: 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)
ENDCOMMENT
NEURON {
SUFFIX cdp5_CAM
USEION ca READ cao, cai, ica WRITE cai
RANGE ica_pmp
RANGE Nannuli, Buffnull2, rf3, rf4, vrat
RANGE CAM0, CAM1C, CAM2C, CAM1N2C, CAM1N, CAM2N, CAM2N1C, CAM1C1N, CAM4
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 Calbindin (2 high and 2 low affinity binding sites)
CBnull= .16 (mM)
nf1 =43.5 (/ms mM)
nf2 =3.58e-2 (/ms)
ns1 =5.5 (/ms mM)
ns2 =0.26e-2 (/ms)
: values for Parvalbumin
PVnull = .08 (mM)
m1 = 1.07e2 (/ms mM)
m2 = 9.5e-4 (/ms)
p1 = 0.8 (/ms mM)
p2 = 2.5e-2 (/ms)
: Calmodulin concentration
CAM_start = 0.03 (mM) :Pepke 2010
: Calmodulin Kinetic parameters. The values are the mean between max and min.
:C-lobe
Kd1C = 0.00965 (mM) : Kd - Equilibrium binding of 1st Ca2+ to CaM C-terminus
K1Coff = 0.04 (/ms) : From 0C to 1C with X ions on N-lobe
K1Con = 5.4 (/mM ms) : From 1C to 0C with X ions on N-lobe
Kd2C = 0.00105 (mM) : Kd - Equilibrium binding of 2nd Ca2+ to CaM C-terminus
K2Coff = 0.00925 (/ms) : From 1C to 2C with X ions on N-lobe
K2Con = 15 (/mM ms) : From 2C to 1C with X ions on N-lobe
:N-lobe
Kd1N = 0.0275 (uM) : Kd - Equilibrium binding of 1st Ca2+ to CaM N-terminus
K1Noff = 2.5 (/ms) : From 0N to 1N with X ions on C-lobe
K1Non = 142.5 (/mM ms) : From 1N to 0N with X ions on C-lobe
Kd2N = 0.00615 (mM) : Kd - Equilibrium binding of 2nd Ca2+ to CaM N-terminus
K2Noff = 0.75 (/ms) : From 1N to 2N with X ions on C-lobe
K2Non = 175 (/mM ms) : From 2N to 1N with X ions on C-lobe
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)
CB (mM)
CB_f_ca (mM)
CB_ca_s (mM)
CB_ca_ca (mM)
PV (mM)
PV_ca (mM)
PV_mg (mM)
:State for the Calmodulin
CAM0 (mM)
:C-lobe mainly
CAM1C (mM)
CAM2C (mM)
CAM1N2C (mM)
:N-Lobe Mainly
CAM1N (mM)
CAM2N (mM)
CAM2N1C (mM)
:One ion on C-lobe and one on N-lobe
CAM1C1N (mM)
:CaM complete
CAM4 (mM)
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()
CB = ssCB( kdf(), kds())
CB_f_ca = ssCBfast( kdf(), kds())
CB_ca_s = ssCBslow( kdf(), kds())
CB_ca_ca = ssCBca( kdf(), kds())
PV = ssPV( kdc(), kdm())
PV_ca = ssPVca(kdc(), kdm())
PV_mg = ssPVmg(kdc(), kdm())
:Calmodulin
CAM0 = CAM_start
CAM1C = 0
CAM2C = 0
CAM1N2C = 0
CAM1N = 0
CAM2N = 0
CAM2N1C = 0
CAM1C1N = 0
CAM4 = 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 CB CB_f_ca CB_ca_s CB_ca_ca PV PV_ca PV_mg CAM0 CAM1C CAM2C CAM1N2C CAM1N CAM2N CAM2N1C CAM1C1N CAM4}
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)
:Calbindin
~ ca + CB <-> CB_ca_s (nf1*dsqvol, nf2*dsqvol)
~ ca + CB <-> CB_f_ca (ns1*dsqvol, ns2*dsqvol)
~ ca + CB_f_ca <-> CB_ca_ca (nf1*dsqvol, nf2*dsqvol)
~ ca + CB_ca_s <-> CB_ca_ca (ns1*dsqvol, ns2*dsqvol)
:Paravalbumin
~ ca + PV <-> PV_ca (m1*dsqvol, m2*dsqvol)
~ mg + PV <-> PV_mg (p1*dsqvol, p2*dsqvol)
:Calmodulin
:C-lobe
~ ca + CAM0 <-> CAM1C (K1Con*dsqvol, K1Coff*dsqvol)
~ ca + CAM1C <-> CAM2C (K2Con*dsqvol, K2Coff*dsqvol)
~ ca + CAM2C <-> CAM1N2C (K1Non*dsqvol, K1Noff*dsqvol)
~ ca + CAM1N2C <-> CAM4 (K2Non*dsqvol, K2Noff*dsqvol)
:N-lobe
~ ca + CAM0 <-> CAM1N (K1Non*dsqvol, K1Noff*dsqvol)
~ ca + CAM1N <-> CAM2N (K2Non*dsqvol, K2Noff*dsqvol)
~ ca + CAM2N <-> CAM2N1C (K1Con*dsqvol, K1Coff*dsqvol)
~ ca + CAM2N1C <-> CAM4 (K2Con*dsqvol, K2Coff*dsqvol)
:Mixed C and N lobes
~ ca + CAM1C <-> CAM1C1N (K1Non*dsqvol, K1Noff*dsqvol)
~ ca + CAM1N <-> CAM1C1N (K1Con*dsqvol, K1Coff*dsqvol)
~ ca + CAM1C1N <-> CAM1N2C (K2Con*dsqvol, K2Coff*dsqvol)
~ ca + CAM1C1N <-> CAM2N1C (K2Non*dsqvol, K2Noff*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)))
}
FUNCTION ssCB( kdf(), kds()) (mM) {
ssCB = CBnull/(1+kdf()+kds()+(kdf()*kds()))
}
FUNCTION ssCBfast( kdf(), kds()) (mM) {
ssCBfast = (CBnull*kds())/(1+kdf()+kds()+(kdf()*kds()))
}
FUNCTION ssCBslow( kdf(), kds()) (mM) {
ssCBslow = (CBnull*kdf())/(1+kdf()+kds()+(kdf()*kds()))
}
FUNCTION ssCBca(kdf(), kds()) (mM) {
ssCBca = (CBnull*kdf()*kds())/(1+kdf()+kds()+(kdf()*kds()))
}
FUNCTION kdf() (1) {
kdf = (cainull*nf1)/nf2
}
FUNCTION kds() (1) {
kds = (cainull*ns1)/ns2
}
FUNCTION kdc() (1) {
kdc = (cainull*m1)/m2
}
FUNCTION kdm() (1) {
kdm = (mginull*p1)/p2
}
FUNCTION ssPV( kdc(), kdm()) (mM) {
ssPV = PVnull/(1+kdc()+kdm())
}
FUNCTION ssPVca( kdc(), kdm()) (mM) {
ssPVca = (PVnull*kdc())/(1+kdc()+kdm())
}
FUNCTION ssPVmg( kdc(), kdm()) (mM) {
ssPVmg = (PVnull*kdm())/(1+kdc()+kdm())
}