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Myelin increases resistance across the cell membrane

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atyy
#37
Sep25-08, 02:44 PM
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Quote Quote by somasimple View Post
50 turns of myelin (50*d) and a length that is 2000 time longer (2000*A).
Yes, myelin allows the total capacitance of an internode and a node to be roughly the same even though the internode is ~1000 longer than the node.
Moonbear
#38
Sep25-08, 05:03 PM
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Quote Quote by somasimple View Post
DaleSpam,
Give the results in our example.
50 turns of myelin (50*d) and a length that is 2000 time longer (2000*A).
Your question is rather ambiguous the way it is worded. Length of what? What "result" are you asking to have explained?
somasimple
#39
Sep26-08, 12:06 AM
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A visual perhaps?
Time constant for internode is, at least, 120 longer in that case.
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somasimple
#40
Sep26-08, 12:11 AM
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You're right. Normally a cylindrical capacitor must be computed that way but biologists do not.
http://butler.cc.tut.fi/~malmivuo/bem/bembook/21/21.htm
It does not change the length segment problem.
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atyy
#41
Sep26-08, 01:55 AM
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Quote Quote by somasimple View Post
A visual perhaps?
Time constant for internode is, at least, 120 longer in that case.
Quote Quote by somasimple View Post
It does not change the length segment problem.
Time constant~RC, so if you include R (membrane resistance)?
somasimple
#42
Sep26-08, 02:01 AM
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http://www.physicsforums.com/showpos...66&postcount=1
Myelin increases resistance across the cell membrane by a factor of 5,000 and decreases capacitance by a factor of 50.
If C and R are increased then...
Of course the internal axonal resistance remains unchanged but since its length did.
atyy
#43
Sep26-08, 02:08 AM
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Quote Quote by somasimple View Post
http://www.physicsforums.com/showpos...66&postcount=1

If C and R are increased then...
Of course the internal axonal resistance remains unchanged but sinceits length did.
So your point is that the numbers in wikipedia are wrong?
somasimple
#44
Sep26-08, 02:14 AM
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Quote Quote by atyy View Post
Yes, myelin allows the total capacitance of an internode and a node to be roughly the same even though the internode is ~1000 longer than the node.
Are you serious?
I do not contest... numbers.
atyy
#45
Sep26-08, 02:19 AM
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Are you serious?
I do not contest... numbers.
Yes - but only "same order of magnitude" - Koch: Even though the length of the interaxial node is typically 1000 times larger than the node, its total capacitance has the same order of magnitude.

But Koch is talking about the frog axon: made up of 250 myelin layers
somasimple
#46
Sep26-08, 02:21 AM
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Quote Quote by atyy View Post
Yes - but only "same order of magnitude" - Koch: Even though the length of the interaxial node is typically 1000 times larger than the node, its total capacitance has the same order of magnitude.
Someone is wrong: Is it Mathematics or Pr C Koch?
Edit: 250 turns does not change anything since 250 < 1000
atyy
#47
Sep26-08, 02:25 AM
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Quote Quote by somasimple View Post
Someone is wrong: Is it Mathematics or Pr C Koch?
Edit: 250 turns does not change anything since 250 < 1000
Order of magnitude means correct to within a factor of <10 (I usually think ~3-4)

So I think we need better numbers, and from the same species - not some squid, some frog, and some rabbit ...

Edit: not squid - that's not myelinated
somasimple
#48
Sep26-08, 04:56 AM
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Quote Quote by atyy View Post
Order of magnitude means correct to within a factor of <10 (I usually think ~3-4)
But Rm varies inversely to Cm and they are linked...
You may test a simple linear function:
Rm=f(C)=-a(C)+b
atyy
#49
Sep26-08, 05:33 AM
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Quote Quote by somasimple View Post
But Rm varies inversely to Cm and they are linked...
You may test a simple linear function:
Rm=f(C)=-a(C)+b
Yes, that's why I said:
Quote Quote by atyy View Post
Edit: But there is something very fishy with this explanation. Time constant Tm~RmCm. What's the point of decreasing Cm, but increasing Rm by the same amount?

Edit: Another part of the puzzle. Space constant Lm~Rm/Ra
There are other equations in Koch's book where Cm enters, for example in the frequency-dependent length constant, but it always enters in the combination RmCm, so if the primary job of myelin is to change capacitance, I don't see how it affects anything.

That's why I was thinking about the length constant (frequency-independent component) ~Rm/Ra, where Ra is the axial resistance. The length constant determines how signals decay over distance, so to conduct in the internode where sodium channels are low, and signals cannot be actively boosted, the length constant has to be increased, perhaps by increasing Rm with myelination. Unfortunately, this increases the time constant ~RmCm - unless you decrease the capacitance by the same amount, which I think myelin does. However, most expositions do not feature the length constant, and they also say that the job of myelin is to increase the time constant, not to keep it the same. So I don't understand what's going on.
somasimple
#50
Sep26-08, 05:43 AM
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Quote Quote by Atyy
That's why I was thinking about the length constant (frequency-independent component) ~Rm/Ra, where Ra is the axial resistance.
If you reject Cm then you reject the whole theory...
Quote Quote by Atyy
So I don't understand what's going on.
I do... but I can't say anything on this site without being thunder lightened by modos.
atyy
#51
Sep26-08, 05:54 AM
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Quote Quote by somasimple View Post
If you reject Cm then you reject the whole theory...
Yes, and no. I think the decrease in Cm is required to offset the increase in Rm, so that the time constant remains the same. There are no outright contradictions between what I'm saying and the standard explanations. BUT there are enough differences in emphasis that I should look at the equations carefully and see whether the apparent lack of contradiction between the two explanations is due to a real similarity in the underlying mathematics, or just due to chance. But those details are not in Koch's book.

Quote Quote by somasimple View Post
I do... but I can't say anything on this site without being thunder lightened by modos.
Maybe to be careful, you should say "at least one modo (singular)".
somasimple
#52
Sep26-08, 06:19 AM
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Quote Quote by atyy View Post
Maybe to be careful, you should say "at least one modo (singular)".
I can't. It is out of my capacitance and resistance.
atyy
#53
Sep26-08, 06:21 AM
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Quote Quote by somasimple View Post
I can't. It is out of my capacitance and resistance.
somasimple
#54
Sep26-08, 07:27 AM
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Quote Quote by atyy View Post
Order of magnitude means correct to within a factor of <10 (I usually think ~3-4)
with the function:
The minimal value found with 250 turns is a Time Constant that is multiplied by a factor 20.
the worst is... 1250
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