www.neuron.yale.edu

Hi folks,

These are some questions I had about Electrotonic Analysis.
And below that, you will find Ted's response. Hope this helps someone else who has similar doubts.

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Hi Ted,

I have some questions from the electrotonic analysis ?
Hoping that you can give some advice and guidance....

On the frequency tool, the tutorial says that this tool is used to study electrical coupling between two points in the cell.

So lets say we inject at the soma and measure at the dendrite for example and lets assume that this is done at DC.

The tutorial also says that "An electrode is attached to the cell, but not necessarily where the signal is produced. The electrode may be used with a current clamp to inject current and record fluctuations in membrane potential Vm, or with a voltage clamp that records the clamp current Ic that is needed to regulate Vm. "

a ) so for the log frequency vs log A(which is log of voltage inject/measure)
....does this mean that we are looking for the log A for a range of frequencies ?
and based on a basic neuron, when I injected into the soma and measured at the end of a dendrite , i find at high frequency the log A is high, that is to say that the measured signal is decreasing ?
Another point I was wondering is ....what are we injecting ? Since there are distinct numbers on the figure, I am assuming that the software is injecting some "pre-set" current ? Also, as to the measuring, are we just placing an electrode at the point of measure and merely the reading the voltage at that site ?

b ) as for the log frequency vs input impedance...
I noticed that for a simple 5 dendrite neuron , that the input impedance at the soma was of the lowest value, input impedance seen from any of the dendrites is much higher ? Also, in general at higher frequencies the input impedance becomes lower, has this do with the fact that Zc=1/Wc, and and as frequency increases, the impedance becomes lower....
also, does the soma see a lesser input impedance because of some sort of capacitance in serial arrangement ?

Also, the given definition for input impedance is : input impedance ZN (local voltage change)/(local current injection)

I can understand measuring the voltage change with an electrode, but what is the local current injection value and where can i find this, also, is the original voltage the rest potential ie -65mV ??

c ) and as for the log frequency vs Z transfer,
Z transfer is given as :
transfer impedance Zc (local voltage change)/(remote current injection)
equal to
(remote voltage change)/(local current injection)

I noticed, that the highest value of Z transfer is when both the injection and measurement sites are the same ... ?
This sort of makes sense because, obviously, the highest spike in voltage occurs at th point where the current is injected ....and for point further down stream the effect is sort of softened ....but what is the significance of this Z transfer for neural communication?
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Ted's response
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> So lets say we inject at the soma and measure at the dendrite for
> example and lets assume that this is done at DC.

Except none of your questions are about DC, are they?

> The tutorial also says that "An electrode is attached to the cell,
but
> not necessarily where the signal is produced. The electrode may be
used
> with a current clamp to inject current and record fluctuations in
> membrane potential Vm, or with a voltage clamp that records the clamp
> current Ic that is needed to regulate Vm. "
>
> a ) so for the log frequency vs log A(which is log of voltage
> inject/measure)

It's log(Attenuation) (dependent variable) vs. log10 of frequency
(independent variable).

> ....does this mean that we are looking for the log A for a ran! ge of
> frequencies ?

Yes, where -1 means 0.1 Hz, 0 means 1 Hz, 1 means 10 Hz etc. Don't
forget that log(A) is base e, i.e. along the Y axis 1 means an e-fold
attenuation.

> and based on a basic neuron, when I injected into the soma and
measured
> at the end of a dendrite , i find at high frequency the log A is
high,
> that is to say that the measured signal is decreasing ?

Yes. Lots of attenuation means lots of signal loss.

> Another point I was wondering is ....what are we injecting ? Since
there
> are distinct numbers on the figure, I am assuming that the software
is
> injecting some "pre-set" current ? Also, as to the measuring, are we
> just placing an electrode at the point of measure and merely the
reading
> the voltage at that site ?

Nothing is actually injected. The differential equations that describe
the system in the time domain are transformed to algebraic equations
that describe it in the frequency domain (Laplace transformation).
Those algebraic equations are solved to discover the input and transfer
impedances at each frequency, for each node in the model. From these
impedances, all of the signal transfer ratios are computed. This is
called frequency domain analysis and it is orders of magnitude faster
than running frequency domain simulations with sinusoidal currents.

The "include dstate/dt contribution" button is useful for models that
have voltage-gated currents. When this is turned on, NEURON actually
takes the voltage- and time-dependence of active currents into
account by doing a numerical perturbation that is equivalent to
applying a small voltage change.

