Nernst Equation and Action Potential Help.

[AMSRebel]

Questions regarding action potential:

(1) Why isn't the membrane potential of sodium +60 mV as would be calculated using the Nernst equation? Looking at the AP graph in my book, I see it peaks out at +40 mV instead.

(2) Does the Nernst equation describes the membrane potential acquired when the electro-gradient is sufficient enough in strength to stop the concentration gradient?

(3) From what I understand, the Nernst equation describes the potential voltage attained when the cell is permeable to only one ion, right?

My thoughts:

The Nernst equation is used to calculate the voltage, or charge differential, across a membrane, given that the membrane is permeable to one ion. This charge differential is similar to potential energy in its capacity to do "work". When we plug in the concentration values of sodium across the cell membrane into the Nernst equation, we find that the equilibrium voltage potential is +60 mV. This number is the membrane potential inside of the cell. Furthermore, I use the word “equilibrium”, given that the initial concentrations that we plug are derived from “normal” physiological conditions. Additionally, this is the voltage inside of the cell when the concentration gradient cancels out the opposing electro-gradient.

Now, in one of my books, it writes that the concentration gradient is actually stronger, in effect. That’s why we have ion leakage and require the sodium-potassium pump, to restore normal physiological conditions. That’s a bit confusing to me, because I thought this is the point where the electro cancels out the chemical gradient. If we have further leakage, then the electro isn’t powerful enough, just yet.

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[theonlytycrane]

Let's contextualize this as a simple setup in a neuron cell body: Na+ / K+ ATPase is pumping 3 Na+ out and taking 2 K+ in. This creates a net positive charge outside of the cell (and net negative charge inside of the cell). Outside of the cell there's excess Na+ and inside the cell there's excess K+. K+ leaks out of the cell due to potassium-leak channels, but the Na+ / K+ pump continually uses energy (ATP) to maintain a cell potential. There eventually exists an equilibrium point where the Na+ / K+ pump and K+ leak channels counteract each other equally to establish a resting potential measured inside the cell relative to the outside. This is usually something like -70 mV.

If the above makes sense the link below will explain how to incorporate the nernst equation. At the equilibrium state, ions are moving in and out of the cell, but the net movement is 0 and the equation let's you calculate the voltage based on concentrations.

link: http://www.physiologyweb.com/lectur...e_potential_nernst_equilibrium_potential.html

 

[ImDiene0412]

Questions regarding action potential:

(1) Why isn't the membrane potential of sodium +60 mV as would be calculated using the Nernst equation? Looking at the AP graph in my book, I see it peaks out at +40 mV instead.

(2) Does the Nernst equation describes the membrane potential acquired when the electro-gradient is sufficient enough in strength to stop the concentration gradient?

(3) From what I understand, the Nernst equation describes the potential voltage attained when the cell is permeable to only one ion, right?

My thoughts:

The Nernst equation is used to calculate the voltage, or charge differential, across a membrane, given that the membrane is permeable to one ion. This charge differential is similar to potential energy in its capacity to do "work". When we plug in the concentration values of sodium across the cell membrane into the Nernst equation, we find that the equilibrium voltage potential is +60 mV. This number is the membrane potential inside of the cell. Furthermore, I use the word “equilibrium”, given that the initial concentrations that we plug are derived from “normal” physiological conditions. Additionally, this is the voltage inside of the cell when the concentration gradient cancels out the opposing electro-gradient.

Now, in one of my books, it writes that the concentration gradient is actually stronger, in effect. That’s why we have ion leakage and require the sodium-potassium pump, to restore normal physiological conditions. That’s a bit confusing to me, because I thought this is the point where the electro cancels out the chemical gradient. If we have further leakage, then the electro isn’t powerful enough, just yet.

1.) The membrane potential of Na+ "peaks out" once the membrane potential reaches the equilibrium potential for Na+, because there will be no more influx of Na+. From my understanding, the membrane potential of Na+ calculated from the Nernst Equation is ONLY taking into account influx of Na+; however, in reality, K+ is also leaving the cell (which depolarizes it) making the "real" membrane potential less than the "theoretical". Same goes for using the Nernst equation to calculate the membrane potential for K+ in a resting cell: the Nernst equation will predict a membrane potential of ~ -87 mV vs. the -80 mV "observed" in a cell because it is only taking into account the potential difference (voltage) created by K+ and not the small amount of Na+ that is entering the cell (polarizing the cell and making it more positive).

2.) The Nernst Equation is used to find and exact value for voltage (in this case membrane potential, but also for exact cell voltages in gen chem) and quantifies the effects of concentration on cell voltage- large or small. There is no amount of "electro-gradient sufficiency" that must be met in order for the equation to work, you just have to interpret it according to what is going on in the cell.

3.) Yes, the Nernst Equation is only taking one ion into account at a time. In some cases, such as K+ in "resting" cell this number is still very close, because the cell is much more permeable to K+ than Na+ (PK+ >>> PNa+) and therefore, it is the K+ gradient that is responsible for the potential. The less this is the case, the less accurately the Nernst Equation will quantify voltage.

4.) According to Wikipedia, "voltage is the difference in electric potential energybetween two points per unit electric charge. The voltage between two points is equal to the work done per unit of chargeagainst a static electric field to move the test charge between two points and is measured in units of volts" So yes, the greater the charge difference, the greater the voltage and the greater its ability to do work. Imagine plugging in an infinitely small number into the bottom of the equation for K+ inside the cell ( V= 2.3 (RT/ZF) log [K+] outside/[K+] inside ), voltage would approach infinity. My book also says the the concentration gradient has a stronger affect. What I took from that, is that the "greater force of the gradient" is the reason K+ flows out of a "resting" cell (and down its concentration gradient). If the positive voltage were equal to the force of the K+ gradient, there would be no movement of K+ outside of the cell and resting membrane potential would be much higher than ~ -80 (and probably a lot more difficult to depolarize). Between the "force" of the gradient causing K+ to flow out of the cell, the positive voltage build up (from the diffusion of K+) wanting to "push" K+ back in, and the Na+/K+ ATPase pump, a resting cell "equilibrates" at around -80 mV.

Hope this helps, sorry it was long winded!