spike propagation in a branched cell

[Quentin]

Hi all,

I am trying to simulate a linear fiber with a central axon, a soma and a peripheral axon.
I used the dimensions given in Rattay et al, 2001, Hear Res.:
central.diam=2 um, peripheral.diam=1um, soma.L =20 and soma.diam =30.

However when using these parameters I am facing unexpected behaviors:
1/ I plotted the potential as a function of distance across my cell and it seems that action potentials initiated (IClamp at one node) at the periphery cannot pass the soma.

2/ In the opposite AP initiated in the central axon (IClamp at one central node) propagate in both directions, and antidromic spikes CAN pass the soma.

3/ when using extracellular stimulation (which is my objective) it seems that AP are initiated at both extremities resulting in an antidromic central spike and orthodromic peripheral spike both ending at the soma.

I'd be glad to hear your advice to either fix these problems or understand why it yields such outcomes.
Thanks a lot.
Q.

[ted]

About the model cell: what are the lengths and spatial discretization of its axons, how did you decide what discretization to specify, and what is the cell's topology?

About the computational experiments: what results did you expect?

[Quentin]

Thanks for your answer. Here are details on the cell topology:

[node-internode-...-node-Soma-node-internode...-node]
soma: diam =30, L =20µm
central axon :
- diam = 2 µm
- 11 nodes, L = 1.5 µm
- 10 internodes, L = 100 µm

peripheral axon :
- diam = 1 µm
- 6 nodes, L = 1.5 µm
- 5 internodes, L = 100 µm

all sections are ruled by HH mechanism + Ra = 70 Ohm.cm + xtra + extracellular
Cm = 0.01 for internodes and 1 nodes and soma.
gnabar_hh = 1.2 for nodes and 0.12 for internodes and soma.

I used the d_lambda rule with d_lambda = 0.03 according to the recommandations in the ModelView window.

I ran a few more tests to understand what is going on here and I have new insights compared to my previous post.
When I play with the electrode-cell distance I can in some cases find results that I am able to understand and explain.
eg. when AP are generated close to the electrode and can propagate through the cell.

But in other cases I sometimes end up with another AP initiated at the central extremity that goes in the opposite direction. When plotting the potential at a peripheral node it results in a double spike 1 is generated in this region the other travel from the central axon with a slight delay.
In the end I almost met all my expectations:
1/ AP generated at the nodes that are closest to the stimulating electrode
2/ AP to propagate along axons and through the soma
3/ spikes to be delayed by the presence of the soma.

you might still help me understand why I still get a "central" AP even when my electrode is located at the very periphery?

here is an example I cannot explain:
1/ I place the electrode in front of the most peripheral node => AP is generated at this node propagates through the peripheral axon but cannot pass the soma
2/ my electrode is still in front of that peripheral node but slightly further => I end up with the same AP PLUS another one coming from the other end of the fiber...

thank you for your help,
best,
Quentin

[ted]

Here are details on the cell topology:

OK, just needed to make sure the model's soma was between the two axons.

Cm = 0.01 for internodes and 1 nodes and soma.

"1 nodes"? Does this mean "node of Ranvier," and if it does, why would any node of Ranvier have the same specific capacitance as the adjacent interndode? Or do you mean "node" in the mathematical sense, i.e. one of the points in space at which NEURON computes membrane potential?

gnabar_hh = 1.2 for nodes and 0.12 for internodes and soma.

The relatively low channel density at the soma may be relevant to one of the observations in your first message.

I used the d_lambda rule with d_lambda = 0.03 according to the recommandations in the ModelView window.

So spatial discretization is more than adequate. If the spatial grid is too coarse, excitability and conduction velocity are both artifactually reduced.

I ran a few more tests to understand what is going on here and I have new insights compared to my previous post.

One of those new insights is probably about this:

I plotted the potential as a function of distance across my cell and it seems that action potentials initiated (IClamp at one node) at the periphery cannot pass the soma.

2/ In the opposite AP initiated in the central axon (IClamp at one central node) propagate in both directions, and antidromic spikes CAN pass the soma.

The peripheral axon is only 1 um in diameter, so it can't generate much depolarizing current. Because the soma is electrically compact and has a very large surface area compared to an identical length of 1 um diameter axon, orthodromic spikes run into a big capacitive load when they hit the soma. That, and the relatively low Na channel density of the soma (which reduces excitability of the soma) may account for conduction failure of orthodromic spikes.


Now, about extracellular stimulation, which can produce puzzling results.

3/ when using extracellular stimulation (which is my objective) it seems that AP are initiated at both extremities resulting in an antidromic central spike and orthodromic peripheral spike both ending at the soma.

You haven't mentioned stimulus waveform or polarity, or whether it is produced by monopolar or bipolar electrodes. Monopolar stimulation is spatially much less selective than bipolar and can produce lots of interesting phenomena. Some spatial configurations of electrode and nerve, and temporal profiles of stimulus current, are more likely to elicit rebound excitation (historically called "anode break excitation") than direct excitation. I'm using the term "direct excitation" to refer to depolarization that occurs while the extracellular current is being applied. Rebound excitation happens in situations where the stimulus current makes membrane hyperpolarize, so that after the current stops the membrane potential springs back toward rest but overshoots and results in a spike. Some spike mechanisms are relatively resistant to rebound excitation. However, the HH mechanism is rather prone to rebound or anode break spiking, because at rest there is a significant activation of gk and inactivation of gna. Hyperpolarization both gna inactivation and gk activation. When the hyperpolarizing current stops, v rises quickly toward rest, na channels open quickly and accelerate this rise, but gk lags well behind--and that can make v overshoot enough to trigger a spike.

