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. 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
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.