COMMENT
This file, ca_soma_cylind_shells.mod, for Quadroni and Knopfel 1994, was modified from
cadifus.mod from Chapter 9 Hines and Carnevale NEURON
This file is identical to the other ca_*.mod files except has
the number of annulli, Nannuli (number of compartments) set to 25.
ENDCOMMENT
: Calcium ion accumulation with radial and longitudinal diffusion
NEURON {
SUFFIX ca_soma_cyl
USEION ca READ cai, ica WRITE cai
GLOBAL vrat : vrat must be GLOBAL --see INITIAL block
: however B which in cadifus.mod was called TotalBuffer may be and is here RANGE
RANGE K2f_ex, K2f_ATPase, B
RANGE i_Na_Ca_ex, i_ATPase, I : Na Ca exchanger can pump one Ca out for 3 Na's
: that enter the cell.
: the ATPase current pumps Ca out of the cell by
: using up ATP
}
DEFINE Nannuli 50 : must be >=2 (i.e. at least shell and core)
UNITS {
(molar) = (1/liter)
(mM) = (millimolar)
(um) = (micron)
(mA) = (milliamp)
(mV) = (millivolt)
FARADAY = (faraday) (10000 coulomb)
PI = (pi) (1)
}
PARAMETER {
DCa = 0.6 (um2/ms)
: Ca buffer reaction rates :
k1buf = 30 (/mM ms) : these rates from Sala and Hernandez-Cruz 1990
k2buf = 0.03 (/ms) : and are labeled f and b in
: Quadroni and Knopfel 1994 p. 1916
B = 0.025 (mM) : this is [B] in Quadroni and Knopfel 94 Table 4
: compare above with these rates from
: k1buf = 100 (/mM ms) : Yamada et al. 1989
: k2buf = 0.1 (/ms)
: B = 0.003 (mM)
K2f_ex = 0 : should be 2*FARADAY*3.3e-13 (mA/cm2mM2): Quadroni and Knopfel 94
: K2f_ex = 5e-6 (mA/cm2mM2): a value from Lytton and Sejnowski's (LS '91) 5e-6
: (Soma value only - dendrites are different)
cao = 2 (mM) : [Ca]_outside is set constant because it
: doesn't change in this simulation.
E_1 = 0.01315 (/mV) : Quadroni and Knopfel 94
E_2 = 0.0255 (/mV) : "
nai = 7.6 (mM) : " : (LS's '91 = 10 mM)
nao = 152 (mM) : " : (LS's '91 = 140 mM)
K2f_ATPase = 0 : 2*FARADAY*2.65e-9 (mA/cm2) : type A soma only : dendrites and type B cell different
f_ATPase = 100 (/mM ms) : simply called f for forward rate in Quadroni Knopfel
b_ATPase = 0.005 (/ms) : 1994 - this one is just called b for backward
}
ASSIGNED {
v (mV)
diam (um)
ica (mA/cm2)
I (mA/cm2) : same as ica but used for diagnostic purposes
i_Na_Ca_ex (mA/cm2)
i_ATPase (mA/cm2)
cai (mM)
vrat[Nannuli] (1) : dimensionless
: numeric value of vrat[i] equals the volume
: of annulus iof a 1um diameter cylinder
: multiply by diam^2 to get volume per um length
Kd (/mM)
B0 (mM)
}
STATE {
: ca[0] is equivalent to cai
: ca[] are very small, so specify absolute tolerance
ca[Nannuli] (mM) <1e10>
CaBuffer[Nannuli] (mM)
Buffer[Nannuli] (mM)
n (1)
}
BREAKPOINT {
SOLVE states METHOD cnexp
i_Na_Ca_ex = -K2f_ex * (nai^3 * cao * exp(E_1 * v) - nao^3 * cai * exp(-E_2*v))
i_ATPase = K2f_ATPase * n
I= ica : diagnostic purposes only
SOLVE state METHOD sparse
}
DERIVATIVE states {
: compute state variable n at present v and t
n' = f_ATPase * cai * (1 - n) - b_ATPase * n
}
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
}
n = f_ATPase * cai / (f_ATPase * cai + b_ATPase)
Kd = k1buf/k2buf
B0 = B/(1 + Kd*cai)
FROM i=0 TO Nannuli-1 {
cai = 5e-5 : arbitrary initialization
ca[i] = cai
Buffer[i] = B0
CaBuffer[i] = B - B0
}
}
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)*4*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}
: LONGITUDINAL_DIFFUSION i, DCa*diam*diam*vrat[i] {ca}
~ ca[0] << ( (-ica - i_Na_Ca_ex - i_ATPase)*PI*diam/(2*FARADAY))
: ica is Ca current from hva or lva or both
: i_Na_Ca_ex is the current from Na-Ca exhanger
: i_ATPase is the current from Ca-ATPase
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]
}