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100 lines
2.4 KiB
100 lines
2.4 KiB
TITLE decay of submembrane calcium concentration |
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: Internal calcium concentration due to calcium currents and pump. |
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: Differential equations. |
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: This file contains two mechanisms: |
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: 1. Simple model of ATPase pump with 3 kinetic constants (Destexhe 1992) |
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: Cai + P <-> CaP -> Cao + P (k1,k2,k3) |
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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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: 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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: 2. Simple first-order decay or buffering: |
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: Cai + B <-> ... |
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: which can be written as: |
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: dCai/dt = (cainf - Cai) / taur |
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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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: All variables are range variables |
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: Written by Alain Destexhe, Salk Institute, Nov 12, 1992 |
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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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