Realistic current clamp electrode (balance bridge artifact)

[jaambros]

Does anybody know of a "realistic" current clamp model that incorporates electrode resistance and capacitance?

I have some experimental current patch clamp recordings with artifacts at the beggining and end of the current pulse (I believe these are known as bridge balance artifacts) and I want to recreate the artifacts in my NEURON model.

[ted]

Easily done with the Linear Circuit Builder. Decide how to represent your electrode and
whether or not you want to include compensation circuitry.

The simplest electrode model is an equivalent L circuit--lumps the series resistance
into a single element, and lumps the electrode capacitance into a single element that
spans from the "headstage" end of that resistor (the end that is not attached to the
cell) to ground. You'll find an example of this in chapter 3 of The NEURON Book, where
it is paired with a simple capacitive compensation circuit.

A slightly more complex electrode representation is an equivalent T, in which the
series resistance is split into two halves, the electrode capacitance spanning from
their junction to ground. This can better mimic the "abrupt" jump of observed V that
occurs at the start and end of current pulses. I have presented this model, sans any
compensation circuitry, in the NEURON course at past meetings of the Society for
Neuroscience, and have also used it in a model that includes circuitry for compensation
of series resistance and electrode capacitance.

Toss in limited gain-bandwidth product for the headstage and compensation amplifiers,
and you're starting to emulate the complexities of the real world.

All of this is quite easy to implement using the GUI, and it is also easy to combine
the GUI with a hoc-implemented cell. I'll send you some of these via separate email.

[eacheon]

Easily done with the Linear Circuit Builder. Decide how to represent your electrode and
whether or not you want to include compensation circuitry.

The simplest electrode model is an equivalent L circuit--lumps the series resistance
into a single element, and lumps the electrode capacitance into a single element that
spans from the "headstage" end of that resistor (the end that is not attached to the
cell) to ground. You'll find an example of this in chapter 3 of The NEURON Book, where
it is paired with a simple capacitive compensation circuit.

A slightly more complex electrode representation is an equivalent T, in which the
series resistance is split into two halves, the electrode capacitance spanning from
their junction to ground. This can better mimic the "abrupt" jump of observed V that
occurs at the start and end of current pulses. I have presented this model, sans any
compensation circuitry, in the NEURON course at past meetings of the Society for
Neuroscience, and have also used it in a model that includes circuitry for compensation
of series resistance and electrode capacitance.

Toss in limited gain-bandwidth product for the headstage and compensation amplifiers,
and you're starting to emulate the complexities of the real world.

All of this is quite easy to implement using the GUI, and it is also easy to combine
the GUI with a hoc-implemented cell. I'll send you some of these via separate email.

Ted, is this later more complex model available with any resources? Is the old NEURON course available on line? I found this:
http://www.neuron.yale.edu/course/lincir1/lincir1.html
not sure if it is what you meant, (it is a two-electrode voltage clamp).

I am trying to implement a realistic voltage clamp / current clamp with patch pipette electrode. The compensation is not the major concern since the data were sample without specific compensation. Not sure what to read as a first introduction...

[ted]

The SEClamp class, which is built into NEURON, is a voltage source in series with
a resistor. Think of it as a model of an electrode that has series resistance but no
capacitance, attached to a "perfect single electrode clamp device." You only need to
use the Linear Circuit Builder if you want to take electrode capacitance or limited
frequency response of the single electrode clamp device into account.

Before doing any modeling of electrodes, headstages, clamps etc., it is essential to
have a clear qualitative grasp of the underlying theory. The old Axon Guide presents
this stuff in a very approachable way, particularly in the first three chapters. Molecular
Devices swallowed up Axon Instruments, but wisely are still giving away the Axon
Guide--you can get the pdf from
http://www.moleculardevices.com/pages/i ... guide.html

The mechanics of using the Linear Circuit Builder are described in this excerpt from the
NEURON summer course http://www.neuron.yale.edu/course/lincir1/arrange.html . This
particular excerpt presents the Linear Circuit Buider in the context of an exercise
http://www.neuron.yale.edu/course/lincir1/lincir1.html that involves implementing a very
simple model of a two electrode voltage clamp, with significant electrical separation
between the voltage sensing and current passing electrodes, but it should be enough
to get you going.

