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### Recording the total input current to the soma

Posted: Thu Sep 22, 2016 6:00 pm
Hi, I am trying to make use of this model as described in Bahl A, Stemmler MB, Herz AV, Roth A (2012), within Python.

Basically, I want to record the total amount of input current flowing into the soma (but not anything internal to the soma).

I found that I can add the lines:

Code: Select all

``````cell.soma.insert('extracellular')
...
current = cell.soma(0).i_membrane
``````
But this seems to include some currents internal to the soma, since it rises every time the neuron spikes. See for example, a plot of the neuron's current + spikes for a constant input. How can I get only the combined input current to the soma?

Thanks.

### Re: Recording the total input current to the soma

Posted: Thu Sep 22, 2016 10:23 pm
I want to record the total amount of input current flowing into the soma (but not anything internal to the soma).
Not sure I know what you mean. Are you referring to currents generated by synapses that are attached to the soma, or do you mean axial current that flows between the soma and adjacent parts of the cell?

### Re: Recording the total input current to the soma

Posted: Fri Sep 23, 2016 2:42 am
Not sure I know what you mean. Are you referring to currents generated by synapses that are attached to the soma
Yes. I'm basically trying to get the current that goes into the soma from the dendritic tree.

### Re: Recording the total input current to the soma

Posted: Fri Sep 23, 2016 10:41 am
So you want axial current flow between the soma and the neurites that are attached to it. In pseudocode, assuming that no section has nseg >= 1e3,

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``````iax = 0
for each section that is attached to the soma
iax += (v(0.001) - v(0))/ri(0.001)``````
where iax is in nA, v is in mV, and the function ri(x) returns the axial resistance between the node at the center of the segment that contains x and its parent node. If x<1/nseg then x lies in the first segment and ri(x) returns the axial resistance between the center of the first segment and the node at 0.

Let me know if you have related questions, e.g. how to implement this pseudocode in Python, or how to calculate the time course of iax most efficiently.

### Re: Recording the total input current to the soma

Posted: Thu Mar 30, 2017 11:12 am
Hi Ted,

I have a few follow-up questions. Briefly, I’m trying to do the same thing Aaron was doing - i.e. probe the current flowing into the somatic compartment (nseg=1) from the dendritic tree, which in our NEURON model is a single dendritic compartment (nseg=5). I’m interested in comparing the behavior of a leaky-integrate-and-fire neuron with the behavior of this NEURON model when the current fed into the LIF, J, is equal to the current flowing out of the bioneuron’s dendrite and into its soma. I need to investigate this current separately from the spiking behavior of the cell: if J depends on V_soma, I will not be able to make the two inputs equivalent, since the voltage equations for the LIF neuron (a point neuron with no adaptation) are obviously different than for our NEURON model (which include multiple ion channels, etc.).

Is it theoretically possible to probe the current without referencing the voltage of the somatic compartment? I haven’t been able to figure out what equations govern the current flowing between two compartments, and whether this depends on the relative voltages of the compartments. I know NEURON uses the cable equation to propagate voltage between segments within a compartment, but is this also true between compartments? Could you direct me to any NEURON literature that discusses these mechanisms mathematically?

Is current always derived from voltage and resistance in NEURON, or is it tracked explicitly? If it is tracked explicitly, is it possible to grab the value that is transmitted from the dendrite to the soma, but not the backpropagating signals?

I gather from your previous answer that one way to compute this current is to use Ohm’s Law on the previous segment: V_dendrite=I_dendrite*resistance_axial_dendrite. But you wrote that I_axial=(V_dendrite-V_soma)/R_axial_dendrite. Why do you also include a term for the voltage of the soma (at the segment closest to the dendrite, assuming V_dendrite(0)=V_soma(1))? Implementing your suggested probe (or any probe that calculates current from voltage) gives a current that fluctuates wildly with the bioneuron’s spiking, which doesn’t seem to reflect the dendritic current flowing into the soma. It may accurately reflect the current transfer between the two compartments, given that that current is backpropagating to the dendrites after after an action potential is initiated, but I’m only interested in the dendrite-to-soma direction.

Thanks, let me know if anything is unclear or you need more information on the code / NEURON model.

Peter Duggins

### Re: Recording the total input current to the soma

Posted: Thu Mar 30, 2017 2:20 pm
psipeter wrote:I need to investigate this current separately from the spiking behavior of the cell: if J depends on V_soma, I will not be able to make the two inputs equivalent, since the voltage equations for the LIF neuron (a point neuron with no adaptation) are obviously different than for our NEURON model (which include multiple ion channels, etc.).
And that's why what you ask for is an impossibility. Current flow from one location to another depends on the resistance between those points and the potential difference between them.
Is it theoretically possible to probe the current without referencing the voltage of the somatic compartment?
No, but I repeat myself.
I haven’t been able to figure out what equations govern the current flowing between two compartments, and whether this depends on the relative voltages of the compartments.
The equation is called Ohm's law.
I know NEURON uses the cable equation to propagate voltage between segments within a compartment, but is this also true between compartments?
It's not voltage that propagates. It's charge. The movement of charge is driven by an electrical potential gradient, just like the movement of mass in a gravitational field is driven by a gravitational potential gradient (on the earth's surface, we recognize that as difference in elevation), the movement of solute in a solution is driven by chemical potential gradient (which is roughly proportional to concentration gradient), the movement of gas or a liquid is driven by pressure gradient, and the movement of heat is driven by temperature gradient.
Could you direct me to any NEURON literature that discusses these mechanisms mathematically?
Chapters 3 and 4 of The NEURON Book contain some useful information.
Is current always derived from voltage and resistance
Yes.
in NEURON
Yes. A neuron is a physical system and obeys the laws of physics, so a mechanistic model of a neuron must also obey the equations that describe the laws of physics.
or is it tracked explicitly?
NEURON solves a set of equations of the form Cy' = b where y are state variables, such as membrane potential, whose values are calculated by numerical integration. The axial currents are implicit in the C and b matrices; their values are never computed explicitly. If you need them, you have to calculate them yourself.
I gather from your previous answer that one way to compute this current is to use Ohm’s Law on the previous segment: V_dendrite=I_dendrite*resistance_axial_dendrite. But you wrote that I_axial=(V_dendrite-V_soma)/R_axial_dendrite.
No, I wrote

Code: Select all

``````iax = 0
for each section that is attached to the soma
iax += (v(0.001) - v(0))/ri(0.001)``````
where v(0.001) is the membrane potential at the middle of the first segment of a section, v(0) is the potential at that section's 0 end, and ri(0.001) is the axial resistance between the middle of the section's first segment and its 0 end.
Implementing your suggested probe (or any probe that calculates current from voltage) gives a current that fluctuates wildly with the bioneuron’s spiking
True.
which doesn’t seem to reflect the dendritic current flowing into the soma.
The formula calculates the current that flows between the soma and the section. That's a fact. Laws of physics and all that.
It may accurately reflect the current transfer between the two compartments, given that current is backpropagating to the dendrites after an action potential is initiated, but I’m only interested in the dendrite-to-soma direction.
Do whatever you like. Just be prepared to defend your choice to whomever has the duty of reviewing your manuscripts and grant proposals.