Understanding pump current in Calcium dynamics model

[Haroon]

Hi,

I have a question related to the pump model (Example 8) of Hines and Carnevale: Expanding NEURON with NMODL.

If i understood correctly, the expression
~ ca[0] << (-(ica - ica_pmp_last)*PI*diam/(2*FARADAY))
gives us the calcium concentration at the outermost shell at any time step t, where ica_pmp_last is current due to pump at time step t-1. What i don't understand is why we need to exclude the net pump current computed at previous time sep?

At each time step, all the reactions in kinetic scheme should take care of change in ca[0] due to pump, diffusion and buffering. Right?

Haroon

[ted]

To quote the last sentence on the bottom of page 259 of The NEURON Book:
"Since the total Ca2+ current ica contains the pump current from the previous step, ica_pmp_last must be subtracted from it to prevent the pump current from being counted twice."

[Haroon]

I think i am missing the point. How ica includes pump current in the code? In my case i want to get ica from Calcium channel and just want to get rid of calcium out of the system, without actually increasing cao (assuming cao to be constant), so actually i don't compute ica_pmp and exclude following expressions from the code

CONSERVE pump+pumpca = TotalPump*parea*(1e10)
ica_pmp = 2*FARADAY*(f_flux_b_flux)/parea


My code is simply

~ ca[0] + pump <-> pumpca (k1*parea*(1e10), k2*parea*(1e10))
~ pumpca <-> pump (k3*parea*(1e10), 0)
~ ca[0] << (-ica*PI*diam/(2*FARADAY))

Is it that NEURON implicitly accounts for all the currents associated with exchange of calcium ions across the membrane and assigns it to ica? because in my case i don't want to see the pump current, i am only interested in ca[0].

Thanks for explaining basic concepts!

Haroon

[ted]

If i understood correctly, the expression
~ ca[0] << (-(ica - ica_pmp_last)*PI*diam/(2*FARADAY))
gives us the calcium concentration at the outermost shell

The statement tells NMODL how to calculate the flux of calcium into compartment [0] that is attributable to transmembrane calcium current other than the current generated by the pump itself. This is just one of the calcium fluxes that affect compartment [0]. The others are the fluxes specified by
ca[0] + pump <-> pumpca
and
ca[0] <-> ca[1]


There are two processes to be represented: transmembrane calcium flux, and accumulation of cai.
The implementational choices are:
1. specify them in separate mechanisms
2. specify them in the same mechanism

Case 1: ca pump and ca accumulation are specified in separate mechanisms.

The pump mechanism will have a
USEION ca READ cai WRITE ica
statement (or USEION ca READ cao, cai WRITE ica if the pump is affected by cao). It must have such a statement in order to respond to changes in cai by generating a transmembrane flux of ca that can then be discovered by some other mechanism.

That calcium accumulation mechanism will contain a
USEION ca READ cai, ica WRITE cai
statement. This mechanism merely keeps track of how much calcium has entered or left the cell, and uses that information to compute cai. It does not need to WRITE ica because it does not generate a transmembrane calcium flux.

Case 2: ca pump and ca accumulation are specified in one mechanism.

The NEURON block will contain this statement
USEION ca READ cai, ica WRITE cai, ica
(or USEION ca READ cao, cai, ica WRITE cai, ica if the pump is affected by cao)
In this case it is necessary to prevent the pump-generated transmembrane flux from being counted twice.

exclude following expressions from the code

CONSERVE pump+pumpca = TotalPump*parea*(1e10)

The purpose of a CONSERVE statement is to ensure strict numerical conservation. Convergence and accuracy will be compromised if this statement is omitted.

In my case i want to get ica from Calcium channel and just want to get rid of calcium out of the system, without actually increasing cao (assuming cao to be constant)

so don't bother implementing an accumulation mechanism for cao.

i don't compute ica_pmp

OK, leave it out if you like, and don't include WRITE ica in the USEION ca statement. This imposes the assumption that the pump is electrically silent. Ca pumps in erythrocytes are electrogenic, and there is some evidence for electrogenic ca transport in neurons as well. This will also eliminate your only direct measure of the pump's activity. How do you propose to test your model to make sure the pump is working properly (let alone debug it)?

[ted]

How do you propose to test your model to make sure the pump is working properly (let alone debug it)?

You could, of course, just calculate the current and make it a RANGE variable, but not WRITE it. That way it will be available via hoc, but it will not affect charge balance.

Prompted by your questions, I have reviewed the discussion of this mechanism in The NEURON Book and found that the first sentence of the last paragraph on page 259 is incorrect and needs to be revised in the next edition. See
Discussion of calcium pump on page 259
viewtopic.php?f=22&t=316&p=5735#p6156
Thanks for raising these issues!

[Haroon]

Thanks Ted!

I am tuning parameters for my pump now and using data from Maeda et al 1999; Neuron, to calibrate it properly.

Haroon