This zip file
http://www.neuron.yale.edu/ftp/ted/neur ... amples.zip
contains three examples of simplified patch clamp instrumentation modeled with the
Linear Circuit Buider. Read the readme.txt file first. These are all current clamps, but it
woudn't be hard for you to cobble up your own voltage clamp circuit.

[eacheon]

The SEClamp class, which is built into NEURON, is a voltage source in series with
a resistor. Think of it as a model of an electrode that has series resistance but no
capacitance, attached to a "perfect single electrode clamp device." You only need to
use the Linear Circuit Builder if you want to take electrode capacitance or limited
frequency response of the single electrode clamp device into account.

Thanks for the detailed instruction. I do want to take electrode capacitance and maybe filter properties of electrodes into consideration. But may I ask how do people deal with non-infinite "seal resistance"? I read some of the materials mentioned above but did not find it mentioned. Is seal resistance not affecting the shapes of the traces recorded (simply division), under the hypothesis that it is constant?

[ted]

how do people deal with non-infinite "seal resistance"? I read some of the materials mentioned above but did not find it mentioned.

Too bad nobody seems to be teaching this stuff. The answer to your question "how do
people deal with . . . " is somewhere in the primary literature about patch clamp. However,
it's not hard to devise a rational way to represent an imperfect seal in a model. First ask
yourself these two questions:
1. Where is the seal located?
2. If the seal is imperfect, what are its biophysical properties? i.e. is it like an ion channel
(has a nonzero reversal potential, i-v relationship possibly nonlinear or time-varying), or is
it more like a nonspecific leak (just a linear resistor from the site of electrode attachment
to the bath ground).

Nuts. I answered question 1 for you.

[eacheon]

how do people deal with non-infinite "seal resistance"? I read some of the materials mentioned above but did not find it mentioned.

Too bad nobody seems to be teaching this stuff. The answer to your question "how do
people deal with . . . " is somewhere in the primary literature about patch clamp. However,
it's not hard to devise a rational way to represent an imperfect seal in a model. First ask
yourself these two questions:
1. Where is the seal located?
2. If the seal is imperfect, what are its biophysical properties? i.e. is it like an ion channel
(has a nonzero reversal potential, i-v relationship possibly nonlinear or time-varying), or is
it more like a nonspecific leak (just a linear resistor from the site of electrode attachment
to the bath ground).

Nuts. I answered question 1 for you.

All right, I guess it is a nonspecific leak. Correct me if I get it wrong, since I'm going to regard it as a linear resistor.

But sorry I have more questions regarding the "patch clamp example" I was directed to:

1. Is the "series resistance" mentioned in these models actually alias of "the resistance of pipette", or " the resistance of pipette" and "the residual resistance of the ruptured patch" (as "access resistance")?

2. Why is the "equivalent T" a better electrode model than "equivalent L"? Is it justified that the electrode capacitor is connected to half of the voltage drop on the series resistance?

The data I am working with are in somewhat different configuration with many ppl have, where the pipette is sunk into brain for ~10 mm and that produces huge capacitance and since cells membrane is ruptured by zapping I suppose the residual resistance of the ruptured patch is also huge. I am suspecting this electrode capacitance might be differently modeled than the "equivalent T".

[ted]

All right, I guess it is a nonspecific leak. Correct me if I get it wrong, since I'm going to regard it as a linear resistor.

Yep.

1. Is the "series resistance" mentioned in these models actually alias of "the resistance of pipette", or " the resistance of pipette" and "the residual resistance of the ruptured patch" (as "access resistance")?

In theory it should be the latter. Practice is another matter; do you know of an
experimental method for measuring "the residual resistance of the ruptured patch" ?

Why is the "equivalent T" a better electrode model than "equivalent L"?

The question is how to represent distributed electrode resistance and stray capacitance.
A rough approximation is to lump each into a single element (resistor and capacitor), but
then the question is where should the lumped capacitor be located. The problem with
plunking it at one end or the other of the resistance is that most of the distributed
capacitance isn't particularly close to either of those locations--most of it is in between
them. That's why putting it in the middle is better. You can also think about it this way:
If we represent stray capacitance by a lumped capacitor located at the distal end, the
voltage at the proximal end--which is attached to the preamp--would perfectly follow the
membrane potential of the cell (because there would be no current flow through the
electrode resistance, hence the voltage at its proximal and distal ends would be dentical).
So there would be no need to compensate for electrode capacitance. We know this
doesn't happen in the real world, so it's not how we should represent electrode
capacitance in our models.
If on the other hand the lumped capacitor were all located at the proximal end, it would be
possible to perfectly compensate for the electrode capacitance. But this doesn't happen
in the real world either, so it's not a good way to represent the effects of electrode
capacitance.
The third alternative is to place it somewhere in between. Dead center is a reasonable
choice, in the absence of any basis for picking some other location. This representation
gives us a model that needs capacitance compensation, but does not allow perfect
compensation. More faithful to the world in which we live, so a better way to model
electrode capacitance.

