# Homework Help: GHK equation

1. Dec 20, 2009

### af86

1. The problem statement, all variables and given/known data

Have to determine permeabilities $$\alpha$$ and $$\beta$$ (PNa/PK and PCl/PK)

as well as internal concentrations of Na+, K+ and Cl-

I have calculated different membrane voltages according to the external concentration (when altering one ion, the other two were set to zero).

2. Relevant equations

Ki = {(A2 + 4Co2)1/2 + A}/2

ψ = (kT/q) ln (Co/Ki)

and GHK equation:
VR = kT/qln {Ko*+*αNao*+*βCli/Ki+*αNai*+*βClo}

3. The attempt at a solution

I am having trouble calculating the internal concentrations for K, Cl and Na. I have the membrane voltages and the concentrations between 0mM and 300mM in 5mM increments.

I think once I am able to calculate that, I might be able to figure out the rest.

Thanks

2. Dec 20, 2009

### denverdoc

af86,
me again. What can you control--as I understand it the voltages for any set of external concentrations are known, unknown are the permeabilities and internal concentrations?

3. Dec 20, 2009

### af86

I can control external concentration of Na, Cl and K. Which then produces/outputs a membrane voltage.

4. Dec 20, 2009

### denverdoc

How did you determine alpha and beta?

5. Dec 20, 2009

### af86

I haven't...that's another part of the question I'm stuck on

6. Dec 20, 2009

### denverdoc

Then basically you have 6 unknowns and an unlimited number of combinations/voltages. It can be done purely algebraically, but ugh. Much better if you have matlab and can set it up to to either try to solve the inverse matrix of the simultaneous equations (you'd need to input 5 eqns and results, or better yet to try a best fit using a bigger data set.

Let me show you how you can go about doing it for 4 unkwowns assume Chloride permeability is zero.

So, lets start with a small amt of K, say 5 mM, and Na=0

GHK can be written as

10^(Em/58)= 5/(ki+A*Nai)

Then we set Ko = 0, and Na = 5 then 10^Em/58=(5*A)/(k1+A*Nai)

Then maybe something like Na and K=5 then 10^Em/58 = (5+5*A)/(k1+A*Nai)

By manipulating the various eqns, you can eventually tease out A, Nai and Ki.

Naturaly it is worse for the 3 ion case. You just need to add more combos and do a lot more algebra. 58 is for 20 C if, your experiment is at 37, then the RT/FZ= 61.5

Like I said this is where a good curve fitting routine would be the best approach IMO.

7. Jan 2, 2010

### af86

Denverdoc,

Sorry it's taken me so long to reply - unfortunately I do not have matlab and don't know how to use it, any other suggestions - I don't mind if its time consuming to calculate it...a nice easy procedure would be great - I'm still really stuck on this.

Thanks

8. Jan 5, 2010

### af86

Hi again,

So I have managed to figure out the internal concentrations of each external concentration. Do I then take the average? Or do I just choose a set external concentration (e.g. 100mM) for all ions?

Also, from here, how can I calculate PK, PNa and PCl? Which will then allow me to find the permeabilities, alpha and beta. Actually, I have assumed that PK is one for this question. So it is just PNa and PCl I need help in finding.

Thanks