> b ) as for the log frequency vs input impedance...
> I noticed that for a simple 5 dendrite neuron , that the input
impedance
> at the soma was of the lowest value, input impedance seen from any of
> the dendrites is much higher ?

Yes. Was this a surprise? Much more membrane is "electrically close"
to the soma, than to any point on a dendrite. The more membrane that
is electrically close to the measurement site, the lower the input
impedance is. Why is this true?

> Also, in general at higher frequencies
> the input impedance becomes lower, has this do with the fact that
> Zc=1/Wc,

You got it.

> and and as frequency increases, the impedance becomes lower....
> also, does the soma see a lesser input impedance because of some sort
of
> capacitance in serial arrangement ?

You're close to answering the question I asked above. A big cell
has lower input impedance than a small cell with identical membrane
and cytoplasm, because the big cell has more membrane capacitance
and ion channels that the signal can leak out of. Somatic input
impedance is lower than dendritic input impedance because there's
a lot of membrane (more capacitance and ion channels) near the
soma than there is near most dendritic locations.

Here's another question for you:
suppose you have a cell that looks like this--
From left to right:
thin axon, medium small soma with one or two dendrites arising from it,
long apical branch that gives rise to a big distal apical tuft with
lots of branches (in other words, something like an olfactory bulb
mitral cell).
Where will input impedance be smallest: at the soma, or at the base
of the apical tuft? Or might it be small in both locations?

> Also, the given definition for input impedance is :
> input impedance Z_N (local voltage change)/(local current injection)
>
> I can understand measuring the voltage change with an electrode, but
> what is the local current injection value and where can i find this,
> also, is the original voltage the rest potential ie -65mV ??

More good questions. This dialog should really be on the NEURON Forum.
From what I wrote above, you already know that there isn't actually
any current being injected.
The membrane potential is whatever exists at the time you make your
measurement. If you have a cell with voltage-gated channels, you
should at least click on the RunControl's Init button to make sure
that everything is in its resting state at -65 mV (or whatever value
you specified next to the Init button). You can now see what the
cell's properties are at rest. Then you can run a simulation,
stop at any time, and click on the impedance tool's Redraw button
to see what has happened as a result of voltage- and/or time-dependent
conductance changes. For a bit of fun, you might click on the
Extras button and select Movie mode, then click on Init & Run.
This can be very dramatic if you're using the Shape impedance tool
to watch the neuromorphic rendering of the cell's electrotonic
architecture.

> c ) and as for the log frequency vs Z transfer,
> Z transfer is given as :
> transfer impedance Z_c (! local voltage change)/(remote current
injection)
> equal to
> (remote voltage change)/(local current injection)

Transfer impedance is symmetric. This is a hallmark of a linear
system. Neurons can have very linear properties, over a fairly
wide range of membrane potentials, as long as you stay below
spike threshold. The common opinion is that a cell can be fit
by a linear approximation over a narrow range, e.g. 5 or 10 mV,
but if you look at the IV plots of real neurons you'll be
surprised at how linear many cells are over 20 mV, 30 mV, or
even wider ranges (e.g. neocortical pyramidal cells).

Even cells that have a lot of h current can be quite linear.
This doesn't mean that their membrane potential doesn't show
the typical "h current sag" during sustained current injection.
But look at papers (e.g. by Jeff Magee) that involved simultaneous
dual patch recording at somatic and dendritic sites, separated by
tens or hundreds of microns. You'll see figures in which the
authors inject a current at the soma and record v in the dendrite,
and then injected the same current in the dendrite and recorded v
at the soma. The v traces have nearly identical amplitudes and
time courses. This means that transfer impedance was symmetric
even though the cells are loaded with voltage gated, time dependent
channels that were affected by the injected current, and the
voltage changes definitely were too big to be called "small
signals." Pretty surprising, if you ask me. It's almost as
surprising that neither the authors nor the reviewers noticed
or understood the implication of this finding (the implication
is that subthreshold signal spread in these anatomically and
biophysically complex cells is well described by a linear
approximation).

Did I forget to mention that a linear system can be time-varying?
Many neuroscientists seem unaware of that fact.

> I noticed, that the highest value of Z transfer is when both the
> injection and measurement sites are the same ... ?
> This sort of makes sense because, obviously, the highest spike in
> voltage occurs at th point where the current is injected ....and for
> point further down stream the effect is sort of softened

You answered your own question.

