Calcium current through NMDA receptor

[to]

I would like to add an NMDA receptor with a realistic calcium permeability as a point process to my model synapse. All NMDA mechanisms I can find use the NONSPECIFIC_CURRENT i, which does not change any intracellular ion concentrations.
My first question is: Can I combine NONSPECIFIC_CURRENT i with a USEION ca statement in my NMDA mechanism, or should I handle Na+, K+ and Ca++ ions separately?
A second question: How can I plot a NONSPECIFIC_CURRENT i from a point process?

[ted]

I would like to add an NMDA receptor with a realistic calcium permeability as a point process to my model synapse. All NMDA mechanisms I can find use the NONSPECIFIC_CURRENT i, which does not change any intracellular ion concentrations.

If you want to make it a pure Ca current, comment out the
NONSPECIFIC_CURRENT i
and insert
USEION ca READ eca WRITE ica
You'll need to make several other changes, but do them one at a time, testing at
each step to ensure that you're getting what you expected to get. For example,
1. The NEURON block probably declares e as a RANGE variable, but you won't
be using it, so get rid of it.
2. It also probably declares i as a RANGE variable. Change that to ica. Also change i
to ica in the ASSIGNED and BREAKPOINT blocks.
3. You'll need to add
eca (mV)
to the ASSIGNED block.

That's enough to make a synaptic mechanism with a pure Ca current.

If you want to have this be a mixed current, add whatever USEION or
NONSPECIFIC_CURRENT declarations you need, along with their conductances
etc.. If N ionic species are involved, you'll find it more convenient to specify a
total synaptic conductance and have N-1 parameters in the range 0-1 that specify
the fraction that is attributable to each ion (you'll need to bulletproof this by adding
some code to an INITIAL block that ensures that the sum of these parameters is <= 1).
Then the current for each ion will be, for example,
ica = g*fca*(v-eca)
ina = g*fna*(v-ena)
i = g*(1-fca-fna)*(v-e)
where g is governed by whatever kinetics you specified.

How can I plot a NONSPECIFIC_CURRENT i from a point process?

Just make sure that each current component, whether nonspecific or attributable to
a specific ionic species, is declared as a RANGE variable. All RANGE variables are
accessible to hoc.

[NeuroRhythms]

So if we know from experimental work that the Ca++ current flowing through the NMDA receptor is 10% of the total current, is it safe/scientifically valid to make the claim that the permeability of Ca is 10% the total conductance flowing through a channel? Immediately I'd think not, but this has been done before by other groups. Suggestions?

[ted]

Immediately I'd think not

Because?

[NeuroRhythms]

I am just looking at units in the .mod file. How can you take a microS value, place it in the GHK equation where a current value should be and get a permeability value?

[NeuroRhythms]

my original wording was imprecise. "permeability of Ca is 10% the total conductance flowing through a channel?" there is no conductance flow, that should really read, "is it valid to simply say that since 10% of the current is Ca++ then permeability of Ca++ is 10 percent the conductance of the channel?"

[NeuroRhythms]

This is how it exists in a published model

Code: Select all

ASSIGNED {	: parameters needed to solve DE
	ica (mA/cm2)	:calcium current, which will be add to the total Ca current together with ica in 'car.mod'
	v (mV)          :spine head membrane potential
	i (mA/cm2)		:balance current to the ica through NMDA
	g (uS)          :conductance of nmda(not include the effect of Mg block)
	Pca (cm/s)		:Ca permeability of NMDA, it's obtained from gnmda by multiplied with P=0.1*gnmda*(v-e_nmda)/GHK at -65mV
	
	inmda (mA/cm2)	:equal to -i2_nmda which is the total nmda current's density, the direction is changed to be easier compared with i_canmda in this file.  
	gnmda	(uS)	:cunduction of nmda(include the Mg effect), to be easier plot out by just click the 'plot what'button 
	iampa	(mA/cm2):total current of ampa, the direction is changed to be easier compared with i_canmda in this file.  
	gampa	(uS)	:cunductance of ampa
	itotal (mA/cm2)	:total current flow into spinehead (only the aciviated channel current is considered),the direction is chosen the same as i_canmda in this file.  
	irtype (mA/cm2)	:r_type current
	f               :Ca current fraction in nmda current
}

INITIAL {

	P  = (1-exp(-65*-0.0755))/(10*Area*14564*(50e-09-(2e-03*exp(-65*-0.0755))))*k	:converting conductance to permaebility 
}


