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### Simplifying myelin-node on long axons

Posted: **Fri Oct 09, 2015 12:25 pm**

by **CYUlysses**

Hi all,

I am currently dealing with a network model of many excitatory cells with relatively long axons (reaching over 1000 um) and intermittent myelin sheath structures. The motivation of this population model is to study the effect of extracellular stimulation on a cell population with different kinds of synapses.

Since the total number of cells is large, I am thinking of simplifying the node area as only one compartment, and simplify the electric property of the myelin sheath as perfect insulators with no additional capacitance.

I then came to think that because the specific axial resistance is assumed to be constant, can such simplified model be further simplified as a long single section divided into n segments, where n is the number of nodes? This makes the assumption that the internode length stays relatively constant throughout the axon, and some specific membrane properties channel mechanisms may be adjusted linearly based on the segment lengths.

Is the nseg simplification valid? Is there any caveat that I should be wary of?

Thanks a lot!

Best,

### Re: Simplifying myelin-node on long axons

Posted: **Fri Oct 09, 2015 9:33 pm**

by **ted**

Time to ask yourself a lot of questions.

Does a cell's axon matter? Is it exposed to the field? Is it where the spike is initiated? If not, does it affect membrane potential at the spike trigger zone? If not, why include it?

On the other hand, does it add much to the total computational complexity of a model cell? Have you calculated the the relative computational complexities attributable to axonal compartments vs. non-axonal compartments? Computational complexity is roughly proportional to the total number of ordinary differential equations (ODEs) that must be numerically integrated. Each compartment has a minimum complexity of 1 even if it's passive (because the discretized cable equation has an ODE that governs v) . If active currents are present, increase that by the total number of ODEs in all of the NMODL-specified mechanisms that are present. Example: a section with nseg = 3 that has hh has a complexity of 3*(3+1) = 12 where the first 3 is because there are 3 compartments, the second 3 is because hh has three ODEs (for m, h, and n), and the 1 is for the cable equation. A dendritic section that has an A current, an H current, a delayed rectifier, and a sodium current may have a complexity of nseg*(2+2+1+3) = 8*nseg. Usually dendrites account for most of a cell's compartments, and axons for relatively few, especially if they're myelinated (for a fiber diameter of 1 um, there's only about 1 node of Ranvier per 200-300 um of axon length, so a 1000 um long axon will have 3 to 5 nodes of Ranvier).

I then came to think that because the specific axial resistance is assumed to be constant, can such simplified model be further simplified as a long single section divided into n segments, where n is the number of nodes?

That's a nice trick. I don't think it would reduce overall complexity of your model cell significantly, not if it's a pyramidal cell with lots of dendritic branches.

### Re: Simplifying myelin-node on long axons

Posted: **Tue Oct 13, 2015 2:26 pm**

by **CYUlysses**

Thanks for your detailed and informative reply!

ted wrote:
Does a cell's axon matter? Is it exposed to the field? Is it where the spike is initiated? If not, does it affect membrane potential at the spike trigger zone? If not, why include it?

The axon is what actually matters in this model, since it is commonly agreed that extracellular stimulation yields spike initiation on the major axons.

ted wrote:
On the other hand, does it add much to the total computational complexity of a model cell? Have you calculated the the relative computational complexities attributable to axonal compartments vs. non-axonal compartments?

As the axons are the major focus of spike generation, the dendrites in this model are reduced to several major branches of apical and basal dendrites with reduced lengths; the allowed synapse distance is increased to compensate for the reduction's impact. The active channel mechanisms are maintained for now, but I am not sure whether the electrotonic length requirement can be relaxed for this simulation: after all, the role of dendrites here in this model is mainly to pass synaptic signals along to the soma. Moreover, the synapses that synapse on soma and axon initial segments are of larger interest.

ted wrote:That's a nice trick. I don't think it would reduce overall complexity of your model cell significantly, not if it's a pyramidal cell with lots of dendritic branches.

And here because the pyramidal cell is modeled with reduced dendritic morphology but rather involved axon structures (the longest spanning over 1000 um), if reducing the node to a single compartment is a valid simplification, then computational complexity can be significantly reduced.

The above are my thoughts and assumptions, and I would be grateful if you can point out anything that you think is wrong..

### Re: Simplifying myelin-node on long axons

Posted: **Tue Oct 13, 2015 3:47 pm**

by **ted**

OK, axons are the most important part of the model. What is "a lot of compartments" to you? According to the d_lambda rule, a 1 um diameter axon with

Ra 100 ohm cm

cm 1 uf/cm2

needs compartments that are no longer than about 27 um, but myelination reduces effective cm and allows longer compartments, e.g. if cm is 0.1 uf/cm2 they can be up to about 77 um long, and if cm is 0.01 uf/cm2 they can be as long as 200 um. I seem to recall that a 1 um diameter myelinated axon has internodes that are ~200 to 250 um long, so I'd design my model to have internodes that are <= 200 um long so a 1 mm length of unbranched axon would need only 5 nodes of Ranvier and 5 internodes--each of which requires only one compartment. 10 compartments isn't a lot, so I can only presume that your axons are highly ramified.

My own inclination would be to avoid tricky approximations and just take the computational hit. If the time required to execute a single run is way too long, you might try multithreaded execution. That's usually easy to do (generally doesn't require changes to source code, as long as mod files are threadsafe) and it's a convenient way to speed things up by a factor ~2 to ~3 or 3.5 (depending on the number of cores on your PC or Mac). If you have to do a bunch of simulations with different parameters, e.g. for optimization or exploration of parameter space, you could use bulletin-board style parallelization which will get you almost exactly an N-fold speedup where N is the number of cores that you allocate to the task. And if you need more than your local hardware can handle, only run on your PC or Mac during program development and debugging, then use the Neuroscience Gateway Portal

http://www.nsgportal.org/ when it comes time to grind out a lot of results. Getting an account is quick and easy, and you automatically get a pile of free CPU time (50,000 CPU hours) and can ask for (and get) more if you start to run out. User interface is very simple.

### Re: Simplifying myelin-node on long axons

Posted: **Tue Oct 13, 2015 5:53 pm**

by **CYUlysses**

I see! Very helpful and insightful advice. Thanks a lot!