Different Axial Resistance for different ions

[ziemek]

Hey!

Is it possible to somehow define different axial resistances (Ra) for different ions? I want to use it for simplified diffusion of calcium restricted by ER (and I don't want to use RxD), so I would like to have default Ra for all ions and Ra_ca2+ for calcium ions.

I think we are dealing with non-specific current between compartments, right? So I assume that's the catch :)

Is there any workaround I can think of? I will be very grateful for your help!

[ted]

Hey!

Relax, there's no need to be so formal.

Is it possible to somehow define different axial resistances (Ra) for different ions?

Everything is possible through programming, but the set of "everything" has many members that are ugly and awkward. You're asking for something that could easily belong to the "ugly and awkward" subset.

You and I may know that electrochemical potential gradients drive the movement of ions in a solution, but NEURON treats electrical current flow between adjacent compartments (segments) without attributing that current to any ionic species. That's OK for ions that are abundant, like na or k or cl, but not so good for ions whose concentrations are much smaller, like intracellular ca.

Even so, NMODL's LONGITUDINAL_DIFFUSION can be used to implement representations of ionic fluxes in cytoplasm that are driven by concentration gradients--for example, see Example 9.8: Calcium diffusion with buffering in chapter 9 of The NEURON Book (preprint available here https://www.neuron.yale.edu/ftp/ted/boo ... xedref.pdf). Diffusion has a much shorter length constant than electrical signals do, so you'll want to experiment with nseg to make sure that spatial error doesn't cause qualitative changes in simulation results. I should mention that LONGITUDINAL_DIFFUSION has only first order precision.

I want to use it for simplified diffusion of calcium restricted by ER

If one assumes that calcium occupies some fraction k of cytoplasmic volume, this factor could be included in the NMODL file's KINETIC block, e.g. in the COMPARTMENT and LONGITUDINAL_DIFFUSUION statements
diam*diam*vrat
would be changed to
k*diam*diam*vrat
Similarly,
dsq = diam*diam
would have to be changed to
dsq = k*diam*diam
And the right hand side of the very first kinetic statement would have to become
~ ca[0] << (-ica etc.)/k

Now, what to do about the effect of electrical potential gradients on calcium movement in cytoplasm? I suppose it is possible to use NMODL to implement a density mechanism that employs POINTERs to discover the electrical potentials in adjacent compartments and uses those values (plus path lengths, cross sectional areas, and ionic mobility, which are all discoverable during model setup) to calculate the corresponding calcium fluxes. I'd be concerned about accuracy (net electrically-driven flux between any pair of adjacent compartments would be a small difference between two much larger numbers), stability, and computational overhead. My preference would be to ask myself "what would Josef (Švejk) do?" and try to get away with saying something like

"This is intended to be a simplified representation of ca diffusion restricted to ER. Omitting the effect of longitudinal electrical potential gradient on cytoplasmic ca movement is one of the simplifications I am willing to make for the sake of sanity."