### Impedance vs Frequency Plot- DC & AC Current - Gap Junctions

Posted:

**Thu Jul 12, 2012 3:14 pm**Hi,

I was using the GUI tool to plot Impedance vs Frequency spectrum for a number of models:

(a) a simple passive cell

(b) two of these same cells connected via gap junctions (Gap Junctions were modeled in NMODL as purely resisitive - as described in NEURON book)

(c) two of these same cells connected via a resistor using Linear Circuit Builder (basically equivalent to above but different approach)

[As expected results for models (b) and (c) turned out to be pretty identical]

(d) two of these same cells connected via a resistor and capacitor in parallel using Linear Circuit Builder (a gap junction having both a resistive and capacitive component)

Then just for verification, I tried testing for a few values of f (10hz, 100hz, 1000hz) using a sinusoidal input (used Izap.mod with f0=f1) and for f=0Hz, (i.e. DC) by using IClamp - Zin calculated in all cases as as v(x)/i(x) at the peak/steady state. For the latter I supposed that as f tends to 0Hz (f->0Hz) on the Impedance spectrum, Zin converges to a finite value and this would be equivalent to Rin. All the values matched pretty perfectly for the model of a simple passive cell. But there were significant differences for f (10hz, 100hz, 1000hz) when gap junctions came into the picture. And there was a bigger difference in Zin as (f->0Hz) and Rin(IClamp) (33 Mohms vs 1838 MOhms).

I was wondering why this difference takes place in the models having gap junctions. In the NEURON documentation, under Impedance -> Compute -> Bugs, it states: "The calculation is incomplete in the presence of nonlocal mechanisms such as gap junctions". I can list down my questions from here as:

1> What does that statement exactly mean (why is there an issue with mechanims such as gap junctions) and does it have something to do with whats observed in the above models?

2> If yes, then does it mean that the Impedance vs Frequency plot obtained for models with gap junctions is incorrect?

3> If yes, what alternative would you suggest to obtain an Impedance spectrum for such models using gap junctions as point processes?

4> The Impedance spectrum for models (c) and (d) were identical (right to the last decimal); even for absurdly large values of gap junctional capacitance. Found it surprising that the presence of a capacitor (even when given large values) failed to produce any effect on the Impedance spectrum. Why so? Am I missing something?

I was trying to have a go and look through the code where Impedance Class was implemented. But I was unable to locate the same. I was having one other query, but it seemed more appropriate to post it separately as it wasn't entirely related.

Thanks,

Shailesh Appukuttan

I was using the GUI tool to plot Impedance vs Frequency spectrum for a number of models:

(a) a simple passive cell

(b) two of these same cells connected via gap junctions (Gap Junctions were modeled in NMODL as purely resisitive - as described in NEURON book)

(c) two of these same cells connected via a resistor using Linear Circuit Builder (basically equivalent to above but different approach)

[As expected results for models (b) and (c) turned out to be pretty identical]

(d) two of these same cells connected via a resistor and capacitor in parallel using Linear Circuit Builder (a gap junction having both a resistive and capacitive component)

Then just for verification, I tried testing for a few values of f (10hz, 100hz, 1000hz) using a sinusoidal input (used Izap.mod with f0=f1) and for f=0Hz, (i.e. DC) by using IClamp - Zin calculated in all cases as as v(x)/i(x) at the peak/steady state. For the latter I supposed that as f tends to 0Hz (f->0Hz) on the Impedance spectrum, Zin converges to a finite value and this would be equivalent to Rin. All the values matched pretty perfectly for the model of a simple passive cell. But there were significant differences for f (10hz, 100hz, 1000hz) when gap junctions came into the picture. And there was a bigger difference in Zin as (f->0Hz) and Rin(IClamp) (33 Mohms vs 1838 MOhms).

I was wondering why this difference takes place in the models having gap junctions. In the NEURON documentation, under Impedance -> Compute -> Bugs, it states: "The calculation is incomplete in the presence of nonlocal mechanisms such as gap junctions". I can list down my questions from here as:

1> What does that statement exactly mean (why is there an issue with mechanims such as gap junctions) and does it have something to do with whats observed in the above models?

2> If yes, then does it mean that the Impedance vs Frequency plot obtained for models with gap junctions is incorrect?

3> If yes, what alternative would you suggest to obtain an Impedance spectrum for such models using gap junctions as point processes?

4> The Impedance spectrum for models (c) and (d) were identical (right to the last decimal); even for absurdly large values of gap junctional capacitance. Found it surprising that the presence of a capacitor (even when given large values) failed to produce any effect on the Impedance spectrum. Why so? Am I missing something?

I was trying to have a go and look through the code where Impedance Class was implemented. But I was unable to locate the same. I was having one other query, but it seemed more appropriate to post it separately as it wasn't entirely related.

Thanks,

Shailesh Appukuttan