COMMENT
IP3 accumulation with breakdown and radial and longitudinal diffusion
patterned after cadifus
ENDCOMMENT
NEURON {
SUFFIX ip3cum
USEION ip3 READ ip3i, iip3 WRITE ip3i VALENCE 1
GLOBAL vrat : vrat must be GLOBAL--see INITIAL block
}
DEFINE Nannuli 4
UNITS {
(molar) = (1/liter)
(mM) = (millimolar)
(uM) = (micromolar)
(um) = (micron)
(mA) = (milliamp)
FARADAY = (faraday) (coulomb)
PI = (pi) (1)
}
PARAMETER {
DIP3 = 0.283 (um2/ms)
kdegr = 0.14e-3 (/ms) : degredation rate
}
CONSTANT {
ip3i0 = 0.16e-3 (mM) : [IP3]0 initial and resting ip3i conc
}
ASSIGNED {
diam (um)
iip3 (mA/cm2)
ip3i (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
}
STATE {
: ip3[0] is equivalent to ip3i
: ip3[] are very small, so specify absolute tolerance
ip3[Nannuli] (mM) <1e-6>
}
BREAKPOINT { SOLVE state METHOD sparse }
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
}
ip3i = ip3i0
FROM i=0 TO Nannuli-1 {
ip3[i] = ip3i
}
}
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] {ip3 ip3i0}
LONGITUDINAL_DIFFUSION i, DIP3*diam*diam*vrat[i] {ip3}
~ ip3[0] << (-iip3*PI*diam*(1e4)/FARADAY) : -iip3 is IP3 production at the cell membrane
FROM i=0 TO Nannuli-2 {
~ ip3[i] <-> ip3[i+1] (DIP3*frat[i+1], DIP3*frat[i+1])
}
dsq = diam*diam
FROM i=0 TO Nannuli-1 {
dsqvol = dsq*vrat[i]
~ ip3[i] <-> ip3i0 (kdegr*dsqvol, kdegr*dsqvol)
}
ip3i = ip3[0]
}