Cross-Sectional Area of Axon

[drXanthine]

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TBR states that the ability of a given neuron to conduct a current depends "on the cross-sectional area of that neuron." Looking around online, I found that the number of ions per unit length is greater in large diameter neurons; this is obvious. I also read that the ions are thus able to move farther along the axon before leaking back across the membrane.

If the cross-sectional area is larger, however, I would think it would take more ions to generate the same potential difference as in the smaller diameter neuron. Although the number of ions has increased, the number of ions per unit volume, has remained the same. It is the concentrations that affect the potential, not just the number of ions.

The only thing I can think of is that the number of ions (concentration * pir^2) increases faster than the area through which they can leak out (2*pi*r). Thoughts?

 

[chill3]

Well you are right, membrane voltage is determined via concentration distribution of ions across the membrane as well as the individual conductance for each ion. This was explained in the Goldman-Hodgkin-Katz equation. Now the actual ability to conduct current was tackled by "cable theory." Just like in electronics, current is directly proportional to the resistance of the wire (neuron). The larger diameter neuron simply has a lower internal resistance and can transfer charge faster down its length. Obviously there are some nice partial differential equations that can help explain this, but for MCAT purposes you would never need to know it.

Hope this helps

 

[mcloaf]

What makes you think that it would be the absolute number or ions rather than their concentration that would be held constant as cross sectional area increases?

 

[drXanthine]

chill3: Ok, that actually makes a lot of sense. I wasn't thinking about modeling the axon as a wire. If that's the case, it's similar to the equation R = rho * L / A. Now that sure sounds like an MCAT question!

mcloaf: I don't think that. It is the concentration that is held constant, not the absolute number of ions.

 

[mcloaf]

chill3: Ok, that actually makes a lot of sense. I wasn't thinking about modeling the axon as a wire. If that's the case, it's similar to the equation R = rho * L / A. Now that sure sounds like an MCAT question!

mcloaf: I don't think that. It is the concentration that is held constant, not the absolute number of ions.

Heh, sorry, now that I read back again I'm not sure how I missed that the first time around.

Anyway, chill3 had it right in that modeling the neuron as a wire is the best way to think about this effect.