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cal4.mod
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cal4.mod
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:Modified from NEURON implementation of Fink et al., 2000
NEURON {
SUFFIX cal4
USEION ca READ cao, ica WRITE cai, ica
USEION ip3 READ ip3i VALENCE 1
RANGE ica_pmp,ca1, ca2,alpha,beta,ca3,gamma,ip3ca, DCa,jip3
GLOBAL vrat, TBufs, KDs, TBufs, TBufm, KDm, factor
}
DEFINE Nannuli 4
UNITS {
(mol) = (1)
(molar) = (1/liter)
(uM) = (micromolar)
(mM) = (millimolar)
(um) = (micron)
(mA) = (milliamp)
FARADAY = (faraday) (10000 coulomb)
PI = (pi) (1)
}
PARAMETER {
cai0 = 50e-6(mM)
cath = 0.2e-3 (mM) : threshold for ca pump activity
gamma = 8 (um/s) : ca pump flux density
jmax = 3.5e-3 (mM/ms)
caer = 0.400 (mM)
Kip3 = 0.8e-3 (mM)
Kact = 0.3e-3 (mM)
kon = 2.7 (/mM-ms)
Kinh = 0.2e-3 (mM)
alpha = 1 (1) : relative abundance of ER mechanisms : alpha only specific for ip3 receptor,
beta = 1(1) :introducing beta to take care of other ER mechanisms(SERCA and leak channel density)
vmax =1e-4 (mM/ms) :1e-4 revised
Kp = 0.27e-3 (mM)
DCa = 0.22 (um2/ms) :Fink et al 2000
TBufs = 0.45 (mM)
kfs = 1000 (/mM-ms) : try these for now
KDs = 10 (uM)
TBufm = 0.075 (mM)
kfm = 1000 (/mM-ms) : try these for now
KDm = 0.24 (uM)
DBufm = 0.050 (um2/ms)
factor = 0.019 (1)
}
ASSIGNED {
diam (um)
ica (mA/cm2)
cai (mM)
jip3 (mM/ms)
ca1 (mM)
ca2 (mM)
ca3 (mM)
ica_pmp (mA/cm2)
ica_pmp_last (mA/cm2)
parea (um) :pump area peer unit length
sump (mM)
cao (mM)
ip3i (mM)
jchnl (mM/ms)
vrat[Nannuli] (1)
L[Nannuli] (mM/ms) adjusted so that
: jchnl + jpump + jleak = 0 when ca = 0.05 uM and h = Kinh/(ca + Kinh)
bufs_0 (mM)
bufm_0 (mM)
ip3ca (mM)
}
CONSTANT { volo = 1e10 (um2) }
STATE {
ca[Nannuli] (mM) <1e-7>
hc[Nannuli]
ho[Nannuli]
bufs[Nannuli] (mM) <1e-3>
cabufs[Nannuli] (mM) <1e-7>
bufm[Nannuli] (mM) <1e-4>
cabufm[Nannuli] (mM) <1e-8>
ip3cas [Nannuli] (mM)
}
BREAKPOINT {
SOLVE state METHOD sparse
ica_pmp_last = ica_pmp
ica = ica_pmp
}
LOCAL factors_done, jx
INITIAL {
if (factors_done==0) {
factors_done= 1
factors()
}
cai = cai0
jip3=0
bufs_0 = KDs*TBufs/(KDs + (1000)*cai0)
bufm_0 = KDm*TBufm/(KDm + (1000)*cai0)
FROM i=0 TO Nannuli-1 {
ca[i] = cai
bufs[i] = bufs_0
cabufs[i] = TBufs - bufs_0
bufm[i] = bufm_0
cabufm[i] = TBufm - bufm_0
}
ica=0
ica_pmp = 0
ica_pmp_last = 0
FROM i=0 TO Nannuli-1 {
ho[i] = Kinh/(ca[i]+Kinh)
hc[i] = 1-ho[i]
jx = (-vmax*ca[i]^2 / (ca[i]^2 + Kp^2))
jx = jx + jmax*(1-(ca[i]/caer)) * ( (ip3i/(ip3i+Kip3)) * (ca[i]/(ca[i]+Kact)) * ho[i] )^3
L[i] = -jx/(1 - (ca[i]/caer))
}
sump = cath
parea = PI*diam
}
LOCAL frat[Nannuli]
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
KINETIC state {
COMPARTMENT i, diam*diam*vrat[i] {ca bufs cabufs bufm cabufm sump}
COMPARTMENT volo {cao}
LONGITUDINAL_DIFFUSION i, DCa*diam*diam*vrat[i] {ca}
LONGITUDINAL_DIFFUSION i, DBufm*diam*diam*vrat[i] {bufm cabufm}
:cell membrane ca pump
~ ca[0] <-> sump ((0.001)*parea*gamma*u(ca[0]/(1 (mM)), cath/(1 (mM))), (0.001)*parea*gamma*u(ca[0]/(1 (mM)), cath/(1 (mM))))
ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea
: all currents except cell membrane ca pump
~ ca[0] << (-(ica - ica_pmp_last)*PI*diam*factor/(2*FARADAY)) : ica is Ca efflux
: radial diffusion
FROM i=0 TO Nannuli-2 {
~ ca[i] <-> ca[i+1] (DCa*frat[i+1], DCa*frat[i+1])
}
: buffering
dsq = diam*diam
FROM i=0 TO Nannuli-1 {
dsqvol = dsq*vrat[i]
~ ca[i] + bufs[i] <-> cabufs[i] (kfs*dsqvol, (0.001)*KDs*kfs*dsqvol)
:~ ca[i] + bufm[i] <-> cabufm[i] (kfm*dsqvol, (0.001)*KDm*kfm*dsqvol) :to simulate high affinity dyes, used only for the simplified 3 cylinder model in the paper
}
:SERCA pump, channel
FROM i=0 TO Nannuli-1 {
dsqvol = dsq*vrat[i]
: pump
~ ca[i] << (-dsqvol*beta*vmax*ca[i]^2 / (ca[i]^2 + Kp^2))
: channel
~ hc[i] <-> ho[i] (kon*Kinh, kon*ca[i])
~ ca[i] << ( dsqvol*alpha*jmax*(1-(ca[i]/caer)) * ( (ip3i/(ip3i+Kip3)) * (ca[i]/(ca[i]+Kact)) * ho[i] )^3 )
: leak
~ ca[i] << (dsqvol*beta*L[i]*(1 - (ca[i]/caer)))
~ ip3cas[i] << (dsqvol*alpha*jmax*(1-(ca[i]/caer)) * ( (ip3i/(ip3i+Kip3)) * (ca[i]/(ca[i]+Kact)) * ho[i] )^3 )
}
jip3 = ( dsqvol*alpha*jmax*(1-(ca[0]/caer)) * ( (ip3i/(ip3i+Kip3)) * (ca[0]/(ca[0]+Kact)) * ho[0] )^3 )
: ip3ca=0
: FROM i=0 TO Nannuli-1 {
: ip3ca=ip3ca+ip3cas[i]
: }
ip3ca=ip3cas[0]
cai = ca[0]
ca1 = ca[1]
ca2 = ca[2]
ca3 = ca[3]
}
FUNCTION u (x, th) {
if (x>th) {
u = 1
} else {
u = 0
}
}