TITLE Calcium ion accumulation and diffusion
: The internal coordinate system is set up in PROCEDURE coord_cadifus()
: and must be executed before computing the concentrations.
: 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[NANN-1] being the concentration at the exact center
NEURON {
SUFFIX cadifus
USEION ca READ cao, cai, ica WRITE cai, ica
GLOBAL vol, Buffer0
RANGE ipump
}
DEFINE NANN 4
UNITS {
(mol) = (1)
(molar) = (1/liter)
(mM) = (millimolar)
(um) = (micron)
(mA) = (milliamp)
FARADAY = (faraday) (10000 coulomb)
PI = (pi) (1)
}
PARAMETER {
DFree = .6 (um2/ms)
diam (um)
cao (mM)
ica (mA/cm2)
k1buf = 500 (/mM-ms)
k2buf = 0.5 (/ms)
k1=1.e10 (um3/s)
k2=50.e7 (/s) : k1*50.e-3
k3=1.e10 (/s) : k1
k4=5.e6 (um3/s) : k1*5.e-4
area (um2)
}
CONSTANT { volo=1 (liter)}
ASSIGNED {
cai (mM)
vol[NANN] (1) : gets extra cm2 when multiplied by diam^2
ipump (mA/cm2)
last_ipump (mA/cm2)
}
STATE {
ca[NANN] (mM) <1.e-5> : ca[0] is equivalent to cai
CaBuffer[NANN] (mM)
Buffer[NANN] (mM)
pump (mol/cm2) <1.e-3>
pumpca (mol/cm2) <1.e-15>
}
LOCAL totpump, kd,totbuf
INITIAL {
totpump=0.2
pump=totpump/(1+1.e-18*k4*cao/k3)
pumpca=2.e-22
ipump=0
totbuf=1.2
kd=k2buf/k1buf
FROM i=0 TO NANN-1 {
ca[i] = cai
CaBuffer[i] =(totbuf*ca[i])/(kd+ca[i])
Buffer[i] = totbuf - CaBuffer[i]
}
}
BREAKPOINT {
SOLVE state METHOD sparse
last_ipump=ipump
ica = ipump
}
LOCAL coord_done
INITIAL {
if (coord_done == 0) {
coord_done = 1
coord()
}
: note Buffer gets set to Buffer0 automatically
: and CaBuffer gets set to 0 (Default value of CaBuffer0) as well
FROM i=0 TO NANN-1 {
ca[i] = cai
}
}
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 ca[0] is at edge of cell
: ca[NANN-1] is at center of cell
r = 1/2 :starts at edge (half diam)
dr2 = r/(NANN-1)/2 :half thickness of annulus
vol[0] = 0
frat[0] = 2*r
FROM i=0 TO NANN-2 {
vol[i] = vol[i] + PI*(r-dr2/2)*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]*1(um) {ca CaBuffer Buffer}
COMPARTMENT (1.e10)*area {pump pumpca}
COMPARTMENT (1.e15)*volo {cao}
~ ca[0] << (-(ica-last_ipump)*PI*diam*frat[0]*1(um)/(2*FARADAY))
FROM i=0 TO NANN-2 {
~ ca[i] <-> ca[i+1] (DFree*frat[i+1]*1(um), DFree*frat[i+1]*1(um))
}
dsq = diam*diam*1(um)
FROM i=0 TO NANN-1 {
dsqvol = dsq*vol[i]
~ ca[i] + Buffer[i] <-> CaBuffer[i] (k1buf*dsqvol,k2buf*dsqvol)
}
~ca[0] + pump <-> pumpca ((1.e-11)*k1*area, (1.e7)*k2*area)
~pumpca <-> pump + cao ((1.e7)*k3*area, (1.e-11)*k4*area)
ipump = 2*FARADAY*(f_flux-b_flux)/area
cai = ca[0]
}
COMMENT
At this time, conductances (and channel states and currents are
calculated at the midpoint of a dt interval. Membrane potential and
concentrations are calculated at the edges of a dt interval. With
secondorder=2 everything turns out to be second order correct.
ENDCOMMENT