Thin myelinated fibers

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calu
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Thin myelinated fibers

Post by calu » Thu Apr 28, 2016 1:26 pm

Dear all,

I need to simulate thin (0.2 - 3µm) myelinated fibers of the autonomic nervous system. For larger (motor) ones (>5.7µm), the McIntyre model seems to be today's standard. However when simply extrapolating the parameters to smaller diameters, strange effects like muliple action potentials following one excitation arise. One can tweak the parameters to let the axon spike normally but I wonder if there is a physiologically plausible model for thin myelinated axons out there I am not aware of.

Thanks for any hints.

ted
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Re: Thin myelinated fibers

Post by ted » Sun May 01, 2016 12:53 pm

calu wrote:the McIntyre model seems to be today's standard.
AFAIK there is no "standard model" for myelinated axons--at least, nothing with the stature of the HH squid axon model. Several different computational models for myelinated axons have been proposed. Also, models tend to be species-specific, not to mention differences between central and peripheral axons. You might want to consider some of the models developed by Waxman and his collaborators, and consult recent reviews to see what else may be available.
when simply extrapolating the parameters to smaller diameters, strange effects like muliple action potentials following one excitation arise.
Risky business, extrapolating parameters. Are you sure your diameters aren't outside the fitted range? Best to base models on specific experimental observations.

Have you adjusted spatial discretization? Narrower diameter neurites require a finer spatial grid than larger diameter neurites do.

WRT repeated spiking, what kind of stimulus are you using? Is its duration too long, amplitude too large? Experimentalists find the threshold stimulus, then use an "experimental" stimulus that is twice as large.

calu
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Re: Thin myelinated fibers

Post by calu » Thu May 12, 2016 12:03 pm

Thanks Ted and sorry for the late reply.

I tried out your suggestions and still have mutliple APs, with just over threshold stimuli.

I now assume that the effect arises from a simplification the McIntyre model applies. There are no fast K+-channels in the internodal compartments that are observed in peripheral axons. This causes the potential of these comparments to stay very high. I will try to add them (first need to get a little used to MODL writing) and report back here.

ted
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Re: Thin myelinated fibers

Post by ted » Thu May 12, 2016 3:24 pm

calu wrote:I now assume that the effect arises from a simplification the McIntyre model applies. There are no fast K+-channels in the internodal compartments that are observed in peripheral axons. This causes the potential of these comparments to stay very high.
Two questions.
1. Why would that be more of a problem for small diameter than large diameter?
2. Why would prolonged depolarization not simply cause depolarization block?
I will try to add them (first need to get a little used to MODL writing) and report back here.
Which McIntyre model do you mean? The one used for
McIntyre CC, Richardson AG, Grill WM (2002)
Modeling the excitability of mammalian nerve fibers:
influence of afterpotentials on the recovery cycle.
J Neurophysiol 87:995-1006
https://senselab.med.yale.edu/ModelDB/s ... model=3810
has a mod file called AXNODE.mod which describes a mechanism that generates voltage-gated spike sodium, persistent sodium, and potassium currents, not to mention a leak current with constant conductance. According to ModelDB's ModelView feature, gkbar_axnode has a value of 0.08 S/cm2.

So there should be no need to write any NMODL code at all. Just
1. make sure that gkbar_axnode is nonzero in all sections into which axnode has been inserted
and
2. if necessary, use hoc statements to adjust its value to overcome the persistent post-spike depolarization.

This procedure makes it easy to set the value of gkbar_axnode:

Code: Select all

proc setgk() {
  forall for (x,0) if (ismembrane("axnode")) gkbar_axnode(x) = $1
}
As a nonsense example,
setgk(PI)
will set gkbar_axnode to 3.1415... S/cm2 wherever axnode has been inserted.

