Calculating number of ion channels in lipid bilayer

[af86]

Homework Statement

Calculate number of channels present in a lipid bilayer


q = 1.6^-19; D (diffusion constant) = 1.2E-9; C (Concentration); 4.36; k = 1.38E-23; T=298; d = 2.5E-9

Therefore G₁ = 1.27E-17

Channel area = 7.07E-18

measured conductance (from injecting Na+ concentration of 100mM) = 149.24uS

Homework Equations

G1 (conductance) = q^2DC/kTd

Gm = g/$$\pi$$r^2

The Attempt at a Solution

Conductance of a single channel = 1.27E-12 x 7.07E-18
Number of channels = Gm/G1 ??

Calculating the number of channels is what is getting to me. I have the area of the channel, and I have a measured conductance from injecting a concentration

Thanks!

 

[denverdoc]

The conductances sum as you mention. I would think that N = Gm/G1 just as you suppose. Did you not get the right answer?

 

[af86]

Yep. Tried that and my answer came out a few order of magnitudes out...double and triple checked all my work and still..could be that the answer given is incorrect.
Thanks!

 

[denverdoc]

Not sure and without access to my books/notes, may be unable to help here: in your modelling, do you assume that a leak conductance is present?

 

[af86]

Thanks denverdoc.

I figured it out (I think). But yes, leak conductance was taken into account; I think the only way to go is to divide Gm/G1.

Cheers

 

[denverdoc]

Your welcome for what is is was worth--amazing how much one forgets--once upon a time,many moons ago, I was a post doc in an electrophysiology lab.

 

[af86]

So I thought I figured this out - but I haven't!

I have some values, as a test, and I can't seem to get it right.

Can anybody please help!? I know it uses the equations above, but something is going wrong in the last step when I'm trying to calculate the number of channels and conductance...I know what the answers should be; number of channels is 3E6


Data:

bilayer area = 1.1E-6m²
bilayer thickness = 2.5E-9m
channel radius = 1.5E-9m
channel thickness = 2.5E-9
diffusion constant = 1.2E-9
dielectric constant = 2.3
change in energy (i.e $$\Delta$$U or sometimes $$\Delta$$E)

can anybody help please?