# Problems understanding membrane potential

I understand that membrane potential is the difference of the extracellular and intracellular ionic charges, due to their concentrations. We say that the extracellular space has a charge of 0 and then take the membrane potential with respect to the extracellular space. The intracellular space is normally around -60mV due to more negative charges being in the cell than the extracellular space.

This is how I understand membrane potential.

From this understanding, it is hard for me to see why I can't get this right:

We work with a regular cell with potassium 120mM inside and 4.5mM outside.

Say that we increase the intracellular concentration of potassium by 10 mM, a +1 valence ion which contributes to POSITIVE membrane potential.

What I envision is that as we put more positive ions in the cell, the cell is now more positive in regard to the extracellular matrix. However the Nernst equation states that the membrane potential actually gets MORE NEGATIVE!! http://www.physiologyweb.com/calculators/nernst_potential_calculator.html

What is it that I am misunderstanding? Thank you.

• An increase of the intracellular concentration of potassium decreases the membrane potential, i.e. makes it more negative. The Nernst equation provides the potential required 'to keep' the ions from flowing out of the cell, down their gradient. You shouldn't view those positively charged ions within the cell as positively contributing to the membrane potential. It's the contrary, the Nernst equation provides the potential to maintain the electrochemical equilibrium, as if it needs to stop the ions from flowing out of the cell (you need a negative potential to oppose + charged ions). Oct 17, 2014 at 2:29

I think this question has more to do with kinetics / transport phenomenons than biology, but that's okay, everything is connected especially my computer to the internet. ;-)

The basic idea behind transport phenomenons is that there will always be a flux of quantitative properties (e.g. charges, particle number, entropy, volume, etc...) where the qualitative properties like (electrical potential, chemical potential, temperature, pressure, etc...) have a gradient in space (note that kinetics of chemical reactions can be described similarly without the space gradient part).

In this case we are talking about electrochemical potential gradient and ion flux. It is very important to recognize that the electrochemical potential is not the same as the electric potential. It has a chemical component, so the result will depend on both charge and concentration gradients. By a single ion channel system (e.g. Na⁺ channel only) you can count the potential of each side of the membrane using the Nernst equation, by a system with multiple ion channels it is more complicated, so in that case you have to use the Goldman equation. So at the end you can say something like one side has a potential of x[mV] and the other side has a potential of y[mV] and so the difference is: d[mV] = x[mV] - y[mV]

The sign of d depends on x or y has a greater value. By single ion channel systems this expresses an x → y direction so by positive d the cation flow direction is x → y and by negative d it is y → x. By anion flow it is the opposite.

By cells we use the out → in direction by counting the membrane potential. We can count the potentials using the

• Nernst equation: $$E_m = \frac{RT}{zF} \times ln \left(\frac{c_{out}}{c_{in}}\right)$$ or the
• Goldman equation: $$E_m = \frac{RT}{F} \times ln \left(\frac{p_{K^+}.[K^+]_{out} + p_{Na^+}.[Na^+]_{out} + p_{Cl^-}.[Cl^-]_{in}} {p_{K^+}.[K^+]_{in} + p_{Na^+}.[Na^+]_{in} + p_{Cl^-}.[Cl^-]_{out}}\right)$$ where

• $Em$ is the membrane potential
• $z$ is the ion charge
• $[X]$ is the ion concentration
• $p_X$ is the relative membrane permeability for the actual ion

and so on...

So for example by an average human cell in blood plasma, assuming that the inside of the membrane has a small negative charge

• the Na⁺ has a positive effect (positive charge, high out → in concentration gradient, low out → in charge gradient),
• the K⁺ has a negative effect (positive charge, high in → out concentration gradient, low out → in charge gradient),
• the Cl¯ has a negative effect (negative charge, high out → in concentration gradient, low in → out charge gradient)
• the Mg⁺⁺ has a small positive effect (positive charge, low out → in concentration gradient, low out → in charge gradient)

on the membrane potential. It is hard to find an ion in this case which flow is charge gradient dominated instead of concentration gradient...

I understand that membrane potential is the difference of the extracellular and intracellular ionic charges, due to their concentrations.

The (sign and) value of the membrane potential is not determined by the charge gradient because the concentration gradients usually have a much bigger effect on it. The cells maintain these concentration gradients by using up energy.

We work with a regular cell with potassium 120mM inside and 4.5mM outside.

Say that we increase the intracellular concentration of potassium by 10 mM, a +1 valence ion which contributes to POSITIVE membrane potential.

In your case K⁺ has a negative effect on the membrane potential, because of the high concentration gradient with reverse direction. So decreasing the concentration gradient will increase the membrane potential.

• @WYSIWYG Thanks the edit, I did not know it is possible to use an equation description language. Oct 17, 2014 at 14:03
• yeah it is $\TeX$ Oct 19, 2014 at 9:08
• So basically K has a negative effect because of its gradient. What if I'd put 100mM outside and only 5mM inside? Shouldn't the gradient now change and the effect be opposite?
– Paze
Oct 20, 2014 at 17:07
• Yes it will be then positive. ln a/b = - ln b/a Oct 20, 2014 at 17:24
• I can't seem to replicate this effect with the tool in the link you posted in another question: nernstgoldman.physiology.arizona.edu/using If I put 100mM outside and test the slider for inside around 100mM it still just goes one way.
– Paze
Oct 20, 2014 at 17:29

I think inf3rno's answer is very complete, so I will just be adding some notes that might help OP understanding what's happening.

Say that we increase the intracellular concentration of potassium by 10 mM, a +1 valence ion which contributes to POSITIVE membrane potential.

Let's say we do that, in an in vitro cell model, using a syringe with only K⁺ ions. What would happen?

What I envision is that as we put more positive ions in the cell, the cell is now more positive in regard to the extracellular matrix.

And that is true, at least instantly. However, due to the differences in concentration gradients, the K⁺ would quickly flow out until electrochemical balance was restored. This would lead to an increase in K⁺ concentration outside our cell model so, in the end, the net charge would decrease inside the cell.

So you can think of the Nernst equation as a mathematical model to the cell in equilibrium.

• "However, due to the differences in concentration gradients, the K⁺ would quickly flow out until electrochemical balance was restored. ... So you can think of the Nernst equation as a mathematical model to the cell in equilibrium. " - Yes that's true. Oct 17, 2014 at 14:01