> ....but what is
> the significance of this Z transfer for neural communication?

Very simple. Transfer impedance is the best predictor of the
effect of synaptic location on synaptic efficacy. This is
a consequence of these two facts:
1. Peak depolarization at the synaptic trigger zone is the
primary determinant of whether or not an epsp will trigger
a spike. This is easily shown by computational modeling.
2. Most synapses act like current sources, not voltage sources.
Also easily shown by computational modeling.

Therefore, despite everything you might find in textbooks, hear
in the classroom, or read in most journal articles, voltage
attenuation is not a useful predictor of the effect of synaptic
location on synaptic efficacy. The best predictor is transfer
impedance, which tells you how strongly a current, injected at
one point in the cell, will affect membrane potential throughout
the cell. See
Jaffe, D.B. and Carnevale, N.T. Passive normalization of
synaptic integration influenced by dendritic architecture.
Journal of Neurophysiology 82:3268-3285, 1999.

So if you want to understand how the distribution of synaptic
inputs over the surface of a cell will affect the spiking
output of that cell, study the spatial variation of
transfer impedance from a reference point located at the
cell's spike trigger zone (since transfer impedance between
any two points is independent of the direction of signal
propagation, the transfer impedance from any point to the
soma is the same as from the soma to that point).

Really, this should all be on the Forum, where it would do
someone else some good. You have no idea how widespread
misunderstandings on these issues are.

--Ted

Hi Ted,

In response to your two questions in the previous message :
"Where will input impedance be smallest: at the soma, or at the base
of the apical tuft? Or might it be small in both locations?"

I would think that there is more membrane seen at the base of the apical tuft ....due to the dendrite and such, there would be a smaller input impedance here...Is this the right way of thinking about it ?

Now for the portion about the input impedance :
"The membrane potential is whatever exists at the time you make your
measurement. If you have a cell with voltage-gated channels, you
should at least click on the RunControl's Init button to make sure
that everything is in its resting state at -65 mV (or whatever value
you specified next to the Init button). You can now see what the
cell's properties are at rest. Then you can run a simulation,
stop at any time, and click on the impedance tool's Redraw button
to see what has happened as a result of voltage- and/or time-dependent
conductance changes. For a bit of fun, you might click on the
Extras button and select Movie mode, then click on Init & Run.
This can be very dramatic if you're using the Shape impedance tool
to watch the neuromorphic rendering of the cell's electrotonic
architecture."

I tried doing this with one of my cells.

Initially the resting voltage is at -65mV. The Zin was about 40 ( I am thinking the unit is Mohms right ?, as the current is in nA and the voltage is in mV ....). Assuming, I do a current clamping of the cell,
amp = 2nA and duration 5 ms --> Zin increases slightly...
Any amount of amplitude increase, yielded no higher Zin.

now, I also tried amp=2nA, but this time, duration was at 10ms, the Zin decreased to about 30 Mohms (note I am looking at the Zin at 1Hz--> for simplicity)

next I did amp=2nA and duration 15ms, Zin at 1Hz= 23 M ohms

Then when the duration is up to about 30ms, when there is repetitive spiking, the Zin goes back up to about 40Mohms.

This is a little puzzling to me -- as in why this happens.
This is my reasoning, and I would appreciate it if you could tell me if I am in the right line of thinking.

Firstly, why did the Zin increase although slightly when I tried clamping it 2nA ?
is it because Zin=(local voltage change)/(local current injection)
So, assuming, given there is a spike from -65mV at rest to +40mV ...this causes the increase in the Zin.

Next, further increase in amplitude of current injection for that same duration does not increase Zin , this to me is odd, because spiking this time was higher than +40mV ....but is the Zin retained then due to current injection increase....ie some sort of ratio between the 2 parameters is maintained ?

"for the part where I tried amp=2nA, but this time, duration was at 10ms, the Zin decreased to about 30 Mohms (note I am looking at the Zin at 1Hz--> for simplicity)"
-- > This and this point there after, I do not understand....

ideally is a lower value of Zin a desirable matter, as in signal is more favorably received into the cell ?

Meena wrote: "Where will input impedance be smallest: at the soma, or at the base
of the apical tuft? Or might it be small in both locations?"

I would think that there is more membrane seen at the base of the apical tuft ....due to the dendrite and such, there would be a smaller input impedance here...Is this the right way of thinking about it ?

