voltage and calcium dependent channel

[udi]

Hi,
I want to describe a voltage dependent channels (e.g KDr, KM) as voltage AND calcium dependent in a way that calcium INHIBITS the channel. The "degree" of inhibition is defined according to the following function:

y = A * ((cai*X))/ (((cai*X)) + (Z)) ;
A,Z,X are defined elsewhere).


what parameter in the mod file should I multiply by 'y' ?

for example: in the mod file which describes the M current:
:
:
USEION ca READ cai
:
:
BREAKPOINT {
SOLVE states METHOD cnexp
ik = gkbar * m * (v - ek)
}

DERIVATIVE states {
rates(v) : change to ---- > rates(v,cai) ?
m' = (m_inf - m) / tau_m
}

INITIAL {
:
:
:
rates(v)
m = m_inf
}

PROCEDURE rates( v(mV) ) { LOCAL a,b

a = 1e-4 * (v+30) / ( 1 - exp(-(v+30)/9) )
b = -1e-4 * (v+30) / ( 1 - exp( (v+30)/9) )
tau_m = 1 / (a + b) / tadj
m_inf = a / (a + b)
}

Should it be m, m' or a,b ?

Thanks,
--Udi.

[ted]

Here's how to think about it:
You have some function f(cai) that varies between 0 and 1, which represents the effect of
cai on the "availability" of your voltage-gated k channels. This is quite analogous to the h
variable in the HH model of the sodium current. The only difference is that f() is an
instantaneous function of cai.

So all you have to do is
ik = gkbar * m * f(cai) * (v - ek)

[udi]

Thanks for your answer.

I did as you said and here is the related parts from the mod file:
--------------------------------------------------------------------
NEURON {
USEION k READ ek WRITE ik
USEION ca READ cai
}

PARAMETER {
cai (mM)
IC50 = 0.0001004 (mM)
A = .868
n = 1.03
frc = 1
ikk
}

BREAKPOINT {
SOLVE states METHOD cnexp
y = A * ((cai*frc)^n)/ (((cai*frc)^n) + (IC50^n))
z=(1-y)
ikk = gkbar * m * (v - ek)
ik = ikk*z
}

DERIVATIVE states {
rates(v,cai)
m' = ((m_inf - m) / tau_m)
}

PROCEDURE rates( v(mV), cai(mM) ) {
LOCAL a,b

a = 1e-4 * (v+30) / ( 1 - exp(-(v+30)/9) )
b = -1e-4 * (v+30) / ( 1 - exp( (v+30)/9) )
tau_m = (1 / (a + b) / tadj)
m_inf = (a / (a + b))
}
--------------------------------------------------------------------

After adding this mechanism I ran the simulation for the previous conductance value of Im (before this current becomes Ca++ dependent) and the cell was depolarized, as expected. BUT - when I increased gbar of Im in order to hyperpolarize the cell, it became even MORE depolarized.
What is the reason?

Thanks in advance,

--Udi.

[ted]

After adding this mechanism I ran the simulation for the previous conductance value of Im (before this current becomes Ca++ dependent) and the cell was depolarized, as expected. BUT - when I increased gbar of Im in order to hyperpolarize the cell, it became even MORE depolarized.

Are you saying that increasing this mechanism's gbar hyperpolarized the
cell when this mechanism was not Ca dependent, but depolarized it after
you made it Ca dependent? If so, what happens when you reduce A to 0?


This won't fix the problem, but it will save you future grief:

Code: Select all

 a = 1e-4 * (v+30) / ( 1 - exp(-(v+30)/9) )
b = -1e-4 * (v+30) / ( 1 - exp( (v+30)/9) )
tau_m = (1 / (a + b) / tadj)
m_inf = (a / (a + b))

will produce a bunch of msgs about divide by 0 errors, or numeric
overflow of a, b, tau_m, and m_inf, whenever v is very close to -30. The
RHS of the definitions of a and b should call a function that uses
L'hospital's rule whenever v+30 is close to 0.


Here's a suggestion that will make your code more readable in the Forum:
Preserving code formatting
https://www.neuron.yale.edu/phpBB2/viewtopic.php?t=493

[udi]

Are you saying that increasing this mechanism's gbar hyperpolarized the
cell when this mechanism was not Ca dependent, but depolarized it after
you made it Ca dependent?

Yes I am...

If so, what happens when you reduce A to 0?

In this case, z=1, as it was when the mecahnism wasn't Ca dependent. But how does it help??

Thanks for the other tips.

--Udi.

[ted]

Are you saying that increasing this mechanism's gbar hyperpolarized the
cell when this mechanism was not Ca dependent, but depolarized it after
you made it Ca dependent?

Yes I am...

So the NMODL code that did not include the y and ikk stuff worked
properly.

If so, what happens when you reduce A to 0?

In this case, z=1, as it was when the mecahnism wasn't Ca dependent. But how does it help??

I wasn't asking what happened to z. The point of my question was to find
out how your model behaves when A is 0.

[udi]

I wasn't asking what happened to z. The point of my question was to find
out how your model behaves when A is 0.

In this case (A = 0) it behaves like the mechanism (I_m) is NOT calcium dependent: increasing gbar hyperpolarizes the cell, decreasing gbar depolarizes the cell.

[ted]

At this point the most effective way to proceed will be for you to zip up
just the files that are necessary to reproduce this problem and email the
zip file to me at
ted dot carnevale at yale dot edu
so I can try to figure out what's wrong. Since I'm away from Yale and must
use a slow modem connection, please don't send dll, .o, or .c files--just the
hoc, mod, and ses files that are essential to reproduce the symptom.