: Calcium ion accumulation with endogenous buffers, DCM and pump
COMMENT
The basic code of Example 9.8 and Example 9.9 from NEURON book was adapted as:
1) Extended using parameters from Schmidt et al. 2003.
2) Pump rate was tuned according to data from Maeda et al. 1999
3) DCM was introduced and tuned to approximate the effect of radial diffusion
Reference: Anwar H, Hong S, De Schutter E (2010) Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cell. Cerebellum*
*Article available as Open Access
PubMed link: http://www.ncbi.nlm.nih.gov/pubmed/20981513
Written by Haroon Anwar, Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 2010.
Contact: Haroon Anwar (anwar@oist.jp)
Modified by Stefano Masoli, Department Brain and Behavioral Sciences, University of Pavia, 2015
1) Buffer for Granule cell model 2015, without Parvalbumin and Calretinin instead of Calbindin.
ENDCOMMENT
NEURON {
SUFFIX cdp5_CR
USEION ca READ cao, cai, ica WRITE cai
RANGE ica_pmp
RANGE Nannuli, Buffnull2, rf3, rf4, vrat, cainull, CR, CR_1C_0N, CR_2C_2N, CR_1V, CRnull
RANGE TotalPump
}
UNITS {
(mol) = (1)
(molar) = (1/liter)
(mM) = (millimolar)
(um) = (micron)
(mA) = (milliamp)
FARADAY = (faraday) (10000 coulomb)
PI = (pi) (1)
}
PARAMETER {
Nannuli = 10.9495 (1)
celsius (degC)
cainull = 45e-6 (mM)
mginull =.59 (mM)
: values for a buffer compensating the diffusion
Buffnull1 = 0 (mM)
rf1 = 0.0134329 (/ms mM)
rf2 = 0.0397469 (/ms)
Buffnull2 = 60.9091 (mM)
rf3 = 0.1435 (/ms mM)
rf4 = 0.0014 (/ms)
: values for benzothiazole coumarin (BTC)
BTCnull = 0 (mM)
b1 = 5.33 (/ms mM)
b2 = 0.08 (/ms)
: values for caged compound DMNPE-4
DMNPEnull = 0 (mM)
c1 = 5.63 (/ms mM)
c2 = 0.107e-3 (/ms)
: values for Calretinin (6 sites but only 5 active) (2*2 cooperative sites and 1 single indipendent site)
CRnull = 0.9 (mM):0.7-1.2
nT1 = 1.8 (/ms mM)
nT2 = 0.053 (/ms)
nR1 = 310 (/ms mM)
nR2 = 0.02 (/ms)
nV1 = 7.3 (/ms mM)
nV2 = 0.24 (/ms)
:pumps
kpmp1 = 3e-3 (/mM-ms)
kpmp2 = 1.75e-5 (/ms)
kpmp3 = 7.255e-5 (/ms)
TotalPump = 1e-9 (mol/cm2)
}
ASSIGNED {
diam (um)
ica (mA/cm2)
ica_pmp (mA/cm2)
parea (um) : pump area per unit length
parea2 (um)
cai (mM)
cao (mM)
mgi (mM)
vrat (1)
}
:CONSTANT { cao = 2 (mM) }
STATE {
: ca[0] is equivalent to cai
: ca[] are very small, so specify absolute tolerance
: let it be ~1.5 - 2 orders of magnitude smaller than baseline level
ca (mM) <1e-3>
mg (mM) <1e-6>
Buff1 (mM)
Buff1_ca (mM)
Buff2 (mM)
Buff2_ca (mM)
BTC (mM)
BTC_ca (mM)
DMNPE (mM)
DMNPE_ca (mM)
:calretinin
CR (mM)
CR_1C_0N (mM)
CR_2C_0N (mM)
CR_2C_1N (mM)
CR_1C_1N (mM)
CR_0C_1N (mM)
CR_0C_2N (mM)
CR_1C_2N (mM)
CR_2C_2N (mM)
CR_1V (mM)
:pumps
pump (mol/cm2) <1e-15>
pumpca (mol/cm2) <1e-15>
}
BREAKPOINT {
SOLVE state METHOD sparse
}
LOCAL factors_done
INITIAL {
factors()
ca = cainull
mg = mginull
Buff1 = ssBuff1()
Buff1_ca = ssBuff1ca()
Buff2 = ssBuff2()