That is the right way to think about it. Of course, it's always a good idea to test one's
intuition--in this case by looking at a plot of the spatial variation of Zin.

The Zin was about 40 ( I am thinking the unit is Mohms right ?

Correct.

Firstly, why did the Zin increase although slightly when I tried clamping it 2nA ?
is it because Zin=(local voltage change)/(local current injection)

Yes. I don't know what voltage-gated currents are in your model, but there must be
something that transiently flattens the IV plot when the model is slightly depolarized.

So, assuming, given there is a spike from -65mV at rest to +40mV ...this causes the increase in the Zin.

Next, further increase in amplitude of current injection for that same duration does not increase Zin , this to me is odd, because spiking this time was higher than +40mV ....but is the Zin retained then due to current injection increase....ie some sort of ratio between the 2 parameters is maintained ?

I don't understand what you mean in either of these paragraphs.

"for the part where I tried amp=2nA, but this time, duration was at 10ms, the Zin decreased to about 30 Mohms (note I am looking at the Zin at 1Hz--> for simplicity)"
-- > This and this point there after, I do not understand....

Are you asking why there was an initial increase of Zin, followed by a decrease?
If so, I can only guess because I don't have your model to play with. One guess is
that there is a weak depolarization-activated inward current that turns on early.
This would account for the initial flattening of the IV curve (a strong inward current
would produce a dip (N shape, negative resistance region) in the curve). Then, with
time, a more slowly activating outward current turns on, obliterating the dip and
increasing the slope of the IV curve. Of course, the "usual suspects" that might
underlie these changes would be spike gna and gk.

ideally is a lower value of Zin a desirable matter, as in signal is more favorably received into the cell ?

Trying to infer the functional consequences of Zin changes is an iffy proposition, but
here's a stab at it for this particular example:
While it is true that decreasing Zin might allow larger synaptic current to enter the
cell, it would do this by reducing PSP amplitude. Since spikes are generated by
voltage-gated currents, lower PSP amplitude means that synaptic inputs would have
less ability to drive spiking. Also, lower Zin generally means faster decay of membrane
potential transients, so integration time is shorter. This reduces the ability of repeated
EPSPs to summate.

I am trying to wrap my head around the Zin and Z transfer concept.

You mentioned that a reduced Zin would allow a larger synaptic current ito enter the cell at the expense of the PSP. I comprehend that.

So lets say we have a very high Zin at a given point, could I assume that would deter any current from entering that point ??

In which case, are we then looking at an ideal value for Zin that is not too high nor too low for entry of synaptic current, which does not drastically reduce the PSP, that ultimately drive a good amount of spiking etc?

Next is about the Z transfer....Suppose my objective is too look a cell and its many pathways and determine which way the signal is being transferred out of the cell .....

I played with one neuron, I checked all the pathways....
I guessed that one pathway (it had a long axon) was how the signal was being transmitted out of the cell....and this pathway had the least Ztransfer value... ( inject at Point A and measure at point B)
All the other pathways had the same Z transfer (almost)

code:
So, can I say the pathway with the least Z transfer value ( ie between the soma and point B) is how the signal is being transmitted outwards ?

I would also say the other dendrites around the soma, would serve as an efficient synaptic location ?

Thanks,
Meena

I am trying to wrap my head around the Zin and Z transfer concept.

You mentioned that a reduced Zin would allow a larger synaptic current ito enter the cell at the expense of the PSP. I comprehend that.

So lets say we have a very high Zin at a given point, could I assume that would deter any current from entering that point ??

In which case, are we then looking at an ideal value for Zin that is not too high nor too low for entry of synaptic current, which does not drastically reduce the PSP, that ultimately drive a good amount of spiking etc?

Next is about the Z transfer....Suppose my objective is too look a cell and its many pathways and determine which way the signal is being transferred out of the cell .....

I played with one neuron, I checked all the pathways....
I guessed that one pathway (it had a long axon) was how the signal was being transmitted out of the cell....and this pathway had the least Ztransfer value... ( inject at Point A and measure at point B)
All the other pathways had the same Z transfer (almost)

code:
So, can I say the pathway with the least Z transfer value ( ie between the soma and point B) is how the signal is being transmitted outwards ?

I would also say the other dendrites around the soma, would serve as an efficient synaptic location ?

Thanks,
Meena

Meena wrote:So lets say we have a very high Zin at a given point, could I assume that would deter any current from entering that point ??