BREAKPOINT {
	g = g2_nmda	:[uS]
	Pca = P*g	:[cm/s]
	ica = Pca*14564*v*(50e-09-(2e-03*exp(v*-0.0755)))/(1-exp(v*-0.0755))*1/(1+(exp(0.08(/mV) * -v)*(mg / 0.69)))	:ca current density through NMDAr in [mA/cm2]
	i = -Pca*14564*v*(50e-09-(2e-03*exp(v*-0.0755)))/(1-exp(v*-0.0755))*1/(1+(exp(0.08(/mV) * -v)*(mg / 0.69)))	:balance current density of ca current through nmda
	
	:14564=(z^2*F^2)/(R*T); -0.0755 = -z*F/RT in [1/mV] where z=2,F=96500 in[C/mol], R=8.31 in[J/K*mol], T=308 in[K] 
	:and everything should be normalizied to [mV], 0.088 and 0.7474 is from our blocking experiment data fitting.
	

I am bothered by the P statement. Why not just put in I-NMDA and attain a permeability that way. If you know it is 10% of that, just divide by 10.

[NeuroRhythms]

Oh I see since the P formula does not contain E values, and therefore has units of C/J or 1/V, you can simply multiply it by a conductance value?

[ted]

my original wording was imprecise. "permeability of Ca is 10% the total conductance flowing through a channel?" there is no conductance flow, that should really read, "is it valid to simply say that since 10% of the current is Ca++ then permeability of Ca++ is 10 percent the conductance of the channel?"

No, it would only be valid to say that 10% of the current is carried by Ca. Currents depend not only on channel conductance or permeability, but also on driving force. Now, if a 1 mV change in membrane potential produces a change of ica that is 10% of the change of total membrane current, then it would be correct to infer that, at that particular membrane potential +- 1 mV or so, calcium conductance is 10% of total membrane conductance.

But your real question is whether it makes sense to talk about conductance as a parameter of a current that is described in terms of the GHK formalism, and that's a different matter altogether.

[ted]

since the P formula does not contain E values, and therefore has units of C/J or 1/V, you can simply multiply it by a conductance value?

I am not familiar with the model you are talking about. What rationale do the authors provide for any of this in the paper? That's the first place to turn for explanations.

[NeuroRhythms]

The paper is Grunditz et al. 2008. JNeurosci. 2008 Dec 10;28(50):13457-66.

ModelDB: http://senselab.med.yale.edu/ModelDb/sh ... del=116769
JNeurosci.org: http://www.jneurosci.org/content/28/50/13457
Pubmed.gov: http://www.ncbi.nlm.nih.gov/pubmed/1907 ... t=Abstract

Verbatim from supplemental material:

"Approximately 10% of the current through NMDA channels is carried by calcium (Jahr and Stevens, 1993). Therefore, at a membrane potential of -65 mV, the calculated PCa,NMDA is 10% of the total NMDA channel conductance (gNMDA)."

I've scoured over this document many times. That is the all there is for rationale.

[ted]

I've scoured over this document many times. That is the all there is for rationale.

There is more, although it is not entirely explicit; have you examined the supplementary material?

Of course in strict terms it is incorrect to say
"at a membrane potential of -65 mV, the calculated PCa,NMDA is 10% of the total NMDA channel conductance (gNMDA)". However, channel conductance can be measured empirically, and from that measurement it may be possible to determine permeability. The first question is whether the finding attributed to Jahr and Stevens 1993 pertains to total current through NMDA channels, in which it is an assertion about chord conductance for a particular membrane potential, or whether it pertains to d(NMDA channel current)/dv at a particular membrane potential, in which case it is an assertion about slope conductance. If they were writing about chord conductance*, then you know that
Ica = fGHK(cai, cao, v, eca) = 0.1*Itotal
where Itotal is the total NMDA receptor current, Ica is the ca component of that, and fGHK is the right hand side of the equation that begins I_{Ca_NMDA} = . . . on page 3 of grunditz2008's supplemental "legends" pdf. fGHK is the product of P_Ca,NMDA (henceforth simply PCa) and many other terms. From this it is possible to determine PCa. Your task is to read the supplemental materials, verify that its fGHK is indeed the GHK formula for calcium current, and then verify that the mod file properly caculates PCa (that includes making sure that the membrane potential assumed in fGHK is indeed the membrane potential at which Itotal was measured) and uses it in the relevant equations elsewhere in that file. Don't get hung up on whether they call some intermediate result a "conductance" or something else. If you think they made a mistake, fine, and f you decide their work produces a correct result, despite some terminology that may have been a bit loose, then also fine. Don't just take their assertion for granted if it isn't immediately obvious to you that they were right--but in deciding whether they were or weren't, there's some algebra and a bit of reasoning to wade through.