Buff2_ca = ssBuff2ca()
BTC = ssBTC()
BTC_ca = ssBTCca()
DMNPE = ssDMNPE()
DMNPE_ca = ssDMNPEca()
:to calculate the steady state of each protein at starting point
CR = CRnull
CR_1C_0N = 0
CR_2C_0N = 0
CR_2C_1N = 0
CR_1C_1N = 0
CR_0C_1N = 0
CR_0C_2N = 0
CR_1C_2N = 0
CR_2C_2N = 0
CR_1V = 0
parea = PI*diam
parea2 = PI*(diam-0.2)
ica = 0
ica_pmp = 0
: ica_pmp_last = 0
pump = TotalPump
pumpca = 0
cai = ca
}
PROCEDURE factors() {
LOCAL r, dr2
r = 1/2 : starts at edge (half diam)
dr2 = r/(Nannuli-1)/2 : full thickness of outermost annulus,
vrat = PI*(r-dr2/2)*2*dr2 : interior half
r = r - dr2
}
LOCAL dsq, dsqvol : can't define local variable in KINETIC block
: or use in COMPARTMENT statement
KINETIC state {
COMPARTMENT diam*diam*vrat {ca mg Buff1 Buff1_ca Buff2 Buff2_ca BTC BTC_ca DMNPE DMNPE_ca CR CR_1C_0N CR_2C_0N CR_2C_1N CR_0C_1N CR_0C_2N CR_1C_2N CR_1C_1N CR_2C_2N CR_1V}
COMPARTMENT (1e10)*parea {pump pumpca}
:pump
~ ca + pump <-> pumpca (kpmp1*parea*(1e10), kpmp2*parea*(1e10))
~ pumpca <-> pump (kpmp3*parea*(1e10), 0)
CONSERVE pump + pumpca = TotalPump * parea * (1e10)
ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea
: all currents except pump
: ica is Ca efflux
~ ca << (-ica*PI*diam/(2*FARADAY))
:RADIAL DIFFUSION OF ca, mg and mobile buffers
dsq = diam*diam
dsqvol = dsq*vrat
~ ca + Buff1 <-> Buff1_ca (rf1*dsqvol, rf2*dsqvol)
~ ca + Buff2 <-> Buff2_ca (rf3*dsqvol, rf4*dsqvol)
~ ca + BTC <-> BTC_ca (b1*dsqvol, b2*dsqvol)
~ ca + DMNPE <-> DMNPE_ca (c1*dsqvol, c2*dsqvol)
:Calretinin
:Slow state
~ ca + CR <-> CR_1C_0N (nT1*dsqvol, nT2*dsqvol)
~ ca + CR_1C_0N <-> CR_2C_0N (nR1*dsqvol, nR2*dsqvol)
~ ca + CR_2C_0N <-> CR_2C_1N (nT1*dsqvol, nT2*dsqvol)
:fast state
~ ca + CR <-> CR_0C_1N (nT1*dsqvol, nT2*dsqvol)
~ ca + CR_0C_1N <-> CR_0C_2N (nR1*dsqvol, nR2*dsqvol)
~ ca + CR_0C_2N <-> CR_1C_2N (nT1*dsqvol, nT2*dsqvol)
:complete
~ ca + CR_2C_1N <-> CR_2C_2N (nR1*dsqvol, nR2*dsqvol)
~ ca + CR_1C_2N <-> CR_2C_2N (nR1*dsqvol, nR2*dsqvol)
:mixed
~ ca + CR_1C_0N <-> CR_1C_1N (nT1*dsqvol, nT2*dsqvol)
~ ca + CR_0C_1N <-> CR_1C_1N (nT1*dsqvol, nT2*dsqvol)
~ ca + CR_1C_1N <-> CR_2C_1N (nR1*dsqvol, nR2*dsqvol)
~ ca + CR_1C_1N <-> CR_1C_2N (nR1*dsqvol, nR2*dsqvol)
:Fith site
~ ca + CR <-> CR_1V (nV1*dsqvol, nV2*dsqvol)
cai = ca
mgi = mg
}
FUNCTION ssBuff1() (mM) {
ssBuff1 = Buffnull1/(1+((rf1/rf2)*cainull))
}
FUNCTION ssBuff1ca() (mM) {
ssBuff1ca = Buffnull1/(1+(rf2/(rf1*cainull)))
}
FUNCTION ssBuff2() (mM) {
ssBuff2 = Buffnull2/(1+((rf3/rf4)*cainull))
}
FUNCTION ssBuff2ca() (mM) {
ssBuff2ca = Buffnull2/(1+(rf4/(rf3*cainull)))
}
FUNCTION ssBTC() (mM) {
ssBTC = BTCnull/(1+((b1/b2)*cainull))
}
FUNCTION ssBTCca() (mM) {
ssBTCca = BTCnull/(1+(b2/(b1*cainull)))
}
FUNCTION ssDMNPE() (mM) {
ssDMNPE = DMNPEnull/(1+((c1/c2)*cainull))
}
FUNCTION ssDMNPEca() (mM) {
ssDMNPEca = DMNPEnull/(1+(c2/(c1*cainull)))
}