Extracellular potassium increase

[Function]

Hi everyone

 

I was once again wondering something about an extracellular potassium increase.

Of course, at the very moment of the injection, it's quite obvious that the influenced cells (or their membrane potential) are being hyperpolarized - they are, to say, relatively getting more negatively charged in comparison to their surrounding.

 

However, great Goldman teaches us that after a new equilibrium has been reached, the cells will, compared to the initial situation without the potassium increase, be depolarized.

 

My question is thus: how is this equilibrium exactly reached and how so is the resting membrane potential more positive, compared relatively to the initial situation?

 

I'm afraid this isn't quite explained in my textbook physiology (a small textbook written by my professor in physiology to teach us the basic mechanics of this wonderful discipline).

 

Thanks!

 

F.

 

EDIT: how long would it generally take a membrane potential to, considering an injection of x mL K:

• Go from momentarily hyperpolarization to the initial resting membrane potential?
• Go from the initial resting membrane potential to the long-term depolarization?

Edited June 26, 2015 by Function

[CPG]

Your question is confusing and not very specific, making it difficult to provide a direct answer. What are we injecting K+ into? Intracellularly or to the extracellular environment (blood, artificial physiological saline, etc)? If it's the extracellular environment, what is the concentration of the K⁺ solution you are adding? What is the volume of the solution to which you are adding it... etc. Perhaps I'm not understanding correctly but I fail to see why cells would hyperpolarize at the moment of injection. Help me out here, and I can probably clear up some confusion.

Regardless of the specifics, this should help with a general understanding that should help:

 

Start by examining the Nernst Potential. This allows you to predict the equilibrium potential (membrane potential at equilibrium, also called Reversal Potential) for a single type of ion: in this case, K⁺. This equation is based on the relevant biophysics and as long as we assume temperature does not change, all the values are constants as listed in the wiki link. The variables here are extracellular ion concentration and intracellular ion concentration. When K⁺ channels are open, they will move the membrane potential towards its equilibrium potential. You can see in the equation that increasing [K⁺] outside the cell will shift the equilibrium potential to a more positive voltage.

 

 

Note: You mentioned Goldman, so if you're dealing with the Goldman-Hodgkin-Katz equation, you can think of that as essentially this same concept for multiple ions.

 

At a hyperpolarized resting potential, neurons tend to be most permeable to K⁺, so the reversal potential of K⁺ has the most influence over the resting potential. With the shift in the potassium equilibrium potential (E_K) K⁺ flux across the membrane will move the potential to this new value, which is a more depolarized potential.

[Function]

What are we injecting K+ into?

 

Extracellular fluid, let's say blood plasm.

 

 

what is the concentration of the K⁺ solution you are adding? What is the volume of the solution to which you are adding it...

 

Let's say you're injecting 0,01 L of 0,1 M KCl in 5 L of blood with normal haematocrit values.

 

 

Perhaps I'm not understanding correctly but I fail to see why cells would hyperpolarize at the moment of injection. Help me out here, and I can probably clear up some confusion.

 

Note that I am very clearly restricting the hyperpolarization to the moment right at and right after injection of potassium solution, making the cells relatively speaking more negatively charged as compared to the situation before injection - thus hyperpolarizing them.

Edited June 28, 2015 by Function

[CPG]

The convention is to define the extracellular solution as 0 Volts and compare the intracellular solution to that. So you are correct if you were thinking that adding solely positive charges (eg pure potassium) and nothing else to the extracellular solution it would change the net charge and cause the membrane potential to be hyperpolarized. Trying to do that would be dangerous, so please don't try it on me! See this youtube video for what that would look like.

 

I think by focusing the question on one ion, it is easy to temporarily forget that you're adding a potassium salt that has an equal number of anions (Cl-) for every cation (K+). The transmembrane voltage at any given instant is a result of differential distribution of charged particles on different sides of the membrane. The net charge inside versus the net charge outside is what is going to determine the charges that get distributed across the membrane. In the solution you have added the (+) and (-) charges are in equal proportion so the net charge (Q) of the extracellular solution as a whole does not change.

 

If you had an intracellular electrode recording from inside a cell, you would see a slow and steady depolarization of the membrane potential. The reason for this would be that under normal conditions the membrane would be most permeable to K+, so it would exert the most influence on membrane potential. With the concentration change, you have shifted the point at which it reaches equilibrium. How long this would take would mainly depend on blood circulation and diffusion.

 

Honestly, I think the best way to get a feel for this (if you don't have an electrophysiology rig and animals at your disposal) is to check out this simulator. Launch it, and to get conditions similar to the human body choose Goldman @ 37degC. Once you have that open, you can fiddle with concentrations and permeability and see what happens to the membrane potential of a simulated cell. It's very cool and once you figure out what the buttons do it makes some complex ideas very intuitive. Check it out! http://www.nernstgoldman.physiology.arizona.edu/

[Function]

Thank you very much for this extended contribution. +2

[Xalatan]

The RMP for a neuron sits around -70mV, and the major contribution to the RMP is K channels. This means At rest the inside of the cell is more negative than the outside by 70mV. Intracellular K sits at around 145mmol/L where as extraxellular k is around 4mmol/L. So naturally there is a constant flux of k out of the cell, the RMP being maintained by na/k atpase pump. If it weren't for the na/k atpase the RMP would tend towards k's equilibrium potential of around -90mV.

 

Let's say you increase extracellular k. This will decrease the electrochemical gradient for the potassium to efflux out of the cell. Less K going out of the cell means intracellular k will increase. Since k determines the RMP, having more cations in the cytoplasm will increase the net charge in the cell relative to the outside, by definition increasing the resting membrane potential and depolarising the cell.