In theory but never in practice.

Here's how to think about the relationship between Zin and synaptic charge entry:
the electrical equivalent circuit that relates Zin to synaptic current flow iis From Ohm's law, is(t) = Es / (Zin + (1/gs(t))) (ignoring for the moment the
fact that Zin is not purely resistive). From experimental observations it
turns out that, except for a very few special cases, the resistance 1/gs(t)
is very much larger than Zin. So much larger that is(t) is within just a few
percent of Es * gs(t) (another way of saying this is that the peak epsp
amplitude is only a small fraction of the driving force for charge entry).

An aside: an incidental consequence of 1/gs(t) >> Zin is that we can ignore
the fact that Zin may not be purely resistive--because, with little error, we
can ignore Zin.

Back to the main track:
So Zin is never large enough to have much effect on either peak synaptic current
or the total synaptic charge that enters a cell.

In which case, are we then looking at an ideal value for Zin that is not too high nor too low for entry of synaptic current, which does not drastically reduce the PSP, that ultimately drive a good amount of spiking etc?

No. Never. Synaptic current is nearly independent of Zin. The only reason you might
want Zin to be large is if you want to affect local voltage-gated currents. The
experimental manipulations that induce dendritic spiking that precedes somatic spiking
involve completely artificial stimulation of very large numbers of synapes in a narrow
time window. Does this ever happen in a live animal in the absence of artificial
stimulation or an epileptic seizure? If it does, maybe it happens in the context of
something that is especially important (a particularly salient environmental stimulus,
perhaps).

The literature contains a lot of silly stuff about "impedance matching" and "impedance
mismatch" but that's just a bunch of bafflegab. Impedance match/mismatch is important
in the context of radio or microwave transmission lines, when you want to maximize
power transfer and eliminate signal reflections. It has no relevance to cellular
neurophysiology, where the issue isn't power transfer, it's how big a voltage signal
you can induce at one location as a consequence of current or charge entry at some
other location.

can I say the pathway with the least Z transfer value ( ie between the soma and point B) is how the signal is being transmitted outwards ?

Good question. The answer is no. The conclusion that such an observation supports
is that A and B are relatively poorly coupled, unless there is some means of active
signal transfer (spike propagation) between them. For all you know, the somatic and
tuft regions operate relatively independently of each other, doing some kind of local
processing. Maybe the apical tuft has its own output via dendrodendritic synapses.
Or maybe it doesn't, in which case the only time the soma "hears" much from it is
when the tuft is driven by highly synchronous inputs to fire a dendritic spike, which
is big enough to force a significant amount of current down that long skinny apical
trunk to the soma.

Alternatively, maybe this is one of those cells whose axon arises from a dendrite,
in which case wouldn't it be interesting if the apical tuft were the site of axon origin?
Then the cell's output would be relatively independent of what's converging onto the
soma, unless the soma is driven strongly enough to fire a spike that can then force
some charge up to the tuft.

I would also say the other dendrites around the soma, would serve as an efficient synaptic location ?

Yes, in terms of influencing the somatic membrane potential, and shaping the firing
pattern of an axon that might arise from the soma.

Hi again....

If the case is such that I cannot relate Zin to strength of synaptic current and Ztransfer to the direction that the signal is being transferred...

I was just wondering ....

Lets say, I have a not so well characterized neuron...like the NTS neuron..
How do I recognise for example the axon of that neuron?
Does the axon have any specific properties (electrical) that can be recognised given that I have this neuron and I don't know where the axon is ?

Is there any literature that talks about how we can go about distinguishing
the differents parts of the neuron (like the dendrite, axon) in an electrical sense ?

Thanks,
Meena

In general, axons in mammalian CNS are <= 1um in diameter. The orientation and
branching pattern typically look very different from dendrites of the same cell. Some
are myelinated, but myelination may not start until some distance from the soma. It
is taught that axons usually arise from the soma, but there are several cell classes
in which the axon commonly arises from a dendrite.

There lots of reports of recordings from dendrites, but few reports of recordings from
axons in the mammalian CNS. Consequently axonal electrical properties are not well
characterized.

Axons are often poorly visualized, perhaps because they are hard to see because of
their narrow diameter and a tendency to be poorly stained. Few morophometric data sets
contain extensive axonal data.

For more info about axons, talk to a neuroanatomist, especially one who has done
quantitative reconstructions of neurons.