TITLE decay of internal calcium concentration
:
: Internal calcium concentration due to calcium currents and pump.
: Differential equations.
:
: Simple model of ATPase pump with 3 kinetic constants (Destexhe 92)
: Cai + P <-> CaP -> Cao + P (k1,k2,k3)
: A Michaelis-Menten approximation is assumed, which reduces the complexity
: of the system to 2 parameters:
: kt = * k3 -> TIME CONSTANT OF THE PUMP
: kd = k2/k1 (dissociation constant) -> EQUILIBRIUM CALCIUM VALUE
: The values of these parameters are chosen assuming a high affinity of
: the pump to calcium and a low transport capacity (cfr. Blaustein,
: TINS, 11: 438, 1988, and references therein).
:
: Units checked using "modlunit" -> factor 10000 needed in ca entry
:
: VERSION OF PUMP + DECAY (decay can be viewed as simplified buffering)
:
: All variables are range variables
:
:
: This mechanism was published in: Destexhe, A. Babloyantz, A. and
: Sejnowski, TJ. Ionic mechanisms for intrinsic slow oscillations in
: thalamic relay neurons. Biophys. J. 65: 1538-1552, 1993)
:
: Written by Alain Destexhe, Salk Institute, Nov 12, 1992
:
: "The normal resting [Ca2+]i lies in the range of 30 to 200 nM
: in living cells." (Hille 2001)
: Parameter changes by Paulo Aguiar and Mafalda Sousa, IBMC, May 2008
: pauloaguiar@fc.up.pt; mafsousa@ibmc.up.pt
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
SUFFIX CaIntraCellDyn
USEION ca READ ica, cai WRITE cai
RANGE cai_new, depth, cai_inf, cai_tau
}
UNITS {
(molar) = (1/liter) : moles do not appear in units
(mM) = (millimolar)
(um) = (micron)
(mA) = (milliamp)
(msM) = (ms mM)
FARADAY = (faraday) (coulomb)
}
PARAMETER {
depth = 0.1 (um) : depth of shell
cai_tau = 2.0 (ms) : rate of calcium removal
cai_inf = 50.0e-6 (mM) : equilibrium intracellular calcium concentration
cai (mM)
}
STATE {
cai_new (mM)
}
INITIAL {
cai_new = cai_inf
}
ASSIGNED {
ica (mA/cm2)
drive_channel (mM/ms)
}
BREAKPOINT {
SOLVE state METHOD euler
}
DERIVATIVE state {
drive_channel = - (10000) * ica / (2 * FARADAY * depth)
if (drive_channel <= 0.) { drive_channel = 0. } : cannot pump inward
cai_new' = drive_channel + (cai_inf-cai_new)/cai_tau
cai = cai_new
}