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
AMPA_DynSyn.mod
CaIntraCellDyn.mod
GABAa_DynSyn.mod *
GABAb_DynSyn.mod *
HH2.mod *
iCaAN.mod *
iCaL.mod *
iKCa.mod *
iNaP.mod *
mGluR_DynSyn.mod
NK1_DynSyn.mod *
NMDA_DynSyn.mod *
herreroscatter.m
interneuron.hoc *
loadsynapticcurrents.m
mosinit.hoc
screenshot.jpg
WDR.hoc
wdr_spike_times.dat *
wdr-complete-model.hoc
wdr-complete-model.ses
wdr-complete-model-exportsyns.hoc
                            
//Created by Paulo Aguiar [pauloaguiar@fc.up.pt]

// IMPORTANT NOTE:
// The iKCa current is not necessary but provide an idea on how activity control can be achieved.
// The early, but truncated increase in the evoked APs results from the interaction between NK1R and iKCa
// Remove the iKCa, but renormalize the inputs, if you want a slow and monotonic increase in the evoked APs

// CREATE INTERNEURON

begintemplate Interneuron

public soma, dendrite, hillock, axon

create soma, dendrite, hillock, axon

proc init() {
    
    create soma
    soma {    
	nseg = 3  
	L = 20.0
	diam = 20.0
	
	//HH channels: iNat and iK
	insert HH2 {
	    gnabar_HH2 = 0.08
	    gkbar_HH2 = 0.02
	    vtraub_HH2 = -55.0
	}
	
	//intracellular Ca dynamics
	insert CaIntraCellDyn {
	    depth_CaIntraCellDyn = 0.1
	    cai_tau_CaIntraCellDyn = 1.0
	    cai_inf_CaIntraCellDyn = 50.0e-6
	}
	
	//potassium current dependent on intracellular calcium concentration 
	insert iKCa {
	    gbar_iKCa = 0.002 //0.002
	}
	
	ek = -70.0
	
	Ra = 150.0
	
	insert pas
	g_pas = 4.2e-5
	e_pas = -65.0
    }
    
    create dendrite
    dendrite {    
	nseg = 5    
	L = 500.0  
	diam = 4.0
	
	//intracellular Ca dynamics
	insert CaIntraCellDyn {
	    depth_CaIntraCellDyn = 0.1
	    cai_tau_CaIntraCellDyn = 2.0
	    cai_inf_CaIntraCellDyn = 50.0e-6
	}
	
	//potassium current dependent on intracellular calcium concentration 
	insert iKCa {
	    gbar_iKCa = 0.002 //0.002
	}
	
	ek = -70.0
	
	Ra = 150.0
	
	insert pas
	g_pas = 4.2e-5
	e_pas = -65.0
    }
    
    
    create hillock
    hillock {   
	nseg = 3  
	L = 3.0
	diam(0:1) = 2.0:1.0
	
	//HH channels: iNa,t and iK
	insert HH2 {
	    gnabar_HH2 = 0.1
	    gkbar_HH2 = 0.04
	    vtraub_HH2 = -55.0
	}
	
	Ra = 150.0
	
	insert pas
	g_pas = 4.2e-5
	e_pas = -65.0
    }
    
    create axon
    axon {    
	nseg = 5
	L = 1000.0
	diam = 1.0
	
	//HH channels: iNa,t and iK
	insert HH2 {
	    gnabar_HH2 = 0.1
	    gkbar_HH2 = 0.04	//0.06
	    vtraub_HH2 = -55
	}
	
	Ra = 150.0
	
	insert pas
	g_pas = 4.2e-5
	e_pas = -65.0
    }
    
    
    //CONNECTIONS
    soma connect hillock(0),1
    hillock connect axon(0),1
    soma connect dendrite(0),0 
    
}

endtemplate Interneuron





//************************************************************************************
//UNITS	    
//Category									Variable			Units
//Time											t							[ms]
//Voltage										v							[mV]
//Current										i							[mA/cm2] (distributed)	[nA] (point process)
//Concentration							ko, ki, etc.	[mM]
//Specific capacitance			cm						[uf/cm2]
//Length										diam, L				[um]
//Conductance								g							[S/cm2] (distributed)	[uS] (point process)
//Cytoplasmic resistivity		Ra						[ohm cm]
//Resistance								Ri						[10E6 ohm]

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