: modified by Jay Coggan for K diffusion
TITLE Calcium ion accumulation with longitudinal and radial diffusion
: The internal coordinate system is set up in PROCEDURE coord_cadifus()
: The scale factors set up in this procedure do not have to be recomputed
: when diam or DFree are changed.
: The amount of calcium in an annulus is ca[i]*diam^2*vol[i] with
: ca[0] being the second order correct concentration at the exact edge
: and ca[NANN1] being the concentration at the exact center
: modified by j coggan
NEURON {
SUFFIX kdifus
:USEION k READ ko, ki, ik WRITE ki, ik
USEION k READ ko, ki, ik WRITE ki
RANGE ikbar
GLOBAL vol :, Buffer0
}
DEFINE NANN 4
UNITS {
(molar) = (1/liter)
(mM) = (millimolar)
(um) = (micron)
(mA) = (milliamp)
FARADAY = (faraday) (10000 coulomb)
PI = (pi) (1)
}
PARAMETER {
DFree = .6 (um2/ms)
diam (um)
ko (mM)
ik (mA/cm2)
k1buf (/mMms)
k2buf (/ms)
ikbar (mA/cm2)
ki0 = 150 (mM)
}
ASSIGNED {
ki (mM)
vol[NANN] (1) : gets extra cm2 when multiplied by diam^2
}
STATE {
k[NANN] (mM) : k[0] is equivalent to cai
KBuffer[NANN] (mM)
Buffer[NANN] (mM)
}
BREAKPOINT {
SOLVE state METHOD sparse
ik = ikbar
}
LOCAL coord_done
INITIAL {
if (coord_done == 0) {
coord_done = 1
coord()
}
: note Buffer gets set to Buffer0 automatically
: and KBuffer gets set to 0 (Default value of KBuffer0) as well
FROM i=0 TO NANN1 {
k[i] = ki0
}
}
LOCAL frat[NANN] : gets extra cm when multiplied by diam
PROCEDURE coord() {
LOCAL r, dr2
: cylindrical coordinate system with constant annuli thickness to
: center of cell. Note however that the first annulus is half thickness
: so that the concentration is second order correct spatially at
: the membrane or exact edge of the cell.
: note k[0] is at edge of cell
: k[NANN1] is at center of cell
r = 1/2
:starts at edge (half diam)
dr2 = r/(NANN1)/2 :half thickness of annulus
vol[0] = 0
frat[0] = 2*r
FROM i=0 TO NANN2 {
vol[i] = vol[i] + PI*(rdr2/2)*2*dr2 :interior half
r = r  dr2
frat[i+1] = 2*PI*r/(2*dr2) :exterior edge of annulus
: divided by distance between centers
r = r  dr2
vol[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
KINETIC state {
COMPARTMENT i, diam*diam*vol[i] {k KBuffer Buffer}
LONGITUDINAL_DIFFUSION j, DFree*diam*diam*vol[j] {k}
~ k[0] << (ik*PI*diam*frat[0]/(FARADAY))
FROM i=0 TO NANN2 {
~ k[i] <> k[i+1] (DFree*frat[i+1], DFree*frat[i+1])
}
dsq = diam*diam
FROM i=0 TO NANN1 {
dsqvol = dsq*vol[i]
~ k[i] + Buffer[i] <> KBuffer[i] (k1buf*dsqvol,k2buf*dsqvol)
}
:ki = k[3]
ki = (k[0] + k[1] + k[2] + k[3])/4
}
