Regarding connection to ground under extracellular

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shailesh
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Joined: Thu Mar 10, 2011 12:11 am

Regarding connection to ground under extracellular

Post by shailesh » Wed Mar 18, 2015 7:09 am

Hi,

I again have some query regarding the use of extracellular. I am trying to model a long axon having hh and extracellular mechanism with the connection to ground available at only at one of the terminals (say 1-end). The other end (0-end) of the axon is stimulated via IClamp and I keep track of the .v, .vext[0], i_membrane at several segments along the length. I have set Ra/Re = 4 (with proper units, I believe).

I find that as soon as the stimulus starts, I can immediately see a depolarization at both the 0 and 1 ends, but no change simultaneously at the segments inbetween. The response at the 1-end is smaller (sub-threshold) than the 0-end (AP). If I change Ra/Re = 1, then identical responses are observed at both ends, and AP's are subsequently generated at the other segments from both ends.

I am unable to figure out why I see an instantaneous depolarization at the end of the axon (opposite to the site of stimulus), especially with the intermediate segments remaining at rest. I suppose the query is conceptual. Any help would be appreciated. Thanks in advance!

p.s. My thoughts right now are that the current injection (IClamp) takes place between the specified point and the ground, and thus current flows out of the segment connected to ground (here the 1-end) while it is injected at the specified site (0-end). But if so, how can I implement my model without having this issue, i.e. such as to have two separate grounds - one for the model and one for the stimulus?

My HOC code:

Code: Select all

load_file("nrngui.hoc")

create axon
axon {
	L = 5000
	diam = 1
	nseg = L+1

	cm = 1
	Ra = 100

	insert hh	
	//insert pas
	//e_pas = -65
}

objref stim
stim = new IClamp(0)
stim.del = 2.5
stim.amp = 0.25
stim.dur = 0.5

tstop = 25

xopen("session_test.ses")

// ----- Extracellular Implementation -----

//Define
ratio_Ra_by_Re = 4

proc setExtra() {	
	axon {
		insert extracellular
		xc[0] = 0
		xc[1] = 0		
		
		xg[0] = 1e-9	// Infinite Resistance
		xg[1] = 1e-9	// Infinite Resistance
		
		/*		
		To connext start (0) terminal to ground
		xg[0](0) = 1e9
		xg[1](0) = 1e9
		*/
		
		//To connext end (1) terminal to ground
		xg[0](1) = 1e9	//	No Resistance
		xg[1](1) = 1e9 	//	No Resistance
		
		xraxial[0] = ((Ra / ratio_Ra_by_Re)/(PI*((diam*1e-4/2)^2))) * 1e-6
		xraxial[1] = 1e9  // Infinite Resistance
	}
	
	print "_________________________________________"
	print "Extracellular Mechanism Inserted"
	print "_________________________________________"
}
setExtra()

xpanel("Run Simulation")
	xlabel("Run Simulation")
	xbutton("Run", "run()")
	xvalue("ratio_Ra_by_Re", "ratio_Ra_by_Re", 1, "setExtra()")
xpanel(400, 750)

ted
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Re: Regarding connection to ground under extracellular

Post by ted » Wed Mar 18, 2015 5:52 pm

shailesh wrote:as soon as the stimulus starts, I can immediately see a depolarization at both the 0 and 1 ends, but no change simultaneously at the segments inbetween . . .
. . . I am unable to figure out why I see an instantaneous depolarization at the end of the axon (opposite to the site of stimulus), especially with the intermediate segments remaining at rest.
A very good question. Certainly good for a lab discussion, or for an instructor to apply the Socratic Method. Maybe even good enough to use in a doctoral candidate's qualifying exam.

Doubtless you are looking at v, and not seeing any change in v in the segments for which xg[0] and [1] are very small. Suggest you re-read the Programmer's Reference documentation of the extracellular class, then see what the stimulus does to the value of vext.

