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 potassium current
:
:   Ca++ dependent K+ current IC responsible for slow AHP
:   Differential equations
:
:   Model based on a first order kinetic scheme
:
:       + n cai <->     (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)
:   ---------------------------------------------
:
:   This current models the "slow" IK[Ca] (IAHP): 
:      - potassium current
:      - 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.
:   See also: http://www.cnl.salk.edu/~alain , http://cns.fmed.ulaval.ca
:   modifications by Yiota Poirazi 2001 (poirazi@LNC.usc.edu)
:   taumin = 0.5 ms instead of 0.1 ms	

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

NEURON {
    SUFFIX iKCa
    USEION k READ ek WRITE ik
    USEION ca READ cai
    RANGE gk, gbar, m_inf, tau_m
    GLOBAL beta, cac
}


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


PARAMETER {
    v                 (mV)
    celsius = 36      (degC)
    ek      = -80     (mV) 
    cai     = 50.0e-6 (mM)            : initial [Ca]i
    gbar    = 0.01    (mho/cm2)
    beta    = 0.03    (1/ms)          : backward rate constant
    :cac     = 0.025   (mM)            : middle point of activation fct    
    cac     = 0.001   (mM)            : middle point of activation fct    
    taumin  = 0.1     (ms)            : minimal value of the time cst
    gk
}


STATE {m}        : activation variable to be solved in the DEs       

ASSIGNED {       : parameters needed to solve DE 
    ik      (mA/cm2)
    m_inf
    tau_m   (ms)
    tadj
}
BREAKPOINT { 
    SOLVE states METHOD derivimplicit
    gk = gbar*m*m*m     : maximum channel conductance
    ik = gk*(v - ek)    : potassium current induced by this channel
}

DERIVATIVE states { 
    evaluate_fct(v,cai)
    m' = (m_inf - m) / tau_m
}

UNITSOFF
INITIAL {
    :
    :  activation kinetics are assumed to be at 22 deg. C
    :  Q10 is assumed to be 3
    :
    tadj = 3 ^ ((celsius-22.0)/10) : temperature-dependent adjastment factor
    evaluate_fct(v,cai)
    m = m_inf
}

PROCEDURE evaluate_fct(v(mV),cai(mM)) {  LOCAL car
    car = (cai/cac)^2
    m_inf = car / ( 1 + car )      : activation steady state value
    tau_m =  1 / beta / (1 + car) / tadj
    if(tau_m < taumin) { tau_m = taumin }   : activation min value of time cst
}
UNITSON

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