Effects of spinal cord stimulation on WDR dorsal horn network (Zhang et al 2014)

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Accession:168414
" ... To study the mechanisms underlying SCS (Spinal cord stimulation), we constructed a biophysically-based network model of the dorsal horn circuit consisting of interconnected dorsal horn interneurons and a wide dynamic range (WDR) projection neuron and representations of both local and surround receptive field inhibition. We validated the network model by reproducing cellular and network responses relevant to pain processing including wind-up, A-fiber mediated inhibition, and surround receptive field inhibition. ..." See paper for more.
Reference:
1 . Zhang TC, Janik JJ, Grill WM (2014) Modeling effects of spinal cord stimulation on wide-dynamic range dorsal horn neurons: influence of stimulation frequency and GABAergic inhibition. J Neurophysiol 112:552-67 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism:
Cell Type(s): Wide dynamic range neuron;
Channel(s):
Gap Junctions:
Receptor(s): GabaA; AMPA; NMDA; Glutamate; Glycine;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s):
Implementer(s): Zhang, Tianhe [tz5@duke.edu];
Search NeuronDB for information about:  GabaA; AMPA; NMDA; Glutamate; Glycine;
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ZhangEtAl2014
Critical Mod Files
AMPA_DynSyn.mod
B_A.mod
B_DR.mod
B_NA.mod
CaIntraCellDyn.mod *
GABAa_DynSyn.mod *
GABAb_DynSyn.mod *
Glycine_DynSyn.mod
HH2.mod *
HH2new.mod *
iCaAN.mod *
iCaL.mod
iKCa.mod *
iNaP.mod *
KDR.mod
KDRI.mod
NK1_DynSyn.mod *
NMDA_DynSyn.mod *
SS.mod
vsource.mod *
                            
TITLE Slow Ca-dependent cation current
:
:   Ca++ dependent nonspecific cation current ICAN
:   Differential equations
:
:   Model based on a first order kinetic scheme
:
:      <closed> + n cai <-> <open>	(alpha,beta)
:
:   Following this model, the activation fct will be half-activated at 
:   a concentration of Cai = (beta/alpha)^(1/n) = cac (parameter)
:
:   The mod file is here written for the case n=2 (2 binding sites)
:   ---------------------------------------------
:
:   Kinetics based on: Partridge & Swandulla, TINS 11: 69-72, 1988.
:
:   This current has the following properties:
:      - inward current (non specific for cations Na, K, Ca, ...)
:      - activated by intracellular calcium
:      - NOT voltage dependent
:
:   A minimal value for the time constant has been added
:
:   Ref: Destexhe et al., J. Neurophysiology 72: 803-818, 1994.
:
:   Modifications by Arthur Houweling for use in MyFirstNEURON
:
:   Some parameter changes by Paulo Aguiar (pauloaguiar@fc.up.pt):
:   tau_factor = 40 => parameter beta	changes from 2.0e-3 to 5.0e-5
:		cac = 0.5e-3 (before was 1.0e-3)

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

NEURON {
	SUFFIX iCaAN
	USEION can READ ecan WRITE ican VALENCE 1
	USEION ca READ cai
        RANGE gbar, m_inf, tau_m
	RANGE ican
	GLOBAL beta, cac, taumin
}


UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
	(molar) = (1/liter)
	(mM) = (millimolar)
}


PARAMETER {
	v		  (mV)
	celsius		  (degC)
        dt                (ms)
	ecan	= -20	  (mV)		: reversal potential
	cai		  (mM)
	gbar	= 0.00025 (mho/cm2)
	beta	= 2.0e-3  (1/ms)	: backward rate constant (original value)

	tau_factor = 40         : scaling factor allowing tuning

	:cac	= 1.0e-3  (mM)		: middle point of activation fct  (original value)
	cac		= 5e-4	  (mM)		: middle point of activation fct

	taumin	= 0.1	  (ms)		: minimal value of time constant
	
	:parameter tau_factor and cac were set to produce tau_m ~ 2000(ms) at cai=cac and celsius=36;
	:implications of parameters change when cai=cac:
	: -> BEFORE (beta=2.0e-3;tadj=4.66) => tau_m ~ 50   ms
	: -> AFTER  (beta=5.0e-5;tadj=4.66) => tau_m ~ 2000 ms
	:
	:also cac was reduced to half, from 1.0 uM to 0.5 uM
}


STATE {
	m
}

ASSIGNED {
	ican	(mA/cm2)
	m_inf
	tau_m	(ms)
	tadj
}

BREAKPOINT { 
	SOLVE states :METHOD euler
	ican = gbar * m*m * (v - ecan)
}

:DERIVATIVE states {
:       evaluate_fct(v,cai)
:
:       m'= (m_inf-m) / tau_m 
:}
  
PROCEDURE states() {
        evaluate_fct(v,cai)
	
        m = m + ( 1-exp(-dt/tau_m) )*(m_inf-m)
	:printf("\n iCAN tau_m=%g", tau_m)

}

UNITSOFF
INITIAL {
:
:  activation kinetics are assumed to be at 22 deg. C
:  Q10 is assumed to be 3
:
	tadj = 3.0 ^ ((celsius-22.0)/10)

	evaluate_fct(v,cai)
	m = m_inf
}


PROCEDURE evaluate_fct(v(mV),cai(mM)) {  LOCAL alpha2

	alpha2 = beta * (cai/cac)^2
	
	tau_m = tau_factor / (alpha2 + beta) / tadj		: tau_m = tau_factor / ( beta * (1 + (cai/cac)^2) ) / tadj
	
	m_inf = alpha2 / (alpha2 + beta)							: m_inf = (cai/cac)^2 / ( 1 + (cai/cac)^2 )

	if(tau_m < taumin) { tau_m = taumin }					: min value of time cst

}
UNITSON

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