NetCon & total neuronal current

[Tsirogiannis]

In a detailed model, we need to calculate the total current flowing through the membrane of a neuron, in order to calculate the local field potential around it.

To this end, on the one hand we have created the following NMODL mechanism:

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TITLE cumI.mod

UNITS {
	(mV) = (millivolt)
	(mA) = (milliamp)
}

NEURON {
	SUFFIX cumI
	USEION na READ ina
	USEION k READ ik
	USEION ca READ ica
	RANGE cumi
}

PARAMETER {
	ina (mA/cm2)
	ik (mA/cm2)
	ica (mA/cm2)
	ipas (mA/cm2)
}

ASSIGNED { 
	cumi (mA/cm2)
}

BREAKPOINT {
	cumi=ina+ik+ica+ipas
}

In the hoc code, this is added to our neuron template:

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begintemplate STNcell
public soma,nclist

create soma
objectvar f, nclist

proc init() {local i, me

    create soma

    nclist = new List()

   soma {
      nseg = 1
      cm=100
      L=25
      diam=25
      
      // channels

    insert cumI
...   }
}
endtemplate STNcell

On the other hand, the neuron receives synaptic input, using the NetCon object:

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GPEcell STNcell.nclist.append(new NetCon(&GPEcell.soma.v(.5),synapseGPE_STN,0,delay_GPE_STN,w_GABA_GPE_STN))	

During the simulation, the current flowing through the NetCon object is recorded:

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GPE_STN_vec.record(&synapseGPE_STN.i)

After the end of the simulation, the total current through the STN neuron is calculated by adding the cumI and the NetCon currents:

Code: Select all

totiSTN_soma.mul(area(0.5)*0.01)
LFPvec.resize(totiSTN_soma.size)
LFPvec.add(totiSTN_soma)

totiGPE_STN.resize(LFPvec.size)
LFPvec[i].add(GPE_STN_vec)

Do we really have to add both these current sources in order to find the total current, or NetCon current changes are somehow reflected in the ion channel mechanisms of the neuron, that are included in the above mentioned cumI mechanism?

Thank you!

[ted]

cumi=ina+ik+ica+ipas

Not the way to do it. (1) Ignores all currents carried by other ions. (2) Ignores capacitive current. (3) Ignores all NONSPECIFIC_CURRENT contributions to membrane current. (4) ipas will never have a nonzero value.

What you need to do is insert extracellular into all sections whose membrane current you care about. Then membrane current density will be available to you as i_membrane, and this value will include contributions from membrane capacitance plus all all ionic species and all NONSPECIFIC_CURRENTs. For each compartment in your model you will have to multiply i_membrane by segment area to get net membrane current, i.e. current in absolute units rather than density units.

During the simulation, the current flowing through the NetCon object is recorded

Current does not flow through a NetCon object. It flows through a synaptic mechanism, such as an ExpSyn or Exp2Syn. But you don't have to anything special to deal with synaptic currents, since NEURON automatically factors them into extracellular's i_membrane.

Tell me, are your neurons single compartment models, or do they have multiple compartments? If they are single compartment models, i_membrane will always be 0. This is an unavoidable consequence of Gauss's theorem.

Do we really have to add both these current sources in order to find the total current, or NetCon current changes are somehow reflected in the ion channel mechanisms of the neuron, that are included in the above mentioned cumI mechanism?

[/quote]This question is moot even if one substites "ExpSyn or Exp2Syn" for "NetCon." The way to determine transmembrane current is to insert extracellular and then use i_membrane.

[Tsirogiannis]

Thank you for your response.
I still have some questions on that:

(1) Are there any other ions that should be considered, if all channels incorporated in the neuron model use only Na, K & Ca? (our caase)

(3) Same as (1), NONSPECIFIC_CURRENT(s) are missed only if they have been defined in the model, is this correct? (no such currents in our model)

Finally, the neuron models are actually single compartmental.

So, since in this case i_membrane is always 0, what would be the correct way to record reliably the total membrane current in each neuron of our model?

[ted]

(1) Are there any other ions that should be considered, if all channels incorporated in the neuron model use only Na, K & Ca?

Nope. Nothing goes into a model that the user didn't put there. Just be sure to check the USEION statements in your mod files, and any Channel Builders that may be involved.

(3) Same as (1), NONSPECIFIC_CURRENT(s) are missed only if they have been defined in the model, is this correct?

Yes, but be sure to check your mod files and Channel Builders.

Finally, the neuron models are actually single compartmental.

So, since in this case i_membrane is always 0, what would be the correct way to record reliably the total membrane current in each neuron of our model?

Unless you are using a current or voltage clamp to inject current into your model cells, total membrane current will be 0, because for a single compartment model
sum of all ionic currents = -1 * membrane capacitive current
So if you want to know total ionic current for a section called foo, it's just -foo.i_cap(0.5).

If you are injecting current into a cell, total membrane current for that particular cell will be equal to the injected current (but flowing in the opposite direction).

[Tsirogiannis]

I 'm not sure whether I have udnerstood exactly how I should treat such a case (single compartmental model) in order to obtain the total current flowing through the membrane of a cell.
From your answers I deduce that apart from the currents of the various channels and the synaptic connections, we should also add the i_cap current. Or is i_cap equal to the whole of the membrane current? (which I can't see how it can be true, by the way)

Thanks again.

[ted]

I 'm not sure whether I have udnerstood exactly how I should treat such a case (single compartmental model) in order to obtain the total current flowing through the membrane of a cell.

Total membrane current of a cell is the sum of all currents that flow through the membrane of that cell. It can be defined as the surface integral of all transmembrane currents. In the absence of some extrinsic source, such as current spreading via gap junctions from another cell, or current injected into the cell through an electrode inserted into the cell or a patch electrode, total membrane current will be 0 regardless of the size of the cell. This means that total transmembrane ionic current must be equal and of opposite sign to total transmembrane capacitive current.

In a multicompartmental model of a cell, the total transmembrane current for a particular compartment may be nonzero. However, if that is the case, in the absence of gap junctions or electrodes that inject current into the model, the sum of the transmembrane currents of all other compartments must be equal and opposite so that the total transmembrane current for the entire model is 0. And, of course, total transmembrane ionic and capacitive currents must be equal and of opposite sign. Again, the only exception is if there are one or more gap junctions or electrodes that inject current directly into the model.

In a single compartment model of a cell, since there is only one compartment, that compartment's total transmembrane current must be zero. And you already know what I was going to say about ionic and capacitive current, and the effect of gap junctions or electrodes.