By the way, did you make sure that your code sets celsius to 37?

calu
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Re: Thin myelinated fibers

Post by calu » Thu May 12, 2016 4:40 pm

Hi,
Two questions.
1. Why would that be more of a problem for small diameter than large diameter?
Because the node length does not scale with diameter, but the distance between nodes does. So the relation of (membrane area of node)/(membrane area of internodal compartments) ~ (inward current during AP)/(leakage outward current) rises. If I reduce the node length, the multiple AP problem goes away. But this is not observed even in very small myelinated axons.
2. Why would prolonged depolarization not simply cause depolarization block?
By depolarisation block you mean inactivation after several spikes? That happens, yes. But already the second spike does not seem like a physiologically realistic behaviour.
Which McIntyre model do you mean? The one used for
McIntyre CC, Richardson AG, Grill WM (2002)
Modeling the excitability of mammalian nerve fibers:
influence of afterpotentials on the recovery cycle.
J Neurophysiol 87:995-1006
https://senselab.med.yale.edu/ModelDB/s ... model=3810
Yes.

has a mod file called AXNODE.mod which describes a mechanism that generates voltage-gated spike sodium, persistent sodium, and potassium currents, not to mention a leak current with constant conductance. According to ModelDB's ModelView feature, gkbar_axnode has a value of 0.08 S/cm2.
The axnode membrane mechanism only gets inserted into the nodes, not the internodal compartments. But I will build on that model to 'code by example' and add the potassium channels. In fact McIntyre integrated those for axons in the CNS:

McIntyre CC, Grill WM, Sherman DL, Thakor NV (2004)
Cellular effects of deep brain stimulation: model-based analysis of activation and inhibition
J Neurophysiol. 91(4):1457-69

Unfortunately the corresponding files are not available in the database. But maybe this one for a more recent paper will help me. https://senselab.med.yale.edu/ModelDB/S ... del=151460

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Re: Thin myelinated fibers

Post by ted » Thu May 12, 2016 5:44 pm

calu wrote:
1. Why would that be more of a problem for small diameter than large diameter?
Because the node length does not scale with diameter, but the distance between nodes does. So the relation of (membrane area of node)/(membrane area of internodal compartments) ~ (inward current during AP)/(leakage outward current) rises.
Good point.
2. Why would prolonged depolarization not simply cause depolarization block?
By depolarisation block you mean inactivation after several spikes? That happens, yes. But already the second spike does not seem like a physiologically realistic behaviour.
Introducing voltage-gated gk into the internodal membrane adds complexity to the model but may not have much effect on its dynamics because of the resistance of the pathways that separate the external surface of the axon from the external medium.

Here are three other measures that would not add new differential equations to the model but should reduce its propensity to fire repeatedly after a single stimulus.

1. Decrease gnapbar_axnode. I suspect this will be most effective.
2. Increase gkbar_axnode.
3. Decrease gnabar_axnode.

Any of these changes is likely to affect resting potential, hyperpolarizing the nodes in particular, but inserting a potassium conductance into the internodes might have a larger effect.

calu
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Re: Thin myelinated fibers

Post by calu » Thu May 12, 2016 5:59 pm

Here are three other measures that would not add new differential equations to the model but should reduce its propensity to fire repeatedly after a single stimulus.

1. Decrease gnapbar_axnode. I suspect this will be most effective.
2. Increase gkbar_axnode.
3. Decrease gnabar_axnode.
Yes, this should be effective, too, you are right. Then again I did not find papers that reported a smaller channel density/ opening probablity for thinner axons. While on the other hand fast K+-channels between nodes have been reported (e.g. Röper and Schwartz 1989). So I prefer to follow this physiological route despite its increased complexity. Also the shape of a single AP might be affected by the measures you propose, right? But I will try it out.

Thanks!

ted
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Re: Thin myelinated fibers

Post by ted » Fri May 13, 2016 10:08 am

calu wrote:
the shape of a single AP might be affected by the measures you propose, right?
Persistent sodium conductance accounts for only a very small fraction of total sodium channel density. Eliminating it entirely is unlikely to have a significant effect on spike amplitude or time course.

calu
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Re: Thin myelinated fibers

Post by calu » Sun May 15, 2016 3:39 pm

Hi,

I tried both your proposed method of changing g[...]bar and mine of inserting a fast potassium channel in the FLUT segments. By increasing gkbar_axnode by 50%, I could eliminate the multiple action potentials. With my method, only very high (unrealistic, more than 10 times higher than observed) values of gkbar of the fast channels could keep the nodes from spiking again. Then also the shape of afterpotentials was significantly changed. So I will keep the gkbar_axnode reduced as you proposed.

Thank you for your help!

ted
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Re: Thin myelinated fibers

Post by ted » Sun May 15, 2016 11:58 pm

Interesting. Does reducing persistent sodium channel density have bad side-effects, e.g. on resting membrane potential, or spike threshold, amplitude, or duration? If so, can they be compensated by increasing the non-persistent sodium channel density?

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