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101 lines
2.4 KiB
101 lines
2.4 KiB
2 years ago
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TITLE decay of submembrane calcium concentration
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:
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: Internal calcium concentration due to calcium currents and pump.
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: Differential equations.
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:
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: This file contains two mechanisms:
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:
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: 1. Simple model of ATPase pump with 3 kinetic constants (Destexhe 1992)
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:
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: Cai + P <-> CaP -> Cao + P (k1,k2,k3)
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:
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: A Michaelis-Menten approximation is assumed, which reduces the complexity
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: of the system to 2 parameters:
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: kt = <tot enzyme concentration> * k3 -> TIME CONSTANT OF THE PUMP
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: kd = k2/k1 (dissociation constant) -> EQUILIBRIUM CALCIUM VALUE
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: The values of these parameters are chosen assuming a high affinity of
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: the pump to calcium and a low transport capacity (cfr. Blaustein,
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: TINS, 11: 438, 1988, and references therein).
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:
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: For further information about this this mechanism, see Destexhe, A.
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: Babloyantz, A. and Sejnowski, TJ. Ionic mechanisms for intrinsic slow
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: oscillations in thalamic relay neurons. Biophys. J. 65: 1538-1552, 1993.
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:
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:
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: 2. Simple first-order decay or buffering:
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:
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: Cai + B <-> ...
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:
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: which can be written as:
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:
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: dCai/dt = (cainf - Cai) / taur
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:
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: where cainf is the equilibrium intracellular calcium value (usually
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: in the range of 200-300 nM) and taur is the time constant of calcium
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: removal. The dynamics of submembranal calcium is usually thought to
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: be relatively fast, in the 1-10 millisecond range (see Blaustein,
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: TINS, 11: 438, 1988).
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:
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: All variables are range variables
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:
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: Written by Alain Destexhe, Salk Institute, Nov 12, 1992
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:
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INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
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NEURON {
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SUFFIX cadyn
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USEION ca READ ica, cai WRITE cai
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RANGE depth,kt,kd,cainf,taur
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}
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UNITS {
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(molar) = (1/liter) : moles do not appear in units
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(mM) = (millimolar)
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(um) = (micron)
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(mA) = (milliamp)
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(msM) = (ms mM)
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}
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CONSTANT {
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FARADAY = 96489 (coul) : moles do not appear in units
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}
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PARAMETER {
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depth = .1 (um) : depth of shell
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taur = 1e10 (ms) : remove first-order decay
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cainf = 1.4e-1 (mM)
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kt = 1e-4 (mM/ms)
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kd = 1e-4 (mM)
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}
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STATE {
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cai (mM)
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}
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INITIAL {
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cai = kd
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}
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ASSIGNED {
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ica (mA/cm2)
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drive_channel (mM/ms)
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drive_pump (mM/ms)
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}
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BREAKPOINT {
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SOLVE state METHOD cnexp
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}
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DERIVATIVE state {
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drive_channel = - (10000) * ica / (2 * FARADAY * depth)
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if (drive_channel <= 0.) { drive_channel = 0. } : cannot pump inward
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drive_pump = -kt * cai / (cai + kd ) : Michaelis-Menten
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cai' = drive_channel + drive_pump + (cainf-cai)/taur
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}
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