I am using the calcium diffusion and buffering mechanism presented as Example 8 of the NMODL expanded documentation, with the additions specified in the Example 9 that add a calcium pump (the complete code is below).

In addition, I have an L-type calcium channel mechanism which provides some calcium entry.

The section in which I am inserting it has variable diameter (diam(0:1)=6:0.5, nseg=50, L=500) and I am not sure whether that is a good idea given some particuarities of the mechanism. The result of the simulation is a constant increase of calcium at the narrowest end of the section, something that does not happen when simulating with a section of constant diameter. I have noticed, though, that with constant diameter the steady state calcium concentration increases as the diameter decreases, indicating that what I am seeing is a normal consequence of the geometry.

I have tried to compensate it with a variable density of the calcium channel or with a variable value for some parameter such as buffer concentration or pump density, and it seems to work.

Does anybody think that there is a more 'wise' way of dealing with this?

Any help will be greatly appreciated.

Code: Select all

```
: Calcium ion accumulation with radial and longitudinal diffusion + calcium pump
: Hines and Carnevale:Expanding NEURON with NMODL, Examples 8 & 9
NEURON {
SUFFIX cdp
USEION ca READ cao, cai, ica WRITE cai, ica
RANGE ica_pmp
GLOBAL vrat, TotalBuffer, TotalPump
}
DEFINE Nannuli 4
UNITS {
(mol) = (1)
(molar) = (1/liter)
(mM) = (millimolar)
(um) = (micron)
(mA) = (milliamp)
FARADAY = (faraday) (10000 coulomb)
PI = (pi) (1)
}
PARAMETER {
DCa = 0.6 (um2/ms)
k1buf = 100 (/mM-ms) : Yamada et al. 1989
k2buf = 0.1 (/ms)
TotalBuffer = 0.003 (mM)
k1 = 1 (/mM-ms)
k2 = 0.005 (/ms)
k3 = 1 (/ms)
k4 = 0.005 (/mM-ms)
TotalPump = 1e-14 (mol/cm2) : to eliminate pump, set TotalPump to 0 in hoc
}
ASSIGNED {
diam (um)
ica (mA/cm2)
cai (mM)
vrat[Nannuli] : numeric value of vrat[i] equals the volume
: of annulus i of a 1um diameter cylinder
: multiply by diam^2 to get volume per um length
Kd (/mM)
B0 (mM)
cao (mM)
ica_pmp (mA/cm2)
parea (um)
}
CONSTANT { volo = 1e10 (um2) }
STATE {
: ca[0] is equivalent to cai
: ca[] are very small, so specify absolute tolerance
ca[Nannuli] (mM) <1e-10>
CaBuffer[Nannuli] (mM)
Buffer[Nannuli] (mM)
pump (mol/cm2)
pumpca (mol/cm2)
}
BREAKPOINT {
SOLVE state METHOD sparse
ica = ica_pmp
}
LOCAL factors_done
INITIAL {
if (factors_done == 0) { : flag becomes 1 in the first segment
factors_done = 1 : all subsequent segments will have
factors() : vrat = 0 unless vrat is GLOBAL
}
Kd = k1buf/k2buf
B0 = TotalBuffer/(1 + Kd*cai)
FROM i=0 TO Nannuli-1 {
ca[i] = cai
Buffer[i] = B0
CaBuffer[i] = TotalBuffer - B0
}
parea = PI*diam
pump = TotalPump/(1 + (cai*k1/k2))
pumpca = TotalPump - pump
}
LOCAL frat[Nannuli] : scales the rate constants for model geometry
PROCEDURE factors() {
LOCAL r, dr2
r = 1/2 : starts at edge (half diam)
dr2 = r/(Nannuli-1)/2 : full thickness of outermost annulus,
: half thickness of all other annuli
vrat[0] = 0
frat[0] = 2*r
FROM i=0 TO Nannuli-2 {
vrat[i] = vrat[i] + PI*(r-dr2/2)*2*dr2 : interior half
r = r - dr2
frat[i+1] = 2*PI*r/(2*dr2) : outer radius of annulus
: div by distance between centers
r = r - dr2
vrat[i+1] = PI*(r+dr2/2)*2*dr2 : outer half of annulus
}
}
LOCAL dsq, dsqvol : can't define local variable in KINETIC block
: or use in COMPARTMENT statement
KINETIC state {
COMPARTMENT i, diam*diam*vrat[i] {ca CaBuffer Buffer}
COMPARTMENT (1e10)*parea {pump pumpca}
COMPARTMENT volo {cao}
LONGITUDINAL_DIFFUSION i, DCa*diam*diam*vrat[i] {ca}
:pump
~ ca[0] + pump <-> pumpca (k1*parea*(1e10), k2*parea*(1e10))
~ pumpca <-> pump + cao (k3*parea*(1e10), k4*parea*(1e10))
CONSERVE pump + pumpca = TotalPump * parea * (1e10)
ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea
: all currents except pump
~ ca[0] << (-(ica - ica_pmp)*PI*diam/(2*FARADAY))
FROM i=0 TO Nannuli-2 {
~ ca[i] <-> ca[i+1] (DCa*frat[i+1], DCa*frat[i+1])
}
dsq = diam*diam
FROM i=0 TO Nannuli-1 {
dsqvol = dsq*vrat[i]
~ ca[i] + Buffer[i] <-> CaBuffer[i] (k1buf*dsqvol, k2buf*dsqvol)
}
cai = ca[0]
}
```