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.

Equilibrium is very important...but also, when you talk about changing [K]e it is not usually associated with a K flux, rather adding K to the bath (or wherever). There are situations when the accumulation of extracellular K following prolonged activation of K channels can change the local concentrations enough to cause a significant change in EK..situations where there is a barrier to K diffusion (muscle fascia) or maybe a particularly tortuous cell membrane (like a Xenopus oocyte).

Dear Kevin

You are comparing two completely different situations. During repolarization, K+ will go out of cell thus, hyperpolarize the call. However, following an increase in extracellular K+, the K+ ourflux will be decreased (because of a decrease in chemical gradient for K+ ocncentration) and thus the membrane potential will be depolarized. On the other hand, an increase in K+ outflux will hyperpolarize and a decrease in K+ outflux will depolarize the cell. These are one phenomenon in two different situations. In both, the K+ ions trends to reach their equilibriub state.

The amount of K that effluxes from a neuron during the falling phase of an AP is enough to significantly change Vm, but relatively little with respect to the actual ionic concentration gradient. Consider that if you voltage clamp a neuron at a positive voltage for several seconds you will continue to see K exit the cell as an outward current until you hyperpolarize again. That is because even with seconds of outward K efflux, it still doesn't dramatically drive down the gradient. Only a few million ions have to cross the membrane to alter Vm.

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#

To add to the other answers: it is more helpful to think in terms of conductances, when wanting to understand these phenomena. The momentary voltage is (in a simplified version) a weighted sum of the driving forces (differences between the Nernst potentials and the membrane voltage); the weights are the conductances for the ions (based on the permeability). The driving force E(K)-V(m) changes with e.g. changes in extracellular K+ concentration, which then changes the V(m). However, during an action potential, post-synaptic potential etc. the conductances change (not the driving force), which result in the observed and recorded change in membrane voltage. In practice of course also the membrane capacitance comes into play slowing down the voltage change, but it does not change the direction.

The key point to understand the situation is the permeability. If certain ion channel is inactive or deactivated, you can not expect the ion flow cross the member. Under such circumstances, at least for this kind of ion, there won't be potential build up.

The activation of the ion channel is a dynamic procedure, either by ligand or by voltage change, so you can not expect the Goldman-Hodgkin-Katz equation will have a stable value for a certain time span. A lot of subtypes of potassium and sodium channel presented on the cell member, they have different properties. That's why we need a lot of pharmacological tools to dissect ion channel of interests.

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.

Please note that during action potential the permeability for K and permeability for Na are different form that during the resting state. Try to calculate Vm at resting state when PK=40PNa, and next calculate Vm during the beginning of the action potential curve when PNa = 20PK (at this moment Na channel are opening), and go along the entire the curve of the action potential when the relationship between PNa and PK are constantly chaining.

Another way to simplify: K outward flux during the AP or the liking K channels make the membrane more negative in the intra cellular side. While, increase of extra cellular K by external sources reduces the efflux of positive charges making the intra cellular membrane side less negative and more excitable or prone to depolarizing.

In fact, the elevation of potassium concentration in the extracellular space has been shown to be a crucial factor in several types of epilepsy such as status epilepticus the most severe form of epilepsy; potassium lateral diffusion could explain this phase-synchronized state of individual cell activity leading to production of rhythmical activity The mechanism underlying phase synchronization is still unknown. However, it has to involve potassium diffusion coupling. The source of the increasing extracellular potassium is often assumed to be intracellular compartment of glia cells. However, another important source of potassium resides within blood where potassium concentration (5 mM) is higher than that in cerebrospinal fluid (CSF; 2.9 mM). Normally, the blood–brain barrier (BBB) prevents potassium in blood from reaching the brain tissues. A break in the BBB is a possible aetiologic mechanism in epileptogenesis.

I agree with Javad Mirnajafi-Zadeh in both conditions K+ out flux does the same thing: bring the membrane potential to more negative potential ( toward K+ equilibrium potential of K+). In high extracellular K+ condition, the depolarized potential you see is not due to K+ outflux, which still brings the membrane potential but due to high K+, in another word, a positive potential, added to the outside of membrane.

Kevin,

The quick answer to your perceptive question is that during a single action potential the total efflux of potassium ions is only 3-4 picomoles per square centimeter; since the external concentration of potassium ions is, for example, 4 millimolar, the potassium efflux normally has negligible effect upon the potassium concentration in the external solution.

In both conditions K+ out flux does the same thing: bring the membrane potential to more negative potential ( toward K+ equilibrium potential of K+, hyperpolarization). In high extracellular K+ condition, the depolarized potential you see is not due to K+ outflux, which still brings the membrane potential to more negative potential ( toward K+ equilibrium potential of K+, hyperpolarization) but due to high K+, in another word, the positive charges, added to the outside of membrane. In addition, in high extracellular K+ condition, K+ outflux decreases but there is no K+ intflux.

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.

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.

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

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.

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).

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.

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.

Or any first year textbook in physiology

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

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!