Membrane capacitance and Nernst potential

[somasimple]

Hi all,
Is there any relation between the membrane capacitance and the Nernst potential?

Refs:
membrance capacitance
http://www.cnbc.cmu.edu/~bard/passive2/node5.html
Nernst potential
http://en.wikipedia.org/wiki/Nernst_equation#Nernst_potential

 

[Cincinnatus]

A good, short and easy to read reference on this is chapter 5 of Peter Dayan and Larry Abbott's book Theoretical Neuroscience.

Actually, you can find a discussion of these things even in the huge Kandel and Squire books.

 

[somasimple]

I'm owning the https://www.amazon.com/gp/product/0838577016/?tag=pfamazon01-20but there is not a direct response about the question.
Neither in this one;
https://www.amazon.com/dp/0262100533/?tag=pfamazon01-20
or that one
https://www.amazon.com/dp/0878933212/?tag=pfamazon01-20
These three books are unable to give a simple response...

 

[Cincinnatus]

If I remember correctly, the discussion you are looking for is in an appendix in the Kandel book.

 

[somasimple]

If I remember correctly, the discussion you are looking for is in an appendix in the Kandel book.

Thanks, but there is quite nothing (pages 1280..1287).
The chapters 7 to 9 (pages 125 170) describe the events/properties of a neuron but not a single relation between these important equations.

 

[Andy Resnick]

Are you referring to the cable equation? There's a derivation in Sten-Knudsen's "biological membranes" on pages 486-492 (roughly), but it's not clear if the voltage in that can be directly replaced with the Nernst potential. I think it can, and the text appears to call the voltage the 'membrane potential', but the Nernst equation is an equilibrium condition, not a dynamic one.

 

[somasimple]

I'm only asking about the membrane potential in quiet conditions (aka resting potential).
something like that :

 

[Andy Resnick]

Now I'm confused about what you are asking. Are you wondering if the last line is valid?

 

[somasimple]

Membrane acts as a capacitor so it stores a charge (ionic difference between interior and exterior).
The second equation computes the reversal voltage that exists between the two sides because of a ionic difference (concentration gradient).
There must/may be something that relies the two equations, no?

 

[Andy Resnick]

I think you are re-discovering the cable equation:

http://en.wikipedia.org/wiki/Cable_theory

 

[somasimple]

Andy,
Do you really think that?
A capacitor is able to express only one tension in relation with one charge. A charge is a finite quantity.
In the second equation, the charge is related to a ratio. A ratio is dimensionless somewhere.
So you may have an infinity of concentrations that give the same ratio.
Because you may multiply the nominator and the denominator by a a value k without changing the tension.
Secondly you may obtain a huge tension with very low quantities of charges/concentrations. That is against the principles of physics. (See Calcium).
And lastly, the Nernst equation was designed to work with RedOx chemical reactions. The transposition with a single ion may be inaccurate.

 

[Andy Resnick]

I'm not sure what you mean by 'tension'. The potential jump across the membrane?

Likewise, your post in general is confusing- there are multiple statements that are not quite true and not quite false.

 

[somasimple]

I meant the reversal potential (difference between the two sides):

Likewise, your post in general is confusing- there are multiple statements that are not quite true and not quite false.

Something that is not quite true is not quite false!
Something that is not quite false is not quite false!
Something that is not quite false is quite true.
What statements are quite false or true?

 

[somasimple]

I'll help you a bit:

http://en.wikipedia.org/wiki/Nernst_equation

The potential across the cell membrane that exactly opposes net diffusion of a particular ion through the membrane is called the Nernst potential for that ion. As seen above, the magnitude of the Nernst potential is determined by the ratio of the concentrations of that specific ion on the two sides of the membrane. The greater this ratio, the greater the tendency for the ion to diffuse in one direction, and therefore the greater the Nernst potential required to prevent the diffusion.

At very low concentrations of the potential determining ions, the potential predicted by Nernst equation tends to ±infinity. This is physically meaningless because, under such conditions, the exchange current density becomes very low, and then other effects tend to take control of the electrochemical behavior of the system.

from
https://www.amazon.com/gp/product/0781760038/?tag=pfamazon01-20
pages 64..66 => see picture => Ca⁺⁺ is just at very low concentrations and creates a huge potential that contradicts the limitations of the above equation.