: 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_CAM
USEION ca READ cao, cai, ica WRITE cai
USEION con_2c WRITE con_2ci VALENCE 1
RANGE ica_pmp
RANGE Nannuli, Buffnull2, rf3, rf4, vrat, cainull, CR, CR_1C_0N, CR_2C_2N, CR_1V, CRnull
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 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)
: 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
: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)
con_2ci (mM)
}
: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)
: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)
: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
: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 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)
: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
con_2ci = CAM2C
}
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)))
}