Mathematical model for windup (Aguiar et al. 2010)

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Accession:128559
"Windup is characterized as a frequency-dependent increase in the number of evoked action potentials in dorsal horn neurons in response to electrical stimulation of afferent C-fibers. ... The approach presented here relies on mathematical and computational analysis to study the mechanism(s) underlying windup. From experimentally obtained windup profiles, we extract the time scale of the facilitation mechanisms that may support the characteristics of windup. Guided by these values and using simulations of a biologically realistic compartmental model of a wide dynamic range (WDR) neuron, we are able to assess the contribution of each mechanism for the generation of action potentials windup. ..."
Reference:
1 . Aguiar P, Sousa M, Lima D (2010) NMDA channels together with L-type calcium currents and calcium-activated nonspecific cationic currents are sufficient to generate windup in WDR neurons. J Neurophysiol 104:1155-66 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Wide dynamic range neuron;
Channel(s): I Na,p; I Na,t; I L high threshold; I N; I K; I K,Ca;
Gap Junctions:
Receptor(s): GabaA; AMPA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; MATLAB;
Model Concept(s): Activity Patterns; Action Potentials;
Implementer(s):
Search NeuronDB for information about:  GabaA; AMPA; NMDA; I Na,p; I Na,t; I L high threshold; I N; I K; I K,Ca;
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WDR-Model
readme.html
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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
:
: "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 derivimplicit
}

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
}

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