COMMENT
This file, ca_dist.mod or ca_prox.mod, for Quadroni and Knopfel 1994, was modified
from cadifus.mod from Chapter 9 Hines and Carnevale NEURON
These files ca_dist.mod, ca_prox.mod, only have differences in number
of annuli, Nannuli, for distal dendrites (5 prox vs 2 dist compartments)
and of course in the suffix names ( ca_dist and ca_prox).
Here ca diffusion in a cylinder is modeled along with an ATPase pump
(the real pump consumes ATP as it pumps Ca out of the cell) and a
Na/Ca exchanger (each real exchanger pumps 1 Ca ions out of the cell for
3 Na ions let into the cell)
ENDCOMMENT
: Calcium ion accumulation with radial (and uncommentable longitudinal) diffusion
NEURON {
SUFFIX ca_dist : ***************************************
USEION ca READ cai, ica WRITE cai : note that the membrane ica is approximated as
: not being changed by the little ATPase pump and the Na/Ca exchangers
: and therefore ica is not written to with WRITE by this mechanism
NONSPECIFIC_CURRENT ifake : used to move the calc. of the breakpt. to same t as other currents
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
}
DEFINE Nannuli 2 : 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 (/mMms) : Yamada et al. 1989
: k2buf = 0.1 (/ms)
: B = 0.003 (mM)
K2f_ex = 4.85e-13 (mA/cm2mM2): Quadroni and Knopfel 94 (distal dendrite A type cells)
: this above value will be overwritten to give each section it's proper value.
: int the Q+R 94 files this is done through bothcells4.ses
cao = 2 (mM) : 2e-3 (M) : [Ca]_outside is set constant to 2mM because it
: doesn't change in this simulation (thought to be approx true in real).
E_1 = 0.01315 (/mV) : Quadroni and Knopfel 94
E_2 = 0.0255 (/mV) : "
nai = 7.6 (mM) : "
nao = 152 (mM) : "
K2f_ATPase = 9.2625897e-06 (mA/cm2 mM4) : 9.6e-11 (/umol ms cm2) : type A distal dendrites only
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
mM2M = 1e-3 (1) : mM to M conversion for cai concentration in rate eq
}
ASSIGNED {
v (mV)
diam (um)
ica (mA/cm2)
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)
ifake (mA/cm2) : fake current used to make solver move
: calculation of breakpt. to same time as currents.
}
STATE {
: ca[0] is equivalent to cai
: ca[] are very small, so specify absolute tolerance
ca[Nannuli] (mM) <1e-6>
CaBuffer[Nannuli] (mM) <1e-6>
Buffer[Nannuli] (mM) <1e-6>
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
SOLVE state METHOD sparse
ifake=0 : causes solver to execute the breakpoint block at the
: same time as the calculation of the other currents
}
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 : initialization value of 50 uM
ca[i] = cai : keep stored values of cai in millimolar units
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)*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}
: 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 efflux from lva and hva mechanisms
: i_Na_Ca_ex is the flux from Na-Ca exhanger
: i_ATPase is the flux 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]
}