pump kinetic scheme

[ted]

You don't really want to do either of those things unless you can point to experimental biological evidence that they happen in real cells.

[menica]

Dear ted
Indeed I cannot prove it biologically but I need to have a system that works in this way: input Iclamp current modified the membrane very, this change induces the activation of the voltage gated na channel , the nai increases. The change in nai activates the na pump. The pump is active until when the nai comes back to its initial value. Any help in order to achieve this will be very helpful. I tryed to change the pump mechanism in this way: ipump-bar=constant*(nai-nai0) but i have the same behaviour.

Menica

[ted]

What you do is up to you, but the principled approach is to make as few assumptions as necessary. Your sodium transport mechanism pumpnatau produces zero sodium flux through the cell membrane when nai equals nai0_pumpnatau. If the net transmembrane sodium flux caused by all other mechanisms is nonzero when the cell is at rest, then the resting nai will necessarily deviated from nai0_pumpnatau. That's an inescapable fact. The simplest way to eliminate this offset is to add a new mechanism that produces a transmembrane sodium flux that is constant and opposite in direction to the flux produced by all other mechanisms at rest. The justification for adding such a mechanism is simple.
1. The real cell must have a steady nai at rest, and so must the model cell
2. The model cell contains representations of only a subset of all the things that are going on in the real cell that would affect nai. If nai in the model cell at rest does not settle to the same nai as in the real cell, then the model cell must have omitted "something" that affects nai.
3. The simplest way to compensate for omission of that "something" is to represent it as a constant source of sodium flux. In the absence of any more specific knowledge, there is no basis for presuming anything more complicated.

Here's an electroneutral sodium flux mechanism:

Code: Select all

: an electroneutral transmembrane sodium flux
NEURON {
  SUFFIX naflux
  USEION na WRITE ina
  NONSPECIFIC_CURRENT i  
  RANGE amp
}
PARAMETER {
  amp = 0 (milliamp/cm2)  : negative is inward
}
ASSIGNED {
  ina (milliamp/cm2)
  i (milliamp/cm2)
}
BREAKPOINT {
  ina = amp
  i = -ina
}

Insert naflux into every section that has your sodium pump, and you're almost done. All you need then is a custom initialization that sets amp_naflux to the correct value in every segment that has your sodium pump.

And here is a custom initialization that will do the job. Put the following code into a file called initnaflux.hoc.

Code: Select all

proc init() {
  forall if (ismembrane("naflux")) amp_naflux = 0
  finitialize(v_init)
  forall if (ismembrane("naflux")) {
    for (x,0) {
      amp_naflux(x) = -ina(x)
      i_naflux(x) = ina(x) // preserve electoneutrality
  }
  if (cvode.active()) {
    cvode.re_init()
  } else {
    fcurrent()
  }
  frecord_init()
}

Finally, at the end of your own model setup code, but before any statement that launches a simulation, insert
load_file("initnaflux.hoc")

[menica]

Dear Ted,
I tried out your solution, but it doesn't seem to solve the problem. the nai is not coming back at nai0

Best
Menica

[ted]

I won't have the opportunity to look into this until after I return from the SFN meeting later this week or early next week.

[menica]

Dear Ted,
thanks!
In the meantime, I tried to solve the problem in the other way. I add more complexity to the model (I add the K HH channel and leakage currents for Na, K and non-specific ion, in this way the sodium channel close once the stimulus is over).
I obtained the more or less desired behavior. Still, I have problems: starting from the time point where the nai drops to 0 I observe an oscillatory behavior of the inapump. I think this is own to the fact that I force ipump_bar to be 0 when nai<=nai0, when it is, looking at the equation, = ipumpmax/2.
Then, I changed the ipump_bar equation in the derivative state

if(nai <= nai0 ){
ipump_bar = 0
}else{
ipump_bar = ipumpmax*(1/(1 + pow(km/nai,n)))
}

in this way:
ipump_bar=ipumpmax(nai-nai0). (with adjusted values of the ipumpmax parameter)

I eliminate the oscillatory behavior but I am wondering if this is the correct way to proceed or would be better to eliminate the oscillatory behavior somehow when using the Michaelis-Menten formalism.
The units are not correct.

Best
Menica