It can be useful to examine the temporal evolution of space plots of v, gna, gk, m^3 and h (no need to plot n^4 because gk is proportional to n^4). NEURON's gui makes it very easy to set up such graphs. If you have any problem doing that, let me know.

here is an example I cannot explain:
1/ I place the electrode in front of the most peripheral node => AP is generated at this node propagates through the peripheral axon but cannot pass the soma
2/ my electrode is still in front of that peripheral node but slightly further => I end up with the same AP PLUS another one coming from the other end of the fiber...

This is a perfect situation for demonstrating the utility of having a convenient user interface for interactive simulations. Are you using hoc or Python?

[Quentin]

Dear Ted, I apologize for the late answer.

Thanks for your explanations on the HH mechanism.

I ran hundreds of tests to make sure that each step was operated properly. And I also re-read Rattay et al 2001, Hear Res. I made sure the geometry and biophysics of my model was exactly as in their study and it finally works. I also noted that in this paper they mention that the propagation of spikes is highly dependent on the cell properties and that they had to play with the internode length, the number of myelin layers etc. to achieve AP propagation all along the cell.

Concerning the extracellular stimulation, the most central and peripheral nodes still seem very sensible. I have to place the stimulating electrode (monopolar) very close to the neuron to be sufficiently selective and create an AP at the closest node. Here again playing with the last nodes length seems necessary... I am still working on it

I still have troubles to understand several behaviors.
1/ when an AP in created and travels along the cell the spike amplitude is large where it is created and then decreases because a small part of the energy is lost in the internodes. But I always see an increase the the spike amplitude around the soma, at the most peripheral and at the most central nodes (same thing occurs with an IClamp).

2/ might be a newby question... When an AP is created at a given place and travels along the cell, does the spike necessarily opens the Na and K channels in all the nodes it passes through?

NB: I am coding this in .hoc

Best
Quentin

[ted]

Here again playing with the last nodes length seems necessary

I'm not sure why that would be so.

I still have troubles to understand several behaviors.
1/ when an AP in created and travels along the cell the spike amplitude is large where it is created

I often see models in which a gigantic stimulus is used to elicit a spike--a stimulus large enough and long enough to contaminate the resulting action potential at the spike trigger zone. Is that what's happening with your model? How much of the membrane potential at the spike initiation zone is due to stimulus artifact? (hint: reduce stimulus duration to 0.1 or 0.2 ms, and adjust stimulus amplitude so that it is no more than 2 x threshold). To what extent does sealed end effect contribute to the amplitude of the spike at the spike trigger zone? (are you familiar with sealed end effect?)

and then decreases because a small part of the energy is lost in the internodes.

Decreases where? at non-terminal nodes? or are you referring to membrane potential along the internodes? To what extent is the apparent decrease of peak depolarization at non-terminal nodes due to sealed end effect?

I always see an increase the the spike amplitude around the soma, at the most peripheral and at the most central nodes

What role does sealed end effect play at the most peripheral and central nodes? Does capacitive load have anything to do with the difference between membrane potential at the soma and membrane potential at nodes that are not adjacent to the soma?

2/ might be a newby question... When an AP is created at a given place and travels along the cell, does the spike necessarily opens the Na and K channels in all the nodes it passes through?

Why don't you plot gna and gk vs. t at all nodes?

[Quentin]

Thanks for your answer.

I often see models in which a gigantic stimulus is used to elicit a spike--a stimulus large enough and long enough to contaminate the resulting action potential at the spike trigger zone. Is that what's happening with your model?

I use different types of stimuli but the most basic one for my tests is a monophasic pulse, 0.1ms long and just above threshold
and comparable behaviors occurs using both IClamp and extracellular stimulation.

To what extent does sealed end effect contribute to the amplitude of the spike at the spike trigger zone? (are you familiar with sealed end effect?)

No I realize I do not know much about boundary conditions. Since I do not simulate the propagation up to the central system do you think I should add another section at the central extremity? May be with a large Cm so that the energy diffuses on its surface without affecting AP propagation.

Decreases where? at non-terminal nodes? or are you referring to membrane potential along the internodes? To what extent is the apparent decrease of peak depolarization at non-terminal nodes due to sealed end effect?

Whatever the stimulus (Iclamp or extracellular) and what ever the location of the initial spike, the voltage at the most peripheral node, the most central node and the soma are always slightly higher than at the other nodes.

Does capacitive load have anything to do with the difference between membrane potential at the soma and membrane potential at nodes that are not adjacent to the soma?

I guess this is the point. The geometry of the cell in this model has a non-uniform distribution of length for both nodes and internodes along the cell. When using a uniform geometry (forall "nodes" {L=2.5} and forall "myelin" {L=250} ) AP struggle to pass the highly capacitive soma but the spikes have similar amplitudes.
However, the authors in Rattay et al. 2001 reported that different lengths have to be introduced to reproduce a "natural" behavior.
e.g. presomatic and postsomatic nodes have to be longer as well as a longer peripheral terminal.
So I guess my issue is inherent of the present model.

Why don't you plot gna and gk vs. t at all nodes?

I did and I saw this but I simply wondered if this was an expected phenomenon.

Thanks again