: $Id: cp2.mod,v 1.6 1998/08/16 20:43:54 billl Exp $
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 = <tot enzyme concentration> * 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
:

INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

NEURON {
	SUFFIX Cad
	USEION Ca READ iCa, Cai WRITE Cai VALENCE 2
	RANGE depth,kt,kd,Cainf,taur,k,Cainf2,taur2
}

UNITS {
	(molar) = (1/liter)			: moles do not appear in units
	(mM)	= (millimolar)
	(um)	= (micron)
	(mA)	= (milliamp)
	(msM)	= (ms mM)
}

CONSTANT {
	FARADAY = 96489		(coul)		: moles do not appear in units
:	FARADAY = 96.489	(k-coul)	: moles do not appear in units
}

PARAMETER {
	depth	= .1	(um)		: depth of shell
	taur	= 700	(ms)		: rate of calcium removal
	taur2	= 70	(ms)		: rate of calcium removal
	Cainf	= 1e-8	(mM)
	Cainf2	= 5e-5	(mM)
	Cainit  = 5e-5
	kt	= 1	(mM/ms)		: estimated from k3=.5, tot=.001
	kd	= 5e-4	(mM)		: estimated from k2=250, k1=5e5
        k       = 1
}

STATE {
	Cai		(mM) <1e-8> : to have tolerance of .01nM
}

INITIAL {
	Cai = Cainit
}

ASSIGNED {
	iCa		(mA/cm2)
	drive_channel	(mM/ms)
	drive_pump	(mM/ms)
}
	
BREAKPOINT {
	SOLVE state METHOD cnexp
}

DERIVATIVE state { 
	drive_channel =  - (k*10000) * iCa / (2 * FARADAY * depth)
	if (drive_channel<=0.) { drive_channel = 0. }: cannot pump inward
:	drive_pump = -tot * k3 * Cai / (Cai + ((k2+k3)/k1) )	: quasistat
	drive_pump = -kt * Cai / (Cai + kd )		: Michaelis-Menten
	Cai' = drive_channel+drive_pump+(Cainf-Cai)/taur+(Cainf2-Cai)/taur2
}