bioelectricity: A Quantitative Approach. Second Edition. New York, NY: Kluwer Academic - Plenum Publishers, 2000.
Particularly, look at the Sodium and Potassium currents - they reflect the changes in the conductances, and hence, the permeabilities of the two ions during the action potential. You may then apply derived values of permeabilities to the GHK equation.
More
VOTE
The membrane potential does not change instantaneous upon adding extracellular KCl, but the resting (equilibrium) potential does (assuming the time for the KCl to distribute in the ECS is small). Since the reversal potentials change, the currents change and so the membrane potential moves towards the new resting potential.
The membrane potential does not change instantaneous upon adding extracellular KCl, but the resting (equilibrium) potential does (assuming the time for the KCl to distribute in the ECS is small). Since the reversal potentials change, the currents change and so the membrane potential moves towards the new resting potential.
More
VOTE
In addition to the links and thoughtful discussion, a simple diagram of changes in conductance during the action potential can be useful as a visual reminder. It is the changes in these currents from "rest" that are particularly informative, as a simple model of the relative change in ionic currents being integrated accounts for the basic phenomenon. It may be entertaining to keep in mind, that Hodgkin-Huxley performed empirical fitting to arrive at the equations for the giant squid axon.
http://www.bio.miami.edu/tom/courses/bil255/bil255goods/action_potential.html
In addition to the links and thoughtful discussion, a simple diagram of changes in conductance during the action potential can be useful as a visual reminder. It is the changes in these currents from "rest" that are particularly informative, as a simple model of the relative change in ionic currents being integrated accounts for the basic phenomenon. It may be entertaining to keep in mind, that Hodgkin-Huxley performed empirical fitting to arrive at the equations for the giant squid axon.
http://www.bio.miami.edu/tom/courses/bil255/bil255goods/action_potential.html
More
VOTE
APs are unlikely to change de concentrations of K, and also, during an AP the flux for K tends to move the membrane potential toward the Nernst potential for K (decrease for the most part).
APs are unlikely to change de concentrations of K, and also, during an AP the flux for K tends to move the membrane potential toward the Nernst potential for K (decrease for the most part).
More
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Or any first year textbook in physiology
Or any first year textbook in physiology
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Indeed, a potassium current induces a hyperpolarization. A prolonged potassium current is needed to change the extracellular concentration. Note that a prolonged current can only take place when it is balanced by an inward sodium flux, (or outward chlorine flux). In both cases, the nett current is approximately zero (else charge neutrality would be violated, or the membrane voltage would go extremely high/low). The resting membrane voltage slowly depolarizes however, because the Nernst/reversal potentials change.
This change in extracellular potassium plays a major role in epilepsy and cortical spreading depression. This is modeled and explained in e.g.
Kager, Wadman, Somjen 2000: http://biomedphys.sgu.ru/TMP/CSD_literature/Kager_2000.pdf
Cressman et al. 2009: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2704057/
Zandt et al. 2011: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0022127
Indeed, a potassium current induces a hyperpolarization. A prolonged potassium current is needed to change the extracellular concentration. Note that a prolonged current can only take place when it is balanced by an inward sodium flux, (or outward chlorine flux). In both cases, the nett current is approximately zero (else charge neutrality would be violated, or the membrane voltage would go extremely high/low). The resting membrane voltage slowly depolarizes however, because the Nernst/reversal potentials change.
This change in extracellular potassium plays a major role in epilepsy and cortical spreading depression. This is modeled and explained in e.g.
Kager, Wadman, Somjen 2000: http://biomedphys.sgu.ru/TMP/CSD_literature/Kager_2000.pdf
Cressman et al. 2009: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2704057/
Zandt et al. 2011: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0022127
More
VOTE
There is always a confusion thinking on AP. During AP the concentration of the key ions (Na+ and K+) on the cytoplasmic and the extracellular sides of the membrane does not change very much. This is actually very important because it allows fast repolarisation and repetitive AP. During AP what change is the possibility of the ion to move through the membrane, which is refered to as permeability coefficient. This coefficient (for each ion) changes very much because the open probability of the ion channels increase. Using the Goldman equation to calculate the membrane potential during the AP, it is not necessary to consider changes in the concentration of the ions. one considers only the changes in the permeability. This is a very beautiful consideration of the membrane and the Goldman equation.
There is always a confusion thinking on AP. During AP the concentration of the key ions (Na+ and K+) on the cytoplasmic and the extracellular sides of the membrane does not change very much. This is actually very important because it allows fast repolarisation and repetitive AP. During AP what change is the possibility of the ion to move through the membrane, which is refered to as permeability coefficient. This coefficient (for each ion) changes very much because the open probability of the ion channels increase. Using the Goldman equation to calculate the membrane potential during the AP, it is not necessary to consider changes in the concentration of the ions. one considers only the changes in the permeability. This is a very beautiful consideration of the membrane and the Goldman equation.
More
VOTE