Is it justified that the electrode capacitor is connected to half of the voltage drop on the series resistance?

Beg your pardon. One side of the capacitor is grounded; the other side is at a potential
halfway between true Vm and Vi, where Vi is the voltage that appears at the input to the
headstage preamp. Vi = Vm + epsilon, where epsilon is the voltage drop along the
electrode resistance, so the ungrounded side of the lumped capacitor sees
Vm + epsilon/2, not epsilon/2.

The data I am working with are in somewhat different configuration with many ppl have, where the pipette is sunk into brain for ~10 mm and that produces huge capacitance and since cells membrane is ruptured by zapping I suppose the residual resistance of the ruptured patch is also huge. I am suspecting this electrode capacitance might be differently modeled than the "equivalent T".

Depends on many factors. Are you using a driven shield, or do you bother coating the
electrode (except for the last mm or so)? If not, maybe you can calculate how axial
resistance and stray capacitance vary along the business end of your electrodes.
You know what kind of glass you're using, so can determine its dielectric constant.
You also can measure the resistivity of the pipette solution. All you need to know is
how lumen diameter and wall thickness vary within 1-2 cm of the patch end. Then a
little calculus and you have a completely rational basis for the electrode's equivalent
circuit.

[eacheon]

In theory it should be the latter. Practice is another matter; do you know of an
experimental method for measuring "the residual resistance of the ruptured patch" ?

The experimenters retract the electrodes a little after finishing patch-recording from a cell, and do an I-V curve of the electrode, hopefully I can get an idea about the portion of "series resistance" and that of "residual resistance of the ruptured patch" from these recordings.

You can also think about it this way:
If we represent stray capacitance by a lumped capacitor located at the distal end, the
voltage at the proximal end--which is attached to the preamp--would perfectly follow the
membrane potential of the cell (because there would be no current flow through the
electrode resistance, hence the voltage at its proximal and distal ends would be dentical).
So there would be no need to compensate for electrode capacitance. We know this
doesn't happen in the real world, so it's not how we should represent electrode
capacitance in our models.

Sorry, I did not get the part "because there would be no current flow through the electrode" and all the following reasoning. Did you mean at least when current clamping at 0 we cannot put the lumped capacitor at the distal end?

Depends on many factors. Are you using a driven shield, or do you bother coating the
electrode (except for the last mm or so)? If not, maybe you can calculate how axial
resistance and stray capacitance vary along the business end of your electrodes.
You know what kind of glass you're using, so can determine its dielectric constant.
You also can measure the resistivity of the pipette solution. All you need to know is
how lumen diameter and wall thickness vary within 1-2 cm of the patch end. Then a
little calculus and you have a completely rational basis for the electrode's equivalent
circuit.

This is interesting. We did not use any driven shield or things similar. I think I will have a look and see what values I get.

Also, it is feasible to model this electrode as a cable (a section in NEURON) with modified Ra, C, for the part of electrode filled with internal solution but without wire in it?

[ted]

Sorry, I did not get the part "because there would be no current flow through the electrode" and all the following reasoning. Did you mean at least when current clamping at 0 we cannot put the lumped capacitor at the distal end?

First definitions to make sure we're using the same words.
Distal end is the end of the pipette that attaches to the cell.
Proximal end is the end that attaches to the headstage preamp.

Now to address your question: "Did you mean at least when current clamping at 0 we
cannot put the lumped capacitor at the distal end?"
The distributed resistance and capacitance of the electrode act like a low pass filter. The
effect of the electrode on the signal that gets to the preamp cannot be modeled by putting
the lumped electrode capacitance at the distal end of the electrode.

it is feasible to model this electrode as a cable (a section in NEURON) with modified Ra, C, for the part of electrode filled with internal solution but without wire in it?

Feasible, but the most convenient way to represent it is with an equivalent T circuit in
the Linear Circuit Builder.