The dimension problem of the difusion

Extending NEURON to handle reaction-diffusion problems.

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ylzang
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The dimension problem of the difusion

Hello, I have a simple problem, but I am not sure about the answer. If I used both the radial and longitudinal diffusion in my calcium buffering model. Then this diffusion is 2D, right?
ted
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Re: The dimension problem of the difusion

Yes, but you need to think about whether your model requires the grid to be symmetric, that is, whether you must make sure that compartment lengths are the same size as radial shell thickness.
ylzang
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Joined: Sun Mar 08, 2015 3:38 am

Re: The dimension problem of the difusion

Thanks Ted. I am considering the problem of real calcium diffusion. For example, as you know the BK current will sense calcium to be activated. With recent experiments, BK current only sense the P type calcium current near it. In this case, do you think the following will make sense? Separate the cylinder to many shells and each shell has a dr about 10 nm. Then BK senses the calcium in different shells to account for the distance between BK channel and P type calcium channel.
In this case, of course the longitudinal grid can not be the same as the radial grid, otherwise this problem will be too huge and can not be computed.
ted
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Re: The dimension problem of the difusion

ylzang wrote:With recent experiments, BK current only sense the P type calcium current near it. In this case, do you think the following will make sense? Separate the cylinder to many shells and each shell has a dr about 10 nm. Then BK senses the calcium in different shells to account for the distance between BK channel and P type calcium channel.
Doesn't make sense at all. For each cluster of P and BK channels, you need to represent what happens in a roughly hemispherical volume that has a radius on the order of 1 um or less. Can't do that with annuli. If that level of detailed is required, you either must
(1) represent each P + BK complex as a discrete entity like a point process
or
(2) reformulate the conceptual model so that many P + BK complexes over the surface of a segment can be treated as an ensemble of a large number of individual complexes. Then you will be able to use a density mechanism to represent the behavior of the ensemble.