Spoiler Alert! Remember that v is transmembrane potential, not the absolute potential of the interior of a section. If extracellular has been inserted, the potential at the outer surface of the section is the potential at the floating node of a voltage divider. The ungrounded node of the voltage divider is at the absolute potential inside the cell, and the grounded node is at 0. The resistance of the upper limb of the divider is the membrane resistance of the cell, which although large is still finite. The resistance of the lower limb (path from just outside the axonal membrane to ground) is enormous because the xgs are so small and xraxial is by default 1e9. The absolute potential at the junction of these two limbs will be very nearly equal to the absolute potential of the interior of the cell, so the transmembrane potential will be vanishingly small.

shailesh
Posts: 104
Joined: Thu Mar 10, 2011 12:11 am

Re: Regarding connection to ground under extracellular

Post by shailesh » Thu Mar 19, 2015 9:36 am

Thanks for suggesting to apply the voltage-divider rule. That cleared a lot of questions. To ease things further I replaced the HH with pas and then observed the plots for vint, vext, vm and i_membrane... and then the picture began to emerge. All the intermediate segments had their vint and vext equal (as you pointed out), and thus no vm, as also indicated by i_membrane = 0 at these locations.

But I am left wondering whether I have fumbled in interpreting my model. I imagine the electrical equivalent circuit (for my HOC code in the earlier post; pas in place of hh; ratio_Ra_by_Re=1) to be such:
Image
when
xc[0] = 0
xc[1] = 0
xg[0] = 1e-9 (only at 1-end = 1e9)
xg[1] = 1e-9 (only at 1-end = 1e9)
xraxial[0] : is set such that Ra = Re (so no longer at the default value)
xraxial[1] = 1e9

With Ra=Re here in the figure, each of the trans-membrane pathways (from the site of current current injection to ground) are identical: Rm + 4(Ra or Re). So, I would expect membrane current, and thus change in vm, at each of the segments.

With increased diameter (10 or 100um; so as to have smaller absolute values of resistances), I see that even the intermediate segments exhibit a healthy change in vm with a slower time course (expected as per cable theory). But what I find surprising is the response of the 1-terminal, which shows a response identical to the 0-end... as if the two terminals are short-circuited, though I can't answer where and why. Apologies if I am missing the obvious.
Image

ted
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Re: Regarding connection to ground under extracellular

Post by ted » Thu Mar 19, 2015 11:41 am

Note that the units of xraxial are megohms/cm, not the units of resistivity (ohm cm). The resistance in megohms between two adjacent external nodes in the same section is xraxial * L/nseg * 1e-4 where the 1e-4 scale factor converts um to cm. You may already know that ri(x) returns the axial resistance in megohms between the center of the segment containing x and its parent segment.

shailesh
Posts: 104
Joined: Thu Mar 10, 2011 12:11 am

Re: Regarding connection to ground under extracellular

Post by shailesh » Thu Mar 19, 2015 1:01 pm

I believe I got that conversion correct in my HOC code with the statement:

Code: Select all

xraxial[0] = ((Ra / ratio_Ra_by_Re)/(PI*((diam*1e-4/2)^2))) * 1e-6
To verify (with pas instead of hh and ratio_Ra_by_Re=1):
xraxial[0]*L*1e-4/nseg = 1.2729849
ri(0.9999) = 1.2729849

So not sure where I have faltered.

shailesh
Posts: 104
Joined: Thu Mar 10, 2011 12:11 am

Re: Regarding connection to ground under extracellular

Post by shailesh » Sun Mar 22, 2015 11:41 am

Any suggestions on what could be wrong here?

hines
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Re: Regarding connection to ground under extracellular

Post by hines » Wed Apr 01, 2015 10:04 am

I believe the behavior of your circuit is correct. It is always helpful to plot vext and vext+v.
Note that the current coming into the interior on the left is always equal to the current leaving the exterior on the right. So there is a kind of symmetry and one
expects for your circuit v(x) == v(1-x).
I feel that would be the case for propagated action potential as well if you made the xraxial match with the Ra. ie the ap would be generated on both ends and collide in the middle.

shailesh
Posts: 104
Joined: Thu Mar 10, 2011 12:11 am

Re: Regarding connection to ground under extracellular

Post by shailesh » Wed Apr 01, 2015 11:45 am

Yes that indeed happens. If I change Ra/Re = 1, then identical responses are observed at both ends, and AP's are subsequently generated at the other segments from both ends. Viewing the circuit as a whole, I suppose it is natural to observe such a response. The two ends turn out to be symmetric, as you rightly pointed out.

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