[Function]

Aye, I did understand the concept already, but thank you anyway for your answer! It might be enlightening to other users too!

 

Would be a huge problem if I wouldn't understand this by now, since we're taking on the cardiovascular system, respiration, kidneys and urinary tracts in 10 days; and understanding the fundamentals of electrical systems is quite necessary for this ^^

[Xalatan]

Nice one! i wonder how this concept applies to the pathology of hyperkalaemia and cardiac arrhythmia? Supposedly myocytes or the SA node may be more prone to depolarise, setting off the voltage gated na channels leading to increased cardiac irritability? But I'm reading wiki and it says above a k concentration na channels paradoxically inactivates, setting off ventricular pacing and v arrhythmias... I wonder how the VG na channels works exactly...

Good luck for your exam! I'm sure you would fly through. Did the testing taste question come up?

[Function]

Indeed, I see that hyperkalemia generally leads to activation + inactivation of VG Na-channels; you may appreciate the structure of Na-channels, comprising of an M-gate, and an H-gate; the M-gate opening very quickly at certain treshold depolarization (treshold of opening = -65 mV), and the H-gate closing very slowly, closing increasingly with depolarization; the depolarization of the membranes by K may be so fast, I think, that the time between opening the M-gate, and closing the H-gate, becomes insignificantly small. Hyperkalemia thus slows down the action potentials.

 

Note that in general, hyperkalemia results in arrhythmias by, as mentioned before, depolarizing the membrane, but that it slows down and weakens depolarization during those arrhythmic action potentials (which results in a decreased P-wave in the ECG, meaning a much weaker atrial depolarization), and that it significantly enhances the repolarization (T-wave) because the relative ease it gets from the closed Na channels, at the end of the action potential, which in turn gives calcium less chance to build up and cause the 'plateau' (ST-segment) of the action potential, during which the muscle cells contract.

 

In conclusion: hyperkalemia (1) causes arrhythmias by overall depolarization of the cell membranes, (2) slows down and weakens depolarization during action potentials, (3) enhances repolarization at the end of the contraction and (4) shortens the contraction

 

Fun facts: a plasmic kalemia of +5,5 mM will give you these arrhythmias; a kalemia of +8 mM will cause a heart block (not necessarily an arrest, but an arrest of the conduction at certain conductive tissues; cause will probably be the complete inactivation of all Na channels)

 

--

 

Thank you for the luck - I'm not so sure I'll fly through it, but rather hobble through it my interests in the cardiovascular system are by far not as great as my interests in the central nervous system, of which the exam was (strangely enough for a lot of students) - nice.

The taste testing question did not come up Might've been a too ambiguous question to be posed on an MCQ exam (all our exams are MCQ, sadly enough)

Edited January 18, 2016 by Function

[Xalatan]

Hey that's very well explained. So the VGNaCs have two gates, M activates with depolarisation and H inactivates with depolarisation in a delayed manner. That's very tight control for Na influx. Thank you very much hyperkalaemic arrhythmia is well described. Good stuff!

Yeah interesting point about the distinction between 5.5mmol/L and 8mmol/L. I suppose that's how a lethal injection of KCl works - it raises serum K so high that it just shuts down all the H-gated Na channels leading to lethal asystole.

 

Thing about cardiorespiratory systems is, in many ways the principles of autonomic nervous system apply to both those organs, so being well versed in the CNS helps out a lot. Renal to a lesser degree since the RAA system may be the major focus.

[Function]

Please review my last comment: the easy repolarization would not be because of greater efflux, in hyperkalemia, and that is quite logic, but I think because of the ease of hyperpolarization since Na channels are already closed; might need some feedback on this one from someone with a more fundamental knowledge of the heart electricity.

 

Speaking of RAAS, I've developed a huge aversion for the renal physiology in the last few months since it was given to us I've never been a huge fan of metabolism, truth be told

 

If I may, I'd suggest you to buy Ganong's Review of Medical Physiology (most recent ed.), it is the book our professors refer to in their courses and notes (of course, the paper courses by our professors form the main thing, we use handbooks if we don't understand something), and these things are, as far as I'm aware of, very well explained in it.

 

Should you show more interest in the CNS, my professor strongly advised me, and thus I did, to buy "Principles of Neural Science" by Eric Kandel (Nobel Prize, 2000) et al. (5th ed.); it gives you a very profound explanation on the understanding of the CNS, slightly more applied to the physiological aspect of it

[Xalatan]

Difficult to say what exactly is the cause of the tall tented T waves in hyperkalaemia, chances are it's not due to hyperepolarisation from K efflux since extracellular K is higher. Also not sure if it is related to VGNaC changes since action potentials are all or none responses by nature. If Phase 0 Na influx is inactivated then there may be no subsequent phases I, II, and III.

 

It may have something to do with the calcium influx during ventricular repolarisation from VGCC. This study observes serum calcium levels are inversely proportional to T wave height. http://ndt.oxfordjournals.org/content/17/9/1639.abstract?ijkey=c72f861993db16339c41fd8c7b6ff6b9167e12cd&keytype2=tf_ipsecsha. Makes sense to me because calcium antagonises K efflux to give the plateau phase.

So, hypocalcaemia with less calcium entry should give a relatively larger repolarisation effort from K efflux, which may cause an exaggerated T wave.

 

Yeah Renal physiology is a grind. Ganong is a really good resource book, many thanks for recommending it to me! Will take a look at Kandel, iirc it's quite a tome!