Changing resistivity over axon length

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mganguly
Posts: 29
Joined: Sun May 03, 2015 7:05 pm

Changing resistivity over axon length

Post by mganguly »

Hi,

I understand resistivity is a section variable and is constant over an entire section. https://www.neuron.yale.edu/neuron/stat ... ry.html#Ra

I wanted to know if its possible to make resistivity dependent on the axon length.
Eg: If an axon has 500 nodes, the first 250 nodes have a certain value of resistivity and the second set of 250 nodes have another value of resistivity.

Mohit

ted
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Re: Changing resistivity over axon length

Post by ted »

You mention "nodes" so I suppose you're working with a model of a myelinated axon, so you're referring to nodes of Ranvier. The most reasonable way to build a model of a myelinated axon is as a chain of sections in which every other section represents a node of Ranvier and the others represent internodes. You can use whatever algorithm you like to assign the properties of these sections. If Ra is supposed to depend on anatomical distance from the 0 end of the root section, then I'd suggest using NEURON's distance() function instead of section index. If your section names are of the form node and internode, and node[0] is the root section, then this should work:

Code: Select all

// $1 is Ra for proximal sections
// $2 is Ra for distal sections
// $3 specifies the distance that separates proximal and distal sections
// example: setRa(35.4, 70.8, 200)
// means proximal sections are closer than 200 um
// and have Ra = 35.4, while distal sections have Ra = 70.8
proc setRa() {
  node[0] distance()
  forall {
    if (distance(0.5)<$3) {
      Ra = $1
    } else {
      Ra = $2
    }
  }
}

mganguly
Posts: 29
Joined: Sun May 03, 2015 7:05 pm

Re: Changing resistivity over axon length

Post by mganguly »

Thanks for the reply.

What if I use an unmyelinated axon and instead of varying properties over sections, I aim to vary properties over segments ? Or should I use the distance function in that case ?

Mohit

ted
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Re: Changing resistivity over axon length

Post by ted »

mganguly wrote:What if I use an unmyelinated axon and instead of varying properties over sections, I aim to vary properties over segments ?
You can do that for parameters that are range variables, but Ra is not a range variable. It is a section variable. That means it has the same value from one end of a section to the other. If you need Ra to change abruptly at some distance, then that point must be the distal end of a parent section and the proximal end of a child section. If you want Ra to be a "continuous" function of distance along the axon model, you need to represent the axon by a chain of sections. It would be best to break the axon into N sections of equal length (and of course each section should be discretized using the d_lambda approach).

How big should N be? That is an empirical question, which can only be answered by performing a series of simulations and comparing results. I would follow this protocol:

Code: Select all

set N = 1
build a model that has the axon broken into N sections
run a simulation and save results as "new results"
Repeat
  copy "new results" to "previous results"
  set N = 3*N
  build a model that has the axon broken into N sections
  run a simulation and save results as "new results"
Until you judge that the difference between new results and previous results is insignificant
should I use the distance function
Not necessary if Ra is simply a step function of distance. Absolutely necessary if Ra varies continuously with distance.

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