## Intracellular potassium depletion

Extending NEURON to handle reaction-diffusion problems.

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yuzhou
Posts: 7
Joined: Fri Apr 29, 2016 10:44 pm

### Intracellular potassium depletion

I want to simulate intracellular K+ depletion by outward K+ current in a semi-sphere space with radius of 1 uM and volume of 2.1 um3. The outward K+ current is set to be 5 nA with duration of 3 ms, which equals to an efflux of 1.55e-16 mole of K+. Thus the intracellular K+ should be reduced by 74 mM. I wrote the following mechanism to simulate change of intracellular K+ by this outward K+ current. The extracellular [K+] is assumed to be constant.

Code: Select all

``````COMMENT
Modified from the code posted at
https://www.neuron.yale.edu/phpBB/viewtopic.php?f=16&t=1938&p=7158&hilit=intracellular+concentration#p7158
ENDCOMMENT

NEURON {
SUFFIX kiacc
USEION k READ ik WRITE ki,ko
RANGE ki0,ko0
}

UNITS {
(mV) = (millivolt)
(mA) = (milliamp)
(molar) = (1/liter)
(mM) = (millimolar)
}

PARAMETER {
ki0   = 160  (mM)      :   Initial K conc within the section
ko0   = 160  (mM)      :   Initial K conc in Extracellular space
}

ASSIGNED {
ik (mA/cm2)
diam (micron)
ko (mM)
}

INITIAL {
ki = ki0
}

STATE {
ki (mM)
}

BREAKPOINT {
SOLVE state METHOD cnexp
}

DERIVATIVE state {
ko=ko0
}
``````

Simulation using this mechanism shows that with 160 mM K+ on both sides the intracellular [K+] was only reduced by less than 5 mM (160 -> 155.5 mM) by above K+ current in a single compartment cell with L and diam of 1.386 um.

P.S. Here is the screenshot of the simulation. ted
Posts: 5819
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
Contact:

### Re: Intracellular potassium depletion

yuzhou wrote:I want to simulate intracellular K+ depletion by outward K+ current in a semi-sphere space with radius of 1 uM
1uM is generally used to mean 1 micromolar. You apparently meant 1 um (one micron).

Assuming that the surface through which potassium current flows is a hemisphere with radius 1 um, your model has the same volume and surface area as a section with diameter
diam = 4*4.2/PI = 5.3476061 um
and length
L = 1/(2*diam) = 0.093499781um
And its surface area is 1.5707963 um2.
The outward K+ current is set to be 5 nA with duration of 3 ms, which equals to an efflux of 1.55e-16 mole of K+
The current is very definitely not a rectangular current pulse--the plot of soma.ik shows a distinct lag between the onset of soma.ik and the time that its numerical value converges on 5). But the real problem is this: the units of soma.ik are in mA/cm2, not nA. Even if the current were exactly 5 mA/cm2, the net current is only about
5mA/cm2 * 1.6 um2 * 1e-8 cm2/um2 = 8e-8 mA = 0.08 nA
which is a lot smaller than 5 nA.

The NMODL code for your potassium accumulation mechanism is pretty good but could be a bit better--

This mechanism doesn't actually use ko or ko0 so the USEION and RANGE statements in its NEURON block should be

Code: Select all

``````   USEION k READ ik WRITE ki
RANGE ki0``````
and all the other statements that involve ko or ko0 can be deleted.
But that's pretty minor stuff.

Here's something much more important: with an ion accumulation mechanism described by differential equations, a large efflux from a small compartment can force concentration to become < 0 in a single time step if the mechanism uses cnexp. That will crash the simulation because ionic equilibrium potential cannot be calculated. To prevent this, change
SOLVE state METHOD cnexp
to
SOLVE state METHOD derivimplicit
yuzhou
Posts: 7
Joined: Fri Apr 29, 2016 10:44 pm

### Re: Intracellular potassium depletion

Dear Ted,

Thank you so much for pointing out my mistakes on current unit and NMODL coding. Now the simulation works as expected.

Yu