Ephaptic connections in network

[staceyw]

I'm trying to add ephaptic connections to a ~100 neuron network. I'd like to have one group of them produce a net output, and have the other group "see" it. Unfortunately, the network is a parallel context version, and I'm not sure how to even start. I do not need very sophisticated devices here, just a way of collecting the outputs of that group and then multiplying it by some parameter as an input current. I would be happy with a very arbitrary measure.

I have thought of 2 ways. One is to piggyback onto my working parallel-style gap junctions. The problems there are 1) they introduce conductance to the cells and I can see a big difference when the conductances are high--not a great model of ephaptic connections, and 2) I would need N^2 connection statements. The gap junctions use the halfgap.mod in the following style, connecting reciprocally to each cell.
pnm.pc.target_var(&g.vgap, $3)
pnm.pc.source_var(&v(.5), $4)
If there is a clever way to fool this mechanism into injecting current without changing conductance, I'd be happy with it.


The other way is that perhaps it can be done with a direct injected current into each cell, that takes as a factor the summed currents of all cells (which I am already recording and writing anyway). This would clearly be better, though I'm not sure exactly how to "collect" all the cells' data at each time step in pnm.pc.

[ted]

So by "ephaptic" you really mean "ephaptic"--coupling mediated by extracellular field?

[staceyw]

Yes, ephaptic field effects. It is a CNS model of pyramidal cells. Axons are not really a part of it. I am modeling the effect of bursting cells on their neighbors--essentially the local currents produced by active cells, and how they might recruit nearby cells. These effects become more prominent when the extracellular space is reduced--i.e. when the cells are closer together for a lower 1/r field effect. There are several papers by J. Jefferys lab talking about such effects in high frequency oscillations.

But I'm really looking for an arbitrary method of producing the effect, rather than a very specific parameter set.

What I'm looking for is:
injected current in cell B = some factor * output current in cell A.

I can settle for some approximations of the Cell A output.

[ted]

What I'm looking for is:
injected current in cell B = some factor * output current in cell A.

I can settle for some approximations of the Cell A output.

It's up to you, but be careful--lots of devils lurk in trying to approximate the contributions of a cell to extracellular field. An initially plausible but probably fatally flawed strategy would be to rely on somatic membrane current (insert extracellular into the soma, then multiply i_membrane by area of that segment). This would be easy to implement in NMODL with a statement in a BREAKPOINT block (so it would occur automatically at every time step, and be performed by compiled code). The flaw is that somatic current grossly overemphasizes the contribution of spike currents while grossly underestimating the effect of synaptic currents.

Your proposed effect on the "target" cell could be implemented with a point process defined by NMODL code that delivers a NONSPECIFIC_CURRENT i to the segment to which it is attached. The questions here are how best to couple the "outputs" of all cells to every instance of this mechanism, and how to tell every instance of this mechanism what weight to apply to each cell's "ouput."

I'm not sure exactly how to "collect" all the cells' data at each time step

ParallelTransfer seems like the tool for this
http://www.neuron.yale.edu/neuron/stati ... elTransfer
The amount of data to be exchanged is proportional to the square of the number of cells, unless you impose a simplification like "each cell is influenced only by its N nearest neighbors".

[hines]

ephaptic coupling is best handled by the LinearMechanism class.
http://www.neuron.yale.edu/neuron/stati ... inmod.html
See http://senselab.med.yale.edu/modeldb/Sh ... model=3676
for an example of use in ephaptic coupling of axons. In these cases, the extracellular mechanism
is used only so that there is an extracellular node adjacent to the membrane in each compartment
(xg = 0 and raxial=1e9)
and then the LinearMechanism is used to connect resistors (and capacitors if you need them) between those
extracellular nodes.

The advantage of the LinearMechanism class is that it is numerically stable regardless of the strength of
coupling. I would get everything working with LinearMechanism before doing computational experiments
with paralellism using the parallel transfer functions which are tantamount to using a modified euler method
to handling the coupling.