*--If they weren't writing about chord conductance, then they were writing about slope conductance. Now you need to know the actual ionic conductance gnonca associated with the non-Ca component of the NMDA current, and you have to derive the derivative of the GHK current formula with respect to membrane potential, and then the relevant formula becomes
Dv fGHK(cai, cao, v, eca) = 0.9*gnonca
where Dv x is just another way of writing dx/dv.

[NeuroRhythms]

Yes I did indeed read the supplemental material. All that follows the statement that I quoted is the GHK equation. What is peculiar about this model is the what is exactly in the .mod file.

I have posted it again here. From the file, CaNMDA.mod:

Code: Select all

INITIAL {

	P  = (1-exp(-65*-0.0755))/(10*Area*14564*(50e-09-(2e-03*exp(-65*-0.0755))))*k	:converting conductance to permaebility 
}


BREAKPOINT {
	g = g2_nmda	:[uS]
	Pca = P*g	:[cm/s]
	ica = Pca*14564*v*(50e-09-(2e-03*exp(v*-0.0755)))/(1-exp(v*-0.0755))*1/(1+(exp(0.08(/mV) * -v)*(mg / 0.69)))	:ca current density through NMDAr in [mA/cm2]
	i = -Pca*14564*v*(50e-09-(2e-03*exp(v*-0.0755)))/(1-exp(v*-0.0755))*1/(1+(exp(0.08(/mV) * -v)*(mg / 0.69)))	:balance current density of ca current through nmda
	
	:14564=(z^2*F^2)/(R*T); -0.0755 = -z*F/RT in [1/mV] where z=2,F=96500 in[C/mol], R=8.31 in[J/K*mol], T=308 in[K] 
	:and everything should be normalizied to [mV], 0.088 and 0.7474 is from our blocking experiment data fitting.
	

This model has two .mod files related to the NMDA receptor. You first have the NMDA receptor, a nonspecific ion point process with a conductance value, g2_NMDA reported in microS. That value is global variable in nmda.mod and an external variable in the CaNMDA.mod file. They first declare this statement P. It is not a permeability, it is a conversion factor. 0.0755 is (-z*F/RT) and 14564 is (z^2*F^2)/(RT). Also these numbers have been divided by 1000 to get mV rather than V. k is a scaling factor to turn the current from nA to mA. This value looks very much like the GHK equation but there is no voltage value in the denominator. There is voltage values in the exponentials, it is -65 mV. Also in the denominator they divide by 10, this is the 10% issue, and divide by the area. You need to get cm in there some how that makes sense. They then take this value with -65 mV in the exponentials, and then multiply it by g in the BREAKPOINT section, where g =g2_NMDA. This value p*g they call PCa. They then feed it into the GHK equation and calculate ICa on a voltage dependent basis. This seems quite weird because g is voltage dependent but P this scaling factor is not. It is as if the value is normalized by the value at -65. This just seems bizarre to me.

[NeuroRhythms]

I'll leave it at that.

[ted]

Well, to be fair to the authors of the model, this

"they were writing about chord conductance
. . .
From this it is possible to determine PCa."

is what they were trying to do. The code is not the most beautiful, and the comments are not the most explicit, true, but this assignment statement in the INITIAL block
P = (1-exp(-65*-0.0755))/(10*Area*14564*(50e-09-(2e-03*exp(-65*-0.0755))))*k
is just the GHK current equation rearranged to solve for P, but missing a multiplicative factor: the actual NMDA current at -65 mV. There are many other peculiarities in the code that invite inspection--where does the g2_nmda come from, and why is canmda implemented as a density mechanism rather than as a point process (my guess is that they just wanted something that would emulate a background level of tonic ampaergic input that activates NMDA receptors, but that should be verified by reading the paper)--but it sure looks like their intent was use a measure of NMDA current at a particular membrane potential as a means to estimate PCa, and that at least the formal structure of the statement that assigns a value to P is OK.